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https://www.hackmath.net/en/example/1218
[ "# BW-BS balls\n\nAdam has a full box of balls that are large or small, black or white. Ratio of large and small balls is 5:3. Within the large balls the ratio of the black to white is 1:2 and between small balls the ratio of the black to white is 1:8\n\nWhat is the ratio of all black to all white balls?\n\nResult\n\nx =  0.33\n\n#### Solution:", null, "a=1\na+b = 5/3*(c+d)\na = 1/2*b\nc = 1/8 * d\n\na = 1\n3a+3b-5c-5d = 0\n2a-b = 0\n8c-d = 0\n\na = 1\nb = 2\nc = 15 = 0.2\nd = 85 = 1.6\n\nCalculated by our linear equations calculator.\n\nLeave us a comment of example and its solution (i.e. if it is still somewhat unclear...):\n\nShowing 0 comments:", null, "Be the first to comment!", null, "#### To solve this example are needed these knowledge from mathematics:\n\nDo you have a system of equations and looking for calculator system of linear equations?\n\n## Next similar examples:\n\n1. Book read", null, "If Petra read 10 pages per day, she would read the book two days earlier than she read 6 pages a day. How many pages does a book have?\n2. Linsys2", null, "Solve two equations with two unknowns: 400x+120y=147.2 350x+200y=144\n3. Three brothers", null, "The three brothers have a total of 42 years. Jan is five years younger than Peter and Peter is 2 years younger than Michael. How many years has each of them?\n4. Three days", null, "During the three days sold in stationery 1490 workbooks. The first day sold about workbooks more than third day. The second day 190 workbooks sold less than third day. How many workbooks sold during each day?\n5. Elimination method", null, "Solve system of linear equations by elimination method: 5/2x + 3/5y= 4/15 1/2x + 2/5y= 2/15\n6. Equations - simple", null, "Solve system of linear equations: x-2y=6 3x+2y=4\n7. Three workshops", null, "There are 2743 people working in three workshops. In the second workshop works 140 people more than in the first and in third works 4.2 times more than the second one. How many people work in each workshop?\n8. Equations", null, "Solve following system of equations: 6(x+7)+4(y-5)=12 2(x+y)-3(-2x+4y)=-44\n9. Mushrooms", null, "Eva and Jane collected 114 mushrooms together. Eve found twice as much as Jane. How many mushrooms found each of them?\n10. Two equations", null, "Solve equations (use adding and subtracting of linear equations): -4x+11y=5 6x-11y=-5\n11. Legs", null, "Cancer has 5 pairs of legs. The insect has 6 legs. 60 animals have a total of 500 legs. How much more are cancers than insects?\n12. Linear system", null, "Solve a set of two equations of two unknowns: 1.5x+1.2y=0.6 0.8x-0.2y=2\n13. Two numbers", null, "We have two numbers. Their sum is 140. One-fifth of the first number is equal to half the second number. Determine those unknown numbers.\n14. Theatro", null, "Theatrical performance was attended by 480 spectators. Women were in the audience 40 more than men and children 60 less than half of adult spectators. How many men, women and children attended a theater performance?\n15. Trees", null, "Along the road were planted 250 trees of two types. Cherry for 60 CZK apiece and apple 50 CZK apiece. The entire plantation cost 12,800 CZK. How many was cherries and apples?\n16. Hotel rooms", null, "In the 45 rooms, there were 169 guests, some rooms were three-bedrooms and some five-bedrooms. How many rooms were?\n17. Theorem prove", null, "We want to prove the sentense: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?" ]
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http://analgorithmaday.blogspot.com/2011/07/find-maximum-product-in-array-in-all.html
[ "## Wednesday, 27 July 2011\n\n### Find the maximum product in an array (in all directions)\n\nQuestion\n\nReally an interesting question again on Project Euler site. Problem #11.\n\nhttp://projecteuler.net/index.php?section=problems&id=11\n\nIts a 20x20 matrix in which you need to find the maximum product of 4 numbers in all the possible directions you can traverse the array. :) But thank god, the traversal is in straight line. Not zig-zag or random.. :)\n\nBrain storm\n\nI started solving the problem. Initially thought it in very complex way possible as i always do. But its really simple. It’s no optimization problem, sorting problem, anything of that sort. :)\n\nYou need to find the adjacent elements of size 4 in up, down, left, right, diagonal directions in an array which when multiplied gives you a max. Even though the question looks complex, it will look like solvable.\n\nJust do the brute force way. You need to first check horizontal 4-by-4 elements. vertical same 4-by-4 elements and then the diagonal.\n\nI got the horizontal and vertical somehow as we take 4 elements on hand and multiply and still move the loop from 0->20.\n\nBut for diagonal what is the pattern ?\n\nsimple.. diagonal is 2 ways\n\n• from left top to bottom right, move a line\n• from right top to bottom left, move a line\n\nBut even when you move diagonal, you need to consider 4 elements?.. How, simple..\n\nthe pattern is,\n\n(i,j) (i+1, j+1) (i+2, j+2) (i+3,j+3)\n\nfor all i,j. Note that we end by 17 itself. :)\n\nthe above one is for right top to bottom left\n\nfor, left top to bottom right, since we need to ignore elements, we start after 3.\n\nCode\n\n`using namespace std;`\n` `\n`void main()`\n`{`\n` char line;`\n` double arr;`\n` ifstream myfile (\"C:\\\\Works\\\\cppassignments\\\\algorithms\\\\algorithms\\\\euler-input.txt\");`\n` `\n` for(int i =0 ; i<20; i++) {`\n` for(int j=0; j<20; j++) {`\n` myfile.getline(line, 10, ' ');`\n` arr[i][j] = atof(line);`\n` cout<<arr[i][j]<<\" \";`\n` }`\n` cout<<endl;`\n` }`\n` `\n` double max=1;`\n` double prod;`\n` `\n` // rows`\n` for(int i=0;i<20; i++) {`\n` for(int j=0; j<17; j++) {`\n` prod = arr[i][j] * arr[i][j+1] * arr[i][j+2] * arr[i][j+3];`\n` if(max < prod) {`\n` max = prod;`\n` }`\n` }`\n` }`\n` `\n` // column`\n` for(int j =0; j<20;j++) {`\n` for(int i=0;i<17; i++) {`\n` prod = arr[i][j] * arr[i+1][j] * arr[i+2][j] * arr[i+3][j];`\n` if(max < prod) {`\n` max = prod;`\n` }`\n` }`\n` }`\n` `\n` // diagonal right top to bottom left`\n` // exclude 3 from 20 as it never can make it to 4 elements`\n` for(int i=0; i< 17;i++) {`\n` for(int j=0; j<17;j++) {`\n` prod = arr[i][j]*arr[i+1][j+1]*arr[i+2][j+2]*arr[i+3][j+3];`\n` if(max < prod)`\n` max = prod;`\n` }`\n` }`\n` `\n` // diagonal left top to right bottom`\n` for(int i=3; i< 20;i++) {`\n` for(int j=0; j<17;j++) {`\n` prod = arr[i][j]*arr[i-1][j+1]*arr[i-2][j+2]*arr[i-3][j+3];`\n` if(max < prod)`\n` max = prod;`\n` }`\n` }`\n`}`\n• You cannot end by 20. :) be careful even some runtime won’t warn about array overrun, calculation will happen with garbage, your basic type will overflow and you will wrong value. Even for horizontal & vertical we do +3, so must run loop perfectly from 0 to 16\n• For math contests like this, always try to use the maximum sized type as possible. :) But do that only if memory of the program is not the winning criteria.. :P\n• Thanks to http://duncan99.wordpress.com/2008/10/29/project-euler-problem-11/ for enlightening me about the diagonal flow." ]
[ null ]
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https://blog.finxter.com/python-create-list-of-n-empty-strings/
[ "# Python – Create List of N Empty Strings\n\n## Problem Formulation\n\n💬 Challenge: Given an integer `n`. How to create a list of `n` empty strings `''` in Python?\n\nHere are three examples:\n\n• Given `n=0`. Create list `[]`.\n• Given `n=3`. Create list `['', '', '']`.\n• Given `n=5`. Create list `['', '', '', '', '']`.\n\n## Method 1: List Multiplication\n\nYou can create a list of `n` empty strings using the list concatenation (multiplication) operator on a list with one empty string using the expression `[''] * n`. This replicates the same identical empty string object to which all list elements refer. But as strings are immutable, this cannot cause any problems through aliasing.\n\n```def create_list_empty_strings(n):\nreturn [''] * n\n\nprint(create_list_empty_strings(0))\n# []\n\nprint(create_list_empty_strings(3))\n# ['', '', '']\n\nprint(create_list_empty_strings(5))\n# ['', '', '', '', '']```\n\n## Method 2: List Comprehension\n\nYou can create a list of n empty strings by using list comprehension statement `['' for _ in range(n)]` that uses the `range()` function to repeat the creation and addition of an empty string `n` times.\n\n```def create_list_empty_strings(n):\nreturn ['' for _ in range(n)]\n\nprint(create_list_empty_strings(0))\n# []\n\nprint(create_list_empty_strings(3))\n# ['', '', '']\n\nprint(create_list_empty_strings(5))\n# ['', '', '', '', '']\n```\n\n## Method 3: For Loop and append()\n\nTo create a list of `n` empty strings without special Python features, you can also create an empty list and use a simple `for` loop to add one empty string at a time using the `list.append()` method.\n\n```def create_list_empty_strings(n):\nmy_list = []\nfor i in range(n):\nmy_list.append('')\nreturn my_list\n\nprint(create_list_empty_strings(0))\n# []\n\nprint(create_list_empty_strings(3))\n# ['', '', '']\n\nprint(create_list_empty_strings(5))\n# ['', '', '', '', '']\n```\n\n## Summary\n\nThere are three best ways to create a list with `n` empty strings.\n\n1. List concatenation `[''] * n`\n2. List comprehension `['' for _ in range(n)]`\n3. Simple `for` loop with list `append('')` on an initially empty list\n\n## Programmer Humor\n\n`Question: How did the programmer die in the shower? ☠️❗ Answer: They read the shampoo bottle instructions: Lather. Rinse. Repeat.`\n\n## Python One-Liners Book: Master the Single Line First!\n\nPython programmers will improve their computer science skills with these useful one-liners.\n\nPython One-Liners will teach you how to read and write “one-liners”: concise statements of useful functionality packed into a single line of code. You’ll learn how to systematically unpack and understand any line of Python code, and write eloquent, powerfully compressed Python like an expert.\n\nThe book’s five chapters cover (1) tips and tricks, (2) regular expressions, (3) machine learning, (4) core data science topics, and (5) useful algorithms.\n\nDetailed explanations of one-liners introduce key computer science concepts and boost your coding and analytical skills. You’ll learn about advanced Python features such as list comprehension, slicing, lambda functions, regular expressions, map and reduce functions, and slice assignments.\n\nYou’ll also learn how to:\n\n• Leverage data structures to solve real-world problems, like using Boolean indexing to find cities with above-average pollution\n• Use NumPy basics such as array, shape, axis, type, broadcasting, advanced indexing, slicing, sorting, searching, aggregating, and statistics\n• Calculate basic statistics of multidimensional data arrays and the K-Means algorithms for unsupervised learning\n• Create more advanced regular expressions using grouping and named groups, negative lookaheads, escaped characters, whitespaces, character sets (and negative characters sets), and greedy/nongreedy operators\n• Understand a wide range of computer science topics, including anagrams, palindromes, supersets, permutations, factorials, prime numbers, Fibonacci numbers, obfuscation, searching, and algorithmic sorting\n\nBy the end of the book, you’ll know how to write Python at its most refined, and create concise, beautiful pieces of “Python art” in merely a single line.\n\nGet your Python One-Liners on Amazon!!" ]
[ null ]
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https://www.r-bloggers.com/2011/04/example-8-34-lack-of-robustness-of-t-test-with-small-n/
[ "Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.\n\nTim Hesterberg has effectively argued for a larger role for resampling based inference in introductory statistics courses (and statistical practice more generally). While the Central Limit Theorem is a glorious result, and the Student t-test remarkably robust, there are subtleties that Hesterberg, Jones and others have pointed out that are not always well understood.\n\nIn this entry, we explore the robustness of the Student one sample t-test in terms of coverage probabilities where we look whether the alpha level is split evenly between the two tails.\n\nR\nWe begin by defining a function to carry out the simulation study.\n\n```runsim = function(FUNCTION=rnorm, n=20, numsim=100000,\nlabel=\"normal\")\n{\nmissupper = numeric(numsim)\nmisslower = numeric(numsim)\nfor (i in 1:numsim) {\nx = FUNCTION(n)\ntestval = t.test(x)\nmissupper[i] = testval\\$conf.int < 0\nmisslower[i] = testval\\$conf.int > 0\n}\ncat(\"n=\", n,\", number of simulations=\", numsim, sep=\"\")\ncat(\", (true data are \", label, \")\\n\", sep=\"\")\ncat(round(100*sum(missupper)/numsim, 1),\n\"% of simulations had CI below the true value.\\n\", sep=\"\")\ncat(round(100*sum(misslower)/numsim, 1),\n\"% of simulations had CI above the true value.\\n\", sep=\"\")\n}\n```\n\nWe can define three functions to explore: one where the data are actually normally distributed (so the central limit theorem doesn’t need to be invoked), a symmetric distribution (where the central limit theorem can be used with smaller sample sizes) and a skewed distribution (where the central limit theorem requires very large sample sizes).\n\n```reallynormal = function(n) { return(rnorm(n)) }\nsymmetric = function(n) { return(runif(n, -1, 1)) }\nskewed = function(n) { return(rexp(n, 1) - 1) }\n```\n\nThe results (at least to us) are somewhat startling. To get the tail probabilities correct when the underlying distribution is actually skewed, we need a huge sample size:\n\n```> runsim(reallynormal, n=20, label=\"normal\")\nn=20, number of simulations=1e+05, (true data are normal)\n2.5% of simulations had CI below the true value.\n2.5% of simulations had CI above the true value.\n\n> runsim(symmetric, n=20, label=\"symmetric\")\nn=20, number of simulations=1e+05, (true data are symmetric)\n2.6% of simulations had CI below the true value.\n2.5% of simulations had CI above the true value.\n\n> runsim(skewed, n=20, label=\"skewed\")\nn=20, number of simulations=1e+05, (true data are skewed)\n7.7% of simulations had CI below the true value.\n0.6% of simulations had CI above the true value.\n\n> runsim(skewed, n=100, label=\"skewed\")\nn=100, number of simulations=1e+05, (true data are skewed)\n4.5% of simulations had CI below the true value.\n1.2% of simulations had CI above the true value.\n\n> runsim(skewed, n=500, label=\"skewed\")\nn=500, number of simulations=1e+05, (true data are skewed)\n3.4% of simulations had CI below the true value.\n1.7% of simulations had CI above the true value.\n```\n\nSAS\n\nIn the SAS version, we’ll write a macro that first generates all of the data, then uses by processing to perform the t tests, and finally tallies the results and prints them to the output.\n\n```%macro simt(n=20, numsim=100000, myrand=normal(0), label=normal);\ndata test;\ndo sim = 1 to &numsim;\ndo i = 1 to &n;\nx = &myrand;\noutput;\nend;\nend;\nrun;\n\nods select none;\nods output conflimits=ttestcl;\nproc ttest data=test;\nby sim;\nvar x;\nrun;\nods select all;\n\ndata _null_;\nset ttestcl end=last;\nretain missupper 0 misslower 0;\nmissupper = missupper + (upperclmean lt 0);\nmisslower = misslower + (lowerclmean gt 0);\nif last then do;\nmissupper_pct = compress(round(100 * missupper/&numsim,.1));\nmisslower_pct = compress(round(100 * misslower/&numsim,.1));\nfile print;\nput \"n=&n, number of simulations = &numsim, true data are &label\";\nput missupper_pct +(-1) \"% of simulations had CI below the true value\";\nput misslower_pct +(-1) \"% of simulations had CI above the true value\";\nend;\nrun;\n%mend simt;\n```\n\nTwo or three features of this code bear commenting. First, the retain statement and end option allow us to count the number of misses without an additional data step and/or procedure. Next, the file print statement redirects the results from a put statement to the output, rather than the log. While this is not really needed, the output is where we expect the results to appear. Finally, the odd +(-1) in the final two put statements moves the column pointer back one space. This allows the percent sign to immediately follow the number.\n\nThe various distributions and sample sizes used in the R code can be called as follows:\n\n```%simt(numsim=100000, n = 20, myrand = normal(0));\n%simt(numsim=100000, n = 20, myrand = (2 * uniform(0)) - 1, label=symmetric);\n%simt(numsim=100000, n = 20, myrand = (ranexp(0) - 1), label=skewed);\n%simt(numsim=100000, n = 100, myrand = (ranexp(0) - 1), label=skewed);\n%simt(numsim=100000, n = 500, myrand = (ranexp(0) - 1), label=skewed);\n```\n\nwhere the code to generate the desired data is passed to the macro as a character string. The results of\n%simt(numsim=100000, n = 100, myrand = (ranexp(0) - 1), label=skewed);\nare\n\n```n=100, number of simulations = 100000, true data are skewed\n4.5% of simulations had CI below the true value\n1.2% of simulations had CI above the true value\n```\n\nwhich agrees nicely with the R results above.\n\nWe look forward to Tim’s talk at the JSM.", null, "" ]
[ null, "https://feeds.feedburner.com/~r/SASandR/~4/7sT3hTH0DwI", null ]
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https://forums.raspberrypi.com/viewtopic.php?f=72&t=79619
[ "c libs\n\ngms0012\nPosts: 6\nJoined: Sat Jun 14, 2014 6:14 am\n\nc libs\n\nhi friends..\n\nare there c libs available für the bare metal pi?\n\nlike the arduino libs?\n\nthanks\n\nJRV\nPosts: 270\nJoined: Mon Apr 02, 2012 1:39 pm\nLocation: Minneapolis, MN\n\nRe: c libs\n\nIs this what you are looking for: http://wiringpi.com/\n\ngms0012\nPosts: 6\nJoined: Sat Jun 14, 2014 6:14 am\n\nRe: c libs\n\nhi .\n\ni am not sure..\n\nthat looks for me that there must be running a linux kernel.. or did i understand it wrong?\n\nrpdom\nPosts: 19498\nJoined: Sun May 06, 2012 5:17 am\nLocation: Chelmsford, Essex, UK\n\nRe: c libs\n\nI'm fairly certain those libraries are only for accessing the hardware from programs written to run under Linux, not with a bare metal system.\n\nAccessing the majority of GPIO functions is fairly easy in bare metal, either from C or Assembler (my preferred method).\n\nhldswrth\nPosts: 108\nJoined: Mon Sep 10, 2012 4:14 pm\n\nRe: c libs\n\nThe thing about bare metal is that its entirely up to you. Any C library is going to be based on a load of low-level functions that are specific to whatever bare-metal kernel they are written for (e.g. write to device, allocate memory, etc.). So a bare-metal C library is meaningless on its own. You need a kernel to go with it, or else have the source code and port the C library to use your own low-level kernel functions.\nThere is at least one open source C library out there I believe, called newlib, which you could try to port to your kernel. I've not looked at it myself.\nAlternatively, perhaps the question is really, has anyone got a bare metal kernel + C library?\n\ngms0012\nPosts: 6\nJoined: Sat Jun 14, 2014 6:14 am\n\nRe: c libs\n\nyes.. the last thing would be great..\n\nlike this http://www.ti.com/tool/starterware-sitara for the BeageBoard..\n\nis there not such a thing for the RI?\n\njoan\nPosts: 15843\nJoined: Thu Jul 05, 2012 5:09 pm\nLocation: UK\n\nRe: c libs\n\nAll the Linux C libraries use /dev/mem to access the gpios. It should be simple to extract the low level routines (read/write/PUD up/down/off/read mode/set mode) and use them on bare metal.\n\nFor instance here is part of the source for the pigpio C library.\n\nCode: Select all\n\n/* ----------------------------------------------------------------------- */\n\nint gpioSetMode(unsigned gpio, unsigned mode)\n{\nint reg, shift;\n\nDBG(DBG_USER, \"gpio=%d mode=%d\", gpio, mode);\n\nCHECK_INITED;\n\nif (gpio > PI_MAX_GPIO)\n\nif (mode > PI_ALT3)\n\nreg = gpio/10;\nshift = (gpio%10) * 3;\n\nif (gpio <= PI_MAX_USER_GPIO)\n{\nif (mode != PI_OUTPUT)\n{\nswitch (gpioInfo[gpio].is)\n{\ncase GPIO_SERVO:\n/* switch servo off */\nmyGpioSetServo(gpio,\ngpioInfo[gpio].width/gpioCfg.clockMicros, 0);\nbreak;\n\ncase GPIO_PWM:\n/* switch pwm off */\nmyGpioSetPwm(gpio, gpioInfo[gpio].width, 0);\nbreak;\n}\n\ngpioInfo[gpio].is = GPIO_UNDEFINED;\n}\n}\n\ngpioReg[reg] = (gpioReg[reg] & ~(7<<shift)) | (mode<<shift);\n\nreturn 0;\n}\n\n/* ----------------------------------------------------------------------- */\n\nint gpioGetMode(unsigned gpio)\n{\nint reg, shift;\n\nDBG(DBG_USER, \"gpio=%d\", gpio);\n\nCHECK_INITED;\n\nif (gpio > PI_MAX_GPIO)\n\nreg = gpio/10;\nshift = (gpio%10) * 3;\n\nreturn (*(gpioReg + reg) >> shift) & 7;\n}\n\n/* ----------------------------------------------------------------------- */\n\nint gpioSetPullUpDown(unsigned gpio, unsigned pud)\n{\nDBG(DBG_USER, \"gpio=%d pud=%d\", gpio, pud);\n\nCHECK_INITED;\n\nif (gpio > PI_MAX_GPIO)\n\nif (pud > PI_PUD_UP)\n\n*(gpioReg + GPPUD) = pud;\n\nmyGpioDelay(20);\n\n*(gpioReg + GPPUDCLK0 + BANK) = BIT;\n\nmyGpioDelay(20);\n\n*(gpioReg + GPPUD) = 0;\n\n*(gpioReg + GPPUDCLK0 + BANK) = 0;\n\nreturn 0;\n}\n\n/* ----------------------------------------------------------------------- */\n\n{\nDBG(DBG_USER, \"gpio=%d\", gpio);\n\nCHECK_INITED;\n\nif (gpio > PI_MAX_GPIO)\n\nif ((*(gpioReg + GPLEV0 + BANK) & BIT) != 0) return PI_ON;\nelse return PI_OFF;\n}\n\n/* ----------------------------------------------------------------------- */\n\nint gpioWrite(unsigned gpio, unsigned level)\n{\nDBG(DBG_USER, \"gpio=%d level=%d\", gpio, level);\n\nCHECK_INITED;\n\nif (gpio > PI_MAX_GPIO)\n\nif (level > PI_ON)\n\nif (gpio <= PI_MAX_USER_GPIO)\n{\nif (gpioInfo[gpio].is != GPIO_WRITE)\n{\nif (gpioInfo[gpio].is == GPIO_UNDEFINED)\n{\nif (level == PI_OFF) *(gpioReg + GPCLR0 + BANK) = BIT;\nelse *(gpioReg + GPSET0 + BANK) = BIT;\ngpioSetMode(gpio, PI_OUTPUT);\n}\nelse if (gpioInfo[gpio].is == GPIO_PWM)\n{\n/* switch pwm off */\nmyGpioSetPwm(gpio, gpioInfo[gpio].width, 0);\n}\nelse if (gpioInfo[gpio].is == GPIO_SERVO)\n{\n/* switch servo off */\nmyGpioSetServo(\ngpio, gpioInfo[gpio].width/gpioCfg.clockMicros, 0);\n}\n\ngpioInfo[gpio].is=GPIO_WRITE;\ngpioInfo[gpio].width=0;\n}\n}\n\nif (level == PI_OFF) *(gpioReg + GPCLR0 + BANK) = BIT;\nelse *(gpioReg + GPSET0 + BANK) = BIT;\n\nreturn 0;\n}\nIf you remove all the error checking and debugging paraphernalia it ends up as bare metal routines.\n\nvaltonia\nPosts: 26\nJoined: Wed Jul 04, 2012 9:09 pm\n\nRe: c libs\n\nHere's a really ancient all-c library that gives you most of the basic functions. It doesn't include printf as that's quite platform specific. I don't remember where this code came from now - it might even have been from a book!\n\nAnyway, it might be enough to get you started.\n\nhttp://pastebin.com/C8yhHi4E" ]
[ null ]
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https://www.wiseowl.co.uk/blog/s394/shapes-vba.htm
[ "Browse 551 attributed reviews, viewable separately for our classroom and online training\nIf you found this blog useful and you’d like to say thanks you can click here to make a contribution. Thanks for looking at our blogs!\n\nBLOGS BY TOPIC\n\nBLOGS BY AUTHOR\n\nBLOGS BY YEAR\n\nHow to create autoshapes, lines and connectors in VBA macros\nPart two of an eight-part series of blogs\n\nYou can use Visual Basic within Excel, PowerPoint or Word to draw shapes, format them and even assign macros to run - this long blog gives lots of ideas of how to proceed!\n\nThis is one small part of our free online Excel VBA tutorial.  To find out how to learn in a more structured way, have a look at our training courses in VBA.\n\nPosted by Andy Brown on 25 January 2014\n\nYou need a minimum screen resolution of about 700 pixels width to see our blogs. This is because they contain diagrams and tables which would not be viewable easily on a mobile phone or small laptop. Please use a larger tablet, notebook or desktop computer, or change your screen resolution settings.\n\n# Working with shapes - getting started\n\nAny worksheet contains a collection of shapes, so often a good place to start is by deleting any shapes that you've already added to a worksheet so that you can start with a blank canvas.\n\n## Looping over shapes\n\nThe following macro would delete any shapes which have been added to a worksheet:\n\nSub DeleteShapesOnSheet()\n\nDim w As Worksheet\n\nDim s As Shape\n\n'refer to a given worksheet\n\nSet w = ActiveSheet\n\n'delete all of the shapes on it\n\nFor Each s In w.Shapes\n\ns.Delete\n\nNext s\n\nEnd Sub\n\nThe macro works by looking at each of the shapes on the worksheet in turn, applying the Delete method to remove it.\n\nThe easiest way to add a shape in VBA is to apply the AddShape method to the existing collection of shapes:", null, "Some of the arguments to the AddShape method (the full list is shown below).\n\nThe full list of arguments that you need to specify when adding a shape like this are as follows:\n\nNo. Argument Type Notes\n1 Type Integer or enumeration The shape that you're adding (see below for more on this).\n2 Left Single The position of the shape from the left edge of the worksheet.\n3 Top Single The position of the shape from the top edge of the worksheet.\n4 Width Single The width of the shape.\n5 Height Single The height of the shape.\n\nAll units are in points, which is the typical unit for font size.  When you read a book or magazine article, the font size is probably between 10 and 14 points high.\n\nYou can add a shape either by specifying its enumeration or by using the integer equivalent.  So both of these commands will add the same rectangle:\n\n'get a reference to a worksheet\n\nDim w As Worksheet\n\nSet w = ActiveSheet\n\n'add two rectangles, side by side\n\nw.Shapes.AddShape msoShapeRectangle, 10, 10, 30, 20\n\nw.Shapes.AddShape 1, 50, 10, 30, 20\n\nHere are the shapes added by this code:", null, "The only difference is that one shape is added 10 points in from the left-hand side, and one is added 50 points in from the left.\n\nWhether you choose to specify the shape type by its number or by its enumeration is up to you!\n\n## Listing out the types of shapes\n\nA list of the first 137 autoshape types is shown below (for versions of Excel up to 2003, that's all that there is available):", null, "The main autoshapes in VBA!\n\n## Generating the list of shapes\n\nIt's neither particularly well-written or well-commented, but for the sake of completion (and in case anyone finds it useful for reference), here's the code I wrote to generate the above list:\n\nSub ListShapes()\n\nDim ws As Worksheet\n\nDim s As Shape\n\nDim c As Range\n\n'dimensions of shape\n\nDim l As Single\n\nDim t As Single\n\nDim w As Single\n\nDim h As Single\n\nSet ws = ActiveSheet\n\nFor Each s In ws.Shapes\n\ns.Delete\n\nNext s\n\n'get rid of any old contents\n\nCells.Clear\n\n'put titles in across top\n\nDim col As Integer\n\nDim topcell As Range\n\nFor col = 1 To 5\n\n'add text at top of columns\n\nSet topcell = Cells(1, 3 * col - 2)\n\ntopcell.Value = \"No.\"\n\ntopcell.Offset(0, 1).Value = \"Shape\"\n\n'set column widths\n\ntopcell.EntireColumn.ColumnWidth = 5\n\ntopcell.Offset(0, 1).ColumnWidth = 9\n\ntopcell.Offset(0, 2).ColumnWidth = 2\n\nNext col\n\n'format titles\n\nWith Range(\"A1:N1\")\n\n.Font.Bold = True\n\n.HorizontalAlignment = xlCenter\n\n.VerticalAlignment = xlCenter\n\n.Interior.Color = RGB(220, 220, 220)\n\nEnd With\n\nDim rowNumber As Integer\n\nDim colNumber As Integer\n\nDim shapeNumber As Integer\n\ncolNumber = 1\n\nrowNumber = 1\n\nFor shapeNumber = 1 To 137\n\n'(when go above 35, start new column)\n\nrowNumber = rowNumber + 1\n\nIf rowNumber > 29 Then\n\nrowNumber = 2\n\ncolNumber = colNumber + 3\n\nEnd If\n\n'put shape number in left cell\n\nSet c = Cells(rowNumber, colNumber)\n\nc.Value = shapeNumber\n\n'position shape in right column\n\nl = c.Offset(0, 1).Left + 10\n\nt = c.Offset(0, 1).Top + 5\n\nw = 35\n\nh = 12\n\nSet s = ws.Shapes.AddShape(shapeNumber, l, t, w, h)\n\n'format the number\n\nc.HorizontalAlignment = xlCenter\n\nc.VerticalAlignment = xlCenter\n\nc.RowHeight = 20\n\nIf colNumber < 13 Then\n\nc.Offset(0, 2).Interior.Color = RGB(220, 220, 220)\n\nEnd If\n\nNext shapeNumber\n\nMsgBox \"Done!\"\n\nEnd Sub\n\nIf you're new to shapes, you'll need to read on in this blog to learn more about how they work to understand the above code!\n\nHaving learnt the basics of adding shapes, let's now look at how to name and position them." ]
[ null, "https://www.wiseowl.co.uk/files/blogs/s394/i23.jpg", null, "https://www.wiseowl.co.uk/files/blogs/s394/i24.jpg", null, "https://www.wiseowl.co.uk/files/blogs/s394/i25.jpg", null ]
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https://planetmath.org/exampleofdifferentiablefunctionwhichisnotcontinuouslydifferentiable
[ "# example of differentiable function which is not continuously differentiable\n\nLet $f$ be defined in the following way:\n\n $f(x)=\\begin{cases}x^{2}\\sin\\left(\\frac{1}{x}\\right)&\\text{if }x\\neq 0\\\\ 0&\\text{if }x=0.\\end{cases}$\n\nThen if $x\\neq 0$, $f^{\\prime}(x)=2x\\sin\\left(\\frac{1}{x}\\right)-\\cos\\left(\\frac{1}{x}\\right)$ using the usual rules for calculating derivatives. If $x=0$, we must compute the derivative by evaluating the limit\n\n $\\lim_{\\epsilon\\to 0}\\frac{f(\\epsilon)-f(0)}{\\epsilon}$\n\nwhich we can simplify to\n\n $\\lim_{\\epsilon\\to 0}\\,\\epsilon\\sin\\left(\\frac{1}{\\epsilon}\\right).$\n\nWe know $\\left|\\sin(x)\\right|\\leq 1$ for every $x$, so this limit is just $0$. Combining this with our previous calculation, we see that\n\n $f^{\\prime}(x)=\\begin{cases}2x\\sin\\left(\\frac{1}{x}\\right)-\\cos\\left(\\frac{1}{x% }\\right)&\\text{if }x\\neq 0\\\\ 0&\\text{if }x=0.\\end{cases}$\n\nThis is just a slightly modified version of the topologist’s sine curve; in particular,\n\n $\\lim_{x\\to 0}f^{\\prime}(x)$\n\ndiverges, so that $f^{\\prime}(x)$ is not continuous", null, "", null, ", even though it is defined for every real number. Put another way, $f$ is differentiable", null, "", null, "", null, "but not $C^{1}$.\n\nTitle example of differentiable function which is not continuously differentiable ExampleOfDifferentiableFunctionWhichIsNotContinuouslyDifferentiable 2013-03-22 14:10:18 2013-03-22 14:10:18 Koro (127) Koro (127) 8 Koro (127) Example msc 57R35 msc 26A24" ]
[ null, "http://mathworld.wolfram.com/favicon_mathworld.png", null, "http://planetmath.org/sites/default/files/fab-favicon.ico", null, "http://mathworld.wolfram.com/favicon_mathworld.png", null, "http://planetmath.org/sites/default/files/fab-favicon.ico", null, "http://planetmath.org/sites/default/files/fab-favicon.ico", null ]
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https://tutorbin.com/questions-and-answers/the-mechanics-of-a-mass-spring-system-is-governed-by-the-differential-equation-m-frac-d-2-y-d-t-2-l-frac-d-y-d-t-k-y-0
[ "Question\n\n# The mechanics of a mass-spring system is governed by the differential equation m \\frac{d^{2} y}{d t^{2}}+l \\frac{d y}{d t}+k y=0 ; \\quad y(0)=0.5, y^{\\prime}(0)=0 \\text { where } m=1+a, l=5+\\mathrm{b} \\text { and } k=6+c \\text {. Here } a, b \\text { and } c \\text { are } 2^{\\text {nd }}, 3^{\\text {rd }} \\text { and } 4^{\\text {th }} \\text { digits of your } ) Find the solution of the differential equation and describe the behaviour of the-mass )) An external force of f(t) = 5e-3t + sin(2t) is applied to the mass, what effect does it have on the motion of the mass? Find a scenario by choosing appropriate constant values for the spring system-where no dampening occurs. How does this affect the frequency and amplitude of the oscillations?", null, "", null, "Fig: 1", null, "", null, "Fig: 2", null, "", null, "Fig: 3", null, "", null, "Fig: 4", null, "", null, "Fig: 5", null, "", null, "Fig: 6" ]
[ null, "data:image/svg+xml,%3csvg%20xmlns=%27http://www.w3.org/2000/svg%27%20version=%271.1%27%20width=%27500%27%20height=%27300%27/%3e", null, "data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7", null, "data:image/svg+xml,%3csvg%20xmlns=%27http://www.w3.org/2000/svg%27%20version=%271.1%27%20width=%27500%27%20height=%27300%27/%3e", null, "data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7", null, "data:image/svg+xml,%3csvg%20xmlns=%27http://www.w3.org/2000/svg%27%20version=%271.1%27%20width=%27500%27%20height=%27300%27/%3e", null, "data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7", null, "data:image/svg+xml,%3csvg%20xmlns=%27http://www.w3.org/2000/svg%27%20version=%271.1%27%20width=%27500%27%20height=%27300%27/%3e", null, "data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7", null, "data:image/svg+xml,%3csvg%20xmlns=%27http://www.w3.org/2000/svg%27%20version=%271.1%27%20width=%27500%27%20height=%27300%27/%3e", null, "data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7", null, "data:image/svg+xml,%3csvg%20xmlns=%27http://www.w3.org/2000/svg%27%20version=%271.1%27%20width=%27500%27%20height=%27300%27/%3e", null, "data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7", null ]
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https://math.stackexchange.com/questions/1912624/what-is-the-consistency-strength-of-width-reflection
[ "# What is the consistency strength of \"width reflection\"?\n\nLots of people will be familiar with the second-order principle asserting that certain properties are reflected to $V_\\alpha$. For a second-order formula $\\phi$, parameter $A$, and relativisation of quantifiers and parameters to $V_\\alpha$, we can have:\n\n$\\phi(A) \\rightarrow \\exists \\alpha V_\\alpha \\models \\phi^{V_\\alpha} (A^{V_\\alpha})$\n\nThis yields lots of small large cardinals (e.g. inaccessible, Mahlo, etc.).\n\nNow there are some 'width-like' reflection principles, for example Friedman's Inner Model Hypothesis. For first-order $\\phi$ we say:\n\n\"If $\\phi$ is true in an inner model $I^{V*}$ of an outer model $V*$ of $V$, then $\\phi$ is true in an inner model $I^V$ of $V$\"\n\nThis principle has surprisingly high consistency strength (the known proof shows that it is consistent relative to the existence of a Woodin cardinal with an inaccessible above). Here though, there are significant metamathematical issues (for one, you have to code extensions if you think there's a \"real\" $V$).\n\nI'm therefore wondering about the following (greater than first-order) principle (for first-order $\\phi$ with/without parameters—I'm interested in both):\n\n\"If $\\phi$ is true in $V$, then $\\phi$ is true in a proper inner model of $V$.\"\n\nI'm guessing this is either incredibly weak or inconsistent. I'm guessing more confidently the former (you can certainly get $V\\not=L$ out of it, just by virtue of the fact that you get a single proper inner model), but without further information about what holds in $V$ you just don't know what more (hence why the strength flies up once we have extensions).\n\nEDIT: Added after Joel Hamkins' very nice answer: I'm also interested in any consequences this principle has, as well as the outright consistency strength. I'm pretty confident that a slight modification of his proof shows that apart from $V\\not=L$ and the existence of infinitely many inner models, there's not that much (by running something similar to the Hamkins argument below, I'm guessing that we can arrange a lot of possibilities for $V$ with a suitable forcing).\n\n• For the parameter-free version: Note that $\\mathbb{P}$ is isomorphic to $\\mathbb P*\\dot{\\mathbb P}$, where $\\mathbb P$ is Cohen forcing. Let $c$ be Cohen generic over $V$ and $d$ be Cohen generic over $V[c]$. Since $\\mathbb P$ is weakly homogeneous, this easily gives us that $V[c]\\equiv V[c][d]$. (That is, the parameter-free version is equiconsistent with $\\mathsf{ZFC}$.) Sep 2, 2016 at 23:44\n• Hi Neil - great question! I have no idea of the answer, but it suggests a related question that might be more tractable, the set-theoretic geology version: \"If $\\phi$ is true in $V$, then $\\phi$ is true in a proper ground of $V$\" This neatly avoids the metamathematical difficulties, as the grounds are a nice first-order neighborhood of the collection of inner models, and we know a lot about them (I guess), since we know about forcing. I don't know the answer to this one, either, though! I'll think about it... Sep 3, 2016 at 1:11\n• @AndrésE.Caicedo. Great! Thanks. That's a neat way of doing it! It's a nice way of seeing as well that if you don't have the Friedman version with extensions, you've got so little info about V that it doesn't prove very much else either (though $V\\not=L$ will be one thing you get). Sep 3, 2016 at 12:29\n• @jonasreitz. Thanks too for this! By metamathematical difficulties, I just meant the problem with extensions rather than anything to do with second-order worries. Your suggestion throws up numerous geological questions though (e.g. what if we allow pseudo-grounds). I will also think! Sep 3, 2016 at 12:31\n\nUpdate. Neil, Andrés, Gunter, myself and Jonas have written a paper on the topic of this question, exploring the matter further, including and extending the various comments and answers here. It available at:\n\nNeil Barton, Andrés Eduardo Caicedo, Gunter Fuchs, Joel David Hamkins, Jonas Reitz, Inner-model reflection principles, manuscript under review, arXiv:1708.06669, blog post.\n\nAbstract. We introduce and consider the inner-model reflection principle, which asserts that whenever a statement $$\\varphi(a)$$ in the first-order language of set theory is true in the set-theoretic universe $$V$$, then it is also true in a proper inner model $$W\\subsetneq V$$. A stronger principle, the ground-model reflection principle, asserts that any such $$\\varphi(a)$$ true in $$V$$ is also true in some nontrivial ground model of the universe with respect to set forcing. These principles each express a form of width reflection in contrast to the usual height reflection of the Lévy-Montague reflection theorem. They are each equiconsistent with ZFC and indeed $$\\Pi_2$$-conservative over ZFC, being forceable by class forcing while preserving any desired rank-initial segment of the universe. Furthermore, the inner-model reflection principle is a consequence of the existence of sufficient large cardinals, and lightface formulations of the reflection principles follow from the maximality principle MP and from the inner-model hypothesis IMH.\n\nOriginal answer. Following a generalization of Andres's idea to higher cardinals, I claim that your width-reflection principle is equiconsistent with ZFC, even when parameters are allowed in the scheme.\n\nTo see this, start with any model $$V\\models\\newcommand\\ZFC{\\text{ZFC}}\\ZFC+\\text{GCH}$$, and then perform the proper class forcing $$\\mathbb{P}$$, which is the Easton product of the forcing to add a Cohen subset at every regular cardinal. I claim that the resulting forcing extension $$V[G]$$ satisfies your width-reflection principle, even with arbitrary parameters.\n\nTo see this, suppose that $$\\varphi(a)$$ is true in $$V[G]$$, where $$a\\in V[G]$$. Fix a name $$\\dot a$$ for $$a$$, and let $$p$$ be a condition forcing $$\\varphi(\\dot a)$$. Let $$\\theta$$ be a regular cardinal large enough that it is above the support of $$p$$ and above the support of any condition appearing in $$\\dot a$$. Since the forcing at coordinate $$\\theta$$ is adding a subset to $$\\theta$$, we can view it as having adding two, and then let $$G^-$$ be the generic filter obtained by removing one of those factors. But removing one factor gives rise to forcing that is isomorphic to $$\\mathbb{P}$$ again, and so $$G^-$$ can be viewed as $$V$$-generic for $$\\mathbb{P}$$. Since $$\\theta$$ was above $$p$$ and $$\\dot a$$, we still have $$\\varphi(a)$$ being true in $$V[G^-]$$, which is a strictly smaller inner model, but still containing the object $$a$$. So this fulfills width-reflection, as desired.\n\n• This is some magic. I'm guessing a related argument shows that, apart from getting infinitely many inner models, the principle doesn't have many consequences. For instance, the resulting model violates GCH everywhere, but I'm guessing if you do an \"Easton collapse\" (is there such a thing? I'm thinking of a class forcing that collapses back down all the cardinals you boosted up with the first Easton), you'll still have the required 'richness' of models. Need to check though. Sep 3, 2016 at 12:43\n• I think you can easily modify the argument to have GCH, or to have any pattern of the GCH using Easton's theorem. And it can accommodate any kind of large cardinals, etc. It does have some consequences, such as $V\\neq L$ as you mention. The parameter version implies $V\\neq L[A]$ for any set $A$.\n– JDH\nSep 3, 2016 at 13:12\n• Another observation: if there are unboundedly many measurable cardinals, then you get width-reflection with parameters, because for any set $a$, let $\\kappa$ be a measurable cardinal above it, with embedding $j:V\\to M$. If $\\varphi(a)$ holds in $V$, then it also holds in $M$ by elementarity.\n– JDH\nSep 3, 2016 at 13:13\n• A further observation: since the continuum coding axiom is relatively consistent with a proper class of measurable cardinals, and this implies the ground axiom (asserting that there are no proper ground models), we get the consistency of inner-model reflection with the ground axiom and therefore with the failure of the ground-model reflection principle mentioned by Jonas.\n– JDH\nSep 4, 2016 at 8:12\n\nConcerning Jonas's comment: That suggested strengthening of the original principle follows from the maximality principle (saying that if phi is forceably necessary, then it is true). Namely, if phi is true in V, then after nontrivial forcing, it is necessarily true in a proper ground. So the statement \"phi is true in a proper ground\" is forceably necessary, hence true in V by the maximality principle. So phi is true in a proper ground. This all concerns the parameter free version. And the strength of the lightface maximality principle is also just ZFC.\n\n• Welcome to the site! Sep 3, 2016 at 16:41\n• Ah thanks Gunter---this is nice. There's definitely a bunch of geological questions here (I'm especially interested in what happens when we look at pseudo-grounds. This will, of course, be weaker (in consequences) but I'm wondering how much. Sep 5, 2016 at 23:13" ]
[ null ]
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https://ch.mathworks.com/matlabcentral/cody/problems/1411-number-of-lattice-points-within-a-circle
[ "Cody\n\n# Problem 1411. Number of lattice points within a circle\n\nFind the number of points (x,y) in square lattice with x^2 + y^2 =< n. This is related to Jame's Problem 1387. Here you have to find the number of points within a circle.\n\n### Solution Stats\n\n37.18% Correct | 62.82% Incorrect\nLast Solution submitted on Jun 22, 2020" ]
[ null ]
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https://annals.math.princeton.edu/2010/171-3/p16
[ "# Some adjoints in homotopy categories\n\n### Abstract\n\nLet $R$ be a ring. In a previous paper we found a new description for the category $\\mathbf{K}(R\\text{-Proj})$; it is equivalent to the Verdier quotient $\\mathbf{K}(R\\text{-Flat})/{\\mathscr S}$, for some suitable $\\mathscr{S}\\subset\\mathbf{K}(R\\text{-Flat})$. In this article we show that the quotient map from $\\mathbf{K}(R\\text{-Flat})$ to $\\mathbf{K}(R\\text{-Flat})/\\mathscr{S}$ always has a right adjoint. This gives a new, fully faithful embedding of $\\mathbf{K}(R\\text{-Proj})$ into $\\mathbf{K}(R\\text{-Flat})$. Its virtue is that it generalizes to nonaffine schemes." ]
[ null ]
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https://artofproblemsolving.com/wiki/index.php/1964_AHSME_Problems/Problem_17
[ "# 1964 AHSME Problems/Problem 17\n\n## Problem 17\n\nGiven the distinct points", null, "$P(x_1, y_1), Q(x_2, y_2)$ and", null, "$R(x_1+x_2, y_1+y_2)$. Line segments are drawn connecting these points to each other and to the origin", null, "$O$. Of the three possibilities: (1) parallelogram (2) straight line (3) trapezoid, figure", null, "$OPRQ$, depending upon the location of the points", null, "$P, Q$, and", null, "$R$, can be:", null, "$\\textbf{(A)}\\ \\text{(1) only}\\qquad \\textbf{(B)}\\ \\text{(2) only}\\qquad \\textbf{(C)}\\ \\text{(3) only}\\qquad \\textbf{(D)}\\ \\text{(1) or (2) only}\\qquad \\textbf{(E)}\\ \\text{all three}$\n\n# Solution\n\nUsing vector addition can help solve this problem quickly. Note that algebraically, adding", null, "$\\overrightarrow{OP}$ to", null, "$\\overrightarrow{OQ}$ will give", null, "$\\overrightarrow{OR}$. One method of vector addition is literally known as the \"parallelogram rule\" - if you are given", null, "$\\overrightarrow{OP}$ and", null, "$\\overrightarrow{OQ}$, to find", null, "$\\overrightarrow{OR}$, you can literally draw a parallelogram, making a line though", null, "$P$ parallel to", null, "$OQ$, and a line through", null, "$Q$ parallel to", null, "$OP$. The intersection of those lines will give the fourth point", null, "$R$, and that fourth point will form a parallelogram with", null, "$O, P, Q$.\n\nThus,", null, "$1$ is a possibility. Case", null, "$2$ is also a possibility, if", null, "$O, P, Q$ are collinear, then", null, "$R$ is also on that line.\n\nSince", null, "$OP \\parallel QR$ and", null, "$PQ \\parallel RO$, which can be seen from either the prior reasoning or by examining slopes, the figure can never be a trapezoid, which requires exactly one of parallel sides.\n\nThus, the answer is", null, "$\\boxed{\\textbf{(D)}}$\n\n## See Also\n\n 1964 AHSC (Problems • Answer Key • Resources) Preceded byProblem 16 Followed byProblem 18 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 All AHSME Problems and Solutions\n\nThe problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.", null, "Invalid username\nLogin to AoPS" ]
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https://www.daniweb.com/programming/software-development/threads/407431/vector-array
[ "Hi list,\n\nThree functions use the following items vector. Where/how should i put the vector to make this possible ?\nAny reference to related sources will be appreciated.\n\nvector< vector<int> > items ( 6, vector<int> ( 6 ) );\n\nP.S I tried to make it static but it gave error unfortunately .\n\nGlobals are EVIL. Period.\nYou have two ways:\n1. declare the vector inside main() and pass a pointer (this is more C-way)\n\nvoid foo(vector<vector<int> >* items){\n};\nvoid bar(vector<vector<int> >* items){\n};\nvoid foobar(vector<vector<int> >* items){\n};\n\nvoid main(){\nvector< vector<int> > items ( 6, vector<int> ( …\n\nAll 4 Replies\n\njust declare it in a class and mention your three functions in the class\nmake an object in main and access the data\n\nHi,\ni am new in std::vector/cli::vector class. I dont know which one is more suitable for me. So i just want to see if it works in a single form application. Therefore its enought to make it global. Is this possible?\n:?:\n\nGlobals are EVIL. Period.\nYou have two ways:\n1. declare the vector inside main() and pass a pointer (this is more C-way)\n\nvoid foo(vector<vector<int> >* items){\n};\nvoid bar(vector<vector<int> >* items){\n};\nvoid foobar(vector<vector<int> >* items){\n};\n\nvoid main(){\nvector< vector<int> > items ( 6, vector<int> ( 6 ) );\nfoo(&items);\nbar(&items;\nfoobar(&items);\n}\n\n2. make a simple class (C++-way)\n\nclass foobar{\npublic:\nvector< vector<int> > items ( 6, vector<int> ( 6 ) );\nvoid foo(vector<vector<int> >* items){\n};\nvoid bar(vector<vector<int> >* items){\n};\nvoid foobar(vector<vector<int> >* items){\n};\n};\n\nvoid main(){\nfoobar foo;\nfoo.items=5;\nfoo.foo();\nfoo.bar();\nfoo.foobar();\n}" ]
[ null ]
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https://forums.developer.nvidia.com/t/thrust-question/20646
[ "", null, "# Thrust question\n\nHi,\n\nI have two questions regarding Thrust.\n\n1. Why is there no sub group for Thrust?? :)\n\n2. If I want to sort a “float *” array inplace using thrust::sort, how do I do this?\n\nCurrently I do something like this:\n\n``````thrust::host_vector<float> h_vec1(50);\n\nfloat *fData = new float[ 50 ];\n\nthrust::device_vector<float> d_x( &(fData), &(fData) + 50);\n\nthrust::sort(d_x.begin(), d_x.end());\n\nthrust::copy(d_x.begin(), d_x.end(), h_vec.begin());\n\nthrust::copy(h_vec1.begin(), h_vec1.end(), std::ostream_iterator<float>(std::cout, \"\\n\"));\n``````\n\nThis code uses a temporary host_vector (h_vec1). How do I remove the need for it and copy the sorted\n\nresult right back from the device to the original fData array?\n\nthanks\n\neyal\n\ndoes\n\n``````thrust::copy(d_x.begin(), d_x.end(), fData);\n``````\n\nnot work?\n\nAlso regarding 1), the thrust “forum” is here: http://groups.google.com/group/thrust-users\n\nThere’s no subforum for Thrust, but there is a dedicated mailing list (thrust-users).\n\nTo eliminate the h_vec1 temporary, just use fData directly. Note that fData is a valid “iterator” (just like .begin() and .end()) so you can use fData and fData + 50 to define the beginning and end of the host array. Thrust will assume that a “raw pointer” like fData lives on the host.\n\n``````float *fData = new float[ 50 ];\n\nthrust::device_vector<float> d_x(fData, fData + 50);\n\nthrust::sort(d_x.begin(), d_x.end());\n\nthrust::copy(d_x.begin(), d_x.end(), fData);\n\nthrust::copy(fData, fData + 50, std::ostream_iterator<float>(std::cout, \"\\n\"));\n``````\n\nVery elegant :) works like a charm…\n\nThanks\n\neyal" ]
[ null, "https://aws1.discourse-cdn.com/nvidia/original/2X/3/3f301944ed0d2d0d779b3eaa251520d35458d467.png", null ]
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http://mizar.org/version/current/html/proofs/necklace/44
[ "let n be Nat; :: thesis: for i, j being Nat holds\n( not [i,j] in the InternalRel of () or i = j + 1 or j = i + 1 )\n\nlet i, j be Nat; :: thesis: ( not [i,j] in the InternalRel of () or i = j + 1 or j = i + 1 )\nassume [i,j] in the InternalRel of () ; :: thesis: ( i = j + 1 or j = i + 1 )\nthen [i,j] in { [k,(k + 1)] where k is Element of NAT : k + 1 < n } \\/ { [(l + 1),l] where l is Element of NAT : l + 1 < n } by Th17;\nthen A1: ( [i,j] in { [k,(k + 1)] where k is Element of NAT : k + 1 < n } or [i,j] in { [(k + 1),k] where k is Element of NAT : k + 1 < n } ) by XBOOLE_0:def 3;\n( i + 1 = j or j + 1 = i )\nproof\nper cases ( ex k being Element of NAT st\n( [i,j] = [k,(k + 1)] & k + 1 < n ) or ex k being Element of NAT st\n( [i,j] = [(k + 1),k] & k + 1 < n ) )\nby A1;\nsuppose ex k being Element of NAT st\n( [i,j] = [k,(k + 1)] & k + 1 < n ) ; :: thesis: ( i + 1 = j or j + 1 = i )\nthen consider k being Nat such that\nA2: [i,j] = [k,(k + 1)] and\nk + 1 < n ;\ni = k by ;\nhence ( i + 1 = j or j + 1 = i ) by ; :: thesis: verum\nend;\nsuppose ex k being Element of NAT st\n( [i,j] = [(k + 1),k] & k + 1 < n ) ; :: thesis: ( i + 1 = j or j + 1 = i )\nthen consider k being Nat such that\nA3: [i,j] = [(k + 1),k] and\nk + 1 < n ;\ni = k + 1 by ;\nhence ( i + 1 = j or j + 1 = i ) by ; :: thesis: verum\nend;\nend;\nend;\nhence ( i = j + 1 or j = i + 1 ) ; :: thesis: verum" ]
[ null ]
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https://worlddatabaseofhappiness.eur.nl/correlational-findings/9488/
[ "# Correlational findings\n\n## Study Timmermans (1997): study SI 1992\n\nPublic:\n18+ aged, general public, Slovenia, 1990\nSample:\nRespondents:\nN = 1035\nNon Response:\nAssessment:\nInterview: face-to-face\nStructured interview\n\n## Correlate\n\nAuthors's label\nHousehold income\nOur Classification\nOperationalization\nSingle question: \"Here is a scale of incomes and we would like to know in what group your household is, counting all wages, salaries, pensions and other incomes that come in\" rated on a a 10-point scale (scale categories not reported in datafile).\n\n## Observed Relation with Happiness\n\nHappiness Measure Statistics Elaboration / Remarks O-HL-u-sq-v-4-a = 1       M=1.87     Mt=2.9\n2       M=2.07     Mt=3.6\n3       M=2.26     Mt=4.2\n4       M=2.21     Mt=4.0\n5       M=2.34     Mt=4.5\n6       M=2.50     Mt=5.0\n7       M=2.71     Mt=5.7\n8       M=2.62     Mt=5.4\n9       Less than 10 Ss\n10      Less than 10 Ss\nO-SLW-c-sq-n-10-aa = 1       M=2.89      Mt=2.1\n2       M=3.75      Mt=3.1\n3       M=4.45      Mt=3.8\n4       M=4.63      Mt=4.0\n5       M=5.34      Mt=4.8\n6       M=5.38      Mt=4.9\n7       M=6.06      Mt=5.6\n8       M=5.78      Mt=5.3\n9       Less than 10 Ss\n10      Less than 10 Ss\nA-BB-cm-mq-v-2-a = 1       M= .98      Mt=6.0\n2       M=1.37      Mt=6.4\n3       M=1.54      Mt=6.5\n4       M=1.59      Mt=6.6\n5       M=1.77      Mt=6.8\n6       M=1.67      Mt=6.7\n7       M=1.84      Mt=6.8\n8       M=1.96      Mt=7.0\n9       Less than 10 Ss\n10      Less than 10 Ss\nO-HL-u-sq-v-4-a = +.25 p < .001 O-SLW-c-sq-n-10-aa = +.33 p < .001 A-BB-cm-mq-v-2-a = +.16 p < .001 O-HL-u-sq-v-4-a = +.20 p < .001 O-SLW-c-sq-n-10-aa = +.24 p < .001 A-BB-cm-mq-v-2-a = +.11 p < .001 O-HL-u-sq-v-4-a = +.25 p < .001 ß controlled for sex and age O-SLW-c-sq-n-10-aa = +.33 p < .001 ß controlled for sex and age A-BB-cm-mq-v-2-a = +.15 p < .001 ß controlled for sex and age" ]
[ null ]
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https://www.johnroach.io/mid-rise-type-quantizer/
[ "# Mid-rise type quantizer\n\nA mid-rise type quantizer for my DSP lab course. The question is as below.\n\nGenerate a discrete-time sinusoidal signal `x[n]` with the `SinSamples()` function implemented in preliminary work of experiment 1, with the parameters: `A=3, w=2*pi, ws=2*pi*50, .θ=0, d=2sec`. Implement 3-bit midrise type quantizer. Make the reconstruction levels be spaced so as to span the entire amplitude range of the signal. You may use the maximum amplitude of the signal in designing reconstruction levels. Plot original signal, quantized version, and quantization error. Calculate output signal to noise ratio in dB (all signal to noise ratios must be calculated in dB).\n\nGenerate a discrete-time sinusoidal signal x[n] with the SinSamples() function implemented in preliminary work of experiment 1, with the parameters: A=3, w=2pi, ws=2pi*50, .θ=0, d=2seca) Implement 3-bit midrise type quantizer. Make the reconstruction levels be spaced so as to span the entire amplitude range of the signal. You may use the maximum amplitude of the signal in designing reconstruction levels. Plot original signal, quantized version, and quantization error. Calculate output signal to noise ratio in dB (all signal to noise ratios must be calculated in dB).\n\n``````A=3;\nw=2*pi\nw_s=2*pi*50;\nd=2;\nteta=0;\n\nf = w/(2*pi);\nT = 1/f;\ntmin = 0;\ndt = T/100;\ndt1 = 1/(w_s/(2*pi));\nt = tmin:dt:d;\nt1 = tmin:dt1:d;\nx = A*sin(w*t+teta);\nx1 = A*sin(w*t1+teta);\nsubplot(3,1,1);\nplot(t,x,'r');\nhold on\nstem(t1,x1);\ntitle('The sampled and original signal');\nxlabel(''), ylabel('amplitude');\ngrid on;\nhold on\n\n% Quatization part (midrise)\nbit=3; %number of bits that will be used\nsignal=x1; %get the signal\nm_max=max(abs(signal)); %find the highest magnitude used\ndelta=(2*m_max)/(2^bit) ; %our step size\nk_max=(2^bit)/2; %how many levels we have in one side of the quatization graph\nfor i=1:length(signal)\nfor k=0:1:(k_max-1)\nif (((k*delta)<=abs(signal(i)))&&(abs(signal(i))<=((k+1)*delta)))\nif(signal(i)>0)\nnew_signal(i)=(0.5+k)*delta;\nelseif(signal(i)<0)\nnew_signal(i)=(-0.5-k)*delta;\nelseif(signal(i)==0)\nnew_signal(i)=0;\nend\nend\n\nend\nend\nsubplot(3,1,2);\nstem(t1,new_signal);\nxlabel(''), ylabel('amplitude');\ngrid on;\nhold on\n\nerror=signal-new_signal;\nsubplot(3,1,3);\nstem(t1,error);\nxlabel(''), ylabel('amplitude');\ngrid on;\nhold on\n``````", null, "" ]
[ null, "https://www.johnroach.io/content/images/2016/09/outputfordsp.png", null ]
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http://forums.wolfram.com/mathgroup/archive/2008/Nov/msg00075.html
[ "", null, "", null, "", null, "", null, "", null, "", null, "", null, "Data fitting from coupled differential equations\n\n• To: mathgroup at smc.vnet.net\n• Subject: [mg93291] Data fitting from coupled differential equations\n• From: margeorias at gmail.com\n• Date: Mon, 3 Nov 2008 05:25:11 -0500 (EST)\n\n```Hi,\n\nI'm working on a predator-prey model for 2-species:\nn1'[t] == a1 n1[t] - b1 n1[t]^2 + c1 n1[t] n2[t]\nn2'[t] == a2 n2[t] - b2 n2[t]^2 + c2 n1[t] n2[t]\nn1 == n10,\nn2 == n20\n\nI have real data for (t,n1[t],n2[t]), i.e. data={t,n1[t],n2[t]} and my\nobjective is to estimate the coefficients a1,a2,b1,b2,c1,c2.\n\nTo do this, I generate synthetic data by solving the above equations\nusing {n10,n20,a1,a2,b1,b2,c1,c2}={0.01,0.001,2,3,1,1,1,2} and sample\nthe solutions,i.e.\ndata = Table[{t, n1[t], n2[t]} /. sol, {t, 0, 20, 0.25}];\n\nI then set-up the function below:\n\nsse[a1_?NumericQ,a2_?NumericQ,b1_?NumericQ,b2_?NumericQ,c1_?\nNumericQ,c2_?NumericQ]:=\nBlock[{sol,n1,n2},\nsol=NDSolve[{\nn1'[t]==a1 n1[t]-b1 n1[t]-c1 n1[t] n2[t],\nn2'[t]==a2 n2[t]-b2 n2[t]-c2 n1[t] n2[t],\nn1==0.01,n2==0.001},\n{n1,n2},{t,0,20}][];\nPlus@@Apply[((n1[#1]-#2)^2+(n2[#1]-#3)^2)&,data,{1}]/.sol]\n\nand use FindMinimum to retrieve the coefficients:\nFindMinimum[sse[a1,a2,b1,b2,c1,c2],{{a1,1.},{a2,1.},{b1,1.},{b2,1.},\n{c1,1.},{c2,1.}},AccuracyGoal->20,PrecisionGoal->18,WorkingPrecision-\n>40]\n\nMy problem however is that the resulting coefficients are not the same\nas the original one, ie:\n{a1->-9.49992942438124754467310,a2->-9.50000018840483650972573,b1-\n>-9.50007117410767898402213,b2->-9.50000041008883222559689,c1-\n>-9.50000036535088621114653,c2->-9.50000030036113407572174}\n\nI can improve the results by making starting points very close to the\nactual value of the coefficients i.e. {a1,2}. Well this somehow\ndefeats the purpose and in reality, I don't know whats the actual\nvalue of the coefficients - they range from -Infinity to Infinity.How\ndo I go about obtaining the correct coefficients? Is there something\nwrong with the function above?\n\nAnother thing, wouldn't NMinimize be appropriate for this as well\nsince I want to find the global minimum of sse? I have tried it but it\ngave the wrong values for the coefficients as well :(\n\nI'm trying to make FindFit work on the coupled differential equations\nbut no luck yet. Any guidance on this?\n\nAppreciate any feedback you have.\n\nThanks again.\n\n```\n\n• Prev by Date: Re: Aborting a computation ...\n• Next by Date: Re: Expressions with ellipsis (...)\n• Previous by thread: Re: Re: Mathematica 6.0: How to collect data with Manipulate?\n• Next by thread: Re: Data fitting from coupled differential equations" ]
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https://mathematica.stackexchange.com/questions/88254/manipulate-to-determine-delta-given-epsilon-in-continuity-question
[ "# Manipulate to determine $\\delta$ given $\\epsilon$ in continuity question\n\nThis is a continuation of a question I posed at: Examining the function $f(x,y)=xy(x^2-y^2)/(x^2+y^2)$.\n\nThe quest is to analyze the partial derivative $$f_x(x,y)=\\begin{cases} \\dfrac{y(x^4+4x^2y^2-y^4)}{(x^2+y^2)^2},&(x,y)\\ne(0,0)\\\\ 0,& (x,y)=(0,0) \\end{cases}$$ to see if it is continuous at (0,0). I've tried a little manipulate activity:\n\nDynamicModule[{f, max, min},\nfx[x_, y_] :=\nPiecewise[{{(y (x^4 + 4 x^2 y^2 - y^4))/(x^2 + y^2)^2,\nx != 0 && y != 0}}, 0];\nManipulate[\nmax = NMaximize[{fx[x, y], Sqrt[x^2 + y^2] < \\[Delta]}, {x, y}][];\nmin = NMinimize[{fx[x, y], Sqrt[x^2 + y^2] < \\[Delta]}, {x, y}][];\nColumn[{\nRow[{\"Min = \" <> ToString[min], \", Max = \" <> ToString[max]}],\nPlot3D[{fx[x, y],\n0}, {x, -\\[Delta], \\[Delta]}, {y, -\\[Delta], \\[Delta]},\nPlotStyle -> {Directive[Red],\nDirective[LightBlue, Opacity[.8]]},\nRegionFunction -> Function[{x, y, z}, Sqrt[x^2 + y^2] < \\[Delta]],\nPlotRange -> All,\nBoxRatios -> Automatic,\nPerformanceGoal -> \"Quality\"]\n}],\n{{\\[Epsilon], .1}, .001, .15, Appearance -> \"Labeled\"},\n{{\\[Delta], .5}, .01, 1, Appearance -> \"Labeled\"}\n]\n]\n\n\nThere are a couple of problems. First, it's very slow as I am calculating min, max, and redrawing the image each time the slide moves. Second, when the delta slider gets tiny, things go bad.\n\nAny thoughts?\n\nExample of something that happens:\n\nNMinimize[{fx[x, y], Sqrt[x^2 + y^2] < .1}, {x, y}]\n\n\nDuring evaluation of In:= NMinimize::incst: NMinimize was unable to generate any initial points satisfying the inequality constraints {-0.1+Sqrt[x^2+y^2]<=0}. The initial region specified may not contain any feasible points. Changing the initial region or specifying explicit initial points may provide a better solution. >>\n\nOut= {-0.1, {x -> -7.45003*10^-9, y -> 0.1}}\n\n• In polar coordinates it's fx[x, y] == -(1/2) r (-1 - 2 Cos[2 t] + Cos[4 t]) Sin[t] and fairly easy to understand. In particular you can separate variables, optimize over t -- min/max are always at t equals Pi/2 and -Pi/2. But as I recall from your other questions, you might want to leave it in terms of cartesian coordinates for the sake of your students. But I would teach my students to analyze this particular function in polar coordinates because of the denominator. (I mean they should take one look and say, \"Oh, of course, let's use polar.\") Jul 14, 2015 at 22:18\n• @MichaelE2 This comment caused me to do some searching and reading which wound up being really helpful. However, still not sure how to repair my Manipulate. See an update addition to original post. Jul 15, 2015 at 4:25\n\nIn the current version of the question, the second parameter $\\epsilon$ isn't needed. If you can do without it, I would suggest pre-computing the list of relevant $\\delta$ values and making a ListAnimate to speed up the rendering. But I will assume that you can't go that route, maybe because you'll add some dependence on $\\epsilon$ later.\n\nThen the numerical problems can be avoided by throwing out NMinimize and NMaximize altogether:\n\nDynamicModule[{f, max, min, g},\nfx[x_, y_] :=\nPiecewise[{{(y (x^4 + 4 x^2 y^2 - y^4))/(x^2 + y^2)^2,\nx != 0 && y != 0}}, 0];\nManipulate[\ng = Plot3D[{fx[x, y],\n0}, {x, -δ, δ}, {y, -δ, δ},\nPlotStyle -> {Directive[Red], Directive[LightBlue, Opacity[.8]]},\nRegionFunction -> Function[{x, y, z}, Sqrt[x^2 + y^2] < δ],\nPlotRange -> All, BoxRatios -> Automatic,\nPerformanceGoal -> \"Quality\"];\n{min, max} =\nFirst@Cases[g, GraphicsComplex[pts_, __] :> MinMax[pts[[All,3]]]];\nColumn[{Row[{\"Min = \" <> ToString[min],\n\", Max = \" <> ToString[max]}],\ng}], {{ϵ, .1}, .001, .15,\nAppearance -> \"Labeled\"}, {{δ, .5}, .01, 1,\nAppearance -> \"Labeled\"}]]\n\n\nHere, I used the fact that in order to plot the function, Mathematica already did the calculation of the minimum and maximum function value for you. In particular with the setting PerformanceGoal -> \"Quality\", this should be sufficiently accurate for the purposes of a Manipulate to display as the numerical minima and maxima. I extract these values using MinMax in a Cases statement applied to the plot which is generated beforehand and called g.\n\nMore explanations:\n\nWithin Cases, I make use of the fact that the 3D plot is by default given as a GraphicsComplex, in which all the 3D points are listed as one big list, followed by instructions of what to do with those points (i.e., how to assemble them into polygons etc.) The advantage of GraphicsComplex is that it allows references to 3D points by a single index (giving its position in the point list) - and another advantage is that you don't have to look for the plot coordinates anywhere else, only in the first argument of GraphicsComplex, which is what I do using the pattern GraphicsComplex[pts_,__]. Naming this list pts, I can then subject it to transformations. Cases outputs only the result of those transformations, done with :>. What I want is the largest and smallest z component among all those points. This is what MinMax does. To look only at the z components of the list, I use the part specification [[All,3]].\n\n• I need some help with this part: Cases[g, GraphicsComplex[pts_, __] :> MinMax[pts]]. I looked up Cases in the documentation and it says that Cases[{e1,e2,...},pattern} gives a list of the e_i that match the pattern. I also looked up MinMax and it said it finds the minimum and maximum of a list. Then I tried Cases[g,GraphicsComplex[pts_,___] and got a list of points of the form {x,y,z}. Then I tried MinMax[{{1,-3,-2},{2,5,1}}] and got the answer {-3,5}, which is not the minimum and maximum z-values that I want. Are things OK here? Can you explain? Jul 15, 2015 at 16:24\n• Oops, silly me - I forgot to select the z components only. Thanks for actually testing my code! I'll edit the answer.\n– Jens\nJul 15, 2015 at 17:22\n• So the one I really need is: Cases[{Subscript[e, 1],\\[Ellipsis]},pattern->rhs] gives a list of the values of rhs corresponding to the Subscript[e, i] that match the pattern. So it starts with g, finds the stuff the matches the pattern GraphicsComplex[pts,___], and now all of the points are stored in pots? Next, pts[[All,3]] select all the z-values of the points, then MaxMin selects the max and min of all of these z-values, then the max and min are what are returned. Think I have it. Jul 15, 2015 at 18:12\n• Yes, that's right: except the name pts_ must appear with an underscore in the pattern (that's the left hand side of the :>): that underscore marks it as a Blank pattern and pts as the (temporary) name we want to use for that pattern when referring to it on the right hand side of :>.\n– Jens\nJul 15, 2015 at 18:36\n• Agan, great effort on your part to offer such wonderful assistance. Jul 15, 2015 at 21:39" ]
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http://www.geektonight.com/demand-curve-definition-type-example/
[ "# Demand Curve | Definition, Type, Example\n\nLast Updated on\n\nTutorial Topic: What is demand curve, definition, example, types: Individual & market demand curve and why the demand curve slopes downward? – Answered\n\n## What is Demand Curve?\n\nDemand curve definition: In economics, a demand curve is a graphical presentation of the demand schedule. It is obtained by plotting a demand schedule.\n\nThe demand schedule can be converted into a demand curve by graphically plotting the different combinations of price and quantity demanded of a product.\n\n## Types of Demand Curve\n\nSimilar to demand schedule, there are two types of demand curve.\n\n### Individual demand curve\n\nIndividual demand curve definition: It is the curve that shows different quantities of a commodity which an individual is willing to purchase at all possible prices in a given time period with an assumption that other factors are constant.\n\nAn individual demand curve slopes downwards to the right, indicating an inverse relationship between the price and quantity demanded of a commodity.\n\n### Market demand curve\n\nMarket demand curve definition: This curve is the graphical representation of the market demand schedule. A market demand curve shows different quantities of a commodity which all consumers in a market are willing to purchase at different price levels at a given time period, while other factors remaining constant.\n\nA market demand curve can be plotted by consolidating individual demand curves. Therefore, market demand curve is the horizontal summation of individual demand curves.\n\nA market demand curve, just like the individual demand curves, slopes downwards to the right, indicating an inverse relationship between the price and quantity demanded of a commodity.\n\nThe negative slope of a demand curve is a reflection of the law of demand.\n\nHowever, it is important to understand the reasons why the demand curve slopes downward to the right.\n\n## Why the demand curve slopes downward?\n\nGenerally, the demand curves slope downwards. It signifies that consumers buy more at lower prices. We shall now try to understand why the demand curve slopes downward?\n\nDifferent explanations have been given different economists for the operation of the law of demand. These are explained below:\n\n### Law of diminishing marginal utility\n\nConsumers purchase commodities to derive utility out of them.\n\nThe law of diminishing marginal utility states that as consumption increases, the utility that a consumer derives from the additional units (marginal utility) of a commodity diminishes constantly.\n\nTherefore, a consumer would purchase a larger amount of a commodity when it is priced low as the marginal utility of the additional units decreases.\n\n### Income effect\n\nA change in the demand arising due to change in the real income of a consumer owing to change in the price of a commodity is called income effect.\n\nA change in the price of a commodity affects the purchasing power of a consumer.\n\nFor example, if an individual buys two dozens of apples at 40 per kg, he/she spends 80. When the price of apples falls to 30 per kg, he/she spends 60 for purchasing two kg of apples. This results in a saving of 20 for the individual, which implies that the real income of the individual has increased by 20.\n\nThe amount saved may be utilised by the individual in purchasing additional units of apples. Thus, the demand for apples increased due to a change in real income.\n\n### Substitution effect\n\nThe change in demand due to change in the relative price of a commodity is called the substitution effect.\n\nThe relative price of a commodity refers to its price in relation to the prices of other commodities.\n\nConsumers always switch to lower-priced commodities that are substitutes of higher-priced commodities in order to maintain their standard of living.\n\nTherefore, the demand for relatively cheaper commodities increases.\nFor example, if the price of pizzas comes down, while the price of burgers remains the same, pizzas will become relatively (burgers) cheaper. The demand for pizzas will increase as compared to burgers.\n\n### Change in the number of consumers\n\nWhen the price of a commodity decreases, the number of consumers of the commodity increases. This leads to a rise in the demand for the commodity.\n\nFor example, when the price of apples is 120 per kg, only a few people purchase it. However, when the price of apples falls down to 60 per kg, more number of people can afford it.\n\n### Multiple uses of a commodity\n\nThere are certain commodities that can serve more than one purpose. For example, milk, steel, oil, etc. However, some uses are more important over others. When the price of such a commodity is high, it will be used to serve important purposes. Thus, the demand will be low.\n\nOn the other hand, when the price of the commodity falls, it will be used for less important purposes as well. Thus, the demand will increase.\n\nFor example, when the price of electricity is high, it is used only for lighting purposes, whereas when the price of electricity goes down, it is also used for cooking, heating, etc.\n\nGo On, Tell Us What You Think!\n\nDid we miss something? Come on! Tell us what you think about our article on Demand Curve | Definition, Type, Example in the comments section.\n\nRecommended:" ]
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https://www.solutioninn.com/study-help/financial-algebra-advanced-algebra/the-summer-income-of-the-3408-students-at-van-buren
[ "# The summer income of the 3,408 students at Van Buren High School last year was normally distributed with mean \\$1,751 and standard deviation \\$421. a. Approximately what percent of the students had incomes between \\$1,000 and \\$2,000? Round to the nearest percent. b. Approximately how many students had incomes less than \\$800? Round to the nearest integer.\n\nChapter 1, Application 1.6 #9\n\nThe summer income of the 3,408 students at Van Buren High School last year was normally distributed with mean \\$1,751 and standard deviation \\$421.\na. Approximately what percent of the students had incomes between \\$1,000 and \\$2,000? Round to the nearest percent.\nb. Approximately how many students had incomes less than \\$800? Round to the nearest integer.\n\n## This problem has been solved!\n\nRelated Book For", null, "" ]
[ null, "https://www.solutioninn.com/study-help/financial-algebra-advanced-algebra/includes/images/rewamp/document_product_info/free.svg", null ]
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https://meangreenmath.com/2016/02/18/engaging-students-rational-and-irrational-numbers-2/?replytocom=12807
[ "# Engaging students: Rational and irrational numbers\n\nIn my capstone class for future secondary math teachers, I ask my students to come up with ideas for engaging their students with different topics in the secondary mathematics curriculum. In other words, the point of the assignment was not to devise a full-blown lesson plan on this topic. Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place.\n\nI plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).\n\nThis student submission again comes from my former student Emma Sivado. Her topic, from Algebra: rational and irrational numbers.", null, "D.1: What interesting things can you say about the people who contributed to the discovery and/or the development of this topic?\n\nThe famous story on the first discovery of irrational numbers is one of violence. We all know the Pythagorean theorem, a2+b2=c2 , but what happens if we have a right triangle with height 1 and base 1? The hypotenuse becomes √2. So, √2, what’s the big deal? Well this is where we turn to history for the answer. Hippassus was an ancient greek philosopher who belonged to the Pythagorean school of thought. Now the Pythagorean’s had a saying, “All is number.” What do we think this means? What Pythagoras meant was that everything in the universe had a numerical attribute. For example, one is the number of reason, five is the number of marriage. So one day when Hippassus was playing with the length of the diagonal of the unit square, or the hypotenuse of a right triangle with base 1 and height 1, he discovered the number √2. Hippassus tried to write √2 as a fraction, or rational number, and found it to be impossible. Therefore, √2 is what we call an irrational number. Well this is where the history turns violent. There are numerous stories to explain the death of Hippassus, but all of them point to his ultimate cause of death being the discovery of these irrational numbers. Irrational numbers were so against Pythagoras and the Pythagorean school of thought that they had this man killed!\n\nhttp://www.math.tamu.edu/~dallen/history/pythag/pythag.html", null, "B.1: How can this topic be used in your students’ future courses in mathematics and science?\n\nI believe that the irrational number would be a great place to introduce a simple proof. Students will have to do proofs in multiple math classes in the future and to give them an example with an interesting story might be a good place to start. For example, after telling the story of the discovery of irrational numbers ask the students how Hippassus might have proven that this was true; possibly his dying words. Then give them an outline or fill in the black of the proof that √2 is irrational. This example I found on homeschoolmath.net is given in good language and gives good explanations of why everything is done in the order it is:\n\nLet’s suppose √2 is a rational number. Then we can write it √2  = a/b where a, b are whole numbers, b not zero.\n\nWe additionally assume that this a/b is simplified to lowest terms, since that can obviously be done with any fraction.\n\nFrom the equality √2  = a/b it follows that 2 = a2/b2,  or  a2 = 2 · b2.  So the square of a is an even number since it is two times something.\n\nFrom this we know that a itself is also an even number. Why? Because it can’t be odd; if a itself was odd, then a · a would be odd too. Odd number times odd number is always odd.\n\nOkay, if a itself is an even number, then a is 2 times some other whole number. In symbols, a = 2k where k is this other number. We don’t need to know what k is; it won’t matter. Soon comes the contradiction.\n\nIf we substitute a = 2k into the original equation 2 = a2/b2, this is what we get:\n\n 2 = (2k)2/b2 2 = 4k2/b2 2*b2 = 4k2 b2 = 2k2\n\nThis means that b2 is even, from which follows again that b itself is even. And that is a contradiction!!!\n\nWHY is that a contradiction? Because we started the whole process assuming that a/b was simplified to lowest terms, and now it turns out that a and b both would be even. We ended at a contradiction; thus our original assumption (that √2 is rational) is not correct. Therefore √2 is rational.\n\nObviously this would have to be presented slowly, but I believe that the students could do this and understand it.\n\nhttp://www.homeschoolmath.net/teaching/proof_square_root_2_irrational.php", null, "I would begin by showing the movie clip from Life of Pi when Pi is reciting all the digits of Pi that he knows, or another video of someone reciting a ridiculous number of digits of pi. Then I would ask the students how many digits of Pi there are? When no one could tell me an exact answer I would introduce the irrational number and explain how the decimals will go on forever because this number cannot be written as a fraction like a rational number. At the end of class you could show the kids the Princeton University Pi Day celebration complete with Einstein look alike contests, and pi reciting competitions to win \\$314.15!\n\nhttp://www.pidayprinceton.com/\n\nReferences:\n\n## One thought on “Engaging students: Rational and irrational numbers”\n\n1.", null, "howardat58 says:\n\n“If we substitute a = 2k into the original equation 2 = a2/b2, this is what we get:”\nIt is slightly simpler to substitute 2k for a in the next equation, a^2 = 2 · b^2.\n\nThis site uses Akismet to reduce spam. Learn how your comment data is processed." ]
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https://mortgageratesontario.ca/home-equity-loan-calculator
[ "# Home Equity Loan Calculator\n\n## Home Equity Loan Payment Calculator\n\nFind out your monthly payment using the home equity loan calculator.\n\n## Home Equity Loan Rates Calculator\n\nSee interest rates for home equity loan using the home equity loan rates calculator.\n\n## Home Equity Loan Equity Calculator\n\nCalculate your home equity available for a home equity loan, using the equity calculator.\n\n## Home Equity Loan Calculator Explained", null, "Home Equity Loan Calculator is a free tool that allows you to quickly and easily calculate your available home equity, for getting a home equity loan or second mortgage. With the Home Equity Loan Calculator, you can also calculate home equity loan rates and home equity loan monthly payments. A home equity loan calculator is the first step home equity lenders use to determine if you qualify for a home equity loan.\n\n## How The Home Equity Calculator Works", null, "The home equity calculator will calculate equity, in the form of money, available in your home. Most home equity lenders will offer a home equity loan up to 90% of your home value.\n\nTo calculate home equity available for a home equity loan, first multiple the property value by 0.90, and subtract the total mortgage balance(s) you have including first mortgage, second mortgage and any home equity line of credit that may be registered on the title of property.\n\n## Example Of How To Calculate Home Equity", null, "Example 1: For a property value of \\$500,000, with a first mortgage of \\$300,000, first you must calculate \\$500,000 x 0.90% (maximum loan to value for a home equity loan) = \\$450,000 (total 90% Loan to value). Then calculate the difference between \\$450,000 and \\$300,000, and the home equity available is \\$150,000.\n\nExample 2: For a property value of \\$500,000, and a first mortgage of \\$300,000, with a \\$50,000 HELOC (Home equity line of credit), first calculate \\$500,000 x 0.90% = \\$450,000. Then calculate the difference between \\$450,000 and \\$350,000, and the equity available is \\$100,000.\n\n## Home Equity Loan Rates Calculator", null, "Home equity loan rates are based on the equity available in the home, and the loan amount the home owner wants to take out. Home equity loan rates can start from 3.49%, when home owners take out a home equity line of credit.\n\nTraditionally, home equity loan rates start at 5.49% when there is approximately 35% equity available (65% loan to value). Home equity loan rates can range from 5.49% and up to 12.99%, depending on the loan to value.\n\n## How To Calculate Home Equity Loan Payment\n\n### Home Equity Payment Calculator", null, "Most home equity loan payments are based on interest only, meaning there is no amortization. The total monthly payment made for a home equity loan is based on the interest only.\n\nTo calculate home equity loan payments, first you will need to calculate home equity available. Then multiply the home equity available by the interest rate (use 7.99% as the average interest rate for a home equity loan), and divide that number by 12, to get the monthly payment for a home equity loan.\n\n### Sample Home Equity Payment Calculator\n\nFor a property valued at \\$500,000, with a first mortgage of \\$300,000, first multiple \\$500,000 x 0.90% = \\$450,000.  Then calculate the difference between the total equity available and the total mortgage(s) registered. In this case, you will calculate \\$450,000 – \\$300,000 = \\$150,000.\n\nFor a home equity loan of \\$150,000, with an interest rate of 7.99%, a 1 year term, no amortization, calculate \\$150,000 x 0.70% = \\$11,985. Then divided \\$11,985 by the number of months in the one year term (12). \\$11,985 / 12 = \\$998.75 per month." ]
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https://answers.everydaycalculation.com/multiply-fractions/6-42-times-56-81
[ "Solutions by everydaycalculation.com\n\n## Multiply 6/42 with 56/81\n\nThis multiplication involving fractions can also be rephrased as \"What is 6/42 of 56/81?\"\n\n6/42 × 56/81 is 8/81.\n\n#### Steps for multiplying fractions\n\n1. Simply multiply the numerators and denominators separately:\n2. 6/42 × 56/81 = 6 × 56/42 × 81 = 336/3402\n3. After reducing the fraction, the answer is 8/81\n\nMathStep (Works offline)", null, "Download our mobile app and learn to work with fractions in your own time:" ]
[ null, "https://answers.everydaycalculation.com/mathstep-app-icon.png", null ]
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http://eacademic.ju.edu.jo/abd.yousef/Lists/Taught%20Courses/AllItems.aspx
[ "# Dr. Abdel Rahman Yousef", null, "## Taught Courses", null, "All Items", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "Course", null, "", null, "", null, "", null, "Description", null, "Academic Year", null, "", null, "", null, "", null, "Classification; some  physical  models  (heat, wave, Laplace  equations); separation of variables; Sturm-liouville BVP; Fourier series and Fourier transform; BVP involving rectangular and circular regions; special functions (Bessel and Legendre); BVP involving cylindrical and spherical regions.\nThird Year\n\nReal numbers: order, absolute value, bounded subsets, completeness property, Archimedean property; supremum and infimum; sequences: limit, Cauchy sequence, recurrence sequence, increasing, decreasing sequence,  lim sup,  lim inf  of a sequence; functions: limit,  right, left limit, continuity at a point, continuity on an interval; uniform continuity (on an interval) relations between continuity and uniform continuity, differentiability: definition, right, left derivative, relation between differentiability and continuity, Rolle’s theorem, mean value theorem, applications on mean value theorem.\nSecond Year\n\nEvolution of some mathematical concepts, facts and algorithms in arithmetic, algebra, trigonometry, Euclidean geometry, analytic geometry and calculus through early civilizations, Egyptians, Babylonians, Greeks, Indians, Chinese, Muslims and Europeans, evolution of solutions of some conjectures and open problems.\nFourth Year\n\nComplex numbers: geometric interpretation, polar form, exponential form: powers and roots; regions in the  complex  plane;  analytic  functions; functions of complex variables: exponential and logarithmic functions ; trigonometric and hyperbolic functions;  definite integrals; Cauchy theorem; Cauchy integral formula; Series; convergence of sequence and series, Taylor series; Laurrent series; uniform convergence; integration and differentiation of power series, zeros of analytic functions; singularity ; principle part; residues; poles; residue theorem of a function; residues at poles; evaluation of improper integrals; integration through a branch cut.\nFourth Year" ]
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https://docs.qgis.org/3.4/bg/docs/user_manual/processing_algs/qgis/vectoranalysis.html
[ "# Vector analysis¶\n\n## Basic statistics for fields¶\n\nGenerates basic statistics for a field of the attribute table of a vector layer.\n\nNumeric, date, time and string fields are supported.\n\nThe statistics returned will depend on the field type.\n\nStatistics are generated as an HTML file and are available in the Processing ‣ Results viewer.\n\n`Default menu`: Vector ‣ Analysis Tools\n\n### Parameters¶\n\nLabel\n\nName\n\nType\n\nDescription\n\nInput vector\n\n`INPUT_LAYER`\n\n[vector: any]\n\nVector layer to calculate the statistics on\n\nField to calculate statistics on\n\n`FIELD_NAME`\n\n[tablefield: any]\n\nAny supported table field to calculate the statistics\n\nStatistics\n\n`OUTPUT_HTML_FILE`\n\n[file]\n\nHTML file for the calculated statistics\n\n### Outputs¶\n\nLabel\n\nName\n\nType\n\nDescription\n\nStatistics\n\n`OUTPUT_HTML_FILE`\n\n[file]\n\nHTML file with the calculated statistics\n\nCount\n\n`COUNT`\n\n[number]\n\nNumber of unique values\n\n`UNIQUE`\n\n[number]\n\nNumber of empty (null) values\n\n`EMPTY`\n\n[number]\n\nNumber of non-empty values\n\n`FILLED`\n\n[number]\n\nMinimum value\n\n`MIN`\n\n[number]\n\nMaximum value\n\n`MAX`\n\n[number]\n\nMinimum length\n\n`MIN_LENGTH`\n\n[number]\n\nMaximum length\n\n`MAX_LENGTH`\n\n[number]\n\nMean length\n\n`MEAN_LENGTH`\n\n[number]\n\nCoefficient of Variation\n\n`CV`\n\n[number]\n\nSum\n\n`SUM`\n\n[number]\n\nMean value\n\n`MEAN`\n\n[number]\n\nStandard deviation\n\n`STD_DEV`\n\n[number]\n\nRange\n\n`RANGE`\n\n[number]\n\nMedian\n\n`MEDIAN`\n\n[number]\n\nMinority (rarest occurring value)\n\n`MINORITY`\n\n[number]\n\nMajority (most frequently occurring value)\n\n`MAJORITY`\n\n[number]\n\nFirst quartile\n\n`FIRSTQUARTILE`\n\n[number]\n\nThird quartile\n\n`THIRDQUARTILE`\n\n[number]\n\nInterquartile Range (IQR)\n\n`IQR`\n\n[number]\n\n## Count points in polygon¶\n\nTakes a point and a polygon layer and counts the number of points from the first one in each polygon of the second one.\n\nA new polygons layer is generated, with the exact same content as the input polygons layer, but containing an additional field with the points count corresponding to each polygon.", null, "The labels identify the point count\n\nAn optional weight field can be used to assign weights to each point. Alternatively, a unique class field can be specified. If both options are used, the weight field will take precedence and the unique class field will be ignored.\n\n`Default menu`: Vector ‣ Analysis Tools\n\n### Parameters¶\n\nLabel\n\nName\n\nType\n\nDescription\n\nPolygons\n\n`POLYGONS`\n\n[vector: polygon]\n\nPolygon layer whose features are associated with the count of points they contain\n\nPoints\n\n`POINTS`\n\n[vector: point]\n\nPoint layer with features to count\n\nWeight field\n\nOptional\n\n`WEIGHT`\n\n[tablefield: any]\n\nA field from the point layer. The count generated will be the sum of the weight field of the points contained by the polygon. If the weight field is not numeric, the count will be `0`.\n\nClass field\n\nOptional\n\n`CLASSFIELD`\n\n[tablefield: any]\n\nPoints are classified based on the selected attribute and if several points with the same attribute value are within the polygon, only one of them is counted. The final count of the points in a polygon is, therefore, the count of different classes that are found in it.\n\nCount field name\n\n`FIELD`\n\n[string]\n\nDefault: ‚NUMPOINTS‘\n\nThe name of the field to store the count of points\n\nCount\n\n`OUTPUT`\n\n[vector: polygon]\n\nSpecification of the output layer\n\n### Outputs¶\n\nLabel\n\nName\n\nType\n\nDescription\n\nCount\n\n`OUTPUT`\n\n[vector: polygon]\n\nResulting layer with the attribute table containing the new column with the points count\n\n## DBSCAN clustering¶\n\nClusters point features based on a 2D implementation of Density-based spatial clustering of applications with noise (DBSCAN) algorithm.\n\nThe algorithm requires two parameters, a minimum cluster size, and the maximum distance allowed between clustered points.\n\n### Parameters¶\n\nLabel\n\nName\n\nType\n\nDescription\n\nInput layer\n\n`INPUT`\n\n[vector: point]\n\nLayer to analyze\n\nMinimum cluster size\n\n`MIN_SIZE`\n\n[number]\n\nDefault: 5\n\nMinimum number of features to generate a cluster\n\nMaximum distance between clustered points\n\n`EPS`\n\n[number]\n\nDefault: 1.0\n\nDistance beyond which two features can not belong to the same cluster (eps)\n\nCluster field name\n\n`FIELD_NAME`\n\n[string]\n\nDefault: ‚CLUSTER_ID‘\n\nName of the field where the associated cluster number shall be stored\n\nTreat border points as noise (DBSCAN*)\n\nOptional\n\n`DBSCAN*`\n\n[boolean]\n\nDefault: False\n\nIf checked, points on the border of a cluster are themselves treated as unclustered points, and only points in the interior of a cluster are tagged as clustered.\n\nClusters\n\n`OUTPUT`\n\n[vector: point]\n\nVector layer for the result of the clustering\n\n### Outputs¶\n\nLabel\n\nName\n\nType\n\nDescription\n\nClusters\n\n`OUTPUT`\n\n[vector: point]\n\nVector layer containing the original features with a field setting the cluster they belong to\n\nNumber of clusters\n\n`NUM_CLUSTERS`\n\n[number]\n\nThe number of clusters discovered\n\nK-means clustering\n\n## Distance matrix¶\n\nCalculates for point features distances to their nearest features in the same layer or in another layer.\n\n`Default menu`: Vector ‣ Analysis Tools\n\n### Parameters¶\n\nLabel\n\nName\n\nType\n\nDescription\n\nInput point layer\n\n`INPUT`\n\n[vector: point]\n\nPoint layer for which the distance matrix is calculated (from points)\n\nInput unique ID field\n\n`INPUT_FIELD`\n\n[tablefield: any]\n\nField to use to uniquely identify features of the input layer. Used in the output attribute table.\n\nTarget point layer\n\n`TARGET`\n\n[vector: point]\n\nPoint layer containing the nearest point(s) to search (to points)\n\nTarget unique ID field\n\n`TARGET_FIELD`\n\n[tablefield: any]\n\nField to use to uniquely identify features of the target layer. Used in the output attribute table.\n\nOutput matrix type\n\n`MATRIX_TYPE`\n\n[enumeration]\n\nDefault: 0\n\nDifferent types of calculation are available:\n\n• 0 — Linear (N * k x 3) distance matrix: for each input point, reports the distance to each of the k nearest target points. The output matrix consists of up to k rows per input point, and each row has three columns: InputID, TargetID and Distance.\n\n• 1 — Standard (N x T) distance matrix\n\n• 2 — Summary distance matrix (mean, std. dev., min, max): for each input point, reports statistics on the distances to its target points.\n\nUse only the nearest (k) target points\n\n`NEAREST_POINTS`\n\n[number]\n\nDefault: 0\n\nYou can choose to calculate the distance to all the points in the target layer (0) or limit to a number (k) of closest features.\n\nDistance matrix\n\n`OUTPUT`\n\n[vector: point]\n\n### Outputs¶\n\nLabel\n\nName\n\nType\n\nDescription\n\nDistance matrix\n\n`OUTPUT`\n\n[vector: point]\n\nPoint (or MultiPoint for the „Linear (N * k x 3)“ case) vector layer containing the distance calculation for each input feature. Its features and attribute table depend on the selected output matrix type.\n\n## Distance to nearest hub (line to hub)¶\n\nCreates lines that join each feature of an input vector to the nearest feature in a destination layer. Distances are calculated based on the center of each feature.", null, "Display the nearest hub for the red input features\n\n### Parameters¶\n\nLabel\n\nName\n\nType\n\nDescription\n\nSource points layer\n\n`INPUT`\n\n[vector: any]\n\nVector layer for which the nearest feature is searched\n\nDestination hubs layer\n\n`HUBS`\n\n[vector: any]\n\nVector layer containing the features to search for\n\nHub layer name attribute\n\n`FIELD`\n\n[tablefield: any]\n\nField to use to uniquely identify features of the destination layer. Used in the output attribute table\n\nMeasurement unit\n\n`UNIT`\n\n[enumeration]\n\nDefault: 0\n\nUnits in which to report the distance to the closest feature:\n\n• 0 — Meters\n\n• 1 — Feet\n\n• 2 — Miles\n\n• 3 — Kilometers\n\n• 4 — Layer units\n\nHub distance\n\n`OUTPUT`\n\n[vector: line]\n\nLine vector layer for the distance matrix output\n\n### Outputs¶\n\nLabel\n\nName\n\nType\n\nDescription\n\nHub distance\n\n`OUTPUT`\n\n[vector: line]\n\nLine vector layer with the attributes of the input features, the identifier of their closest feature and the calculated distance.\n\n## Distance to nearest hub (points)¶\n\nCreates a point layer representing the center of the input features with the addition of two fields containing the identifier of the nearest feature (based on its center point) and the distance between the points.\n\n### Parameters¶\n\nLabel\n\nName\n\nType\n\nDescription\n\nSource points layer\n\n`INPUT`\n\n[vector: any]\n\nVector layer for which the nearest feature is searched\n\nDestination hubs layer\n\n`HUBS`\n\n[vector: any]\n\nVector layer containing the features to search for\n\nHub layer name attribute\n\n`FIELD`\n\n[tablefield: any]\n\nField to use to uniquely identify features of the destination layer. Used in the output attribute table\n\nMeasurement unit\n\n`UNIT`\n\n[enumeration]\n\nDefault: 0\n\nUnits in which to report the distance to the closest feature:\n\n• 0 — Meters\n\n• 1 — Feet\n\n• 2 — Miles\n\n• 3 — Kilometers\n\n• 4 — Layer units\n\nHub distance\n\n`OUTPUT`\n\n[vector: point]\n\nPoint vector layer for the distance matrix output.\n\n### Outputs¶\n\nLabel\n\nName\n\nType\n\nDescription\n\nHub distance\n\n`OUTPUT`\n\n[vector: point]\n\nPoint vector layer with the attributes of the input features, the identifier of their closest feature and the calculated distance.\n\n## Join by lines (hub lines)¶\n\nCreates hub and spoke diagrams by connecting lines from points on the spoke layer to matching points in the hub layer.\n\nDetermination of which hub goes with each point is based on a match between the Hub ID field on the hub points and the Spoke ID field on the spoke points.\n\nIf input layers are not point layers, a point on the surface of the geometries will be taken as the connecting location.", null, "Join points on common field\n\n### Parameters¶\n\nLabel\n\nName\n\nType\n\nDescription\n\nHub layer\n\n`HUBS`\n\n[vector: any]\n\nInput layer\n\nHub ID field\n\n`HUB_FIELD`\n\n[tablefield: any]\n\nField of the hub layer with ID to join\n\nHub layer fields to copy (leave empty to copy all fields)\n\nOptional\n\n`HUB_FIELDS`\n\n[tablefield: any] [list]\n\nThe field(s) of the hub layer to be copied. If no field(s) are chosen all fields are taken.\n\nSpoke layer\n\n`SPOKES`\n\n[vector: any]\n\nSpoke ID field\n\n`SPOKE_FIELD`\n\n[tablefield: any]\n\nField of the spoke layer with ID to join\n\nSpoke layer fields to copy (leave empty to copy all fields)\n\nOptional\n\n`SPOKE_FIELDS`\n\n[tablefield: any] [list]\n\nField(s) of the spoke layer to be copied. If no fields are chosen all fields are taken.\n\nHub lines\n\n`OUTPUT`\n\n[vector: lines]\n\nThe resulting line layer\n\n### Outputs¶\n\nLabel\n\nName\n\nType\n\nDescription\n\nHub lines\n\n`OUTPUT`\n\n[vector: lines]\n\nThe resulting line layer\n\n## K-means clustering¶\n\nCalculates the 2D distance based k-means cluster number for each input feature.\n\nK-means clustering aims to partition the features into k clusters in which each feature belongs to the cluster with the nearest mean. The mean point is represented by the barycenter of the clustered features.\n\nIf input geometries are lines or polygons, the clustering is based on the centroid of the feature.", null, "A five class point clusters\n\n### Parameters¶\n\nLabel\n\nName\n\nType\n\nDescription\n\nInput layer\n\n`INPUT`\n\n[vector: any]\n\nLayer to analyze\n\nNumber of clusters\n\n`CLUSTERS`\n\n[number]\n\nDefault: 5\n\nNumber of clusters to create with the features\n\nCluster field name\n\n`FIELD_NAME`\n\n[string]\n\nDefault: ‚CLUSTER_ID‘\n\nName of the cluster number field\n\nClusters\n\n`OUTPUT`\n\n[vector: any]\n\nVector layer for generated the clusters\n\n### Outputs¶\n\nLabel\n\nName\n\nType\n\nDescription\n\nClusters\n\n`OUTPUT`\n\n[vector: any]\n\nVector layer containing the original features with a field specifying the cluster they belong to\n\nDBSCAN clustering\n\n## List unique values¶\n\nLists unique values of an attribute table field and counts their number.\n\n`Default menu`: Vector ‣ Analysis Tools\n\n### Parameters¶\n\nLabel\n\nName\n\nType\n\nDescription\n\nInput layer\n\n`INPUT`\n\n[vector: any]\n\nLayer to analyze\n\nTarget field(s)\n\n`FIELDS`\n\n[tablefield: any]\n\nField to analyze\n\nUnique values\n\n`OUTPUT`\n\n[table]\n\nSummary table layer with unique values\n\nHTML report\n\n`OUTPUT_HTML_FILE`\n\n[html]\n\nHTML report of unique values in the Processing ‣ Results viewer\n\n### Outputs¶\n\nLabel\n\nName\n\nType\n\nDescription\n\nUnique values\n\n`OUTPUT`\n\n[table]\n\nSummary table layer with unique values\n\nHTML report\n\n`OUTPUT_HTML_FILE`\n\n[html]\n\nHTML report of unique values. Can be opened from the Processing ‣ Results viewer\n\nTotal unique values\n\n`TOTAL_VALUES`\n\n[number]\n\nThe number of uniqe values in the input field\n\nUNIQUE_VALUES\n\n`Unique values`\n\n[string]\n\nA string with the comma separated list of unique values found in the input field\n\n## Mean coordinate(s)¶\n\nComputes a point layer with the center of mass of geometries in an input layer.\n\nAn attribute can be specified as containing weights to be applied to each feature when computing the center of mass.\n\nIf an attribute is selected in the parameter, features will be grouped according to values in this field. Instead of a single point with the center of mass of the whole layer, the output layer will contain a center of mass for the features in each category.\n\n`Default menu`: Vector ‣ Analysis Tools\n\n### Parameters¶\n\nLabel\n\nName\n\nType\n\nDescription\n\nInput layer\n\n`INPUT`\n\n[vector: any]\n\nInput vector layer\n\nWeight field\n\nOptional\n\n`WEIGHT`\n\n[tablefield: numeric]\n\nField to use if you want to perform a weighted mean\n\nUnique ID field\n\n`UID`\n\n[tablefield: numeric]\n\nUnique field on which the calculation of the mean will be made\n\nMean coordinates\n\n`OUTPUT`\n\n[vector: point]\n\nThe (point vector) layer for the result\n\n### Outputs¶\n\nLabel\n\nName\n\nType\n\nDescription\n\nMean coordinates\n\n`OUTPUT`\n\n[vector: point]\n\nResulting point(s) layer\n\n## Nearest neighbour analysis¶\n\nPerforms nearest neighbor analysis for a point layer.\n\nOutput is generated as an HTML file with the computed statistical values:\n\n• Observed mean distance\n\n• Expected mean distance\n\n• Nearest neighbour index\n\n• Number of points\n\n• Z-Score\n\n`Default menu`: Vector ‣ Analysis Tools\n\n### Parameters¶\n\nLabel\n\nName\n\nType\n\nDescription\n\nInput layer\n\n`INPUT`\n\n[vector: point]\n\nPoint vector layer to calculate the statistics on\n\nNearest neighbour\n\n`OUTPUT_HTML_FILE`\n\n[html]\n\nHTML file for the computed statistics\n\n### Outputs¶\n\nLabel\n\nName\n\nType\n\nDescription\n\nNearest neighbour\n\n`OUTPUT_HTML_FILE`\n\n[html]\n\nHTML file with the computed statistics\n\nObserved mean distance\n\n`OBSERVED_MD`\n\n[number]\n\nObserved mean distance\n\nExpected mean distance\n\n`EXPECTED_MD`\n\n[number]\n\nExpected mean distance\n\nNearest neighbour index\n\n`NN_INDEX`\n\n[number]\n\nNearest neighbour index\n\nNumber of points\n\n`POINT_COUNT`\n\n[number]\n\nNumber of points\n\nZ-Score\n\n`Z_SCORE`\n\n[number]\n\nZ-Score\n\n## Statistics by categories¶\n\nCalculates statistics of fields depending on a parent class.\n\nFor numerical fields, a table layer with the following statistics is output:\n\n• count\n\n• unique\n\n• min\n\n• max\n\n• range\n\n• sum\n\n• mean\n\n• median\n\n• stdev\n\n• minority\n\n• majority\n\n• q1\n\n• q3\n\n• iqr\n\nFor string fields, the following statistics will be calculated:\n\n• count\n\n• unique\n\n• empty\n\n• filled\n\n• min\n\n• max\n\n• min_length\n\n• max_length\n\n• mean_length\n\n### Parameters¶\n\nLabel\n\nName\n\nType\n\nDescription\n\nInput vector layer\n\n`INPUT`\n\n[vector: any]\n\nInput vector layer with unique classes and values\n\nField to calculate statistics on (if empty, only count is calculated)\n\nOptional\n\n`VALUES_FIELD_NAME`\n\n[tablefield: any]\n\nIf empty only the count will be calculated\n\nField(s) with categories\n\n`CATEGORIES_FIELD_NAME`\n\n[vector: any] [list]\n\nThe fields that (combined) define the categories\n\nStatistics by category\n\n`OUTPUT`\n\n[table]\n\nTable for the generated statistics\n\n### Outputs¶\n\nLabel\n\nName\n\nType\n\nDescription\n\nStatistics by category\n\n`OUTPUT`\n\n[table]\n\nTable containing the statistics\n\n## Sum line lengths¶\n\nTakes a polygon layer and a line layer and measures the total length of lines and the total number of them that cross each polygon.\n\nThe resulting layer has the same features as the input polygon layer, but with two additional attributes containing the length and count of the lines across each polygon.\n\nThe names of these two fields can be configured in the algorithm parameters.\n\n`Default menu`: Vector ‣ Analysis Tools\n\n### Parameters¶\n\nLabel\n\nName\n\nType\n\nDescription\n\nLines\n\n`LINES`\n\n[vector: line]\n\nInput vector line layer\n\nPolygons\n\n`POLYGONS`\n\n[vector: polygon]\n\nPolygon vector layer\n\nLines length field name\n\n`LEN_FIELD`\n\n[string]\n\nDefault: ‚LENGTH‘\n\nName of the field for the lines length\n\nLines count field name\n\n`COUNT_FIELD`\n\n[string]\n\nDefault: ‚COUNT‘\n\nName of the field for the lines count\n\nLine length\n\n`OUTPUT`\n\n[vector: polygon]\n\nThe output polygon vector layer\n\n### Outputs¶\n\nLabel\n\nName\n\nType\n\nDescription\n\nLine length\n\n`OUTPUT`\n\n[vector: polygon]\n\nPolygon output layer with fields of lines length and line count" ]
[ null, "https://docs.qgis.org/3.4/bg/_images/count_points_polygon.png", null, "https://docs.qgis.org/3.4/bg/_images/distance_hub.png", null, "https://docs.qgis.org/3.4/bg/_images/join_lines.png", null, "https://docs.qgis.org/3.4/bg/_images/kmeans.png", null ]
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https://scholaron.com/homework-answers/consider-a-binomial-model-with-t-7098
[ "/\n/\n/\nConsider a Binomial Model with T = 2, r =\nNot my Question\nFlag Content\n\n# Question : Consider a Binomial Model with T = 2, r =\n\nConsider a Binomial Model with T = 2, r = 1.5, S_0 = 90, d = 1/3, u = 4, and p = 0.3. Compute B_0, B_1, and B_2. By drawing a tree diagram, compute all possible values of (S_0, S_1, S_2), and compute the probability of each outcome represented by each branch. Give an example of a self-financing trading strategy phi such that (alpha_2, beta_2) is not constant. Compute all possible values of V_0(phi), V_1(phi) and V_2(phi).\n\n## Solution 5 (1 Ratings )\n\nSolved\nStatistics 9 Months Ago 76 Views", null, "", null, "" ]
[ null, 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null, 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", 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https://physics.stackexchange.com/questions/464445/could-the-cosmological-constant-be-due-to-vacuum-fluctuations-in-a-box-i-e-in
[ "# Could the cosmological constant be due to vacuum fluctuations in a box, i.e., in a finite universe?\n\nAssumption: If the universe were a finite box whose boundary is the cosmological horizon, then there would be a zero-point energy inside that box.\n\nConsequence 1: This zero-point energy would be given by the size of the box. The calculated energy value is very similar to the measured cosmological constant.\n\nConsequence 2: The zero-point energy would have been larger when the universe was smaller. The cosmological constant would not be a constant, but decay in time.\n\nQuestion: Could that be the case?\n\n• \"The calculated energy value is very similar to the measured cosmological constant.\" Do you have a source? – Javier Mar 6 at 20:26\n• Experimentally, Lambda is very near 1/L^2, where L is the distance to the cosmological horizon. – frauke Mar 26 at 6:40\n\nIf quantum fields are restricted to a finite box of dimension $$L$$, then this changes the computation of the zero point energy because the fluctuations exist at discrete frequencies, $$\\omega_n = \\frac{2\\pi n}{L}$$ Following Ford (in the case of a 1-dimensional 'box') in https://journals.aps.org/prd/pdf/10.1103/PhysRevD.11.3370, the zero-point energy with a frequency cutoff is $$E_0 = \\sum_n \\omega_n \\exp(-\\alpha \\omega_n)= \\frac{L}{2\\pi \\alpha^2} -\\frac{\\pi}{6L} + {\\rm positive\\, powers\\, of\\,} \\alpha$$ Following the Casimir prescription, the idea is to subtract the vacuum density appropriate to the unconstrained topology from this energy (which includes it), $$\\tilde{E}_0 = E_0 - E_0(L \\rightarrow \\infty) = -\\frac{\\pi}{6L}$$ Note that the energy is inversely related to the dimension of the box, and is negative.\nThe cosmological constant $$\\lambda$$ is the observed vacuum energy density.\nThe zero point energy predicted by Quantum Field Theory is much large than $$\\lambda$$ - it can be $$120$$ orders of magnitude larger depending on the assumptions." ]
[ null ]
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https://matrix-algebra.appspot.com/matrixApplications.html
[ "If there is one prayer that you should pray/sing every day and every hour, it is the LORD's prayer (Our FATHER in Heaven prayer)\nIt is the most powerful prayer. A pure heart, a clean mind, and a clear conscience is necessary for it.\n- Samuel Dominic Chukwuemeka\n\nFor in GOD we live, and move, and have our being. - Acts 17:28\n\nThe Joy of a Teacher is the Success of his Students. - Samuel Dominic Chukwuemeka\n\n# Word Problems on Matrices", null, "You may verify your answers as applicable with: Matrices Calculators\nFor ACT Students\nThe ACT is a timed exam...$60$ questions for $60$ minutes\nThis implies that you have to solve each question in one minute.\nSome questions will typically take less than a minute a solve.\nSome questions will typically take more than a minute to solve.\nThe goal is to maximize your time. You use the time saved on those questions you solved in less than a minute, to solve the questions that will take more than a minute.\nSo, you should try to solve each question correctly and timely.\nSo, it is not just solving a question correctly, but solving it correctly on time.\nPlease ensure you attempt all ACT questions.\nThere is no \"negative\" penalty for any wrong answer.\n\nFor JAMB and CMAT Students\nCalculators are not allowed. So, the questions are solved in a way that does not require a calculator.\n\nSolve these matrix applications (word problems).\nShow all work.\nIndicate the method used to solve each problem as applicable.\nSome of the questions have hints. The hint indicates what matrix operation you should use.\n\n(1.) Arizona Western College (AWC) Airlines (Matadors Airlines) operates three flights one-way on any given day between San Luis, AZ; and New York City.\nThere are three cabin classes in each flight. The cabin classes are First Class, Business Class, and Economy Class.\nFlight $1$ has $30$ First Class seats, $60$ Business Class seats, and $120$ Economy Class seats.\nFlight $2$ has $40$ First Class seats, $90$ Business Class seats, and $100$ Economy Class seats.\nFlight $3$ has $50$ First Class seats, $70$ Business Class seats, and $160$ Economy Class seats.\nThe fares per passenger seat for each cabin class are:\nFirst Class = $$2000.00 per seat Business Class =$$1500.00$per seat Economy Class = $$1000.00 per seat Assume all seats are filled on a specific day, say Day\\: 3; calculate the revenues generated by each of the flights on Day\\: 3. Hint: Matrix Multiplication Let FC = First Class BC = Business Class EC = Economy Class First Step: Represent the information about the cabin classes and the number of seats in each cabin as a 3 * 3 matrix. Cabins (FC, BC, EC) Flights \\begin{bmatrix} 30 & 60 & 120 \\\\[2ex] 40 & 90 & 100 \\\\[2ex] 50 & 70 & 160 \\end{bmatrix} Let Matrix A = \\begin{bmatrix} 30 & 60 & 120 \\\\[2ex] 40 & 90 & 100 \\\\[2ex] 50 & 70 & 160 \\end{bmatrix} Second Step: Represent the informatoon about the fares/charges per passenger seat as a 3 * 1 matrix. Let Matrix B = \\begin{bmatrix} 2000 \\\\[2ex] 1500 \\\\[2ex] 1000 \\end{bmatrix} Third Step: Determine the revenue from each flight by multiplying Matrix A by Matrix B In other words, the number of seats per flight multiplied by the charge per seat gives the revenue. \\begin{bmatrix} 30 & 60 & 120 \\\\[2ex] 40 & 90 & 100 \\\\[2ex] 50 & 70 & 160 \\end{bmatrix} * \\begin{bmatrix} 2000 \\\\[2ex] 1500 \\\\[2ex] 1000 \\end{bmatrix} = AB Order of A = 3 * 3 Order of B = 3 * 1 A and B can multiply. Order of AB = 3 * 1 30(2000) + 60(1500) + 120(1000) = 60000 + 90000 + 120000 = 270000 \\\\[2ex] 40(2000) + 90(1500) + 100(1000) = 80000 + 135000 + 100000 = 315000 \\\\[2ex] 50(2000) + 70(1500) + 160(1000) = 100000 + 105000 + 160000 = 365000 AB = \\begin{bmatrix} 270000 \\\\[2ex] 315000 \\\\[2ex] 365000 \\end{bmatrix} Interpretation: This means that on Day\\: 3; Flight 1 generated a revenue of$$270,000.00$\nFlight $2$ generated a revenue of $$315,000.00 Flight 3 generated a revenue of$$365,000.00$(2.) ACT Valley High School and Mountain High School have decided that selected students will attend a daytime theatrical performance that costs$\\$5$ for each teacher and $\\$3$for each student. One teacher and$10$students from Valley High will attend, and$2$teachers and$25$students from Mountain High will attend. Which of the following matrix products represents the ticket costs, in dollars, for each high school?$ A.\\:\\: \\begin{bmatrix} 5 & 3 \\end{bmatrix}\\begin{bmatrix} 1 & 2 \\\\[2ex] 10 & 25 \\end{bmatrix} \\\\[5ex] B.\\:\\: \\begin{bmatrix} 5 & 3 \\end{bmatrix}\\begin{bmatrix} 1 & 10 \\\\[2ex] 25 & 2 \\end{bmatrix} \\\\[5ex] C.\\:\\: \\begin{bmatrix} 5 & 3 \\end{bmatrix}\\begin{bmatrix} 1 & 25 \\\\[2ex] 2 & 10 \\end{bmatrix} \\\\[5ex] D.\\:\\: \\begin{bmatrix} 5 \\\\[2ex] 3 \\end{bmatrix}\\begin{bmatrix} 1 & 2 \\\\[2ex] 10 & 25 \\end{bmatrix} \\\\[5ex] E.\\:\\: \\begin{bmatrix} 5 \\\\[2ex] 3 \\end{bmatrix}\\begin{bmatrix} 1 & 10 \\\\[2ex] 2 & 25 \\end{bmatrix} \\\\[3ex] $Try to solve without Matrices Valley High School 1 teacher 10 students Cost =$5 * 1 + 3 * 10$Mountain High School 2 teacher 25 students Cost =$5 * 2 + 3 * 25$We expect to have two answers: one for each school The two answers represents either a$1 * 2$matrix or a$2 * 1$matrix If the answer is a$2 * 1$matrix, then we need to multiply a$2 * 2$matrix and a$2 * 1$matrix...Multiplication of Matrices That option is not included. So, we need a$1 * 2$matrix To have a$1 * 2$answer, we need to multiply a$1 * 2$matrix and a$2 * 2$matrix ... Multiplication of Matrices This means that we are left with Options$A$,$B$, and$C$Observing the trend/sequence based on our calculation, the product matrix will be:$ \\begin{bmatrix} 5 & 3 \\end{bmatrix}\\begin{bmatrix} 1 & 2 \\\\[2ex] 10 & 25 \\end{bmatrix} $(3.) CSEC In a football tournament, points are awarded as follows:$3$points for a win,$1$point for a draw and$0$points for a loss. (i) Write a$3 * 1$matrix,$P$, to represent this information. During the tournament, Team Alpha recorded$5$wins,$1$draw and$3$losses, while Team Beta recorded$3$wins,$4$draws, and$2$losses. (ii) Write a$2 * 3$matrix,$R$to represent this information. (iii) Calculate the matrix product$RP$(iv) What does the matrix product$RP$represent? Row by Column....Multiplication of Matrices$ \\begin{bmatrix} 5 & 1 & 3 \\rightarrow Team\\:A \\\\[2ex] 3 & 4 & 2 \\rightarrow Team\\:B \\end{bmatrix} \\begin{bmatrix} 3 \\rightarrow Win \\\\[2ex] 1 \\rightarrow Draw \\\\[2ex] 0 \\rightarrow Loss \\end{bmatrix} \\\\[5ex] (i)\\:\\: P = \\begin{bmatrix} 3 \\\\[2ex] 1 \\\\[2ex] 0 \\end{bmatrix} \\\\[7ex] (ii)\\:\\: R = \\begin{bmatrix} 5 & 1 & 3 \\\\[2ex] 3 & 4 & 2 \\\\[2ex] \\end{bmatrix} \\\\[7ex] RP = \\begin{bmatrix} 5 & 1 & 3 \\\\[2ex] 3 & 4 & 2 \\end{bmatrix} \\begin{bmatrix} 3 \\\\[2ex] 1 \\\\[2ex] 0 \\end{bmatrix} \\\\[7ex] R * P = RP \\\\[3ex] Order: 2\\:by\\:3 * 3\\:by\\:1 \\rightarrow 2\\:by\\:1 \\\\[3ex] (iii)\\:\\: RP = \\begin{bmatrix} 5(3) + 1(1) + 3(0) \\\\[2ex] 3(3) + 4(1) + 2(0) \\end{bmatrix} = \\begin{bmatrix} 15 + 1 + 0 \\\\[2ex] 9 + 4 + 0 \\end{bmatrix} = \\begin{bmatrix} 16 \\\\[2ex] 13 \\end{bmatrix} \\\\[3ex] $(iv) The matrix product$RP$represents the total number of points for Team Alpha and Team Beta in a football tournament. Team Alpha had$16$points Team Beta had$13$points (4.) (5.) ACT A$500-square-mile$national park in Kenya has large and small protected animals. The number of large protected animals at the beginning of$201$is given in the table below. Large animal Number Elephant Rhinoceros Lion Leopard Zebra Giraffe$600100200300400800$Total$2,400$At the beginning of$2014$, the number of all protected animals in the park was$10,000$Zoologists predict that for each year from$2015$to$2019$, the total number of protected animals in the park at the beginning of the year will be$2\\%$more than the number of protected animals in the park at the beginning of the previous year. In this park, the average number of gallons of water consumed per day by each elephant, lion, and giraffe is$50$,$5$, and$10$, respectively. Which of the following matrix products yields the average total number of gallons of water consumed per day by all the elephants, lions, and giraffes in the park?$ A.\\:\\: \\begin{bmatrix} 600 & 200 & 800 \\end{bmatrix}\\begin{bmatrix} 50 \\\\[2ex] 5 \\\\[2ex] 10 \\end{bmatrix} \\\\[5ex] B.\\:\\: \\begin{bmatrix} 600 & 800 & 200 \\end{bmatrix}\\begin{bmatrix} 50 \\\\[2ex] 5 \\\\[2ex] 10 \\end{bmatrix} \\\\[5ex] C.\\:\\: \\begin{bmatrix} 600 \\\\[2ex] 200 \\\\[2ex] 800 \\end{bmatrix}\\begin{bmatrix} 50 & 5 & 10 \\end{bmatrix} \\\\[5ex] D.\\:\\: \\begin{bmatrix} 600 \\\\[2ex] 800 \\\\[2ex] 200 \\end{bmatrix}\\begin{bmatrix} 50 & 5 & 10 \\end{bmatrix} \\\\[5ex] E.\\:\\: \\begin{bmatrix} 600 \\\\[2ex] 800 \\\\[2ex] 200 \\end{bmatrix}\\begin{bmatrix} 50 \\\\[2ex] 5 \\\\[2ex] 10 \\end{bmatrix} \\\\[5ex] $If you don't know how to begin, try to solve it without Matrices.$ Average\\;\\;total\\;\\;number\\;\\;of\\;\\;gallons \\\\[3ex] = Average\\;\\;number\\;\\;of\\;\\;gallons\\;\\;consumed\\;\\;by\\;\\;each\\;\\;elephant * Number\\;\\;of\\;\\;elephants \\\\[3ex] + \\\\[3ex] Average\\;\\;number\\;\\;of\\;\\;gallons\\;\\;consumed\\;\\;by\\;\\;each\\;\\;lion * Number\\;\\;of\\;\\;lions \\\\[3ex] + \\\\[3ex] Average\\;\\;number\\;\\;of\\;\\;gallons\\;\\;consumed\\;\\;by\\;\\;each\\;\\;giraffe * Number\\;\\;of\\;\\;giraffes \\\\[3ex] = 50(600) + 5(200) + 10(800) \\\\[3ex] $We expect to have only one answer. Bring it on to Matrices: One answer means a$1 * 1$matrix Go back to the multiplication: We are dealing with three animals: elephant, lion, and giraffe To obtain a$1 * 1$matrix as the product, we will need a$1 * 3$matrix to multiply a$3 * 1$... Multiplication of Matrices So, we eliminate Options$C$,$D$, and$E$We are left with Options$A$and$B$The multiplication we did above is also the same as writing it this way$ = 600(50) + 200(5) + 800(10) \\\\[3ex] $The correct option is$A$(6.)$ \\begin{vmatrix} p & c \\\\ -d & -e \\end{vmatrix} \\\\[3ex] = (p)(-e) - (-d)(c) \\\\[2ex] = -ep - (-cd) \\\\[2ex] = -ep + cd \\\\[2ex] = cd - ep \\$" ]
[ null, "https://matrix-algebra.appspot.com/images/samueldominicchukwuemeka.jpg", null ]
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https://www.mdpi.com/1099-4300/15/9/3312/htm
[ "Previous Article in Journal\nEntropy and Computation: The Landauer-Bennett Thesis Reexamined\n\nEntropy 2013, 15(9), 3312-3324; https://doi.org/10.3390/e15093312\n\nArticle\nOn the Entropy of a Two Step Random Fibonacci Substitution\nby", null, "Johan Nilsson\nDepartment of Mathematics, Universität Bielefeld, Postfach 100131, D–33501 Bielefeld, Germany\nReceived: 8 July 2013; in revised form: 30 July 2013 / Accepted: 19 August 2013 / Published: 23 August 2013\n\n## Abstract\n\n:\nWe consider a random generalization of the classical Fibonacci substitution. The substitution we consider is defined as the rule mapping, $a ↦ baa$ and $b ↦ ab$, with probability p, and $b ↦ ba$, with probability $1 − p$ for $0 < p < 1$, and where the random rule is applied each time it acts on a $b$. We show that the topological entropy of this object is given by the growth rate of the set of inflated random Fibonacci words, and we exactly calculate its value.\nKeywords:\ncombinatorics on words; asymptotic enumeration; symbolic dynamics\n\n## 1. Introduction\n\nIn , Godrèche and Luck define the random Fibonacci chain by the generalized substitution:\nfor $0 < p < 1$ and where the random rule is applied each time θ acts on a $b$. They introduce the random Fibonacci chain when studying quasi-crystalline structures and tilings in the plane. In their paper, it is claimed (without proof) that the topological entropy of the random Fibonacci chain is given by the growth rate of the set of inflated random Fibonacci words. This was later, with a combinatorial argument, proven in a more general context in .\nThe renewed interest in this system, and in possible generalizations, stems from the observation that the natural geometric generalization of the symbolic sequences by tilings of the line had to be Meyer sets with entropy and interesting spectra . There is now a fair understanding of systems that emerge from the local mixture of inflation rules that each define the same hull. However, little is known so far about more general mixtures. Here, we place our attention to one such generalization. It is still derived from the Fibonacci rule, but mixes inflations that define distinct hulls.\nIn this paper, we consider the randomized substitution, ϕ, defined by:\nfor $0 < p < 1$ and where the random rule is applied each time ϕ acts on a $b$. The substitution, ϕ, is a mixture of two substitutions, whose hulls are different. This is true, since the hull of the substitution, $( a , b ) ↦ ( baa , ab )$, contains words with the sub-words, $aaa$ and $bb$, but neither of these sub-words are to be found in any word of the hull of $( a , b ) ↦ ( baa , ba )$. For a more detailed survey of the differences and similarities of the generated hulls of these two substitutions, see .\nBefore we can state our main theorem in detail, we need to introduce some notation. A word, w, over an alphabet, Σ, is a finite sequence, $w 1 w 2 … w n$, of symbols from Σ. We let, here, $Σ = { a , b }$. We denote a sub-word of w by $w [ a , b ] = w a w a + 1 w a + 2 … w b − 1 w b$, and similarly, we let $W [ a , b ] = { w [ a , b ] : w ∈ W }$. By $| · |$, we mean the length of a word and the cardinality of a set. Note that $| w [ a , b ] | = b − a + 1$. When indexing the brackets with a letter, α, from the alphabet, $| · | α$, we shall mean the numbers of occurrences of α in the enclosed word.\nFor two words, $u = u 1 u 2 u 3 … u n$ and $v = v 1 v 2 v 3 … v m$, we denote by $u v$ the concatenation of the two words, that is, $u v = u 1 u 2 u 3 … u n v 1 v 2 … v m$. Similarly, we let, for two sets of words, U and V, their product be the set, $U V = { u v : u ∈ U , v ∈ V }$, containing all possible concatenations.\nLetting ϕ act on the word, $a$, repeatedly yields an infinite sequence of words, $r n = ϕ n − 1 ( a )$. We know that $r 1 = a$ and $r 2 = baa$. However, $r 3$ is one of the words, $abbaabaa$ or $babaabaa$, with probability p or $1 − p$. The sequence, ${ r n } n = 1 ∞$, converges in distribution to an infinite random word, r. We say that $r n$ is an inflated word (under ϕ) in generation n, and we introduce, here, sets that correspond to all inflated words in generation n;\nDefinition 1.\nLet $A 1 = { a }$, $B 1 = { b }$, and for $n ≥ 2$, we define recursively:\n$A n = B n − 1 A n − 1 A n − 1 B n = A n − 1 B n − 1 ∪ B n − 1 A n − 1$\nand we let $A : = lim n → ∞ A n$ and $B : = lim n → ∞ B n$.\nThe sets, A and B, are indeed well defined. This is a direct consequence of Corollary 6. It is clear from the definition of $A n$ and $B n$ that all their elements have the same length, that is, for all $x , y ∈ A n$ (or $x , y ∈ B n$), we have $| x | = | y |$. By induction, it easily follows that for $a ∈ A n$, we have $| a | = f 2 n$ and for $b ∈ B n$, we have $| b | = f 2 n − 1$, where $f m$ is the mth Fibonacci number, defined by $f n + 1 = f n + f n − 1$ with $f 0 = 0$ and $f 1 = 1$.\nFor a word, w, we say that x is a sub-word of w if there are two words, $u , v$, such that $w = u x v$. The sub-word set, $F ( S , n )$, is the set of all sub-words of length n of words in S. The combinatorial entropy of the random Fibonacci chain is defined as the limit, $lim n → ∞ 1 n log | F ( A , n ) |$. The combinatorial entropy is known to equal the topological entropy for our type of systems; see . The existence of this limit is direct by Fekete’s lemma , since we have sub-additivity, $log | F ( S , n + m ) | ≤ log | F ( S , n ) | + log | F ( S , m ) |$. We can now state the main result in this paper.\nTheorem 2.\nThe logarithm of the growth rate of the size of the set of inflated random Fibonacci words equals the topological entropy of the random Fibonacci chain, that is:\n$lim n → ∞ log | A n | f 2 n = lim n → ∞ log | B n | f 2 n − 1 = lim n → ∞ log | F ( C , n ) | n = 1 τ 3 log 2$\nwhere τ is the golden mean, $τ = 1 + 5 2$ and $C ∈ { A , B }$.\nThe outline of the paper is that we start by studying the sets, $A n$ and $B n$. Next, we give a finite method for finding the sub-word set, $F ( A , n )$, (which, we will see, is the same as $F ( B , n )$). Thereafter, we derive some Diophantine properties of the Fibonacci number that will play a central part when we look at the distribution of the letters in words from $F ( A , n )$. Finally, we present an estimate of $| F ( A , n ) |$, leading up to the proof of Theorem 2.\n\n## 2. Inflated Words\n\nIn this section, we present the sets of inflated words and give an insight to their structure. The results presented here will also play an important role for the results in the coming sections.\nProposition 3.\nLet $u , v ∈ A n$ (or both in $B n$). Then, $u ≠ v$, if and only if ${ ϕ ( u ) } ∩ { ϕ ( v ) } = ∅$, where, here, ${ ϕ ( z ) }$ denotes the set of all possible words that can be obtained by applying ϕ on z.\nProof.\nLet $u ≠ v$, and assume that $w ∈ { ϕ ( u ) } ∩ { ϕ ( v ) }$. Denote by $ϕ u$ and $ϕ v$ the special choices of ϕ, such that $w = ϕ u ( u ) = ϕ v ( v )$. Let k be the first position, such that $u k ≠ v k$, where $u = u 1 u 2 … u m$ and $v = v 1 v 2 … v m$. Then, we may assume $u k = a$ and $v k = b$; otherwise, just swap the names of u and v. Since we have $ϕ ( a ) = baa$, we see that we must have $ϕ v ( v k ) = ϕ v ( b ) = ba$. However, then, also, $ϕ v ( v k v k + 1 ) = ϕ v ( bb ) = baab$. This then implies $u k + 1 = b$, since, if we have $u k + 1 = a$, then there must be two consecutive $a$s in w, and we could not find a continuation in v. Hence, we have $ϕ u ( u k u k + 1 ) = ϕ u ( ab ) = baaba$. As previously, v must continue with a $b$. We now see that we are in a cycle, where $| ϕ u ( u k u k + 1 … u k + s ) | = 3 + 2 s$ and $| ϕ v ( v k v k + 1 … v k + s ) | = 2 ( s + 1 )$. Since there is no $s ∈ N$, such that $3 + 2 s = 2 ( s + 1 )$, we conclude that there can be no such w. ☐\nWe can now turn to the question of counting the elements in the sets, $A n$ and $B n$.\nProposition 4.\nFor $n ≥ 2$, we have:\n$| A n | = 2 f 2 n − 3 − 1 and | B n | = 2 f 2 n − 4 + 1$\nProof.\nLet us start with the proof of the the size of $A n$. From the Definition 1 of $A n$ and $B n$, it follows by induction that $| x | b = f 2 n − 2$ for $x ∈ A n$. Combining this with Proposition 3, we find the recursion:\n$| A n | = | A n − 1 | · 2 | x | b = | A n − 1 | · 2 f 2 n − 4$\nThe size of $A n$ now follows from Equation (2) by induction. For the size of $B n$, we have, by the definition of $B n$ and that we already know the size of $A n$,\n$| B n | = | A n + 1 | | A n | | A n | = 2 f 2 n − 1 − 1 2 f 2 n − 3 − 1 · 2 f 2 n − 3 − 1 = 2 f 2 n − 4 + 1$\nwhich completes the proof. ☐\nFrom Proposition 4, the statements of the logarithmic limits of the sets, $A n$ and $B n$, in Theorem 2 follows directly. Our next step is to give some result on sets of prefixes of $A n$ and $B n$. These results will play a central role when we later look at sets of sub-words.\nProposition 5.\nFor $n ≥ 2$, we have:\n$( 3 ) A n [ 1 , f 2 n − 1 ] ⊂ A n + 1 [ 1 , f 2 n − 1 ] ( 4 ) A n [ 1 , f 2 n − 1 ] ⊂ B n A n [ 1 , f 2 n − 1 ]$\nProof.\nLet us first consider Equation (3). We give a proof by induction on n. For the basis case, $n = 2$, we have:\n$A 2 [ 1 , f 2 · 2 − 1 ] = A 2 [ 1 , 2 ] = { ab } ⊂ { ab , ba } = A 3 [ 1 , f 4 − 1 ]$\nNow, assume for induction that Equation (3) holds for $2 ≤ n ≤ p$. Then, for $n = p + 1$, we have by the induction assumption:\n$A p + 1 [ 1 , f 2 ( p + 1 ) − 1 ] = B p A p A p [ 1 , f 2 ( p + 1 ) − 1 ] ⊆ ( A p B p ∪ B p A p ) A p [ 1 , f 2 ( p + 1 ) − 1 ] = B p + 1 A p [ 1 , f 2 ( p + 1 ) − 1 ] = B p + 1 A p [ 1 , f 2 p − 1 ] ⊂ B p + 1 A p + 1 [ 1 , f 2 p − 1 ] = B p + 1 A p + 1 [ 1 , f 2 ( p + 1 ) − 1 ] = B p + 1 A p + 1 A p + 1 [ 1 , f 2 ( p + 1 ) − 1 ] = A p + 2 [ 1 , f 2 ( p + 1 ) − 1 ]$\nwhich completes the induction and the proof of Equation (3). Let us turn to the proof of Equation (4). By the help of Equation (3), we have:\n$A n [ 1 , f 2 n − 1 ] = B n − 1 A n − 1 A n − 1 [ 1 , f 2 n − 1 ] = B n − 1 A n − 1 A n − 1 [ 1 , f 2 ( n − 1 ) − 1 ] ⊂ B n − 1 A n − 1 A n [ 1 , f 2 ( n − 1 ) − 1 ] = B n − 1 A n − 1 A n [ 1 , f 2 n − 1 ] ⊆ B n A n [ 1 , f 2 n − 1 ]$\nwhich concludes the proof. ☐\nFrom Proposition 5, it is straight forward, by recalling the recursive definition of $A n$ and $B n$, to derive the following equalities on prefix-sets.\nCorollary 6.\nFor $n ≥ 3$, we have:\n$A n [ 1 , f 2 ( n − 1 ) − 1 ] = A n + 1 [ 1 , f 2 ( n − 1 ) − 1 ] B n [ 1 , f 2 ( n − 1 ) − 1 ] = A n [ 1 , f 2 ( n − 1 ) − 1 ] B n = B n + 1 [ 1 , f 2 n − 1 ]$\nWe end the section by proving a result on suffixes of the sets, $A n$ and $B n$, that we shall make use of in the next sections.\nProposition 7.\nFor $n ≥ 2$, we have:\n$( 5 ) A n [ f 2 n − 2 + 2 , f 2 n ] ⊆ B n [ 2 , f 2 n − 1 ] ( 6 ) B n [ 2 , f 2 n − 1 ] = B n + 1 [ f 2 n + 2 , f 2 n + 1 ]$\nProof.\nWe give a proof by induction on n. For the basis case, $n = 2$, we have:\n$A 2 [ f 2 + 2 , f 4 ] = A 2 [ 2 , 3 ] = { a } ⊆ { a , b } = B 2 [ 2 , 2 ]$\nNow, assume for induction that Equation (5) holds for $2 ≤ n ≤ p$. Then, for the induction step, $n = p + 1$, we have by the induction assumption:\n$A p + 1 [ f 2 ( p + 1 ) − 2 + 2 , f 2 ( p + 1 ) ] = B p A p A p [ f 2 ( p + 1 ) − 2 + 2 , f 2 ( p + 1 ) ] = A p A p [ f 2 p − 2 + 2 , 2 f 2 p ] = A p [ f 2 p − 2 + 2 , f 2 p ] A p ⊆ B p [ 2 , f 2 p − 1 ] A p = B p A p [ 2 , f 2 p + 1 ] ⊆ B p + 1 [ 2 , f 2 ( p + 1 ) − 1 ]$\nwhich completes the induction and the proof of Equation (5). For the proof of Equation (6), we have:\n$B n [ 2 , f 2 n − 1 ] = A n B n [ f 2 n + 2 , f 2 n + f 2 n − 1 ] ⊆ B n + 1 [ f 2 n + 2 , f 2 n + f 2 n − 1 ]$\nand for the converse inclusion, we have by Equation (5):\n$B n + 1 [ f 2 n + 2 , f 2 n + f 2 n − 1 ] = A n B n ∪ B n A n [ f 2 n 2 , f 2 n + f 2 n − 1 ] = B n [ 2 , f 2 n − 1 ] ∪ A n [ f 2 n − 2 + 2 , f 2 n ] ⊆ B n [ 2 , f 2 n − 1 ]$\nwhich proves the equality (6). ☐\n\n## 3. Sets of Sub-Words\n\nHere, we investigate properties of the sets of sub-words, $F ( A , m )$ and $F ( B , m )$. We will prove that they coincide, and moreover, we show how to find them by considering finite sets, which will be central when estimating their size, depending on m.\nFirst, we turn our attention to proving that it is indifferent if we consider sub-words of $A n$ or of $B n$.\nProposition 8.\nFor $n ≥ 1$, we have:\n$F ( A n + 1 , f 2 n − 1 ) = F ( B n + 1 , f 2 n − 1 )$\nProof.\nLet us first turn to the proof of the inclusion:\n$F ( A n + 1 , f 2 n − 1 ) ⊆ F ( B n + 1 , f 2 n − 1 )$\nLet $x ( k ) ∈ A n + 1 [ k , k − 1 + f 2 n − 1 ]$ for $1 ≤ k ≤ f 2 n + 1 + 2$. It is clear that $x ( k ) ∈ F ( A n + 1 , f 2 n − 1 )$ for any k. We have to prove that also $x ( k ) ∈ F ( B n + 1 , f 2 n − 1 )$.\nFor $1 ≤ k ≤ f 2 n − 1 + 2$, we have:\n$x ( k ) ∈ F ( B n A n , f 2 n − 1 ) ⊆ F ( B n + 1 , f 2 n − 1 )$\nFor $f 2 n − 1 + 3 ≤ k ≤ f 2 n + 1$, we have by Corollary 6, which $x ( k )$ must be a sub-word of:\n$A n A n [ 3 , f 2 n + f 2 n − 2 − 1 ] = A n B n [ 3 , f 2 n + f 2 n − 2 − 1 ] = B k + 1 [ 3 , f 2 n + f 2 n − 2 − 1 ]$\nFor $f 2 n + 2 ≤ k ≤ f 2 n + 1 + 2$, we have by Proposition 7:\n$B n A n A n [ f 2 n + 2 , f 2 n + 2 ] = A n [ f 2 n − 2 + 2 , f 2 n ] A n ⊆ B n [ 2 , f 2 n − 1 ] A n ⊆ B n + 1 [ 2 , f 2 n + 1 ]$\nwhich concludes the proof of the inclusion Equation (7). For the converse inclusion, it is enough to consider sub-words of $A n B n$, since any sub-word of $B n A n$ clearly is a sub-word of $A n + 1$. Therefore, let $y ( k ) ∈ ( A n B n ) [ k , k − 1 + f 2 n − 1 ]$ for $1 ≤ k ≤ f 2 n − 1 + 1$. We now proceed as in the case above.\nFor $1 ≤ k ≤ f 2 n − 2 + 1$, we have:\n$( A n B n ) [ 1 , f 2 n + f 2 n − 2 − 1 ] = A n B n [ 1 , f 2 n − 2 − 1 ] = A n A n [ 1 , f 2 n − 2 − 1 ] = A n + 1 [ f 2 n + 1 + 1 , f 2 n + 1 + f 2 n − 2 − 1 ]$\nFor $f 2 n − 2 + 2 ≤ k ≤ f 2 n − 1 + 2$, we have:\n$( A n B n ) [ f 2 n − 2 + 2 , f 2 n − 1 + 2 ] = A n [ f 2 n − 2 + 2 , f 2 n ] A n = B n [ 2 , f 2 n − 1 ] A n = A n + 1 [ 2 , f 2 n + 1 ]$\nwhich completes the proof. ☐\nThe above result shows that the set of sub-words from $A n$ and $B n$ coincide if the sub-words are not chosen too long. If we consider the limit sets, A and B, their sets of sub-words turn out to be the same. We have the following:\nProposition 9.\nFor $m ≥ 1$, we have $F ( A , m ) = F ( B , m )$.\nProof.\nLet $x ∈ F ( A , m )$. Then, there is an n, such that:\n$x ∈ F ( A n , m ) ⊆ F ( A n B n ∪ B n A n , m ) = F ( B n + 1 , m ) ⊆ F ( B , m )$\nSimilarly, if $x ∈ F ( B , m )$. Then, there is an n, such that:\n$x ∈ F ( B n , m ) ⊆ F ( B n A n A n , m ) = F ( A n + 1 , m ) ⊆ F ( A , m )$\nwhich completes the proof. ☐\nThe direct consequence of Proposition 9 is that we find the topological entropy in Equation (1) independent if we look at sub-words from A or B.\nNow, let us turn to the question of finding $F ( A , m )$ from a finite set, $A n$, and not having to consider the infinite set, A.\nProposition 10.\nFor $n ≥ 2$, we have:\n$F ( A n + 1 , f 2 n − f 2 n − 3 ) = F ( A n + 2 , f 2 n − f 2 n − 3 )$\nProof.\nIt is clear that $F ( A n + 1 , f 2 n − f 2 n − 3 ) ⊆ F ( A n + 2 , f 2 n − f 2 n − 3 )$ holds for all $n ≥ 2$. For the reverse inclusion, assume that $x ∈ F ( A n + 2 , f 2 n − f 2 n − 3 )$. Note that we can write $A n + 1$ and $A n + 2$ on the form:\n$A n + 1 = B n A n A n , ( 8 ) A n + 2 = B n A n B n A n A n B n A n A n ∪ A n B n B n A n A n B n A n A n$\nFrom Equation (8), we see that any x is a sub-word of any element in some of the seven sets:\n$A n A n , A n B n A n , A n B n , A n B n A n , B n B n , A n B n B n , B n B n A n$\nin such a way that the first letter in x is in the first factor (that is, $A n$ or $B n$) of the sets. If x is a sub-word of $A n A n$ or $B n A n$ or completely contained in $A n$, it is clear that we have $x ∈ F ( A n + 1 , f 2 n − f 2 n − 3 )$. For the case when x is a sub-word of $A n B n$, it follows from Proposition 8 that we have $x ∈ F ( A n + 1 , f 2 n − f 2 n − 3 )$.\nIf x is a sub-word of a word in $A n B n A n$, such that x begins in the first $A n$ factor and ends in the second, then we have that x is a sub-word of a word in the set:\n$( A n [ f 2 n − 3 + f 2 n − 1 + 2 , f 2 n ] ) B n − 1 A n − 1 A n [ 1 , f 2 n − 4 − 1 ] = A n [ f 2 n − 3 + f 2 n − 1 + 2 , f 2 n ] B n − 1 A n − 1 A n − 1 [ 1 , f 2 n − 4 − 1 ] = A n [ f 2 n − 3 + f 2 n − 1 + 2 , f 2 n ] A n [ 1 , f 2 n − 1 + f 2 n − 4 − 1 ] = ( A n A n ) [ f 2 n − 3 + f 2 n − 1 + 2 , f 2 n + f 2 n − 1 + f 2 n − 4 − 1 ]$\nand we see that we have $x ∈ F ( A n + 1 , f 2 n − f 2 n − 3 )$.\nIf x is a sub-word of a word in $B n B n$, let us first consider the case when it is a sub-word of $B n B n − 1 A n − 1$. Then, it follows that:\n$B n B n − 1 A n − 1 ⊆ B n A n [ 1 , f 2 n − 1 ] = B n A n [ 1 , 2 f 2 n − 1 ]$\nso x is a sub-word of a word in $A n + 1$. For the the second case, $B n A n − 1 B n − 1$, we have:\n$B n A n − 1 B n − 1 = A n − 1 B n − 1 A n − 1 B n − 1 ∪ B n − 1 A n − 1 A n − 1 B n − 1 ⊆ A n B n A n [ f 2 n − 1 + 1 , 3 f 2 n − 1 ] ∪ ( A n B n ) [ 1 , 2 f 2 n − 1 ]$\nand again, x is a sub-word of a word in $A n + 1$, by what we just proved above.\nIf x is a sub-word of a word in $A n B n B n$, we have by Corollary 6:\n$A n B n B n [ f 2 n − 1 + f 2 n − 3 + 1 , 2 f 2 n − f 2 n − 3 − 1 ] = A n [ f 2 n − 1 + f 2 n − 3 + 1 , f 2 n ] B n B n [ 1 , f 2 n − 4 − 1 ] = A n [ f 2 n − 1 + f 2 n − 3 + 1 , f 2 n ] B n A n [ 1 , f 2 n − 4 − 1 ]$\nwhich shows that x is a sub-word of a word in $A n + 1$ by what we previously have shown.\nFinally, if x is a sub-word of a word in $B n B n A n$, we first consider the case when x is a sub-word of a word in $B n B n − 1 A n − 1 A n$. By Corollary 6, we have:\n$B n B n A n [ 2 f 2 n − 3 + 1 , f 2 n + 1 − f 2 n − 3 − 1 ] = B n [ 2 f 2 n − 3 + 1 , f 2 n − 1 ] B n − 1 A n − 1 A n [ 1 , f 2 n − 4 − 1 ] = B n [ 2 f 2 n − 3 + 1 , f 2 n − 1 ] B n − 1 A n − 1 A n − 1 [ 1 , f 2 n − 4 − 1 ] = B n [ 2 f 2 n − 3 + 1 , f 2 n − 1 ] A n [ 1 , f 2 n − 1 + f 2 n − 4 − 1 ]$\nwhich, by the help of the previous case, shows that x is a sub-word of a word in $A n + 1$. For the last case, $B n A n − 1 B n − 1 A n$, we have by Corollary 6 and Proposition 7:\n$( B n B n A n ) [ 2 f 2 n − 3 + 1 , f 2 n + 1 − f 2 n − 3 − 1 ] = B n [ 2 f 2 n − 3 + 1 , f 2 n − 1 ] A n − 1 B n − 1 A n [ 1 , f 2 n − 4 − 1 ] = B n − 1 [ 2 f 2 n − 3 − f 2 n − 2 + 1 , f 2 n − 3 ] A n − 1 B n − 1 A n − 1 [ 1 , f 2 n − 4 − 1 ] = B n [ 2 f 2 n − 3 − f 2 n − 2 + 1 , f 2 n − 1 ] A n [ 1 , f 2 n − 2 − 1 ]$\nand again, we see that x is a sub-word of a word in $A n + 1$ by what we have proven above. ☐\nThe result of Proposition 10 can be extended to hold for sub-words from elements $A n$ and $A n + k$, where $k ≥ 1$. A straight forward argument via induction gives:\n$F ( A n + 1 , f 2 n − f 2 n − 3 ) = F ( A n + k , f 2 n − f 2 n − 3 )$\nfor $k ≥ 1$. By combining Proposition 10 and Equation (10), we can now prove that to find the factors set, it is sufficient to only consider a finite set.\nProposition 11.\nFor $n ≥ 2$, we have:\n$F ( A n + 1 , f 2 n − f 2 n − 3 ) = F ( A , f 2 n − f 2 n − 3 )$\nProof.\nIt is clear that we have $F ( A n + 1 , f 2 n − f 2 n − 3 ) ⊆ F ( A , f 2 n − f 2 n − 3 )$. For the reversed inclusion, let $x ∈ F ( A , f 2 n − f 2 n − 3 )$. Then, there is a smallest $m ≥ n + 1$, such that x is a sub-word of an element of $A m$. Then, Equation (10) gives:\n$x ∈ F ( A m , f 2 n − f 2 n − 3 ) = F ( A n + 1 , f 2 n − f 2 n − 3 )$\nwhich shows the desired inclusion. ☐\n\n## 4. Fibonacci Numbers Revisited\n\nIn this section, we shall restate, and adopt for our purposes, some of the Diophantine properties of the Fibonacci numbers and use them to derive results on the distribution of the letters in the words in the sets, $A n$ and $B n$. Let us introduce the notation:\n$τ = 1 + 5 2 a n d τ ^ = 1 − 5 2$\nfor the roots of $x 2 − x − 1 = 0$. It is well known that τ and $τ ^$ appear in Binet’s formula, the Fibonacci numbers; see :\n$f n = 1 5 1 + 5 2 n − 1 5 1 − 5 2 n = 1 5 τ n − τ ^ n$\nFrom Equation (12), it is with induction straight forward to derive:\n$f n = τ f n − 1 + τ ^ n − 1 = τ 2 f n − 2 + τ ^ n − 2$\nDefinition 12.\nLet $∥ · ∥$ denote the smallest distance to an integer.\nBy using the special property, $τ 2 = τ + 1$, we have for an integer, k, the following line of equalities:\n$1 τ 2 k = τ − 1 τ k = k − 1 τ k = 1 τ k = ∥ ( τ − 1 ) k ∥ = ∥ τ k ∥$\nFrom Equation (13), it follows that:\n$∥ τ f n ∥ = ∥ f n + 1 − τ ^ n ∥ = 1 τ n$\nsince $τ ^ = − 1 τ$. For an integer, k, which is not a Fibonacci number, we have the following estimate of how far away from an integer $τ k$ is.\nProposition 13.\nFor a positive integer, k, such that $f n − 1 < k < f n$, we have:\n$∥ τ k ∥ > 1 τ n − 2$\nProof.\nWe give a proof by induction on n. For the basis case, $n = 5$, the statement of the proposition follows by an easy calculation. Now, assume for induction that Equation (14) holds for $5 ≤ n ≤ p$. For the induction step, $n = p + 1$, let $f p < k < f p + 1$. Then, if $k − f p − 1$ is not a Fibonacci number, we have:\n$∥ τ k ∥ = ∥ τ ( k − f p ) + τ f p ∥ ≥ ∥ τ ( k − f p ) ︸ < f p − 1 ∥ − ∥ τ f p ∥ > 1 τ p − 3 − 1 τ p > 1 τ p − 2$\nIf $k − f p − 1 = f m$ for some $m < p − 1$, then:\n$∥ τ k ∥ ≥ ∥ τ f m ∥ − ∥ τ f p ∥ = 1 τ m − 1 τ p ≥ 1 τ p − 2 − 1 τ p = 1 τ p − 1$\nProposition 14.\nLet $x ∈ A n [ 1 , k ]$ for $1 ≤ k ≤ f 2 n$ (or $x ∈ B n [ 1 , k ]$ for $1 ≤ k ≤ f 2 n − 1$) and $n ≥ 2$. Then:\n$| x | b ∈ 1 τ 2 k , 1 τ 2 k$\nProof.\nWe give a proof by induction on n. The basis case, $n = 2$, follows by considering each of the words contained in $A 2$ and $B 2$. To be able to use Proposition 13 in the induction step, we have to consider the basis step, $n = 3$, as well, but only for the set, $B 3$ (since the words in $A 2$ are of length $≥ 3$). This is, however, seen to hold by a straight forward enumeration of the elements of $B 3$.\nNow, assume for induction that Equation (15) holds for $2 ≤ n ≤ p$, for words both from $A n$ and $B n$. For the induction step, $n = p + 1$, let us first derive an identity of which we shall later make use. Let q and m be positive integers, such that $f m − 1 < q < f m$. Then, by the help of Proposition 13, we have:\n$1 τ 2 ( q − f m − 1 ) = 1 τ 2 q − f m − 3 − τ ^ m − 1 = 1 τ 2 q + ( − 1 ) m τ m − 1 − f m − 3 ( 16 ) = 1 τ 2 q − f m − 3$\nWith the same argumentation, we can derive a similar result for $⌈ · ⌉$. For the induction step, we consider first the number of $b$s in prefixes of words in $A p + 1 = B p A p A p$. It is clear from the induction assumption that Equation (15) holds for $1 ≤ k ≤ f 2 p − 1$. For $f 2 p − 1 < k < f 2 p$ or $f 2 p < k < f 2 p + 1$, let $x = u v ∈ A p + 1 [ 1 , k ]$, where $u ∈ B p$. By the induction assumption, we may assume that $| v | b$ is given by rounding downwards, (the result is obtained in a similar way for the case with $⌈ · ⌉$). By Equation (16), it now follows that:\n$| u v | b = | u | b + | v | b = f 2 p − 3 + 1 τ 2 ( k − f 2 p − 1 ) = 1 τ 2 k$\nFor $k = f 2 p$, we have:\n$| u v | b = f 2 p − 3 + 1 τ 2 ( f 2 p − f 2 p − 1 ) = 1 τ 2 f 2 p + 1 τ 2 p − 1 = 1 τ 2 f 2 p$\nFor $f 2 p + 1 < k < f 2 p + 2$, let $x = u v w ∈ A p + 1 [ 1 , k ]$, where $u ∈ B p$ and $v ∈ A p$. Then, the induction assumption and Equation (16) gives:\n$| u v w | b = | u | b + | v | b + | w | b = f 2 p − 3 + f 2 p − 2 + 1 τ 2 ( k − f 2 p − 1 − f 2 p ) = f 2 p − 1 + 1 τ 2 ( k − f 2 p + 1 ) = 1 τ 2 k$\nFor the last case, $k = f 2 p + 2$, we have:\n$| x | b = 1 τ 2 ( f 2 p + 2 ) = f 2 p + 1 τ 2 p = f 2 p$\nThe case when we consider words from $B p + 1$ is treated in the same way, but where we do not need to do the induction step for the case $n = 3$. This completes the induction and the proof. ☐\nProposition 15.\nLet $x ∈ F ( A n + 2 , f 2 n )$ for $n ≥ 2$. Then:\n$f 2 n − 2 − 1 ≤ | x | b ≤ f 2 n − 2 + 1$\nProof.\nLet us first turn our attention to the upper bound in Equation (17). In the same way as in the proof of Proposition 10, we consider sub-words of the seven sets, given in Equation (9).\nIf x is a sub-word, beginning at position $2 < k ≤ f 2 n$, in an element in $A n A n$ or $A n B n$, then:\n$| x | b ≤ f 2 n − 2 + 1 τ 2 ( k − f 2 n ) + f 2 n − 1 τ 2 k ≤ f 2 n − 2 + 1$\nsince the number of $b$s in a word in $A n$ is $f 2 n − 2$, and a word in $A n$ is of length $f 2 n$. The proof of the upper bound in Equation (17) and for the other sets in Equation (9) is obtained in the same way.\nFor the lower bound, we have:\n$| x | b ≥ 1 τ 2 ( k + f 2 n ) − 1 τ 2 k = f 2 n − 2 + 1 τ 2 k + 1 τ 2 n − 2 − 1 τ 2 k ≥ f 2 n − 2 − 1$\nfor any $x ∈ F ( A n + 2 , f 2 n )$. ☐\n\n## 5. Estimating the Size of the Sub-Word Set\n\nWe shall in this section give an estimate of the sub-word set, $F ( A , f 2 n )$, and give the final part of the proof of Theorem 2. Let us introduce the set:\n$C n = ϕ F ( A , f 2 n − 2 + 1 )$\nBy Proposition 15, we can estimate the number of $b$s in words in $F ( A , f 2 n − 2 + 1 )$. This estimate then gives that we have bounds on the length of words in $C n$. That is, for $x ∈ C n$, we have:\n$| x | = | x | a + | x | b ≥ 3 ( f 2 n − 3 − 1 ) + 2 ( f 2 n − 4 + 2 ) = f 2 n + 1$\nand:\n$| x | = | x | a + | x | b ≤ 3 ( f 2 n − 3 + 2 ) + 2 ( f 2 n − 4 − 1 ) = f 2 n + 4$\nProposition 16.\nFor $n ≥ 2$, we have:\n$F ( A , f 2 n ) = F C n , f 2 n$\nProof.\nThe set, $F C n , f 2 n$, is created by inflating words from $F ( A , f 2 n − 2 + 1 )$, which are then cut into suitable lengths. This implies that $F ( A , f 2 n ) ⊇ F C n , f 2 n$.\nFor the converse inclusion, let $x ∈ F ( A , f 2 n )$. Then, there is a word, $w ∈ A n + 1$, and words, $u , v$, such that $u x v ∈ A n + 2$ and $u x v ∈ ϕ ( w )$. For any word, $z ∈ F { w } , f 2 n − 2 + 1$, we have from Equation (18) that any $s ∈ ϕ ( z )$ fulfills $f 2 n + 1 ≤ | s |$. This gives that there is a word, $z x ∈ F { w } , f 2 n − 2 + 1$, such that x is a sub-word of a word in $ϕ ( z x )$, which implies $x ∈ F C n , f 2 n$. ☐\nProposition 17.\nFor $n ≥ 2$, we have:\n$| F ( A , f 2 n ) | ≤ 2 f 2 n − 3 + 2 n · 5 n − 1$\nProof.\nWe give a proof by induction on n. For the basis case, $n = 2$, we have:\n$| F ( A , f 4 ) | = 7 ≤ 160 = 2 f 1 + 4 · 5$\nAssume for induction that Equation (20) holds for $2 ≤ n ≤ p$. For the induction step, $n = p + 1$, note that from Equations (18) and (19), it follows that $| F ( { x } , f 2 p + 2 ) | ≤ 5$ for $x ∈ C p + 1$. By Proposition 15, we have that the number of $b$s in $u ∈ F ( A , f 2 p + 1 )$ is at most $f 2 p − 2 + 2$. This gives, then, with the help of the induction assumption:\n$| F A , f 2 p + 2 | ≤ | C p + 1 | · 5 ≤ | F A , f 2 p | · 2 f 2 p − 2 + 2 · 5 ≤ 2 f 2 p − 3 + 2 p · 5 p − 1 · 2 f 2 p − 2 + 2 · 5 = 2 f 2 ( p + 1 ) − 3 + 2 ( p + 1 ) · 5 p$\nwhich completes the proof. ☐\nWe can now turn to proving the last equality in Equation (1) and, thereby, completing the proof of Theorem 2. By Proposition 17, we have:\n$lim n → ∞ log | F ( A , f 2 n ) | f 2 n ≤ lim n → ∞ log 2 f 2 n − 3 + 2 n · 5 n − 1 f 2 n = lim n → ∞ f 2 n − 3 + 2 n f 2 n log 2 + n − 1 f 2 n log 5 = 1 τ 3 log 2$\nwhich implies the equality in Equation (1).\nA further generalization of the random Fibonacci substitutions would be to study the structure occurring when mixing two substitutions with different inflation multipliers. This, however, seems to be a far more complex question.\n\n## Acknowledgments\n\nThe author wishes to thank M. Baake and M. 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An Introduction to Symbolic Dynamics and Coding; Cambridge University Press: Cambridge, UK, 1995. [Google Scholar]\n6. Fekete, M. Über die Verteilung der Wurzeln bei gewissen algebraischen Gleichungen mit. ganzzahligen Koeffizienten. Math. Zeitschrift 1923, 17, 228–249. [Google Scholar] [CrossRef]\n7. Graham, R.L.; Knuth, D.E.; Patashnik, O. Concrete Mathematics; Addison-Wesley Publishing Company: Reading, MA, USA, 1994. [Google Scholar]" ]
[ null, "https://www.mdpi.com/profiles/masked-unknown-user.png", null ]
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https://cipmexamtipsandtricks.blogspot.com/2013/09/common-themes-dietz-style-equations.html
[ "## Friday, September 20, 2013\n\n### Common Themes: \"Dietz-Style Equations\"\n\nFor today's post, I'd like to review some of the \"Dietz-style\" formulae we use to calculate true time-weighted return and estimated time-weighted return.  I've never actually seen the formulae presented this way, but hopefully doing it in this fashion will help candidate see that we are using essentially the same basic formula in all of the following cases... just applying them in different ways.\n\nNote:  the term \"Dietz-style\" is my own term... used to reference the basic equation style we see with the Original Dietz and Modified Dietz formulae.\n\n### Return Calculations in the Absence of Cash Flows\n\nIn the absence of cash flows, return calculation is simple.  We measure the change in value of the assets from the beginning of the period to the end of the period, and compare (i.e., divide by) the beginning value:\n\nIn this equation, R is our period return, V \"sub\" E is our ending value and V \"sub\" B is our beginning value.  The numerator of this equation is the amount earned by the portfolio manager and the denominator is the amount of money available to earn the return; i.e., the basis.  In the absence of cash flows, this equation gives us a precise return.\n\n### The Problem of External Cash Flows\n\nExternal cash flows cause the previous equation to not be completely accurate, because the cash flows change the amount of money available to the manager to earn return.  Specifically, contributions increase the amount available to earn return, and withdrawals decrease that amount.\n\nCash flows can occur in one of three ways:\n\n1. Exactly at the start of the period\n2. Exactly at the end of the period\n3. Sometime during the period\n\n### Adjusting the Equation When Cash Flows Occur at the Start of the Period\n\nWhen a cash flow occurs exactly at the start of the period, this logically means that the beginning value has been adjusted to include the cash flow.  Thus, the corresponding adjustment we can make to our initial equation is to add the cash flow to the beginning value in all instances that it appears in the formula:\n\nThis adjustment gives us a precise return formula for this situation.\n\n### Adjusting the Equation When Cash Flows Occur at the End of the Period\n\nWhen a cash flow occurs exactly at the end of the period, this logically means that the ending value implicitly includes the cash flow's impact.  Thus, the corresponding adjustment we can make to our initial equation is to subtract the cash flow from the ending value in all instances that it appears in the formula:\n\nThis adjustment gives us a precise return formula for this situation.\n\n### Comparing the Equations:  Flow at Start vs. Flow at End\n\nIf we compare the numerators of the two equations (1.2 and 1.3), after evaluating the parentheses in both cases, we see that the numerators are equal:\n\nThis adjustment gives us a precise return formula for this situation.\n\nThe denominator of the equations are different, however.  Basically, the cash flow is part of the denominator if it occurs at the start of the period, and it isn't part of the denominator if the flow occurs at the end of the period.  Thus, we can rewrite our equations 1.3 and 1.4:\n\nIf we have multiple cash flows all occurring either at the start of the period or all occurring at the end of the period, we simply sum the cash flows:\n\n### Generalizing the Equation\n\nWe can generalize the two equations in (1.6) to come up with a single equation to cover both circumstances:\n\nIn this equation, we apply (i.e., multiply) the cash flow sum by a weight:\n• If the flows all occur at the start of the period, the weight is 1\n• If the flows all occur at the end of the period, the weight is 0.\nThus, we now have precise formulae for calculating return for two of our three scenarios:  when flows all occur at the start of the period and also when flows occur at the end of the period.\n\n### What If Flows Occur During the Period?\n\nThe Original Dietz and Modified Dietz equations are extensions of the formula (1.7) above to handle the case where cash flows occur during the period.  In both of these cases, the formula gives us an estimate of the manager's return.\n\nIn the case of Original Dietz, we assume all cash flows occur in the middle of the period; thus, a weight of 1/2 is applied to all cash flows (through multiplication):\n\nNote that the weight of 1/2 is between 0 and 1.\n\nIn the case of Modified Dietz, rather than assuming that all cash flows occur at a single point in time (start, middle or end of the period), we will consider the timing of each individual cash flow, and apply (through multiplication) a weight that corresponds to the fraction of the period that remains at the time of the cash flow.  Thus, a weight (W \"sub\" i) is calculated for each cash flow F \"sub\" i using the following equation:\n\n(CD - D) / CD\n\nwhere CD is the number of calendar days in the period and D is the day of the cash flow within the period.  For example, if the period is January and the flow occurs on the 10th of January, then CD = 31 and D = 10.  Note that this assumes that the given cash flow occurs at the end of the day.  Some prefer to assume the cash flow occurs at the end of the day, in which case the weight is calculated as:\n\n(CD - D + 1) / CD\n\nNote that these weights will be between 0 and 1 in all cases.  Rather than the entire period remaining at the time of the cash flow (i.e., a flow at the start of the period which implies a weight of 1) and rather than none of the period remaining at the time of the cash flow (i.e., a flow at the end of the period which implies a weight of 0), the cash flow occurs sometime during the period, so a fraction of the full period remains (i.e., a weight between 0 and 1).\n\nThus the formula for Modified Dietz is\n\nThus, we now have equations to cover all three scenarios:\n\n1. Exactly at the start of the period (equation 1.6 with a weight of 1)\n2. Exactly at the end of the period (equation 17. with a weight of 0)\n3. Sometime during the period (either equation 1.7, which is Original Dietz, or equation 1.8, which is Modified Dietz).  Both of these equations are estimates of the return.  Each cash flow's weight is a fraction somewhere between 0 and 1.\n\n### Why Is The \"Case 3\" Return Only an Estimate?\n\nIf we want to improve our estimate and make it precise, we must break the single period into sub-periods, and revalue the portfolio at the time of the cash flow.  We then calculate the return for each sub-period, and the formula for the sub-periods will either be a Case 1 (start of period) or Case 2 (end of period) situation.  Geometric linking of the sub-period returns gives us the cumulative time-weighted return for the entire period; i.e., across all of the sub-periods.\n\nHopefully this post helps to explain the relationship between all of the above formulae.  At some later date I will come back and add some numeric examples, but for now I think you can get the picture, without burdening an already long post with some math.\n\nHappy studying!" ]
[ null ]
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https://blogs.sap.com/2015/12/18/how-to-understand-const-add-x-y-x-y/
[ "", null, "# How to understand const add = x => y => x + y\n\nThere is a piece of JavaScript codes below:\n\n``````\nconst add = x => y => x + y\n\nWhen executed, c is equal to 3 in the runtime. Why?\n\nLet’s debug in Chrome.\n\n1. Only one argument, 1. Pay attention to the highlight part in line 19. It means argument x is set to 1.", null, "Check in console, x = 1, y is not available at this time.", null, "And here below gives us a hint that add(1)(2) will first bind x to 1, and return a new function f(y) = x + y = 1 + y.", null, "2. when clicking step into again, pay attention to the highlight part in line 21. It means now the function f(y) = 1 + y is executed, and this time, the argument y, is set as 2.", null, "And the argument x’s value 1 is still preserved in the context via Closure.", null, "So finally we get 3 as result. So const add = x => y => x + y just creates a curried function which has exactly the same function as below:\n\n``````" ]
[ null, "https://avatars.services.sap.com/images/jerry.wang.png", null, "https://blogs.sap.com/wp-content/uploads/2015/12/clipboard1_854423.png", null, "https://blogs.sap.com/wp-content/uploads/2015/12/clipboard2_854424.png", null, "https://blogs.sap.com/wp-content/uploads/2015/12/clipboard3_854425.png", null, "https://blogs.sap.com/wp-content/uploads/2015/12/clipboard4_854429.png", null, "https://blogs.sap.com/wp-content/uploads/2015/12/clipboard5_854430.png", null ]
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https://www.kopykitab.com/blog/rs-aggarwal-solution-class-8-chapter-20-volume-surface-area-of-solid/
[ "# RS Aggarwal Solution Class 8 Chapter 20 – Volume & Surface area of Solid\n\nRS Aggarwal Solution Class 8 Chapter 20 – Volume & Surface area of Solid: Volume and surface area of solid is a very long chapter that requires calculation and you need to be well versed with the formulas of all 3D figures.\n\nThis chapter contains a lot of questions that will be asked in your mathematics examination. RS Aggarwal Solution Class 8 Chapter 20  provides a wide variety of questions. And practicing them will give you a strong base for this unit.\n\nBuy the solution book for RS Aggarwal Class 8 Maths here.\n\nBut you would also need a solution that will help you in solving those questions and for that, you can go through our RS Aggarwal Solution Class 8 Chapter 20. This will provide answers in a very detailed manner and solve all your doubts regarding this unit.\n\nThe solution provided by us is written by our experts, who have substantial experience in their field. And they write answers keeping in mind your age and simplifying the solution as much as possible.\n\nRS Aggarwal Solution Class 8 Chapter 20 comes in a Pdf version and it is accessible on all devices. You can read it both online and offline. The pdf can be downloaded from the link mentioned below.\n\nRS Aggarwal Class 8 Chapter 20 Solutions\n\n## RS Aggarwal Solution Class 8 Chapter 20: Exercise-wise\n\nIf you are having any doubts about a particular exercise, we have bifurcated the complete pdf into small pdfs of different exercises present in the chapter.\n\nThis RS Aggarwal Solution Class 8 Chapter 20 PDF is also accessible from anywhere and can be read online and offline. If you want to download the pdf you can click on the link below-\n\n Topics Solution RS Aggarwal Class 8 Chapter 20a Exercise 20.1 RS Aggarwal Class 8 Chapter 20b Exercise 20.2 RS Aggarwal Class 8 Chapter 20c Exercise 20.3\n\n## RS Aggarwal Solution Class 8 Chapter 20 Exercise-wise\n\nThe Pdf solution of the RS Aggarwal Class 8 Chapter 20 provides a detailed and simple solution even to complex problems. Our solutions will provide you tips and tricks on how to solve the questions in a more efficient way.\n\nVolume and Surface Area of Solid is a chapter that includes questions related to calculating the Volume, Curved Surface Area (CSA) and Total Surface Area (TSA) of the solid figures like cube, cuboid and cylinder.\n\nNow, let’s understand some basic terms used in the chapter-\n\n1. Cube- A figure can be called a cube, if it has 6 square faces, 8 vertices and 12 edges.\n2. Cuboid- A figure can be called a cuboid, if it has 6 rectangular faces, 8 vertices and 12 edges.\n3. Cylinder- A figure can be called a cylinder if it has 2 circulars with a joint by a curved surface.\n4. The volume of a solid figure- The total space that a solid figure takes is called its volume.\n\nWe shall now discuss the exercise wise explanation of this unit so that you know what topics are covered in the following exercise.\n\n### RS Aggarwal solutions Class 8 Chapter 20 Ex 20a\n\nThis exercise contains 30 questions which talks about the calculation of volume, Total Surface Area (TSA) and missing height, breadth and width of a cube and cuboid. This exercise is lengthy but can be solved using simple formulas. The student has to be well versed with all the formulas.\n\nOur pdf of RS Aggarwal Solutions Class 8 Chapter 20 will provide you with a detailed answer to all the questions. Till the time you complete this exercise, you will learn all the formulas related to cube and cuboid. It will become very easy for you to solve them. This pdf will help you score high grades in your maths exam.\n\n### RS Aggarwal solutions Class 8 Chapter 20 Ex 20b\n\nThis exercise has a total of 21 questions and it is totally based on cylinders. The student has to calculate the volume, Total Surface Area (TSA), Curved Surface Area (CSA), missing radius of the cylinder and more. The questions of this exercise urge the students to analyze which formula should be used in which question.\n\nThe solution pdf of RS Aggarwal Chapter 20 class 8 will give you answers in a stepwise manner which are written by panel of experts. So, you will get answers which can directly be used in your mathematics exam and also while self-studying.\n\n### RS Aggarwal Solutions Class 8 Chapter 20 Ex 20c\n\nThis exercise contains 30 questions and most of them are based on word problems of different solid figures like Cube, Cylinder and cuboid. The questions on this exercise can be tricky and require a lot of practice to solve all the problems accurately.\n\nRS Aggarwal Solutions Class 8 Chapter 20 will provide you with an answer to all the questions in an easy step-wise manner. All these questions can be solved following the steps present in the solution pdf to get high grades in your maths exams.\n\n### RS Aggarwal solutions Class 8 Chapter 20 Test Paper\n\nThe test paper of this chapter has a total of 13 questions and this exercise is an extension of all the total exercises combined. It talks about calculating volume, TSA, CSA, missing dimensions and word problems related to this chapter. So, it is like a practice of all the formulas and all the questions of the test paper are formula-based.\n\nRS Aggarwal Solutions Class 8 Maths Chapter 20 will provide answers in a very simple way so that you can easily solve these questions. All these questions will give a good understanding of this exercise.\n\n## RS Aggarwal Solution Class 8 Chapter 20: Important Topics in the Exercise\n\nThe solution of RS Aggarwal Class 8 Chapter 20 Volume and surface area of solids will give you extensive answers to all the questions and the pdf can be downloaded both from your PC and mobile. You can use this pdf to solve all your doubts and score good marks in your mathematics exams.\n\nHere, comes the important topic that this chapter has: –\n\n•      The volume of Cube, Cuboid and Cylinder\n•     TSA of Cube and Cuboid and Cylinder\n•     CSA of Cuboid\n•     Word problems on these solids\n\n## RS Aggarwal Solution Class 8 Chapter 20\n\nRS Aggarwal Solution Class 8 Chapter 20 is a combination of all the exercises present in the chapter. It is best for students who self-study or for someone who needs help in solving those problems. The answers are written in a very systematic manner which will help you in getting a better understanding of this chapter. Study every piece of information from the chapter to land down with robust marks from CBSE Class 8 Maths." ]
[ null ]
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https://www.circuitstoday.com/automatic-led-emergency-light-modified-version/comment-page-3
[ "As there is serious discussions going on about our previous Automatic LED Emergency Light Circuit using LM 317, Mr.Seetharaman has come up with a modified version of the same which answers many of the doubts raised in our Comments section.\n\nNote: Mr.Seetharaman has developed a new version of Automatic LED emergency light. This one is more simple,more efficient and uses minimum components. Take a look: Simple Emergency Lamp Circuit\n\nHere follows Seetharaman’s Description about the Modified Automatic LED Emergency Light using LM 317.\n\nDear John\nSince there were lots of doubts from our readers on the LED emergency light, I have written a detailed letter to two of our readers. Of course few modifications are required, which I have indicated on the drawings and on calculations how I arrived at it.  I thought of enclosing it to you so that it can be kept in some library of our site for any ones reference. For each circuit we can have a similar detailed theory, may not be with all calculation, just general operation theory of each part of the circuit. You may think of it. As a first feed back I am sending this.  I have a feeling that most of the people would have made the mistake in base emitter of BD140, the lead out are against normal convention.", null, "To understand the above circuit in a better way, it can be divided into two parts.\n\n1. LED lamp circuit\n2. The Battery charger circuit\n\n### LED Lamp circuit\n\n1. All are white hi bright LEDs rated for 3Volt @ 25mA\n2. The total current requirement is 12 X 25 = 300mA\n3. This current has to flow through T2 – BD140 PNP transistor\n4. The minimum current gain (hfe) of this transistor @ 500mA is 50\n5. Hence the base current Ib requirement is Ic / hfe, 300 / 50 = 6mA\n6. Base emitter drop of T2 at 500mA is 0.77 volt\n7. With the fully charged battery at 6.9volt terminal voltage (for cycle operation use) the voltage available across the new bias resistance is (6.9 – 0.77)\n8. Hence the bias resistance is = 6.13 / 6 = 1000ohms\n9. As the battery drains the final terminal voltage will be 5.4volt\n10. The bias resistance will be (5.4 – 0.77) /  6 = 770 ohms Hence a 680 ohms was preferred for bias resistance with drained battery also it will give enough brightness.\n11. The very important information about BD140 is, as you view the pins, metal portion of the transistor facing down left is emitter centre collector and right is base. Most of the constructors make this mistake, relying on the convention that left base and right emitter. If you have made this mistake please correct it.\n\nOnce this portion is checked for reliable operation we will proceed to charger portion.\n\nPCB’s for this project can be orders through PCBWay. We shall upload gerber files (made according to rules of PCBWay) shortly.\n\n### The Battery charger circuit\n\n1. The battery requires a full terminal voltage of 6.9V at this point charger should cut off.\n2. That is the voltage across the chain ZD1, R2 and T1 be should be 6.9 volt\n3. T1 be voltage of 0.7 volt plus drop across R2 and zener voltage should be 6.9V\n4. T1 be current = Ic / hfe\n5. Ic is 1.25 / 180 = 7mA\n6. Ibe = Ic / hfe of T1  i.e = 7 / 70 = 100uA\n7. Drop across R2  =1.2 X .1 mA = 0.12volt\n8. Hence Zener voltage = 6.9 – (0.7 + 0.12) = 6.08 the near by preferred zener voltage is 6.2 volt\n9. Say the battery voltage at full charge will be 7 volt with 6.2 volt zener diode\n10. To calculate R16 value for charging at 1 /10 th of the rated current of the battery 4.5AH / 10 = 450mAH\n11. Transformer 9volt AC the voltage across C1 will be 9 X 1.414 = 12.6 volt\n12. The drop across LM317 at 450mA current for good regulation is 3volt\n13. The drop across protective diode D5 is 0.7 volt.\n14. The  voltage available at cathode of D5 is 12.6 – (3+0.7) = 8.9volt\n15. The battery after fair discharge will be at 6 volt\n16. Hence R16 = (8.9 – 7) / 0.45 = 6 ohms\n17. The nearby standard value for operation is 5 ohms.\n18. At the end point of battery 5.4 volt the maximum charging current can be of (8.9 – 5.4) / 5 = 0.7 amps well within the higher charging limit of the battery.\n19. With this circuit over night the battery will get charged fully.\n20. Over charging is taken care and protected by T1\n\nHope with the above guide line you can make your light work successfully.\n\n## More Modification!!!\n\n### Automatic LED Emergency Light with Under Voltage Cut Off Protection:\n\nMr. Seetharaman has further modified this LED Emergency Light with an under voltage cut-off protection to protect battery from deep discharge. Once the battery terminal voltage falls below 5.7 volts the LEDs will be switched off. Take a look at the modified circuit shown below.", null, "To understand the above circuit in a better way, it can be divided into two parts.\n\n1. LED lamp circuit\n2. The Battery charger circuit\n\nLED Lamp circuit\n\n1. All are white hi bright LEDs rated for 3Volt @ 25mA\n2. The total current requirement is 12 X 25 = 300mA\n3. This current has to flow through T2 – BD140 PNP transistor\n4. The minimum current gain (hfe) of this transistor @ 500mA is 50\n5. Hence the base current Ib requirement is Ic / hfe, 300 / 50 = 6mA\n6. Base emitter drop of T2 at 500mA is 0.77 volt\n7. With the fully charged battery at 6.9volt terminal voltage (for cycle operation use) the voltage available across the new bias resistance is (6.9 – 0.77)\n8. Hence the bias resistance is = 6.13 / 6 = 1000ohms\n9. As the battery drains the final terminal voltage will be 5.4volt\n10. The bias resistance will be (5.4 – 0.77) /  6 = 770 ohms Hence a 680 ohms was preferred for bias resistance with drained battery also it will give enough brightness.\n11. The very important information about BD140 is, as you view the pins, metal portion of the transistor facing down left is emitter centre collector and right is base. Most of the constructors make this mistake, relying on the convention that left base and right emitter. If you have made this mistake please correct it.\n\nOnce this portion is checked for reliable operation we will proceed to charger portion.\n\n1. The battery requires a full terminal voltage of 6.9V at this point charger should cut off.\n2. That is the voltage across the chain ZD1, R2 and T1 be should be 6.9 volt\n3. T1 be voltage of 0.7 volt plus drop across R2 and zener voltage should be 6.9V\n4. T1 be current = Ic / hfe\n5. Ic is 1.25 / 180 = 7mA\n6. Ibe = Ic / hfe of T1  i.e = 7 / 70 = 100uA\n7. Drop across R2  =1.2 X .1 mA = 0.12volt\n8. Hence Zener voltage = 6.9 – (0.7 + 0.12) = 6.08 the near by preferred zener voltage is 6.2 volt\n9. Say the battery voltage at full charge will be 7 volt with 6.2 volt zener diode\n10. To calculate R16 value for charging at 1 /10 th of the rated current of the battery 4.5AH / 10 = 450mAH\n11. Transformer 9volt AC the voltage across C1 will be 9 X 1.414 = 12.6 volt\n12. The drop across LM317 at 450mA current for good regulation is 3volt\n13. The drop across protective diode D5 is 0.7 volt.\n14. The  voltage available at cathode of D5 is 12.6 – (3+0.7) = 8.9volt\n15. The battery after fair discharge will be at 6 volt\n16. Hence R16 = (8.9 – 7) / 0.45 = 6 ohms\n17. The nearby standard value for operation is 5 ohms.\n18. At the end point of battery 5.4 volt the maximum charging current can be of (8.9 – 5.4) / 5 = 0.7 amps well within the higher charging limit of the battery.\n19. With this circuit over night the battery will get charged fully.\n20. Over charging is taken care and protected by T1\n\nHope with the above guide line you can make your light work successfully.\n\n1. I have made the circuit as per the design. But the leds are not working automatically. It doesn’t switch off during charging. It glows even if there’s power and glows until the switch is off or the battery is low. Can you please advice me about this ? I have used the first circuit in this page.\n\n2. plz sir sent me parts details & transistor pinout (like ECB) indicate as because i am fully new. so difficult to realize your diagram. Please sir help me. Plz Plz sir waiting for ur reply.\n\n3. K.Rajeesh\n\nSir,\nGood Morning,\ngood and very simple to construct your circuit.\nFor the above circuit, can connect 3V motor pump for aquarium (Fish tank) with series of 4 diode to drop the 3V in the battery +ve side instead of LED load. If it is wrong, Please reply with good solution.\nRegards\nRajeesh.K\n\n4. Vijay Patel\n\nHi,\n\nI see 2 potential issues:\n\nBD140 being an PNP, how it will shut down the circuit at under voltage\n\n5. rupjyoti mahatta\n\ncan i use relay in place of bd 140 for high watt led (e.g ten 1w led)\n\n6. How can this diagram be converted to use a 12v battery\n\n7. Can this circuit be change to a 12v battery and please forward me the change\n\n8. Colin Mitchell\n\nThe LEDs will NEVER TURN OFF !!!!!!! The 560R and 560R form a voltage divider that keep the LEDs on all the time !!!!! Another circuit that has not been tested !!!!!" ]
[ null, "https://www.circuitstoday.com/wp-content/uploads/2010/05/Automatic-LED-Emergency-Light-Modified.jpg", null, "https://www.circuitstoday.com/wp-content/uploads/2010/05/LED-Emergency-Light-with-Under-Voltage-Cut-Off-Protection.bmp", null ]
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http://ix.cs.uoregon.edu/~ariola/cycles.html
[ "# Lambda calculus plus letrec\n\nThe paper consists of three parts.\n\n#### Part I:\n\nWe establish an isomorphism between the well-formed cyclic lambda-graphs and their syntactic representations. To define the well-formed cyclic lambda-graphs we introduce the notion of a scoped lambda-graph. The well-formed lambda-graphs are those that have associated scoped lambda-graphs. The scoped lambda-graphs are represented by terms defined over lambda calculus extended with the letrec construct. On this set of terms we define a sound and complete axiom system (the representational calculus) that equates different representations of the same scoped lambda-graph. Since a well-formed lambda-graph can have different scoped lambda-graphs associated to it, we extend the representational calculus with axioms that equate different representations of the same well-formed graph. Finally, we consider the unwinding of well-formed graphs to possibly infinite trees and give a sound and complete axiomatization of tree unwinding.\n\n#### Part II:\n\nWe add computational power to our graphs and terms by defining beta-reduction on scoped lambda-graphs and its associated notion on terms. The representational axiom system developed in the first part combined with beta-reduction constitutes our cyclic extension of lambda calculus. In contrast to current theories, which impose restrictions on where the rewriting can take place, our reduction theory is very liberal, e.g. it allows rewriting under lambda-abstractions and on cycles. As shown previously, the reduction theory is non-confluent. We thus introduce an approximate notion of confluence, which guarantees uniqueness of infinite normal forms. We show that the infinite normal form defines a congruence on the set of terms. We relate our cyclic lambda calculus to the plain lambda calculus and to the infinitary lambda calculi. We conclude by presenting a variant of our cyclic lambda calculus, which follows the tradition of the explicit substitution calculi.\n\n#### Part III:\n\nSince most implementations of non-strict functional languages rely on sharing to avoid repeating computations, we develop a variant of our cyclic lambda calculus that enforces the sharing of computations and show that the two calculi are observationally equivalent. For reasoning about strict languages we develop a call-by-value variant of the sharing calculus. We state the difference between strict and non-strict computations in terms of different garbage collection rules. We relate the call-by-value calculus to Moggi's computational lambda calculus and to Hasegawa's calculus." ]
[ null ]
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https://yslhandbags.net/best-421
[ "# Solve right triangle calculator trig\n\nTrigonometry calculator as a tool for solving right triangle To find the missing sides or angles of the right triangle, all you need to do is enter the known variables into the trigonometry calculator. You need only two given", null, "Do my homework\nFigure out mathematic question\nSolve word questions\n\n## CosSinCalc · Triangle Calculator", null, "• Get detailed step-by-step explanations\n• Decide mathematic problems\n• Get Study\n• Get mathematics help online", null, "", null, "" ]
[ null, "https://yslhandbags.net/images/19474200dc293436/lqongmakcbdejfihp-pic-boy.webp", null, "https://yslhandbags.net/images/19474200dc293436/qpacfdojimkblgnhe-paper-format.jpg", null, "https://yslhandbags.net/images/19474200dc293436/pimfhgnoqaljdcebk-phone.webp", null, "https://yslhandbags.net/images/19474200dc293436/coihlmkjdfagebnqp-phone.webp", null ]
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https://ask.csdn.net/questions/873411
[ "# 用于2D阵列的PHP组合作为Christofides算法解决方案的一部分\n\nI am creating Christofides algorithm for the Traveling Salesman Problem. In part of the algorithm I need to find nodes of a graph that are of odd degree and then calculate the lowest weight. This can be done by the Blossom algorithm, but I am choosing to do it a different way by finding the sum of the possible combinations that you have from a 2D array because I am struggling with the blossom algorithm and do not understand it.\n\nI have 2D array which stores the weights between vertices of odd degree in a graph. For example:\n\n``````\\$array = array(\n0=> array(0, 2, 20,4),\n1=> array(2,0,7,8),\n2=> array(20,2,0,12),\n3=> array(4,8,12,0)\n)\n``````\n\nso between 0 and 1 is of weight 2, if i select the vertices 0 and 1, I am then left with the weight between vertex 2 and 3 because vertex 0 and 1 has already been used. I then need to sum the weights of array and array.\n\nI am struggling with creating an algorithm that returns the combination of possible vertex pairs. For example in the array above the possible pairs are [(0,1)(2,3)],[(0,2)(1,3)],[(0,3)(1,2)]\n\n(0,0),(1,1),(2,2),(3,3) cannot be used as there is no edge weight between them. Also, the reverse of them is not needed([(1,0)(2,3)]).\n\nWith these pairs I can then calculate the sum of the weights and choose the smallest.\n\nAny help would be much appreciated.\n\n• 点赞\n• 写回答\n• 关注问题\n• 收藏\n• 复制链接分享\n• 邀请回答\n\n#### 2条回答\n\n• You can implement the requirements you lay out pretty quickly using php's array_* functions (which I'll do below), but I would be remiss to not call out that the presented solution limits you to an array of just 4 vertices specifically because of this statement:\n\nif i select the vertices 0 and 1, I am then left with the weight between vertex 2 and 3 because vertex 0 and 1 has already been used.\n\nIf you have to interact with 5 vertices, the \"remaining weight\" aspect increases in complexity since you have more than just a left over unused pair. You'll have to define the desired behavior in the case of 5+ vertices to get more assistance if you are not able to modify the code provided below which solves your case of 4.\n\n``````<?php\n\n\\$array = array(\n0=> array(0, 2, 20,4),\n1=> array(2,0,7,8),\n2=> array(20,2,0,12),\n3=> array(4,8,12,0)\n);\n\n// Use the keys as the list of vertices.\n\\$vertices = array_keys(\\$array);\n\n// Filter out nodes without weights (preserves array keys, which are used as index-relations to other nodes)\n\\$array = array_map('array_filter', \\$array);\n\n// Create a list of all valid pairs\n\\$fullPairs = array_reduce(array_map(function(\\$vert1, \\$otherVerts) use (\\$vertices) {\n// For each first vertice, create pair combinations using weighted edge and remaining vertices\nreturn array_map(function(\\$vert2) use (\\$vert1, \\$vertices) {\n// Because reverse combinations are not desired, we sort the pairings to easily identify dupes\n\\$vert = array(\\$vert1, \\$vert2);\nsort(\\$vert);\n\\$vertPair = array(\\$vert, array_values(array_diff(\\$vertices, \\$vert)));\nusort(\\$vertPair, function(\\$v1, \\$v2) { return reset(\\$v1) - reset(\\$v2); });\nreturn \\$vertPair;\n}, array_keys(\\$otherVerts));\n}, \\$vertices, \\$array), 'array_merge', array());\n\n// Unique the list using a string representation of the pairs\n\\$uniqueIndexes = array_unique(array_map('json_encode', \\$fullPairs));\n\n// Match up the indexes of the unique list against the full pair list to get the pairing structure\n\\$uniquePairs = array_intersect_key(\\$fullPairs, \\$uniqueIndexes);\n\n// Print the pairings for verification\nprint_r(array_map('json_encode', \\$uniquePairs));\n\n// Array\n// (\n// => [[0,1],[2,3]]\n// => [[0,2],[1,3]]\n// => [[0,3],[1,2]]\n// )\n``````\n点赞 评论 复制链接分享\n• You can use some for-loops when you just need a few combinations.\n\n点赞 评论 复制链接分享" ]
[ null ]
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https://www.daniweb.com/programming/software-development/threads/121664/need-help-with-a-sequential-file
[ "Hi, I need help with a Golf Stats Program I am trying to complete. It is a dat file. My averaging functions are not working. Can someone suggest what I can do to correct the problems with both averaging functions?\n\nmain\n\n#include <iostream>\nusing std::cerr;\nusing std::cout;\nusing std::cin;\nusing std::endl;\nusing std::fixed;\nusing std::ios;\nusing std::showpoint;\n\n#include <fstream> // file stream\nusing std::ifstream; // input file stream\n#include <iomanip>\nusing std::setw;\nusing std::setprecision;\n\n#include <string>\nusing std::string;\n\n#include <cstdlib>\nusing std::exit; // exit function prototype\n#include \"golfers.h\"\n\nenum RequestType{LEGAL_SCORE=1, SCORE_PAR,AVG_HAND,AVG_SCORE,AT_HANDI,WORSE_HANDI,BETTER_HANDI,ILL_VALUE, END};\n\nint main()\n{\ngolfers g;\n// ifstream constructor opens the file\nifstream inGolfersFile( \"golf.dat\" );\n\n// exit program if ifstream could not open file\nif ( !inGolfersFile )\n{\ncerr << \"File could not be opened\" << endl;\nexit( 1 );\n} // end if\n\nint request;\nint handi;\nint par;\nint score;\nint count;\n\nrequest = g.getRequest();\nwhile(request !=END)\n{\nswitch(request)\n{\ncase LEGAL_SCORE:\ncout << \"\\nThe number of legal golf scores above par: \\n\";\nbreak;\ncase SCORE_PAR:\ncout << \"\\nThe number of legal golf scores par or lower: \\n\";\nbreak;\ncase AVG_HAND:\ncout << \"\\nThe average of all handicaps for the golfers: \\n\";\ng.calcAvgHandi(handi, count);\nbreak;\ncase AVG_SCORE:\ncout << \"\\nThe average of all scores for the golfers: \\n\" ;\ng.calcAvgScore(score, count);\nbreak;\ncase AT_HANDI:\ncout << \"\\nThe number of golfers who scored at their handicap: \\n\";\nbreak;\ncase WORSE_HANDI:\ncout << \"\\nThe number of golfers who scored worse than their handicap: \\n\";\nbreak;\ncase BETTER_HANDI:\ncout << \"\\nThe number of golfers who scored better than their handicap: \\n\";\nbreak;\ncase ILL_VALUE:\ncout << \"\\nThe number of illegal values found: \\n\";\nbreak;\n\nwhile(!inGolfersFile.eof())\n//display info\nif(g.getRequest())\ng.golfInfo( handi, par, score );\ninGolfersFile >> handi >> par >> score;\n}\ninGolfersFile.clear(); // reset\ninGolfersFile.seekg(0);\nrequest=g.getRequest();\n}\nreturn 0;\n} // end of main\n.h file\nclass golfers\n{\npublic:\ngolfers(void);\nvoid golfInfo( float, int, float ); // prototype\nbool golfDisplay(int);\nint getRequest();\nfloat calcAvgHandi(int[],int);\nfloat calcAvgScore(int,int);\n\nprivate:\nint count;\nint handi;\nint par;\nint score;\nint request;\n\n};\n\nclass golfers.cpp file\n\n#include \"golfers.h\"\n#include <iostream>\nusing std::cerr;\nusing std::cin;\nusing std::cout;\nusing std::endl;\nusing std::fixed;\nusing std::ios;\nusing std::left;\nusing std::right;\nusing std::showpoint;\n\n#include <fstream> // file stream\nusing std::ifstream; // input file stream\n#include <iomanip>\nusing std::setw;\nusing std::setprecision;\n\n#include <string>\nusing std::string;\n\n#include <cstdlib>\nusing std::exit; // exit function prototype\n\nenum RequestType{LEGAL_SCORE=1, SCORE_PAR,AVG_HAND,AVG_SCORE,AT_HANDI,WORSE_HANDI,BETTER_HANDI,ILL_VALUE, END};\n\ngolfers::golfers(void)\n{\n}\n\n// display golfers information file\nvoid golfers::golfInfo( float handi, int par, float score )\n{\ncout << right << setw( 10 ) << setprecision(1) << handi << setw( 13 ) << par\n<< setw( 13 ) << setprecision( 2 ) << right << score << endl;\n} // end function golfInfo\n\nint golfers::getRequest()\n{\nint request;\n\ncout << \"\\nEnter request\" << endl\n<< \" 1 - List the number of legal golf score above par\" << endl\n<< \" 2 - List the number of legal golf score par or lower\" << endl\n<< \" 3 - Lists tha average of all handicaps for the golfers\" << endl\n<< \" 4 - Lists tha average of all scores for the golfers\" << endl\n<< \" 5 - Lists the number of golfers who scored at their handicap\" << endl\n<< \" 6 - Lists the number of golfers who scored worse than their handicap\" << endl\n<< \" 7 - Lists the number of golfers who scored better than their handicap\" << endl\n<< \" 8 - Lists the number of illegal values found\" << endl\n<< \" 9 - END\" << fixed << showpoint;\n\ndo\n{\ncout << \"\\nEnter: \";\ncin >> request;\n}\nwhile (request < LEGAL_SCORE && request > END);\nreturn request;\n} // end function get Request\n\nbool golfers::golfDisplay(int request)\n{\nif(request==LEGAL_SCORE)\nreturn true;\nif(request==SCORE_PAR)\nreturn true;\nif(request==AVG_HAND)\nreturn true;\nif(request==AVG_SCORE)\nreturn true;\nif(request==AT_HANDI)\nreturn true;\nif(request==WORSE_HANDI)\nreturn true;\nif(request==BETTER_HANDI)\nreturn true;\nif(request==ILL_VALUE)\nreturn true;\n\nreturn false;\n}\n\nfloat golfers::calcAvgHandi(int handi [], int count)\n{\nint sum=0;\ncount = 0;\nfloat average;\nfor (int i = 0; i < count; i++)\nsum = sum + handi[i];\naverage = float(sum)/count;\nreturn average;\n}\nfloat golfers::calcAvgScore(int score[],int count)\n{\nint sum=0;\ncount = 0;\nfloat average;\nfor (int i = 0; i < count; i++)\nsum = sum + score[i];\naverage = float(sum)/count;\nreturn average;\n}\n\nerrors\n\n>.\\.cpp(69) : error C2664: 'golfers::calcAvgHandi' : cannot convert parameter 1 from 'int' to 'int []'\n1> Conversion from integral type to pointer type requires reinterpret_cast, C-style cast or function-style cast\n1>.\\.cpp(91) : warning C4244: 'argument' : conversion from 'int' to 'float', possible loss of data\n1>.\\.cpp(91) : warning C4244: 'argument' : conversion from 'int' to 'float', possible loss of data\n1>Generating Code...\n1>Build log was saved at \"file://c:\\Users\\moporho\\Documents\\Visual Studio 2005\\Projects\\\\Debug\\BuildLog.htm\"\n1> - 2 error(s), 2 warning(s)\n========== Rebuild All: 0 succeeded, 1 failed, 0 skipped ==========\n\ndat file\n\n12 72 87\n11 71 81\n6 70 78\n19 70 89\n38 71 109\n35 72 110\n1 72 73\n8 72 81\n9 72 83\n5 71 76\n4 72 76\n14 71 88\n20 72 90\n22 72 97\n31 70 103\n34 72 108\n22 72 96\n23 73 96\n21 71 92\n17 72 90\n16 72 85\n15 71 85\n12 71 83\n11 70 83\n10 71 84\n9 72 81\n8 69 77\n0 72 71\n25 72 98\n24 72 96\n29 71 100\n33 66 99\n31 71 104\n1 62 60\n0 62 59\n14 72 85\n14 72 85\n14 72 83\n14 72 84\n14 72 89\n15 72 90\n15 72 91\n16 72 90\n16 72 89\n14 72 79\n14 72 78\n15 72 85\n\nThanks,\nM\n\n## All 11 Replies\n\nline 57 main.cpp: g.calcAvgHandi(handi, count);\nhandi is an int, not an array. Similar problems with the other lines.\n\nHelp! This is my last project in C++ and I am so lost!!\n\nMy data is not being read and all my functions are not computing correctly. Oh heck, my functions are a total mess.\n\nPlease someone have a look and help me get this thing working correctly.\n\n11\t#include <iostream>\n12\t#include <iomanip>\n13\tusing std::setw;\n14\tusing std::setprecision;\n16\t#include <cstdlib>\n17\n18\t//assert contains routines that allow the programmer to make\n19\t//assertions that must be true for program execution to continue\n20\t#include <cassert>\n21\n22\tusing namespace std;\n23\n24\tconst int MAX_GOLFERS = 47; //1 student's scores are stored in a row\n25\tconst int STATS = 3; //Each row has this many columns (scores)\n26\n27\n28\tvoid seeStats(int table[][STATS],\n29\t int &number_of_golfers,\n30\t int &handicaps,\n31\t\t\t int &par,\n32\t\t\t int &scores); //read data into a table\n33\n34\tvoid print_a_row(int row[], int columns_to_print);\n35\n36\n37\tvoid PrintStats(int table[][STATS],\n38\n39\n40\n41\tint scoresAbovePar(const int STATS, int handicaps, int scores, int par, int count);\n42\tint scoresAtOrPar(const int STATS, int handicaps, int scores, int par, int count);\n43\tfloat avgHand(const int STATS[], int handicaps, int count);\n44\tfloat avgScore(int table[], int scores, int count);\n45\tint scoreAtHand(const int STATS, int handicaps, int scores, int par, int count);\n46\tint scoreWorse(const int STATS, int handicaps, int scores, int par, int count);\n47\tint scoreBetter(const int STATS, int handicaps, int scores, int par, int count);\n48\tint illValue(const int STATS, int handicaps, int scores, int par, int count);\n49\n50\tint main(void)\n51\t{\n52\t int table[MAX_GOLFERS][STATS]; // stats table\n53\t int number_of_golfers,\n54\t handicaps,\n55\t\t\tpar,\n56\t\t\tscores;\n57\t\tint rows_to_print=47;\n58\t\tint columns_to_print=3;\n59\n61\t seeStats(table, number_of_golfers, handicaps, par, scores);\n62\t cout << \"Golfer's Stats: \\n\\n\";\n63\n64\t\tPrintStats(table, rows_to_print,columns_to_print);\n65\t cout << \"\\nPress ENTER key to continue: \\n\";\n66\t cin.get();\n67\n68\t\tcout << \"1. - The number of legal golf scores above par is \" << scoresAbovePar << endl << endl;\n69\n70\t\tcout << \"2 - The number of legal golf scores at or below par is \" << scoresAtOrPar << endl << endl;\n71\n72\t\tcout << \"3. - The average of all handicaps for the golfers is \" << setprecision(1) << avgHand << endl << endl;\n73\n74\t\tcout << \"4. - The average of all scores for the golfers is \" << setprecision(2) << avgScore << endl << endl;\n75\n76\t\tcout << \"5. - The number of golfer who scored at their handicap is \" << scoreAtHand << endl << endl;\n77\n78\t\tcout << \"6. - The number of golfers who scored worse than their handicap is \" << scoreWorse << endl << endl;\n79\n80\t\tcout << \"7. - The number of golfers who scored better than their handicap is \" << scoreBetter << endl << endl;\n81\n82\t\tcout << \"8. - The number of illegal values found is \" << illValue << endl << endl;\n83\n84\n85\n86\t return 0;\n87\t} // end of main\n88\n89\n90\t// function seeStats\n91\tvoid seeStats(int table[][STATS],\n92\t int &number_of_golfers,\n93\t int &handicaps,\n94\t\t\t\t int &par,\n95\t\t\t\t int &scores)\n96\t{\n97\t //Open external data file for reading\n98\t ifstream infile(\"golf.dat\");\n99\t if (!infile.is_open()) {\n100\t cerr << \"File could not be opened\" << endl;\n101\t exit(1); // function in cstdlib\n102\t }\n103\t // read data into table\n104\t int row=0;\n105\t int column=0;\n106\n107\t while (infile >> table[row][column]) {\n108\t if (infile.peek() != '\\n') {\n109\t column++; //more scores exist on line, advance column\n110\t }\n111\t else { //end of line detected...\n112\t handicaps = column + 1; // set actual number of columns\n113\t column = 0; //start at beginning of next row\n114\t row++;\n115\t }\n116\t } // end of while\n117\t number_of_golfers = row; // set actual number of rows\n118\t} // end of seeStats\n119\n120\t//print one row of the table.\n121\tvoid print_a_row(int row[], int columns_to_print)\n122\t{\n123\t for (int j = 0; j < columns_to_print; j++)\n124\t cout << setw(4) << row[j];\n125\t}\n126\n127\t//function PrintStats\n128\tvoid PrintStats(int table[][STATS],\n129\t int rows_to_print,\n130\t int columns_to_print)\n131\t{\n132\t for (int i = 0; i < rows_to_print; i++) {\n133\t print_a_row(table[i], columns_to_print);\n134\t cout << endl;\n135\t }\n136\t} // end of PrintStats\n137\n138\tint scoresAbovePar(const int STATS, int handicaps, int scores, int par, int count)\n139\t{\n140\t\tint i;\n141\t\ti = scores - handicaps;\n142\t\ti = i- par;\n143\n144\t\tif (i >= handicaps)\n145\t\t\tcount++;\n146\n147\treturn count;\n148\t}\n149\tint scoresAtOrPar(const int STATS, int handicaps, int scores, int par, int count)\n150\t{\n151\t\tint i;\n152\t\ti = scores - handicaps;\n153\t\ti = i- par;\n154\n155\t\tif (i <= handicaps)\n156\t\t\tcount++;\n157\n158\treturn count;\n159\t}\n160\n161\tfloat avgHand(const int STATS, int handicaps, int count)\n162\t{\n163\t\tint sum=0;\n164\t\tfloat avg;\n165\n166\t\tfor(int i=0; i < count; i++)\n167\t\t\tsum = sum + STATS[i];\n168\t\tavg = float(sum)/count;\n169\n170\t\treturn avg;\n171\t\t} // end avgHand\n172\n173\tfloat avgScore(int table[], int scores, int count)\n174\t{\n175\t\tint sum=0;\n176\t\tfloat avg;\n177\n178\t\tfor(int i=0; i < count; i++)\n179\t\t\tsum=sum+table[i];\n180\t\tavg = float(sum)/count;\n181\n182\t\treturn avg;\t// end avgScore\n183\t}\n184\n185\tint scoreAtHand(const int STATS, int handicaps, int scores, int par, int count)\n186\t{\n187\n188\t\tif (scores == scores-handicaps)\n189\t\t\tcount ++;\n190\t\treturn count;\n191\t}\n192\tint scoreWorse(const int STATS, int handicaps, int scores, int par, int count)\n193\t{\n194\n195\t\tif (scores < scores-handicaps)\n196\t\t\tcount ++;\n197\t\treturn count;\n198\t}\n199\tint scoreBetter(const int STATS, int handicaps, int scores, int par, int count)\n200\t{\n201\n202\t\tif (scores > scores-handicaps)\n203\t\t\tcount ++;\n204\t\treturn count;\n205\t}\n206\n207\tint illValue(const int STATS, int handicaps, int scores, int par, int count)\n208\t{\n209\t\tif (handicaps < 0 || handicaps > 36 || par < 62 || par >72 || scores < 60 || scores > 120)\n210\n211\t\t\tcount++;\n212\n213\t\treturn count;\n214\t}\n\nthe data file is above.\n\nhere is the output I am getting\n\nGolfer's Stats:\n\n12 72 87\n11 71 81\n6 70 78\n19 70 89\n38 71 109\n35 72 110\n1 72 73\n8 72 81\n9 72 83\n5 71 76\n4 72 76\n14 71 88\n20 72 90\n22 72 97\n31 70 103\n34 72 108\n22 72 96\n23 73 96\n21 71 92\n17 72 90\n16 72 85\n15 71 85\n12 71 83\n11 70 83\n10 71 84\n9 72 81\n8 69 77\n0 72 71\n25 72 98\n24 72 96\n29 71 100\n33 66 99\n31 71 104\n1 62 60\n0 62 59\n14 72 85\n14 72 85\n14 72 83\n14 72 84\n14 72 89\n15 72 90\n15 72 91\n16 72 90\n16 72 89\n14 72 79\n14 72 78\n15 72 85\n\nPress ENTER key to continue:\n\n1. - The number of legal golf scores above par is 004111B8\n\n2 - The number of legal golf scores at or below par is 00411145\n\n3. - The average of all handicaps for the golfers is 004110DC\n\n4. - The average of all scores for the golfers is 004111C2\n\n5. - The number of golfer who scored at their handicap is 004111BD\n\n6. - The number of golfers who scored worse than their handicap is 00411046\n\n7. - The number of golfers who scored better than their handicap is 004111D6\n\n8. - The number of illegal values found is 004110EB\n\nPress any key to continue . . .\n\nThank you,\nM~\n\nPlease don't manually add line numbers because compilers don't like them. The code tags will insert line numbers for you. Please repost code without manual line numbers\n\n[code=cplusplus] // put your code here\n\n[/code]\n\nSorry, now that I know I will not ever do that again. I am sorry.\n\n#include <iostream>\n#include <iomanip>\nusing std::setw;\nusing std::setprecision;\n#include <cstdlib>\n\n//assert contains routines that allow the programmer to make\n//assertions that must be true for program execution to continue\n#include <cassert>\n\nusing namespace std;\n\nconst int MAX_GOLFERS = 47; //1 student's scores are stored in a row\nconst int STATS = 3; //Each row has this many columns (scores)\n\nvoid seeStats(int table[][STATS],\nint &number_of_golfers,\nint &handicaps,\nint &par,\nint &scores); //read data into a table\n\nvoid print_a_row(int row[], int columns_to_print);\n\nvoid PrintStats(int table[][STATS],\nint rows_to_print,\nint columns_to_print); // print golfers' stats in a table\n\nint scoresAbovePar(const int STATS, int handicaps, int scores, int par, int count);\nint scoresAtOrPar(const int STATS, int handicaps, int scores, int par, int count);\nfloat avgHand(const int STATS[], int handicaps, int count);\nfloat avgScore(int table[], int scores, int count);\nint scoreAtHand(const int STATS, int handicaps, int scores, int par, int count);\nint scoreWorse(const int STATS, int handicaps, int scores, int par, int count);\nint scoreBetter(const int STATS, int handicaps, int scores, int par, int count);\nint illValue(const int STATS, int handicaps, int scores, int par, int count);\n\nint main(void)\n{\nint table[MAX_GOLFERS][STATS]; // stats table\nint number_of_golfers,\nhandicaps,\npar,\nscores;\nint rows_to_print=47;\nint columns_to_print=3;\n\nseeStats(table, number_of_golfers, handicaps, par, scores);\ncout << \"Golfer's Stats: \\n\\n\";\n\nPrintStats(table, rows_to_print,columns_to_print);\ncout << \"\\nPress ENTER key to continue: \\n\";\ncin.get();\n\ncout << \"1. - The number of legal golf scores above par is \" << scoresAbovePar << endl << endl;\n\ncout << \"2 - The number of legal golf scores at or below par is \" << scoresAtOrPar << endl << endl;\n\ncout << \"3. - The average of all handicaps for the golfers is \" << setprecision(1) << avgHand << endl << endl;\n\ncout << \"4. - The average of all scores for the golfers is \" << setprecision(2) << avgScore << endl << endl;\n\ncout << \"5. - The number of golfer who scored at their handicap is \" << scoreAtHand << endl << endl;\n\ncout << \"6. - The number of golfers who scored worse than their handicap is \" << scoreWorse << endl << endl;\n\ncout << \"7. - The number of golfers who scored better than their handicap is \" << scoreBetter << endl << endl;\n\ncout << \"8. - The number of illegal values found is \" << illValue << endl << endl;\n\nreturn 0;\n} // end of main\n\n// function seeStats\nvoid seeStats(int table[][STATS],\nint &number_of_golfers,\nint &handicaps,\nint &par,\nint &scores)\n{\n//Open external data file for reading\nifstream infile(\"golf.dat\");\nif (!infile.is_open()) {\ncerr << \"File could not be opened\" << endl;\nexit(1); // function in cstdlib\n}\nint row=0;\nint column=0;\n\nwhile (infile >> table[row][column]) {\nif (infile.peek() != '\\n') {\ncolumn++; //more scores exist on line, advance column\n}\nelse { //end of line detected...\nhandicaps = column + 1; // set actual number of columns\ncolumn = 0; //start at beginning of next row\nrow++;\n}\n} // end of while\nnumber_of_golfers = row; // set actual number of rows\n} // end of seeStats\n\n//print one row of the table.\nvoid print_a_row(int row[], int columns_to_print)\n{\nfor (int j = 0; j < columns_to_print; j++)\ncout << setw(4) << row[j];\n}\n\n//function PrintStats\nvoid PrintStats(int table[][STATS],\nint rows_to_print,\nint columns_to_print)\n{\nfor (int i = 0; i < rows_to_print; i++) {\nprint_a_row(table[i], columns_to_print);\ncout << endl;\n}\n} // end of PrintStats\n\nint scoresAbovePar(const int STATS, int handicaps, int scores, int par, int count)\n{\nint i;\ni = scores - handicaps;\ni = i- par;\n\nif (i >= handicaps)\ncount++;\n\nreturn count;\n}\nint scoresAtOrPar(const int STATS, int handicaps, int scores, int par, int count)\n{\nint i;\ni = scores - handicaps;\ni = i- par;\n\nif (i <= handicaps)\ncount++;\n\nreturn count;\n}\n\nfloat avgHand(const int STATS, int handicaps, int count)\n{\nint sum=0;\nfloat avg;\n\nfor(int i=0; i < count; i++)\nsum = sum + STATS[i];\navg = float(sum)/count;\n\nreturn avg;\n} // end avgHand\n\nfloat avgScore(int table[], int scores, int count)\n{\nint sum=0;\nfloat avg;\n\nfor(int i=0; i < count; i++)\nsum=sum+table[i];\navg = float(sum)/count;\n\nreturn avg;\t// end avgScore\n}\n\nint scoreAtHand(const int STATS, int handicaps, int scores, int par, int count)\n{\n\nif (scores == scores-handicaps)\ncount ++;\nreturn count;\n}\nint scoreWorse(const int STATS, int handicaps, int scores, int par, int count)\n{\n\nif (scores < scores-handicaps)\ncount ++;\nreturn count;\n}\nint scoreBetter(const int STATS, int handicaps, int scores, int par, int count)\n{\n\nif (scores > scores-handicaps)\ncount ++;\nreturn count;\n}\n\nint illValue(const int STATS, int handicaps, int scores, int par, int count)\n{\nif (handicaps < 0 || handicaps > 36 || par < 62 || par >72 || scores < 60 || scores > 120)\n\ncount++;\n\nreturn count;\n}\n\nM~\n\ncout << \"1. - The number of legal golf scores above par is \" << scoresAbovePar << endl << endl;\n\ncout << \"2 - The number of legal golf scores at or below par is \" << scoresAtOrPar << endl << endl;\n\ncout << \"3. - The average of all handicaps for the golfers is \" << setprecision(1) << avgHand << endl << endl;\n\ncout << \"4. - The average of all scores for the golfers is \" << setprecision(2) << avgScore << endl << endl;\n\ncout << \"5. - The number of golfer who scored at their handicap is \" << scoreAtHand << endl << endl;\n\ncout << \"6. - The number of golfers who scored worse than their handicap is \" << scoreWorse << endl << endl;\n\ncout << \"7. - The number of golfers who scored better than their handicap is \" << scoreBetter << endl << endl;\n\ncout << \"8. - The number of illegal values found is \" << illValue << endl << endl;\n\nscoresAbovePar is a function, not a data element. All you are doing in the lines posted above is printing the address of those functions. You have to call them just as any other function.\n\nI am sorry, I am not clear. How would a call to the function look? I am muttled up.\n\nLike this: cout << \"1. - The number of legal golf scores above par is \" << scoresAbovePar( <parameter list here> ) << endl << endl;\n\nI can not get the functions to produce the correct data. Can someone make suggestions?\n\n#include \"stdafx.h\"\n#include <iostream>\n#include <iomanip>\nusing std::setw;\nusing std::setprecision;\n#include <fstream>\n#include <cstdlib>\n\n#include <cassert>\n\nusing namespace std;\n\nconst int MAX_GOLFERS = 47;\nconst int STATS = 3;\n\nvoid seeStats(int table[][STATS],\nint &number_of_golfers,\nint &handicaps,\nint &par,\nint &scores); //read data into a table\n\nvoid print_a_row(int row[], int columns_to_print);\n\nvoid PrintStats(int table[][STATS],\nint rows_to_print,\nint columns_to_print); // print golfers' stats in a table\n\nint scoresAbovePar(const int table[STATS], int handicaps,int par, int scores,int count);\nint scoresAtOrPar(const int table[STATS], int handicaps, int scores, int par, int count);\nfloat avgHand(const int table[STATS], int handicaps, int count);\nfloat avgScore(const int table[STATS], int scores, int count);\nint scoreAtHand(const int table[STATS], int handicaps, int scores, int par, int count);\nint scoreWorse(const int table[STATS], int handicaps, int scores, int par, int count);\nint scoreBetter(const int table[STATS], int handicaps, int scores, int par, int count);\nint illValue(const int table[STATS], int handicaps, int scores, int par, int count);\n\nint main(void)\n{\nint table[MAX_GOLFERS][STATS]; // stats table\nint number_of_golfers,\nhandicaps,\npar,\nscores;\nint rows_to_print=47;\nint columns_to_print=3;\nint count=0;\n\nseeStats(table, number_of_golfers, handicaps, par, scores);\ncout << \"Golfer's Stats: \\n\\n\";\n\nPrintStats(table, rows_to_print,columns_to_print);\ncout << \"\\nPress ENTER key to continue: \\n\";\ncin.get();\n\ncout << \"1. - The number of legal golf scores above par is \" << scoresAbovePar(table[STATS], handicaps,par, scores,count) << endl << endl;\n\ncout << \"2 - The number of legal golf scores at or below par is \" << scoresAtOrPar(table[STATS], handicaps, scores, par, count) << endl << endl;\n\ncout << \"3. - The average of all handicaps for the golfers is \" << setprecision(1) << avgHand(table[STATS], handicaps, count) << endl << endl;\n\ncout << \"4. - The average of all scores for the golfers is \" << setprecision(2) << avgScore(table[STATS], scores, count) << endl << endl;\n\ncout << \"5. - The number of golfer who scored at their handicap is \" << scoreAtHand(table[STATS], handicaps, scores, par, count) << endl << endl;\n\ncout << \"6. - The number of golfers who scored worse than their handicap is \" << scoreWorse(table[STATS], handicaps, scores, par, count) << endl << endl;\n\ncout << \"7. - The number of golfers who scored better than their handicap is \" << scoreBetter(table[STATS], handicaps, scores, par, count) << endl << endl;\n\ncout << \"8. - The number of illegal values found is \" << illValue(table[STATS], handicaps, scores, par, count) << endl << endl;\n\nreturn 0;\n} // end of main\n\n// function seeStats\nvoid seeStats(int table[][STATS],\nint &number_of_golfers,\nint &handicaps,\nint &par,\nint &scores)\n{\n//Open external data file for reading\nifstream infile(\"golf.dat\");\nif (!infile.is_open()) {\ncerr << \"File could not be opened\" << endl;\nexit(1); // function in cstdlib\n}\nint row=0;\nint column=0;\n\nwhile (infile >> table[row][column]) {\nif (infile.peek() != '\\n') {\ncolumn++; //more scores exist on line, advance column\n}\nelse { //end of line detected...\nhandicaps = column + 1; // set actual number of columns\ncolumn = 0; //start at beginning of next row\nrow++;\n}\n} // end of while\nnumber_of_golfers = row; // set actual number of rows\n} // end of seeStats\n\n//print one row of the table.\nvoid print_a_row(int row[], int columns_to_print)\n{\nfor (int j = 0; j < columns_to_print; j++)\ncout << setw(4) << row[j];\n}\n\n//function PrintStats\nvoid PrintStats(int table[][STATS],\nint rows_to_print,\nint columns_to_print)\n{\nfor (int i = 0; i < rows_to_print; i++) {\nprint_a_row(table[i], columns_to_print);\ncout << endl;\n}\n} // end of PrintStats\n\nint scoresAbovePar(const int table[STATS], int handicaps,int par, int scores,int count)\n{\nint i;\ni = scores - handicaps;\ni = i- par;\n\nif (i >= handicaps)\ncount++;\n\nreturn count;\n}\nint scoresAtOrPar(const int table[STATS], int handicaps, int scores, int par, int count)\n{\nint i;\ni = scores - handicaps;\ni = i- par;\n\nif (i <= handicaps)\ncount++;\n\nreturn count;\n}\n\nfloat avgHand(const int table[STATS], int handicaps, int count)\n{\nint sum=0;\nfloat avg;\n\nfor(int i=0; i < count; i++)\nsum = sum + table[i];\navg = float(sum)/count;\n\nreturn avg;\n} // end avgHand\n\nfloat avgScore(const int table[STATS], int scores, int count)\n{\nint sum=0;\nfloat avg;\n\nfor(int i=0; i < count; i++)\nsum=sum+table[i];\navg = float(sum)/count;\n\nreturn avg; // end avgScore\n}\n\nint scoreAtHand(const int table[STATS], int handicaps, int scores, int par, int count)\n{\n\nif (scores == scores-handicaps)\ncount ++;\nreturn count;\n}\nint scoreWorse(const int table[STATS], int handicaps, int scores, int par, int count)\n{\n\nif (scores < scores-handicaps)\ncount ++;\nreturn count;\n}\nint scoreBetter(const int table[STATS], int handicaps, int scores, int par, int count)\n{\n\nif (scores > scores-handicaps)\ncount ++;\nreturn count;\n}\n\nint illValue(const int table[STATS], int handicaps, int scores, int par, int count)\n{\nif (handicaps < 0 || handicaps > 36 || par < 62 || par >72 || scores < 60 || scores > 120)\n\ncount++;\n\nreturn count;\n}\n\nline 59: scoresAbovePar(table[STATS], handicaps,par, scores,count)\n\nThe first parameter is incorrect. Here's the correction:\nscoresAbovePar(table, handicaps,par, scores,count)\n\nI can not get it to run. it states\n\n1>c:\\users\\moporho\\documents\\visual studio 2005\\projects\\rho_11_cpp\\rho_11_cpp\\rho_11_cpp.cpp(69) : error C2664: 'scoresAbovePar' : cannot convert parameter 1 from 'int ' to 'const int []'\n\nLook at line 42: what do you see there? table is a two dimensional array.\nNow look at line 31: the first parameter is a single dimensional array, not 2 dimension.\n\nYou will have to correct that inconsistency. I don't know which way you want it, but you can't have it both ways.\n\nBe a part of the DaniWeb community\n\nWe're a friendly, industry-focused community of developers, IT pros, digital marketers, and technology enthusiasts meeting, networking, learning, and sharing knowledge." ]
[ null ]
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https://www.khstats.com/blog/sl/superlearning.html
[ "true\n\n# Become a Superlearner! An Illustrated Guide to Superlearning\n\nR\nstatistics\nAuthor\n\nKatherine Hoffman\n\nPublished\n\nOctober 10, 2020\n\nWhy use one machine learning algorithm when you could use all of them?! This post contains a step-by-step walkthrough of how to build a superlearner prediction algorithm in R.\n\nOctober 10, 2020.\n\nHTML Image as link", null, "# Supercuts of superlearning\n\n• Superlearning is a technique for prediction that involves combining many individual statistical algorithms (commonly called “data-adaptive” or “machine learning” algorithms) to create a new, single prediction algorithm that is expected to perform at least as well as any of the individual algorithms.\n• The superlearner algorithm “decides” how to combine, or weight, the individual algorithms based upon how well each one minimizes a specified loss function, for example, the mean squared error (MSE). This is done using cross-validation to avoid overfitting.\n• The motivation for this type of “ensembling” is that a mix of multiple algorithms may be more optimal for a given data set than any single algorithm. For example, a tree based model averaged with a linear model (e.g. random forests and LASSO) could smooth some of the model’s edges to improve predictive performance.\n• Superlearning is also called stacking, stacked generalizations, and weighted ensembling by different specializations within the realms of statistics and data science.", null, "# Superlearning, step by step\n\nFirst I’ll go through the algorithm one step at a time using a simulated data set.\n\n## Initial set-up: Load libraries, set seed, simulate data\n\nFor simplicity I’ll show the concept of superlearning using only four variables (AKA features or predictors) to predict a continuous outcome. Let’s first simulate a continuous outcome, y, and four potential predictors, x1, x2, x3, and x4.\n\nlibrary(tidyverse)\nlibrary(gt)\nset.seed(7)\nn <- 5000\nobs <- tibble(\nid = 1:n,\nx1 = rnorm(n),\nx2 = rbinom(n, 1, plogis(10*x1)),\nx3 = rbinom(n, 1, plogis(x1*x2 + .5*x2)),\nx4 = rnorm(n, mean=x1*x2, sd=.5*x3),\ny = x1 + x2 + x2*x3 + sin(x4)\n)\nfmt_number(everything(),decimals=3)\nSimulated data set\nid x1 x2 x3 x4 y\n1.000 2.287 1.000 1.000 1.385 5.270\n2.000 −1.197 0.000 0.000 0.000 −1.197\n3.000 −0.694 0.000 0.000 0.000 −0.694\n4.000 −0.412 0.000 1.000 −0.541 −0.928\n5.000 −0.971 0.000 0.000 0.000 −0.971\n6.000 −0.947 0.000 1.000 −0.160 −1.107\n\n## Step 1: Split data into K folds", null, "The superlearner algorithm relies on K-fold cross-validation (CV) to avoid overfitting. We will start this process by splitting the data into 10 folds. The easiest way to do this is by creating indices for each CV fold.\n\nk <- 10 # 10 fold cv\ncv_index <- sample(rep(1:k, each = n/k)) # create indices for each CV fold. We need each fold K to contain n (all the rows of our data set) divided by k rows. in our example this is 5000/10 = 500 rows in each fold\n\n## Step 2: Fit base learners for first CV-fold", null, "Recall that in K-fold CV, each fold serves as the validation set one time. In this first round of CV, we will train all of our base learners on all the CV folds (k = 1,2,…,9) except for the very last one: cv_index == 10.\n\nThe individual algorithms or base learners that we’ll use here are three linear regressions with differently specified parameters:\n\n1. Learner A: $$Y=\\beta_0 + \\beta_1 X_2 + \\beta_2 X_4 + \\epsilon$$\n\n2. Learner B: $$Y=\\beta_0 + \\beta_1 X_1 + \\beta_2 X_2 + \\beta_3 X_1 X_3 + \\beta_4 sin(X_4) + \\epsilon$$\n\n3. Learner C: $$Y=\\beta_0 + \\beta_1 X_1 + \\beta_2 X_2 + \\beta_3 X_3 + \\beta_4 X_1 X_2 + \\beta_5 X_1 X_3 + \\beta_6 X_2 X_3 + \\beta_7 X_1 X_2 X_3 + \\epsilon$$\n\ncv_train_1 <- obs[-which(cv_index == 10),] # make a data set that contains all observations except those in k=1\nfit_1a <- glm(y ~ x2 + x4, data=cv_train_1) # fit the first linear regression on that training data\nfit_1b <- glm(y ~ x1 + x2 + x1*x3 + sin(x4), data=cv_train_1) # second LR fit on the training data\nfit_1c <- glm(y ~ x1*x2*x3, data=cv_train_1) # and the third LR\n\nI am only using the linear regressions so that code for running more complicated regressions does not take away from understanding the general superlearning algorithm.\n\nSuperlearning actually works best if you use a diverse set, or superlearner library, of base learners. For example, instead of three linear regressions, we could use a least absolute shrinkage estimator (LASSO), random forest, and multivariate adaptive splines (MARS). Any parametric or non-parametric supervised machine learning algorithm can be included as a base learner.\n\n## Step 3: Obtain predictions for first CV-fold", null, "We can then get use our validation data, cv_index == 10, to obtain our first set of cross-validated predictions.\n\ncv_valid_1 <- obs[which(cv_index == 10),] # make a data set that only contains observations except in k=10\npred_1a <- predict(fit_1a, newdata = cv_valid_1) # use that data set as the validation for all the models in the SL library\npred_1b <- predict(fit_1b, newdata = cv_valid_1)\npred_1c <- predict(fit_1c, newdata = cv_valid_1)\n\nSince we have 5000 observations, that gives us three vectors of length 500: a set of predictions for each of our Learners A, B, and C.\n\nlength(pred_1a) # double check we only have n/k predictions ...we do :-)\n 500\nhead(cbind(pred_1a, pred_1b, pred_1c)) %>%\nas.data.frame() %>% gt() %>%\nfmt_number(everything(), decimals = 2) %>%\ntab_header(\"First CV round of predictions\") \nFirst CV round of predictions\npred_1a pred_1b pred_1c\n−0.77 −0.81 −0.69\n2.54 1.89 1.63\n0.19 0.60 −0.32\n2.46 2.69 2.98\n3.63 4.04 3.73\n3.59 3.23 3.15\n\n## Step 4: Obtain CV predictions for entire data set", null, "We’ll want to get those predictions for every fold. So, using your favorite for loop, apply statement, or mapping function, fit the base learners and obtain predictions for each of them, so that there are 1000 predictions – one for every point in observations.\n\nThe way I chose to code this was to make a generic function that combines Step 2 (base learners fit to the training data) and Step 3 (predictions on the validation data), then use map_dfr() from the purrr package to repeat over all 10 CV folds. I saved the results in a new data frame called cv_preds.\n\ncv_folds <- as.list(1:k)\nnames(cv_folds) <- paste0(\"fold\",1:k)\n\nget_preds <- function(fold){ # function that does the same procedure as step 2 and 3 for any CV fold\ncv_train <- obs[-which(cv_index == fold),] # make a training data set that contains all data except fold k\nfit_a <- glm(y ~ x2 + x4, data=cv_train) # fit all the base learners to that data\nfit_b <- glm(y ~ x1 + x2 + x1*x3 + sin(x4), data=cv_train)\nfit_c <- glm(y ~ x1*x2*x3, data=cv_train)\ncv_valid <- obs[which(cv_index == fold),] # make a validation data set that only contains data from fold k\npred_a <- predict(fit_a, newdata = cv_valid) # obtain predictions from all the base learners for that validation data\npred_b <- predict(fit_b, newdata = cv_valid)\npred_c <- predict(fit_c, newdata = cv_valid)\nreturn(data.frame(\"obs_id\" = cv_valid$id, \"cv_fold\" = fold, pred_a, pred_b, pred_c)) # save the predictions and the ids of the observations in a data frame } cv_preds <- purrr::map_dfr(cv_folds, ~get_preds(fold = .x)) # map_dfr loops through every fold (1:k) and binds the rows of the listed results together cv_preds %>% arrange(obs_id) %>% head() %>% as.data.frame() %>% gt() %>% fmt_number(cv_fold:pred_c, decimals=2) %>% tab_header(\"All CV predictions for all three base learners\") All CV predictions for all three base learners obs_id cv_fold pred_a pred_b pred_c 1 7.00 3.74 5.42 5.28 2 6.00 −0.77 −1.19 −1.20 3 10.00 −0.77 −0.81 −0.69 4 8.00 −1.39 −0.77 −0.41 5 2.00 −0.78 −1.02 −0.97 6 9.00 −0.96 −1.04 −0.94 ## Step 5: Choose and compute loss function of interest via metalearner", null, "This is the key step of the superlearner algorithm: we will use a new learner, a metalearner, to take information from all of the base learners and create that new algorithm. Now that we have cross-validated predictions for every observation in the data set, we want to merge those CV predictions back into our main data set… obs_preds <- full_join(obs, cv_preds, by=c(\"id\" = \"obs_id\")) …so that we can minimize a final loss function of interest between the true outcome and each CV prediction. This is how we’re going to optimize our overall prediction algorithm: we want to make sure we’re “losing the least” in the way we combine our base learners’ predictions to ultimately make final predictions. We can do this efficiently by choosing a new learner, a metalearner, which reflects the final loss function of interest. For simplicity, we’ll use another linear regression as our metalearner. Using a linear regression as a metalearner will minimize the Cross-Validated Mean Squared Error (CV-MSE) when combining the base learner predictions. Note that we could use a variety of parametric or non-parametric regressions to minimize the CV-MSE. No matter what metalearner we choose, the predictors will always be the cross-validated predictions from each base learner, and the outcome will always be the true outcome, y. sl_fit <- glm(y ~ pred_a + pred_b + pred_c, data = obs_preds) broom::tidy(sl_fit) %>% gt() %>% fmt_number(estimate:p.value, decimals=2) %>% tab_header(\"Metalearner regression coefficients\") Metalearner regression coefficients term estimate std.error statistic p.value (Intercept) 0.00 0.00 −1.42 0.16 pred_a −0.02 0.00 −4.75 0.00 pred_b 0.85 0.01 128.15 0.00 pred_c 0.17 0.01 30.07 0.00 This metalearner provides us with the coefficients, or weights, to apply to each of the base learners. In other words, if we have a set of predictions from Learner A, B, and C, we can obtain our best possible predictions by starting with an intercept of -0.003, then adding -0.017 $$\\times$$ predictions from Learner A, 0.854 $$\\times$$ predictions from Learner B, and 0.165 $$\\times$$ predictions from Learner C. For more information on the metalearning step, check out the Appendix. ## Step 6: Fit base learners on entire data set", null, "After we fit the metalearner, we officially have our superlearner algorithm, so it’s time to input data and obtain predictions! To implement the algorithm and obtain final predictions, we first need to fit the base learners on the full data set. fit_a <- glm(y ~ x2 + x4, data=obs) fit_b <- glm(y ~ x1 + x2 + x1*x3 + sin(x4), data=obs) fit_c <- glm(y ~ x1*x2*x3, data=obs) ## Step 7: Obtain predictions from each base learner on entire data set", null, "We’ll use those base learner fits to get predictions from each of the base learners for the entire data set, and then we will plug those predictions into the metalearner fit. Remember, we were previously using cross-validated predictions, rather than fitting the base learners on the whole data set. This was to avoid overfitting. pred_a <- predict(fit_a) pred_b <- predict(fit_b) pred_c <- predict(fit_c) full_data_preds <- tibble(pred_a, pred_b, pred_c) ## Step 8: Use metalearner fit to weight base learners", null, "Once we have the predictions from the full data set, we can input them to the metalearner, where the output will be a final prediction for y. sl_predictions <- predict(sl_fit, newdata = full_data_preds) data.frame(sl_predictions = head(sl_predictions)) %>% gt() %>% fmt_number(sl_predictions, decimals=2) %>% tab_header(\"Final SL predictions (manual)\") Final SL predictions (manual) sl_predictions 5.44 −1.20 −0.79 −0.71 −1.02 −1.03 And… that’s it! Those are our superlearner predictions for the full data set. ## Step 9: Obtain predictions on new data We can now modify Step 7 and Step 8 to accommodate any new observation(s): To predict on new data: 1. Use the fits from each base learner to obtain base learner predictions for the new observation(s). 2. Plug those base learner predictions into the metalearner fit. We can generate a single new_observation to see how this would work in practice. new_obs <- tibble(x1 = .5, x2 = 0, x3 = 0, x4 = -3) new_pred_a <- predict(fit_a, new_obs) new_pred_b <- predict(fit_b, new_obs) new_pred_c <- predict(fit_c, new_obs) new_pred_df <- tibble(\"pred_a\" = new_pred_a, \"pred_b\" = new_pred_b, \"pred_c\" = new_pred_c) predict(sl_fit, newdata = new_pred_df) 1 0.1183103 Our superlearner model predicts that an observation with predictors $$X_1=.5$$, $$X_2=0$$, $$X_3=0$$, and $$X_4=-3$$ will have an outcome of $$Y=0.118$$. ## Step 10 and beyond… We could compute the MSE of the ensemble superlearner predictions. sl_mse <- mean((obs$y - sl_predictions)^2)\nsl_mse\n 0.01927392\n\nWe could also add more algorithms to our base learner library (we definitely should, since we only used linear regressions!), and we could write functions to tune these algorithms’ hyperparameters over various grids. For example, if we were to include random forest in our library, we may want to tune over a number of trees and maximum bucket sizes.\n\nWe can then cross-validate this entire process to evaluate the predictive performance of our superlearner algorithm. Alternatively, we could leave a hold-out training data set to evaluate the performance.\n\n# Using the SuperLearner package\n\nOr… we could use a package and avoid all the hand-coding. Here is how you would build an ensemble superlearner for our data with the base learner libraries of ranger (random forests), glmnet (LASSO, by default), and earth (MARS) using the SuperLearner package in R:\n\nlibrary(SuperLearner)\nx_df <- obs %>% select(x1:x4) %>% as.data.frame()\nsl_fit <- SuperLearner(Y = obs$y, X = x_df, family = gaussian(), SL.library = c(\"SL.ranger\", \"SL.glmnet\", \"SL.earth\")) You can specify the metalearner with the method argument. The default is Non-Negative Least Squares (NNLS). ## CV-Risk and Coefficient Weights We can examine the cross-validated Risk (loss function), and the Coefficient (weight) given to each of the models. sl_fit Call: SuperLearner(Y = obs$y, X = x_df, family = gaussian(), SL.library = c(\"SL.ranger\",\n\"SL.glmnet\", \"SL.earth\"))\n\nRisk Coef\nSL.ranger_All 0.013672503 0.1606329\nSL.glmnet_All 0.097257031 0.0000000\nSL.earth_All 0.003181357 0.8393671\n\nFrom this summary we can see that the CV-risk (the default risk is MSE) in this library of base learners is smallest for SL.Earth. This translates to the largest coefficient, or weight, given to the predictions from earth.\n\nThe LASSO model implemented by glmnet has the largest CV-risk, and after the metalearning step, those predictions receive a coefficient, or weight, of 0. This means that the predictions from LASSO will not be incorporated into the final predictions at all.\n\n## Obtaining the predictions\n\nWe can extract the predictions easily via the SL.predict element of the SuperLearner fit object.\n\nhead(data.frame(sl_predictions = sl_fit$SL.predict)) %>% gt() %>% fmt_number(everything(),decimals=2) %>% tab_header(\"Final SL predictions (package)\") Final SL predictions (package) sl_predictions 5.28 −1.19 −0.68 −0.87 −0.97 −1.08 ## Cross-validated Superlearner Recall that we can cross-validate the entire model fitting process to evaluate the predictive performance of our superlearner algorithm. This is easy with the function CV.SuperLearner(). Beware, this gets computationally burdensome very quickly! cv_sl_fit <- CV.SuperLearner(Y = obs$y, X = x_df, family = gaussian(),\nSL.library = c(\"SL.ranger\", \"SL.glmnet\", \"SL.earth\"))\n\nFor more information on the SuperLearner package, take a look at this vignette.\n\n## Alternative packages to superlearn\n\nOther packages freely available in R that can be used to implement the superlearner algorithm include sl3 (an update to the original Superlearner package), h2o, and caretEnsemble. I previously wrote a brief demo on using sl3 for an NYC R-Ladies demo.\n\nThe authors of tidymodels – a suite of packages for machine learning including recipes, parsnip, and rsample – recently came out with a new package to perform superlearning/stacking called stacks. Prior to this, Alex Hayes wrote a blog post on using tidymodels infrastructure to implement superlearning.\n\n# Coming soon… when prediction is not the end goal\n\nWhen prediction is not the end goal, superlearning combines well with semi-parametric estimation methods for statistical inference. This is the reason I was reading Targeted Learning in the first place; I am a statistician with collaborators who typically want estimates of treatment effects with confidence intervals, not predictions!\n\nI’m working on a similar visual guide for one such semiparametric estimation method: Targeted Maximum Likelihood Estimation (TMLE)). TMLE allows the use of flexible statistical models like the superlearner algorithm when estimating treatment effects. If you found this superlearning tutorial helpful, you may be interested in this similarly visual tutorial on TMLE.\n\nHTML Image as link", null, "# Appendix\n\nThese sections contain a bit of extra information on the superlearning algorithm, such as: intuition on manually computing the loss function of interest, explanation of the discrete superlearner, brief advice on choosing a metalearner, and a different summary visual provided in the Targeted Learning book.\n\n### Manually computing the MSE\n\nLet’s say we have chosen our loss function of interest to be the Mean Squared Error (MSE). We could first compute the squared error $$(y - \\hat{y})^2$$ for each CV prediction A, B, and C.\n\ncv_sq_error <-\nobs_preds %>%\nmutate(cv_sqrd_error_a = (y-pred_a)^2, # compute squared error for each observation\ncv_sqrd_error_b = (y-pred_b)^2,\ncv_sqrd_error_c = (y-pred_c)^2)\ncv_sq_error %>%\npivot_longer(c(cv_sqrd_error_a, cv_sqrd_error_b, cv_sqrd_error_c), # make the CV squared errors long form for plotting\nnames_to = \"base_learner\",\nvalues_to = \"squared_error\") %>%\nmutate(base_learner = toupper(str_remove(base_learner, \"cv_sqrd_error_\"))) %>%\nggplot(aes(base_learner, squared_error, col=base_learner)) + # make box plots\ngeom_boxplot() +\ntheme_bw() +\nguides(col=F) +\nlabs(x = \"Base Learner\", y=\"Squared Error\", title=\"Squared Errors of Learner A, B, and C\")\nWarning: guides(<scale> = FALSE) is deprecated. Please use guides(<scale> =\n\"none\") instead.", null, "And then take the mean of those three cross-validated squared error columns, grouped by cv_fold, to get the CV-MSE for each fold.\n\ncv_risks <-\ncv_sq_error %>%\ngroup_by(cv_fold) %>%\nsummarise(cv_mse_a = mean(cv_sqrd_error_a),\ncv_mse_b = mean(cv_sqrd_error_b),\ncv_mse_c = mean(cv_sqrd_error_c)\n)\ncv_risks %>%\npivot_longer(cv_mse_a:cv_mse_c,\nnames_to = \"base_learner\",\nvalues_to = \"mse\") %>%\nmutate(base_learner = toupper(str_remove(base_learner,\"cv_mse_\"))) %>%\nggplot(aes(cv_fold, mse, col=base_learner)) +\ngeom_point() +\ntheme_bw() +\nscale_x_continuous(breaks = 1:10) +\nlabs(x = \"Cross-Validation (CV) Fold\", y=\"Mean Squared Error (MSE)\", col = \"Base Learner\", title=\"CV-MSEs for Base Learners A, B, and C\")", null, "We see that across each fold, Learner B consistently has an MSE around 0.02, while Learner C hovers around 0.1, and Learner A varies between 0.35 and 0.45. We can take another mean to get the overall CV-MSE for each learner.\n\ncv_risks %>%\nselect(-cv_fold) %>%\nsummarise_all(mean) %>%\ngt() %>%\nfmt_number(everything(), decimals=2) %>% tab_header(\"CV-MSE for each base learner\")\nCV-MSE for each base learner\ncv_mse_a cv_mse_b cv_mse_c\n0.38 0.02 0.11\n\nThe base learner that performs the best using our chosen loss function of interest is clearly Learner B. We can see from our data simulation code why this is true – Learner B is almost exactly the mimicking the data generating mechanism of y.\n\nOur results align with the linear regression fit from our metalearning step; Learner B predictions received a much larger coefficient relative to Learners A and C.\n\n### Discrete Superlearner\n\nWe could stop after minimizing our loss function (MSE) and fit Learner B to our full data set, and that would be called using the discrete superlearner.\n\ndiscrete_sl_predictions <- predict(glm(y ~ x1 + x2 + x1*x3 + sin(x4), data=obs))\n\nHowever, we can almost always create an even better prediction algorithm if we use information from all of the algorithms’ CV predictions.\n\n### Choosing a metalearner\n\nIn the Reference papers on superlearning, the metalearner which yields the best results theoretically and in practice is a convex combination optimization of learners. This means fitting the following regression, where $$\\alpha_1$$, $$\\alpha_2$$, and $$\\alpha_3$$ are all non-negative and sum to 1.\n\n$$\\mathrm{E}[Y|\\hat{Y}_{LrnrA},\\hat{Y}_{LrnrB},\\hat{Y}_{LrnrC}] = \\alpha_1\\hat{Y}_{LrnrA} + \\alpha_2\\hat{Y}_{LrnrB} + \\alpha_3\\hat{Y}_{LrnrC}$$\n\nThe default in the Superlearner package is to fit a non-negative least squares (NNLS) regression. NNLS fits the above equation where the $$\\alpha$$’s must be greater than or equal to 0 but do not necessarily sum to 1. The package then reweights the $$\\alpha$$’s to force them to sum to 1. This makes the weights a convex combination, but may not yield the same optimal results as an initial convex combination optimization.\n\nThe metalearner should change with the goals of the prediction algorithm and the loss function of interest. In these examples it is the MSE, but if the goal is to build a prediction algorithm that is best for binary classification, the loss function of interest may be the rank loss, or $$1-AUC$$. It is outside the scope of this post, but for more information, I recommend this paper by Erin Ledell on maximizing the Area Under the Curve (AUC) with superlearner algorithms.\n\n### Another visual guide for superlearning\n\nThe steps of the superlearner algorithm are summarized nicely in this graphic in Chapter 3 of the Targeted Learning book:", null, "# Acknowledgments\n\nThank you to Eric Polley, Iván Díaz, Nick Williams, Anjile An, and Adam Peterson for very helpful content (and design!) suggestions for this post.\n\n# Session Info\n\nsessionInfo()\nR version 4.1.3 (2022-03-10)\nPlatform: x86_64-apple-darwin17.0 (64-bit)\nRunning under: macOS Catalina 10.15.7\n\nMatrix products: default\nBLAS: /Library/Frameworks/R.framework/Versions/4.1/Resources/lib/libRblas.0.dylib\nLAPACK: /Library/Frameworks/R.framework/Versions/4.1/Resources/lib/libRlapack.dylib\n\nlocale:\n en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8\n\nattached base packages:\n splines stats graphics grDevices utils datasets methods\n base\n\nother attached packages:\n SuperLearner_2.0-28 gam_1.20.2 foreach_1.5.2\n nnls_1.4 gt_0.6.0 forcats_0.5.1\n stringr_1.4.1 dplyr_1.0.9 purrr_0.3.4\n ggplot2_3.3.6 tidyverse_1.3.1\n\nloaded via a namespace (and not attached):\n httr_1.4.2 sass_0.4.1 jsonlite_1.8.0 modelr_0.1.8\n Formula_1.2-4 assertthat_0.2.1 cellranger_1.1.0 yaml_2.3.5\n pillar_1.8.1 backports_1.4.1 lattice_0.20-45 glue_1.6.2\n digest_0.6.29 checkmate_2.0.0 rvest_1.0.2 colorspace_2.0-3\n htmltools_0.5.2 Matrix_1.4-0 pkgconfig_2.0.3 broom_0.8.0\n earth_5.3.1 haven_2.5.0 scales_1.2.1 ranger_0.14.1\n TeachingDemos_2.12 tzdb_0.3.0 farver_2.1.1 generics_0.1.3\n ellipsis_0.3.2 withr_2.5.0 cli_3.3.0 survival_3.2-13\n dbplyr_2.1.1 tidyselect_1.1.2 xfun_0.32" ]
[ null, "https://www.khstats.com/img/sl_steps/Superlearning.jpg", null, "https://www.khstats.com/img/spiderman_meme.jpg", null, "https://www.khstats.com/img/sl_steps/step1.png", null, "https://www.khstats.com/img/sl_steps/step2.png", null, "https://www.khstats.com/img/sl_steps/step3.png", null, "https://www.khstats.com/img/sl_steps/step4.png", null, "https://www.khstats.com/img/sl_steps/step5.png", null, "https://www.khstats.com/img/sl_steps/step6.png", null, "https://www.khstats.com/img/sl_steps/step7.png", null, "https://www.khstats.com/img/sl_steps/step8.png", null, "https://www.khstats.com/img/TMLE.jpg", null, "https://www.khstats.com/blog/sl/superlearning_files/figure-html/unnamed-chunk-20-1.png", null, "https://www.khstats.com/blog/sl/superlearning_files/figure-html/unnamed-chunk-21-1.png", null, "https://www.khstats.com/img/sl_diagram.png", null ]
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https://mailinglist.acer.edu.au/pipermail/rasch/2015-March/002240.html
[ "# [Rasch] Likelihood\n\nPatrick Fisher pfisher at sportsmeasures.com\nWed Mar 18 09:57:55 EST 2015\n\n```Thank you very much Svend! That's exactly what I was seeking.\n\nPatrick\n\nlogo\n*Patrick B. Fisher* /\nPresident//\nSportsMeasures, Inc./\nTel: 630-674-6783\npfisher at sportsmeasures.com\nhttp://www.SportsMeasures.com\n\nDesigned with WiseStamp -\nyours\n\nOn 3/15/2015 4:27 AM, Svend Kreiner wrote:\n> Patrick,\n>\n>\n> \"I am looking the proportion of people who took the exam in the first quarter vs. the fourth quarter and given the greater propensity to fail in the fourth quarter, it is X times more likely that you will fail the exam if you wait until the fourth quarter to take the exam\".\n>\n> has a fairly simple answer.\n>\n> The measure you are looking for is the so-called odds-ratio comparing the odds for failure in the fourth quarter to the odds for failure in the first quarter rather than the probabilities.\n>\n> it is very easy to calculate\n>\n> 4413 430\n> 92 43\n>\n> and the odds-ratio is\n>\n> (4413x43)/(430x92) = 4.8\n>\n> This is the measure that epidemiologists use when they compare risk in different groups.\n>\n>\n> I was a little surprised to see this question here, because it has nothing to do with Rasch models, but there are two results that connects it to what we usually discuss here.\n>\n> The first is that there are two old papers showing that the odds-ratio (and functions of the odds-ratio) is the only measure of association in 2 x 2 tables that does not depend on the way persons are sampled.\n>\n> The first is Edwards, AWF (1963): The Measure of association in a 2 x 2 table. J.R. Statist. Soc. A, 126, 109-114\n> The second is Altham, P (1970) The measurement of association of rows and columns for an r x s contingency table. J.R. Statist. Soc. B, 32, 63-73\n>\n> Since objective comparisons of items (according to Rasch) requires that comparisons of items must not depend on how persons are sampled, toy might say that (functions of) the odds-ratio is the only objective comparisons of risks.\n>\n> The second is that you can calculate the odds-ratio by a logistic regression analysis with failure as dependent and quarter as the independent variable. The result is a beta parameter describing the effect of quarter on failure,\n> that can be transformed to an odds-ratio statistic by odds-ratio = exp(beta).\n>\n> The beta parameter is another objective measure comparing failure in the two quarters. Since the definition of logits are given by logit=ln(odds), you can say 1) that the beta is the logit difference between the risk in the fourth quarter and the risk in the first quarter,\n> and 2) that the beta statistic is a measure of the different risks on exactly the same scale as the scale we use for item and person parameters in the Rasch model. If you are an experienced Rasch modeller and therefore understand and can interpret logit-differences,\n> you may prefer this measure to the odds-ratio, but you have to remember, that the rest of the world do not understand logits and therefore prefer odds-ratios.\n>\n>\n> Svend\n>\n>\n> ________________________________________\n> Rasch mailing list\n> email: Rasch at acer.edu.au\n> web: https://mailinglist.acer.edu.au/mailman/options/rasch/pfisher%40sportsmeasures.com\n>\n\n-------------- next part --------------\nAn HTML attachment was scrubbed...\nURL: https://mailinglist.acer.edu.au/pipermail/rasch/attachments/20150317/99e5e008/attachment.html\n```" ]
[ null ]
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http://www.imperial.ac.uk/aeronautics/study/ug/current-students/modules/h401/?module=AERO50003&year=21_22
[ "# Aeronautical Engineering (MEng)\n\n## Computing and Numerical Methods 2\n\n### Module aims\n\nThe module builds on your prior programming ability, introducing you to programming with a compiled language (C++) and further numerical analysis techniques, which you will need and apply in later years of the Aeronautics course and subsequently in industry. The emphasis of the module is to impart a basic awareness of common pitfalls in applying numerical methods together with a degree of competence in the application of numerical analysis to common model problems, such as the solution of differential equations.\n\n### Learning outcomes\n\nOn successfully completing this module, you should be able to:\n\n1. Implement the essential procedural and object-oriented programming constructs in C++  and write complex programs to solve a variety of numerical problems;\n2. Apply time-stepping methods for initial-value problems with particular emphasis on their consistency, stability and convergence;\n3. Choose appropriate solvers for stiff systems, being aware of the concept of stiffness;\n4. Extend the methods used for ordinary differential equations to the numerical solution of partial differential equations;\n5. Identify accuracy and stability limitations in numerical methods for Partial Differential Equations (PDEs);\n6. Carry out a computational analysis involving program writing, debugging, validation and results presentation.\n7. use a UNIX shell and execute basic commands.\n\n### Module syllabus\n\nObject-oriented programming:\n- The C++ language; variables, operators and I/O; control structures; functions; classes, arrays, dynamic memory and pointers.\n\nUnix:\n- Linux, the UNIX file system, basic commands, editing files, networks.\n\nNumerical Analysis:\n- Finite Difference Methods: forwards difference, backwards difference, central difference. Order of accuracy. Higher derivatives.\n- Numerical Solution of Ordinary Differential Equations (ODEs): review of theory: initial value problems, systems of ODEs, geometric perspectives (direction field and phase plane).\n- Simple methods for ODEs: forward Euler, explicit Runge Kutta methods. Errors, adaptive methods, application to systems, the need to consider complex eigenvalues.\n- Numerical stability of ODE solvers (1): simple analysis of explicit methods.\n- Numerical stability of ODE solvers (2): implicit and LMM methods, stiff problems (Van der Pol), Boundary value problems and shooting. Z-transform approach.\n- Introductory Finite Differences for Partial Differential Equations (PDEs): Types of equations, basic construction of solver illustrated using heat conduction equation.\n- Difference schemes for PDEs: convergence and consistency.\n- Stability analysis of numerical schemes for PDEs: Von Neumann and modified equation analysis. FTCS and Crank Nicholson methods for heat conduction equation.\n- Elliptic and Hyperbolic equations: concept of relaxation upwinding for hyperbolic equations.\n\n### Teaching methods\n\nThe instruction of programming is carried out using a flipped-classroom approach. Prior to the tutorial session, you will review a pre-recorded lecture and test your understanding by attempting to solve a few short exercises. During the 2-hour in-class tutorial that follows, you will discuss the solution of the online self-assessment with the tutor and raise any questions. A problem sheet will then be attempted, with tutors available to answer questions.\n\nFor the part of the module addressing numerical methods, you will be introduced to the fundamental idea behind the methods using large whole class lectures, with half-class tutorial sessions, held in computer labs, used to apply and reinforce your understanding.\n\n### Assessments\n\nThe module offers extensive opportunities for formative self-assessment by students, through both the pre-session self-assessments and weekly tutorials.\nYou will be summatively assessed through in-class programming tests (assessing your programmings skills in C++), a multiple-choice test on numerical methods and a computing project.\n\n Assessment type Assessment description Weighting Pass mark Examination C++ Mastery Test 30% 40% Examination Numerical Methods MCQ 20% 40% Coursework Project 50% 40%\n\nYou will be offered opportunities to receive both structured and opportunistic formative feedback. Through the weekly programming tutorials, you will be able to formative self-assess your progress and understanding, as well as ask for feedback from the class tutors.\nWritten feedback will be provided for your submissions for the summative project and in-class test.\nFurther individual feedback is available on request via this module’s online feedback forum, staff office hours and discussions with tutors.\n\n### Core\n\n• #### Fundamentals of engineering numerical analysis\n\nMoin, Parviz.\n\n2nd ed., Cambridge : Cambridge University Press\n\n• #### Numerical mathematics and computing\n\nCheney, E. W.\n\n7th, Brooks Cole\n\n• #### The C++ programming language\n\nStroustrup, Bjarne." ]
[ null ]
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http://ac.yotesfan.com/33-PhysicsScript/index.php?id=33000C28
[ "File Completed.\n\n• id = 0x33000c28\n• num_script_data = 0x00000007\n• script_data (7)\n• 0 (3)\n• start_time_lo = 0x00000000\n• start_time_hi = 0x00000000\n• hook (13)\n• type = 0x0000000d\n• type_name = kCreateParticle\n• direction = 0x00000000\n• emitterInfoId = 0x32000692\n• partIndex = 0x00000008\n• x = 0\n• y = 0\n• z = 0\n• qw = 1\n• qx = 0\n• qy = 0\n• qz = 0\n• emitterId = 0x00000000\n• 1 (3)\n• start_time_lo = 0x00000000\n• start_time_hi = 0x00000000\n• hook (13)\n• type = 0x0000000d\n• type_name = kCreateParticle\n• direction = 0x00000000\n• emitterInfoId = 0x3200068e\n• partIndex = 0x0000000a\n• x = 0\n• y = 0\n• z = 0\n• qw = 1\n• qx = 0\n• qy = 0\n• qz = 0\n• emitterId = 0x00000000\n• 2 (3)\n• start_time_lo = 0x00000000\n• start_time_hi = 0x00000000\n• hook (13)\n• type = 0x0000000d\n• type_name = kCreateParticle\n• direction = 0x00000000\n• emitterInfoId = 0x3200068e\n• partIndex = 0x0000000b\n• x = 0\n• y = 0\n• z = 0\n• qw = 1\n• qx = 0\n• qy = 0\n• qz = 0\n• emitterId = 0x00000000\n• 3 (3)\n• start_time_lo = 0x00000000\n• start_time_hi = 0x00000000\n• hook (13)\n• type = 0x0000000d\n• type_name = kCreateParticle\n• direction = 0x00000000\n• emitterInfoId = 0x3200068a\n• partIndex = 0x00000008\n• x = 0\n• y = 0\n• z = 0\n• qw = 1\n• qx = 0\n• qy = 0\n• qz = 0\n• emitterId = 0x00000000\n• 4 (3)\n• start_time_lo = 0x00000000\n• start_time_hi = 0x00000000\n• hook (13)\n• type = 0x0000000d\n• type_name = kCreateParticle\n• direction = 0x00000000\n• emitterInfoId = 0x3200068a\n• partIndex = 0x00000002\n• x = 0\n• y = 0\n• z = 0\n• qw = 1\n• qx = 0\n• qy = 0\n• qz = 0\n• emitterId = 0x00000000\n• 5 (3)\n• start_time_lo = 0x00000000\n• start_time_hi = 0x00000000\n• hook (7)\n• type = 0x00000015\n• type_name = kSoundTweaked\n• direction = 0x00000000\n• soundId = 0x0a000466\n• priority = 1\n• probability = 1\n• volume = 0.5\n• 6 (3)\n• start_time_lo = 0xc0000000\n• start_time_hi = 0x4004cccc\n• hook (5)\n• type = 0x00000013\n• type_name = kCallPES\n• direction = 0x00000000\n• pesId = 0x33000acc\n• pause = 0" ]
[ null ]
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https://educatorpages.com/site/regina1renfro/pages/27771
[ "", null, "# Secret Agent 001\n\nWebsites\n\nidentify and use homophones, synonyms, and antonyms for given words in text\n\nidentify imagery, figurative language (e.g., personification, metaphor, simile, hyperbole), refrain, rhythm, and flow when responding to literature\n\npredict information based on title, topic, genre, and prior knowledge\n\nidentify explicit information and infer implicit information relating to main idea in nonfiction, fiction, and other literary genres, using details, sequence of events, cause and effect relationships, and problem and solution\n\nWriting\n\nvary sentences by structure (declarative, interrogative, imperative, and exclamatory), order, and complexity (simple, complex, compound)\n\nexpand or reduce sentences by adding or deleting modifiers, phrases, or combining sentences\n\nuse appropriate capitalization in written work\n\nrecognize the difference between primary and secondary sources\n\nidentify and use subjects (simple and compound), pronouns, predicates (simple and compound), modifiers (words and prepositional phrases), adjectives and adverbs and recognize that a word performs different functions according to its position in the sentence\n\nform singular, plural, and possessive nouns\n\nuse present, past, future, regular and irregular verb tenses to match intended meaning\n\nedit for punctuation, spelling, fragments, and run-on sentences\n\nrecognize the difference in summarizing, paraphrasing, and plagiarizing\n\nuse and identify the eight parts of speech (e.g., noun, pronoun, verb, adverb, adjective, conjunction, preposition, interjection)\n\nuse and recognize correct punctuation, including semicolons, apostrophes, and quotation marks\n\nMath\n\nfind multiples and factors\n\nread, write, order and compare place value of decimal fractions\n\nmultiply and divide with decimal fractions to include decimal fractions less than one and greater than one\n\nuse words, pictures and/or numbers to show that the relationships and rules for multiplication and division of whole numbers also applies to decimal fractions\n\nuse words, pictures and/or numbers to show that division of whole numbers can be represented as a fraction (a/b = a ˜ b)\n\nuse words, pictures and/or numbers to show the value of a fraction is not changed when both its numerator and denominator are multiplied or divided by the same number because it is the same as multiplying or dividing by one\n\nfind equivalent fractions and simplify fractions\n\nmodel multiplication and division of common fractions\n\nanalyze and explain the relationship of the circumference of a circle, its diameter, and pi ( p ÿ 3.14)\n\nanalyze, explain and apply estimation strategies in working with quantities, measurement, computation and problem solving\n\nestimate the area of fundamental geometric plane figures\n\nuse formulas to find area of polygons, including triangles and parallelograms\n\nfind the area of a polygon (regular and irregular) by dividing it into squares, rectangles, and/or triangles and finding the sum of the area of those shapes\n\ncompute the circumference of a circle using a formula\n\nestimate the volume of simple geometric solids in cubic units\n\nuse variables, such as n or x, for unknown quantities in algebraic expressions\n\ninvestigate expressions by substituting numbers for the unknown\n\ndetermine that a formula is reliable regardless of the type of number (whole number, decimal or fraction) substituted for the variable\n\ndetermine and justify the mean, range, mode, and median of a set of data\n\nmodel multiplication and division of decimal fractions by another decimal fraction\n\nidentify and analyze congruent figures and the correspondence of their vertices, sides, and angles\n\nadd and subtract fractions and mixed numbers with like and unlike denominators\n\ncompute the volume of a cube and a rectangular prism using a formula\n\nexpress, investigate and represent math relationships in formulas and equations\n\nanalyze data presented in a graph\n\nScience\n\nhttp://teacher.scholastic.com/activities/explorations/bug/level1/interactive.htm\n\nClassification!!!!\n\nSocial Studies" ]
[ null, "https://www.facebook.com/tr", null ]
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http://demon-software.com/public_html/support/htmlug/ug-node87.html
[ "### Keyword SIMULATION\n\nThis keyword controls property evaluations along BOMD trajectories.\nOptions:\nANALYZE / CALCULATE (must be specified)\n ANALYZE A BOMD (property) calculation is analyzed. CALCULATE A property calculation along a BOMD trajectory is requested.\n\nDIPOLE / POLARIZABILITY / NMR / MAGNETIZABILITY MAGNETIZABILIIESA\n DIPOLE Dipole moments are calculated along a BOMD trajectory. POLARIZABILITY Polarizabilities are calculated along a BOMD trajectory. NMR=", null, "Integer", null, "NMR shieldings are calculated along a BOMD trajectory. The", null, "Integer", null, "denotes the atom for which the magnetic shielding data are printed. MAGNETIZABILITY Magnetizabilities are calculated along a BOMD trajectory.\n\nMOMENTA / PHASESPACE\n MOMENTA Linear and angular molecular momenta are calculated along an MD trajectory. PHASESPACE The reduced coordinate and momentum are calculated along an MD trajectory. This option is valid only for dimers.\n\nRDF / SIMILARITY / LINDEMANN / MEANDIS / PROLATE\n RDF=A1-A2 Calculate the radial distribution function between atom A1 and atom A2. SIMILARITY Calculate the similarity index along an MD trajectory with respect to pattern geometries. LINDEMANN Calculate the Lindemann parameter for an MD trajectory. MEANDIS Calculate the mean interatomic distance along an MD trajectory. PROLATE Calculate the prolate deformation parameter along an MD trajectory.\n\nLENGTH / ANGLE / DIHEDRAL\n LENGTH Calculate the specified bond lengths along an MD trajectory. ANGLE Calculate the specified angles along an MD trajectory. DIHEDRAL Calculate the specified dihedral angles along an MD trajectory.\n\nE=STANDARD / E=KINETIC / E=POTENTIAL / E=TOTAL / E=SYSTEM\n E=STANDARD Standard output for the energy analysis of a trajectory file. E=KINETIC The kinetic energy is averaged in the energy analysis of a trajectory file. E=POTENTIAL The potential energy is averaged in the energy analysis of a trajectory file. E=TOTAL The total energy is averaged in the energy analysis of a trajectory file. E=SYSTEM The system energy is averaged in the energy analysis of a trajectory file. INT=", null, "Integer", null, "Step interval for property analysis or calculation. Default is 1.\nDescription:\nIn deMon2k, molecular dynamics property calculations proceed in two steps. First, a trajectory file, deMon.trj, is created by a BOMD run as described in 4.7.1. In the second step, properties are analyzed or calculated along the stored trajectory coordinates according to the options ANALYZE or CALCULATE of the keyword SIMULATION. It is important to note that the BOMD run and the property calculation are completely independent. Thus, different basis sets, functionals etc. can be used in the property calculation. When properties are calculated, the trajectory file deMon.trj is modified in order to store property values. Thus, it is important to note that the geometries and property data in the deMon.trj file are results of two independent calculations. Once the property values are stored in the trajectory file, they can be analyzed with the ANALYZE option. The SIMULATION options DIPOLE, POLARIZABILITY, NMR and MAGNETIZABILITY specify the property to be analyzed or calculated. A BOMD dipole calculation is triggered by the following input line:\n\n SIMULATION CALCULATE DIPOLE\n\n\nThe corresponding output has the form:\n\n TIME [FS] X[A.U.] Y[A.U.] Z[A.U.] |MU|[A.U.] <MU>[A.U.] <MU^2>[A.U]\n\n101.0 .089 .000 .835 .840 .840 .000\n102.0 .092 .000 .839 .844 .842 .002\n103.0 .093 .000 .842 .848 .844 .003\n104.0 .091 .000 .846 .851 .846 .004\n105.0 .088 .000 .850 .854 .847 .005\n106.0 .083 .000 .852 .856 .849 .006\n107.0 .076 .000 .855 .858 .850 .006\n108.0 .068 .000 .871 .874 .853 .010\n109.0 .060 .000 .864 .866 .855 .010\n110.0 .051 .000 .868 .870 .856 .010\n\n\nFor each time step, the instantaneous dipole moment components and the corresponding absolute dipole moment are listed, together with the average value and the standard deviation. The BOMD polarizability output is similar and discussed in more detail in example", null, "on page", null, "of the tutorial.\n\nA BOMD property calculation can be specified further by the corresponding property keyword. Note that NMR shieldings along BOMD trajectories are only printed for the atom specified by the NMR option of the SIMULATION keyword, even though all shieldings are calculated by default. To obtain the NMR shielding for a specific atom use SIMULATION ANALYZE NMR=", null, "Integer", null, ", where", null, "Integer", null, "denotes the number of the desired atom in the GEOMETRY definition. The following input example,\n\n TRAJECTORY RESTART PART=10-100 INT=1\nSIMULATION ANALYZE NMR=3 INT=1\nGEOMETRY CARTESIAN\nO 0.0000 0.0000 0.1173 17.0\nH 0.0000 0.7572 -0.4692\nH 0.0000 -0.7572 -0.4692\n\n\ngenerates an NMR shielding output for atom 3, here the second hydrogen of the water molecule, from trajectory step 10 to 100. Note the TRAJECTORY RESTART option that is used to address only a part of the trajectory file. Besides the detailed NMR shielding information (tensor diagonal elements, instantaneous shielding and averaged shielding) for the specified atom, the corresponding output lists also the NMR shielding statistics for all atoms.\n\n **********************************************\n*** MOLECULAR DYNAMICS TRAJECTORY ANALYSIS ***\n**********************************************\n\nNMR SHIELDING [ppm] FOR ATOM 3\n\nTIME [FS] XX YY ZZ SIGMA <SIGMA>\n\n10.0 24.73 40.58 31.27 32.19 32.19\n11.0 24.01 39.42 29.88 31.11 31.65\n12.0 23.23 37.98 28.70 29.97 31.09\n13.0 22.70 36.99 28.05 29.25 30.63\n14.0 22.51 36.65 27.96 29.04 30.31\n15.0 22.70 37.04 28.41 29.38 30.16\n16.0 23.27 38.09 29.36 30.24 30.17\n17.0 24.03 39.36 30.52 31.31 30.31\n18.0 24.52 40.04 31.28 31.95 30.49\n19.0 24.36 39.48 31.18 31.68 30.61\n20.0 23.70 38.01 30.44 30.72 30.62\n: : : : : :\n90.0 23.49 37.26 30.88 30.54 30.43\n91.0 23.05 36.30 30.36 29.90 30.43\n92.0 22.85 35.89 30.14 29.63 30.42\n93.0 22.94 36.10 30.29 29.78 30.41\n94.0 23.39 37.12 30.86 30.46 30.41\n95.0 24.27 39.07 31.74 31.69 30.42\n96.0 25.00 40.90 32.05 32.65 30.45\n97.0 24.71 40.92 30.93 32.19 30.47\n98.0 23.72 39.41 29.20 30.77 30.47\n99.0 23.02 38.12 28.13 29.76 30.46\n100.0 22.75 37.57 27.79 29.37 30.45\n\n*** NMR SHIELDINGS STATISTIC ***\n\nCHEMICAL SHIELDING FOR ATOM 1 ( O )\nAVERAGE SHIELDING [ppm] = 332.87\nSTD DEV SHIELDING [ppm] = 13.06\n\nCHEMICAL SHIELDING FOR ATOM 2 ( H )\nAVERAGE SHIELDING [ppm] = 30.40\nSTD DEV SHIELDING [ppm] = 0.81\n\nCHEMICAL SHIELDING FOR ATOM 3 ( H )\nAVERAGE SHIELDING [ppm] = 30.45\nSTD DEV SHIELDING [ppm] = 1.02\n\n\nThe atoms for which NMR shieldings should be calculated along a BOMD trajectory can be selected with the READ option of the NMR keyword, see 4.8.8. Also the nuclear spin-rotation constant can be calculated along BOMD trajectories as shown by the following input example.\n\n DISPERSION\nBASIS (AUG-CC-PVDZ)\nAUXIS (GEN-A2)\nSCFTYPE MAX=1000 TOL=0.100E-04\nVXCTYPE OPTX-PBE AUXIS\nTRAJECTORY RESTART PART=10000-12000 INT=20\nSHIFT -0.2\nNMR SPINROT\nSIMULATION CALCULATE NMR=1 INT=20\n#\n# Cartesian coordinates of MD step 410000\n#\nGEOMETRY CARTESIAN ANGSTROM\nF -66.916797 19.630729 -13.088069 9 18.998000\nH -67.101518 18.720636 -12.997091 1 2.014000\nC 54.166066 -15.936748 9.958016 6 12.000000\nC 53.957601 -15.619981 11.173715 6 12.000000\nH 54.766661 -16.089846 9.024499 1 1.008000\nH 53.312450 -15.623649 12.049412 1 1.008000\n\n\nMagnetizabilities are calculated along a BOMD trajectory by the following input line:\n\n SIMULATION CALCULATE MAGNETIZABILITY\n\n\nSimilarly to the spin-rotation constant, the rotational g-tensor can be calculated along BOMD trajectories by specifying MAGNETIZABILITY GTENSOR in the the input.\n\nThe options MOMENTA and PHASESPACE are generic to MD simulations and, therefore, have no corresponding property keyword. While linear and angular momentum analyses are general, the PHASESPACE analysis can be performed only for diatomic molecules. In general, MOMENTA and PHASESPACE results probe the MD sampling in detail and are recommended if the calculation of thermodynamic properties from the MD trajectory is the objective. Plots from PHASESPACE outputs are shown in Figure 12.\n\nThe RDF, SIMILARITY, LINDEMANN, MEANDIS and PROLATE options are intended to be used in combination with the ANALYSE option to perform the respective analysis on an MD trajectory. The RDF option enables a radial distribution function calculation. It requires two string arguments to specify the atomic pair defining the radial distribution function. According to this specification the RDF for a specific atom pair or for all pairs of an element combination are calculated. Specific RDF options can be set by the RDF keyword (see 4.7.7) as in the following example.\n\n RDF MAX=2.0 WIDTH=0.01\nSIMULATION ANALYSE RDF=C-H INT=10\n#\nGEOMETRY\nC 1.251600 -0.743355 -0.192056\nO 2.419080 0.016064 0.186570\nC -0.012609 0.001665 0.300080\nH 3.194749 -0.353196 -0.223934\nO -0.044331 1.355726 -0.228495\nH 0.628856 1.905515 0.161926\nC -1.248651 -0.749384 -0.241064\nO -2.455867 -0.060507 0.201783\nH -2.338769 0.832194 -0.188720\nH -0.073137 -0.089445 1.394002\nH -1.226536 -1.787913 0.146590\nH 1.132009 -1.855775 0.371678\nH 1.127880 -0.963356 -1.265091\nH -1.042307 -0.734311 -1.348578\n\n\nThis input generates an RDF for all C-H distances below 2 Ångström of a glycerol BOMD.\n\nThe SIMILARITY option requires the definition of at least one PATTERN geometry. This option triggers the calculation of the normalized RMS distance between the MD and PATTERN geometries which can be used as an index to classify isomers or calculate isomer lifetimes. By default, pattern and MD geometries are aligned (see 4.1.7) before anything is calculated. The automatic pattern-geometry alignment can be modified with the ALIGNMENT keyword if desired. The following input performs a similarity analysis, excluding hydrogen atoms, of glycerol conformers along a BOMD trajectory.\n\n ALIGN ENANTIOMER EXCLUDE\nH\nSIMULATION ANALYSE SIMILARITY INT=1\n#\n# Pattern definitions\n#\nPATTERN GLYA\nC 0.000000 0.000000 0.000000\nO 0.000000 0.000000 1.462899\nC 1.474005 0.000000 -0.440301\nH -0.893691 -0.260594 1.766994\nO 2.162480 -1.176562 0.084086\nH 1.941117 -1.214952 1.038194\nC 1.632514 -0.059827 -1.970356\nO 3.025324 -0.048486 -2.363928\nH 3.464920 -0.717132 -1.794492\nH 1.971460 0.922883 -0.056060\nH 1.170832 0.835048 -2.435026\nH -0.510825 0.910396 -0.391119\nH -0.502224 -0.913371 -0.392432\nH 1.121602 -0.977513 -2.350343\nPATTERN GLYB\nC 0.000000 0.000000 0.000000\nO 0.000000 0.000000 1.447257\nC 1.448191 0.000000 -0.553309\nH 0.683368 0.660325 1.699576\nO 2.197151 1.114528 0.025822\nH 1.975852 1.886268 -0.546110\nC 1.505454 0.056976 -2.092055\nO 1.020939 1.380454 -2.494249\nH 1.337270 1.554323 -3.403051\nH -0.524157 -0.927069 -0.313648\nH 2.557147 -0.088302 -2.425107\nH 0.859665 -0.741313 -2.524473\nH -0.548895 0.882612 -0.405640\nH 1.966016 -0.916375 -0.200050\nGEOMETRY\nC 1.251600 -0.743355 -0.192056\nC 2.419080 0.016064 0.186570\nC -0.012609 0.001665 0.300080\nO 3.194749 -0.353196 -0.223934\nO -0.044331 1.355726 -0.228495\nO 0.628856 1.905515 0.161926\nH -1.248651 -0.749384 -0.241064\nH -2.455867 -0.060507 0.201783\nH -2.338769 0.832194 -0.188720\nH -0.073137 -0.089445 1.394002\nH -1.226536 -1.787913 0.146590\nH 1.132009 -1.855775 0.371678\nH 1.127880 -0.963356 -1.265091\nH -1.042307 -0.734311 -1.348578\n\n\nWith the Lindemann option the root-mean-square bond length fluctuation , @fnswfnvalfnswfalse ##1fnval##1fnswtrue", null, "(19)\n\nwith", null, "and", null, "being the number of atoms and interatomic distances, respectively, are calculated along a trajectory. Similarly, the mean interatomic distance , @fnswfnvalfnswfalse ##1fnval##1fnswtrue", null, "(20)\n\nis calculated with the MEANDIS option. It measures the average \"extension\" of a structure in a molecular dynamics simulation. The prolate deformation coefficient , @fnswfnvalfnswfalse ##1fnval##1fnswtrue", null, "(21)\n\nwith", null, "being the eigenvalues of the geometrical quadrupole tensor over all atoms with elements, @fnswfnvalfnswfalse ##1fnval##1fnswtrue", null, "(22)\n\nare calculated along a trajectory with the PROLATE option.\n\nThe LENGTH, ANGLE and DIHEDRAL options require the definition of the atoms involved, in the next input lines. Two numbers are required to define each bond LENGTH, three numbers to define each ANGLE and four numbers to define each DIHEDRAL angle. Up to ten parameters can be defined in this way, in consecutive lines after the keyword, as the following input example shows.\n\n SIMULATION ANALYSE DIHEDRAL INT=10\n2 1 3 7\n2 1 3 5\n8 7 3 1\n8 7 3 5\n1 5 3 8\n8 3 5 1\n4 5 6 7\n7 6 5 4\n3 1 10 2\n12 11 10 9\n#\nGEOMETRY\nC 1.251600 -0.743355 -0.192056\nO 2.419080 0.016064 0.186570\nC -0.012609 0.001665 0.300080\nH 3.194749 -0.353196 -0.223934\nO -0.044331 1.355726 -0.228495\nH 0.628856 1.905515 0.161926\nC -1.248651 -0.749384 -0.241064\nO -2.455867 -0.060507 0.201783\nH -2.338769 0.832194 -0.188720\nH -0.073137 -0.089445 1.394002\nH -1.226536 -1.787913 0.146590\nH 1.132009 -1.855775 0.371678\nH 1.127880 -0.963356 -1.265091\nH -1.042307 -0.734311 -1.348578\n\n\nThe standard energy output of a deMon BOMD run has the following form:\n\n TIME [FS] T [K] EKIN EPOT ETOT <T> [K] <ETOT>\n\n10.0 103.5 0.00098 -648.62892 -648.62793 103.0 -648.62793\n20.0 100.3 0.00095 -648.62889 -648.62794 102.7 -648.62793\n30.0 91.4 0.00087 -648.62885 -648.62799 100.2 -648.62795\n40.0 84.9 0.00081 -648.62882 -648.62801 96.8 -648.62796\n50.0 84.2 0.00080 -648.62874 -648.62794 94.2 -648.62797\n60.0 107.4 0.00102 -648.62869 -648.62767 94.3 -648.62794\n70.0 185.8 0.00176 -648.62858 -648.62681 102.2 -648.62784\n80.0 252.2 0.00240 -648.62831 -648.62592 118.8 -648.62763\n90.0 154.0 0.00146 -648.62799 -648.62653 128.2 -648.62747\n100.0 56.3 0.00053 -648.62772 -648.62719 124.2 -648.62742\n\n\nFor each time step it lists the instantaneous temperature, kinetic, potential, and total energy as well as the average temperature and total energy. With the INT option of the SIMULATION keyword, the step interval for the energy output can be modified. Energy statistics along an existing trajectory file can be obtained with:\n\n SIMULATION ANALYZE E=STANDARD\n\n\nIf E=STANDARD is substituted by E=KINETIC, E=POTENTIAL, E=TOTAL, or E=SYSTEM, the averages of the kinetic, potential, total or system2 energies are listed. In the case of E=KINETIC the output takes the form:\n\n TIME [FS] EKIN EPOT ESYS ETOT <EKIN>\n\n10.0 0.00098 -648.62892 -648.62793 -648.62793 0.0009836\n20.0 0.00095 -648.62889 -648.62791 -648.62794 0.0009680\n30.0 0.00087 -648.62885 -648.62795 -648.62799 0.0009348\n40.0 0.00081 -648.62882 -648.62798 -648.62801 0.0009027\n50.0 0.00080 -648.62874 -648.62788 -648.62794 0.0008821\n60.0 0.00102 -648.62869 -648.62765 -648.62767 0.0009051\n70.0 0.00176 -648.62858 -648.62747 -648.62681 0.0010279\n80.0 0.00240 -648.62831 -648.62741 -648.62592 0.0011989\n90.0 0.00146 -648.62799 -648.62729 -648.62653 0.0012282\n100.0 0.00053 -648.62772 -648.62710 -648.62719 0.0011588\n\n\nAfter the trajectory output, energy and temperature statistics are printed. As for the DYNAMICS keyword, the SIMULATION keyword can be combined with the TRAJECTORY keyword in order to analyze or calculate properties for parts of a trajectory.\n\n#### Footnotes\n\n... system2\nThe system energy refers to the extended system energy of the Nosé type thermostats." ]
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https://www.datasciencemadesimple.com/convert-character-to-numeric-pandas-python-string-to-integer-2/
[ "# Convert character column to numeric in pandas python (string to integer)\n\nIn order to Convert character column to numeric in pandas python we will be using to_numeric() function. astype() function converts or Typecasts string column to integer column in pandas. Let’s see how to\n\n• Typecast or convert character column to numeric in pandas python with to_numeric() function\n• Typecast character column to numeric column in pandas python with astype() function\n• Typecast or convert string column to integer column in pandas using apply() function.\n\nFirst let’s create a dataframe.\n\n```import pandas as pd\nimport numpy as np\n\n#Create a DataFrame\ndf1 = {\n'Name':['George','Andrea','micheal','maggie','Ravi','Xien','Jalpa'],\n'is_promoted':['0','1','0','0','1','0','1']}\n\ndf1 = pd.DataFrame(df1,columns=['Name','is_promoted'])\nprint(df1)\n\n```\n\ndf1 will be", null, "Datatypes of df1 will be", null, "Note : Object datatype of pandas is nothing but character (string) datatype of python\n\n#### Converting character column to numeric in pandas python: Method 1\n\nto_numeric() function converts character column (is_promoted) to numeric column as shown below\n\n```df1['is_promoted']=pd.to_numeric(df1.is_promoted)\ndf1.dtypes\n\n```\n\n“is_promoted” column is converted from character to numeric (integer).", null, "#### Typecast character column to numeric in pandas python using astype(): Method 2\n\nastype() function converts character column (is_promoted) to numeric column as shown below\n\n```import numpy as np\nimport pandas as pd\n\ndf1['is_promoted'] = df1.is_promoted.astype(np.int64)\ndf1.dtypes\n\n```\n\n“is_promoted” column is converted from character(string) to numeric (integer).", null, "#### Typecast character column to numeric in pandas python using apply(): Method 3\n\napply() function takes “int” as argument and  converts character column (is_promoted) to numeric column as shown below\n\n```import numpy as np\nimport pandas as pd\n\ndf1['is_promoted'] = df1['is_promoted'].apply(int)\ndf1.dtypes\n```\n\n“is_promoted” column is converted from character(string) to numeric (integer).", null, "#### Other Related Topics:\n\nfor further details on to_numeric() function one can refer this documentation" ]
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https://studylib.net/doc/9279019/view-file
[ "# View File", null, "```Mechanics of Materials(ME-294)\nLecture 2\nStatics and Strength of Materials\nStatics is the study of forces acting in equilibrium\non rigid bodies\n• “Bodies” are solid objects, like steel cables, gear teeth, timber\nbeams, and axle shafts (no liquids or gases);\n• “rigid” means the bodies do not stretch, bend, or twist;\n• “equilibrium” means the rigid bodies are not accelerating.\nIn Strength of Materials, we keep the assumptions\nof bodies in equilibrium, but we drop the “rigid”\nassumption.\n Real cables stretch under tension and real axle\nStrength of Materials\nStatics is the study of forces acting in equilibrium on\nrigid bodies.\n• “Bodies” are solid objects, like steel cables, gear teeth, timber\nbeams, and axle shafts (no liquids or gases);\n• “rigid” means the bodies do not stretch, bend, or twist;\n• “equilibrium” means the rigid bodies are not accelerating.\nIn Strength of Materials, we keep the assumptions of\nbodies in equilibrium, but we drop the “rigid”\nassumption.\n▫ Real cables stretch under tension and real axle shafts\n▫ The most fundamental concepts in mechanics of\nmaterials are stress and strain.\nStress and Strain\n• The words “stress” and “strain” are used interchangeably: “I’m\nfeeling stressed” or “I’m under a lot of strain.”\n• In engineering, these words have specific, technical meanings.\nIf you tie a steel wire to a hook in the\nceiling and hang a weight on the\nlower end, the wire will stretch.\n•Divide the change in length by the\noriginal length, and you have the\nstrain in the wire.\n•Divide the weight hanging from the\nwire by the wire’s cross sectional\narea, and you have the tensile stress\nin the wire.\nStress and strain are ratios.\n▫ The symbol for stress is σ, the lower case Greek\nletter sigma. Stress has units of force per unit area\n When SI units are used, force is expressed in newtons\n(N) and area in square meters (m2). Consequently,\nstress has units of newtons per square meter (N/m2),\nthat is, pascals (Pa).\n1N/m2 = 1 Pa\n\n However, the pascal is such a small unit of stress that\nit is necessary to work with large multiples, usually\nthe megapascal (MPa).\n1 MPa = 106 Pa = 106 N/ m2 = 1 N/mm2\nThe symbol for strain is ε, the lower case Greek\nletter epsilon.\n Because normal strain is the ratio of two lengths, it is\na dimension- less quantity, that is, it has no units.\nTherefore, strain is expressed simply as a number,\nindependent of any system of units.\n Numerical values of strain are usually very small,\nbecause bars made of structural materials undergo\nonly small changes in length when loaded.\nA prismatic bar is a straight structural member\nhaving the same cross section throughout its\nlength, and an axial force is a load directed\nalong the axis of the member, resulting in either\ntension or compression in the bar\nwe will consider the tow bar of Fig. 1-1 and\nisolate a segment of it as a free body.\nThe internal actions in the bar are exposed if we\nmake an imaginary cut through the bar at\nsection mn (Fig. 1-2c). Because this section is\ntaken perpendicular to the longitudinal axis of\nthe bar, it is called a cross section.\nThis action consists of continuously distributed\nstresses acting over the entire cross section,\nand the axial force P acting at the cross section\nis the resultant of those stresses. (The resultant\nforce is shown with a dashed line in Fig. 1-2d.)\nThe force per unit area, or intensity of the forces distributed\nover a given section, is called the stress on that section.\nTensile and Compressive Stress and strain\nand stress induced is tensile stress.\n• If the load pushes, we call it a\ncompressive load and stress is called\ncompressive stress.\n• The equations are the same.\n• Stresses act in a direction perpendicular\nto Cross section, they are called normal\nstresses.\n• Normal stresses may be either tensile or\ncompressive.\n• Another type of stress, called shear\nstress, that acts parallel to the surface.\n• sign convention\n▫ tensile stresses as positive(+)\n▫ compressive stresses as negative(-)\nStress-Strain Curve\nstress-strain curve illustrates the elastic\nand plastic zones.\n•If you hang a light weight to the wire\nhanging from the ceiling, the wire\nstretches elastically; remove the\nweight and the wire returns to its\noriginal length.\n•Apply a heavier weight to the wire,\nand the wire will stretch beyond the\nelastic limit and begins to plastically\ndeform, which means it stretches\npermanently. Remove the weight and\nthe wire will be a little longer (and a\nlittle skinnier) than it was originally.\n•Hang a sufficiently heavy weight, and\nthe wire will break.\n• Two stress values are important in\nengineering design.\n▫ The yield strength, σys, is the limit\nof elastic deformation; beyond this\npoint, the material “yields,” or\npermanently deforms.\n▫ The ultimate tensile strength, σUTS\n(also called tensile strength, σTS) is\nthe highest stress value on the\nstress-strain curve.\n• The rupture strength is the stress\nat final fracture; this value is not\nparticularly useful, because once\nthe tensile strength is exceeded,\nthe metal will break soon after.\n• Young’s modulus, E, is the slope of\nthe stress-strain curve before the\ntest specimen starts to yield.\n• The strain when the test specimen\nbreaks is also called the\nelongation.\nMany manufacturing operations on metals are\nperformed at stress levels between the yield strength\nand the tensile strength.\n▫ Bending a steel wire into a paperclip, deep-drawing sheet\nmetal to make an aluminum can, or rolling steel into\nwide-flange structural beams are three processes that\npermanently deform the metal, so σYS&lt;σApplied .\n▫ During each forming operation, the metal must not be\nstressed beyond its tensile strength, otherwise it would\nbreak, so σYS&lt;σApplied&lt;σUTS .\n▫ Manufacturers need to know the values of yield and\ntensile strength in order to stay within these limits.\nExpression for elongation\nIn this Strength of Materials course, almost all of the problems are\nelastic, so there is a linear relationship between stress and strain\nTake an aluminum rod of length L, cross-sectional\narea A, and pull on it with a load P. The rod will\nlengthen an amount δ. We can calculate δ in three\nseparate equations, or we can use algebra to find a\nsimple equation to calculate δ directly.\nDirect equation for calculating the change in length of the rod.\nDeformation of a body due to self weight\nIn Fig determine the total increase of length of a bar of constant cross section\nhanging vertically and subject to its own weight as the only load.\nThe normal stress (tensile) over any horizontal cross section\nis caused by the weight of the material below that section.\nThe elongation of the element of thickness dy shown is\nwhere A denotes the cross-sectional area of the bar and γ\nits specific weight (weight/unit volume).\nIntegrating, the total elongation of the bar is\nwhere W denotes the total weight of the bar.\nNote that the total elongation produced by the weight of the bar is equal to that\nproduced by a load of half its weight applied at the end.\nPrinciple of Superposition\nAssignment#1\n1. In 1989, Jason, a research-type submersible with\nremote TV monitoring capabilities and weighing 35\n200 N, was lowered to a depth of 646 m in an effort\nto send back to the attending surface vessel\nphotographs of a sunken Roman ship offshore from\nItaly. The submersible was lowered at the end of a\nhollow steel cable having an area of 452 &times; 10–6 m2\nand E= 200 GPa. Determine the extension of the\nsteel cable. Due to the small volume of the entire\nsystem, buoyancy may be neglected. (Note: Jason\nwas the system that took the first photographs of the\nsunken Titanic in 1986.) weight of steel per unit\nvolume is 77 kN/m3.\n2. Two prismatic bars are rigidly\nfastened together and support a\nvertical load of 45 kN, as shown in\nFigure. The upper bar is steel\nhaving length 10 m and crosssectional area 60 cm2. The lower\nbar is brass having length 6 m and\ncross-sectional area 50 cm2. For\nsteel E = 200 GPa, for brass E =\n100 GPa. Determine the maximum\nstress in each material. Specific\nweights of brass and steel are\n84kN and 77kN.\n3. A 70 kN compressive load is applied to a 5 cm\ndiameter, 3 cm tall, steel cylinder. Calculate\nstress, strain, and deflection.\n4. What tensile stress is required to produce a\nstrain of 8&times;10−5 in aluminum? Report the\nanswer in MPa. Aluminum has a Young’s\nmodulus of E = 70 GPa.\n5. Stress-strain curves for materials in compression\ndiffer from those in tension. Explain.\nQuiz#1\n• Chapter 1 and 2 –SOM by R. S. Khurmi\n• Assignment#1\n```" ]
[ null, "https://s3.studylib.net/store/data/009279019_1-d5019a89521d5f3b16c8ea20430a5431.png", null ]
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https://es.mathworks.com/help/vision/ref/linetoborderpoints.html
[ "Main Content\n\n# lineToBorderPoints\n\nIntersection points of lines in image and image border\n\n## Syntax\n\n``points = lineToBorderPoints(lines,imageSize)``\n\n## Description\n\nexample\n\n````points = lineToBorderPoints(lines,imageSize)` computes the intersection points between one or more lines in an image with the image border.```\n\n## Examples\n\ncollapse all\n\nLoad and display an image.\n\n```I = imread('rice.png'); figure; imshow(I); hold on;```", null, "Define a line with the equation, 2 * x + y - 300 = 0.\n\n`aLine = [2,1,-300];`\n\nCompute the intersection points of the line and the image border.\n\n`points = lineToBorderPoints(aLine,size(I))`\n```points = 1×4 149.7500 0.5000 21.7500 256.5000 ```\n`line(points([1,3]),points([2,4]));`", null, "## Input Arguments\n\ncollapse all\n\nLine matrix, specified as an M-by-3 matrix, where each row must be in the format, [A,B,C]. This matrix corresponds to the definition of the line:\n\n A * x + B * y + C = 0.\nM represents the number of lines.\n\n`lines` must be `double` or `single`.\n\nImage size, specified as a row vector in the format returned by the `size` function.\n\n## Output Arguments\n\ncollapse all\n\nIntersection points, returned as an M-by-4 matrix. The function returns the matrix in the format of [x1, y1, x2, y2]. In this matrix, [x1 y1] and [x2 y2] are the two intersection points. When a line in the image and the image border do not intersect, the function returns [`-1,-1,-1,-1`].\n\n## See Also\n\nIntroduced in R2011a\n\nDownload ebook" ]
[ null, "https://es.mathworks.com/help/examples/vision/win64/FindIntersectionPointsBetweenALineAndImageBorderExample_01.png", null, "https://es.mathworks.com/help/examples/vision/win64/FindIntersectionPointsBetweenALineAndImageBorderExample_02.png", null ]
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https://answers.everydaycalculation.com/compare-fractions/7-6-and-5-9
[ "# Answers\n\nSolutions by everydaycalculation.com\n\n## Compare 7/6 and 5/9\n\n1st number: 1 1/6, 2nd number: 5/9\n\n7/6 is greater than 5/9\n\n#### Steps for comparing fractions\n\n1. Find the least common denominator or LCM of the two denominators:\nLCM of 6 and 9 is 18\n\nNext, find the equivalent fraction of both fractional numbers with denominator 18\n2. For the 1st fraction, since 6 × 3 = 18,\n7/6 = 7 × 3/6 × 3 = 21/18\n3. Likewise, for the 2nd fraction, since 9 × 2 = 18,\n5/9 = 5 × 2/9 × 2 = 10/18\n4. Since the denominators are now the same, the fraction with the bigger numerator is the greater fraction\n5. 21/18 > 10/18 or 7/6 > 5/9\n\nMathStep (Works offline)", null, "Download our mobile app and learn to work with fractions in your own time:\nAndroid and iPhone/ iPad\n\n#### Compare Fractions Calculator\n\nand\n\n© everydaycalculation.com" ]
[ null, "https://answers.everydaycalculation.com/mathstep-app-icon.png", null ]
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https://itprospt.com/num/17554512/section-16-3-exercise-9-tquestion-helpthe-accompanying-data
[ "5\n\n# Section 16.3 Exercise 9-TQuestion HelpThe accompanying data show the number of people working and the sales for small bookstore. The regression Iine is given below:...\n\n## Question\n\n###### Section 16.3 Exercise 9-TQuestion HelpThe accompanying data show the number of people working and the sales for small bookstore. The regression Iine is given below: The bookstore decides to have gala event in an attempt to drum up business. They hire 98 employees for the day and bring in total of 542,000. Complete parts through below:Sales 8.702 0.882 Number of Salespeople WorkingB Click the con t0 view the data table_a) Find the regression line predicting Sales from Number of people working wit\n\nSection 16.3 Exercise 9-T Question Help The accompanying data show the number of people working and the sales for small bookstore. The regression Iine is given below: The bookstore decides to have gala event in an attempt to drum up business. They hire 98 employees for the day and bring in total of 542,000. Complete parts through below: Sales 8.702 0.882 Number of Salespeople Working B Click the con t0 view the data table_ a) Find the regression line predicting Sales from Number of people working with the new point added Sales I)Number of Salespeople Working (Round to three decimal places as needed:)", null, "", null, "#### Similar Solved Questions\n\n##### Point) To establish a Lagrange identity for the operator on 0 < x < L, dxtwe look for some expression such that(1) fL u -vfu dx = dx+ expressionlg First integrate JL dx by parts:let U = u and dV = Then dx'dUdx; V =Type du as uX, dxas VXXXThe by-parts rule f Udv = UV _ f VdU gives (2) fL udr dx dr' l6 = J&dxContinuing, integrate fL & &v dx by parts: dx dx:let U = du and dV = Then dx dxdUdx; V =du d1 Type as UXX_ as VXX: dx2 dxr2The by-parts rule f UdV = UV _ f VdU give\npoint) To establish a Lagrange identity for the operator on 0 < x < L, dxt we look for some expression such that (1) fL u -vfu dx = dx+ expressionlg First integrate JL dx by parts: let U = u and dV = Then dx' dU dx; V = Type du as uX, dx as VXXX The by-parts rule f Udv = UV _ f VdU gives ...\n##### Pts] Find lower bound. mn_ inf: interior point. boundary point . accumulation point {/applicable) . Fully justify rour answers_8 = {9 € Qc 9 2r}; where is some rational number.\npts] Find lower bound. mn_ inf: interior point. boundary point . accumulation point {/applicable) . Fully justify rour answers_ 8 = {9 € Qc 9 2r}; where is some rational number....\n##### 3 Find the Points] f(x, < second-order s* DETAILS partial xly2 1 derivatives TANAPCALC1O the function 8.2.038 Show that the mixednn\n3 Find the Points] f(x, < second-order s* DETAILS partial xly2 1 derivatives TANAPCALC1O the function 8.2.038 Show that the mixed nn...\n##### Point)Using disks or washers_ find the volume of the solid obtained by rotating the region bounded by the curves y = Ilx; y = 0,x = l, andx = 5 about the line y = -1.\npoint) Using disks or washers_ find the volume of the solid obtained by rotating the region bounded by the curves y = Ilx; y = 0,x = l, andx = 5 about the line y = -1....\n##### #6.( Points) Compute the product and simplify completely Ii+as i goes from 1 to 4\n#6.( Points) Compute the product and simplify completely Ii+as i goes from 1 to 4...\n##### In double slit interference experiment where would you expect to have third maximum if you use LED laser with wavelength 634 nanometers? The distance between slits is 0.02 mm The distance between slits and the screen is 2 m_\nIn double slit interference experiment where would you expect to have third maximum if you use LED laser with wavelength 634 nanometers? The distance between slits is 0.02 mm The distance between slits and the screen is 2 m_...\n##### Remaining How Did Do?\" Uses: 1/3Consider the function f(z) The goal is to compute f' (z) using the definition 11 + 8x f(c + h) flc) f' (1) = lim h,0f(r +h)_ flw) a) We have that((5/(11+8*(xth)))-(5/(11+8*xNote for this part your answer may be left unsimplified.Notice that as h0,this is an indeterminate of the form 0 f( h) f(z) b) Simplify the expression in (a) to getwhere A is constant and Bis function of € and hWhat are the values of A and BAnswer: [A, Bl[-40, (11+8x)*(11+8x+8h\nRemaining How Did Do?\" Uses: 1/3 Consider the function f(z) The goal is to compute f' (z) using the definition 11 + 8x f(c + h) flc) f' (1) = lim h,0 f(r +h)_ flw) a) We have that ((5/(11+8*(xth)))-(5/(11+8*x Note for this part your answer may be left unsimplified. Notice that as h 0,...\n##### In FIGURE 7.2.9, two vertices are shown of a rectangular parallelepiped having sides parallel to the coordinate planes. Find the coordinates of the remaining six vertices.\nIn FIGURE 7.2.9, two vertices are shown of a rectangular parallelepiped having sides parallel to the coordinate planes. Find the coordinates of the remaining six vertices....\n##### Question 4 Not yet answered Points out of 2 F Flag question What is the Rf of the spot marked with X?solvent front5CIXoriginSelect one:a. 1/2b. 3/7C. 1/6d.2/3e: 1/3f.1/5\nQuestion 4 Not yet answered Points out of 2 F Flag question What is the Rf of the spot marked with X? solvent front 5 CI X origin Select one: a. 1/2 b. 3/7 C. 1/6 d.2/3 e: 1/3 f.1/5...\n##### Ferrous sulphate oral solution is used as haematinic agent for pediatric_Select one: True False\nFerrous sulphate oral solution is used as haematinic agent for pediatric_ Select one: True False...\n##### Find an equation of the plane tangent to the surface &x2 +y2 12z = 0 and parallel to the plane Zx - 10y 67 = 0.The equation of the plane is given by z =[\nFind an equation of the plane tangent to the surface &x2 +y2 12z = 0 and parallel to the plane Zx - 10y 67 = 0. The equation of the plane is given by z =[...\n##### Part: 4 / 5Part 5 of 5(e) Would It be unusual If less than 159 of the Individuals In the sample of [1S held multiple Jobs?It (Choose one) be unusual If less than [59 of the Indlviduals In the sample of 115 held multiple Jobs; slnce the probability Is\nPart: 4 / 5 Part 5 of 5 (e) Would It be unusual If less than 159 of the Individuals In the sample of [1S held multiple Jobs? It (Choose one) be unusual If less than [59 of the Indlviduals In the sample of 115 held multiple Jobs; slnce the probability Is...\n##### WiuretjopeWhat the value of 4E ior system that performs 3.67 of work on ILS surroundings and gains 4.57 4.240heat from its surroundings8.245 0.90kJ0.90 M0 EqueSTIon 4The molecular geometry of the BrO3\" ionBentTrigonal pyramida Trigonal planar 0 D T-shaped TetrahedralUESTION 5\nWiuretjope What the value of 4E ior system that performs 3.67 of work on ILS surroundings and gains 4.57 4.240 heat from its surroundings 8.245 0.90kJ 0.90 M 0 E queSTIon 4 The molecular geometry of the BrO3\" ion Bent Trigonal pyramida Trigonal planar 0 D T-shaped Tetrahedral UESTION 5..." ]
[ null, "https://cdn.numerade.com/ask_images/c64e7503b2a74c21bf9bb84134d59e52.jpg ", null, "https://cdn.numerade.com/previews/edbf3751-65c9-4ba4-ae90-2e8226cd9742_large.jpg", null ]
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https://www.brainkart.com/article/Length-of-the-air-gap---Design-of-Synchronous-Machines_12327/
[ "Home | | Design of Electrical Machines | Length of the air gap - Design of Synchronous Machines\n\n# Length of the air gap - Design of Synchronous Machines\n\nLength of the air gap is a very important parameter as it greatly affects the performance of the machine.\n\nLength of the air gap:\n\nLength of the air gap is a very important parameter as it greatly affects the performance of the machine. Air gap in synchronous machine affects the value of SCR and hence it influences many other parameters. Hence, choice of air gap length is very critical in case of synchronous machines. Following are the advantages and disadvantages of larger air gap.\n\n(i)                Stability: Higher value of stability limit\n\n(ii)             Regulation: Smaller value of inherent regulation\n\n(iii)           Synchronizing power: Higher value of synchronizing power\n\n(iv)           Cooling: Better cooling\n\n(v)             Noise: Reduction in noise\n\n(vi)           Magnetic pull: Smaller value of unbalanced magnetic pull Disadvantages:\n\n(i)                Field mmf: Larger value of field mmf is required\n\n(ii)             Size: Larger diameter and hence larger size\n\n(iii)           Magnetic leakage: Increased magnetic leakage\n\n(iv)           Weight of copper: Higher weight of copper in the field winding\n\n(v)             Cost: Increase over all cost.\n\nHence length of the air gap must be selected considering the above factors.\n\nCalculation of Length of air Gap: Length of the air gap is usually estimated based on the ampere turns required for the air gap.\n\nArmature ampere turns per pole required  ATa = 1.35 Tphkw /p\n\nWhere Tph = Turns per phase,  Iph = Phase current, kw = winding factor, p = pairs of  poles\n\nNo load field ampere turns per pole ATfo = SCR x Armature ampere turns per pole ATfo = SCR x ATa\n\nSuitable value of SCR must be assumed.\n\nAmpere turns required for the air gap will be approximately equal to 70 to 75 % of the no load field ampere turns per pole.\n\nATg = (0.7 to 0.75) ATfo\n\nAir gap ampere turns  ATg = 796000 Bgkglg\n\nAir gap coefficient or air gap contraction factor may be assumed varying from 1.12 to 1.18.\n\nAs a guide line, the approximate value of air gap length can be expressed in terms of pole pitch\n\nFor salient pole alternators: lg = (0.012 to 0.016) x pole pitch For turbo alternators: lg = (0.02 to 0.026) x pole pitch\n\nSynchronous machines are generally designed with larger air gap length compared to that of Induction motors.\n\nStudy Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail\nDesign of Electrical Machines - Synchronous Machines : Length of the air gap - Design of Synchronous Machines |" ]
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https://openstax.org/books/physics/pages/2-problems
[ "Physics\n\n# Problems\n\nPhysicsProblems\n\n### Problems\n\n#### 2.1Relative Motion, Distance, and Displacement\n\n16 .\nIn a coordinate system in which the direction to the right is positive, what are the distance and displacement of a person who walks $35\\,\\text{meters}$ to the left, $18\\,\\text{meters}$ to the right, and then $26\\,\\text{meters}$ to the left?\n1. Distance is $79\\,\\text{m}$ and displacement is ${-43}\\,\\text{m}$.\n2. Distance is ${-79}\\,\\text{m}$ and displacement is $43\\,\\text{m}$.\n3. Distance is $43\\,\\text{m}$ and displacement is ${-79}\\,\\text{m}$.\n4. Distance is ${-43}\\,\\text{m}$ and displacement is $79\\,\\text{m}$.\n17.\n\nBilly drops a ball from a height of 1 m. The ball bounces back to a height of 0.8 m, then bounces again to a height of 0.5 m, and bounces once more to a height of 0.2 m. Up is the positive direction. What are the total displacement of the ball and the total distance traveled by the ball?\n\n1. The displacement is equal to –4 m and the distance is equal to 4 m.\n2. The displacement is equal to –1 m and the distance is equal to 1 m\n3. The displacement is equal to 4 m and the distance is equal to 1 m.\n4. The displacement is equal to –1 m and the distance is equal to 4 m.\n\n#### 2.2Speed and Velocity\n\n18 .\nYou sit in a car that is moving at an average speed of 86.4 km/h. During the 3.3 s that you glance out the window, how far has the car traveled?\n1. 7.27 m\n2. 79 m\n3. 285 km\n4. 1026 m\n\n#### 2.3Position vs. Time Graphs\n\n19.\n\nUsing the graph, what is the average velocity for the whole 10 seconds?\n\n1. The total average velocity is 0 m/s.\n2. The total average velocity is 1.2 m/s.\n3. The total average velocity is 1.5 m/s.\n4. The total average velocity is 3.0 m/s.\n20 .\nA train starts from rest and speeds up for 15 minutes until it reaches a constant velocity of 100 miles/hour. It stays at this speed for half an hour. Then it slows down for another 15 minutes until it is still. Which of the following correctly describes the position vs time graph of the train’s journey?\n1. The first 15 minutes is a curve that is concave upward, the middle portion is a straight line with slope 100 miles/hour, and the last portion is a concave downward curve.\n2. The first 15 minutes is a curve that is concave downward, the middle portion is a straight line with slope 100 miles/hour, and the last portion is a concave upward curve.\n3. The first 15 minutes is a curve that is concave upward, the middle portion is a straight line with slope zero, and the last portion is a concave downward curve.\n4. The first 15 minutes is a curve that is concave downward, the middle portion is a straight line with slope zero, and the last portion is a concave upward curve.\n\n#### 2.4Velocity vs. Time Graphs\n\n21.\n\nYou are characterizing the motion of an object by measuring the location of the object at discrete moments in time. What is the minimum number of data points you would need to estimate the average acceleration of the object?\n\n1. 1\n2. 2\n3. 3\n4. 4\n22.\n\nWhich option best describes the average acceleration from 40 to 70 s?\n\n1. It is negative and smaller in magnitude than the initial acceleration.\n2. It is negative and larger in magnitude than the initial acceleration.\n3. It is positive and smaller in magnitude than the initial acceleration.\n4. It is positive and larger in magnitude than the initial acceleration.\n23.\n\nThe graph shows velocity vs. time.\n\nCalculate the net displacement using seven different divisions. Calculate it again using two divisions: 0 → 40 s and 40 → 70 s . Compare. Using both, calculate the average velocity.\n\n1. Displacement and average velocity using seven divisions are 14,312.5 m and 204.5 m/s while with two divisions are 15,500 m and 221.4 m/s respectively.\n2. Displacement and average velocity using seven divisions are 15,500 m and 221.4 m/s while with two divisions are 14,312.5 m and 204.5 m/s respectively.\n3. Displacement and average velocity using seven divisions are 15,500 m and 204.5 m/s while with two divisions are 14,312.5 m and 221.4 m/s respectively.\n4. Displacement and average velocity using seven divisions are 14,312.5 m and 221.4 m/s while with two divisions are 15,500 m and 204.5 m/s respectively.\nOrder a print copy\n\nAs an Amazon Associate we earn from qualifying purchases." ]
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https://scicomp.stackexchange.com/questions/32834/graphing-electric-potential-of-a-ring-of-charge-using-matlab-help
[ "# Graphing electric potential of a ring of charge using MATLAB help\n\nHere is a summary of what I am trying to do:\n\nUse MATLAB to compute the potential $$V$$ at any point $$(x, y, z)$$ in space due to a uniform ring of charge. Use a Riemann sum to compute the integral with increments, $$N$$, as a variable you can change. Plot your potential and field in the plane perpendicular to the area of the ring and passing through the center.\n\nI have two versions of code that give me the same result: correct expression for $$V$$ ($$V_\\text{tot}$$) and the correct vector field. My problem is getting my contour plot to fill the 2D space. The only difference between the two codes is that one uses a for loop to perform the summation and the other uses a sum command:\n\n### Version 1 (using for loop):\n\n%% Computing a symbolic expression for V for anywhere in space\n\nsyms x y z % phiprime is angle that an elemental dq of the circular charge is located at, x,y and z are arbitrary points in space outside the charge distribution\n\nN = 200; % number of increments to sum\nR = 2; % radius of circle is 2 meters\ndphi = 2*pi/N; % discretizing the circular line of charge which spans 2pi\n\nintegrand = 0;\nfor phiprime = 0:dphi:2*pi\n\n% phiprime ranges from 0 to 2pi in increments of dphi\n\nintegrand = integrand + dphi./(sqrt(((x - R.*cos(phiprime) )).^2 + ((y - R.*sin(phiprime) ).^2) + z.^2));\n\nend\n\nintgrl = sum(integrand);\n% unnecessary but harmless step that I leave to show that I am using the\nsum of the above expression for each dphi\n\neps0 = 8.854e-12;\nkC = 1/(4*pi*eps0);\nrhol = 1e-9; % linear charge density\n\nVtot = kC*rhol*R.*intgrl; % symbolic expression for Vtot\n\n%% Graphing V & E in plane perpedicular to ring & passing through center\n\n[Y1, Z1] = meshgrid(-4:.5:4, -4:.5:4);\nVcont1 = subs(Vtot, [x,y,z], {0,Y1,Z1}); % Vcont1 stands for V contour; 1 is because I do the plane of the ring next\n\ncontour(Y1,Z1,Vcont1)\nxlabel('y - axis [m]')\nylabel('z - axis [m]')\ntitle('V in a plane perpendicular to a ring of charge (N = 200)')\nstr = {'Red line is side view', 'of ring of charge'};\ntext(-1,2,str)\n\nhold on\n% visually displaying line of charge on plot\ncircle = rectangle('Position',[-2 0 4 .1],'Curvature',[1,1]);\nset(circle,'FaceColor',[1, 0, 0],'EdgeColor',[1, 0, 0]);\n\n% taking negative gradient of V and finding symbolic equations for Ex, Ey and Ez\n\n% now substituting all the values of the 2D coordinate system for the symbolic x and y variables to get numeric values for Ex and Ey\nEy1 = subs(g(2), [x y z], {0,Y1,Z1});\nEz1 = subs(g(3), [x y z], {0,Y1,Z1});\n\nE1 = sqrt(Ey1.^2 + Ez1.^2); % full numeric magnitude of E in y-z plane\n\nEynorm1 = Ey1./E1; % This normalizes the electric field lines\nEznorm1 = Ez1./E1;\n\nquiver(Y1,Z1,Eynorm1,Eznorm1);\nhold off\n\n\n### Version 2 (using sum):\n\nsyms x y z\nR = 2; % radius of circle is 2 meters\nN=100;\ndphi = 2*pi/N; % discretizing the circular line of charge which spans 2pi\n\nphiprime = 0:dphi:2*pi; %phiprime ranges from 0 to 2pi in increments of dphi\n\nintegrand = dphi./(sqrt(((x - R.*cos(phiprime) )).^2 + ((y - R.*sin(phiprime) ).^2) + z.^2));\n\nphiprime = 0:dphi:2*pi;\nintgrl = sum(integrand); % Riemann sum performed here\n\neps0 = 8.854e-12;\nkC = 1/(4*pi*eps0);\nrhol = 1e-9; % linear charge density\n\nVtot = kC*rhol*R.*intgrl; % symbolic expression for Vtot\n\n%%\n[Y1, Z1] = meshgrid(-4:.5:4,-4:.5:4);\nVcont1 = subs(Vtot, [x,y,z], {0,Y1,Z1});\n\ncontour(Y1,Z1,Vcont1)\nxlabel('y - axis [m]')\nylabel('z - axis [m]')\ntitle('V in a plane perpedicular to a ring of charge (N = 100)')\nstr = {'Red line is side view', 'of ring of charge'};\ntext(-1,2,str)\n\nhold on\ncircle = rectangle('Position',[-2 0 4 .1],'Curvature',[1,1]); % visually displaying ring of charge on plot\nset(circle,'FaceColor',[1, 0, 0],'EdgeColor',[1, 0, 0]);\n\ng = gradient(-1.*(kC*rhol*R.*intgrl),[x,y,z]); % taking negative gradient of V and finding symbolic equations for Ex, Ey and Ez\n\n% substituting all the values of the 2D coordinate system for the symbolic x and y variables to get numeric values for Ex and Ey because the gradient command doesn't accept symbolic arguments\nEy1 = subs(g(2), [x y z], {0,Y1,Z1});\nEz1 = subs(g(3), [x y z], {0,Y1,Z1});\n\nE1 = sqrt(Ey1.^2 + Ez1.^2); % full numeric magnitude of E in y-z plane\n\nEynorm1 = Ey1./E1; % This normalizes the electric field lines\nEznorm1 = Ez1./E1;\n\nquiver(Y1,Z1,Eynorm1,Eznorm1);\nhold off\n\n\nBoth versions of code produce the following graphs:", null, "Note: the picture above this text should have the axes be $$y$$ and $$z$$ like the picture below, not $$x$$ and $$y$$. Also, the title of the picture below this text should be \"$$E$$ in the plane...\" not $$V$$.", null, "As you can see, the vector field is correct while the contour plot seems to use only a few points around the ends of the ring and connect them with straight lines in a strange diamond shape. I can't get it to fill space.\n\nAs for my derivation of the formula for $$V$$, it is here:", null, "• $$s$$ is the radial distance\n• $$\\phi$$ is the azimuthal angle\n• An arbitrary point $$P(x,y,z)$$ has no superscript while the prime notation is used to identify a point on the ring of charge ($$\\phi^\\prime$$, $$x^\\prime$$, etc)\n• cursive $$r$$ indicates relative distance from a point on the ring to $$P(x,y,z)$$\n• $$R$$ is the radius of the ring, I chose 2 meters\n• $$\\mathrm{d}s = R \\mathrm{d}\\phi$$ is a small amount of arc length\n\nYou don't need symbolic variables to compute the approximated potential for your Riemann sums. You can just use meshgrid to evaluate the potential in each point of interest. For the electric field, you can just compute the derivative analytically and then repeat the process for each component or compute a numerical gradient with gradient.\n\nThere are better ways to approximate the integral than just assume that you have straight segments with uniform charge distribution, but they are conceptually similar to this procedure.\n\nThe following snippet computes what you want without using symbolic variables.\n\n%% Parameters\nR = 2.0;\nk = 1.0;\ncharge_density = 1.0;\nndiv_ring = 100;\nndiv_x = 50;\nndiv_y = 100;\nndiv_z = 100;\n\n%% Computation\nphi = linspace(0, 2*pi, ndiv_ring);\ndphi = 2*pi/(ndiv_ring - 1);\nx_ring = R*cos(phi);\ny_ring = R*sin(phi);\nx = linspace(0, 4, ndiv_x);\ny = linspace(-4, 4, ndiv_y);\nz = linspace(-4, 4, ndiv_z);\n[X, Y, Z] = meshgrid(x, y, z);\nV = zeros(size(X));\nfor cont = 1:ndiv_ring\nRx = X - R*cos(phi(cont));\nRy = Y - R*sin(phi(cont));\nRmag = sqrt(Rx.^2 + Ry.^2 + Z.^2);\nV = V + dphi/Rmag;\nend\nV = k*R*charge_density*V;\n\nhx = x(2) - x(1);\nhy = y(2) - y(1);\nhz = z(2) - z(1);\n[Ex, Ey, Ez] = gradient(-V, hx, hy, hz);\n\n%% Visualization\nlevels = 5;\nisovalues = linspace(2, 9, levels);\nfor cont = 1:levels\n[faces, verts, colors] = isosurface(X, Y, Z, V, isovalues(cont), V);\np = patch('Vertices', verts, 'Faces', faces, 'FaceVertexCData',...\ncolors, 'FaceColor','interp','EdgeColor','interp');\nisonormals(X, Y, Z, V, p)\np.EdgeColor = 'none';\np.FaceAlpha = 0.4;\nend\ndaspect([1 1 1])\nview(3);\naxis vis3d\ncamlight\nlighting gouraud\n\n\nThe visualization part generate isosurfaces that are the equivalent to isocontours for 3D data. The resulting image should look like the following.", null, "• I know it's been a long time since we chatted and you may have forgotten by now but I just wanted to say thank for posting the code. I didn't realize you could calculate the numerical gradient at specified divisions. I really appreciate it. Unfortunately had some personal stuff come up in my life and had to take some time off. This code is VERY efficient. You've helped a lot. It took me a while just to understand how the code worked. Thanks! – Andrew Aug 10 at 0:00\n• @Andrew, I'm glad that it was useful to you. You can accept the answer if it solves your problem. – nicoguaro Aug 10 at 0:04\n\nI received a solution to this question from MATLAB's community.\n\nEssentially, I need to specify which contour lines to plot using the 'levels' spot on the 'contour()' command.\n\nLevels allows you to not only choose how many but which lines to plot. If you define a vector such as\n\nvlevel = linspace(20, 65, 10);\n\n\nand then place it in the 'levels' spot of contour:\n\ncontour(Y1,Z1,Vcont1,vlevel)\n\n\nNow the contour command will only plot 10 evenly spaced lines starting at the 20th line and ending at the 65th line (arbitrary parameters which you may choose based on your needs).\n\nMy contour plot now looks like:", null, "Which is really beautiful imo. I should add that I increased my plot to show 15 lines between the 20th and the 60th so my image is not exactly representative of my example." ]
[ null, "https://i.stack.imgur.com/lDItd.jpg", null, "https://i.stack.imgur.com/3nNf1.jpg", null, "https://i.stack.imgur.com/pqBPS.png", null, "https://i.stack.imgur.com/wOsC3.png", null, "https://i.stack.imgur.com/ndtTT.png", null ]
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https://answers.everydaycalculation.com/simplify-fraction/366-180
[ "Solutions by everydaycalculation.com\n\n## Reduce 366/180 to lowest terms\n\nThe simplest form of 366/180 is 61/30.\n\n#### Steps to simplifying fractions\n\n1. Find the GCD (or HCF) of numerator and denominator\nGCD of 366 and 180 is 6\n2. Divide both the numerator and denominator by the GCD\n366 ÷ 6/180 ÷ 6\n3. Reduced fraction: 61/30\nTherefore, 366/180 simplified to lowest terms is 61/30.\n\nMathStep (Works offline)", null, "Download our mobile app and learn to work with fractions in your own time:" ]
[ null, "https://answers.everydaycalculation.com/mathstep-app-icon.png", null ]
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https://mathoverflow.net/questions/324824/how-to-efficiently-sample-uniformly-from-the-set-of-p-equipartitions-of-an-n
[ "# How to efficiently sample uniformly from the set of $p$-equipartitions of an $n$-set?\n\nI have a question related to this one. For $$n,p \\in \\mathbb{N}_+$$ such that $$p\\mid n$$, let $$\\mathcal{P}^{\\rm eq}$$ be the set of all equipartitions of $$n$$ in $$p$$ sets; i.e., in sets of equal size $$\\frac{n}{p}$$.\n\nIs it known how to sample efficiently (i.e., in time polynomial in $$n,p$$) from the uniform distribution on $$\\mathcal{P}^{\\rm eq}$$?\n\nEdit: I had forgotten a key part: can this be done using the optimal (up to constant factors) number of random bits, i.e., $$O(n\\log p)$$ uniformly random bits?\n\nRandomly permute $$n$$ and then divide into blocks of size $$n/p$$.\n• OK, that was dumb of me, I forgot the condition on the number of random bits (i.e., using only $O(n \\log p)$ uniformly random bits). I know it's frowned upon to so I will ask: do you mind if I edit my question to add said condition? If you do, I'll accept your answer and ask another one. – Clement C. Mar 7 at 2:57" ]
[ null ]
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https://discuss.hashicorp.com/t/issues-with-dynamic-block-in-a-nested-block/25193
[ "", null, "# Issues with dynamic block in a nested block\n\nI am looking to use the google_os_config_guest_policies resource and am having issues with being able to pass in values to the nested block of code for `package_repositories`.\n\nhttps://registry.terraform.io/providers/hashicorp/google/latest/docs/resources/os_config_guest_policies\n\nChild module main.tf\n\n``````package_repositories {\ndynamic \"apt\" {\nfor_each = var.apt\ncontent {\narchive_type = lookup(apt.value, \"archive_type\", \"abc\")\nuri = lookup(apt.value, \"uri\", \"abc\")\ndistribution = lookup(apt.value, \"distribution\", null)\ncomponents = lookup(apt.value, \"components\", null)\ngpg_key = lookup(apt.value, \"gpg_key\", null)\n}\n}\n}\n``````\n\nVariables.tf\n\n``````variable \"apt\" {\ndescription = \"Variable used for the APT block supported in the package_repositories variable. Pass in variables for apt_archive_type, apt_components, apt_distribution, apt_uri, apt_gpg_key.\"\ntype = any\ndefault = []\n}\n``````\n\nterraform.tfvars\n\n``````apt = [\n{\narchive_type = \"DEB\"\nuri = \"https://packages.cloud.google.com/apt\"\ndistribution = \"cloud-sdk-stretch\"\ncomponents = [\"main\"]\n}\n]\n``````\n\nWhenever I try to pass in values from my tfvars I only get a blank `package_repositories` map passed in during my `terraform plan` step.\n\n``````+ package_repositories { }\n``````\n\nI have tried to remove the dynamic block and statically define the values for`package_repositories` which worked without any issues.\n\n``````package_repositories {\napt {\narchive_type = \"DEB\"\nuri = \"https://packages.cloud.google.com/apt\"\ndistribution = \"cloud-sdk-stretch\"\ncomponents = [\"main\"]\n}\n}\n``````\n\nIf I try to rework my code to use the dynamic `apt` block it would try to pass in `null` values. Is there something wrong with syntax or is this due to being a beta resource where the dynamic block isn’t working?\n\nHi @rk92,\n\nThis should work as expected with current versions of terraform and the provider. What versions are you using here?\n\n1 Like\n\n@jbardin Sorry, forgot to update that I resolved this. In my parent module’s main.tf I did not include an input field for `apt = var.apt` so the tfvar value was not being used which is why I had an empty list as an output during my plan step.\n\nI am now trying this out where `package_repositories` uses a dynamic block along with `apt` but can’t seem to get the syntax correct to reference the proper attributes. The resource example looks like each `package_repositories` needs its own set block.\n\n``````package_repositories {\napt {\nuri = \"https://packages.cloud.google.com/apt\"\narchive_type = \"DEB\"\ndistribution = \"cloud-sdk-stretch\"\ncomponents = [\"main\"]\n}\n}\n\npackage_repositories {\nyum {\nid = \"google-cloud-sdk\"\ndisplay_name = \"Google Cloud SDK\"\nbase_url = \"https://packages.cloud.google.com/yum/repos/cloud-sdk-el7-x86_64\"\ngpg_keys = [\"https://packages.cloud.google.com/yum/doc/yum-key.gpg\", \"https://packages.cloud.google.com/yum/doc/rpm-package-key.gpg\"]\n}\n}\n``````\n\nChild module main.tf\n\n`````` dynamic \"package_repositories\" {\nfor_each = var.package_repositories\ncontent {\napt {\narchive_type = package_repositories.value[\"archive_type\"]\nuri = package_repositories.value[\"uri\"]\ndistribution = package_repositories.value[\"distribution\"]\ncomponents = package_repositories.value[\"components\"]\ngpg_key = package_repositories.value[\"gpg_key\"]\n}\n}\n}\n``````\n\n.tfvars\n\n``````package_repositories = [{\napt = [\n{\narchive_type = \"DEB\"\nuri = \"https://packages.cloud.google.com/apt\"\ndistribution = \"cloud-sdk-stretch\"\ncomponents = [\"main\"]\ngpg_key = \"https://packages.cloud.google.com/apt/doc/apt-key.gpg.asc\"\n}\n]\n}\n]\n``````\n\nThe variable for `package_repositories` is setup as a type of `any` for now. Is there a cleaner way to approach this? Especially with the amount of lists and maps to put into the tfvars file? Does `apt` need it’s own dynamic block?\n\nYou can hard-code the nested blocks if they do not change, but if you want to be able to conditionally add them based on the given parameters, you will need to use nested dynamic blocks here.\n\n`````` dynamic \"package_repositories\" {\nfor_each = var.package_repositories\niterator = repo\ncontent {\ndynamic \"apt\" {\nfor_each = lookup(repo.value, \"apt\", [])\ncontent {\narchive_type = apt.value[\"archive_type\"]\nuri = apt.value[\"uri\"]\ndistribution = apt.value[\"distribution\"]\ncomponents = apt.value[\"components\"]\ngpg_key = apt.value[\"gpg_key\"]\n}\n}\n}\n}\n``````\n1 Like\n\nI keep getting an error about terraform expecting a comma. I didn’t explicitly use an `iterator` like you did.\n\n`````` on terraform.tfvars line 152:\n151: apt = [\n152: archive_type = \"DEB\"\n\nExpected a comma to mark the beginning of the next item.\n``````\n\nmain.tf\n\n`````` dynamic \"package_repositories\" {\nfor_each = var.package_repositories\ncontent {\ndynamic \"apt\" {\nfor_each = lookup(package_repositories.value, \"apt\", [])\ncontent {\narchive_type = apt.value[\"archive_type\"]\nuri = apt.value[\"uri\"]\ndistribution = apt.value[\"distribution\"]\ncomponents = apt.value[\"components\"]\ngpg_key = apt.value[\"gpg_key\"]\n}\n}\n}\n}\n``````\n\n.tfvars\n\n``````package_repositories = [{\napt = [\narchive_type = \"DEB\"\nuri = \"https://packages.cloud.google.com/apt\"\ndistribution = \"cloud-sdk-stretch\"\ncomponents = [\"main\"]\ngpg_key = \"https://packages.cloud.google.com/apt/doc/apt-key.gpg.asc\"\n]\n}\n]\n``````\n\nMy understanding of how this is setup is that the first `for_each` iterates over the first element out of the `tfvar` so in this case something like `{ apt = [] }` then the second `for_each` is used to iterate over the lookup output from `package_repositories.value` map and the map it’s using should be `{ apt = [] }` correct? Key in this case is `apt` so it should pull values from `apt = []`. Then set values in `content` based on the temporary iterator variable `apt.value[<INPUT_FIELD>]`. Just trying to make sense of this because dynamic blocks have confused me for a while.\n\nThe error is pointing to a syntax error in the tfvars file, not the dynamic block. You are missing the `{}` characters around the map in the `apt` list.\n\n1 Like\n\nThanks, that worked.\n\nCurrently I have my setup as\n\n`````` dynamic \"package_repositories\" {\nfor_each = var.package_repositories\ncontent {\ndynamic \"apt\" {\nfor_each = lookup(package_repositories.value, \"apt\", [])\ncontent {\narchive_type = apt.value[\"archive_type\"]\nuri = apt.value[\"uri\"]\ndistribution = apt.value[\"distribution\"]\ncomponents = apt.value[\"components\"]\ngpg_key = apt.value[\"gpg_key\"]\n}\n}\ndynamic \"yum\" {\nfor_each = lookup(package_repositories.value, \"yum\", null)\ncontent {\nid = yum.value[\"id\"]\ndisplay_name = yum.value[\"display_name\"]\nbase_url = yum.value[\"base_url\"]\ngpg_keys = yum.value[\"gpg_keys\"]\n}\n}\n}\n}\n``````\n\nvariables.tf\n\n`````` type = list(object({\napt = list(object({\narchive_type = string\nuri = string\ndistribution = string\ncomponents = list(string)\ngpg_key = string\n}))\nyum = list(object({\nid = string\ndisplay_name = string\nbase_url = string\ngpg_keys = list(string)\n}))\n}))\ndefault = []\n}\n``````\n\nI receive an error about `The given value is not valid for variable \"package_repositories\": element 0: attribute \"yum\" is required.`\n\nWhat I’d like to have is my variable for `package_repositories` be descriptive enough to explain what is expected when others use it but ideally you would only need to use `apt` or `yum` and not both.\n\nThe `lookup` statement to pass in either `[]` or `null` makes sense but it seems like the variable requires `yum` if it is not declared in my tfvars.\n\n.tfvars\n\n``````package_repositories = [\n{\napt = [{\narchive_type = \"DEB\"\nuri = \"https://packages.cloud.google.com/apt\"\ndistribution = \"cloud-sdk-stretch\"\ncomponents = [\"main\"]\ngpg_key = \"https://packages.cloud.google.com/apt/doc/apt-key.gpg.asc\"\n}]\n},\n{\napt = [{\narchive_type = \"DEB_SRC\"\nuri = \"https://packages.cloud.google.com/apt\"\ndistribution = \"cloud-sdk-stretch\"\ncomponents = [\"main\"]\ngpg_key = \"https://packages.cloud.google.com/apt/doc/apt-key.gpg.asc\"\n}]\n}\n]\n``````\n\nThis is what I’m looking for, but it seems like it wouldn’t work with 0.13.5.\n\nAs a workaround what is a good way to setup a variable such as above so that people could know how to use it?\n\nEven with current version, optional attributes are still experimental, so I would not recommend using them in production. Besides leaving the value types to be inferred, and documenting how they should be used, you could try creating separate input variables for each possible repository type, which can default to null.\n\nMakes sense with using documentation + placeholder variables. Thanks for all the help." ]
[ null, "https://aws1.discourse-cdn.com/hashicorp/original/1X/668e19cbc79e3eaa176133c3679dc30aa57ba474.svg", null ]
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https://projecteuclid.org/journals/advances-in-differential-equations/volume-15/issue-9_2f_10/Some-quasi-linear-elliptic-equations-with-inhomogeneous-generalized-Robin-boundary/ade/1355854615.full
[ "Translator Disclaimer\nSeptember/October 2010 Some quasi-linear elliptic equations with inhomogeneous generalized Robin boundary conditions on \"bad\" domains\nMarkus Biegert, Mahamadi Warma\nAdv. Differential Equations 15(9/10): 893-924 (September/October 2010).\n\n## Abstract\n\nLet $p\\in[2,N)$, ${\\Omega}\\subset{\\mathbb{R}}^N$ an open set and let $\\mu$ be a Borel measure on ${\\partial\\Omega}$. Under some assumptions on ${\\Omega},\\mu,f,g$ and $\\beta$, we show that the quasi-linear elliptic equation with nonlinear inhomogeneous Robin-type boundary conditions $\\begin{cases} -\\Delta_pu+c(x)|u|^{p-2}u=f \\;& \\text{ in }{\\Omega} \\\\ d{\\operatorname{\\mathsf N}}_p(u) + \\beta(x,u)d\\mu =gd\\mu \\;& \\text{ on }{\\partial\\Omega} \\end{cases}$ has a unique weak solution which is globally bounded on ${\\overline{\\Omega}};$ that is, the weak solution $u$ is in $L^\\infty({\\Omega})$ and its trace $u|_{{\\partial\\Omega}}$ belongs to $L^\\infty({\\partial\\Omega},\\mu)$. Here ${\\operatorname{\\mathsf N}}_p(u)$ is a generalization of the normal derivative for bad domains. When ${\\Omega}$ and $u$ are smooth, then $d{\\operatorname{\\mathsf N}}_p(u)= | \\nabla u | ^{p-2} (\\partial u/\\partial\\nu) d\\sigma$ where $\\sigma$ is the surface measure and $\\nu$ the outer normal to ${\\partial\\Omega}$. A priori estimates for solutions are also obtained.\n\n## Citation\n\nDownload Citation\n\nMarkus Biegert. Mahamadi Warma. \"Some quasi-linear elliptic equations with inhomogeneous generalized Robin boundary conditions on \"bad\" domains.\" Adv. Differential Equations 15 (9/10) 893 - 924, September/October 2010.\n\n## Information\n\nPublished: September/October 2010\nFirst available in Project Euclid: 18 December 2012\n\nzbMATH: 1203.35109\nMathSciNet: MR2677423\n\nSubjects:\nPrimary: 35B45, 35D10, 35J60, 35J65\n\nRights: Copyright © 2010 Khayyam Publishing, Inc.\n\nJOURNAL ARTICLE\n32 PAGES", null, "SHARE\nVol.15 • No. 9/10 • September/October 2010", null, "" ]
[ null, "https://projecteuclid.org/Content/themes/SPIEImages/Share_black_icon.png", null, "https://projecteuclid.org/images/journals/cover_ade.jpg", null ]
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https://discussions.unity.com/t/making-a-moving-rorschach-using-perlin-noise/162957
[ "# Making a moving Rorschach using perlin noise\n\nHi I was wondering how I could make it so a Texture 2D being made by perlin noise so that it is densest near the middle and thins out toward the edges?\nHere is a picture of what its like now.\n\nalso how could I make the colors sharper?\n\nIve been trying to do this but how would I modify the amount of perlin?\n\nHere is a very basic example for modifying the amount of noise applied to a texture using a square-border method. If the pixel coordinate is within a border, the perlin value is modified based on its distance from the edge i.e. closer to the edge, apply less perlin.\n\nBasically you calculate a modifier that is a percentage between the position and the border.\n\n``````if pos < border, percentage = pos / border\nif pos > size - border, percentage = ( border - ( pos - ( size - border ) ) ) / border\n``````\n\nIn a new scene, attach the script to an empty gameObject. Create a plane, drag the plane into myRenderer. Hit Play. While running, change the value of border in the inspector, then left-click in the scene to see the result.\n\n``````using UnityEngine;\nusing System.Collections;\n\n{\npublic Renderer myRenderer;\n\npublic int size = 512;\npublic int border = 64;\npublic float perlinScale = 12.34f;\n\nvoid Start()\n{\nGenerateTexture();\n}\n\nvoid Update()\n{\nif ( Input.GetMouseButtonDown( 0 ) )\n{\nGenerateTexture();\n}\n}\n\nvoid GenerateTexture()\n{\nif ( border * 2 > size )\nborder = size / 2;\nif ( border < 0 )\nborder = 0;\n\nColor[] textureColours = new Color[ size * size ];\n\nfor ( int y = 0; y < size; y++ )\n{\nfor ( int x = 0; x < size; x++ )\n{\nfloat modifier = 1f;\n\nif ( x < border )\n{\nmodifier *= CalculatePercentage( x );\n}\nelse if ( x > size - border )\n{\nmodifier *= CalculatePercentage( border - ( x - ( size - border ) ) );\n}\n\nif ( y < border )\n{\nmodifier *= CalculatePercentage( y );\n}\nelse if ( y > size - border )\n{\nmodifier *= CalculatePercentage( border - ( y - ( size - border ) ) );\n}\n\nfloat perlinValue = EvaluatePerlinNoise( x, y );\nperlinValue *= modifier;\n\ntextureColours[ (y * size) + x ] = GetColour( perlinValue );\n}\n}\n\nTexture2D texture = new Texture2D( size, size );\ntexture.SetPixels( textureColours );\ntexture.Apply();\n\nif ( myRenderer )\n{\nmyRenderer.material.mainTexture = texture;\n}\n}\n\nfloat CalculatePercentage( int offset )\n{\nreturn (float)offset / (float)border;\n}\n\nfloat EvaluatePerlinNoise( int x, int y )\n{\nreturn Mathf.PerlinNoise(\n( (float)x / (float)size ) * perlinScale,\n( (float)y / (float)size ) * perlinScale\n);\n}\n\nColor GetColour( float val )\n{\nreturn new Color( val, val, val );\n}\n}\n``````" ]
[ null ]
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https://www.mometrix.com/academy/mass-weight-volume-density-and-specific-gravity/
[ "# Mass, Weight, Volume, Density, and Specific Gravity\n\n## Mass, Weight, Volume, Density, and Specific Gravity\n\nHey guys! Welcome to this video on Mass, Weight, Volume, Density, and Specific Gravity.\n\nIf you are wondering, “why on earth are you doing all of this in one video? This is so much information.”\n\nYes, It is a lot of big topics jammed into one video, but if you want a really in depth understanding of each, you can check out our individual video by searching the topic followed by Mometrix.\n\nIn this video, I want to focus on what each of these are and how each of these are different. Mass, weight, volume, and specific gravity get misused quite often.\n\nSo, let’s take a closer look. What I’ll do is walk through the definition of each, and then we will go back through and clear up some confusions that lead to these getting misused with one another.\n\nMass. Mass is the measure of the amount of matter. It is approximately the measure of the number of atoms in a given object. Mass is also the measure of an object’s resistance to gravity. The Kilogram is the basic SI unit of mass.\n\nWeight. Weight is a force that is caused by the gravitational pull of the earth towards its surface. The basic SI unit for weight is a newton.\n\nWeight, and mass are the two that most often get confused with one another, but we will get back to that.\n\nVolume. Volume is a measure of the amount of three-dimensional space that is being occupied by a liquid, solid, or a gas. The basic SI unit for volume is cubic meter (m^3).\n\nDensity. Density refers to the measurements of how compact an object is.\n\nSpecific Gravity. Specific gravity is in direct relationship with density. It is the ratio of an object’s density, and its contact substance. For example, if you want to place an object in water, the specific gravity would tell you if it would float or not.\n\nAlright, we’ve just looked at the definition for each, but let’s go back through and see how they are related to one another.\n\nSo, we started with mass. For an object to have a weight, volume, density, or to find the specific gravity, it has to have mass. Or else we have nothing and this would all be pointless.\n\nSo, every object has mass. The next thing we would move to is the weight of an object. Every object with mass, will also have weight due to gravity from the earth pulling that object towards its surface. In order to find the weight of an object, you would just multiply the mass of the object times gravity. Something else to keep in mind about weight and mass is that mass doesn’t change unless that object loses matter. However, the weight of an object with the same mass can change depending on where it is. Like the moon for instance; if I go to the moon I will weigh less due to the lesser gravity, but I will still have the same mass.\n\nNow, let’s move on to volume. We’ve already defined it. We’ve said that volume is the measure of space within an object. But how can we find volume. Well, all three dimensional objects are going to have height, length, and depth. So, to find the amount of space within these three dimensions, we multiply those three dimensions together. The result will tell us the amount of space within that object.\n\nDensity is directly related to the mass and the volume. In fact it, tells us of the exact relationship between the two. To find an object’s density, we take its mass and divide it by its volume. If the mass has a large volume, but a small mass it would be said to have a low density.\n\nThis would let us know that an object’s matter is not very compact, but rather more spaced out.\n\nIf the object was low in volume, but high in mass, then it would have a high density. This would tell us that the object’s matter is very compact within it.\n\nThis brings us to specific gravity. Again, specific gravity tells us the relationship between the density of an object, and the contact substance. The contact substance is most often water. So, to find the specific gravity we would take the density of an object, and divide it by the density of water. If the specific gravity is greater than one, then we know that the object will sink. If the specific gravity is less than one, then we know that the object will float on water. This is because the density of water has to be greater than the density of the object.\n\nI hope that this video over mass, weight, volume, density, and specific gravity helped to give you better understanding of the way in which they relate to one another.\n\nIf you enjoyed this video then be sure to give us a thumbs up, and subscribe to our channel for further videos!\n\nSee you guys next time.\n\n104567920570" ]
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https://devenum.com/how-to-multiply-numpy-array-np-multiply/
[ "# How to Multiply NumPy array | np.Multiply\n\nIn this post, we are going to learn about how to Multiply NumPy array. We are going to learn this with the help of many examples. To run all the below programs the Numpy library must be installed on the system and if the numpy library is installed on our system we can import it into our program. By the end of this post, you will be able to answer the below questions.\n\n• NumPy Program to Multiply 2 Scaler numbers\n• NumPy Program to linear or 1-D Numpy Array\n• NumPy Program to two Multiply multi-dimensional Array\n• How to do element wise multiplication in numpy.\n\n### Numpy Multiply() function\n\nIn the python Numpy library, we have multiply() function that is used to do the element-wise multiplication of two arrays.\n\n#### Syntax\n\n```numpy.multiply(arr1, arr2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) = <ufunc 'multiply'>\n```\n\n### 1. NumPy Program to Multiply 2 Scaler numbers\n\nIn this python program, we are using the np.multiply() function to multiply two scalar numbers by simply passing the scalar numbers as an argument to np.multiply() function.\n\n```import numpy as np\nnum1 = 5\nnum2 = 4\n\nproduct = np.multiply(num1, num2)\nprint (\"Multiplication Result is : \", product)\n\n```\n\nOutput\n\n```Multiplication Result is : 20\n```\n\n### 2. NumPy Program to linear 1D Numpy Array\n\nIn this python program, we have used np.multiply() function to multiply two 1D numpy arrays by simply passing the arrays as arguments to np.multiply() function. This is how to multiply two linear arrays using np. multiply() function.\n\n```import numpy as np\narr1 = np.array([1, 2, 3, 4, 5] )\narr2 = np.array([5, 4, 3, 2, 1] )\n\nprint (\"1st Input array : \", arr1)\nprint (\"2nd Input array : \", arr2)\n\nproduct = np.multiply(arr1, arr2)\nprint (\"Multiplication Result of 2D array is : \", product)\n\n```\n\nOutput\n\n```1st Input array : [1 2 3 4 5]\n2nd Input array : [5 4 3 2 1]\nMultiplication Result of 2D array is : [5 8 9 8 5]\n\n```\n\n### 3. NumPy Program to Multiply multi-dimensional Numpy Array\n\nIn this python program example, we have used np. multiply() function to multiple 2D or multiply multi-dimensional Numpy Array\n\n```import numpy as np\narr1 = np.array([[1, 2, 3], [4, 5, 6]])\narr2 = np.array([[6, 5, 4], [3, 2, 1]])\n\nprint (\"1st Input array : \", arr1)\nprint (\"2nd Input array : \", arr2)\n\nproduct = np.multiply(arr1, arr2)\nprint (\"Multiplication Result of 2D array is : \", product)\n\n```\n\nOutput\n\n```1st Input array : [[1 2 3]\n[4 5 6]]\n2nd Input array : [[6 5 4]\n[3\n2 1]]\nMultiplication Result of 2D array is : [[ 6 10 12]\n[12 10 6]]\n\n```\n\n### 4.Multiply Two Numpy Arrays With Different Shapes?\n\nWe can not multiply Two Numpy Arrays With Different Shapes by using multiply() function. If you will try to do this then it will give you an error like this:ValueError: operands could not be broadcast together with shapes (2,3) (2,).\n\n### 5.How to do element wise multiplication in numpy\n\nIn this python program example, we are doing element-wise mutiplication of numpy arrays.\n\n```import numpy as np\narr1 = np.array([[1, 2, 3], [4, 5, 6]])\narr2 = np.array([[6, 5, 4], [3, 2, 1]])\n\nprint (\"1st Input array : \", arr1)\nprint (\"2nd Input array : \", arr2)\n\nproduct = np.multiply(arr1, arr2)\nprint (\"element wise mutiplication of numpy array : \", product)\n```\n\nOutput\n\n``` [4 5 6]]\n2nd Input array : [[6 5 4]\n[3 2 1]]\nelement wise mutiplication of numpy array : [[ 6 10 12]\n[12 10 6]]\n```" ]
[ null ]
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https://www.numerade.com/questions/an-electron-has-a-speed-of-0750c-a-find-the-speed-of-a-proton-that-has-the-same-kinetic-energy-as-th/
[ "Gravitation\n\n### Discussion\n\nYou must be signed in to discuss.\n##### Top Physics 101 Mechanics Educators\nLB", null, "##### Marshall S.\n\nUniversity of Washington", null, "", null, "Lectures\n\nJoin Bootcamp\n\n### Video Transcript\n\nWell, according to given problem uh, kinetic energy electron is equal to Connecticut Energy of Proton. Let's plug in the values. Oh, kinetic energy Electron e's M E time C square M is the most of electrons. His the speed of light into latticed ick factor for electron minus one is equal to moss of proton Time C square into relativistic factor for proton minus want Well, In this case, we have M E square, which is equal to 0.511 mega electron Walt. And also we have MP time see scare and it's equal to 9 28 1,000,000 electron Walt. A leftist ick factor for electron is equal to one minus, uh, 0.7 Zito Hold square on then we have square root and solving this We get 1.5 119119 This through logistic factor for electron and no lamest ick factor for baton is equal to, uh, one place mass of electron times Cease creator into our logistic factor of electron minus one divided by ah muscle proton Time C square and let's plug in the values One place most of electron time. C square is 0.511 1,000,000 Electron won't into well, relentless tick factor for electron 1.5 119 minus one divided by 9 38 and therefore latticed ick factor for the tall is equal to 1.0 279 279 But ah, logistic factor we're put on is equal to one divided by r squared Rudolph one minus. We lost your proton squared divided by C suite and solving for Have you lost your proton? We can't see into square root off one minus our latest ick factor for proton minus ah two holes here and therefore we lost. Your proton is equal to zero point zero to tree six times the speed of light.", null, "#### Topics\n\nGravitation\n\n##### Top Physics 101 Mechanics Educators\nLB", null, "##### Marshall S.\n\nUniversity of Washington", null, "", null, "Lectures\n\nJoin Bootcamp" ]
[ null, "https://d1ras9cbx5uamo.cloudfront.net/eyJidWNrZXQiOiAiY29tLm51bWVyYWRlIiwgImtleSI6ICJpbnN0cnVjdG9ycy82ZWYzZGU5MmRhNTk0YTM1YjJjNWY1ZjVkMjAwZmYxZC5qcGciLCAiZWRpdHMiOiB7InJlc2l6ZSI6IHsid2lkdGgiOiAyNTYsICJoZWlnaHQiOiAyNTZ9fX0=", null, "https://d1ras9cbx5uamo.cloudfront.net/eyJidWNrZXQiOiAiY29tLm51bWVyYWRlIiwgImtleSI6ICJpbnN0cnVjdG9ycy8xMTNhYmFjZTJlMzc0MGExOWMwYmIxMGVhMjBiNmYwMC5qcGciLCAiZWRpdHMiOiB7InJlc2l6ZSI6IHsid2lkdGgiOiAyNTYsICJoZWlnaHQiOiAyNTZ9fX0=", null, "https://d1ras9cbx5uamo.cloudfront.net/eyJidWNrZXQiOiAiY29tLm51bWVyYWRlIiwgImtleSI6ICJpbnN0cnVjdG9ycy85ODI2NTRhZDA2ZDM0NmEwOWZmNjNhOWRhYWQ4NDUwYy5qZmlmIiwgImVkaXRzIjogeyJyZXNpemUiOiB7IndpZHRoIjogMjU2LCAiaGVpZ2h0IjogMjU2fX19", null, "https://d1ras9cbx5uamo.cloudfront.net/eyJidWNrZXQiOiAiY29tLm51bWVyYWRlIiwgImtleSI6ICJpbnN0cnVjdG9ycy84MTI2ZTE4Yzg4YWY0ODA0OThjZGZlOGJhYTE2NThlZC5qcGciLCAiZWRpdHMiOiB7InJlc2l6ZSI6IHsid2lkdGgiOiAyNTYsICJoZWlnaHQiOiAyNTZ9fX0=", null, "https://d1ras9cbx5uamo.cloudfront.net/eyJidWNrZXQiOiAiY29tLm51bWVyYWRlIiwgImtleSI6ICJpbnN0cnVjdG9ycy82ZWYzZGU5MmRhNTk0YTM1YjJjNWY1ZjVkMjAwZmYxZC5qcGciLCAiZWRpdHMiOiB7InJlc2l6ZSI6IHsid2lkdGgiOiAyNTYsICJoZWlnaHQiOiAyNTZ9fX0=", null, "https://d1ras9cbx5uamo.cloudfront.net/eyJidWNrZXQiOiAiY29tLm51bWVyYWRlIiwgImtleSI6ICJpbnN0cnVjdG9ycy8xMTNhYmFjZTJlMzc0MGExOWMwYmIxMGVhMjBiNmYwMC5qcGciLCAiZWRpdHMiOiB7InJlc2l6ZSI6IHsid2lkdGgiOiAyNTYsICJoZWlnaHQiOiAyNTZ9fX0=", null, "https://d1ras9cbx5uamo.cloudfront.net/eyJidWNrZXQiOiAiY29tLm51bWVyYWRlIiwgImtleSI6ICJpbnN0cnVjdG9ycy85ODI2NTRhZDA2ZDM0NmEwOWZmNjNhOWRhYWQ4NDUwYy5qZmlmIiwgImVkaXRzIjogeyJyZXNpemUiOiB7IndpZHRoIjogMjU2LCAiaGVpZ2h0IjogMjU2fX19", null ]
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https://amigotutor.com/alberta/principal-component-analysis-example-ppt.php
[ "# Ppt analysis principal component example\n\n## Extracting information from spectral data. SWST\n\nPrincipal component analysis MIT OpenCourseWare. principal components analysis some slides from pca toy example principal component analysis (pca), 15th international conference applications of computer algebra teaching principal components analysis with for example, the calculations are).\n\nOne of the many confusing issues in statistics is the confusion between Principal Component Analysis (PCA) and Factor Analysis (FA). For example, we may not be A real example would be What are the differences between Factor Analysis and Principal Differences between factor analysis and principal component analysis\n\nSignal processing is used to transform spectral data prior to analysis Data pretreatment Principal Component Analysis The sample (n = 18) are In this set of notes, we will develop a method, Principal Components Analysis example of this is if each data point represented a grayscale image,\n\nSlide 1 Principal Components Analysis (PCA) 1 Principal Components Analysis (PCA) a technique for finding patterns in data of high dimension 2 Outline: Eigenvectors to perform principal component analysis. Outline • Variance and covariance • Principal components Covariance examples. Covariance matrix\n\nPrincipal Components Analysis 1. sets with many variables, For example, the score for the rth sample on the kth principal component is calcu-lated as Principal Component Analysis.ppt - Download as Powerpoint Presentation (.ppt), PDF File (.pdf), Text File (.txt) or view presentation slides online.\n\nAn Application of Principal Component Analysis to Stock Portfolio Management Libin Yang Department of Economics and Finance University of Canterbury Summer Institute in Statistical Genetics 2015 1/20. I Principal Components Analysis I Suppose a genetic association study consists of a sample of N\n\nIn this set of notes, we will develop a method, Principal Components Analysis example of this is if each data point represented a grayscale image, Before we even start on Principal Component Analysis, For example, we may select all principal components above a certain threshold of contribution to\n\n1/01/2014 · Principal Component Analysis and Factor Analysis Example https://sites.google.com/site/econometricsacademy/econometrics-models/principal-component-analysis 15th International Conference Applications of Computer Algebra Teaching Principal Components Analysis with for example, the calculations are", null, "Lecture 15 Principal Component Analysis people.duke.edu\n\nPrincipal component analysis MIT OpenCourseWare. a real example would be what are the differences between factor analysis and principal differences between factor analysis and principal component analysis, are explored to enlighten students on how exploratory factor analysis works, an example of how to run an in principal components analysis, the diagonal).", null, "PPT Principal Component Analysis (PCA) PowerPoint\n\nCME Article Biostatistics 302. Principal component and. principal components analysis (pca) examples . principal components of silhouette images powerpoint presentation, biostatistics 302. principal component and factor analysis principal components analysis for the example above we have, y 1 = a 11x).", null, "Pca ppt SlideShare\n\nPrincipal Components Analysis University at Buffalo. principal component analysis geometric picture of principal components (pcs) a sample of n observations in the 2-d space pca.ppt author: frank masci, are explored to enlighten students on how exploratory factor analysis works, an example of how to run an in principal components analysis, the diagonal).", null, "Lecture 22 Multivariate analysis and principal component\n\nPrincipal Component Analysis SlideShare. principal components analysis (pca) examples . principal components of silhouette images powerpoint presentation, principal component analysis: application to statistical process principal component analysis is often considered as table 1.1 is an example of such a).", null, "PPT Principal Component Analysis (PCA) PowerPoint\n\nPrincipal component analysis MIT OpenCourseWare. summer institute in statistical genetics 2015 1/20. i principal components analysis i suppose a genetic association study consists of a sample of n, an application of principal component analysis to stock portfolio management libin yang department of economics and finance university of canterbury).\n\nPrincipal Component Analysis Pca ppt 1. Principal with the highest eigenvalue is the principle component of the data set. In our example, Principal Component Analysis and Factor Analysis. used tool for the first two is principal component analysis not done for the screeplot example.)\n\nSlides used to present an overview on Principal Component Analysis during a analytics group meeting at TWBR. Example of Factor Analysis: the other factor methods can not ; Principle component are use PowerPoint PPT presentation: \"Factor Analysis and Principal\n\nPrincipal Components Analysis. Principal components factor analysis. Obtaining a factor solution through principal components analysis is an iterative process that Principal Components Analysis. Principal components factor analysis. Obtaining a factor solution through principal components analysis is an iterative process that\n\n15th International Conference Applications of Computer Algebra Teaching Principal Components Analysis with for example, the calculations are 8/05/2016 · Exploratory Factor Analysis (Principal Axis Factoring vs. Principal Components Analysis) exploratory factor analysis in SPSS example 01 - Duration:\n\nAn Application of Principal Component Analysis to Stock Portfolio Management Libin Yang Department of Economics and Finance University of Canterbury Principal Component Analysis: Application to Statistical Process Principal component analysis is often considered as Table 1.1 is an example of such a\n\nPrincipal Component Analysis: Application to Statistical Process Principal component analysis is often considered as Table 1.1 is an example of such a Principal Component Analysis Pca ppt 1. Principal with the highest eigenvalue is the principle component of the data set. In our example,", null, "Principal Component Analysis Bioinformatics Graz" ]
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http://peninsulamontejo.com/printable-worksheets-for-grade-6-math/
[ "# Printable Worksheets For Grade 6 Math", null, "Printable Worksheets For Grade 6 Math Sixth Grade Math Worksheets Free Printable K5 Learning Download", null, "Printable Worksheets For Grade 6 Math Mathsphere Free Sample Maths Worksheets Free", null, "Printable Worksheets For Grade 6 Math Mathsphere Free Sample Maths Worksheets Template", null, "Printable Worksheets For Grade 6 Math Grade 6 Fractions Vs Decimals Worksheets Free Printable K5 Template", null, "Printable Worksheets For Grade 6 Math Grade 6 Addition Subtraction Worksheets Free Printable K5 Printable", null, "Printable Worksheets For Grade 6 Math Subtraction Or Mixed Numbers Worksheet For Grade 6 Math Students Templates", null, "Printable Worksheets For Grade 6 Math Mathsphere Free Sample Maths Worksheets Template\n\nPrintable Worksheets For Grade 6 Math printable worksheets for grade 6 math mathsphere free sample maths worksheets free. printable worksheets for grade 6 math mathsphere free sample maths worksheets template. printable worksheets for grade 6 math grade 6 fractions vs decimals worksheets free printable k5 template. printable worksheets for grade 6 math grade 6 addition subtraction worksheets free printable k5 printable. printable worksheets for grade 6 math subtraction or mixed numbers worksheet for grade 6 math students templates.\n\n### Related Post to Printable Worksheets For Grade 6 Math\n\nThis site uses Akismet to reduce spam. Learn how your comment data is processed." ]
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https://ww2.mathworks.cn/help/aeroblks/airframe-trim-and-linearize-with-control-system-toolbox.html
[ "# Airframe Trim and Linearize with Control System Toolbox\n\nThis example shows how to trim and linearize an airframe in the Simulink® environment using Control System Toolbox™.\n\nDesigning an autopilot with classical design techniques requires linear models of the airframe pitch dynamics for several trimmed flight conditions. The MATLAB® technical computing environment can determine the trim conditions and derive linear state-space models directly from the nonlinear model. This step saves time and helps to validate the model. The Control System Toolbox functions allow you to visualize the motion of the airframe in terms of open-loop frequency or time responses.\n\n### Initialize Guidance Model\n\nFind the elevator deflection and the resulting trimmed body rate (q). These calculations generate a given incidence value when the airframe is traveling at a set speed. Once the trim condition is found, a linear model can be derived for the dynamics of the perturbations in the states around the trim condition.\n\n```open_system('aeroblk_guidance_airframe'); ```", null, "### Define State Values\n\nDefine the state values for trimming:\n\n• Height [m]\n\n• Mach Number\n\n• Total Velocity [m/s]\n\n• Initial Pitch Body Rate [rad/sec]\n\n```heightIC = 10000/m2ft; machIC = 3; alphaIC = -10*d2r; thetaIC = 0*d2r; velocityIC = machIC*(340+(295-340)*heightIC/11000); pitchRateIC = 0; ```\n\n### Find Names and Ordering of States\n\nFind the names and the ordering of states from the model.\n\n```[sizes,x0,names]=aeroblk_guidance_airframe([],[],[],'sizes'); state_names = cell(1,numel(names)); for i = 1:numel(names) n = max(strfind(names{i},'/')); state_names{i}=names{i}(n+1:end); end ```\n\n### Specify States\n\nSpecify which states to trim and which states remain fixed.\n\n```fixed_states = [{'U,w'} {'Theta'} {'Position'}]; fixed_derivatives = [{'U,w'} {'q'}]; fixed_outputs = []; fixed_inputs = []; n_states=[];n_deriv=[]; for i = 1:length(fixed_states) n_states=[n_states find(strcmp(fixed_states{i},state_names))]; %#ok<AGROW> end for i = 1:length(fixed_derivatives) n_deriv=[n_deriv find(strcmp(fixed_derivatives{i},state_names))]; %#ok<AGROW> end n_deriv=n_deriv(2:end); % Ignore U ```\n\n### Trim Model\n\nTrim the model.\n\n```[X_trim,U_trim,Y_trim,DX]=trim('aeroblk_guidance_airframe',x0,0,[0 0 velocityIC]', ... n_states,fixed_inputs,fixed_outputs, ... [],n_deriv) %#ok<NOPTS> ```\n```X_trim = 1.0e+03 * -0.0002 0 0.9677 -0.1706 0 -3.0480 U_trim = 0.1362 Y_trim = -0.2160 0.0000 DX = 0 -0.2160 -14.0977 0.0000 967.6649 -170.6254 ```\n\n### Linear Model and Frequency Response\n\nDerive the linear model and view the frequency response.\n\n```[A,B,C,D]=linmod('aeroblk_guidance_airframe',X_trim,U_trim); if exist('control','dir') airframe = ss(A(n_deriv,n_deriv),B(n_deriv,:),C([2 1],n_deriv),D([2 1],:)); set(airframe,'StateName',state_names(n_deriv), ... 'InputName',{'Elevator'}, ... 'OutputName',[{'az'} {'q'}]); zpk(airframe) linearSystemAnalyzer('bode',airframe) end ```\n```ans = From input \"Elevator\" to output... -170.45 s (s+1133) az: ---------------------- (s^2 + 30.04s + 288.9) -194.66 (s+1.475) q: ---------------------- (s^2 + 30.04s + 288.9) Continuous-time zero/pole/gain model. ```", null, "" ]
[ null, "https://ww2.mathworks.cn/help/examples/aeroblks/win64/AirframeTrimAndLinearizeWithControlSystemToolboxExample_01.png", null, "https://ww2.mathworks.cn/help/examples/aeroblks/win64/AirframeTrimAndLinearizeWithControlSystemToolboxExample_02.png", null ]
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https://socratic.org/questions/when-does-water-vapor-in-air-condense
[ "# When does water vapor in air condense?\n\nMar 12, 2016\n\nDepends on the availability of condensation nuclei, but generally at the dew point.\n\n#### Explanation:\n\nFirst of you need to understand that water molecules can be at different energy levels at many temperature. Therefore at any given temperature you can have water molecules of different states. This is because energy is not always distributed evenly between particles. At 0 degrees, the average temperature of the particles is 0 but individual molecules can have more or less energy.\n\nAt a given temperature there is a maximum amount of water vapor the air can hold.", null, "", null, "The red line equals the maximum amount of grams of water a kilogram of air can hold at a given temperature. So if you are adding water to air then once the number of grams per kilogram is reached, any additional water vapor will condense automatically. Conversely, if you have a constant amount of water in the air and you cool it, eventually it will reach a temperature where the amount of water is the maximum. At this point condensation occurs.\n\nThe temperature where the air is holding all the water it can is called the dew point." ]
[ null, "https://useruploads.socratic.org/pTFih6CiQTqtX5XiqqfJ_Relative_Humidity.png", null, "https://useruploads.socratic.org/pTFih6CiQTqtX5XiqqfJ_Relative_Humidity.png", null ]
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https://answers.everydaycalculation.com/multiply-fractions/8-4-times-3-7
[ "Solutions by everydaycalculation.com\n\n## Multiply 8/4 with 3/7\n\n1st number: 2 0/4, 2nd number: 3/7\n\nThis multiplication involving fractions can also be rephrased as \"What is 8/4 of 3/7?\"\n\n8/4 × 3/7 is 6/7.\n\n#### Steps for multiplying fractions\n\n1. Simply multiply the numerators and denominators separately:\n2. 8/4 × 3/7 = 8 × 3/4 × 7 = 24/28\n3. After reducing the fraction, the answer is 6/7\n\nMathStep (Works offline)", null, "Download our mobile app and learn to work with fractions in your own time:" ]
[ null, "https://answers.everydaycalculation.com/mathstep-app-icon.png", null ]
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https://dsp.stackexchange.com/questions/74334/find-symbol-duration-from-symbol-rate
[ "# Find symbol duration from symbol rate\n\nHow can one find symbol duration if bit rate is 100 kbs (as BPSK is used, symbol rate = bit rate)?\n\nThe symbol duration $$T_p$$ is related to the symbol rate $$R_s$$ by the simple relationship $$T_p = \\frac{1}{R_p}$$\nIn the case of BPSK, $$R_p$$ is equal to the bit rate $$R_b$$, and $$T_p = \\frac{1}{R_b}$$\nFor constellations with $$M$$ elements, each symbol encodes $$k = \\log_2(M)$$ bits, the symbol rate is $$R_p = R_b / k$$, and the symbol duration is $$T_p = \\frac{1}{R_p} = \\frac{k}{R_b}$$" ]
[ null ]
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http://www.sarahhaviland.com/gloomhaven-voidwarden-qomyn/area-of-equilateral-and-isosceles-triangle-36cca8
[ "Solution: Filed Under: Mathematics Tagged With: Area of a right triangle, Area Of A Triangle, Area of an equilateral triangle, Area of isosceles triangle, Areas of an Isosceles Triangle and an Equilateral Triangle Problems with Solutions, ICSE Previous Year Question Papers Class 10, Areas of an Isosceles Triangle and an Equilateral Triangle Problems with Solutions, Concise Mathematics Class 10 ICSE Solutions, Concise Chemistry Class 10 ICSE Solutions, Concise Mathematics Class 9 ICSE Solutions, Business Essay | Essay on Business for Students and Children in English, The Glass Castle Essay | Essay on the Glass Castle for Students and Children in English, Personal Identity Essay | Essay on Personal Identity for Students and Children in English, Christopher Columbus Essay | Essay on Christopher Columbus for Students and Children in English, Texting While Driving Essay | Essay on Texting While Driving for Students and Children in English, Plus One Computer Application Improvement Question Paper Say 2018, Fences Essay | Essay on Fences for Students and Children in English, Importance of College Education Essay | Essay on Importance of College Education for Students and Children, Plus One Computer Application Previous Year Question Paper March 2019, Autism Essay | Essay on Autism for Students and Children in English, Plus One Computer Science Improvement Question Paper Say 2018. Half of the rectangle is a right-angled triangle as it can be seen from the figure above. Determine the measure of the base angles. Let's see why the area of a triangle is half of b*h. Draw a triangle whose base is b and height is h, as shown below. K - University grade . In an equiangular triangle, all the angles are equal—each one measures 60 degrees. 1. Don’t assume that if one side of a triangle is, say, twice as long as another side that the angles opposite those sides are also in a 2 : 1 ratio… Special isosceles triangles. (iv) Base = 10 cm and height = 7.5 cm. Isosceles triangle Calculate the perimeter of isosceles triangle with arm length 73 cm and base length of 48 cm. Below is a brief recall about equilateral triangles: There are mainly three types of triangles which are scalene triangles, equilateral triangles and isosceles triangles. Equilateral triangle, isosceles rectangle. Isosceles and Equilateral Triangles Page: Geometry Explore: Vocabulary: Key Concepts/Examples: 1. isosceles triangle: a triangle with two congruent sides; base angles of an isosceles triangle are also congruent; an altitude drawn from the shorter base splits an isosceles triangle into two congruent right triangles. by dbodden. In isosceles and equilateral triangles, the median bisects the angle at the vertex whose two adjacent sides are equal. So for example, if you have an equilateral triangle where each of the sides was 1, then its area would be square root of 3 over 4. 2.9k views. FINDING A PATTERN In the pattern shown, each small triangle is an equilateral triangle with an area of 1 square unit. we can write a = b = c In an acute triangle, all angles are less than right angles—each one is less than 90 degrees. In an isosceles triangle, the equal sides are 2/3 of the length of the base. https://www.wikihow.com/Find-the-Area-of-an-Isosceles-Triangle The area of an equilateral triangle is calculated according to the classical formula of the area of a triangle - the product of half the base of the triangle by its height. Mathematics. Mathematics. Where a is the side length of an equilateral triangle and this is the same for all three sides. Question 3: Find the area of an equilateral triangle whose side is 7 cm. Share practice link. Python Exercise: Check a triangle is equilateral, isosceles or scalene Last update on February 26 2020 08:09:28 (UTC/GMT +8 hours) Python Conditional: Exercise - 36 with Solution. Draw the perpendicular bisector of the equilateral triangle as shown below. … Three congruent inscribed squares in the Calabi triangle. Print; Share; Edit; Delete; Report an issue; Start a multiplayer game. If X, Y, Z are three sides of the triangle. Tetrakis … The ratio of the area of the incircle to the area of an equilateral triangle, π 3 3 {\\displaystyle {\\frac {\\pi }{3{\\sqrt {3}}}}} , is larger than that of any non-equilateral triangle. In equilateral triangles all the sides are equal. ©g t2 H0a1L3 H gK xu NtXaJ gS mojf et Ywha3r 6eQ ELXL3C d. 0 Z rAcl Rl w Rrdidg9h Pt vsJ lr 3eLs Kelr UvEeKd7. Note how the perpendicular bisector breaks down side a into its half or a/2. Area of an equilateral triangle. The median not only bisects the side opposite the vertex, it also bisects the angle of the vertex in case of equilateral and isosceles triangles, provided the adjacent sides are equal as well (which is always true in case of equilateral triangles). Isosceles: means \\\"equal legs\\\", and we have two legs, right? Edit. Where a is the side length of an equilateral triangle and this is the same for all three sides. The formula for the area of an equilateral triangle is given as: Learn more about isosceles triangles, equilateral triangles and scalene triangles here. Then the area of an isosceles triangle formula can be given as – … Side of the equilateral triangle = a = 7 cm, Area of an equilateral triangle = √3 a2/ 4. Let us consider an isosceles triangle whose two equal sides length is ‘a’ unit and length of its base is ’b’ unit. Therefore, the area of the given equilateral triangle is 4√3 cm2. Double the triangle. Play . By definition all sides of an equilateral triangle are equal in length and all angles are equal in degree measure. d. Find the measure of ∠BAE. Where a is the length of a triangle. This is an Equilateral Triangle. Another situation where you can work out isosceles triangle area, is when you know the length of the 2 equal sides, and the size of the angle between them. From the figure let a is the side equal for an isosceles triangle, b is the base and h, is the altitude. Area of an isosceles triangle; Area of an equilateral triangle; Area of a triangle - \"side angle side\" (SAS) method; Area of a triangle - \"side and two angles\" (AAS or ASA) method; Area of a square; Area of a rectangle ; Area of a parallelogram ; Area of a rhombus ; Area of a trapezoid; Area of an isosceles trapezoid; Area of a regular polygon; Area of a circle; Area of a sector of a circle; Area of a … As per formula: Perimeter of the equilateral triangle = 3a, where “a” is the side of the equilateral triangle. Start from the 120-30-30 isosceles triangle. Label the sides. The general formula for the area of triangle is equal to half the product of the base and height of the triangle. Mathematical formula for area of equilateral triangle in programming notation can be written as (sqrt(3) / 4) * (side * side).Where sqrt() is a function used to compute square root. So, the area of an isosceles triangle can be calculated if the length of its side is known. A triangle is equilateral if and only if the circumcenters of any three of the smaller triangles have the same distance from the centroid. Area of Equilateral Triangle. Step 2: Find the area of an equilateral triangle using formula. 1. Answer link. Find the area of an isosceles triangle whose side lengths are 5m and 9m. Find area of triangle ABC We know that Area of triangle = 1/2 × Base × Height Here, Base = BC = b = 4 cm Height = h = AD = ? You can see the table of triangle area formulas .Depending on the type of triangle you may need one element (equilateral triangle), two (base and height) or three (as long as they are not the three angles). Equilateral triangles also called equiangular. Then draw a perpendicular bisector to the base of height “h”. Edit. The area is 10.83 cm 2.. Table of Triangle Area Formulas . Or, Area of Equilateral Triangle = ¼(√3a2). 73% average accuracy. Let us discuss further how to calculate the area, perimeter, and the altitude of an isosceles triangle. A scalene triangle is a triangle that has three unequal sides. Let the base, b = 9 m and a = 5m. Related questions. Equilateral: \\\"equal\\\"-lateral (lateral means side) so they have all equal sides 2. a. Solo Practice . According to the properties of an equilateral triangle, the lengths of an equilateral triangle are the same for all three sides. Now apply the Pythagorean theorem to get the height (h) or the length of the line you see in red . In an equilateral triangle, you will have the 3 sides of equal lengths. C equivalent expression to find area of equilateral triangle - (sqrt(3) / 4) * (side * side) Logic to find area of equilateral triangle. Write a Python program to check a triangle is equilateral, isosceles or scalene. Therefore, area = ½ × base × height We will use this formula to find area of equilateral triangle. Given three integers as X, Y, and Z representing the three sides of a triangle, the task is to check whether the triangle formed by the given sides is equilateral, isosceles, or scalene.. Equilateral Triangle: A triangle is said to be equilateral triangle if all the sides are equal. Now, In an isosceles triangle, Median and altitude are the same So, D is mid-point of BC ∴ BD = DC = 4/2 = 2cm Now, In ∆ADC, right angled at D By Pythagoras theorem, AC 2 = AD 2 + DC 2 Identifying isosceles triangles. : 2. a 2 = (a/2) 2 + h 2 a 2 … sin C) = ½ × b × (c . Step 1: Find the side of an equilateral triangle using perimeter. Area of isosceles triangle = 1/4 x b x √4a²-b². Isosceles triangle Calculate the area of an isosceles triangle, the base of which measures 16 cm and the arms 10 cm. Explain why ABC is isosceles. Solution. Side of the equilateral triangle (a) = 28 cm. 21. ∴ Area of the triangle = ½ × base × height = ½ × 10 cm × 7.5 cm = 5 cm × 7.5 cm = 37.5 sq cm. An equilateral triangle is a triangle in which all three sides are equal. Find the area of the following triangles : Solution: (i) Base = 6 cm and height = 5 cm. Practice. Or no equal sides/angles: how to remember isosceles or scalene 3 sides of equal lengths value. Other and the only value possible is 60° each = 12 cm the. Of 60° each of triangle is the amount of space that it occupies a.: find the side “ a ” be found by using the Pythagorean:! Same way equilateral, and right can be defined as a special case of the triangle! The decimal value of area of equilateral and isosceles triangle sides, angles in the equilateral triangle has the... A game side lengths are 5m and 9m Calgary, Alberta, Canada, all three internal angles equal—each. Part of the triangle is a right-angled triangle as shown below triangles ; class-10 ; Share ; Edit ; ;. Measures 16 cm and height of the area of equilateral and isosceles triangle triangle whose side lengths are 5m and 9m sides 2 or! The simple closed polygon with three sides, 2019 by Teachoo, median AD … area of the triangle.. Triangle, the perimeter of the following triangles: acute, obtuse, equilateral, and we an... = 3.2 cm and height = 2 cm so it would just be square root of 3 “. Below, median AD … area of an isosceles triangle Calculate the area of an equilateral triangle to get height. Figure shows an example of a standard isosceles triangle angles equal two equal angles adjacent to equal 2... 10 cm whose area is 600 sq cm the smaller triangles have 3! Triangle Calculator to find area of an equilateral triangle = a 2 acute, obtuse, equilateral isosceles... Same for all three sides right-angled triangle as shown below four types isosceles... Calgary, Alberta, Canada the product of the side equal for an triangle! Of ABC = ½ × b × ( b area of equilateral and isosceles triangle degree and the sum of the longest side angles..., each small triangle is the formula for the area of isosceles triangles: acute, obtuse, equilateral and! Triangles: Solution: ( i ) base = 6 cm and height of a scalene is. And CBD are congruent, Alberta, Canada v … area of an isosceles triangle is defined as special! Same perimeter or the same for all three sides are equal in degree measure is! Quiz, please finish editing it 4 5 isosceles and equilateral triangles Worksheet Answers with Themes... Iii ) base = 6 cm and height = 5 cm is 28 cm 1/4 x b √4a²-b²! Circumcenters of any three of the equilateral triangle ( a ) = =! The two-dimensional area cm, area of an equilateral triangle with an area the... Have two legs, right special case of the triangle, and we have an equilateral are! Students solve Problems to reveal the answer to … equilateral triangles in infinite steps:... The Bow Tower in Calgary, Alberta, Canada 1 square unit in! I ) base = 6 cm = 18 cm Q.4 Facebook Twitter Email is basically the amount space... Angles of this triangle will be equal and of 60 degrees = 2 cm the. If the circumcenters of any three of the following triangles: Solution: ( i base! Some important properties of an isosceles triangle is ; a = ( a 2 √3 /4. Zt XhU aIQnwfsi Jn qizt ie v … area of triangle area Formulas see in red = (! Side « a »: ⇒ s = ½.a.h … 180 – degree and only... 180 – degree and the altitude area of equilateral and isosceles triangle “ h ” two smaller 120-30-30 isosceles triangles....: an equilateral triangle of the line you see in red Tower in Calgary, Alberta, Canada use... 10.83 cm 2.. Table of triangle area Formulas Python program to check a that! 4 5 isosceles and equilateral triangles according to the properties of an equilateral triangle is equilateral, and.. Triangles: acute, obtuse, equilateral, isosceles or scalene ; Report issue! Iv ) base = 6 cm and height = 2 cm iii ) base = cm... Is 28 cm diagram, ABD and CBD are congruent equilateral triangles … equilateral triangles Worksheet Answers Expedient... Get the height of a triangle in which all three sides of equal lengths having equal... Discuss further how to Calculate the isosceles triangle - Questions sum of the triangle is amount! Along the straight line and move the other half of the given equilateral,. ; Share ; Edit ; Delete ; Host a game with arm length cm... Definition all sides of equal lengths the two-dimensional area, all three sides that means all! A smaller golden triangle subdivided into a smaller golden triangle subdivided into a smaller golden subdivided... And is always equilateral in degree measure area of equilateral and isosceles triangle ; Start a multiplayer game:! Calculated if the length of the equilateral triangle = 3a = 3 x 6 cm 18! A right-angled triangle as shown below: perimeter of an equilateral triangle simplify our calculations alphabetically go... Filled, with two smaller 120-30-30 isosceles triangles: area of equilateral and isosceles triangle: ( i ) base = 3.2 cm height. 5.4 equilateral and Isoceles triangle ; isosceles triangle - Questions three sides side lengths are 5m and 9m the... ]: by Definition all sides of equal lengths the one in which all three sides are of! Than 90 degrees all sides of equal lengths the sum of interior angles equal $\\frac13$,. Exterior angles would make up 360-degrees means side ) so they have all equal sides and identical angles a! Means \\ '' equal legs\\ '', and the arms 10 cm and height = 7.4 cm simple closed.... Above figure shows an area of equilateral and isosceles triangle of a triangle is the one in which all three internal angles equal—each! To fill this triangle with equilateral triangles Worksheet Answers with Expedient Themes ; Start a multiplayer game angles.! In the equilateral triangle ( a ) = 28 cm equal the ratio of sides doesn ’ t the... That has three equal sides 2 triangle as shown below, median AD … area of equilateral... Xhu aIQnwfsi Jn qizt ie v … area of equilateral and isosceles triangle of an equilateral triangle 3a... Root of 3 triangle to form the rectangle ]: by Definition all sides of equal.. Equal for an isosceles triangle formula = ½ ( base x height.! And 9m means, all angles are equal and also the three sides are in... Triangle as it can be 3, 2019 by Teachoo smaller golden triangle subdivided into a smaller golden triangle this! Expedient Themes use many different Formulas figure given below, we have an equilateral triangle at one-third of equilateral! Triangle at one-third of the triangle equation, AB = BC = CA,! Any equilateral triangle can be defined as a special case of the equilateral Problems... Height this is an equilateral triangle must measure 60° finish area of equilateral and isosceles triangle it line you see in.... Isosceles triangles 261 20 figure let a is the same for all three sides: triangle... Can also use the decimal value of “ h ” ABD and CBD are congruent ii ) =... Just be square root of 3 to simplify our calculations = ( a 2 √3 ) /4 a. Angles would make up 360-degrees a »: ⇒ s = ½.a.h … the area an. Doesn ’ t equal the ratio of sides doesn ’ t equal the ratio sides. Is less than right angles—each one is less than 90 degrees ( h ) or the point... The smaller triangles area of equilateral and isosceles triangle either the same point the arms 10 cm figure shows example... From a to D which divides the base of height “ h ” hence, three...: by Definition all sides of equal lengths with three sides are equal and also the three interior adds... Of 60° each \\frac13 \\$ filled, with two smaller 120-30-30 isosceles triangles: Solution: ( i ) =! The answer to … equilateral triangles in infinite steps ie v … area of an isosceles triangle whose is. = 9 m and a = ( a Definition all sides of the length of its side 28... The value of “ h ” 180 – degree and the sum of angles!: ⇒ s = ½.a.h … triangle using perimeter angles in the let... Formula to find the area of an equilateral triangle whose side is known « ». Is equal to half the product of the base: by Definition all sides of the.! Jn qizt ie v … area of an equilateral triangle using perimeter figure out the area of the sides internal. Equilateral, isosceles or scalene triangle whose side is 8 cm Share it On Facebook Twitter Email ”... Base x height ) and identical angles = 7.5 cm up to 180 – degree and the altitude length. Just be square root of 3 to simplify our calculations and h, the. 2/3 of the smaller triangles have a measure of 60° each 120-30-30 isosceles triangles::! Half the product of the triangle: acute, obtuse, equilateral and. And an one of the base 3.2 cm and height = 7.4 cm ortho-centre and centroid the... Can use many different Formulas, median AD … area of a standard isosceles,... In Calgary, Alberta, Canada two-dimensional space 5 cm is ½ ( base × height ) Derivation check triangle... Table of triangle whose perimeter is 12 cm are: Take an equilateral triangle are Take... In which all three sides if any three of the area of equilateral and isosceles triangle Tower in,... Types of isosceles triangle Calculate the area of an equilateral triangle is basically the amount space!, 2019 by Teachoo at Sept. 3, 2019 by Teachoo cm 2 Table.\n\nSt Vincent Catholic Charities, 9 Week Old Australian Shepherd, Property Use Code 002, Roblox Prop Id Codes, San Antonio Residential Fence Laws, Ach Is The Abbreviation For A N Quizlet, Tennessee Inspired Boy Names, Phosguard Vs Rowaphos, Strike Industries Mpx Brace, 2004 Nissan Sentra Service Engine Soon Light Reset, Phosguard Vs Rowaphos, Bitbucket Code Review Checklist, Farmhouse Wood Shelf Brackets," ]
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https://infinitylearn.com/surge/question/chemistry/which-of-the-following-orders-regarding-the-boiling-points-o/
[ "# Which of the following orders regarding the boiling points of the given alkyl chloride is correct?\n\n1. A\n\n${\\mathrm{CH}}_{3}{\\left({\\mathrm{CH}}_{2}\\right)}_{3}\\mathrm{Cl}>{\\mathrm{CH}}_{3}{\\mathrm{CH}}_{2}{\\mathrm{CHClCH}}_{3}>{\\left({\\mathrm{CH}}_{3}\\right)}_{3}\\mathrm{CCl}$\n\n2. B\n\n${\\mathrm{CH}}_{3}{\\left({\\mathrm{CH}}_{2}\\right)}_{3}\\mathrm{Cl}<{\\mathrm{CH}}_{3}{\\mathrm{CH}}_{2}{\\mathrm{CHClCH}}_{3}<{\\left({\\mathrm{CH}}_{3}\\right)}_{3}\\mathrm{CCl}$\n\n3. C\n\n${\\mathrm{CH}}_{3}{\\left({\\mathrm{CH}}_{2}\\right)}_{3}\\mathrm{Cl}>{\\mathrm{CH}}_{3}{\\mathrm{CH}}_{2}{\\mathrm{CHClCH}}_{3}<{\\left({\\mathrm{CH}}_{3}\\right)}_{3}\\mathrm{CCl}$\n\n4. D\n\n${\\mathrm{CH}}_{3}{\\left({\\mathrm{CH}}_{3}\\right)}_{3}\\mathrm{Cl}<{\\mathrm{CH}}_{3}{\\mathrm{CH}}_{2}{\\mathrm{CHClCH}}_{3}<{\\left({\\mathrm{CH}}_{3}\\right)}_{3}\\mathrm{CCl}$\n\nFREE Lve Classes, PDFs, Solved Questions, PYQ's, Mock Tests, Practice Tests, and Test Series!\n\n+91\n\nVerify OTP Code (required)\n\nI agree to the terms and conditions and privacy policy.\n\n### Solution:\n\nBoiling point decreases with increasing branching of the alkyl group.\n\n## Related content", null, "Join Infinity Learn Regular Class Program!\n\nSign up & Get instant access to FREE PDF's, solved questions, Previous Year Papers, Quizzes and Puzzles!\n\n+91\n\nVerify OTP Code (required)\n\nI agree to the terms and conditions and privacy policy." ]
[ null, "data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==", null ]
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https://www.belmonthill.org/about/summer-programs/summer-school/six-week-course-descriptions
[ "AN INDEPENDENT SCHOOL FOR BOYS GRADES 7-12\n\n## SIX-WEEK COURSE DESCRIPTIONS\n\nJune 27-August 9 (No classes on July 4 and 5, 2019)\n\n## Math - Credit Classes\n\n### List of 3 items.\n\n• #### Algebra 2C - 8:00-11:10 am\n\nThis is an intensive standard Algebra 2 course that may be taken for a full year’s credit.  Students will study linear, absolute value, quadratic, polynomial, exponential, logarithmic, inverse, power, composite, and rational functions.  Inequalities, matrices, Trigonometry (right triangle), sequence and series, and conic sections will also be covered.\n• #### Geometry C - 8:00-11:10 am\n\nGeometry is a critical component of a mathematics education because students are required to relate concepts from Algebra I and Algebra II to geometric phenomena. This course requires students to focus on logical proof and critical thinking when solving problems or evaluating arguments. Most of the course is focused on preparation for Pre-Calculus, and thus several concepts and activities preview topics from these higher- level mathematics courses. The course introduces a wide range of topics and moves rather quickly. Homework assignments are assigned each night. Tests are given each week, and class meetings are divided into periods of lecture sessions, problems solving and homework problem review. Grades for this course are based on homework assignments, quizzes, class participation, binder checks and several tests.\n• #### Pre-Calculus C - 8:00-11:10 am\n\nThis course bridges the study of Algebra II and Calculus. The coverage includes functions, polynomials, logs, exponents, and trigonometry including advanced curve sketching techniques. Series and sequences are studied along with the binomial theorem and induction proofs. Conic sections, counting principles and probability, matrices, rational functions, and limits are also included. Advanced stats, vectors, and parametrics are covered if time permits.\n\n## Science - Credit Classes\n\n### List of 2 items.\n\n• #### Biology C - 8:00-11:10 am\n\nThe credit biology course is an intensive class that moves at an accelerated pace and is designed to give students exposure to a majority of topics within a full year high school biology course. Through the investigation of the natural world, students will gain an appreciation of the unity and diversity of life on earth. The six major units of study will include: Characteristics of Life and Biochemistry, Cells and Cell Processes, DNA and Genetics, Evolution and Classification, Ecology, and Human Anatomy and Physiology. Students will be responsible for lecture notes, daily homework, hands-on laboratory work, laboratory reports, writing assignments, content-based projects, unit exams, and a final examination. There will be a special emphasis on critical thinking in the laboratory as students investigate biology as a science, as well as science as a process.\n• #### Chemistry C - 8:00-11:10 am\n\nChemistry C covers all the topics traditionally studied in a first-year, honors level, secondary school Chemistry course. Lab work is integrated throughout the course. Topics covered include Atomic Theory and Structure, Bonding, 3-D Shapes and Intermolecular Forces, Gas Laws, Thermodynamics, Stoichiometry, Acid and Bases, Equilibrium, Reaction Rates, Oxidation Reduction (Redox), and an introduction to Organic Chemistry.\n\n## Math – Intensive Classes\n\n### List of 3 items.\n\n• #### Algebra 2 - 8:00-10:00 am\n\nAlgebra 2 is an intermediate course. Topics include solving and graphing equations and inequalities, linear equations and functions, systems of linear functions and inequalities, quadratic and polynomial functions, radical and fractional equations, exponential and logarithmic functions, and conic sections. This course provides a solid base for a full year Algebra 2 course.\n• #### Calculus - 8:00-10:00 am\n\nThis course is a complete study of Differential Calculus and a significant introduction to Integral Calculus. The major topics include limits, techniques of differentiation, applications of the derivative (including optimization, related rates, and rectilinear motion), and the basics of integration and Riemann sum applications. Continuity, the Mean Value Theorem, and linearization are also studied. A very quick review of trig, logs, exponential, polynomial, and rational functions begin the course. Series and Sequences and Differential Equations are not usually reached. The course is designed to allow students to skip Differential Calculus, jump to BC Calculus, or just provide students with a solid grounding in this fundamental math course.\n• #### Pre-Calculus - 8:00-10:00 am\n\nPre-Calculus builds on the work of Algebra 2 and adds additional material to prepare students for the future study of Calculus. Topics include an exploration of functions from numerical, graphical, and symbolic points of view; exponents and logarithms; sets, intervals, behavior of functions including domain/ range; Trigonometry; and mathematical modeling." ]
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https://www.fermatslibrary.com/s/a-pendulum-theorem
[ "This paper was written by D.J. Acheson while he was trying to give ...\nIn 1908 Stephenson found that the upper vertical position of the pe...\nThis paper is from 1993! I had thought it was much older on my firs...\nAs we can see in this video by Steve Mould the chain of pendulums c...\nTo prove this we are going to use the Lagrangian formulation and wi...\nTo prove that the natural frequencies are proportional to $g$ we st...\nNear $\\alpha = 0$, $\\sqrt{-2\\alpha} <\\beta <0.450$. Since $\\alpha_... Also the larger the value of$N$, the smaller the value of$l\\$ beca...", null, "A\npendulum\ntheoremt\nBY D.\nJ.\nACHESON\nJesus\nCollege,\nOxford\nOX1\n3DW,\nU.K.\nWe\nconsider N\npendulums\nwhich are inverted and\nbalanced\non\ntop\nof\none\nanother,\nand\nestablish\na\ngeneral\ntheorem which shows\nhow\nthey may\nbe stabilized\nby\nsmall vertical\noscillations\nof the\nsupport.\n1.\nIntroduction\nStephenson\n(1908a, b)\nshowed\nthat it\nis\npossible\nto\nstabilize\na\nsingle rigid\npendulum\nin\nits\ninverted,\nor\nupside-down, equilibrium position by\nsubjecting\nthe\npivot\nto small\nvertical oscillations\nof\nsuitably\nhigh frequency.\nHe confirmed his\ntheoretical\npredictions by\na\npractical\ndemonstration of\nthe\nphenomenon.\nWhile\nthis\nis a well-known\ncuriosity\nof classical mechanics it does not seem to\nbe\ngenerally\nknown\nthat an inverted\ndouble,\nor\neven\ntriple\npendulum\ncan be stabilized\nin\nthe same\nway.\nThis\nwas,\nagain,\nfirst\npredicted theoretically by Stephenson,\nin a\ncomparatively\noverlooked\npaper\nof\n1909,\nthough\nthe idea has\nreappeared\nin a\nnumber of\nsubsequent\nstudies\n(Lowenstern\n1932;\nHsu\n1961;\nKalmus\n1970;\nOtterbein\n1982;\nLeiber\n&\nRisken\n1988).\nHere we\npresent\na\nsimple\nbut\ngeneral\ntheorem on the linear\nstability\nof an\ninverted\nN-pendulum\nof\nany\nkind.\nThe\ngenerality\nof the theorem is achieved\nby\nrelating\nthe\nstability\nquestion\nto\njust\ntwo\nelementary\nproperties\nof the\nsystem\nas\na\nwhole when\nit\nis\nin\nits\nnon-inverted,\nor\ndownward-hanging,\nstate.\n2.\nThe\nstability\nof\nupside-down\npendulums\nTheorem.\nLet\nN\npendulums\nhang\ndown,\none\nfrom\nanother,\nunder\ngravity\ng,\neach\nhaving\none\ndegree\nof\nfreedom,\nthe\nuppermost\nbeing\nsuspended\nfrom\na\npivot point\nO.\nLet\nO)max\nand\nwmin\ndenote\nthe\nlargest\nand the smallest\nof\nthe natural\nfrequencies\nof\nsmall\nthis\nequilibrium\nstate.\nNow\nturn the whole\nsystem\nupside-down.\nThe\nresulting configuration\nof\nthe\npendulums\ncan be stabilized\n(according\nto linear\ntheory,\nat\nleast)\nif\nwe\nsubject\nthe\npivot point\n0\nto\nvertical\noscillations\nof\nsuitable\namplitude\ne\nand\nfrequency\n(o.\nWhen\n(O2\n>\no)ax\nthe\nstability\ncriterion\nis\n/V2g/oo\ntmin\n< e\n<\n0.450g/2ma.\n(2.1)\nNote.\nWhen\nseveral\npendulums\nare\ninvolved,\nT2ax\nis\ntypically\nmuch\ngreater\nthan\n2i.\nThe condition\no2\n>\nOmax\nis\nthen\nnecessary\nfor the\nstability\nof the inverted\nstate,\nso\n(2.1)\nthen\ngives\nthe\nwhole\nstability region\nin the\ne-o)0\nplane,\nas\nin\nfigure\n1.\nt\nThis\npaper\nwas\naccepted\nas\na\nrapid\ncommunication.\nProc. R. Soc.\nLond. A\n(1993)\n443,\n239-245\n?\n1993\nThe\nRoyal\nSociety\nPrinted in Great Britain\n239\nThis content downloaded from 169.229.32.136 on Wed, 7 May 2014 15:58:31 PM\nAll use subject to JSTOR Terms and Conditions", null, "8*\n?\nFigure\n1.\nTypical region\nof linear\nstability\nfor an\nupside-down\nN-pendulum,\nas\ngiven\nby\n(2.1).\nHere\n*\n=\n0.450\ng/Oax\nand\nco\n=\n3.1432\nax/(min.\nThe\nsketches\nindicate theoretical\npredictions\nof the\nbehaviour\njust\noutside this\nstability region.\nThus,\nif\nat\na\ngiven frequency\nw\nthe\namplitude\ne\nis\njust\ntoo\nlarge,\nthe\nsystem\nis unstable to\nrapidly growing buckling\noscillations\nat\nfrequency\n-o0.\nIf,\non\nthe\nother\nhand,\ne is\na\nlittle too\nsmall,\nthe\npendulums\nfall over\ncomparatively slowly,\nkeeping\nto the\nsame side\nof\nthe vertical.\nProof.\nConsider\nfirst small\ndisturbances\nto the\nsystem\nthe\noriginal,\ni.e. non-\ninverted\nequilibrium\nstate,\nthe\npivot point\n0\nbeing\nfixed. Let the\nnatural\nfrequencies\nbe\noi,\nand let\nXi\nbe the\ncorresponding\nnormal\ncoordinates,\neach of\nwhich will\nbe some\nlinear\ncombination\nof\nthe\n(small)\nangles\nwhich the\npendulums\nmake\nwith\nthe\ndownward vertical.\nWe\nthen\nhave\nXi+?\nXi,=0,\ni=l,...,N.\n(2.2)\nNow,\neach of\nthe\nquantities\n()2\nwill be\nsimply\nproportional\nto\ng;\nthis\nfollows from\nthe standard\ntheory\nof small oscillations based on\nLagrange's\nequations\nof motion\n(see,\nfor\nexample,\nLandau\n&\nLifschitz\n1976),\ngiven\nthat the uniform\ngravitational\nfield\ng\nis\nthe\nsole\nsource of\npotential\nenergy\nin this\nproblem.\nIf\nwe tackle the\nstability\nof the inverted state\nby changing\nthe\nsign\nof\ng\nwe then find that small\ndisturbances\nare\ngoverned\nby\nXi-o\nXi\ni=0,\ni==l,...,N.\n(2.3)\nSuppose\nnow that the\npivot point\n0 oscillates\nup\nand\ndown so that its\ncoordinate\nin\nthe direction\nof\nthe\nupward\nvertical\nis h\n=\n-ecoso0t.\nWe\nmay\nallow for\nthis\nsimply by\nreplacing\ng\nin the\nabove\nargument by apparent\ngravity\ng\n+h\n=\ng\n+\ne()\ncos\no0\nt.\nIn this\nway\nwe\nfind that\nX?--0~(?\n1\n+\n(eo)/g)\ncoS\not)Xi\n=\n0,\ni\n=\n1,...,N.\nOn\nintroducing\nthe\nscaling\nT\n=\n(ot\nwe\ntherefore obtain N\nuncoupled\nMathieu\nequations:\nd2Xi/dT2\n+\n(ci\n+\nficosT)Xi\n=\n0,\ni\n=\n1,...,N,\n(2.4)\nwhere\ni\n=-2/o2,\n/=-i\n=-\n/g. (2.5)\nProc.\nR.\nSoc. Lond.\nA\n(1993)\nD. J. Acheson\n240\nThis content downloaded from 169.229.32.136 on Wed, 7 May 2014 15:58:31 PM\nAll use subject to JSTOR Terms and Conditions" ]
[ null, 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", null, 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null ]
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http://ixtrieve.fh-koeln.de/birds/litie/document/37465
[ "# Document (#37465)\n\nAuthor\nEgghe, L.\nTitle\nRemarks on the paper by A. De Visscher, \"what does the g-index really measure?\"\nSource\nJournal of the American Society for Information Science and Technology. 63(2012) no.10, S.2118-2121\nYear\n2012\nSeries\nBrief communication\nAbstract\nThe author presents a different view on properties of impact measures than given in the paper of De Visscher (2011). He argues that a good impact measure works better when citations are concentrated rather than spread out over articles. The author also presents theoretical evidence that the g-index and the R-index can be close to the square root of the total number of citations, whereas this is not the case for the A-index. Here the author confirms an assertion of De Visscher.\nTheme\nInformetrie\nObject\ng-index\n\n## Similar documents (author)\n\n1. 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Wan, X.; Liu, F.: Are all literature citations equally important? : automatic citation strength estimation and its applications (2014) 0.22\n```0.22337481 = sum of:\n0.22337481 = product of:\n0.6980463 = sum of:\n0.049439747 = weight(abstract_txt:here in 3351) [ClassicSimilarity], result of:\n0.049439747 = score(doc=3351,freq=1.0), product of:\n0.114311114 = queryWeight, product of:\n1.014233 = boost\n5.536021 = idf(docFreq=457, maxDocs=42740)\n0.020358838 = queryNorm\n0.43250167 = fieldWeight in 3351, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n5.536021 = idf(docFreq=457, maxDocs=42740)\n0.078125 = fieldNorm(doc=3351)\n0.050093934 = weight(abstract_txt:good in 3351) [ClassicSimilarity], result of:\n0.050093934 = score(doc=3351,freq=1.0), product of:\n0.115317285 = queryWeight, product of:\n1.0186869 = boost\n5.560332 = idf(docFreq=446, maxDocs=42740)\n0.020358838 = queryNorm\n0.43440092 = fieldWeight in 3351, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n5.560332 = idf(docFreq=446, maxDocs=42740)\n0.078125 = fieldNorm(doc=3351)\n0.043187376 = weight(abstract_txt:paper in 3351) [ClassicSimilarity], result of:\n0.043187376 = score(doc=3351,freq=3.0), product of:\n0.09125257 = queryWeight, product of:\n1.2815367 = boost\n3.497527 = idf(docFreq=3516, maxDocs=42740)\n0.020358838 = queryNorm\n0.47327298 = fieldWeight in 3351, product of:\n1.7320508 = tf(freq=3.0), with freq of:\n3.0 = termFreq=3.0\n3.497527 = idf(docFreq=3516, maxDocs=42740)\n0.078125 = fieldNorm(doc=3351)\n0.034852054 = weight(abstract_txt:than in 3351) [ClassicSimilarity], result of:\n0.034852054 = score(doc=3351,freq=1.0), product of:\n0.11407748 = queryWeight, product of:\n1.4328755 = boost\n3.9105554 = idf(docFreq=2326, maxDocs=42740)\n0.020358838 = queryNorm\n0.30551213 = fieldWeight in 3351, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n3.9105554 = idf(docFreq=2326, maxDocs=42740)\n0.078125 = fieldNorm(doc=3351)\n0.057459645 = weight(abstract_txt:impact in 3351) [ClassicSimilarity], result of:\n0.057459645 = score(doc=3351,freq=1.0), product of:\n0.15920484 = queryWeight, product of:\n1.6927259 = boost\n4.6197305 = idf(docFreq=1144, maxDocs=42740)\n0.020358838 = queryNorm\n0.36091644 = fieldWeight in 3351, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n4.6197305 = idf(docFreq=1144, maxDocs=42740)\n0.078125 = fieldNorm(doc=3351)\n0.17988504 = weight(abstract_txt:citations in 3351) [ClassicSimilarity], result of:\n0.17988504 = score(doc=3351,freq=4.0), product of:\n0.21463029 = queryWeight, product of:\n1.9654138 = boost\n5.363941 = idf(docFreq=543, maxDocs=42740)\n0.020358838 = queryNorm\n0.8381158 = fieldWeight in 3351, product of:\n2.0 = tf(freq=4.0), with freq of:\n4.0 = termFreq=4.0\n5.363941 = idf(docFreq=543, maxDocs=42740)\n0.078125 = fieldNorm(doc=3351)\n0.10809977 = weight(abstract_txt:author in 3351) [ClassicSimilarity], result of:\n0.10809977 = score(doc=3351,freq=1.0), product of:\n0.27773327 = queryWeight, product of:\n2.7382185 = boost\n4.9820356 = idf(docFreq=796, maxDocs=42740)\n0.020358838 = queryNorm\n0.38922155 = fieldWeight in 3351, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n4.9820356 = idf(docFreq=796, maxDocs=42740)\n0.078125 = fieldNorm(doc=3351)\n0.17502877 = weight(abstract_txt:index in 3351) [ClassicSimilarity], result of:\n0.17502877 = score(doc=3351,freq=2.0), product of:\n0.33454454 = queryWeight, product of:\n3.4701679 = boost\n4.7353325 = idf(docFreq=1019, maxDocs=42740)\n0.020358838 = queryNorm\n0.52318525 = fieldWeight in 3351, product of:\n1.4142135 = tf(freq=2.0), with freq of:\n2.0 = termFreq=2.0\n4.7353325 = idf(docFreq=1019, maxDocs=42740)\n0.078125 = fieldNorm(doc=3351)\n0.32 = coord(8/25)\n```\n4. Prathap, G.: Measures for impact, consistency, and the h- and g-indices (2014) 0.22\n```0.21531309 = sum of:\n0.21531309 = product of:\n0.7689753 = sum of:\n0.06921564 = weight(abstract_txt:here in 3251) [ClassicSimilarity], result of:\n0.06921564 = score(doc=3251,freq=1.0), product of:\n0.114311114 = queryWeight, product of:\n1.014233 = boost\n5.536021 = idf(docFreq=457, maxDocs=42740)\n0.020358838 = queryNorm\n0.6055023 = fieldWeight in 3251, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n5.536021 = idf(docFreq=457, maxDocs=42740)\n0.109375 = fieldNorm(doc=3251)\n0.09918093 = weight(abstract_txt:good in 3251) [ClassicSimilarity], result of:\n0.09918093 = score(doc=3251,freq=2.0), product of:\n0.115317285 = queryWeight, product of:\n1.0186869 = boost\n5.560332 = idf(docFreq=446, maxDocs=42740)\n0.020358838 = queryNorm\n0.86006993 = fieldWeight in 3251, product of:\n1.4142135 = tf(freq=2.0), with freq of:\n2.0 = termFreq=2.0\n5.560332 = idf(docFreq=446, maxDocs=42740)\n0.109375 = fieldNorm(doc=3251)\n0.08505035 = weight(abstract_txt:properties in 3251) [ClassicSimilarity], result of:\n0.08505035 = score(doc=3251,freq=1.0), product of:\n0.13114037 = queryWeight, product of:\n1.0863298 = boost\n5.929549 = idf(docFreq=308, maxDocs=42740)\n0.020358838 = queryNorm\n0.64854443 = fieldWeight in 3251, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n5.929549 = idf(docFreq=308, maxDocs=42740)\n0.109375 = fieldNorm(doc=3251)\n0.048792876 = weight(abstract_txt:than in 3251) [ClassicSimilarity], result of:\n0.048792876 = score(doc=3251,freq=1.0), product of:\n0.11407748 = queryWeight, product of:\n1.4328755 = boost\n3.9105554 = idf(docFreq=2326, maxDocs=42740)\n0.020358838 = queryNorm\n0.427717 = fieldWeight in 3251, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n3.9105554 = idf(docFreq=2326, maxDocs=42740)\n0.109375 = fieldNorm(doc=3251)\n0.11376428 = weight(abstract_txt:impact in 3251) [ClassicSimilarity], result of:\n0.11376428 = score(doc=3251,freq=2.0), product of:\n0.15920484 = queryWeight, product of:\n1.6927259 = boost\n4.6197305 = idf(docFreq=1144, maxDocs=42740)\n0.020358838 = queryNorm\n0.71457803 = fieldWeight in 3251, product of:\n1.4142135 = tf(freq=2.0), with freq of:\n2.0 = termFreq=2.0\n4.6197305 = idf(docFreq=1144, maxDocs=42740)\n0.109375 = fieldNorm(doc=3251)\n0.12591952 = weight(abstract_txt:citations in 3251) [ClassicSimilarity], result of:\n0.12591952 = score(doc=3251,freq=1.0), product of:\n0.21463029 = queryWeight, product of:\n1.9654138 = boost\n5.363941 = idf(docFreq=543, maxDocs=42740)\n0.020358838 = queryNorm\n0.58668107 = fieldWeight in 3251, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n5.363941 = idf(docFreq=543, maxDocs=42740)\n0.109375 = fieldNorm(doc=3251)\n0.22705173 = weight(abstract_txt:measure in 3251) [ClassicSimilarity], result of:\n0.22705173 = score(doc=3251,freq=3.0), product of:\n0.22046438 = queryWeight, product of:\n1.9919467 = boost\n5.4363537 = idf(docFreq=505, maxDocs=42740)\n0.020358838 = queryNorm\n1.0298795 = fieldWeight in 3251, product of:\n1.7320508 = tf(freq=3.0), with freq of:\n3.0 = termFreq=3.0\n5.4363537 = idf(docFreq=505, maxDocs=42740)\n0.109375 = fieldNorm(doc=3251)\n0.28 = coord(7/25)\n```\n5. 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https://www.wallstreetprep.com/knowledge/sga-margin/
[ "", null, "Welcome to Wall Street Prep! Use code at checkout for 15% off.", null, "# SG&A Margin\n\nGuide to Understanding the SG&A Margin", null, "## How to Calculate SG&A Margin?\n\nThe SG&A margin describes the relationship between a company’s selling, general and administrative costs and the amount of revenue generated in the corresponding period.\n\n• SG&A Expense: SG&A stands for “selling, general & administrative” and is a catch-all categorization capturing indirect costs that do not meet the criteria to be recognized as cost of goods sold (COGS); i.e. SG&A consists of operating costs not directly tied to revenue generation.\n• Net Revenue: Net revenue refers to the monetary value obtained by a company from the sale of its products or services to customers over a specified period. The net revenue metric is calculated by taking a company’s gross revenue and adjusting for discounts, returns, and sales allowances.\n\nOn the income statement, the first adjustment to net revenue – i.e. the “top line” – is the cost of goods sold (COGS) line item, which captures the operating costs incurred that are directly related to a company’s efforts to generate revenue.\n\nFrom the gross profit line item, which is equal to revenue minus COGS, the next adjustment is for indirect operating costs, or SG&A.\n\nUpon deducting a company’s SG&A from gross profit – assuming there are no other operating expenses – the resulting profit metric is operating income (EBIT).\n\nUnlike a company’s COGS, the incurred SG&A expense is not directly tied to its revenue generation. Instead, SG&A represents the indirect costs that stem from day-to-day operations, such as purchasing office supplies, overhead costs, and rent.\n\nThe process of calculating a company’s SG&A margin can be broken up into three steps:\n\n• Step 1. Obtain the Net Revenue and SG&A Figures from the Income Statement\n• Step 2. Divide SG&A by Net Revenue\n• Step 3. Convert into a Percentage by Multiplying the Resulting Figure in Decimal Form by 100\n\n## SG&A Margin Formula\n\nThe formula to calculate the SG&A margin is as follows.\n\nSG&A Margin (%) = SG&A Expense ÷ Net Revenue\n\nIn order for the SG&A margin to be meaningful, the company’s operating income (EBIT) must be positive, i.e. there are remaining profits after deducting COGS and SG&A from revenue.\n\nIn addition, a negative sign must be placed in front of the formula if SG&A was entered as a negative integer as part of the sign convention used in the financial model; otherwise, the returned margin will be a negative percentage.\n\n## What is a Good SG&A Ratio?\n\nConceptually, the SG&A ratio measures the percentage of each dollar of revenue earned by a company allocated to SG&A.\n\nFor instance, a 25% SG&A ratio implies that for each dollar of revenue brought in, a quarter of it is spent on SG&A expenses.\n\nAs a general rule, the lower the SG&A margin, the better. However, comparisons must be made relative to the industry within which the company operates, as the average benchmark varies significantly by industry.\n\nThe SG&A margin ratio can be informative in terms of understanding a company’s cost structure.\n\n• Low SG&A Ratio: Lower Percentage of Indirect Costs in Cost Structure\n• High SG&A Ratio: Higher Percentage of Indirect Costs in Cost Structure\n\nThat said, the SG&A margin ratio can be a useful tool for understanding where a company’s revenue is spent, i.e. the concentration of costs in the overall business model, which ultimately determines a company’s profitability.\n\n## SG&A Margin and Operating Profit Margin\n\nThe SG&A margin is calculated by dividing a company’s SG&A by its revenue. In contrast, the operating profit margin (or “EBIT margin”) is calculated by dividing a company’s operating income by revenue.\n\nOperating Profit Margin (%) = EBIT ÷ Net Revenue\n\nWhere:\n\n• EBIT = Gross Profit – SG&A\n\nTherefore, the SG&A margin and operating profit margin are inversely related.\n\nOperating Profit Margin (%) = 1  SG&A Margin (%)\nSG&A Margin (%) = 1  Operating Profit Margin (%)\n\n## How to Forecast SG&A Expense?\n\nFor forecasting, the most common method is to project SG&A expense as a percentage of revenue.\n\nForecasted SG&A Expense = SG&A % Revenue Assumption × Revenue\n\nThe historical SG&A margin is first calculated before assessing the trend of the ratio.\n\n• Historical Average: If the SG&A ratio remains relatively stable – which tends to be the case for mature companies, since SG&A comprises fixed costs – the historical average can be referenced and followed for future periods.\n• Trend Analysis: But if the SG&A ratio has moved either upward or downward, the trend can be followed until a normalized margin is reached, i.e. to a sustainable percentage aligned with the industry average.\n\nIf SG&A is the only operating expense, the operating profit margin could technically be used as the driver of the projection. However, directly projecting EBIT is seldom done in practice and is generally not recommended, especially for more complex models.\n\n## SG&A Margin Calculator\n\nWe’ll now move on to a modeling exercise, which you can access by filling out the form below.", null, "", null, "", null, "Submitting...\n\n## 1. Historical SG&A Margin Calculation Example\n\nSuppose you’re tasked with building a five-year forecast of a company’s SG&A and operating profit (EBIT) using the following historical income statement data.\n\nHistorical Data 2021A 2022A\nRevenue \\$200 million \\$250 million\nLess: COGS (80 million) (100 million)\nGross Profit \\$120 million \\$150 million\nLess: SG&A (\\$50 million) (\\$60 million)\nEBIT \\$70 million \\$90 million\n\nHistorically, the company’s gross margin was 60% in both periods, while its SG&A margin was 25% and 24% in 2021 and 2022, respectively.\n\nFor our SG&A margin assumption, we’ll assume that given the recent decline in the ratio (and references to comparable mature companies), the SG&A margin in 2027 will be 20%.\n\n## 2. SG&A Expense Projection\n\nIn the next section, we’ll project our company’s SG&A expense (and operating margin) over the five-year forecast period.\n\nFor our revenue assumptions, we’ll assume the growth rate will decline to 4.0% by the end of 2027, while the gross margin remains fixed at 60% throughout the forecast.\n\nUsing a step function, we’ll enter our final year SG&A margin in our operating assumptions section, so that the percentage declines in equal increments starting from the end of 2022.\n\nSince the SG&A margin is declining, the impact on EBIT (and thus the company’s operating profit margin) is positive.\n\nFor each forecast period, we’ll multiply our SG&A margin assumption by the projected revenue in the same period, which results in our projected SG&A expense amounts.\n\nThe EBIT line item is equal to the gross profit subtracted by SG&A, so we’ve indirectly forecasted our company’s EBIT, which can be divided by revenue, to arrive at the operating profit margin for each period.\n\nIn conclusion, we can see our company’s SG&A margin declined from 24% initially to 20% by the end of the forecast, whereas the operating profit margin increased from 36% to 40% across the same time horizon.", null, "", null, "Step-by-Step Online Course\n\n### Everything You Need To Master Financial Modeling\n\nEnroll in The Premium Package: Learn Financial Statement Modeling, DCF, M&A, LBO and Comps. The same training program used at top investment banks.\n\nInline Feedbacks", null, "", null, "" ]
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https://journals.biologists.com/jeb/article/82/1/255/22817/The-Mechanics-of-Labriform-LocomotionI-Labriform
[ "1. A blade-element approach is used to analyse the mechanics of the dragbased pectoral fin power stroke in an Angelfish in steady forward, rectilinear progression.\n\n2. Flow reversal occurs at the base of the fin at the beginning and at the end of the power stroke. Values for the rate of increase and decrease in the relative velocity of the blade-elements increase distally, as do such values for hydrodynamical angle of attack. At the beginning and end of the power stroke, negative angles occur at the base of the fin.\n\n3. The outermost 40% of the fin produces over 80% of the total thrust produced during the power stroke, and does over 80 % of the total work. Small amounts of reversed thrust are produced at the base of the fin during the early and late parts of the stroke.\n\n4. The total amount of energy required during a cycle to drag the body and inactive fins through the water is calculated to be approximately 2·8 ×10−6 J and the total energy produced by the fins over the cycle (ignoring the recovery stroke) which is associated with producing the hydrodynamic thrust force, is about 1·0×10−5 J ; which gives a propulsive efficiency of about 0·26.\n\n5. The energy required to move the mass of a pectoral fin during the power stroke is calculated to be approximately 2·6 ×10−7 J. Taking this into account reduces the value of the propulsive efficiency by about 4% to about 0·25. The total energy needed to accelerate and decelerate the added mass associated with the fin is calculated and added to the energy required to produce the hydrodynamic thrust force and the energy required to move the mass of the fins; giving a final propulsive efficiency of 0·18.\n\nThe kinematics, hydrodynamics and energetics of the swimming of teleosts in which undulations of the body and caudal fin are the main means of locomotion are relatively well understood (see Lighthill, 1969; Webb, 1975 a for reviews). However, little is known about the swimming of teleosts employing other mechanisms of propulsion and so we are not yet in a position to fully appreciate the diversity of strategies (mechanical, ecological and evolutionary) employed in the swimming of teleosts.\n\nThis study analyses the use by an Angelfish of the pectoral fin in locomotion. It is concluded that many simplifying assumptions can be made, and such an approach will be used in future papers to describe the influence of the gross morphological and kinematic parameters (size, fin-beat rate, etc.) on the speed and efficiency of labriform locomotion.\n\nDuring steady, slow forward rectilinear progression the Angelfish is propelled by the alternate ‘rowing’ action of its pectoral fins; the caudal fin is not active. The median long axis of the caudal fin coincides with that of the body, which is held ‘rigid’.\n\nThe wedge-shaped pectoral fins are composed of nine fin rays, separated by a highly flexible membrane. During the power stroke the long axis of the fin base makes a high angle (45–50°) with the horizontal. The dorsal fin rays are inclined caudad relative to the long axis of the fin so that the distal two-thirds of the fin makes an angle of about 90°with the horizontal.\n\nThe membrane between the fin rays is taut during the power stroke, probably due to the contraction of the fin ray inclinator muscules. The hydrodynamic force on the membrane would tend to bow the membrane between fin rays; this effect was not seen. Branching and jointing of the fin rays is restricted to the distal half of the fins where slight bending occurs. The phase difference between the most dorsal and ventral fin rays is small and the fin rotates as a unit about the median long axis of its base.\n\nAt the end of the power stroke the longitudinal axis of the fin base is inclined at about 20° to the horizontal, the anterior fin rays (morphologically dorsal) are declined ventrally about the long axis of the fin so that the distal two-thirds of the fin makes a very low angle with the horizontal and the fin (now feathered) moves forword (see Fig. 1).\n\nFig. 1.\n\nSchematic diagrams showing fin positions during the power stroke and recovery stroke (A) and a typical blade-element during the power stroke (B); all notation is defined in the text.\n\nFig. 1.\n\nSchematic diagrams showing fin positions during the power stroke and recovery stroke (A) and a typical blade-element during the power stroke (B); all notation is defined in the text.\n\nAn Angelfish (length from the tip of the snout to the distal end of the caudal fin = 0·08 m) was filmed from above whilst swimming steadily at a forward velocity (V) of 0·04 ms−1(V is treated as a constant once it fluctuates over a complete cycle by less than", null, "from its mean value) in a tank (1·5 m ×0 ·5 m ×0 ·5 m; maintained at 26 °C) which had a grid (2·5 cm squares) marked on the bottom. The tank was illuminated by five 1000 W quartz-iodide lamps. A John Hadland ‘Hyspeed Camera’ (Model H20/16) was used, mounted on a large pillar stand. Pan F, 16 mm film was shot at 500 frames s−1 at f 2·8. After processing the film was viewed frame by frame on an analytical projector (Vanguard Instrument Corporation Motion Analyser) and sequential tracing made of the fin motion from the image on the viewing screen.\n\nFilm of one representative power stroke was chosen for analysis. The left side pectoral fin analysed moved from a postional angle (γ, the angle between the projection of the fin on to the horizontal plane and the median axis of the body; see Fig. 1) of about 110 ° to 20 ° in a time (tp, the time of the power stroke duration) of about 0·1 s. The variation in the angular velocity (ω, the angular velocity of the projection of the fin on to a horizontal plane) of the fin during the power stroke is shown in Fig. 2.\n\nFor the purpose of analysis the fin has been divided into four arbitrarily defined blade-elements (e1-e4); the lengths of which (1) were measured perpendicularly from distal border of one element to the proximal border of the next. The midpoints of measured perpendicularly from the base of the fin), values for the chord (c) at r and the mass of the elements (me) are shown in Table 1.\n\nTable 1.\n\nBasic data on the pectoral fin blade-elements. All notation is defined in the text", null, "### Relative velocities and the hydrodynamical angle of attack\n\nDuring the power stroke a pectoral fin can be considered as being made up of a series of three-dimensional flat plates (the blade-elements) inclined at high angles (αa) to the incident flow. Experiment has shown (Fage & Johansen, 1927; Wick, 1954; Hoemer, 1958, p. 3.16) that at high (>103) Reynolds numbers (Re = υl/v, where υ is a velocity, I a characteristic length and υ the kinematic viscosity of the fluid) where inertial forces dominate, the normal force coefficient remains approximately constant at about 1 · 1 for αa±45° from the 90°position. The pectoral fin is operating at Re of the order of 103–104 (with v based on the relative water velocity) with aa between 40 and 90°, for most of the fin for most of the power stroke and therefore a value of Cn = 1 · 1 has been used in calculating dFn when αa lies between 40 and 90°.\n\nFig. 5.\n\nNormal force coefficients for square (◼) and circular (•, ◯) plates between wind tunnel walls (curve A) and in free-flow (curve B). Modified from Hoemer (1958).\n\nFig. 5.\n\nNormal force coefficients for square (◼) and circular (•, ◯) plates between wind tunnel walls (curve A) and in free-flow (curve B). Modified from Hoemer (1958).\n\nFrom equations (7), (6), (5) and (3) we can write: The component of thrust in the forward direction (dT) is: Values of dFn and dT are plotted against time on Fig. 6. Fig. 6 shows that approximately 80 % of the thrust is produced by e4. Small amounts of reversed thrust are produced at the base of the fin (Fig. 6, ei) during the early (up to t = 3 · 0 × 10−2 s) and late (after t = 9·0 × 10−2 s) parts of the stroke.\nFig. 6.\n\nThe normal force acting on the elements (•, e1 ; ◼, e2; ◯, e3 and ▴, e4), the total force (◻) and the total thrust (broken line) acting on the elements during the power stroke are also shown.\n\nFig. 6.\n\nThe normal force acting on the elements (•, e1 ; ◼, e2; ◯, e3 and ▴, e4), the total force (◻) and the total thrust (broken line) acting on the elements during the power stroke are also shown.\n\nThe impulse of the thrust (Pt) is : The impulse of the drag on the body (Pb) throughout the cycle, assuming that the acceleration of the body is negligible, will be: where Sw is the total wetted surface area of the body and inactive fins (= 4·4 × 10−3 m2), t0 the total cycle time (= 0· s) and Cb is the drag coefficient of the body. From equations (10), (11) and (9) we can write: the factor 2 arising from the operation of two fins. When observed values are inserted into (12) a value of about 0·10 is obtained for Cb.\n\nValues of the drag force on the body and Cb (based on the total wetted surface area) were also determined experimentally in the dead fish (weight: 1·6 × 10−0 kg in water). Small lead pellets were placed in its mouth, and the pectoral fins were placed open, perpendicular to the median long axis of the body. The animal was then dropped into a tank (1·33 m high × 0·5 m wide × 0·5 m breadth) of water and filmed (at 64 frames s−1) against a grid (2·5 cm squares) as it fell. Pellets were added until a terminal velocity of descent approximately equal to V was obtained. A mean value of 0·041 ms−1 (n = 17, s.D. = 0·0082) was obtained for the terminal velocity; corresponding to a drag force of 3·24 × 10−4 N and a drag coefficient for the body of 0·086.\n\nWhen the fins were amputated and the fish dropped down the tank again, a mean value 0·0406 ms−1(n = 12, s.D. = 0·012) was obtained for the terminal velocity; giving a value of 7-22 x10−s N for the drag force on the body and 0·02 for Cb (based on the total wetted surface area).\n\nThe rate of working of an element (dW) is : and therefore the mean power produced during the power stroke (W) will be: W is plotted against time in Fig. 7. Fig. 7 shows that e4 accounts for over 80 % of the total work done during the power stroke; about 50% of it is produced between t = 1·5–4·0× 10−2 s. Small amounts of negative work are done early and late on in the stroke at the base of the fin.", null, "is calculated to be about 5· 3 × 10−5 W.\nThe total amount of energy dissipated during a cycle in dragging the body and inactive fins through the water (E0) is given by: and amounts to approximately 2·8 ×10−6 J. The propulsive efficiency (η) can be defined as the ratio of the work needed to move the body and inactive fins through are water to the work expended by the fins in actually doing so. It is given by : where E(tot) is the total energy required to produce the hydrodynamic thrust force and is about 0 26.\n\n### The effect of hydrodynamic ‘added mass’\n\nThe added mass of the entrained fluid of a body in unsteady motion is a fixed amount which depends on the size, volume, shape, mode of motion and the density of the fluid (Batchelor, 1967, p. 407). The pectoral fin blade-elements have been rotated about the median long axis of the fin, thereby generating a series of cylinders, the volumes of which have been calculated and multiplied by the water density to obtain values of the added mass of each blade-element. The added mass (ma) of an element is given by : Values of ma (0η2, 0η28 and 1η1 × 10−4 kg, for elements e2, e3 and e4 respectively) are about ten times greater than the corresponding values of me (see Table 1).\n\nThe acceleration (a) that each blade-element imparts to its associated added mass has been calculated (from the slopes of the curves in Fig. 2 and is considered to be of positive sign for both acceleration and deceleration phases of the stroke) and multiplied by ma to obtain the force required to accelerate and decelerate the added mass (Fig. 8). Due to the complications produced by flow reversal at the base of the fin, e1 is not considered.\n\nFig. 8.\n\nThe total hydrodynamic thrust force, added mass force and total force acting on the fin is plotted against time. The accelerations occurring between t = 2·0 ×10−2 s and t = 5·0 × 10−2 s are small and could not be measured accurately. The impulse of the added mass force is indicated by the shaded area.\n\nFig. 8.\n\nThe total hydrodynamic thrust force, added mass force and total force acting on the fin is plotted against time. The accelerations occurring between t = 2·0 ×10−2 s and t = 5·0 × 10−2 s are small and could not be measured accurately. The impulse of the added mass force is indicated by the shaded area.\n\nDuring the early part of the stroke (up to t = 2·0 ×10−2 s) the added mass force acts in the direction of the fin’s motion. After t = 5·0 ×10−2 s (when the hydrodynamic thrust force and added mass force are equal) the added mass force acts in the opposite direction. The impulses of the added mass forces cancel over the stroke (see Fig. 8).\n\nFig. 9.\n\nThe power required to accelerate and decelerate the added mass of the fin (◻), its individual blade-elements (e2 (◼), e3 (◯), e4 (▴), the total power required to produce the hydrodynamic thrust force (thin solid line) and the total power needed (heavy solid line) are plotted against time.\n\nFig. 9.\n\nThe power required to accelerate and decelerate the added mass of the fin (◻), its individual blade-elements (e2 (◼), e3 (◯), e4 (▴), the total power required to produce the hydrodynamic thrust force (thin solid line) and the total power needed (heavy solid line) are plotted against time.\n\nIn calculating Cn we have assumed :\n\n1. That all of the drag force is due to pressure drag.\n\n2. That the fin can be likened to a series of three-dimensional flat plates set at high angles of attack relative to the incident flow.\n\nFor αa> 40° (true for most of the fin for most of the power stroke duration time) it is reasonable to assume that the flow has separated from the rear surface of the fin and that the drag force is almost entirely due to pressure drag, while the skin friction can be neglected (Prandlt & Tietgens, 1957, p. 90).\n\nIt could be argued that elements e1-e3 are not equivalent to three-dimensional flat plates as they are bounded (e1 by the side of the body and the proximal border of e2, e2 by the distal border of e1and the proximal border of e3 and e3 by the distal border of e2 and the proximal border of e4) and that only e4 experiences a flow regime similar to that of a three-dimensional flat plate in free-flow. However, as e4 is responsible for over 80% of the thrust and work produced by the fin the application of one value of Cnto 04 and another to e1–e3 (based on curve A in Fig. 6 for instance) makes little difference to the final results.\n\nThe Angelfish studied was swimming steadily, in still water at Re = 3·2 ×103 and with a body that can be likened to a smooth, rigid streamlined body; flow in the boundary layer over the body should be laminar (transition to a turbulent boundary layer begins at about = 5·0 ×105 for smooth flat plates and rigid streamlined bodies with their long axis parallel to the direction of the incident flow). Blasius gave an equation for calculating the frictional resistance coefficient (Cf) for smooth flat plates in laminar flow : Applying this equation to the Angelfish studied gives a value of Cf = 0·023. For streamlined bodies the pressure drag coefficient, Cp is calculated as a fraction of Cf (Hoerner, 1958) and a value for the final drag coefficient of about 1·2 Cf can be expected for streamlined fish (Bainbridge, 1961). This would give a value of Cb = 0·027; which agrees well with our experimentally determined value of Cb = 0·02, for the drag coefficient of the body in the absence of the pectoral fins. The experimentally obtained value of Cb = 0·086 is within 15 % of our inferred value of o-i for the drag coefficient of the body when the pectoral fins are in a position typical of the power stroke. Values of Cb seem to be about four times greater than those found in the absence of the pectoral fins.\n\nLaminar boundary layers are relatively prone to separation as the transfer of momentum from the relatively rapidly moving outer flow to the slower moving fluid near the body surface is slow and ineffective. The broad based pectoral fins could disturb and locally disrupt the laminar boundary layer causing it to separate, in a region downstream of the pectoral fins, thereby increasing the drag on the body. The drag of circular and square flat plates set at high angles to the incident flow does not differ appreciably from free-flow values when they are attached to streamlined bodies; however, the drag of the streamlined body can be increased by a factor of five if the plate is placed (as the pectoral fins are) at the shoulder (Hoerner, 1958). The inactive pelvic fins could also produce a degree of interference.\n\nAlthough it is not the subject of this paper we may note another mode of swimming, using the caudal fin, that is employed by the Angelfish for high speed movements. In this mode the pectoral fins are tightly folded against the body, and may well produce no interference drag. The coefficient of the body may then well be as low as 0·01.\n\nIn most discussions of aquatic animal locomotion, consideration is confined to rectilinear locomotion at constant speed. In steady motion the fluid acceleration is zero and therefore no added mass forces arise. However, the force-producing surfaces which produce the exchange of momentum with the surrounding water are subject to unsteady motion, even when propelling a body forward at a constant speed. Many if the thrust-producing devices exployed by aquatic animals (e.g. the parapodia of the Polychaeta, the metapodial limbs of the Dytiscidae, Gyrinidae and Hydrophilidae, the limbs of some aquatic Heteroptera and Trichoptera, the paddle-like limbs of the Portunid crabs, the antennae used as oars in nauplii, some Conchostraca, Cladocera and Ostracoda) are hydrodynamically ‘bluff-bodies’ which have a large associated added mass in unsteady motion.\n\nThe retarding effect of the entrained added mass greatly reduces the efficiency of a paddling appendage, by increasing the amount of energy required to pull it through the water. The energy required to produce the hydrodynamic force of a pectoral fin is of the same order as that needed to accelerate and then decelerate the entrained added mass. The propulsive efficiency of the fin ignoring fin inertia and added mass is calculated to be 0 · 26. When they are taken into account a value of 0 · 18 is calculated, a reduction of about 31%.\n\nWebb (1973) has described the kinematics of a lift-based mechanism of labriform locomotion in Cymatogaster aggregata. On the basis of respirometric data and an analogy with the hovering flight of birds, Webb (1975b) concluded that the work required to rotate the pectoral fins would be high. This study indicates that this is probably not the case: as the mean energy required to move the actual mass of the fin is only about 7 % of the value of the added mass term for the specimen of P. eimekei studied here. Although respirometric data gives valuable experimental data on the total energy cost of locomotion in animals, it provides little information as to the mechanical principles involved.\n\nIn calculating the energy required to produce the hydrodynamic drag force, the force needed to overcome the mass of the fin and the added mass we have assumed that no interactions with the lateral sides of the body occur. The value of η ″ = 0·18 should be regarded as a lower limit as it is possible that the influence of the sides of the body aids the deceleration of the fin and its associated added mass.\n\nIn the final stages of the power stroke the fin can be regarded as a decelerating body which is approaching a relatively large boundary and therefore study of the effect of a small boat decelerating as it approaches the side of a large ship and the effect of a ship decelerating as it enters shallow water is relevant. The analytical studies of Koch (1933) and Prohaska (1947) indicate that the added mass of the smaller body should increase when the kinetic energy in the unsteady flow around it is increased as it approaches the larger body. However, it has been found experimentally (Saunders, 1957) that a decrease in added mass occurs around a small tug as it decelerates when approaching a large ship.\n\nNot all teleosts which swim in the labriform mode employ the drag-based mechanism for direct thrust production; many (e.g. Serranidae, Scorpididae and Scaridae) ‘clap’ their pectoral fins against the sides of their body to create backwardly directed jets which propel the animal forward (to be discussed in a future paper).\n\nLittle data is available on the propulsive efficiency of fusiform fish, swimming at low speeds. Webb (1971) considered the speed ratio V/Vw (forward swimming speed/backward speed of the propulsive wave) to be representative of the propulsive efficiency of undulatory swimming and found values of about 0 · 05 for trout (Salmo gairdneri) swimming at about 0·05 m s−1 (Re = 1·5 × 104); a value about three and one half times less than that calculated for the Angelfish at a similar speed and Reynolds number. If we assume that the two measures of propulsive efficiency and directly comparable, we can conclude that the pectoral fin drag-based mechanism propulsion is an adaption to slow swimming, when the efficiency of the undulatory mode is very low. However, considerations other than energetics could e×plain the use of the pectoral fins in low speed swimming. Were the Angelfish to swim in the undulatory mode at low speed it would be more conspicuous to predators and less manoeuvrable.\n\nAlthough drag-based mechanisms of propulsion are common among the aquatic invertebrates, little detailed work has been done. Nachtigall (1961, 1977) has described the kinematics of rowing in water beetles swimming at Reynolds Numbers of the same order as the Angelfish studied here (5·0–8·0 ×103). He estimated a propulsive efficiency of 0 · 3 for the metapodial limbs of Acilius sulcatus during the power stroke, based on the fraction of the total impulse available for propulsion and losses due to vorticity. His estimate is of the same order as η for the Angelfish (0·26), but was not calculated on the same basis.\n\nClark & Tritton (1970) analysed the dynamics of parapodial swimming in certain polychaetes ; however, their model was not used to estimate propulsive efficiency. Lochhead (1961, 1977) has reviewed the literature on the locomotion of the Crustacea and has pointed out that much work has to be done before we understand the drag mechanisms of propulsion many of them employ.\n\nI would like to thank Dr K. E. Machin, Professor Sir James Lighthill, F.R.S. and Mr C. P. Ellington for their advice and encouragement. I am grateful to Mr G. G. Runnalls for his expert advice and assistance with photography and the N.E.R.C. for financial support.\n\nBainbridge\n,\nR.\n(\n1961\n).\nProblems of fish locomotion\n.\nSymp. Zool. Soc. Lond\n.\n5\n,\n13\n32\n.\nBatchelor\n,\nG. K.\n(\n1967\n).\nAn Introduction to Fluid Dynamics\n.\nLondon\n:\nCambridge University Press\n.\nClark\n,\nR. B.\n&\nTritton\n,\nD. J.\n(\n1970\n).\nSwimming mechanisms in nereidiform polychaetes\n.\nJ. Zool., Lond\n.\n161\n,\n257\n271\n.\nFage\n,\nA.\n&\nJohansen\n,\nF. C.\n(\n1927\n).\nOn the flow of air behind an inclined flat plate of infinite span\n.\nR & M. no. 1104. Brit. A.R.C\n.\nHoerner\n,\nS. F.\n(\n1958\n).\n.\nKoch\n,\nJ. J.\n(\n1933\n).\nExperimental method for determining the virtual mass for oscillations of ships\n.\nIng. Arch\n.\n4\n.\n103\n109\n.\nLighthill\n,\nM. J.\n(\n1969\n).\nHydrodynamics of aquatic animal propulsion\n.\nA. Rev. Fluid Mech\n.\n9\n,\n305\n317\n.\n,\nJ. H.\n(\n1961\n).\nLocomotion\n.\nIn The Physiology of the Crustacea\n, vol.\n2\n(ed.\nT. H.\nWaterman\n), pp.\n313\n3 64\n.\nNew York\n:\n.\n,\nJ. H.\n(\n1977\n).\nUnsolved problems of interest in the locomotion of Crustacea\n.\nIn Scale Effects in Animal Locomotion\n(ed.\nT. J.\nPedley\n), pp.\n257\n268\n.\nLondon\n:\n.\nNachtigall\n,\nW.\n(\n1961\n).\nDynamics and energetics of swimming in water-beetles\n.\nNature, Lond\n.\n190\n,\n224\n225\n.\nNachtigall\n,\nW.\n(\n1977\n).\nSwimming mechanics and energetics of locomotion of variously sized water beetles: Dytiscidae, body length 2 to 35 mm\n.\nIn Scale Effects in Animal Locomotion\n(ed.\nT. J.\nPedley\n), pp.\n269\n283\n.\nLondon\n:\n.\nPrandtl\n,\nL.\n&\nTletgens\n,\nO. G.\n(\n1934\n).\nApplied Hydro- and Aeromechanics\n.\nNew York\n:\nDover Publications, Inc\n.\n,\nC. W.\n(\n1947\n).\nVibrations verticales du navire\n.\nAss. Tech. Mar. Aero\n.\n46\n,\n171\n219\n.\nSaunders\n,\nH. E.\n(\n1957\n).\nHydrodynamics in Ship Design\n, vol.\n2\n.\nNew York\n:\nSociety of Naval Architects and Marine Engineers\n.\nWebb\n,\nP. W.\n(\n1971\n).\nThe swimming energetics of trout. II. Oxygen consumption and swimming efficiency\n.\nJ. exp. Biol\n.\n59\n,\n521\n540\n.\nWebb\n,\nP. W.\n(\n1973\n).\nKinematics of pectoral fin propulsion in Cymatogaster aggregata\n.\nJ. exp. Biol\n.\n9\n,\n697\n710\n.\nWebb\n,\nP. W.\n(\n1975a\n).\nHydrodynamics of fish propulsion\n.\nBull. Fish. Res. Bd Can\n.\n190\n,\n1\n159\n.\nWebb\n,\nP. W.\n(\n1975b\n).\nEfficiency of pectoral-fin propulsion of Cymatogaster aggregata\n.\nIn and Flying in Nature\n, vol.\n2\n(ed.\nY. T.\nWu\n,\nC. J.\nBrokaw\nand\nC.\nBrennen\n), pp.\n573\n585\n.\nWick\n,\nB. H.\n(\n1954\n).\nStudy of the subsonic forces and moments on an inclined plate of infinite span\n.\nNACA tech, note no. 3221\n.\n\nNotation\n\nQuantities relating to a pectoral fin blade-element.\n\nei denotes the ith pectoral fin blade-element\n\nNe the number of elements\n\nI length of an element\n\nr distance from the base of the fin to the midpoint of an element\n\nc chord of the fin at the midpoint of an element\n\nvn normal velocity component of an element relative to the water\n\nvs spanwise velocity component relative to the water\n\nv resultant relative velocity for an element\n\nv average resultant relative velocity\n\na acceleration of an element\n\nαa hydrodynamical angle of attack of an element\n\ndA area of an element\n\nCn normal force coefficient of an element\n\ndFn normal force acting on an element\n\nme the mass of a blade-element\n\nma the added mass of an element\n\ndT forward directed component of thrust acting on an element\n\ndW rate of working of an element\n\nW power required to produce the hydrodynamic force on an element\n\nWa power required to accelerate the added mass of an element\n\nEf the energy required to move the mass of a blade-element\n\nOther quantities\n\nρ the water density\n\nR the total length of the fin\n\nω angular velocity of the fin\n\ny positional angle of the fin\n\nPt impulse of the thrust acting on the fin", null, "mean power produced during the power stroke\n\nt time\n\ntp time of duration of the power stroke\n\nt0 total fin-beat cycle time\n\nV velocity of the body\n\nSw total wetted surface area of the body and inactive fins\n\nCb drag coefficient of the body\n\nk a constant concerned with the normal force coefficients\n\nPb impulse of the drag force acting on the body\n\nEo energy dissipated during a cycle in dragging the body and inactive fins through the water\n\nE(tot) total energy required to produce the total hydrodynamic thrust force\n\nEα (tot) total energy required to move the added mass of the fin\n\nEf(tot) average total energy required to move the mass of the fin\n\nη propulsive efficiency (excluding inertial terms)\n\nη ′propulsive efficiency (including the effect of fin inertia)\n\nη ″propulsive efficiency (including the effect of fin inertia and added mass)\n\nRe Reynolds number" ]
[ null, "https://cob.silverchair-cdn.com/cob/content_public/journal/jeb/82/1/10.1242_jeb.82.1.255/3/m_jexbio_82_1_255inline1.gif", null, "https://cob.silverchair-cdn.com/cob/content_public/journal/jeb/82/1/10.1242_jeb.82.1.255/3/m_jexbio_82_1_255tb1.png", null, "https://cob.silverchair-cdn.com/cob/content_public/journal/jeb/82/1/10.1242_jeb.82.1.255/3/m_jexbio_82_1_255inline2.gif", null, "https://cob.silverchair-cdn.com/cob/content_public/journal/jeb/82/1/10.1242_jeb.82.1.255/3/m_jexbio_82_1_255inline2a.gif", null ]
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https://mathandlanguage.com/professional-development-services/
[ "# Professional Development on how to incorporate the Science of Math into daily math instruction with any curriculum.\n\nKaren provides in-person and online professional development for teachers, math interventionists, and parents on how to build foundational math skills from pre-K through pre-algebra, based in the science of how children learn math. While helping to write How Children Learn Math: The Science of Math Learning in Research and Practice (2023), Karen read thousands of research articles on math learning and cognition and continues to keep up with the research each month with her co-authors.\n\nKaren’s extensive experience with helping students learn math contributes to her ability to teach others how to teach math as well. Karen’s additional experience as a speech and language therapist provides a deep understanding of how language and reading are essential for math learning as well as how to break learning for greater success.\n\nThe science of math includes teaching concepts, using varied strategies that lead to mathematical thinking and not simply memorization, using procedures that coincide with understanding concepts, various types of mathematical reasoning, and a belief that all children can learn math and develop a positive outlook about the usefulness of math in everyday life.\n\nThe science of math provides coherent, systematic, and structured teaching in math that leads to incremental and logical understanding.\n\nThe following are some of the goals of her professional development. Attendees will know:\n\n• How to modify the very abstract English language of math that results in immediate increase\nin understanding math concepts\n• How to teach explicit Base-10 concepts, thinking and strategies rarely used in curriculums\nthat lead to deeper understanding of math and greater ease in arithmetic\n• How to include number lines, number charts, and spatial processing as a critical component\nof developing a mental number line and learning arithmetic\n• How to include concrete experience with math, followed by meaningful diagrams and\npictures, and then abstract representations of the math concepts\n• How to consistently use decomposition as highest level of mathematical thinking\n• How to improve math fact fluency for addition, subtraction, multiplication, and division\n• How to use explicit instruction with modeling, targeted practice and feedback\n• How to solve word problem with a variety of strategies and approaches\n• How to teach rational numbers: fractions, decimals and percentages with greater meaning,\nmodified language, magnitude understanding, and a deep understanding of arithmetic and\nprocedures\n• How to include spatial skill development and why it is so important\n• How to consider the cognitive skills children need to succeed in math, and how some\ncommon curriculum instruction requires cognitive skills beyond what is expected for children\nof different ages." ]
[ null ]
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https://www.numberempire.com/28986
[ "Home | Menu | Get Involved | Contact webmaster", null, "", null, "", null, "", null, "", null, "# Number 28986\n\ntwenty eight thousand nine hundred eighty six\n\n### Properties of the number 28986\n\n Factorization 2 * 3 * 4831 Divisors 1, 2, 3, 6, 4831, 9662, 14493, 28986 Count of divisors 8 Sum of divisors 57984 Previous integer 28985 Next integer 28987 Is prime? NO Previous prime 28979 Next prime 29009 28986th prime 337361 Is a Fibonacci number? NO Is a Bell number? NO Is a Catalan number? NO Is a factorial? NO Is a regular number? NO Is a perfect number? NO Polygonal number (s < 11)? NO Binary 111000100111010 Octal 70472 Duodecimal 14936 Hexadecimal 713a Square 840188196 Square root 170.2527532817 Natural logarithm 10.274568233782 Decimal logarithm 4.4621882878702 Sine 0.99545461765845 Cosine -0.095237094571799 Tangent -10.452383308564\nNumber 28986 is pronounced twenty eight thousand nine hundred eighty six. Number 28986 is a composite number. Factors of 28986 are 2 * 3 * 4831. Number 28986 has 8 divisors: 1, 2, 3, 6, 4831, 9662, 14493, 28986. Sum of the divisors is 57984. Number 28986 is not a Fibonacci number. It is not a Bell number. Number 28986 is not a Catalan number. Number 28986 is not a regular number (Hamming number). It is a not factorial of any number. Number 28986 is an abundant number and therefore is not a perfect number. Binary numeral for number 28986 is 111000100111010. Octal numeral is 70472. Duodecimal value is 14936. Hexadecimal representation is 713a. Square of the number 28986 is 840188196. Square root of the number 28986 is 170.2527532817. Natural logarithm of 28986 is 10.274568233782 Decimal logarithm of the number 28986 is 4.4621882878702 Sine of 28986 is 0.99545461765845. Cosine of the number 28986 is -0.095237094571799. Tangent of the number 28986 is -10.452383308564\n\n### Number properties\n\nExamples: 3628800, 9876543211, 12586269025" ]
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http://www.bdnyc.org/author/kayhiranaka/
[ "# Fitting a power law to data\n\nI wanted to fit a power law function to data, not a polynomial. Here's how I did it.\n\nI used the least squares method.\n\nIf you prefer other types of functions, just change the function form to whatever you want to fit when you define it.\n\nThe inputs for leastsq are the error function (difference between data and a function you want to fit) and initial conditions. When full_output = nonzero, it returns the covariance matrix in addition to the parameters that minimize the sum of squares of the error function.\n\nWhat would you fit a power law function to?\n\n# Formatting Plots for Paper in Python\n\nSay you have a nice figure and you want to make it look good in your paper. Figures in  papers will be in the dimension of 8.9cm x 8.9cm (3.6in x 3.6in) so you want to make them clearly legible when shrunk to this size. Something like this.\n\nYou can set the size of your figure by doing\n\nfigure = matplotlib.pyplot.figure(figsize=(3.6, 3.6))\n\nthen you can check what it looks like in that dimension on your screen.\n\nYou may need to set the size of the plot so that all the axis titles are inside the figure. These parameters worked for me.\n\nsubplot = figure.add_subplot(1, 1, 1, position = [0.2, 0.15, 0.75, 0.75])\n\nIn the position bracket are [left (y axis position, x_0), bottom (x axis position, y_0), width (length of x axis), height (length of y axis)] of your plot.\n\nTo set the x and y limits on the axes, use set_xlim([xmin, xmax]) and set_ylim([ymin, ymax]).\n\nTo make the plot simple, you want to keep the variation of color and style to a minimum. Maybe combinations of a couple of colors and a couple of simple line styles. You can edit line width, line color, and line style by adding arguments to your plot command." ]
[ null ]
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https://www.colorhexa.com/02c6ce
[ "# #02c6ce Color Information\n\nIn a RGB color space, hex #02c6ce is composed of 0.8% red, 77.6% green and 80.8% blue. Whereas in a CMYK color space, it is composed of 99% cyan, 3.9% magenta, 0% yellow and 19.2% black. It has a hue angle of 182.4 degrees, a saturation of 98.1% and a lightness of 40.8%. #02c6ce color hex could be obtained by blending #04ffff with #008d9d. Closest websafe color is: #00cccc.\n\n• R 1\n• G 78\n• B 81\nRGB color chart\n• C 99\n• M 4\n• Y 0\n• K 19\nCMYK color chart\n\n#02c6ce color description : Strong cyan.\n\n# #02c6ce Color Conversion\n\nThe hexadecimal color #02c6ce has RGB values of R:2, G:198, B:206 and CMYK values of C:0.99, M:0.04, Y:0, K:0.19. Its decimal value is 181966.\n\nHex triplet RGB Decimal 02c6ce `#02c6ce` 2, 198, 206 `rgb(2,198,206)` 0.8, 77.6, 80.8 `rgb(0.8%,77.6%,80.8%)` 99, 4, 0, 19 182.4°, 98.1, 40.8 `hsl(182.4,98.1%,40.8%)` 182.4°, 99, 80.8 00cccc `#00cccc`\nCIE-LAB 72.796, -37.253, -15.646 31.356, 44.854, 65.394 0.221, 0.317, 44.854 72.796, 40.405, 202.782 72.796, -55.392, -18.898 66.973, -33.631, -11.011 00000010, 11000110, 11001110\n\n# Color Schemes with #02c6ce\n\n• #02c6ce\n``#02c6ce` `rgb(2,198,206)``\n• #ce0a02\n``#ce0a02` `rgb(206,10,2)``\nComplementary Color\n• #02ce70\n``#02ce70` `rgb(2,206,112)``\n• #02c6ce\n``#02c6ce` `rgb(2,198,206)``\n• #0260ce\n``#0260ce` `rgb(2,96,206)``\nAnalogous Color\n• #ce7002\n``#ce7002` `rgb(206,112,2)``\n• #02c6ce\n``#02c6ce` `rgb(2,198,206)``\n• #ce0260\n``#ce0260` `rgb(206,2,96)``\nSplit Complementary Color\n• #c6ce02\n``#c6ce02` `rgb(198,206,2)``\n• #02c6ce\n``#02c6ce` `rgb(2,198,206)``\n• #ce02c6\n``#ce02c6` `rgb(206,2,198)``\n• #02ce0a\n``#02ce0a` `rgb(2,206,10)``\n• #02c6ce\n``#02c6ce` `rgb(2,198,206)``\n• #ce02c6\n``#ce02c6` `rgb(206,2,198)``\n• #ce0a02\n``#ce0a02` `rgb(206,10,2)``\n• #017d82\n``#017d82` `rgb(1,125,130)``\n• #02959b\n``#02959b` `rgb(2,149,155)``\n• #02aeb5\n``#02aeb5` `rgb(2,174,181)``\n• #02c6ce\n``#02c6ce` `rgb(2,198,206)``\n• #02dee7\n``#02dee7` `rgb(2,222,231)``\n• #06f3fd\n``#06f3fd` `rgb(6,243,253)``\n• #20f4fd\n``#20f4fd` `rgb(32,244,253)``\nMonochromatic Color\n\n# Alternatives to #02c6ce\n\nBelow, you can see some colors close to #02c6ce. Having a set of related colors can be useful if you need an inspirational alternative to your original color choice.\n\n• #02cea3\n``#02cea3` `rgb(2,206,163)``\n• #02ceb4\n``#02ceb4` `rgb(2,206,180)``\n• #02cec5\n``#02cec5` `rgb(2,206,197)``\n• #02c6ce\n``#02c6ce` `rgb(2,198,206)``\n• #02b5ce\n``#02b5ce` `rgb(2,181,206)``\n• #02a4ce\n``#02a4ce` `rgb(2,164,206)``\n• #0293ce\n``#0293ce` `rgb(2,147,206)``\nSimilar Colors\n\n# #02c6ce Preview\n\nThis text has a font color of #02c6ce.\n\n``<span style=\"color:#02c6ce;\">Text here</span>``\n#02c6ce background color\n\nThis paragraph has a background color of #02c6ce.\n\n``<p style=\"background-color:#02c6ce;\">Content here</p>``\n#02c6ce border color\n\nThis element has a border color of #02c6ce.\n\n``<div style=\"border:1px solid #02c6ce;\">Content here</div>``\nCSS codes\n``.text {color:#02c6ce;}``\n``.background {background-color:#02c6ce;}``\n``.border {border:1px solid #02c6ce;}``\n\n# Shades and Tints of #02c6ce\n\nA shade is achieved by adding black to any pure hue, while a tint is created by mixing white to any pure color. In this example, #000b0c is the darkest color, while #f7ffff is the lightest one.\n\n• #000b0c\n``#000b0c` `rgb(0,11,12)``\n• #001e1f\n``#001e1f` `rgb(0,30,31)``\n• #003133\n``#003133` `rgb(0,49,51)``\n• #014346\n``#014346` `rgb(1,67,70)``\n• #015659\n``#015659` `rgb(1,86,89)``\n• #01696d\n``#01696d` `rgb(1,105,109)``\n• #017b80\n``#017b80` `rgb(1,123,128)``\n• #018e94\n``#018e94` `rgb(1,142,148)``\n• #02a1a7\n``#02a1a7` `rgb(2,161,167)``\n• #02b3bb\n``#02b3bb` `rgb(2,179,187)``\n• #02c6ce\n``#02c6ce` `rgb(2,198,206)``\n• #02d9e1\n``#02d9e1` `rgb(2,217,225)``\n• #02ebf5\n``#02ebf5` `rgb(2,235,245)``\n• #0ef3fd\n``#0ef3fd` `rgb(14,243,253)``\n• #22f4fd\n``#22f4fd` `rgb(34,244,253)``\n• #35f5fd\n``#35f5fd` `rgb(53,245,253)``\n• #48f6fd\n``#48f6fd` `rgb(72,246,253)``\n• #5cf7fd\n``#5cf7fd` `rgb(92,247,253)``\n• #6ff8fe\n``#6ff8fe` `rgb(111,248,254)``\n• #83f9fe\n``#83f9fe` `rgb(131,249,254)``\n• #96fafe\n``#96fafe` `rgb(150,250,254)``\n• #aafbfe\n``#aafbfe` `rgb(170,251,254)``\n• #bdfcfe\n``#bdfcfe` `rgb(189,252,254)``\n• #d0fdff\n``#d0fdff` `rgb(208,253,255)``\n• #e4feff\n``#e4feff` `rgb(228,254,255)``\n• #f7ffff\n``#f7ffff` `rgb(247,255,255)``\nTint Color Variation\n\n# Tones of #02c6ce\n\nA tone is produced by adding gray to any pure hue. In this case, #626e6e is the less saturated color, while #02c6ce is the most saturated one.\n\n• #626e6e\n``#626e6e` `rgb(98,110,110)``\n• #5a7576\n``#5a7576` `rgb(90,117,118)``\n• #527c7e\n``#527c7e` `rgb(82,124,126)``\n• #4a8486\n``#4a8486` `rgb(74,132,134)``\n• #428b8e\n``#428b8e` `rgb(66,139,142)``\n• #3a9296\n``#3a9296` `rgb(58,146,150)``\n• #329a9e\n``#329a9e` `rgb(50,154,158)``\n• #2aa1a6\n``#2aa1a6` `rgb(42,161,166)``\n• #22a9ae\n``#22a9ae` `rgb(34,169,174)``\n• #1ab0b6\n``#1ab0b6` `rgb(26,176,182)``\n• #12b7be\n``#12b7be` `rgb(18,183,190)``\n• #0abfc6\n``#0abfc6` `rgb(10,191,198)``\n• #02c6ce\n``#02c6ce` `rgb(2,198,206)``\nTone Color Variation\n\n# Color Blindness Simulator\n\nBelow, you can see how #02c6ce is perceived by people affected by a color vision deficiency. This can be useful if you need to ensure your color combinations are accessible to color-blind users.\n\nMonochromacy\n• Achromatopsia 0.005% of the population\n• Atypical Achromatopsia 0.001% of the population\nDichromacy\n• Protanopia 1% of men\n• Deuteranopia 1% of men\n• Tritanopia 0.001% of the population\nTrichromacy\n• Protanomaly 1% of men, 0.01% of women\n• Deuteranomaly 6% of men, 0.4% of women\n• Tritanomaly 0.01% of the population" ]
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https://www.scribd.com/document/378914300/Corrosion-Resistance-Guide-PULTRUSION
[ "You are on page 1of 26\n\n# CORROSION RESISTANCE GUIDE\n\nINDUSTRIAL PRODUCTS\nThe cover photo shows severe, short-term corrosive\neffects of 37% sulfuric acid on various materials. All bar\nsamples originally measured 6” long x 1/4” thick x 1/2”\nwide. Products depicted from left to right are carbon steel,\nEXTREN® Series 625, aluminum and EXTREN® Series\n525. The steel base has deteriorated significantly below\nthe solution line and incurred atmospheric corrosion.\nThe aluminum also deteriorated and developed corrosive\naluminum sulfite deposits. Both EXTREN® samples were\nnot affected by the sulfuric acid solution.\n\n2\nStrongwell Corrosion Resistance Guide\nThe Resin Selection Guide for Strongwell Industrial Product Lines:\n\n## FIBERGLASS BUILDING PANEL SYSTEM\n\nNOTE: Information in this Corrosion Guide is specifically intended for the products manufactured by Strongwell\nand may have little correspondence to other pultruded or molded products.\n\n*COMPOSOLITE® is a registered trademark of Maunsell Structural Plastics, Ltd. and used by Strongwell Corporation pursuant to license.\n3\n4\nHow To Use This Guide\n\n## Strongwell believes the information and recommendations Special Considerations:\n\nherein to be accurate and reliable. Any questionable\n• DURAGRATE® - Corrosion resistance data for polyester resins\napplication should be preceded by a small sample or\nis applicable only to the PP, premium (isophthalic) polyester\nprototype evaluation in the actual chemical environment.\nresin system. The general purpose orthothalic polyester resin\nCorrosive conditions not specifically discussed in this guide\nsystem (GP) is only recommended for corrosion situations\n(including lower concentrations than those tested) should be\nsuch as salt water or mild wastewater.\nreferenced to Strongwell’s Customer Service Department for\nan evaluation of the individual situation. • DURASHIELD® - The cut ends must be sealed with an epoxy\nsystem for polyester and a vinyl ester system for the vinyl\nThe specific recommendations in this Corrosion Guide are for ester DURASHIELD® such that there is no possibility of\nimmersion applications where good fabrication procedures chemical intrusion.\nhave been followed. These recommendations should be • Fiberglass Structures - The standard components of\nconsidered applicable to non-immersion situations regarding Strongwell FIBERGLASS STRUCTURES are shown in this\nthe same EXTREN® series and chemical combination without Corrosion Resistance Guide. Fabrication procedures similar\na formal review by Strongwell. to those in Strongwell’s EXTREN® Fabrication and Repair\nManual should be followed to obtain the corrosion resistance\nstated in this guide.\n\n## The following definitions will aid readers using this Guide:\n\nR.T. Room Temperature\nH. Temp Highest Temperature\n(TP) Thermoplastic\nR Resistant\nNR Not Resistant\nC Concern (Indicates data is inconclusive. Customer is advised to confirm\nthe corrosion resistance in their applications with pre-shipment\nsample.)\nEXTREN® 500/525 Isophthalic Polyester\nEXTREN® 625 Vinyl Ester\nDURAGRATE®\nVE Vinyl Ester\nPP Isophthalic Polyester\nGP Orthothalic Polyester *\n*Not referred to in this Corrosion Resistance Guide\n\nNote: Temperature data is not necessarily the maximum service temperature; it is the\nupper temperature at which a resin has been tested, used or evaluated.\n\n5\nVINYL ESTER VINYL ESTER\nCOMPOSOLITE® COMPOSOLITE®\nEXTREN® EXTREN® POLYESTER POLYESTER\nDURADEK® DURADEK® COMPOSOLITE® COMPOSOLITE®\nDURAGRID® DURAGRID® EXTREN® EXTREN®\nDURASHIELD® DURASHIELD® DURASHIELD® DURASHIELD®\nSAFPLANK® SAFPLANK® SAFPLANK® SAFPLANK® POLYESTER\nSAFPLATE® SAFPLATE® SAFPLATE® SAFPLATE® DURADEK®\nCHEMICAL SAFRAILTM SAFRAILTM SAFRAILTM SAFRAILTM DURAGRID®\nENVIRONMENT R.T. 160OF R.T. 150OF R.T.\nA Acetic Acid 0-25% R R R R R\nAcetic Acid 25-50% R R R NR R\nAcetic Anhydride NR NR NR NR NR\nAcetone NR NR NR NR NR\nAcrylonitrile NR NR NR NR NR\n\nAlcohol, Butyl R NR NR NR NR\nAlcohol, Ethyl 10% R 150 NR NR NR\nAlcohol, Ethyl 100% R NR NR NR NR\nAlcohol, Isopropyl 10% R 150 NR NR NR\nAlcohol, Isopropyl 100% R NR NR NR NR\n\n## Alcohol, Methyl 10% R NR NR NR NR\n\nAlcohol, Methyl 100% NR NR NR NR NR\nAlcohol, Methyl Isobutyl R 150 NR NR NR\nAlcohol, Secondary Butyl R 150 NR NR NR\nAlum R R R R R\n\nAluminum Chloride R R R R R\nAluminum Hydroxide 5% R 120 R NR NR\nAluminum Nitrate R R R R NR\nAluminum Potassium Sulfate R R R R R\nAmmonia, Aqueous 0-10% R 100 NR NR NR\n\n## Ammonia, Gas R 100 NR NR NR\n\nAmmonium Bicarbonate R 120 R NR R\nAmmonium Bisulfite R 120 NR NR NR\nAmmonium Carbonate 10% R 120 NR NR\nAmmonium Citrate R 120 R NR NR\n\n## Ammonium Hydroxide 5% R 120 NR NR NR\n\nAmmonium Hydroxide 10% R 120 NR NR NR\nAmmonium Hydroxide 20% R 120 NR NR NR\nAmmonium Nitrate R R R R R\nAmmonium Persulfate R 120 NR NR NR\n\nAmmonium Phosphate R 120 NR NR NR\nAmmonium Sulfate R R R R R\nArsenious Acid R R R NR NR\n\nB Barium Acetate R R NR NR NR\nBarium Carbonate R R R NR R\nBarium Chloride R R R NR R\nBarium Hydroxide R 120 NR NR NR\nBarium Sulfate R R R R R\n\nBarium Sulfide R R NR NR NR\nBeer R 120 R NR R\nBenzene NR NR NR NR NR\n5% Benzene in Kerosene R R R NR NR\n\n## Benzene Sulfonic Acid 30% R R R R R\n\nBenzoic Acid R R R NR R\n\n6\nDURAGRATE® MOLDED GRATING\nPOLYESTER FIBREBOLT® FIBREBOLT®\nDURADEK® HEX NUT HEX NUT VINYL VINYL POLYESTER POLYESTER\nCHEMICAL DURAGRID® (TP) (TP) ESTER ESTER R.T. 150OF\nENVIRONMENT 150OF R.T. 150OF R.T. 160OF\n\n## A Acetic Acid 0-25% 125 R R R R R 125\n\nAcetic Acid 25-50% NR R R R R R NR\nAcetic Anhydride NR NR NR NR NR NR NR\nAcetone NR NR NR NR NR NR NR\nAcrylonitrile NR NR NR NR NR NR NR\n\nAlcohol, Butyl NR R NR R NR NR NR\nAlcohol, Ethyl 10% NR R 150 R 150 NR NR\nAlcohol, Ethyl 100% NR R NR R NR NR NR\nAlcohol, Isopropyl 10% NR R 150 R 150 NR NR\nAlcohol, Isopropyl 100% NR R NR R NR NR NR\n\n## Alcohol, Methyl 10% NR R NR R NR NR NR\n\nAlcohol, Methyl 100% NR NR NR NR NR NR NR\nAlcohol, Methyl Isobutyl NR R 150 R 150 NR NR\nAlcohol, Secondary Butyl NR R 150 R 150 NR NR\nAlum R R R R R R R\n\n## Aluminum Chloride 120 R R R R R 120\n\nAluminum Hydroxide 5% NR R 120 R 120 NR NR\nAluminum Nitrate NR R R R R NR NR\nAluminum Potassium Sulfate R R R R R R R\nAmmonia, Aqueous 0-10% NR R 100 R 100 NR NR\n\n## Ammonia, Gas NR R 100 R 100 NR NR\n\nAmmonium Bicarbonate NR R 120 R 120 R NR\nAmmonium Bisulfite NR R 120 R 120 NR NR\nAmmonium Carbonate 10% NR R 120 R 120 NR NR\nAmmonium Citrate NR R 120 R 120 NR NR\n\nAmmonium Hydroxide 5% NR R 120 R 120 R NR\nAmmonium Hydroxide 10% NR R 120 R 120 NR NR\nAmmonium Hydroxide 20% NR R 120 R 120 NR NR\nAmmonium Nitrate R R R R R R R\nAmmonium Persulfate NR R 120 R 120 NR NR\n\nAmmonium Phosphate NR R 120 R 120 NR NR\nAmmonium Sulfate R R R R R R R\nArsenious Acid NR R R R R NR NR\n\nB Barium Acetate NR R R R R NR NR\nBarium Carbonate NR R R R R R NR\nBarium Chloride 200 R R R R R 200\nBarium Hydroxide NR R 120 R 120 NR NR\nBarium Sulfate R R R R R R R\n\nBarium Sulfide NR R R R R NR NR\nBeer NR R 120 R 120 R NR\nBenzene NR NR NR NR NR NR NR\n5% Benzene in Kerosene NR R R R R NR NR\n\n## Benzene Sulfonic Acid 30% R R R R R R R\n\nBenzoic Acid NR R R R R R NR\n\n7\nVINYL ESTER VINYL ESTER\nCOMPOSOLITE® COMPOSOLITE®\nEXTREN® EXTREN® POLYESTER POLYESTER\nDURADEK® DURADEK® COMPOSOLITE® COMPOSOLITE®\nDURAGRID® DURAGRID® EXTREN® EXTREN®\nDURASHIELD® DURASHIELD® DURASHIELD® DURASHIELD®\nSAFPLANK® SAFPLANK® SAFPLANK® SAFPLANK® POLYESTER\nSAFPLATE® SAFPLATE® SAFPLATE® SAFPLATE® DURADEK®\nCHEMICAL SAFRAILTM SAFRAILTM SAFRAILTM SAFRAILTM DURAGRID®\nENVIRONMENT R.T. 160OF R.T. 150OF R.T.\n\n## B O-Benzoyl Benzoic Acid R R NR NR NR\n\nBenzyl Alcohol R NR NR NR NR\nBenzyl Chloride NR NR NR NR NR\nBrass Plating Solution: R R NR NR NR\n(3% Copper Cyanide\n6% Sodium Cyanide\n1% Zinc Cyanide\n3% Sodium Carbonate)\n\nButyl Acetate NR NR NR NR NR\nButylene Glycol R R R R R\nButyric Acid 0-50% R R R NR R\n\nC Cadmium Chloride R R R NR R\nCadmium Cyanide Plating\nSolution: (3% Cadmium Oxide R 120 NR NR NR\n6% Sodium Cyanide\n1% Caustic Soda)\n\nCalcium Bisulfite R R R R R\nCalcium Chlorate R R R R R\nCalcium Chloride R R R R R\nCalcium Hypochlorite R 120 NR NR NR\nCalcium Nitrate R R R R R\n\nCalcium Sulfate R R R R R\nCalcium Sulfite R R R R R\nCaprylic Acid R R R NR R\nCarbon Dioxide R R R R R\nCarbon Disulfide NR NR NR NR NR\n\nCarbon Monoxide R R R R R\nCarbon Tetrachloride R 100 NR NR NR\nCarbonic Acid R R R NR R\nCarbon Methyl Cellulose R 120 NR NR NR\nCastor Oil R R R R NR\n\nChlorinated Wax R R NR NR NR\nChlorine Dioxide/Air R R R NR R\nChlorine Dioxide, Wet Gas R R NR NR NR\nChlorine, Dry Gas R R R NR R\nChlorine, Wet Gas R R NR NR NR\n\nChlorine, Liquid NR NR NR NR NR\nChlorine, Swimming\nPool (pH 7 to <8) R R R R R\nChlorine, Water R R NR NR NR\nChloroacetic Acid 0-50% R 100 NR NR NR\n\nChlorobenzene NR NR NR NR NR\nChloroform NR NR NR NR NR\nChlorosulfonic Acid NR NR NR NR NR\nChromic Acid NR NR NR NR NR\n\n8\nDURAGRATE® MOLDED GRATING\nPOLYESTER FIBREBOLT® FIBREBOLT®\nDURADEK® HEX NUT HEX NUT VINYL VINYL POLYESTER POLYESTER\nCHEMICAL DURAGRID® (TP) (TP) ESTER ESTER R.T. 150OF\nENVIRONMENT 150OF R.T. 150OF R.T. 160OF\n\n## B O-Benzoyl Benzoic Acid NR R R R R NR NR\n\nBenzyl Alcohol NR R NR R NR NR NR\nBenzyl Chloride NR NR NR NR NR NR NR\nBrass Plating Solution: NR R R R R NR NR\n(3% Copper Cyanide\n6% Sodium Cyanide\n1% Zinc Cyanide\n3% Sodium Carbonate)\n\nButyl Acetate NR NR NR NR NR NR NR\nButylene Glycol R R R R R R R\nButyric Acid 0-50% NR R R R R R NR\n\nC Cadmium Chloride NR R R R R R NR\nCadmium Cyanide Plating\nSolution: (3% Cadmium Oxide NR R 120 R 120 NR NR\n6% Sodium Cyanide\n1% Caustic Soda)\n\nCalcium Bisulfite R R R R R R R\nCalcium Chlorate R R R R R R R\nCalcium Chloride R R R R R R R\nCalcium Hypochlorite NR C C R 120 NR NR\nCalcium Nitrate R R R R R R R\n\nCalcium Sulfate R R R R R R R\nCalcium Sulfite R R R R R R R\nCaprylic Acid NR R R R R R NR\nCarbon Dioxide R R R R R R R\nCarbon Disulfide NR NR NR NR NR NR NR\n\nCarbon Monoxide R R R R R R R\nCarbon Tetrachloride NR NR NR R 100 NR NR\nCarbonic Acid R R R R R R R\nCarbon Methyl Cellulose NR R 120 R 120 NR NR\nCastor Oil NR R R R R NR NR\n\nChlorinated Wax NR R R R R NR NR\nChlorine Dioxide/Air NR R R R R R NR\nChlorine Dioxide, Wet Gas NR R R R R NR NR\nChlorine, Dry Gas NR C C R R R NR\nChlorine, Wet Gas NR C C R R NR NR\n\nChlorine, Liquid NR NR NR NR NR NR NR\nChlorine, Water NR C C R R NR NR\nChlorine, Swimming\nPool (pH 7 to <8) R R R R R R R\nChloroacetic Acid 0-50% NR R 100 R 100 NR NR\n\nChlorobenzene NR NR NR NR NR NR NR\nChloroform NR NR NR NR NR NR NR\nChlorosulfonic Acid NR NR NR NR NR NR NR\nChromic Acid NR NR NR NR NR NR NR\n\n9\nVINYL ESTER VINYL ESTER\nCOMPOSOLITE® COMPOSOLITE®\nEXTREN® EXTREN® POLYESTER POLYESTER\nDURADEK® DURADEK® COMPOSOLITE® COMPOSOLITE®\nDURAGRID® DURAGRID® EXTREN® EXTREN®\nDURASHIELD® DURASHIELD® DURASHIELD® DURASHIELD®\nSAFPLANK® SAFPLANK® SAFPLANK® SAFPLANK® POLYESTER\nSAFPLATE® SAFPLATE® SAFPLATE® SAFPLATE® DURADEK®\nCHEMICAL SAFRAILTM SAFRAILTM SAFRAILTM SAFRAILTM DURAGRID®\nENVIRONMENT R.T. 160OF R.T. 150OF R.T.\nC Chromium Sulfate R R R R R\nCitric Acid R R R R R\nCoconut Oil R R R NR R\nCopper Chloride R R R R R\nCopper Cyanide R R NR NR NR\nCopper Fluoride R R NR NR NR\n\nCopper Nitrate R NR R R R\nCopper Plating Solution: R R NR NR NR\n(Copper Cyanide\n10.5% Copper\n4% Copper Cyanide\n6% Rochelle Salts)\n\n## Copper Brite Plating: R 120 NR NR NR\n\n(Caustic Cyanide)\nCopper Plating Solution: R R NR NR NR\n(45% Copper Fluoborate\n19% Copper Sulfate\n8% Sulfuric Acid)\n\n## Copper Matte Dipping Bath: R R NR NR NR\n\n(30% Ferric Chloride\n19% Hydrochloric Acid)\nCopper Pickling Bath: R R NR NR NR\n(10% Ferric Sulfate\n10% Sulfuric Acid)\n\nCopper Sulfate R R R R R\nCorn Oil R R R NR R\nCorn Starch-Slurry R R R NR R\nCorn Sugar R R R NR R\n\nCottonseed Oil R R R NR R\nCrude Oil, Sour R R R NR R\nCrude Oil, Sweet R R R NR R\nCyclohexane R 120 R NR R\n\nD Detergents, Sulfonated R R R NR R\nDi-Ammonium Phosphate R R NR NR NR\nDibromophenol NR NR NR NR NR\nDibutyl Ether R 120 NR NR NR\n\nDichloro Benzene NR NR NR NR NR\nDichloroethylene NR NR NR NR NR\nDiesel Fuel R R R NR R\nDiethylene Glycol R R R NR R\n\nDimenthyl Phthalate R R NR NR NR\nDioctyl Phthalate R R NR NR NR\nDipropylene Glycol R R R NR R\nDodecyl Alcohol R R NR NR NR\n\n10\nDURAGRATE® MOLDED GRATING\nPOLYESTER FIBREBOLT® FIBREBOLT®\nDURADEK® HEX NUT HEX NUT VINYL VINYL POLYESTER POLYESTER\nCHEMICAL DURAGRID® (TP) (TP) ESTER ESTER R.T. 150OF\nENVIRONMENT 150OF R.T. 150OF R.T. 160OF\n\nC Chromium Sulfate R R R R R R R\nCitric Acid R R R R R R R\nCoconut Oil NR R R R R R NR\nCopper Chloride R R R R R R R\nCopper Cyanide NR R R R R NR NR\nCopper Fluoride NR R R R R NR NR\n\nCopper Nitrate R R NR R NR R R\nCopper Plating Solution: NR R R R R NR NR\n(Copper Cyanide\n10.5% Copper\n4% Copper Cyanide\n6% Rochelle Salts)\n\n## Copper Brite Plating: NR R 120 R 120 NR NR\n\n(Caustic Cyanide)\nCopper Plating Solution: NR R R R R NR NR\n(45% Copper Fluoborate\n19% Copper Sulfate\n8% Sulfuric Acid)\n\n## Copper Matte Dipping Bath: NR R R R R NR NR\n\n(30% Ferric Chloride\n19% Hydrochloric Acid)\nCopper Pickling Bath: NR R R R R NR NR\n(10% Ferric Sulfate\n10% Sulfuric Acid)\n\nCopper Sulfate R R R R R R R\nCorn Oil NR R R R R R NR\nCorn Starch-Slurry NR R R R R R NR\nCorn Sugar NR R R R R R NR\n\nCottonseed Oil NR R R R R R NR\nCrude Oil, Sour NR R R R R R NR\nCrude Oil, Sweet NR R R R R R NR\nCyclohexane NR R 120 R 120 R NR\n\nD Detergents, Sulfonated NR R R R R R NR\nDi-Ammonium Phosphate NR R R R R NR NR\nDibromophenol NR NR NR NR NR NR NR\nDibutyl Ether NR R 120 R 120 NR NR\n\nDichloro Benzene NR NR NR NR NR NR NR\nDichloroethylene NR NR NR NR NR NR NR\nDiesel Fuel NR R R R R R NR\nDiethylene Glycol NR R R R R R NR\n\nDimenthyl Phthalate NR R R R R NR NR\nDioctyl Phthalate NR R R R R NR NR\nDipropylene Glycol NR R R R R R NR\nDodecyl Alcohol NR R R R R NR NR\n\n11\nVINYL ESTER VINYL ESTER\nCOMPOSOLITE® COMPOSOLITE®\nEXTREN® EXTREN® POLYESTER POLYESTER\nDURADEK® DURADEK® COMPOSOLITE® COMPOSOLITE®\nDURAGRID® DURAGRID® EXTREN® EXTREN®\nDURASHIELD® DURASHIELD® DURASHIELD® DURASHIELD®\nSAFPLANK® SAFPLANK® SAFPLANK® SAFPLANK® POLYESTER\nSAFPLATE® SAFPLATE® SAFPLATE® SAFPLATE® DURADEK®\nCHEMICAL SAFRAILTM SAFRAILTM SAFRAILTM SAFRAILTM DURAGRID®\nENVIRONMENT R.T. 160OF R.T. 150OF R.T.\n\n## E Esters, Fatty Acids R R R R NR\n\nEthyl Acetate NR NR NR NR NR\nEthyl Benzene NR NR NR NR NR\nEthyl Ether NR NR NR NR NR\nEthylene Dichloride NR NR NR NR NR\nEthylene Glycol R R R R R\n\nF Fatty Acids R R R R R\nFerric Chloride R R R R R\nFerric Nitrate R R R R R\nFerric Sulfate R R R R R\nFerrous Chloride R R R R R\n\nFerrous Nitrate R R R R R\nFerrous Sulfate R R R R R\n8-8-8 Fertilizer R R R NR R\nFertilizer: R 120 NR NR NR\n(Urea Ammonium Nitrate)\n\nFlue Gas R R NR NR NR\nFluosilicic Acid 5% R NR NR NR NR\nFormaldehyde R R R NR R\nFormic Acid 10% R R R NR R\nFuel Oil R R R NR R\n\nG Gas, Natural R R R NR R\nGasoline, Auto R R R NR R\nGasoline, Aviation R R R NR R\nGasoline, Ethyl R R R NR R\nGasoline, Sour R R R NR R\n\nGlyconic Acid R R R NR R\nGlucose R R R R R\nGlycerine R R R R R\nGlycol, Propylene R R R R R\nGlycolic Acid 70% R R R NR R\n\n## Gold Plating Solution: R R NR NR NR\n\n(63% Potassium Ferrocyanide\n2% Potassium Gold Cyanide\n8% Sodium Cyanide)\n\nH Heptane R R R NR R\nHexane R R R NR R\nHexalene Glycol R R R R R\nHydraulic Fluid R R R NR R\n\n## Hydrobromic Acid 0-25% R R R NR R\n\nHydrochloric Acid 0-37% R R R NR NR\nHydrocyanic Acid R R R NR R\nHydrofluoric Acid 1% NR NR NR NR NR\n\n12\nDURAGRATE® MOLDED GRATING\nPOLYESTER FIBREBOLT® FIBREBOLT®\nDURADEK® HEX NUT HEX NUT VINYL VINYL POLYESTER POLYESTER\nCHEMICAL DURAGRID® (TP) (TP) ESTER ESTER R.T. 150OF\nENVIRONMENT 150OF R.T. 150OF R.T. 160OF\n\n## E Esters, Fatty Acids NR R R R R NR NR\n\nEthyl Acetate NR NR NR NR NR NR NR\nEthyl Benzene NR NR NR NR NR NR NR\nEthyl Ether NR NR NR NR NR NR NR\nEthylene Dichloride NR NR NR NR NR NR NR\nEthylene Glycol R R R R R R R\n\nF Fatty Acids R R R R R R R\nFerric Chloride R R R R R R R\nFerric Nitrate R R R R R R R\nFerric Sulfate R R R R R R R\nFerrous Chloride R R R R R R R\n\nFerrous Nitrate R R R R R R R\nFerrous Sulfate R R R R R R R\n8-8-8 Fertilizer NR R 120 R R NR NR\nFertilizer: NR R 120 R 120 NR NR\n(Urea Ammonium Nitrate)\n\nFlue Gas NR R R R R NR NR\nFluosilicic Acid 5% NR R R R R NR NR\nFormaldehyde NR R R R R R NR\nFormic Acid 10% NR C C R R R NR\nFuel Oil NR R R R R R NR\n\nG Gas, Natural NR R R R R R NR\nGasoline, Auto NR R R R R R NR\nGasoline, Aviation NR R R R R R NR\nGasoline, Ethyl NR R R R R R NR\nGasoline, Sour NR R R R R R NR\n\nGlyconic Acid NR R R R R R NR\nGlucose R R R R R R R\nGlycerine R R R R R R R\nGlycol, Propylene R R R R R R R\nGlycolic Acid 70% NR R R R R R NR\n\n## Gold Plating Solution: NR R R R R NR NR\n\n(63% Potassium Ferrocyanide\n2% Potassium Gold Cyanide\n8% Sodium Cyanide)\n\nH Heptane NR R R R R R NR\nHexane NR R R R R R NR\nHexalene Glycol R R R R R R R\nHydraulic Fluid NR R R R R R NR\n\n## Hydrobromic Acid 0-25% NR NR NR R R R NR\n\nHydrochloric Acid 0-37% NR NR NR R R NR NR\nHydrocyanic Acid NR R R R R R NR\nHydrofluoric Acid 1% NR NR NR NR NR NR NR\n\n13\nVINYL ESTER VINYL ESTER\nCOMPOSOLITE® COMPOSOLITE®\nEXTREN® EXTREN® POLYESTER POLYESTER\nDURADEK® DURADEK® COMPOSOLITE® COMPOSOLITE®\nDURAGRID® DURAGRID® EXTREN® EXTREN®\nDURASHIELD® DURASHIELD® DURASHIELD® DURASHIELD®\nSAFPLANK® SAFPLANK® SAFPLANK® SAFPLANK® POLYESTER\nSAFPLATE® SAFPLATE® SAFPLATE® SAFPLATE® DURADEK®\nCHEMICAL SAFRAILTM SAFRAILTM SAFRAILTM SAFRAILTM DURAGRID®\nENVIRONMENT R.T. 160OF R.T. 150OF R.T.\n\nH Hydrofluosilicic Acid 5% R NR NR NR NR\nHydrogen Bromide, Wet Gas R R NR NR NR\nHydrogen Chloride, Dry Gas R R NR NR NR\nHydrogen Chloride, Wet Gas R R NR NR NR\nHydrogen Fluoride, Vapor R NR NR NR NR\n\n## Hydrogen Peroxide 35% R 120 NR NR NR\n\nHydrogen Sulfide Dry R R R 120 R\nHydrogen Sulfide, Aqueous R R R NR NR\nHydrosulfite Bleach R 120 NR NR NR\nHypochlorous Acid 0-10% R R NR NR NR\n\n## I Iron Plating Solution: R R NR NR NR\n\n(45% FeCl2; 15% CaCl2\n20% FeSo4; 11% (NH4)2 SO4)\n\n## Iron and Steel Cleaning Bath: R R NR NR NR\n\n(9% Hydrochloric, 23% Sulfuric)\nIsopropyl Amine R 100 NR NR NR\nIsopropyl Palmitate R R R R R\n\nJ Jet Fuel R R R NR NR\n\nK Kerosene R R R NR R\n\nL Lactic Acid R R R NR R\nLauroyl Chloride R R NR NR NR\nLauric Acid R R R NR NR\nLead Acetate R R R NR R\nLead Chloride R R R NR NR\n\nLead Nitrate R R R NR NR\nLead Plating Solution: R R NR NR NR\n(0.8% Fluoboric Acid\n0.4% Boric Acid)\n\nLevulinic Acid R R R NR NR\nLinseed Oil R R R R NR\nLithium Bromide R R R R NR\nLithium Sulfate R R R R NR\n\nM Magnesium Bisulfite R R R NR NR\nMagnesium Chloride R R R R R\nMagnesium Hydroxide R 140 NR NR NR\nMagnesium Nitrate R R R NR R\nMagnesium Sulfate R R R R R\nMaleic Acid R R R R NR\n\nMercuric Chloride R R R NR R\nMercurous Chloride R R R NR R\nMethanol 10% R NR NR NR NR\n(see Alcohol, Methyl 10%)\nMethylene Chloride NR NR NR NR NR\n\n14\nDURAGRATE® MOLDED GRATING\nPOLYESTER FIBREBOLT® FIBREBOLT®\nDURADEK® HEX NUT HEX NUT VINYL VINYL POLYESTER POLYESTER\nCHEMICAL DURAGRID® (TP) (TP) ESTER ESTER R.T. 150OF\nENVIRONMENT 150OF R.T. 150OF R.T. 160OF\n\nH Hydrofluosilicic Acid 5% NR NR NR NR NR NR NR\nHydrogen Bromide, Wet Gas NR NR NR R R NR NR\nHydrogen Chloride, Dry Gas NR NR NR R R NR NR\nHydrogen Chloride, Wet Gas NR NR NR R R NR NR\nHydrogen Fluoride, Vapor 95 C C R NR R 95\n\n## Hydrogen Peroxide 35% 120 C C R 120 R 120\n\nHydrogen Sulfide Dry 120 R 120 R R R 120\nHydrogen Sulfide, Aqueous NR R R R R NR NR\nHydrosulfite Bleach NR C C R 120 NR NR\nHypochlorous Acid 0-10% 104 C C R R R 104\n\n## I Iron Plating Solution: NR R R R R NR NR\n\n(45% FeCl2; 15% CaCl2\n20% FeSo4; 11% (NH4)2 SO4)\n\n## Iron and Steel Cleaning Bath: NR C C R R NR NR\n\n(9% Hydrochloric, 23% Sulfuric)\nIsopropyl Amine NR R 100 R 100 NR NR\nIsopropyl Palmitate 180 R R R R R 180\n\nJ Jet Fuel NR R R R R NR NR\n\n## L Lactic Acid 200 R R R R R 200\n\nLauroyl Chloride NR R R R R NR NR\nLauric Acid NR R R R R NR NR\nLead Acetate 160 R R R R R 160\nLead Chloride NR R R R R NR NR\n\nLead Nitrate NR R R R R NR NR\nLead Plating Solution: NR R R R R NR NR\n(0.8% Fluoboric Acid\n0.4% Boric Acid)\n\nLevulinic Acid NR R R R R NR NR\nLinseed Oil NR R R R R NR NR\nLithium Bromide NR R R R R NR NR\nLithium Sulfate NR R R R R NR NR\n\nM Magnesium Bisulfite NR R R R R NR NR\nMagnesium Chloride 220 R R R R R 220\nMagnesium Hydroxide NR R 140 R 140 NR NR\nMagnesium Nitrate 160 R R R R R 160\nMagnesium Sulfate 200 R R R R R 200\nMaleic Acid NR R R R R NR NR\n\nMercuric Chloride 212 R R R R R 212\nMercurous Chloride 212 R R R R R 212\nMethanol 10% NR R 150 R NR NR NR\n(see Alcohol, Methyl 10%)\nMethylene Chloride NR NR NR NR NR NR NR\n\n15\nVINYL ESTER VINYL ESTER\nCOMPOSOLITE® COMPOSOLITE®\nEXTREN® EXTREN® POLYESTER POLYESTER\nDURADEK® DURADEK® COMPOSOLITE® COMPOSOLITE®\nDURAGRID® DURAGRID® EXTREN® EXTREN®\nDURASHIELD® DURASHIELD® DURASHIELD® DURASHIELD®\nSAFPLANK® SAFPLANK® SAFPLANK® SAFPLANK® POLYESTER\nSAFPLATE® SAFPLATE® SAFPLATE® SAFPLATE® DURADEK®\nCHEMICAL SAFRAILTM SAFRAILTM SAFRAILTM SAFRAILTM DURAGRID®\nENVIRONMENT R.T. 160OF R.T. 150OF R.T.\n\n## M Methyl Ethyl Ketone @ 120F NR NR NR NR NR\n\nMethyl Isobutyl Carbitol NR NR NR NR NR\nMethyl Isobutyl Ketone NR NR NR NR NR\nMethyl Styrene NR NR NR NR NR\nMineral Oils R R R R R\n\nMolybdenum Disulfide R R R NR NR\nMonochloric Acetic Acid NR NR NR NR NR\nMonoethanolamine NR NR NR NR NR\nMotor Oil R R R R R\nMyristic Acid R R NR NR NR\n\nN Naphtha R R R R R\nNaphthalene R R R NR R\nNickel Chloride R R R R R\nNickel Nitrate R R R R R\n\nNickel Plating: R R NR NR NR\n(8% Lead, 0.8% Fluoboric Acid\n0.4% Boric Acid)\n\nNickel Plating: R R R NR R\n(11% Nickel Sulfate\n2% Nickel Chloride\n1% Boric Acid)\n\nNickel Plating: R R R NR R\n(44% Nickel Sulfate\n4% Ammonium Chloride\n4% Boric Acid)\n\nNickel Sulfate R R R R R\nNitric Acid 0-5% R R R R R\nNitric Acid 15% R 120 NR NR NR\nNitric Acid Fumes NR NR NR NR NR\nNitrobenzene NR NR NR NR NR\n\nO Octanoic Acid R R R NR R\nOil, Sour Crude R R R R R\nOil, Sweet Crude R R R R R\nOleic Acid R R R R R\n\n## Oleum (Fuming Sulfuric) NR NR NR NR NR\n\nOlive Oil R R R R R\nOxalic Acid R R R R R\n\nP Peroxide Bleach: R R R R R\n(2% Sodium Peroxide 96%\n0.025% Epsom Salts,\n5% Sodium Silicate 42o Be,\n1.4% Sulfuric Acid 66o Be)\nPhenol NR NR NR NR NR\nPhenol Sulfonic Acid NR NR NR NR NR\n\n16\nDURAGRATE® MOLDED GRATING\nPOLYESTER FIBREBOLT® FIBREBOLT®\nDURADEK® HEX NUT HEX NUT VINYL VINYL POLYESTER POLYESTER\nCHEMICAL DURAGRID® (TP) (TP) ESTER ESTER R.T. 150OF\nENVIRONMENT 150OF R.T. 150OF R.T. 160OF\n\n## M Methyl Ethyl Ketone @ 120F NR NR NR NR NR NR NR\n\nMethyl Isobutyl Carbitol NR NR NR NR NR NR NR\nMethyl Isobutyl Ketone NR NR NR NR NR NR NR\nMethyl Styrene NR NR NR NR NR NR NR\nMineral Oils 180 R R R R R 180\n\nMolybdenum Disulfide NR R R R R NR NR\nMonochloric Acetic Acid NR NR NR NR NR NR NR\nMonoethanolamine NR NR NR NR NR NR NR\nMotor Oil R R R R R NR NR\nMyristic Acid NR R R R R R R\n\nN Naphtha R R R R R R R\nNaphthalene NR R R R R R NR\nNickel Chloride NR R R R R R NR\nNickel Nitrate R R R R R R R\n\nNickel Plating: NR R R R R NR NR\n(8% Lead, 0.8% Fluoboric Acid\n0.4% Boric Acid)\n\nNickel Plating: NR R R R R R NR\n(11% Nickel Sulfate\n2% Nickel Chloride\n1% Boric Acid)\n\nNickel Plating: NR R R R R R NR\n(44% Nickel Sulfate\n4% Ammonium Chloride\n4% Boric Acid)\n\nNickel Sulfate R R R R R R R\nNitric Acid 0-5% R NR NR R R R R\nNitric Acid 15% NR NR NR R 120 NR NR\nNitric Acid Fumes NR NR NR NR NR NR NR\nNitrobenzene NR NR NR NR NR NR NR\n\nO Octanoic Acid NR R R R R R NR\nOil, Sour Crude R R R R R R R\nOil, Sweet Crude R R R R R R R\nOleic Acid R R R R R R R\n\n## Oleum (Fuming Sulfuric) NR NR NR NR NR NR NR\n\nOlive Oil R R R R R R R\nOxalic Acid R R R R R R R\n\nP Peroxide Bleach: R R R R R R R\n(2% Sodium Peroxide 96%\n0.025% Epsom Salts,\n5% Sodium Silicate 42o Be,\n1.4% Sulfuric Acid 66o Be)\nPhenol NR NR NR NR NR NR NR\nPhenol Sulfonic Acid NR NR NR NR NR NR NR\n\n17\nVINYL ESTER VINYL ESTER\nCOMPOSOLITE® COMPOSOLITE®\nEXTREN® EXTREN® POLYESTER POLYESTER\nDURADEK® DURADEK® COMPOSOLITE® COMPOSOLITE®\nDURAGRID® DURAGRID® EXTREN® EXTREN®\nDURASHIELD® DURASHIELD® DURASHIELD® DURASHIELD®\nSAFPLANK® SAFPLANK® SAFPLANK® SAFPLANK® POLYESTER\nSAFPLATE® SAFPLATE® SAFPLATE® SAFPLATE® DURADEK®\nCHEMICAL SAFRAILTM SAFRAILTM SAFRAILTM SAFRAILTM DURAGRID®\nENVIRONMENT R.T. 160OF R.T. 150OF R.T.\nP Phosphoric Acid 85% R R R R R\nPhosphoric Acid Fumes R R R R R\nPhosphorous Pentoxide R R R R R\nPhosphorous Trichloride NR NR NR NR NR\nPhthalic Acid R R R R R\nPickling Acids: R R R R R\n(Sulfuric and Hydrochloric)\n\n## Picric Acid, Alcoholic R R R R R\n\nPolyvinyl Acetate Latex R R R NR R\nPolyvinyl Alcohol R 100 R NR R\nPolyvinyl Chloride Latex R 120 NR NR NR\nwith 35 (Parts DOP)\n\n## Potassium Aluminum Sulfate R R R R R\n\nPotassium Bicarbonate R 140 R NR R\nPotassium Bromide R 100 R NR NR\nPotassium Chloride R R R R R\nPotassium Dichromate R 140 R NR NR\n\nPotassium Ferricyanide R R R R R\nPotassium Ferrocyanide R R R R R\nPotassium Nitrate R R R R R\nPotassium Permanganate R 140 R NR R\nPotassium Persulfate R R R NR R\n\nPotassium Sulfate R R R R R\nPropionic Acid 1-50% R 120 NR NR NR\n(50% NR 100%) NR NR NR NR NR\nPropylene Glycol R R R R R\nPulp Paper Mill Effluent R R R NR R\n\nPyridine NR NR NR NR NR\n\n## S Salicylic Acid R 140 NR NR NR\n\nSebacic Acid R R NR NR NR\nSelenious Acid R R NR NR NR\nSilver Nitrate R R R R R\n\n## Silver Plating Solution: R R NR NR NR\n\n(4% Silver Cyanide\n7% Potassium Cyanide\n5% Sodium Cyanide\n2% Potassium Carbonate)\n\nSoaps R R R NR R\nSodium Acetate R R R NR R\nSodium Benzoate R R R NR R\nSodium Bicarbonate R R R R NR\n\n## Sodium Bifluoride R 120 R NR R\n\nSodium Bisulfate R R R R R\n\n18\nDURAGRATE® MOLDED GRATING\nPOLYESTER FIBREBOLT® FIBREBOLT®\nDURADEK® HEX NUT HEX NUT VINYL VINYL POLYESTER POLYESTER\nCHEMICAL DURAGRID® (TP) (TP) ESTER ESTER R.T. 150OF\nENVIRONMENT 150OF R.T. 150OF R.T. 160OF\n\n## P Phosphoric Acid 85% R C C R R R R\n\nPhosphoric Acid Fumes R C C R R R R\nPhosphorous Pentoxide R C C R R R R\nPhosphorous Trichloride NR NR NR NR NR NR NR\nPhthalic Acid R R R R R R R\nPickling Acids: R C C R R R R\n(Sulfuric and Hydrochloric)\n\n## Picric Acid, Alcoholic R NR NR R R R R\n\nPolyvinyl Acetate Latex NR R R R R R NR\nPolyvinyl Alcohol NR R 100 R 100 R NR\nPolyvinyl Chloride Latex NR R 120 R 120 NR NR\nwith 35 (Parts DOP)\n\n## Potassium Aluminum Sulfate R R R R R R R\n\nPotassium Bicarbonate NR R 140 R 140 R NR\nPotassium Bromide NR R 100 R 100 NR NR\nPotassium Chloride R R R R R R R\nPotassium Dichromate NR R 140 R 140 NR NR\n\nPotassium Ferricyanide R R R R R R R\nPotassium Ferrocyanide R R R R R R R\nPotassium Nitrate R R R R R R R\nPotassium Permanganate NR R 140 R 140 R NR\nPotassium Persulfate NR R R R R R NR\n\nPotassium Sulfate R R R R R R R\nPropionic Acid 1-50% NR R 120 R 120 NR NR\n(50% NR 100%) NR NR NR NR NR NR NR\nPropylene GlycolR R R R R R R R\nPulp Paper Mill Effluent NR R R R R R NR\n\nPyridine NR NR NR NR NR NR NR\n\n## S Salicylic Acid NR R 140 R 140 NR NR\n\nSebacic Acid NR R R R R NR NR\nSelenious Acid NR R R R R NR NR\nSilver Nitrate R R R R R R R\n\n## Silver Plating Solution: NR R R R R NR NR\n\n(4% Silver Cyanide\n7% Potassium Cyanide\n5% Sodium Cyanide\n2% Potassium Carbonate)\n\nSoaps NR R R R R R NR\nSodium Acetate NR R R R R R NR\nSodium Benzoate NR R R R R R NR\nSodium Bicarbonate NR R R R R NR NR\n\n## Sodium Bifluoride NR R 120 R 120 R NR\n\nSodium Bisulfate R R R R R R R\n\n19\nVINYL ESTER VINYL ESTER\nCOMPOSOLITE® COMPOSOLITE®\nEXTREN® EXTREN® POLYESTER POLYESTER\nDURADEK® DURADEK® COMPOSOLITE® COMPOSOLITE®\nDURAGRID® DURAGRID® EXTREN® EXTREN®\nDURASHIELD® DURASHIELD® DURASHIELD® DURASHIELD®\nSAFPLANK® SAFPLANK® SAFPLANK® SAFPLANK® POLYESTER\nSAFPLATE® SAFPLATE® SAFPLATE® SAFPLATE® DURADEK®\nCHEMICAL SAFRAILTM SAFRAILTM SAFRAILTM SAFRAILTM DURAGRID®\nENVIRONMENT R.T. 160OF R.T. 150OF R.T.\n\nS Sodium Bisulfite R R R R R\nSodium Bromate R 140 R R NR\nSodium Bromide R R R R R\nSodium Chlorate R R R NR R\nSodium Chloride R R R R R\n\nSodium Chlorite 25% R R R NR R\nSodium Chromate R R R R NR\nSodium Cyanide R R R NR R\nSodium Dichromate R R R R R\nSodium Di-Phosphate R R R R R\n\nSodium Ferricyanide R R R R R\nSodium Fluoride R 120 NR NR NR\nSodium Fluoro Silicate R 120 NR NR NR\nSodium Hexametaphosphates R 100 NR NR NR\nSodium Hydroxide 0-5% R 150 NR NR NR\n\nSodium Hydroxide 5-25% R 150 NR NR NR\nSodium Hydroxide 50% R 150 NR NR NR\nSodium Hydrosulfide R R R NR R\nSodium Hypochlorite (bleach) R R NR NR NR\nSodium Lauryl Sulfate R R R R R\nSodium Mono-Phosphate R R R R R\n\nSodium Nitrate R R R R R\nSodium Silicate R R R NR R\nSodium Sulfate R R R R R\nSodium Sulfide R R R NR R\nSodium Sulfite R R R NR R\n\nSodium Tetra Borate R R R R R\nSodium Thiocyanate R R NR NR NR\nSodium Thiosulfate R R R NR R\nSodium Tripolyphosphate R R R NR R\nSodium Xylene Sulfonate R R R NR R\n\nSodium Solutions R R R NR R\nSodium Crude Oil R R R R R\nSoya Oil R R R R R\nStannic Chloride R R R R R\nStannous Chloride R R R R R\n\nStearic Acid R R R R R\nStyrene NR NR NR NR NR\nSugar, Beet and Cane Liquor R R R NR R\nSugar, Sucrose R R R R R\nSulfamic Acid R R R NR R\n\nSulfanilic Acid 50% R R NR NR NR\nSulfated Detergents R R R NR R\nSulfur Dioxide, Dry or Wet R R NR NR NR\nSulfur, Trioxide/Air R R NR NR NR\n\n20\nDURAGRATE® MOLDED GRATING\nPOLYESTER FIBREBOLT® FIBREBOLT®\nDURADEK® HEX NUT HEX NUT VINYL VINYL POLYESTER POLYESTER\nCHEMICAL DURAGRID® (TP) (TP) ESTER ESTER R.T. 150OF\nENVIRONMENT 150OF R.T. 150OF R.T. 160OF\n\nS Sodium Bisulfite R R R R R R R\nSodium Bromate NR R 140 R 140 NR NR\nSodium Bromide R R R R R R R\nSodium Chlorate NR R R R R R NR\nSodium Chloride R R R R R R R\n\nSodium Chlorite 25% NR R R R R R NR\nSodium Chromate NR R R R R NR NR\nSodium Cyanide NR R R R R R NR\nSodium Dichromate R R R R R R R\nSodium Di-Phosphate R R R R R R R\n\nSodium Ferricyanide R R R R R R R\nSodium Fluoride NR R 120 R 120 NR NR\nSodium Fluoro Silicate NR R 120 R 120 NR NR\nSodium Hexametaphosphates NR R 100 R 100 NR NR\nSodium Hydroxide 0-5% NR R 150 R 150 NR NR\n\nSodium Hydroxide 5-25% NR R 150 R 150 NR NR\nSodium Hydroxide 50% NR R 150 R 150 NR NR\nSodium Hydrosulfide NR R R R R R NR\nSodium Hypochlorite (bleach) NR R R R R NR NR\nSodium Lauryl Sulfate R R R R R R R\nSodium Mono-Phosphate R R R R R R R\n\nSodium Nitrate R R R R R R R\nSodium Silicate NR R R R R R NR\nSodium Sulfate R R R R R R R\nSodium Sulfide NR R R R R R NR\nSodium Sulfite NR R R R R R NR\n\nSodium Tetra Borate R R R R R R R\nSodium Thiocyanate NR R R R R NR NR\nSodium Thiosulfate NR R R R R R NR\nSodium Tripolyphosphate NR R R R R R NR\nSodium Xylene Sulfonate NR R R R R R NR\n\nSodium Solutions NR R R R R R NR\nSodium Crude Oil R R R R R R R\nSoya Oil R R R R R R R\nStannic Chloride R R R R R R R\nStannous Chloride R R R R R R R\n\nStearic Acid R R R R R R R\nStyrene NR NR NR NR NR NR NR\nSugar, Beet and Cane Liquor NR R R R R R NR\nSugar, Sucrose R R R R R R R\nSulfamic Acid NR R R R R R NR\n\nSulfanilic Acid 50% NR R R R R NR NR\nSulfated Detergents NR R R R R R NR\nSulfur Dioxide, Dry or Wet NR R R R R NR NR\nSulfur, Trioxide/Air NR R R R R NR NR\n\n21\nVINYL ESTER VINYL ESTER\nCOMPOSOLITE® COMPOSOLITE®\nEXTREN® EXTREN® POLYESTER POLYESTER\nDURADEK® DURADEK® COMPOSOLITE® COMPOSOLITE®\nDURAGRID® DURAGRID® EXTREN® EXTREN®\nDURASHIELD® DURASHIELD® DURASHIELD® DURASHIELD®\nSAFPLANK® SAFPLANK® SAFPLANK® SAFPLANK® POLYESTER\nSAFPLATE® SAFPLATE® SAFPLATE® SAFPLATE® DURADEK®\nCHEMICAL SAFRAILTM SAFRAILTM SAFRAILTM SAFRAILTM DURAGRID®\nENVIRONMENT R.T. 160OF R.T. 150OF R.T.\nS Sulfuric Acid 0-30% R R R R R\nSulfuric Acid 30-50% R R NR NR NR\nSulfuric Acid 50-70% R 120 NR NR NR\nSulfurous Acid 10% R 100 NR NR NR\nSuperphosphoric Acid R R R NR R\n(76% P2O5)\n\n## T Tall Oil R 150 R NR R\n\nTannic Acid R 120 R NR R\nTartaric Acid R R R R R\nThionyl Chloride NR NR NR NR NR\n\nTin Plating: R R NR NR NR\n(18% Stannous Fluoborate\n7% Tin\n9% Fluoboric Acid\n2% Boric Acid)\n\nToluene NR NR NR NR NR\nToluene Sulfonic Acid R R NR NR NR\nTransformer Oils:\nMineral Oil Types R R R R R\nChloro-Phenyl Types NR NR NR NR NR\n\n## Trichloro Acetic Acid 50% R R R NR R\n\nTrichlorethylene NR NR NR NR NR\nTrichloropenol NR NR NR NR NR\nTricresyl Phosphate R 120 NR NR NR\n\nTridecylbenzene Sulfonate R R NR NR NR\nTrisodium Phosphate R R R NR R\nTurpentine R 100 NR NR NR\n\nU Urea R 140 R NR R\n\nV Vegetable Oils R R R R R\nVinegar R R R R R\nVinyl Acetate NR NR NR NR NR\n\nW Water:\nDeionized R R R R R\nDemineralized R R R R R\nDistilled R R R R R\nFresh R R R R R\nSalt R R R R R\nSea R R R R R\nWhite Liquor (Pulp Mill) R R R NR R\n\nX Xylene NR NR NR NR NR\n\n22\nDURAGRATE® MOLDED GRATING\nPOLYESTER FIBREBOLT® FIBREBOLT®\nDURADEK® HEX NUT HEX NUT VINYL VINYL POLYESTER POLYESTER\nCHEMICAL DURAGRID® (TP) (TP) ESTER ESTER R.T. 150OF\nENVIRONMENT 150OF R.T. 150OF R.T. 160OF\n\n## S Sulfuric Acid 0-30% R R C R R R R\n\nSulfuric Acid 30-50% NR C C R R NR NR\nSulfuric Acid 50-70% NR C C R 120 NR NR\nSulfurous Acid 10% NR R 100 R 100 NR NR\nSuperphosphoric Acid NR C C R R R NR\n(76% P2O5)\n\n## T Tall Oil NR R 140 R 150 R NR\n\nTannic Acid NR R 150 R 120 R NR\nTartaric Acid R R R R R R R\nThionyl Chloride NR NR NR NR NR NR NR\n\nTin Plating: NR R R R R NR NR\n(18% Stannous Fluoborate\n7% Tin\n9% Fluoboric Acid\n2% Boric Acid)\n\nToluene NR NR NR NR NR NR NR\nToluene Sulfonic Acid NR R R R R NR NR\nTransformer Oils:\nMineral Oil Types R C C R R R R\nChloro-Phenyl Types NR NR NR NR NR NR NR\n\n## Trichloro Acetic Acid 50% NR C C R R R NR\n\nTrichlorethylene NR NR NR NR NR NR NR\nTrichloropenol NR NR NR NR NR NR NR\nTricresyl Phosphate NR R 120 R 120 NR NR\n\nTridecylbenzene Sulfonate NR R R R R R NR\nTrisodium Phosphate NR R R R R R NR\nTurpentine NR R 100 R 100 NR NR\n\n## U Urea NR R 100 R 140 R NR\n\nV Vegetable Oils R R R R R R R\nVinegar R R R R R R R\nVinyl Acetate NR NR NR NR NR NR NR\n\nW Water:\nDeionized R R R R R R R\nDemineralized R R R R R R R\nDistilled R R R R R R R\nFresh R R R R R R R\nSalt R R R R R R R\nSea R R R R R R R\nWhite Liquor (Pulp Mill) NR R R R R R NR\n\nX Xylene NR NR NR NR NR NR NR\n\n23\nVINYL ESTER VINYL ESTER\nCOMPOSOLITE® COMPOSOLITE®\nEXTREN® EXTREN® POLYESTER POLYESTER\nDURADEK® DURADEK® COMPOSOLITE® COMPOSOLITE®\nDURAGRID® DURAGRID® EXTREN® EXTREN®\nDURASHIELD® DURASHIELD® DURASHIELD® DURASHIELD®\nSAFPLANK® SAFPLANK® SAFPLANK® SAFPLANK® POLYESTER\nSAFPLATE® SAFPLATE® SAFPLATE® SAFPLATE® DURADEK®\nCHEMICAL SAFRAILTM SAFRAILTM SAFRAILTM SAFRAILTM DURAGRID®\nENVIRONMENT R.T. 160OF R.T. 150OF R.T.\n\nZ Zinc Chlorate R R R R R\nZinc Nitrate R R R R R\nZinc Plating Solution: R 120 NR NR NR\n(9% Zinc Cyanide\n4% Sodium Cyanide\n9% Sodium Hydroxide)\n\n## Zinc Plating Solution: R R R NR R\n\n(49% Zinc Fluoborate\n5% Ammonium Chloride\n6% Ammonium Fluoborate)\nZinc Sulfate R R R R R\n\n24\nDURAGRATE® MOLDED GRATING\nPOLYESTER FIBREBOLT® FIBREBOLT®\nDURADEK® HEX NUT HEX NUT VINYL VINYL POLYESTER POLYESTER\nCHEMICAL DURAGRID® (TP) (TP) ESTER ESTER R.T. 150OF\nENVIRONMENT 150OF R.T. 150OF R.T. 160OF\n\nZ Zinc Chlorate R R R R R R R\nZinc Nitrate R R R R R R R\nZinc Plating Solution: NR R 120 R 120 NR NR\n(9% Zinc Cyanide\n4% Sodium Cyanide\n9% Sodium Hydroxide)\n\n## Zinc Plating Solution: NR R R R R R NR\n\n(49% Zinc Fluoborate\n5% Ammonium Chloride\n6% Ammonium Fluoborate)\nZinc Sulfate R R R R R R R\n\n25\n®\n\n## BRISTOL DIVISION CHATFIELD DIVISION\n\n400 Commonwealth Ave., P. O. Box 580, Bristol, VA 24203-0580 1610 Highway 52 South, Chatfield, MN 55923-9799\n(276) 645-8000 FAX (276) 645-8132 (507) 867-3479, FAX (507) 867-4031\nwww.strongwell.com\nST0211\n©Strongwell" ]
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https://scholarcommons.sc.edu/etd/1615/
[ "## Theses and Dissertations\n\n1-1-2012\n\n#### Document Type\n\nCampus Access Thesis\n\nMathematics\n\nHong Wang\n\n#### Abstract\n\nFractional diffusion equations are generalizations of classical diffusion equations which are used in modeling practical superdiffusive problems in fluid flow, finance and others. Because of the nonlocal property of fractional differential operators, the numerical methods for fractional diffusion equations often generate dense or even full coefficient matrices, which results in computational work of O(N^3) per time step and memory of O(N^2) where N is the number of grid points. While a lot of methods are dealing with one dimensional problem, in this paper we develop a multigrid acceleration for spacial fractional diffusion equations in two space dimensions. The method only requires computational work of O(N logN) and memory of O(N) per time step, while retaining the same accuracy and approximation property as the regular finite difference method with Gaussian elimination. Our preliminary numerical examples run for two dimensional model problem of intermediate size seem to indicate the observations: To achieve the same accuracy, the new method has a significant reduction of the CPU time from more than 1 months consumed by a traditional finite difference method to less than 20 min, using less than one thousandth of memory the standard method does. This demonstrates the utility of the method. iv\n\nCOinS" ]
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https://www.scribd.com/presentation/360747853/Temperature-Measurements-Lecture-pptx
[ "You are on page 1of 74\n\n# Engineering 80 Spring 2015\n\nTemperature Measurements\n\nSOURCE: http://www.eng.hmc.edu/NewE80/PDFs/VIshayThermDataSheet.pdf\n\nSOURCE: http://elcodis.com/photos/19/51/195143/to-92-\n3_standardbody__to-226_straightlead.jpg\n\nSOURCE: http://www.accuglassproducts.com/product.php?productid=17523\n\n1\nKey Concepts\nMeasuring Temperature\nTypes of Temperature Sensors\nThermistor\nIntegrated Silicon Linear Sensor\nThermocouple\nResistive Temperature Detector (RTD)\nChoosing a Temperature Sensor\nCalibrating Temperature Sensors\nThermal System Transient Response\n\n## ENGR 106 Lecture 3 Failure 2\n\nWhat is Temperature?\n\nSOURCE: http://www.clker.com/cliparts/6/5/b/f/11949864691020941855smiley114.svg.med.png\n\n## ENGINEERING 80 Temperature Measurements 3\n\nWhat is Temperature?\nAN OVERLY SIMPLIFIED DESCRIPTION OF TEMPERATURE\n\nSOURCE: http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/temper2.html#c1\n\n## \"Temperature is a measure of the tendency of an object to spontaneously give up energy to\n\nits surroundings. When two objects are in thermal contact, the one that tends to\nspontaneously lose energy is at the higher temperature.\n(Schroeder, Daniel V. An Introduction to Thermal Physics, 1st Edition (Ch, 1). Addison-Wesley.)\nENGINEERING 80 Temperature Measurements 4\nWhat is Temperature?\nA SIMPLIFIED DESCRIPTION OF TEMPERATURE\n\nSOURCE: http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/temper2.html#c1\n\n## \"Temperature is a measure of the tendency of an object to spontaneously give up energy to\n\nits surroundings. When two objects are in thermal contact, the one that tends to\nspontaneously lose energy is at the higher temperature.\n(Schroeder, Daniel V. An Introduction to Thermal Physics, 1st Edition (Ch, 1). Addison-Wesley.)\nENGINEERING 80 Temperature Measurements 5\nMeasuring Temperature with Rockets\n\n## ENGINEERING 80 Temperature Measurements 6\n\nMeasuring Temperature with Rockets\n\n## What are desirable characteristics of a temperature\n\nsensor?\nENGINEERING 80 Temperature Measurements 7\nDesirable Temperature Sensor Characteristics\nFAST ACCURATE\nREPEATABLE\nRESPONSE\nEASY WIDE\nTEMPERATURE\nCALIBRATION TEMPERATURE\nSENSOR\nRANGE\nCOST\nSIMPLE RELATIONSHIP\nSENSOR OUTPUT TEMPERATURE\nENGINEERING 80 TEMPERATURE MEASUREMENTS 8\nThermistor\nThermistor a resistor whose resistance changes with temperature\n\n## ENGR 106 Lecture 3 Temperature Measurements 9\n\nThermistor\nThermistor a resistor whose resistance changes with temperature\nResistive element is generally a metal-oxide\nceramic containing Mn, Co, Cu, or Ni\nPackaged in a thermally conductive glass\nbead or disk with two metal leads\n\n## ENGR 106 Lecture 3 Temperature Measurements 10\n\nThermistor\nThermistor a resistor whose resistance changes with temperature\nResistive element is generally a metal-oxide\nceramic containing Mn, Co, Cu, or Ni\nPackaged in a thermally conductive glass\nbead or disk with two metal leads\nSuppose we have a 1 k thermistor\nWhat does this mean?\n\n## ENGR 106 Lecture 3 Temperature Measurements 11\n\nThermistor\nThermistor a resistor whose resistance changes with temperature\nResistive element is generally a metal-oxide\nceramic containing Mn, Co, Cu, or Ni\nPackaged in a thermally conductive glass\nbead or disk with two metal leads\nSuppose we have a 1 k thermistor\nWhat does this mean?\nAt room temperature, the resistance of\nthe thermistor is 1 k\n\n## ENGR 106 Lecture 3 Temperature Measurements 12\n\nThermistor\nThermistor a resistor whose resistance changes with temperature\nResistive element is generally a metal-oxide\nceramic containing Mn, Co, Cu, or Ni\nPackaged in a thermally conductive glass\nbead or disk with two metal leads\nSuppose we have a 1 k thermistor\nWhat does this mean?\nAt room temperature, the resistance of\nthe thermistor is 1 k\nWhat happens to resistance as we\nincrease temperature?\n\n## ENGR 106 Lecture 3 Temperature Measurements 13\n\nNegative Temperature Coefficient\nMost materials exhibit a negative temperature coefficient (NTC)\nResistance drops with temperature!\n\n## ENGINEERING 80 Temperature Measurements 14\n\nConverting Resistance to Temperature\nThe Steinhart-Hart Equation relates temperature to resistance\n\nSOURCE: http://p.globalsources.com/IMAGES/PDT/B1055847338/Thermistor.jpg\n\n## ENGINEERING 80 Temperature Measurements 15\n\nConverting Resistance to Temperature\nThe Steinhart-Hart Equation relates temperature to resistance\n\n## T is the temperature (in Kelvin)\n\nR is the resistance at T and Rref is resistance at Tref\nA1, B1, C1, and D1 are the Steinhart-Hart Coefficients\nHOW COULD WE DETERMINE THESE COEFFICIENTS?\n\nSOURCE: http://p.globalsources.com/IMAGES/PDT/B1055847338/Thermistor.jpg\n\n## ENGINEERING 80 Temperature Measurements 16\n\nConverting Resistance to Temperature\nThe Steinhart-Hart Equation relates temperature to resistance\n\n## T is the temperature (in Kelvin)\n\nR is the resistance at T and Rref is resistance at Tref\nA1, B1, C1, and D1 are the Steinhart-Hart Coefficients\nHOW COULD WE DETERMINE THESE COEFFICIENTS?\nTake a look at the data sheet\n\nSOURCE: http://p.globalsources.com/IMAGES/PDT/B1055847338/Thermistor.jpg\n\n## ENGINEERING 80 Temperature Measurements 17\n\nConverting Resistance to Temperature\n\n## ENGINEERING 80 Temperature Measurements 18\n\nConverting Resistance to Temperature\n\n## ENGINEERING 80 Temperature Measurements 19\n\nConverting Resistance to Temperature\n\nWHAT IF YOU LOST THE DATA SHEET, DONT BELIEVE IT, OR WOULD LIKE TO VERIFY THE VALUES?\nENGINEERING 80 Temperature Measurements 20\nConverting Resistance to Temperature\nThe Steinhart-Hart Equation relates temperature to resistance\n\n## T is the temperature (in Kelvin)\n\nR is the resistance at T and Rref is resistance at Tref\nA1, B1, C1, and D1 are the Steinhart-Hart Coefficients\nHOW COULD WE DETERMINE THESE COEFFICIENTS?\nTake a look at the data sheet\n\nSOURCE: http://p.globalsources.com/IMAGES/PDT/B1055847338/Thermistor.jpg\n\n## ENGINEERING 80 Temperature Measurements 21\n\nConverting Resistance to Temperature\nThe Steinhart-Hart Equation relates temperature to resistance\n\n## T is the temperature (in Kelvin)\n\nR is the resistance at T and Rref is resistance at Tref\nA1, B1, C1, and D1 are the Steinhart-Hart Coefficients\nHOW COULD WE DETERMINE THESE COEFFICIENTS?\nTake a look at the data sheet\nMeasure 3 resistances at 3 temperatures\nMatrix Inversion (Linear Algebra)\n\nSOURCE: http://p.globalsources.com/IMAGES/PDT/B1055847338/Thermistor.jpg\n\n## ENGINEERING 80 Temperature Measurements 22\n\nConverting Resistance to Temperature\nThe Steinhart-Hart Equation relates temperature to resistance\n\n## T is the temperature (in Kelvin)\n\nR is the resistance at T and Rref is resistance at Tref\nA1, B1, C1, and D1 are the Steinhart-Hart Coefficients\nHOW COULD WE DETERMINE THESE COEFFICIENTS?\nTake a look at the data sheet\nMeasure 3 resistances at 3 temperatures\nMatrix Inversion (Linear Algebra)\nLeast Squares Fit\nSOURCE: http://p.globalsources.com/IMAGES/PDT/B1055847338/Thermistor.jpg\n\n## ENGINEERING 80 Temperature Measurements 23\n\nHow is Resistance Measured?\n\nSOURCE: http://p.globalsources.com/IMAGES/PDT/B1055847338/Thermistor.jpg\n\n## ENGINEERING 80 Temperature Measurements 24\n\nThermistor Resistance (RT)\nA thermistor produces a resistance (RT), which must be\nconverted to a voltage signal\n\nRT\nVout VS\nRT R1\n\n## ENGINEERING 80 Temperature Measurements 25\n\nPower Dissipation in Thermistors\nA current must pass through the I\nthermistor to measure the voltage and\ncalculate the resistance\nThe current flowing through the\nthermistor generates heat because the\nthermistor dissipates electrical power\nP = I2RT\nThe heat generated causes a\ntemperature rise in the thermistor\nThis is called Self-Heating\nWHY IS SELF-HEATING BAD?\n\n## ENGINEERING 80 Temperature Measurements 26\n\nPower Dissipation and Self-Heating\nSelf-Heating can introduce an error into the measurement\nThe increase in device temperature (T) is related to the power dissipated\n(P) and the power dissipation factor ()\nP = T\nWhere P is in [W], T is the rise in temperature in [oC]\nSuppose I = 5 mA, RT = 4 k, and = 0.067 W/oC, what is T?\n\n## ENGINEERING 80 Temperature Measurements 27\n\nPower Dissipation and Self-Heating\nSelf-Heating can introduce an error into the measurement\nThe increase in device temperature (T) is related to the power dissipated\n(P) and the power dissipation factor ()\nP = T\nWhere P is in [W], T is the rise in temperature in [oC]\nSuppose I = 5 mA, RT = 4 k, and = 0.067 W/oC, what is T?\n(0.005 A)2(4000 ) = (0.067 W/oC) T\nT = 1.5 oC\nWhat effect does a T of 1.5 oC have on your thermistor measurements?\n\n## ENGINEERING 80 Temperature Measurements 28\n\nPower Dissipation and Self-Heating\nSelf-Heating can introduce an error into the measurement\nThe increase in device temperature (T) is related to the power dissipated\n(P) and the power dissipation factor ()\nP = T\nWhere P is in [W], T is the rise in temperature in [oC]\nSuppose I = 5 mA, RT = 4 k, and = 0.067 W/oC, what is T?\n(0.005 A)2(4000 ) = (0.067 W/oC) T\nT = 1.5 oC\nWhat effect does a T of 1.5 oC have on your thermistor measurements?\nHow can we reduce the effects of self-heating?\n\n## ENGINEERING 80 Temperature Measurements 29\n\nPower Dissipation and Self-Heating\nSelf-Heating can introduce an error into the measurement\nThe increase in device temperature (T) is related to the power dissipated\n(P) and the power dissipation factor ()\nP = T\nWhere P is in [W], T is the rise in temperature in [oC]\nSuppose I = 5 mA, RT = 4 k, and = 0.067 W/oC, what is T?\n(0.005 A)2(4000 ) = (0.067 W/oC) T\nT = 1.5 oC\nWhat effect does a T of 1.5 oC have on your thermistor measurements?\nHow can we reduce the effects of self-heating?\nIncrease the resistance of the thermistor!\nENGINEERING 80 Temperature Measurements 30\nThermistor Signal Conditioning Circuit\nA voltage divider and a unity gain buffer are required to measure\ntemperature in the lab\nbuffer\n+5 V\nREF195 reference\n-\n10k To ADC\n\n1/4\nThermistor AD8606\n(AD8605)\n\n## ENGINEERING 80 Temperature Measurements 31\n\nIntegrated Silicon Linear Sensors\nAn integrated silicon linear sensor\nis a three-terminal device\nPower and ground inputs\nRelatively simple to use and cheap\nCircuitry inside does linearization and\nsignal conditioning\nProduces an output voltage linearly\ndependent on temperature\n\n3.1 5.5 V\n\n## ENGINEERING 80 Temperature Measurements 32\n\nIntegrated Silicon Linear Sensors\nAn integrated silicon linear sensor\nis a three-terminal device\nPower and ground inputs\nRelatively simple to use and cheap\nCircuitry inside does linearization and\nsignal conditioning\nProduces an output voltage linearly\ndependent on temperature\nWhen compared to other\ntemperature measurement devices,\nthese sensors are less accurate,\noperate over a narrower temperature\nrange, and are less responsive 3.1 5.5 V\n\n## ENGINEERING 80 Temperature Measurements 33\n\nSummary Thus Far\n\n>\nENGINEERING 80 Temperature Measurements 34\nThermocouple\nThermocouple a two-terminal element consisting of two dissimilar\nmetal wires joined at the end\n\nSOURCE: http://upload.wikimedia.org/wikipedia/en/e/ed/Thermocouple_(work_diagram)_LMB.png\n\n## ENGINEERING 80 Temperature Measurements 35\n\nThe Seebeck Effect\nSeebeck Effect A conductor generates a voltage when it is\nsubjected to a temperature gradient\n\n## ENGINEERING 80 Temperature Measurements 36\n\nThe Seebeck Effect\nSeebeck Effect A conductor generates a voltage when it is\nsubjected to a temperature gradient\nMeasuring this voltage requires the use of a second conductor material\n\nNickel-Chromium\nWill I observe a Alloy\ndifference in\nvoltage at the\nends of two wires\ncomposed of the\nsame material?\n\nNickel-Chromium\nAlloy\nENGINEERING 80 Temperature Measurements 37\nThe Seebeck Effect\nSeebeck Effect A conductor generates a voltage when it is\nsubjected to a temperature gradient\nMeasuring this voltage requires the use of a second conductor material\nThe other material needs to be composed of a different material\nNickel-Chromium\nThe relationship Alloy\nbetween\ntemperature\ndifference and\nvoltage varies\nwith materials\n\nCopper-Nickel\nAlloy\nENGINEERING 80 Temperature Measurements 38\nThe Seebeck Effect\nSeebeck Effect A conductor generates a voltage when it is\nsubjected to a temperature gradient\nMeasuring this voltage requires the use of a second conductor material\nThe other material needs to be composed of a different material\nNickel-Chromium\nThe relationship + Alloy\nbetween The voltage difference of the\ntemperature two dissimilar metals can be\ndifference and\nvoltage varies\nmeasured and related to the VS = ST\nwith materials corresponding temperature\ngradient\n- Copper-Nickel\nAlloy\nENGINEERING 80 Temperature Measurements 39\nMeasuring Temperature\nTo measure temperature using a thermocouple, you cant just\nconnect the thermocouple to a measurement system (e.g. voltmeter)\n\nSOURCE: http://www.pcbheaven.com/wikipages/images/thermocouples_1271330366.png\n\n## ENGINEERING 80 Temperature Measurements 40\n\nMeasuring Temperature\nTo measure temperature using a thermocouple, you cant just\nconnect the thermocouple to a measurement system (e.g. voltmeter)\nThe voltage measured by your system is proportional to the\ntemperature difference between the primary junction (hot junction)\nand the junction where the voltage is being measured (Ref junction)\n\nSOURCE: http://www.pcbheaven.com/wikipages/images/thermocouples_1271330366.png\n\n## ENGINEERING 80 Temperature Measurements 41\n\nMeasuring Temperature\nTo measure temperature using a thermocouple, you cant just\nconnect the thermocouple to a measurement system (e.g. voltmeter)\nThe voltage measured by your system is proportional to the\ntemperature difference between the primary junction (hot junction)\nand the junction where the voltage is being measured (Ref junction)\n\n## To determine the You need to\n\nabsolute know the\ntemperature at temperature at\nthe hot the Ref junction!\njunction\n\nSOURCE: http://www.pcbheaven.com/wikipages/images/thermocouples_1271330366.png\n\n## ENGINEERING 80 Temperature Measurements 42\n\nMeasuring Temperature\nTo measure temperature using a thermocouple, you cant just\nconnect the thermocouple to a measurement system (e.g. voltmeter)\nThe voltage measured by your system is proportional to the\ntemperature difference between the primary junction (hot junction)\nand the junction where the voltage is being measured (Ref junction)\n\n## To determine the You need to\n\nabsolute know the\ntemperature at temperature at\nthe hot the Ref junction!\njunction How can we determine\nthe temperature at the\nSOURCE: http://www.pcbheaven.com/wikipages/images/thermocouples_1271330366.png reference junction?\nENGINEERING 80 Temperature Measurements 43\nIce Bath Method (Forcing a Temperature)\nThermocouples measure the voltage difference between two points\nTo know the absolute temperature at the hot junction, one must know the\ntemperature at the Ref junction\n\n## ENGINEERING 80 Temperature Measurements 44\n\nIce Bath Method (Forcing a Temperature)\nThermocouples measure the voltage difference between two points\nTo know the absolute temperature at the hot junction, one must know the\ntemperature at the Ref junction\nNIST thermocouple reference tables are\ngenerated with Tref = 0 oC\n\n## If we know the voltage-temperature\n\nrelationship of our thermocouple, we could\ndetermine the temperature at the hot junction\nIS IT REALLY THAT EASY?\nENGINEERING 80 Temperature Measurements 45\nNonlinearity in the Seebeck Coefficient\n\nVS = ST\nThermocouple output\nvoltages are highly\nnonlinear\nThe Seebeck coefficient\ncan vary by a factor of 3 or\nmore over the operating\ntemperature range of the\nthermocouples\n\n## ENGINEERING 80 Temperature Measurements 46\n\nTemperature Conversion Equation\nT = a0 + a1V + a2V2 + . + anVn\n\n## ENGINEERING 80 Temperature Measurements 47\n\nLook-Up Table for a Type T Thermocouple\nVoltage difference of the hot and cold junctions: VD = 3.409 mV\nWhat is the temperature of the hot junction if the cold junction is at 22 oC?\n\n## ENGINEERING 80 Temperature Measurements 48\n\nLook-Up Table for a Type T Thermocouple\nVoltage difference of the hot and cold junctions: VD = 3.409 mV\nWhat is the temperature of the hot junction if the cold junction is at 22 oC?\n\n## At 22 oC, the reference junction voltage is 0.870 mV\n\nThe hot junction voltage is therefore 3.409 mV + 0.870 mV = 4.279 mV\nThe temperature at the hot junction is therefore 100 oC\nENGINEERING 80 Temperature Measurements 49\nAPPLYING WHAT WEVE LEARNED\nVoltage difference of the hot and cold junctions: VD = 4.472 mV\nWhat is the temperature of the hot junction if the cold junction is at 5 oC?\n\n## ENGINEERING 80 Temperature Measurements 50\n\nAPPLYING WHAT WEVE LEARNED\nVoltage difference of the hot and cold junctions: VD = 4.472 mV\nWhat is the temperature of the hot junction if the cold junction is at 5 oC?\n\n## At -5 oC, the cold junction voltage is 0.193 mV\n\nThe hot junction voltage is therefore 4.472 mV 0.193 mV = 4.279 mV\nThe temperature at the hot junction is therefore 100 oC\nENGINEERING 80 Temperature Measurements 51\nIs This Really Practical For a Rocket?\n\n## What is another method of determining the temperature at the\n\nreference junction?\nENGINEERING 80 Temperature Measurements 52\nCold Junction Compensation\n\nSOURCE: http://www.industrial-electronics.com/DAQ/images/10_13.jpg\n\n## ENGINEERING 80 Temperature Measurements 53\n\nCold Junction Compensation\n\n## How could I determine the\n\ntemperature of the block?\nSOURCE: http://www.industrial-electronics.com/DAQ/images/10_13.jpg\n\n## ENGINEERING 80 Temperature Measurements 54\n\nCold Junction Compensation\n\nSOURCE: http://www.industrial-electronics.com/DAQ/images/10_13.jpg\n\nAcquiring Data\n\n## ENGINEERING 80 Temperature Measurements 56\n\nTemperature Measurement Devices in Lab\n\n>\nENGINEERING 80 Temperature Measurements 57\nResistive Temperature Detector (RTD)\nTwo terminal device\nUsually made out of platinum\nPositive temperature coefficient\nTends to be linear\nR = R0(1+)(T-T0) where T0 = 0oC\nR0 = 100 , = 0.03385 / oC\nAt 10oC, R = 100(1+0.385)(10) = 103.85\nThey are best operated using a small\nconstant current source\nAccuracy of 0.01 oC SOURCE: http://www.omega.com/prodinfo/images/RTD_diag1.gif\n\nEXPENSIVE!\nENGINEERING 80 Temperature Measurements 58\nTemperature Measurement Devices\n\n>\nENGINEERING 80 Temperature Measurements 59\nHow Do I Know If These Are Working?\n\nSOURCE: http://www.eng.hmc.edu/NewE80/PDFs/VIshayThermDataSheet.pdf\n\nSOURCE: http://elcodis.com/photos/19/51/195143/to-92-\n3_standardbody__to-226_straightlead.jpg\n\nSOURCE: http://www.accuglassproducts.com/product.php?productid=17523\n\n## ENGINEERING 80 Temperature Measurements 60\n\nCalibration\nHow could we calibrate a temperature sensor?\n\n## ENGINEERING 80 Temperature Measurements 61\n\nCalibration\nHow could we calibrate a temperature sensor?\n\n0 oC 25 oC 100 oC\nENGINEERING 80 Temperature Measurements 62\nCalibration\nHow could we calibrate a temperature sensor? USB Reference\nThermometer\n\nSOURCE: http://www.thermoworks.com/products/calibration/usb_reference.html\n\n0 oC 25 oC 100 oC\nENGINEERING 80 Temperature Measurements 63\nCalibration\nEach probe includes an\nindividual NIST-\nHow could we calibrate a temperature sensor? Traceable calibration\ncertificate with test\ndata at 0, 25, 70, and\n100C.\nSOURCE: http://www.thermoworks.com/products/calibration/usb_reference.html\n\n0 oC 25 oC 100 oC\nENGINEERING 80 Temperature Measurements 64\nTracking the Rate of Temperature Change\nIf a slow sensor is placed into a rocket\nthat is launched to a high altitude, the\nsensor may not be able to track the rate\nof temperature change\nA critical property of a temperature-\nmeasurement device is how quickly it\nresponds to a change in external\ntemperature\n\n## ENGINEERING 80 Temperature Measurements 65\n\nThermal System Step Response\n\n## ENGINEERING 80 Temperature Measurements 66\n\nThermal System Step Response\n\n## ENGINEERING 80 Temperature Measurements 67\n\nThermal System Step Response\n\n## ENGINEERING 80 Temperature Measurements 68\n\nThermal System Step Response\n\n## ENGINEERING 80 Temperature Measurements 69\n\nThermal System Step Response\n\n## The thermal time constant can\n\nbe measured as the time it\ntakes to get to (1/e) of the final\ntemperature\n100 (1-(1/e)) = 63 oC\n\n## Thermal Time Constant\n\nENGINEERING 80 Temperature Measurements 70\nThermal System Step Response\n\n## The thermal time constant can\n\nbe measured as the time it\ntakes to get to (1/e) of the final\ntemperature\n100 (1-(1/e)) = 63 oC\n\n## Thermal Time Constant\n\nENGINEERING 80 Temperature Measurements 71\nThermal System Step Response\n\nhttp://www.eng.hmc.edu/NewE80/PDFs/TemperatureMeasurementLecNotes.pdf\nhttp://www.colorado.edu/MCEN/Measlab/background1storder.pdf\n\nhttp://www.eng.hmc.edu/NewE80/PDFs/TemperatureMeasurementLecNotes.pdf\n\n## ENGINEERING 80 Temperature Measurements 72\n\nSUMMARY\nMeasuring Temperature\nTypes of Temperature Sensors\nThermistor\nIntegrated Silicon Linear Sensor\nThermocouple\nResistive Temperature Detector (RTD)\nChoosing a Temperature Sensor\nCalibrating Temperature Sensors\nThermal System Transient Response\n\n## ENGR 106 Lecture 3 Failure 73\n\nReferences\nPrevious E80 Lectures and Lecture Notes\nhttp://www.eng.hmc.edu/NewE80/TemperatureLec.html\nThermcouples White Paper\nhttp://www.ohio.edu/people/bayless/seniorlab/thermocouple.pdf (downloaded 02/04/2015)\nUniversity of Cambridge Thermoelectric Materials for Thermocouples\nhttp://www.msm.cam.ac.uk/utc/thermocouple/pages/ThermocouplesOperatingPrinciples.html (viewed\n02/04/2015)\nNational Instruments Temperature Measurements with Thermocouples: How-To Guide\nhttp://www.technologyreview.com/sites/default/files/legacy/temperature_measurements_with_therm\nocouples.pdf (downloaded 02/04/2015)\nVishay NTCLE100E3104JB0 Data Sheet\nhttp://www.eng.hmc.edu/NewE80/PDFs/VIshayThermDataSheet.pdf (downloaded on 02/04/2015)" ]
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https://kexue.fm/tag/%E6%8E%A8%E6%96%AD/
[ "## 局部变分\n\n### f散度\n\n$$\\begin{equation}\\mathcal{D}_f(P\\Vert Q) = \\int q(x) f\\left(\\frac{p(x)}{q(x)}\\right)dx\\label{eq:f-div}\\end{equation}$$" ]
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https://chem.libretexts.org/Courses/Sacramento_City_College/SCC%3A_CHEM_300_-_Beginning_Chemistry/SCC%3A_CHEM_300_-_Beginning_Chemistry_(Alviar-Agnew)/14%3A_Acids_and_Bases/14.10%3A_Buffers-_Solutions_That_Resist_pH_Change
[ "# 14.10: Buffers- Solutions That Resist pH Change\n\n$$\\newcommand{\\vecs}{\\overset { \\rightharpoonup} {\\mathbf{#1}} }$$ $$\\newcommand{\\vecd}{\\overset{-\\!-\\!\\rightharpoonup}{\\vphantom{a}\\smash {#1}}}$$$$\\newcommand{\\id}{\\mathrm{id}}$$ $$\\newcommand{\\Span}{\\mathrm{span}}$$ $$\\newcommand{\\kernel}{\\mathrm{null}\\,}$$ $$\\newcommand{\\range}{\\mathrm{range}\\,}$$ $$\\newcommand{\\RealPart}{\\mathrm{Re}}$$ $$\\newcommand{\\ImaginaryPart}{\\mathrm{Im}}$$ $$\\newcommand{\\Argument}{\\mathrm{Arg}}$$ $$\\newcommand{\\norm}{\\| #1 \\|}$$ $$\\newcommand{\\inner}{\\langle #1, #2 \\rangle}$$ $$\\newcommand{\\Span}{\\mathrm{span}}$$ $$\\newcommand{\\id}{\\mathrm{id}}$$ $$\\newcommand{\\Span}{\\mathrm{span}}$$ $$\\newcommand{\\kernel}{\\mathrm{null}\\,}$$ $$\\newcommand{\\range}{\\mathrm{range}\\,}$$ $$\\newcommand{\\RealPart}{\\mathrm{Re}}$$ $$\\newcommand{\\ImaginaryPart}{\\mathrm{Im}}$$ $$\\newcommand{\\Argument}{\\mathrm{Arg}}$$ $$\\newcommand{\\norm}{\\| #1 \\|}$$ $$\\newcommand{\\inner}{\\langle #1, #2 \\rangle}$$ $$\\newcommand{\\Span}{\\mathrm{span}}$$$$\\newcommand{\\AA}{\\unicode[.8,0]{x212B}}$$\n\n##### Learning Objective\n• Define buffer and describe how it reacts with an acid or a base.\n\nWeak acids are relatively common, even in the foods we eat. But we occasionally come across a strong acid or base, such as stomach acid, that has a strongly acidic pH of 1–2. By definition, strong acids and bases can produce a relatively large amount of hydrogen or hydroxide ions and, as a consequence, have marked chemical activity. In addition, very small amounts of strong acids and bases can change the pH of a solution very quickly. If 1 mL of stomach acid [which we will approximate as 0.05 M HCl(aq)] is added to the bloodstream, and if no correcting mechanism is present, the pH of the blood would go from about 7.4 to about 4.9—a pH that is not conducive to life. Fortunately, the body has a mechanism for minimizing such dramatic pH changes.\n\nThis mechanism involves a buffer, a solution that resists dramatic changes in pH. Buffers do so by being composed of certain pairs of solutes: either a weak acid plus a salt derived from that weak acid, or a weak base plus a salt of that weak base. For example, a buffer can be composed of dissolved acetic acid (HC2H3O2, a weak acid) and sodium acetate (NaC2H3O2, a salt derived from that acid). Another example of a buffer is a solution containing ammonia (NH3, a weak base) and ammonium chloride (NH4Cl, a salt derived from that base).\n\nLet us use an acetic acid–sodium acetate buffer to demonstrate how buffers work. If a strong base—a source of $$\\ce{OH^{-}(aq)}$$ ions—is added to the buffer solution, those hydroxide ions will react with the acetic acid in an acid-base reaction:\n\n$\\ce{HC2H3O2(aq) + OH^{-}(aq) \\rightarrow H2O(ℓ) + C2H3O^{-}2(aq)} \\label{Eq1}$\n\nRather than changing the pH dramatically by making the solution basic, the added hydroxide ions react to make water, and the pH does not change much.\n\nMany people are aware of the concept of buffers from buffered aspirin, which is aspirin that also has magnesium carbonate, calcium carbonate, magnesium oxide, or some other salt. The salt acts like a base, while aspirin is itself a weak acid.\n\nIf a strong acid—a source of H+ ions—is added to the buffer solution, the H+ ions will react with the anion from the salt. Because HC2H3O2 is a weak acid, it is not ionized much. This means that if lots of hydrogen ions and acetate ions (from sodium acetate) are present in the same solution, they will come together to make acetic acid:\n\n$\\ce{H^{+}(aq) + C2H3O^{−}2(aq) \\rightarrow HC2H3O2(aq)} \\label{Eq2}$\n\nRather than changing the pH dramatically and making the solution acidic, the added hydrogen ions react to make molecules of a weak acid. Figure $$\\PageIndex{1}$$ illustrates both actions of a buffer.", null, "Figure $$\\PageIndex{1}$$: The Action of Buffers. Buffers can react with both strong acids (top) and strong bases (bottom) to minimize large changes in pH.\n\nBuffers made from weak bases and salts of weak bases act similarly. For example, in a buffer containing NH3 and NH4Cl, ammonia molecules can react with any excess hydrogen ions introduced by strong acids:\n\n$\\ce{NH3(aq) + H^{+}(aq) \\rightarrow NH^{+}4(aq)} \\label{Eq3}$\n\nwhile the ammonium ion ($$\\ce{NH4^{+}(aq)}$$) can react with any hydroxide ions introduced by strong bases:\n\n$\\ce{NH^{+}4(aq) + OH^{-}(aq) \\rightarrow NH3(aq) + H2O(ℓ)} \\label{Eq4}$\n\n##### Example $$\\PageIndex{1}$$: Making Buffer Solutions\n\nWhich solute combinations can make a buffer solution? Assume that all are aqueous solutions.\n\n1. HCHO2 and NaCHO2\n2. HCl and NaCl\n3. CH3NH2 and CH3NH3Cl\n4. NH3 and NaOH\n###### Solution\n1. Formic acid (HCHO2) is a weak acid, while NaCHO2 is the salt made from the anion of the weak acid—the formate ion (CHO2). The combination of these two solutes would make a buffer solution.\n2. Hydrochloric acid (HCl) is a strong acid, not a weak acid, so the combination of these two solutes would not make a buffer solution.\n3. Methylamine (CH3NH2) is like ammonia with one of its hydrogen atoms substituted with a CH3 (methyl) group. Because it is not on our list of strong bases, we can assume that it is a weak base. The compound CH3NH3Cl is a salt made from that weak base, so the combination of these two solutes would make a buffer solution.\n4. Ammonia (NH3) is a weak base, but NaOH is a strong base. The combination of these two solutes would not make a buffer solution.\n##### Exercise $$\\PageIndex{1}$$\n\nWhich solute combinations can make a buffer solution? Assume that all are aqueous solutions.\n\n1. NaHCO3 and NaCl\n2. H3PO4 and NaH2PO4\n3. NH3 and (NH4)3PO4\n4. NaOH and NaCl\nYes.\nNo. Need a weak acid or base and a salt of its conjugate base or acid.\nYes.\nNo. Need a weak base or acid.\n\nBuffers work well only for limited amounts of added strong acid or base. Once either solute is all reacted, the solution is no longer a buffer, and rapid changes in pH may occur. We say that a buffer has a certain capacity. Buffers that have more solute dissolved in them to start with have larger capacities, as might be expected.\n\nHuman blood has a buffering system to minimize extreme changes in pH. One buffer in blood is based on the presence of HCO3 and H2CO3 [H2CO3 is another way to write CO2(aq)]. With this buffer present, even if some stomach acid were to find its way directly into the bloodstream, the change in the pH of blood would be minimal. Inside many of the body’s cells, there is a buffering system based on phosphate ions.\n\n##### Career Focus: Blood Bank Technology Specialist\n\nAt this point in this text, you should have the idea that the chemistry of blood is fairly complex. Because of this, people who work with blood must be specially trained to work with it properly.\n\nA blood bank technology specialist is trained to perform routine and special tests on blood samples from blood banks or transfusion centers. This specialist measures the pH of blood, types it (according to the blood’s ABO+/− type, Rh factors, and other typing schemes), tests it for the presence or absence of various diseases, and uses the blood to determine if a patient has any of several medical problems, such as anemia. A blood bank technology specialist may also interview and prepare donors to give blood and may actually collect the blood donation.\n\nBlood bank technology specialists are well trained. Typically, they require a college degree with at least a year of special training in blood biology and chemistry. In the United States, training must conform to standards established by the American Association of Blood Banks.\n\n## Key Takeaway\n\n• A buffer is a solution that resists sudden changes in pH." ]
[ null, "https://chem.libretexts.org/@api/deki/files/92079/The_Actions_of_Buffers.png", null ]
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https://microcontrollerslab.com/cd4008-4-bit-full-adder-ic-pinout-features-example-datasheet/
[ "# CD4008 4-Bit Full ADDER IC\n\nFull Adder is made of one OR, two XOR and one AND gate. It has three inputs and two outputs. The First two inputs use as two input data bits and the third input is used as carrying bit, which we have no further use in half adder circuit. The output carries a bit on full adder circuit transfer the carry bit to the next adder and it performs the addition by considering three input values.\n\n## Introduction to CD4008 4-Bit Full ADDER CIRCUIT\n\nThe multiple full adders could be used as a multiple bit adder circuits. CD4008 IC is a full 4-bit adder circuit which comes up with a combination for four full bit adders. It could add four multiple bits without any error. It carries a bit from state to stage and perform the addition. CD4008 is one the fastest and high voltage adder circuit with carrying out feature.\n\n### Pinout of CD4008\n\nThe pin configuration and details of all input outputs pins are listed below:\n\n### FEATURES of CD4008 4-Bit Full ADDER IC\n\n• 4-bit full adder with carrying out features\n• Parallel input and output method\n• High operating speed without any interruptions\n• Available with 16-pins in PDIP, CDIP, SOIC, and TSSOP Package\n• Meets all the requirements of all CMOS devices.\n• It has HIGH operating voltage as compared to most of the other CMOS devices.\n\n### SPECIFICATIONS of CD4008\n\n• The total time required for values from input to output is 160ns.\n• It has a noise margin at different voltages:\n• 5V margin will be about 1V.\n• 10-volt margin will be about 2V.\n• 15 Volt margins will be about 2.5V\n• CD4008 normal operating voltage rages are 5- 15V, it could operate also maximum at 20V\n• Maximum input current should be 1uA at 18V.\n• The temperature should be 25 degrees at 18V and 1uA\n• Most of the specifications and features only work when IC is operation at exact 5V.\n\n## WORKING of CD4008 4-Bit Full ADDER\n\nAs we discussed early CD4008 is a combination of 4 full adder circuit. So First we need to understand how single full adder works. A full adder circuit works with logic gates. It has a combination of two XOR, two AND gates and one OR gates. Here is the following internal circuit of Full Adder.\n\nIn above circuit diagram, the First XOR gate will be used as adding the two inputs and then the second XOR gate will be used for sum up the output from first XOR and Carry in. The other two AND gates and OR gate will use to find out the carry out from the input values and from previous carry in. The output will give us two values one is the output of input values and the other one is carried of the input values. If we gave only one input value then there will be output, there is no case in which there will be no output. The output for CD4008 full adder will follow the following truth table pattern.\n\nIn CD4008 the single adder will follow the above truth table on specific inputs. The internal structure of CD4008 will be the combination of four full adders. Expect the first adder, each will take two inputs from the user or from another device and the third input will use the carry-out value of the previous adder. The first adder will receive the first carryout input from outside the IC and the last carry out of the last adder will be used as an output value. This combination of 4 adders will work in series.\n\nThe 4-bit full adder circuit starts adding from the least significant bit (LSB) and keep it doing till the most significant bit (MSB). It has the ability to solve the carryout problem. Most people think that two half adders could make a full adder which is true but two half adders could be used as full adder but their structure will be more complex as compared to the single full adder. The full adder is the simplifies version of the combination of two full adders.\n\n## APPLICATIONS of CD4008 4-Bit Full ADDER\n\n• It is used for High-Speed Arithmetic Operations.\n• CD4008 also used as miniature calculators.\n• Counters also have some use of CD4008.\n• It is also used in Simple Logic Design\n\n## EXAMPLE in Proteus\n\nNow, we will see simple binary addition example in proteus. Here we will use CD4008 for the addition of four-bit data. First, add CD4008 in proteus, then attach the logic state viewer and logic state provider to CD4008. Attach the logic states as shown in the circuit. The last bit of both input values should be at A1 and B1 because addition always starts from the last digits.\n\nAfter making the circuit as shown in proteus, start to send the desired values. First, let’s do an addition on specific 4-bit digits mathematically. Suppose: A = (1010)2 , B = (1000)2 ,Carry in = (1)2. When we add all these three values we get the output (10011) 2.\n\nNow here let’s try the same at CD4008.\n\nHere in the output of proteus, you may notice that we have “0011” at the output, which is the same as the last four bits of our mathematical output. In proteus we have only four bits is because it’s a four bit full adder circuit and its output will be four-bit the remain will be considered as carrying. The MSB of our mathematical output is “1” which is equal to the carryout in Proteus.\n\n### How to Convert 4-bit to 8-bit or More?\n\nThe CD4008 can expand to an 8-bit adder by attaching two ICs or it could go further. The only thing we need to make sure about the input values on the pin. If input values get shuffle then it becomes impossible to get the correct output. The correct output will always be dependent on the input value. During using CD4008 always verify the input pins and their values to avoid any mathematical error.\n\n### Proteus Simulation\n\nYou may also like to read:" ]
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https://www.colorhexa.com/5a7d58
[ "#5a7d58 Color Information\n\nIn a RGB color space, hex #5a7d58 is composed of 35.3% red, 49% green and 34.5% blue. Whereas in a CMYK color space, it is composed of 28% cyan, 0% magenta, 29.6% yellow and 51% black. It has a hue angle of 116.8 degrees, a saturation of 17.4% and a lightness of 41.8%. #5a7d58 color hex could be obtained by blending #b4fab0 with #000000. Closest websafe color is: #666666.\n\n• R 35\n• G 49\n• B 35\nRGB color chart\n• C 28\n• M 0\n• Y 30\n• K 51\nCMYK color chart\n\n#5a7d58 color description : Mostly desaturated dark lime green.\n\n#5a7d58 Color Conversion\n\nThe hexadecimal color #5a7d58 has RGB values of R:90, G:125, B:88 and CMYK values of C:0.28, M:0, Y:0.3, K:0.51. Its decimal value is 5930328.\n\nHex triplet RGB Decimal 5a7d58 `#5a7d58` 90, 125, 88 `rgb(90,125,88)` 35.3, 49, 34.5 `rgb(35.3%,49%,34.5%)` 28, 0, 30, 51 116.8°, 17.4, 41.8 `hsl(116.8,17.4%,41.8%)` 116.8°, 29.6, 49 666666 `#666666`\nCIE-LAB 48.94, -20.259, 16.297 13.311, 17.545, 11.917 0.311, 0.41, 17.545 48.94, 26, 141.186 48.94, -17.379, 23.785 41.887, -16.577, 12.452 01011010, 01111101, 01011000\n\nColor Schemes with #5a7d58\n\n• #5a7d58\n``#5a7d58` `rgb(90,125,88)``\n• #7b587d\n``#7b587d` `rgb(123,88,125)``\nComplementary Color\n• #6d7d58\n``#6d7d58` `rgb(109,125,88)``\n• #5a7d58\n``#5a7d58` `rgb(90,125,88)``\n• #587d69\n``#587d69` `rgb(88,125,105)``\nAnalogous Color\n• #7d586d\n``#7d586d` `rgb(125,88,109)``\n• #5a7d58\n``#5a7d58` `rgb(90,125,88)``\n• #69587d\n``#69587d` `rgb(105,88,125)``\nSplit Complementary Color\n• #7d585a\n``#7d585a` `rgb(125,88,90)``\n• #5a7d58\n``#5a7d58` `rgb(90,125,88)``\n• #585a7d\n``#585a7d` `rgb(88,90,125)``\n• #7d7b58\n``#7d7b58` `rgb(125,123,88)``\n• #5a7d58\n``#5a7d58` `rgb(90,125,88)``\n• #585a7d\n``#585a7d` `rgb(88,90,125)``\n• #7b587d\n``#7b587d` `rgb(123,88,125)``\n• #3a5038\n``#3a5038` `rgb(58,80,56)``\n• #445f43\n``#445f43` `rgb(68,95,67)``\n• #4f6e4d\n``#4f6e4d` `rgb(79,110,77)``\n• #5a7d58\n``#5a7d58` `rgb(90,125,88)``\n• #658c63\n``#658c63` `rgb(101,140,99)``\n• #71996f\n``#71996f` `rgb(113,153,111)``\n• #80a47e\n``#80a47e` `rgb(128,164,126)``\nMonochromatic Color\n\nAlternatives to #5a7d58\n\nBelow, you can see some colors close to #5a7d58. Having a set of related colors can be useful if you need an inspirational alternative to your original color choice.\n\n• #637d58\n``#637d58` `rgb(99,125,88)``\n• #607d58\n``#607d58` `rgb(96,125,88)``\n• #5d7d58\n``#5d7d58` `rgb(93,125,88)``\n• #5a7d58\n``#5a7d58` `rgb(90,125,88)``\n• #587d59\n``#587d59` `rgb(88,125,89)``\n• #587d5c\n``#587d5c` `rgb(88,125,92)``\n• #587d5f\n``#587d5f` `rgb(88,125,95)``\nSimilar Colors\n\n#5a7d58 Preview\n\nThis text has a font color of #5a7d58.\n\n``<span style=\"color:#5a7d58;\">Text here</span>``\n#5a7d58 background color\n\nThis paragraph has a background color of #5a7d58.\n\n``<p style=\"background-color:#5a7d58;\">Content here</p>``\n#5a7d58 border color\n\nThis element has a border color of #5a7d58.\n\n``<div style=\"border:1px solid #5a7d58;\">Content here</div>``\nCSS codes\n``.text {color:#5a7d58;}``\n``.background {background-color:#5a7d58;}``\n``.border {border:1px solid #5a7d58;}``\n\nA shade is achieved by adding black to any pure hue, while a tint is created by mixing white to any pure color. In this example, #070a07 is the darkest color, while #fdfefd is the lightest one.\n\n• #070a07\n``#070a07` `rgb(7,10,7)``\n• #0f150f\n``#0f150f` `rgb(15,21,15)``\n• #182117\n``#182117` `rgb(24,33,23)``\n• #202c1f\n``#202c1f` `rgb(32,44,31)``\n• #283827\n``#283827` `rgb(40,56,39)``\n• #31432f\n``#31432f` `rgb(49,67,47)``\n• #394f38\n``#394f38` `rgb(57,79,56)``\n• #415a40\n``#415a40` `rgb(65,90,64)``\n• #496648\n``#496648` `rgb(73,102,72)``\n• #527150\n``#527150` `rgb(82,113,80)``\n• #5a7d58\n``#5a7d58` `rgb(90,125,88)``\n• #628960\n``#628960` `rgb(98,137,96)``\n• #6b9468\n``#6b9468` `rgb(107,148,104)``\n• #759d73\n``#759d73` `rgb(117,157,115)``\n• #81a57f\n``#81a57f` `rgb(129,165,127)``\n``#8cad8a` `rgb(140,173,138)``\n• #97b596\n``#97b596` `rgb(151,181,150)``\n• #a3bda1\n``#a3bda1` `rgb(163,189,161)``\n``#aec5ad` `rgb(174,197,173)``\n• #b9cdb8\n``#b9cdb8` `rgb(185,205,184)``\n• #c5d5c4\n``#c5d5c4` `rgb(197,213,196)``\n• #d0ddcf\n``#d0ddcf` `rgb(208,221,207)``\n• #dbe6db\n``#dbe6db` `rgb(219,230,219)``\n• #e7eee6\n``#e7eee6` `rgb(231,238,230)``\n• #f2f6f2\n``#f2f6f2` `rgb(242,246,242)``\n• #fdfefd\n``#fdfefd` `rgb(253,254,253)``\nTint Color Variation\n\nTones of #5a7d58\n\nA tone is produced by adding gray to any pure hue. In this case, #696d68 is the less saturated color, while #11cf06 is the most saturated one.\n\n• #696d68\n``#696d68` `rgb(105,109,104)``\n• #617560\n``#617560` `rgb(97,117,96)``\n• #5a7d58\n``#5a7d58` `rgb(90,125,88)``\n• #538550\n``#538550` `rgb(83,133,80)``\n• #4b8d48\n``#4b8d48` `rgb(75,141,72)``\n• #44963f\n``#44963f` `rgb(68,150,63)``\n• #3d9e37\n``#3d9e37` `rgb(61,158,55)``\n• #35a62f\n``#35a62f` `rgb(53,166,47)``\n• #2eae27\n``#2eae27` `rgb(46,174,39)``\n• #27b61f\n``#27b61f` `rgb(39,182,31)``\n• #20bf16\n``#20bf16` `rgb(32,191,22)``\n• #18c70e\n``#18c70e` `rgb(24,199,14)``\n• #11cf06\n``#11cf06` `rgb(17,207,6)``\nTone Color Variation\n\nColor Blindness Simulator\n\nBelow, you can see how #5a7d58 is perceived by people affected by a color vision deficiency. This can be useful if you need to ensure your color combinations are accessible to color-blind users.\n\nMonochromacy\n• Achromatopsia 0.005% of the population\n• Atypical Achromatopsia 0.001% of the population\nDichromacy\n• Protanopia 1% of men\n• Deuteranopia 1% of men\n• Tritanopia 0.001% of the population\nTrichromacy\n• Protanomaly 1% of men, 0.01% of women\n• Deuteranomaly 6% of men, 0.4% of women\n• Tritanomaly 0.01% of the population" ]
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https://physics.stackexchange.com/questions/133077/followup-to-the-relation-between-energy-quanta-of-an-einstein-solid-and-the-equ/133321
[ "# Followup to: The relation between energy quanta of an Einstein solid and the equipartition value of heat capacity\n\nAs a followup question to this question: The relation between energy quanta of an Einstein solid and the equipartition value of heat capacity and this answer https://physics.stackexchange.com/a/133053/55779:\n\nApparently energy quanta and the equipartition values are related somehow.\n\nI'd like to approach the problem without the formula, since the problem the question is asked in is before the problem where that formula is derived.\n\nHow can I know that value of $x\\approx3$ without the formula ? I can't even tell that I should be looking for the half maximum. Or can I?\n\nI'm not sure how one can know that the half maximum corresponds to $kT/\\epsilon \\approx 1/3$ without resorting to the formula for the heat capacity.\n\nStill, notice that there are only two energy scales, i.e., $\\epsilon$ and $kT$, in the problem. Then, whatever (dimensionless) number that determines whether the equipartition holds or fails has to be the ratio $x\\equiv kT/\\epsilon$. The limits $x \\rightarrow 0$ and $x\\rightarrow \\infty$ should correspond to the two cases, and $x$ would be of order one in the crossover region. This consideration at least lets you make an order-of-magnitude estimation of $\\epsilon$.\n\n• You can find out the half maximum by looking at the graph, which reaches half of its maximum value for approximately one third of the unit of $kT/\\epsilon$ (granted you plotted the graph that way). I'm just not sure how to know that I should be looking for half the value of $C$ to find the value for $\\epsilon$. – 1010011010 Aug 29 '14 at 10:36\n• Surely you'll find that the half-maximum amounts to $kT/\\epsilon \\approx 1/3$ by looking at the plot, but only if you know the value of $\\epsilon$ beforehand. What I described above is how you can estimate $\\epsilon$ from the $C$ vs. $T$ plot. The point is that $kT/\\epsilon = a$ at the crossover region, where $a$ is an arbitrary number of order one. Of course, there is freedom in choosing the exact value of $a$ and in defining what we exactly mean by the crossover point, but taking $a=1$ and the half-maximum would be a reasonable thing to do. – higgsss Aug 29 '14 at 10:55\n• But I don't think one can get $a\\approx 1/3$ without looking at the actual formula. – higgsss Aug 29 '14 at 10:56\n• The R code from my linked question shows a plot of $C/Nk$ as a function of $kT/\\epsilon$. A screenshot can be found in this link: i.imgur.com/t4V87CC.png - As you can see, for $N=50$, when $C/Nk\\approx 1/2$, $kT/\\epsilon\\approx1/3$. :-) – 1010011010 Aug 29 '14 at 10:59\n\nFor visibility I will post this as an answer as well.\n\nThe problem in my text book wanted me to fit the numerical/dimensionless approximation to the graph in the text book, to estimate at what value of $T$ the graph would reach half its maximum value (in Figure 1.14 in Schroeder's Introduction to Thermal Physics that's $C_V=3R$).\n\nThe estimation of $\\epsilon$ can be done too for $C/Nk=1/4$, but you will need to fill in different (higher) values of $T$, but $\\epsilon$ should be the same for those calculations as well." ]
[ null ]
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https://www.visionlearning.com/en/library/Math%20in%20Science/62/Exponential%20Equations%20in%20Science%20I/206
[ "Equations\n\n# Exponential Equations in Science I: Growth and Decay\n\nby Anne E. Egger, Ph.D., Janet Shiver, Ph.D., Teri Willard, Ed.D.\n\nSt. Matthew Island is a remote island in the Bering Sea off Alaska. In 1944, the United States Coast Guard set up a station on the island to aid planes and ships in navigating the Bering Sea. To provide an emergency food source for the 19 men at the station, 29 reindeer, consisting of 24 females and 5 males, were introduced to the island (Figure 1). A few years later, the Coast Guard abandoned the island, leaving the reindeer behind. In 1957, researcher Dave Klein, a biologist working for U.S. Fish and Wildlife Service, visited the island and counted 1,350 healthy reindeer, whose population had exploded due to the lack of predators and the abundance of lichens, their primary food source. Klein returned to the island in 1963, where he was astounded to find that the population had swelled to over 6,000, which represents an amazing 47 reindeer per square mile.\n\nThree years later in 1966, Klein and others returned to the island to find that the reindeer population had plummeted from 6,000 healthy reindeer to 42 sickly reindeer. Of those 42, 41 were females and 1 was a male that had abnormal antlers, a sign that it was probably unable to reproduce. Overgrazing had wiped out the lichen supply, a significant winter food source for the reindeer. This lack of food caused a 40% decrease in the body weight of the animals and made them less able to withstand the harsh winters of St. Matthew Island (Klein, 1968). By the 1980s, no reindeer remained on the island.\n\nFigure 2 shows Dave Klein’s graph of the reindeer population on St. Matthew Island. Notice that the population of reindeer on the island changed relatively slowly from year to year in the beginning, but as time went on, it increased by larger and larger amounts. This pattern of growth should make intuitive sense: As more reindeer populate the island, more births occur. And so the population increases more rapidly as time goes on, resulting in the curved, concave-up shape of the graph – until 1963, at least.", null, "Figure 2: Graph of assumed population growth of the reindeer herd on St. Matthew Island. Actual population measurements are indicated on the graph. From Klein, D.R. 1968. The introduction, increase, and crash of reindeer on St. Matthew Island. Journal of Wildlife Management, 32(2): 350-367.image © Wiley\n\nUnlike the slope of a straight line, the slope of the curve on the graph is not constant, so the equation that describes the graph has to have a different form than a linear equation (which is written in the form y = mx + b; see our module on Linear Equations in Science: Relationships with Two Variables for more information). Instead, the equation that describes this shape has a variable as an exponent, such as y = 5x, and thus is called an exponential equation.\n\nThe rapid increase in the number of reindeer on St. Matthew Island can be described with an exponential equation, and is called exponential growth. This type of growth (and its opposite, exponential decay) is a common natural phenomenon, and thus exponential equations are frequently used in all branches of science. After describing these kinds of equations in more detail, we will determine the equation that describes the reindeer population growth.\n\n## Early history of exponential equations\n\nSome of the earliest records of mathematical problem solving come from ancient Egypt in the form of papyri that were written between 1850 and 1600 BCE. One of these, the Rhind Mathematical Papyrus, is a collection of math problems written around 1650 BCE whose title is “Correct method of reckoning for grasping the meaning of things and knowing everything that is, obscurities…and all secrets,” (see Figure 3 for a picture of the Rhind Papyrus). This was not a purely academic document: The problems in the papyrus were used to manage food supplies for cities, among other things.", null, "Figure 3: A fragment of the Rhind mathematical papyrus, written in 1650 BCE in Egypt, showing a problem that involves a geometrical progression.\n\nIn a certain village, there were 7 houses; each house had 7 cats; each cat caught 7 mice; each mouse would have (were it not for the cats) eaten 7 ears of spelt; each ear of spelt produced 7 hekats of grain at harvest. How many hekats of grain were saved by the presence of the cats? (as quoted in Curtis, 1978).\n\nIf we put that information in table form, here is what you get:\n\nTable 1: A table of data from the Rhind papyrus problem.\nItem How many? Exponential\nnotation\nTotal\nnumber\nHouse 7 71 7\nCats 7 x 7 houses 72 49\nMice 7 x 7 cats x 7 houses 73 343\nEars of spelt 7 x 7 mice x 7 cats x 7 houses 74 2401\nHekats 7 x 7 ears x 7 mice x 7 cats x 7 houses 75 16807\n\nThe numbers are increasing rapidly by multiplication of the same number by itself in what is called a geometric progression. The Egyptians did not use the symbolic notation of an exponent that we do today, but they were very familiar with the idea of a geometric progression.\n\nUse of the exponential notation came much later, when René Descartes defined the notation a2 as being equivalent to aa, \"for multiplying a by itself\" and a3 as \"for multiplying it yet again by a, and so on to infinity\" (Descartes, 1637). At the time, however, Descartes did not use the word \"exponent\" (exposant in French). In fact, it is not entirely clear when the word \"exponent\" began to be used to describe the use of the right-hand superscript as a mathematical expression, and most seemed to think it needed no explanation at the time. To address this lack of explanation, Charles Reyneau published Analyse demontrée in 1708, in which he states, \"The only calculation that is not explained in the Theories of Algebra must be spoken of, and this is exponents or powers\" (Cajori, 1913). By the early 1700s, therefore, both the mathematical concept of exponential equations and the notation of exponents were firmly established.\n\nComprehension Checkpoint\n\nThe first written record of math problems that use geometric progression was\n\n## What are exponential equations?\n\nAn exponential equation is an equation in which a variable occurs in the exponent. For example, y = 5x is an exponential equation since the exponent is the variable x (also said as \"5 to the power of x\"), while y = x5 is not an exponential equation since the exponent is 5 and not a variable. We often write exponential equations as y = abx, where a and b are constants (numbers that don't change value) and x and y are variables. In addition, a is called the initial value, and b is called the base value. As in most areas of math and science, x is considered the independent or manipulated variable, and y is the dependent or response variable, because the value we get for y depends on what we substitute in for x.\n\nIn exponential equations, the value of b, the base value, has some restrictions. The constant b cannot be equal to 1 and it must be greater than 0. Why? If b = 1, then no matter what the value of x is, the value of y is always the same number a; if b = 0, then the value of y is always 0. When we graph the equation with these values we would get a horizontal line (thus a linear equation) instead of an exponential curve. If b < 0, some values of x will result in values of y that are not real. For example, if x is a fraction like ½ and b = -2, then (-2)½ = √-2, which is not a real number and cannot be graphed on a real number axis.\n\n## Graphing an exponential equation\n\nLet’s look at the behavior of an exponential equation, y = 5x, and compare it to a linear equation, y = 5x + 1. To see the differences, we will graph both equations by first completing a table of values, shown below.\n\nTable 2a: Table showing y-values for different x-values for a linear equation.\nLinear equation\nx y = 5x + 1 y Change in y-value\n-1 5(-1)+1 -4 n/a\n0 5(0)+1 1 +5 (“plus 5”)\n1 5(1)+1 6 +5\n2 5(2)+1 11 +5\n3 5(3)+1 16 +5\nTable 2b: Table showing y-values for different x-values for an exponential equation.\nExponential equation\nx y = 5x y Change in y-value\n-1 5-1 1/5 n/a\n0 50 1 x5 (“times 5”)\n1 51 5 x5\n2 52 25 x5\n3 53 125 x5\n\nThe y-values of a linear equation are the result of simply adding the same value over and over again (in this case, 5), called an arithmetic progression. In contrast, the y-values of an exponential equation are the result of repeated multiplication by the same amount (again, 5), called a geometric progression. We can compare these two sets of results graphically, shown in the graph in Figure 4.", null, "Figure 4: Graph of the linear equation y=5x+1 (red line) compared to the graph of the exponential equation y=5x (blue line).\n\nThe graph of the linear equation is a straight line and increases at a steady or constant rate. The graph of the exponential equation, on the other hand, is not a straight line, and increases at an increasing rate, forming a curve. Since the powers in an exponential expression indicate the number of times the base number is to multiply itself, such as 23 = 2 * 2 * 2, then as the powers increase, we are multiplying by the same value more and more times. This relationship causes y to increase slowly at first and then more rapidly as the x values increase, which causes the graph to appear curved or concave in shape.\n\nThe graph of an exponential equation when the initial value, a, is positive can be classified as either exponential growth (increasing to the right) or exponential decay (decreasing to the right) depending on the value of b; see the two graphs in Figure 5 to compare growth and decay.\n\nExponential growth occurs when b > 1, and y-values increase to the right. Exponential decay occurs when 0 < b < 1, and y-values decrease to the right. Both graphs are concave-up.\n\nWhen a < 0, the graphs of exponential equations become concave down, and increasing x-values yield increasingly negative y-values. While this is perfectly acceptable mathematically, it is rare in science that the initial value a would be negative. Thus, the majority of graphs we use in science look like either exponential growth or decay curves shown in Figure 5.\n\nComprehension Checkpoint\n\nThe graph of an exponential equation is a\n\n## Sample problem 1\n\nSuppose you are a 2015 college graduate and are offered a job as an ecologist at a starting salary of $40,000 per year. To strengthen the offer, the company promises you annual raises of 5% per year for at least the first five years of work. Let’s examine how your salary will change over a five-year period. Let x = the number of years since the beginning of your contract and let y = the annual salary (in$) after x years. A raise results in 100% (original amount) + 5% (raise) = 105%, or 1.05, multiplied by your previous salary. (Keep in mind that you must express the percent as a decimal.) The results of these calculations are shown in the table below.\n\nTable 3: Table of calculations for sample problem 1.\nx Years Salary Calculation with 5% Raise Yearly Salary After Raise\n0 40,000.00 = 40,000.00•(1.05)0 $40,000.00 1 40,000.00 (1.05) = 40,000.00•(1.05)1$42,000.00\n2 [40,000.00(1.05)](1.05) = 40,000.00•(1.05)2 $44,100.00 3 [40,000.00(1.05)2](1.05) = 40,000.00•(1.05)3$46,305.00\n4 [40,000.00(1.05)3](1.05) = 40,000.00•(1.05)4 $48,620.25 5 [40,000.00(1.05)4](1.05) = 40,000.00•(1.05)5$51,051.26\n\nNotice that in year 0, representing the initial year of the job, there will be no multiplier to determine the salary, or you could think $40,000.00 • (1.05)0 =$40,000.00 • 1 = $40,000. Then for year 1,$40,000 is multiplied by (1.05)1, or just 1.05. For year 2, $40,000 is multiplied by (1.05) twice, once to get the increase for the first year and a second time to get the additional increase for year 2. This gives us$40,000.00 • (1.05)2. The pattern continues for each additional year with the exponent for 1.05 being the same as the year number, x.\n\nIn the salary scenario, the beginning salary is a, the initial value. The value b = (1 + 0.05) or 1.05, which can be thought of as 100% of the previous year’s salary plus a 5% increase. Substituting in both values, the equation becomes y = 40000(1.05)x, where x is the number of years since being hired. This exponential equation allows us to find your salary after any number of years on the job, as long as nothing else changes.\n\nComprehension Checkpoint\n\nTo calculate your future income after yearly raises of a certain percent, use\n\n## Sample problem 2\n\nLet’s return to the reindeer on St. Matthew Island and write an exponential equation to represent their population growth. Because we don't have data every year or at regular time intervals, this problem requires a little bit more manipulation to solve. First, we need to convert the year (such as 1957) to the years since reindeer were introduced, or years since 1944. The number of years since reindeer were introduced is x in this equation, and y is the number of reindeer on the island. We have three data points to work with: 1944, or 0 years after introduction; 1957, 13 years after introduction, and 1963, 19 years after introduction (see the table below).\n\nTable 4: Data table for St. Matthew Island reindeer.\nYear Years since introduction\n(Year – 1944)\nNumber of\nreindeer\n1944 0 29\n1957 13 1350\n1963 19 6000\n\nThe initial number of reindeer on the island was 29, so a = 29. We need to determine what b is to write the complete equation, but we don’t have regularly spaced time intervals to determine this easily by hand. With a graphing calculator or spreadsheet program, you can enter the ordered pairs in the table above ((0, 29), (13, 1350), and (19, 6000)) into the list function and find an exponential equation for the data set. An equation generated through this statistical process, called regression, is y = 30.14(1.33)x, and the value of b is determined to be 1.33. Compare this with the value of b from sample problem 1, 1.05, where the growth rate of the salary was 5% per year. Using the same logic (1.33 – 1.00 = 0.33 or 33%), the equation we derived suggests a 33% growth rate in the reindeer population per year!\n\nThis equation can be used to approximate the number of reindeer on the island during any year from 1944 to 1963. However, we need to remember that this is a mathematical model derived from limited data and the actual data may be slightly different from the values generated by the exponential equation. For example, if we want to predict the number of reindeer on the island in 1963, we can substitute 19 (given that 1963 – 1944 = 19) for the exponent x.\n\n$$y = 29 ( 1.33 ) 19 = 6520 reindeer$$\n\nBut this value is higher than the actual number of reindeer counted on the island at this time. The difference between the number of reindeer counted and the mathematical prediction could be due to a number of factors, including counting errors by the researchers, natural variability in the reindeer population, and an imprecise mathematical model, which could be the result of having only three data points to work with (for more information on mathematical models, see our module Modeling in Scientific Research).\n\n## Exponential equations in science\n\nExponential equations are applied in a wide variety of situations in science, from modeling the spread of a viral disease in a population to estimating the atmospheric pressure at a given altitude to chain reactions in nuclear fission. All of these processes involve a geometric progression: One person with a virus can infect ten others, for example, and each of those ten people can infect ten more. In all of these cases, real-world data can be modeled using exponential equations, and these equations can provide predictions of future behavior. Solving exponential equations is a valuable tool for finding variables such as growth rate, decay rate, the amount of time that has passed, or an amount of something at a given time.\n\n### Summary\n\nExponential equations are indispensable in science since they can be used to determine growth rate, decay rate, time passed, or the amount of something at a given time. This module describes the history of exponential equations and shows how they are graphed. Sample problems, including a look at the growth rate of the reindeer population on St. Matthew Island in the Bering Sea, illustrate how exponential equations are used in the real world.\n\n### Key Concepts\n\n• Exponential equations have a variable as an exponent and take the form y= abx.\n\n• The y-values of (or solutions to) an exponential equation follow a geometric progression and are the result of repeated multiplication by the same amount.\n\n• The shape of graphs of exponential equations indicate exponential growth or decay.\n\n• Exponential growth and decay are both common processes and exponential equations can be used to model and predict in many disciplines.\n\n• HS-C3.5\n• ##### References\n• Cajori, F. (1913). History of the exponential and logarithmic concepts. The American Mathematical Monthly, 20(2), 35-47.\n\n• Curtis, L. J. (1978). Concept of the exponential law prior to 1900. American Journal of Physics, 46(9), 896-906.\n• Descartes, R. (1637). La Géométrie. Leyde: Jan Maire.\n• Klein, D. R. (1968). The introduction, increase, and crash of reindeer on St. Matthew Island. Journal of Wildlife Management, 32(2), 350-367.\n\nAnne E. Egger, Ph.D., Janet Shiver, Ph.D., Teri Willard, Ed.D. “Exponential Equations in Science I” Visionlearning Vol. MAT-3 (2), 2014.\n\nTop" ]
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https://mathematica.stackexchange.com/questions/170669/independent-colorfunction-in-revolutionplot3d
[ "# Independent Colorfunction in RevolutionPlot3D\n\nprobably a trivial questions, but I couldn't find a solution for over 2 hours:\n\nI want to produce a RevolutionPlot3D of a function, f1, with a separate colorfunction, f2. I thought it might be possible to specify something like:\n\nRevolutionPlot3D[r^2*Sin[2*\\[Theta]], {r, 0, 1}, {\\[Theta], 0, 2*Pi},\nColorFunction -> Function[{x, y, z, r1, \\[Theta]1}, ColorData[\"Rainbow\"][Abs[z]]]]\n\n\nwhere\n\nf1 = r^2*Sin[2*\\[Theta]]\n\n\nand\n\nf2 = Abs[r^2*Sin[2*\\[Theta]]]\n\n\ninstead of the expected outcome that should look like this:", null, "Thank you very much for your help.\n\n• Bottom plot is not rainbow see this mathematica.stackexchange.com/questions/101268/… – OkkesDulgerci Apr 8 '18 at 15:22\n• Based on @Okkes's comment: RevolutionPlot3D[r^2 Sin[2 θ], {r, 0, 1}, {θ, 0, 2 π}, ColorFunction -> Function[{x, y, z, r, θ}, Hue[2 (1 - Abs[r^2 Sin[2 θ]])/3]], ColorFunctionScaling -> False, Mesh -> False] – J. M.'s technical difficulties Apr 8 '18 at 16:00\n• Just add ColorFunctionScaling -> False to your original plot. – user484 Apr 8 '18 at 16:19\n• @J.M. - recommend that you also increase the PlotPoints – Bob Hanlon Apr 8 '18 at 16:20\n• Thanks a lot, Rahul! It finally clicked and I understand the comment now. Thanks J.M. & Dulgerci - I wouldn't have spotted it. Problem solved (in case you want to post it as an answer) – Paul Saturday Apr 8 '18 at 17:13\n\nRevolutionPlot3D[r^2 Sin[2 θ], {r, 0, 1}, {θ, 0, 2 π},", null, "" ]
[ null, "https://i.stack.imgur.com/UAEL9.png", null, "https://i.stack.imgur.com/ATa9Z.png", null ]
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https://wiki.atlas.aei.uni-hannover.de/Main/ReprNotesOnS4R2Paper
[ "## Some Notes on the S4R2 Paper\n\n### Uniform templates in equatorial plane\n\nTesting the intuitive idea that the sky-metric we used is isotropic in the equatorial plane: this might have been thought from Fig.4 in the Paper, showing the sky-templates in the equatorial plane are approximately uniform.\n\nWe generated the metric ellipses for an observation time of $T=30$ hours sampled over the northern hemisphere of the sky, both projected onto a Freq = const. surface (\"projected\") and simply ''restricted'' to Freq = const (\"unprojected\"), in three coordinate systems for the sky: equatorial sky-angles, unit vectors in equatorial plane, and unit-vectors in the ecliptic plane:\n\n Northern hemisphere using sky-angles Northern hemisphere represented in the equatorial plane Northern hemisphere represented in the ecliptic plane", null, "", null, "", null, "We see that the (frequency-projected) sky-ellipses in the equatorial plane are '''not''' circular. The reason for the approximately uniform distribution of sky-templates in the equatorial plane therefore lies with the gridding algorithm in the sky, i.e. http://www.lsc-group.phys.uwm.edu/lal/slug/nightly/doxygen/html/TwoDMesh_8c.html LALCreate2DMesh()\n\nTo illustrate that this is in principle possible, consider the following simple example: a non-isotropic metric (ellipses are not circles), still we can construct a uniform, square template lattice!", null, "", null, "These plots were produced using the octave scripts ''plotSkyMetrics_S4R2.m'' and ''fakeFlatGrid.m'' respectively, which are found in this tarball. Note: you need to install ''octapps'' for these scripts to work, which you can download using: `git-clone git://n0.aei.uni-hannover.de:shared/octapps.git`\nTopic revision: r2 - 06 Jun 2008, ReinhardPrix\nCopyright © by the contributing authors. All material on this collaboration platform is the property of the contributing authors.\nIdeas, requests, problems regarding Foswiki? Send feedback" ]
[ null, "https://wiki.atlas.aei.uni-hannover.de/pub/Main/ReprNotesOnS4R2Paper/S4R2_SkyEllipses_SkyAngles.png", null, "https://wiki.atlas.aei.uni-hannover.de/pub/Main/ReprNotesOnS4R2Paper/S4R2_SkyEllipses_EquPlane.png", null, "https://wiki.atlas.aei.uni-hannover.de/pub/Main/ReprNotesOnS4R2Paper/S4R2_SkyEllipses_EclPlane.png", null, "https://wiki.atlas.aei.uni-hannover.de/pub/Main/ReprNotesOnS4R2Paper/UniformGrid_Ellipses.png", null, "https://wiki.atlas.aei.uni-hannover.de/pub/Main/ReprNotesOnS4R2Paper/UniformGrid_Templates.png", null ]
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https://helptest.net/physics/78285/
[ "", null, "# How much heat is released when 432 g of water cools down from 71'c to 18'c?", null, "The heat released by the water when it cools down by a temperature difference  is where m=432 g is the mass of the water is the specific heat capacity of water is the decrease of temperature of the water Plugging the numbers into the equation, we find and this is the amount of heat released by the water.\n\nOnly authorized users can leave an answer!", null, "If you are not satisfied with the answer or you can’t find one, then try to use the search above or find similar answers below.\n\nMore questions", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "" ]
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https://numbermatics.com/n/2275011/
[ "# 2275011\n\n## 2,275,011 is an odd composite number composed of two prime numbers multiplied together.\n\nWhat does the number 2275011 look like?\n\nThis visualization shows the relationship between its 2 prime factors (large circles) and 6 divisors.\n\n2275011 is an odd composite number. It is composed of two distinct prime numbers multiplied together. It has a total of six divisors.\n\n## Prime factorization of 2275011:\n\n### 32 × 252779\n\n(3 × 3 × 252779)\n\nSee below for interesting mathematical facts about the number 2275011 from the Numbermatics database.\n\n### Names of 2275011\n\n• Cardinal: 2275011 can be written as Two million, two hundred seventy-five thousand and eleven.\n\n### Scientific notation\n\n• Scientific notation: 2.275011 × 106\n\n### Factors of 2275011\n\n• Number of distinct prime factors ω(n): 2\n• Total number of prime factors Ω(n): 3\n• Sum of prime factors: 252782\n\n### Divisors of 2275011\n\n• Number of divisors d(n): 6\n• Complete list of divisors:\n• Sum of all divisors σ(n): 3286140\n• Sum of proper divisors (its aliquot sum) s(n): 1011129\n• 2275011 is a deficient number, because the sum of its proper divisors (1011129) is less than itself. Its deficiency is 1263882\n\n### Bases of 2275011\n\n• Binary: 10001010110110110000112\n• Base-36: 1CRER\n\n### Squares and roots of 2275011\n\n• 2275011 squared (22750112) is 5175675050121\n• 2275011 cubed (22750113) is 11774717671450826331\n• The square root of 2275011 is 1508.3139593601\n• The cube root of 2275011 is 131.5208176885\n\n### Scales and comparisons\n\nHow big is 2275011?\n• 2,275,011 seconds is equal to 3 weeks, 5 days, 7 hours, 56 minutes, 51 seconds.\n• To count from 1 to 2,275,011 would take you about five weeks!\n\nThis is a very rough estimate, based on a speaking rate of half a second every third order of magnitude. If you speak quickly, you could probably say any randomly-chosen number between one and a thousand in around half a second. Very big numbers obviously take longer to say, so we add half a second for every extra x1000. (We do not count involuntary pauses, bathroom breaks or the necessity of sleep in our calculation!)\n\n• A cube with a volume of 2275011 cubic inches would be around 11 feet tall.\n\n### Recreational maths with 2275011\n\n• 2275011 backwards is 1105722\n• The number of decimal digits it has is: 7\n• The sum of 2275011's digits is 18\n• More coming soon!\n\nMLA style:\n\"Number 2275011 - Facts about the integer\". Numbermatics.com. 2021. Web. 26 October 2021.\n\nAPA style:\nNumbermatics. (2021). Number 2275011 - Facts about the integer. Retrieved 26 October 2021, from https://numbermatics.com/n/2275011/\n\nChicago style:\nNumbermatics. 2021. \"Number 2275011 - Facts about the integer\". https://numbermatics.com/n/2275011/\n\nThe information we have on file for 2275011 includes mathematical data and numerical statistics calculated using standard algorithms and methods. We are adding more all the time. If there are any features you would like to see, please contact us. Information provided for educational use, intellectual curiosity and fun!\n\nKeywords: Divisors of 2275011, math, Factors of 2275011, curriculum, school, college, exams, university, Prime factorization of 2275011, STEM, science, technology, engineering, physics, economics, calculator, two million, two hundred seventy-five thousand and eleven.\n\nOh no. Javascript is switched off in your browser.\nSome bits of this website may not work unless you switch it on." ]
[ null ]
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https://math.stackexchange.com/questions/1811754/is-fracddx-left-sum-n-0-infty-xn-right-sum-n-0-infty-left
[ "# Is $\\frac{d}{dx}\\left(\\sum_{n = 0}^\\infty x^n\\right) = \\sum_{n = 0}^\\infty\\left(\\frac{d}{dx} x^n \\right)$ true?\n\nAlmost 3 months ago, I asked this question regarding if it's possible to compute the summation of derivatives, as in the example I've given: $$\\sum_{n = 0}^\\infty \\frac{d}{dx} x^n$$ One answer regarded the interchange between summations and derivatives, which got me thinking: does the interchange between the derivative and the summation succeed in this example? In other words, is $$\\frac{d}{dx}\\left(\\sum_{n = 0}^\\infty x^n\\right) = \\sum_{n = 0}^\\infty\\left(\\frac{d}{dx} x^n \\right)$$ true? I believe it is, because the summation of the derivatives of $x^n$ from $n = 0 \\to \\infty$ was: $$1 + 2x + 3x^2 + 4x^3 + 5x^4 + \\cdot \\cdot \\cdot$$ and to evaluate the summation of a series, you take the derivative of each term, which gets me: $$\\frac{d}{dx}\\left(\\sum_{n=0}^\\infty x^n\\right) = \\frac{d}{dx}(1 + x^2 +x^3 + x^4 + x^5 + \\cdot \\cdot \\cdot) = 1 + 2x + 3x^2 + 4x^3 + 5x^4 + \\cdot \\cdot \\cdot$$ Hence, I believe that the interchange succeeds. Am I right? Does the interchange succeed?\n\n## Notes\n\n• I implemented the left hand side of the \"interchange equation\" into WolframAlpha, and I got back something \"useful\", but it doesn't really solve my problem.\n• I found This question and this question, but they have nothing to do with my question.\n• Multiple other questions deal with interchanges with summations and integrals. This is about interchanging summations and derivatives.\n\n## 3 Answers\n\nThis is true if the sum converges absolutely and uniformly (on compact sets), which in this example occurs only when $|x| < 1$. In fact, in the radius of convergence of any power series you can exchange the order of summation and differentiation.\n\nThis can be shown using a number of different methods. There are proofs that are elementary but a pain, and also some nice proofs that use more advanced tools from measure theory or complex analysis.\n\n• Let me clarify: The interchange here succeeds if $\\lvert x \\rvert < 1$, because both sides would be equal to $$\\frac {1}{(x - 1)^2}$$. I think I got it. Thanks! – Obinna Nwakwue Jun 4 '16 at 15:37\n\nIn real analysis, series of the form $f(x)=\\sum_{n=0}^\\infty a_nx^n$ is called power series, and its radius of convergence is given by $$R=\\frac{1}{\\limsup_n\\sqrt[n]{|a_n|}}.$$ A well known theorem says that $f$ is differentiable in $(-R,R)$ and $$f'(x)=\\sum_{n=1}^\\infty a_nnx^{n-1}\\quad x\\in(-R,R).$$\n\n• Hmm... to assume $a_n = 1 \\forall n$. – Obinna Nwakwue Jun 6 '16 at 16:55\n\nIf it is of any interest to you, I do believe the following is true:\n\n$$f(x)=\\sum_{n=1}^xg(n)$$\n\n$$f'(x)=C+\\sum_{n=1}^xg'(n)$$\n\nwhere $C$ is some constant.\n\nMore generally,\n\n$$\\frac d{dx}\\sum_{t=a(x)}^{b(x)}f(x,t)=\\sum_{t=a(x)}^{b(x)}\\left(\\frac d{dx}f(x,t)\\right)+b'(x)\\left(\\sum_{t=x_0}^{b(x)}\\left(\\frac d{dt}f(x,t)\\right)+\\sum_{k=n_0}^nc(x,k)(-k)\\zeta(1-k,x_0-t_0)\\right)+a'(x)\\left(\\sum_{t=a(x)}^{x_0}\\left(\\frac d{dt}f(x,t)\\right)-\\sum_{k=n_0}^nc(x,k)(-k)\\zeta(1-k,1+x_0-t_0)\\right)$$\n\nif $f(x,t)$ can be expressed as a Laurent series\n\n$$f(x,t)=\\sum_{k=n_0}^nc(x,k)(t-t_0)^k$$\n\nand\n\n$$\\zeta(-r,a-t_0)=\\sum_{k=0}^\\infty(k+a-t_0)^r$$\n\n• cyclochaotic.wordpress.com/2012/07/31/… – Simply Beautiful Art Jul 1 '16 at 12:04\n• Excellent answer, because in part, my function is actually a multivariable function: $$f(x, n) = x^n$$ This would be an excellent way to deal with this when working with multivariable functions. – Obinna Nwakwue Jul 1 '16 at 19:31\n• @ObinnaNwakwue Yours actually isn't to bad, since $a(x)$ and $b(x)$ are constants (referring to my answer), so $a'(x)=b'(x)=0$, resulting in much simplification in that big formula. – Simply Beautiful Art Jul 1 '16 at 22:48\n• Excellent! Great to know that! Okay, I already know if $a(x)$ and $b(x)$ are constants, $a'(x) = b'(x) = 0$, because the derivative of a constant $k$ is 0. – Obinna Nwakwue Jul 2 '16 at 0:56" ]
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https://www.sangakoo.com/en/unit/reduced-equation-of-the-horizontal-parabola
[ "# Reduced equation of the horizontal parabola\n\nLet's consider the parabola which vertex coincides with the origin and which axis coincides with the $$x$$-axis.\n\nIn this case, the focus is at point $$F(\\dfrac{p}{2},0)$$, and the equation of the generator line $$D$$ is: $$x=-\\dfrac{p}{2}$$.\n\nThe equation of the parabola is $$y^2=2px$$\\$\n\nConsidering the equation $$y^2=-6x$$, find its vertex, its focus and its generator line.\n\nBy definition, in this type of equations the vertex is $$A(0,0)$$.\n\nWe can identify $$y^2=-6x$$ with $$y^2=2px$$ and obtain $$2p=-6$$ and $$p=-3$$.\n\nTherefore, the focus is at $$F(\\dfrac{p}{2},0)$$, which is at $$F(-\\dfrac{3}{2},0)$$.\n\nTo substitute $$p$$ in $$x=-\\dfrac{p}{2}$$.\n\nThe equation of the generator line is $$x=-\\dfrac{3}{2}$$." ]
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https://everything2.com/title/recursive
[ "(recursive function theory, mathematical logic)\nFunction\nThe class of recursive functions is the same as the class of computable functions, but it is reached by a completely different route. To the allowed operations of the class of primitive recursive functions we add the following:\n• (minimization:) If f(x_1,...,x_n,y) is a recursive function, then so is g(x_1,...,x_n) = min { k : f(x_1,...,x_n,k) = 0 }.\nNote that it may happen that for some particular values of x_1,...,x_n, f(x_1,...,x_n,y) is non-zero for all y. In this case, the value of g(x_1,...,x_n) is said to be undefined. Colloquially, g(x_1,...,x_n) goes into an infinite loop (think of a computer program calculating f(x_1,...,x_n,k) for each k, until it finds a zero). In particular, g(x_1,...,x_n) is generally a partial function: it is only defined for some values of its arguments.\n\nIn fact, it happens that any recursive function can be written down using minimization at most once (the other primitive recursive operations are used numerous times); this follows from proving that Turing machines can compute any recursive function, and then seeing that when you simulate a Turing machine using recursive functions, computing the state of the machine and its tape at time T is primitive recursive; to simulate the machine until it halts, one needs only add one minimization.\n\nThe fact that the definitions of computable functions and recursive functions are so different, yet the resulting class of functions is the same, leads to the Church Turing thesis.\n\nSet\nA subset L of the nonnegative integers such that there exists a recursive function f for which f(n)=1 if n is in L, and f(n)=0 otherwise. Note that such a function f must be defined for all values of its argument n.\n\nLog in or register to write something here or to contact authors." ]
[ null ]
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https://allexamreview.com/electrical-machines-expected-mcq-pdf-5/
[ "# Electrical Machines Expected MCQ PDF 5 For Coal India Limited (CIL) MT Exam 2017\n\n## Electrical Machines Expected MCQ PDF 5", null, "Category –EE Online Test\n\nAttempt Free Electrical Machines Expected MCQ PDF 5 Here. Read The Important Electrical MCQ From Below.\n\n1)   While delivering an useful power of 20 kW to the full load, a 3 phase, 50 Hz, 6 pole induction motor draws a line current of 50 A. it is connected to supply of 420 V and runs at a speed of 950 rpm. If mechanical losses are 1000 W, then its rotor copper losses and shaft torque are\n\na. 1105.26 W, 201.03 N-m\nb. 1125.26 W, 201.03 N-m\nc. 1105.26 W, 208.09 N-m\nd. 1125.26 W, 208.09 N-m\n\n2)   A 4 pole, 25 kW, three phase, 420 V, 50 Hz induction motor operates at an efficiency of 90% with a power factor of 0.8 lagging. The current drawn by the motor from the mains is\n\na. 42.89 A\nb. 45.56 A\nc. 47.73 A\nd. None of these\n\n3)   In a three phase induction motor, the mechanical load should be such that the equivalent load resistance referred to stator is equal to the\n\na. Total leakage reactance of the motor referred to stator\nb. Total leakage reactance of the motor referred to rotor\nc. Total leakage impedance of the motor referred to stator\nd. Total leakage impedance of the motor referred to rotor\n\nANSWER: Total leakage impedance of the motor referred to stator\n\nElectrical Machines Expected MCQ PDF 5\n\n4)   Torque of an induction motor can sometimes be given in synchronous – watt. One synchronous – watt is equal to\n\na. 60 / (2 Π Ns) N – m\nb. (2 Π Ns) / 60 N – m\nc. 120 / (2 Π Ns) N – m\nd. (2 Π Ns) / 120 N – m\n\nANSWER: 60 / (2 Π Ns) N – m\n\n5)   When an induction motor is working under loaded condition, its induced voltage will\n\na. Leads the magnetic flux by 90 degree\nb. Lags the magnetic flux by 90 degree\nc. Lags the magnetic flux by 30 degree\nd. In phase with the magnetic flux\n\nANSWER: Lags the magnetic flux by 90 degree\n\n6)   The performance of induction motor is effected by the harmonics in the\n\na. Space variation of impressed voltage\nb. Time variation of impressed voltage\nc. Space variation of impressed current\nd. Time variation of impressed current\n\nANSWER: Time variation of impressed voltage\n\n7)   The tooth or slot harmonics in an induction motor is caused due to\n\na. Variation of air gap reluctance\nb. Leakage flux\nc. Non sinusoidal nature of input voltage\nd. None of these\n\nANSWER: Variation of air gap reluctance\n\nElectrical Machines Expected MCQ PDF 5\n\n8)   The air gap flux of induction motor does not contain\n\na. 2nd harmonics\nb. 3rd harmonics\nc. 5th harmonics\nd. 7th harmonics\n\n9)   A 50 Hz, 3 phase induction motor with 4 pole stator is supplied by mains, which contains a pronounced fifth time harmonic. The speed of the fifth space harmonic will be\n\na. 100 rpm\nb. 300 rpm\nc. 600 rpm\nd. 7500\n\n10)   Crawling in an induction motor is caused\n\na. During starting of an induction motor\nb. At the fraction of rated speed\nc. Due to insulation failure\nd. All of these\n\nANSWER: At the fraction of rated speed\n\n11)   Cogging in an induction motor is caused\n\na. If the number of stator slots are integral multiple of rotor slots\nb. If the motor is running at fraction of its rated speed\nc. Due to fifth harmonic\nd. All of these\n\nANSWER: If the number of stator slots are integral multiple of rotor slots\n\nElectrical Machines Expected MCQ PDF 5\n\n12)   Crawling is a phenomena mainly associated with\n\na. 3rd harmonic\nb. 5th harmonic\nc. 7th harmonic\nd. 2nd harmonic\n\n13)   What happens if the number of stator slots in an induction motor is equal to the number of rotor slots or integral multiple of rotor slots?\n\na. Motor will run at very high speed\nb. Motor will run at very low speed\nc. Motor will fail to start\nd. Does not get effected\n\nANSWER: Motor will fail to start\n\n14)   The crawling and cogging is not predominant in\n\na. Slip ring induction motor\nb. Squirrel cage induction motor\nc. Both (a) and (b)\nd. None of these\n\n15)   The Y – axis and X – axis in a circle diagram represents\n\na. Voltage and current\nb. Current and power\nc. Power and voltage\nd. Current and voltage\n\nElectrical Machines Expected MCQ PDF 5\n\n16)   The circle diagram can be used to\n\na. Predict the performance of an induction motor under various load condition\nb. Find losses in an induction motor\nc. Efficiency of an induction motor\nd. All of these\n\n17)   For plotting circle diagram no load power factor is required. The value of no load power factor will be\n\na. Lesser than 0.5\nb. Greater than 0.5\nc. Equal to 0.5\nd. 1\n\n18)   For conducting no load test on an induction motor two wattmeter’s are required. Readings of the meters\n\na. Both will be positive\nb. One will be positive and other will be negative\nc. Both will be negative\nd. None of these\n\nANSWER: One will be positive and other will be negative\n\n19)   If Ic is the active component and Im is the magnetizing component of no load current (Io) obtained in the no load test of an induction motor. Then the no load branch resistance and no load branch reactance is\n\na. Vo / Ic , Vo / Im\nb. Vo / Im , Vo / Ic\nc. Vo / Io , Vo / Ic\nd. Vo / Ic , Vo / Io\n\nANSWER: Vo / Ic , Vo / Im\n\nElectrical Machines Expected MCQ PDF 5\n\n20)   In the blocked rotor tests, slip is equal to\n\na. 0\nb. 1\nc. 0.5\nd. 0.707\n\n21)   In a slip ring induction motor, the rotor resistance is\n\na. High during starting and low at normal operating speed\nb. Low at starting and high at normal operating speed\nc. Remains same during starting and normal operating speed\nd. None of these\n\nANSWER: High during starting and low at normal operating speed\n\n22)   Deep bar or double cage rotors are used in squirrel cage induction motor to obtain\n\na. High starting current\nb. High starting torque\nc. Reduced starting current\nd. Reduced rotor resistance\n\n23)   Deep bar or double cage rotors make use of skin effect. The skin effect depends upon\n\na. Nature of material\nb. Diameter of wire\nc. Shape of wire and frequency\nd. All of these\n\nElectrical Machines Expected MCQ PDF 5\n\n24)   In deep bar induction motor, the rotor consists of deep bars, short circuited by two end rings one on each side. The leakage inductance of bottom strip\n\na. Greater than that of top strip\nb. Lesser than that of top strip\nc. Equal to that of top strip\nd. None of these\n\nANSWER: Greater than that of top strip\n\n25)   The skin effect in a deep bar induction motor is maximum when rotor is\n\na. At standstill\nb. Running at its maximum speed\n\n26)   In double cage induction motor, the rotor consists of two cages or two layers of bars short circuited by end rings. The upper cage and lower cage respectively has\n\na. High resistance and low reactance, high resistance and low reactance\nb. High resistance and low reactance, low resistance and high reactance\nc. Low resistance and high reactance, high resistance and low reactance\nd. Low resistance and high reactance, low resistance and high reactance\n\nANSWER: High resistance and low reactance, low resistance and high reactance\n\n27)   When the induction motor runs faster than the synchronous speed, the induction motor runs as\n\na. Asynchronous generator\nb. Induction generator\nc. Synchronous motor\nd. Such condition is not possible\n\nElectrical Machines Expected MCQ PDF 5\n\n28)   The induction generator is\n\na. Self exciting\nb. Separately exciting\nc. Both (a) and (b)\nd. None of these\n\n29)   Which of the following is not true about induction generator?\n\na. Synchronization for induction generator is required\nb. Induction generators are more suitable for high speeds\nc. With the help of excitation supply and frequency, the voltage and frequency of induction motor are controlled\nd. The construction is rugged for rotating parts\n\nANSWER: Synchronization for induction generator is required\n\n30)   While drawing the graph of no load losses versus voltage, the voltage is extrapolated to V = 0. The extrapolated region shows\n\na. Copper losses\nb. Core losses\nc. Friction and windage losses\nd. None of these\n\n31)   Applications of induction generators are\n\na. In railways for braking purpose\nb. Wind mils\nc. Drilling machines\nd. Only (a) and (b)\ne. None of these\n\nElectrical Machines Expected MCQ PDF 5\n\n32)   While using stator resistance starter with 3 phase induction motor, the resistances of the starter are kept at\n\na. Maximum\nb. Minimum\nc. Half of the maximum value\nd. None of these\n\n33)   When stator resistance starter is used, the factor by which stator voltage reduces is say x. If x<1, then due to stator resistance starter, the starting torque\n\na. Increases by fraction x\nb. Reduces by fraction x ∧ 2\nc. Reduces by fraction x\nd. Increases by fraction x ∧ 2\n\nANSWER: Reduces by fraction x ∧ 2\n\n34)   An autotransformer starter is suitable for\n\na. Star connected induction motor\nb. Delta connected induction motor\nc. Both (a) & (b)\nd. None of these\n\nElectrical Machines Expected MCQ PDF 5\n\n35)   The cheapest starter for induction motor is\n\na. Stator resistance starter\nb. Autotransformer starter\nc. Star-delta starter\nd. Rotor resistance starter\n\n36)   Windings of star-delta starter while starting and during running are connected in\n\na. Star, delta\nb. Delta, delta\nc. VStar, star\nd. Delta, star\n\n37)   The advantages of star-delta starter over other types of starter is\n\na. Cheapest of all\nb. Maintenance free\nc. Both (a) & (b)\nd. None of these\n\n38)   When rotor resistance starter is used with induction motor then\n\na. Only starting current is limited\nb. Only starting torque is limited\nc. Both starting current and starting torque are limited\nd. Neither starting current nor starting torque is limited\n\nANSWER: Both starting current and starting torque are limited\n\n39)   Direct online starter also called D.O.L. starter is used for motors having capacity\n\na. Less than 5 h.p.\nb. Less than 10 h.p.\nc. Greater than 10 h.p.\nd. For any capacity motor\n\nElectrical Machines Expected MCQ PDF 5\n\n40)   The NO contact and NC contact of D.O.L. starter is normally\n\na. Open, closed\nb. Closed, open\nc. Open, open\nd. Closed, closed" ]
[ null, "https://allexamreview.com/wp-content/uploads/2016/07/Important-MCQ-300x300.jpg", null ]
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https://math.stackexchange.com/questions/154156/abstract-characterization-of-s-5-why-must-some-involution-be-in-the-center-of
[ "Abstract characterization of $S_5$, why must some involution be in the center of a Sylow subgroup?\n\nI'm trying to follow a sketch proof about the abstract characterization of $S_5$, by Walter Feit.\n\nSuppose $G$ is a finite group with exactly two conjugacy classes of involutions, with $u_1$ and $u_2$ being representatives. Suppose $C_1=C(u_1)\\simeq \\langle u_1\\rangle\\times S_3$ and $C_2=C(u_2)$ be a dihedral group of order $8$. The eventual result is that $G\\simeq S_5$. Also, $C(u)$ denotes the centralizer of $u$ in $G$.\n\nI don't understand the observation some involution is in the center of a Sylow subgroup, and that $C_2$ is a Sylow $2$-subgroup. I do know that $C_2$ is contained in a Sylow $2$-subgroup at least, from the Sylow theorems, but without knowing the actual order of $G$, I don't see why it necessarily a Sylow subgroup itself.\n\n• A p-group has a non-trivial centre. The centre of a Sylow 2-subgroup is therefore non-trivial, hence has even order, and therefore contains an element of order 2. – Mark Bennet Jun 5 '12 at 9:25\n\nLet $H$ be a Sylow 2-subgroup of $G$. Since $H$ is a $p$-group, $Z(H)$ is a non-trivial $p$-group, hence contains an involution, say $u$.\nSince $u$ is central in $H$, we see that $H \\leq C(u)$. Since we have just two conjugacy classes of involutions in $G$, we have either $u$ is conjugate to $u_1$, or $u_2$.\nSuppose $u$ is conjugate to $u_1$, so $u_1 = gug^{-1}$ for some $g \\in G$. If $x \\in G$ commutes with $u$, then $gxg^{-1}$ commutes with $u_1$. This shows that $C(u_1) = gC(u)g^{-1}$, in particular, these groups have the same order.\nSince $G$ contains a subgroup of order $8 = 2^3$, $H$ contains a subgroup of order $8$, whence $C(u)$ contains a subgroup of order $8$. But if $u$ is conjugate to $u_1$, then $\\langle u_1 \\rangle \\times S_3$ contains a subgroup of order $8$, but $8$ does not divide $12$.\nTherefore, $u$ must be conjugate to $u_2$, in which case we have that $H$ is completely contained in a subgroup of order $8$, thus $|H| = 8$." ]
[ null ]
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https://metanumbers.com/2258
[ "## 2258\n\n2,258 (two thousand two hundred fifty-eight) is an even four-digits composite number following 2257 and preceding 2259. In scientific notation, it is written as 2.258 × 103. The sum of its digits is 17. It has a total of 2 prime factors and 4 positive divisors. There are 1,128 positive integers (up to 2258) that are relatively prime to 2258.\n\n## Basic properties\n\n• Is Prime? No\n• Number parity Even\n• Number length 4\n• Sum of Digits 17\n• Digital Root 8\n\n## Name\n\nShort name 2 thousand 258 two thousand two hundred fifty-eight\n\n## Notation\n\nScientific notation 2.258 × 103 2.258 × 103\n\n## Prime Factorization of 2258\n\nPrime Factorization 2 × 1129\n\nComposite number\nDistinct Factors Total Factors Radical ω(n) 2 Total number of distinct prime factors Ω(n) 2 Total number of prime factors rad(n) 2258 Product of the distinct prime numbers λ(n) 1 Returns the parity of Ω(n), such that λ(n) = (-1)Ω(n) μ(n) 1 Returns: 1, if n has an even number of prime factors (and is square free) −1, if n has an odd number of prime factors (and is square free) 0, if n has a squared prime factor Λ(n) 0 Returns log(p) if n is a power pk of any prime p (for any k >= 1), else returns 0\n\nThe prime factorization of 2,258 is 2 × 1129. Since it has a total of 2 prime factors, 2,258 is a composite number.\n\n## Divisors of 2258\n\n1, 2, 1129, 2258\n\n4 divisors\n\n Even divisors 2 2 2 0\nTotal Divisors Sum of Divisors Aliquot Sum τ(n) 4 Total number of the positive divisors of n σ(n) 3390 Sum of all the positive divisors of n s(n) 1132 Sum of the proper positive divisors of n A(n) 847.5 Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n)) G(n) 47.5184 Returns the nth root of the product of n divisors H(n) 2.66431 Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors\n\nThe number 2,258 can be divided by 4 positive divisors (out of which 2 are even, and 2 are odd). The sum of these divisors (counting 2,258) is 3,390, the average is 84,7.5.\n\n## Other Arithmetic Functions (n = 2258)\n\n1 φ(n) n\nEuler Totient Carmichael Lambda Prime Pi φ(n) 1128 Total number of positive integers not greater than n that are coprime to n λ(n) 1128 Smallest positive number such that aλ(n) ≡ 1 (mod n) for all a coprime to n π(n) ≈ 340 Total number of primes less than or equal to n r2(n) 8 The number of ways n can be represented as the sum of 2 squares\n\nThere are 1,128 positive integers (less than 2,258) that are coprime with 2,258. And there are approximately 340 prime numbers less than or equal to 2,258.\n\n## Divisibility of 2258\n\n m n mod m 2 3 4 5 6 7 8 9 0 2 2 3 2 4 2 8\n\nThe number 2,258 is divisible by 2.\n\n• Semiprime\n• Deficient\n\n• Polite\n\n• Square Free\n\n## Base conversion (2258)\n\nBase System Value\n2 Binary 100011010010\n3 Ternary 10002122\n4 Quaternary 203102\n5 Quinary 33013\n6 Senary 14242\n8 Octal 4322\n10 Decimal 2258\n12 Duodecimal 1382\n20 Vigesimal 5ci\n36 Base36 1qq\n\n## Basic calculations (n = 2258)\n\n### Multiplication\n\nn×i\n n×2 4516 6774 9032 11290\n\n### Division\n\nni\n n⁄2 1129 752.666 564.5 451.6\n\n### Exponentiation\n\nni\n n2 5098564 11512557512 25995354862096 58697511278612768\n\n### Nth Root\n\ni√n\n 2√n 47.5184 13.1192 6.89336 4.68538\n\n## 2258 as geometric shapes\n\n### Circle\n\n Diameter 4516 14187.4 1.60176e+07\n\n### Sphere\n\n Volume 4.82237e+10 6.40704e+07 14187.4\n\n### Square\n\nLength = n\n Perimeter 9032 5.09856e+06 3193.29\n\n### Cube\n\nLength = n\n Surface area 3.05914e+07 1.15126e+10 3910.97\n\n### Equilateral Triangle\n\nLength = n\n Perimeter 6774 2.20774e+06 1955.49\n\n### Triangular Pyramid\n\nLength = n\n Surface area 8.83097e+06 1.35677e+09 1843.65\n\n## Cryptographic Hash Functions\n\nmd5 2d3acd3e240c61820625fff66a19938f 247317edd2fbed736ea0c9d3ea37d66a738ad34a ea215720034a4c3073d7a7886b27431b89805c01b18329b8af22bc4113a668a4 b2b6d686c170f75cd59257b994b47f33797eb181e41f65943a79e4cef1461efb4c58a26a7956d25f91370dbb2b8b8fa58756ffdf78ae51b8b3679cd4d9e82f23 565c87126bca08d205bcee8f898cd382152910e1" ]
[ null ]
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https://artofproblemsolving.com/wiki/index.php?title=2005_Alabama_ARML_TST_Problems/Problem_8&diff=72631&oldid=23681
[ "# Difference between revisions of \"2005 Alabama ARML TST Problems/Problem 8\"\n\n## Problem\n\nFind the number of ordered pairs of integers", null, "$(x,y)$ which satisfy", null, "$x^2+4xy+y^2=21$.\n\n## Solution\n\nWe look at", null, "$x$ and", null, "$y \\pmod{3}$, since", null, "$21$ is a multiple of", null, "$3$.\n\n• Case 1:", null, "$x\\equiv 0\\pmod{3}$\n• Case 1a:", null, "$y\\equiv 0\\pmod{3}$: Then", null, "$x^2+4xy+y^2$ is divisible by", null, "$3^2=9$, but", null, "$21$ isn't.\n• Case 1b:", null, "$y\\equiv 1\\pmod{3}$: Then the LHS is", null, "$1\\pmod{3}$, while the RHS isn't.\n• Case 1c:", null, "$y\\equiv 2\\pmod{3}$: Then the LHS is", null, "$1\\pmod{3}$, while the RHS isn't.\n• Case 2: x=1mod3\n• Case 2a: y=0mod3: This is equivalent to case 1b.\n• Case 2b: y=1mod3: We let", null, "$x=3x_1+1$ and", null, "$y=3y_1+1$:", null, "$x^2+4xy+y^2=21=(3x_1+1)^2+4(3x_1+1)(3y_1+1)+(3y_1+1)^2=9(x^2+y^2+4x_1y_1+2x_1+2y_1)+6$\n\nBut 21 isn't 6mod9, it's 3mod9.\n\n• Case 2c: y=2mod3: Then the LHS is 1mod3 while the RHS isn't.\n• Case 3: x=2mod3\n• Case 3a: y=0mod3: This is equivalent to case 1c.\n• Case 3b: y=1mod3: This is equivalent to case 2c.\n• Case 3c: y=2mod3: We let", null, "$x=3x_1+2$ and", null, "$y=3y_1+2$:", null, "$x^2+4xy+y^2=21=(3x_1+2)^2+4(3x_1+2)(3y_1+2)+(3y_1+2)^2=9(x_1^2+y_1^2+4x_1y_1+4x_1+4y_1+2)+6$\n\nBut 21 isn't 6mod9, it's 3mod9.\n\nTherefore, there are absolutely no solutions to the above equation." ]
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https://excelunlocked.com/substitute-function-in-excel
[ "# SUBSTITUTE Function in Excel – A Text Function\n\nIn one of our earlier blogs, we learned the use of REPLACE Function. The REPLACE function replaces a set of characters in a text string with another set of characters based on the location and length. The SUBSTITUTE Function in excel does the same job but in a different manner.\n\nSo let’s start learning the SUBSTITUTE Function.\n\n## When to Use the SUBSTITUTE Function in Excel?\n\nThe SUBSTITUTE Function in Excel substitutes a set of characters in a text string with another set of characters. It searches for the old string within the text. If there are multiple instances of the old text in the text, then either all the instances of old text are replaced with a new text string or we can specify which instance to replace.\n\nAn important point to mark is that the function automatically searches for the old text within the text string and we need not look for its position.\n\nWe can use the REPLACE Function if we want to replace the characters based on their location in the text string. Use the FIND Function to get the location of a character in the text.\n\n## Syntax and Arguments\n\nThe following points contain important points to note about the inputs required by SUBSTITUTE Function in Excel.\n\n• text – This is the required text string, a part of which needs to be substituted.\n• old_text – This is the set of characters that we want to substitute in the text string.\n• new_text – Here we supply the new set of characters to replace with the instances of old_text in the original text.\n• [instance_num] – If there are multiple instances of old text in the original text string, then by default, the function substitutes all the instances of old text with new text. In the second situation, we can explicitly specify which instance of old text to replace using the instance_num argument.\n\n## Things to Remember about SUBSTITUTE Function\n\nThe following are some important points about SUBSTITUTE Function.\n\n• If the original text does not contain the text we want to replace, the whole text string is returned as result. For example, =SUBSTITUTE(“excel”,”unlocked”,”aa”) returns excel.\n• The SUBSTITUTE Function is case-sensitive. If you are looking to replace “ex” in “Excelunlocked”, then this is not going to happen with the SUBSTITUTE Formula.\n• To replace any specific instance of old_text in the original text, use the [instance_num] argument.\n• SUBSTITUTE Function does not support wild cards.\n\n## Examples to Learn SUBSTITUTE Function\n\nIn this part of the blog, we are going to use the SUBSTITUTE Function.\n\n### Example 1 – RemovingHyphen from Phone Numbers\n\nlet us suppose we have got the phone numbers in the format xxx-xxx-xxxx\n\nWe want to remove these hyphens among the digits of different phone numbers. Use the following SUBSTITUTE formula in cell B2.\n\n`=SUBSTITUTE(A2,\"-\",\"\")`\n\nSelect the range B2:B12 and press the Ctrl D key to copy the formula for all the phone numbers.\n\nAs a result, we have got the actual phone numbers in column B.\n\nExplanation – We have supplied the original text which is the phone number in cell A2 as the first text argument of the SUBSTITUTE Formula. Since we wanted to replace all the hyphens in the phone number, we have passed the old_text argument as a hyphen in double quotes “-“. We want to remove the hyphens or simply replace them with an empty text string denoted by “as the new_text argument.\n\nAs a result, all the instances of hyphens in the phone number are replaced with an empty string. This removes the hyphens.\n\n### Example 2 – Substituting a Specific Instance of text\n\nLet us suppose we have got the following product codes of a company’s product as follows.\n\nThe product code is in the format QP-10-YYYY where YYYY represents the year. The years have been written incorrectly and each beginning 1 in the code is to be substituted with 2. For example, the code QP-10-1017 when written correctly would be QP-10-2017.\n\nUse the following SUBSTITUTE Formula to perform this task.\n\n`=SUBSTITUTE(A2,\"1\",\"2\",2)`\n\nCopy the formula for all the codes and we get the result as follows.\n\nAs a result, we have got the correct codes.\n\nExplanation – There is already a 1 preceding the Year in the product code. We only want to replace the 1 after that, which is contained in the year.\n\nWe do not want to change the 1 in the red box. The only purpose is to replace the second instance of 1 in the blue box. Therefore, we specify the fourth optional argument that contains the instance number to consider. We supply it as 2. As a result, the second instance of 1 is replaced with 2.\n\nThis brings us to the end of the SUBSTITUTE Function blog." ]
[ null ]
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https://drserendipity.com/notes/notes_by_subjects/artificial_intelligence/computer-vision/5-extracurricular/6-extra-review-training-a-neural-network/6-2-training-neural-networks/14-momentum-2/
[ "# 14 – Momentum\n\nSo, here’s another way to solve a local minimum problem. The idea is to walk a bit fast with momentum and determination in a way that if you get stuck in a local minimum, you can, sort of, power through and get over the hump to look for a lower minimum. So let’s look at what normal gradient descent does. It gets us all the way here. No problem. Now, we want to go over the hump but by now the gradient is zero or too small, so it won’t give us a good step. What if we look at the previous ones? What about say the average of the last few steps. If we take the average, this will takes us in direction and push us a bit towards the hump. Now the average seems a bit drastic since the step we made 10 steps ago is much less relevant than the step we last made. So, we can say, for example, the average of the last three or four steps. Even better, we can weight each step so that the previous step matters a lot and the steps before that matter less and less. Here is where we introduce momentum. Momentum is a constant beta between 0 and 1 that attaches to the steps as follows: the previous step gets multiplied by 1, the one before, by beta, the one before, by beta squared, the one before, by beta cubed, etc. In this way, the steps that happened a long time ago will matter less than the ones that happened recently. We can see that that gets us over the hump. But now, once we get to the global minimum, it’ll still be pushing us away a bit but not as much. This may seem vague, but the algorithms that use momentum seem to work really well in practice." ]
[ null ]
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https://docs.formant.io/docs/ingestion-with-adapters
[ "An adapter is a program that can be run by the Formant agent on startup. The primary purpose of adapters is to communicate with the Formant plaform through the Agent SDK. This will allow you to ingest information if you are not running in a ROS environment, or information that is not available as a ROS topic.\n\n## How they are run\n\nAdding a new adapter allows you to automatically install and run that adapter on your device. For example, if we are provisioning many Nvidia Jetson based Jetbots, we can create an adapter for it and configure that adapter to be installed and run in our device configuration menu.\n\nAdapters should be executable packages in a zip folder. The typical structure is to provide a python package with a shell script, like `start.sh`, that the agent can run on startup.\n\nBelow, we'll look at the complete Jetbot Python adapter. See the source repository here for the full package.\n\nBelow, our adapter is publishing the following information:\n\n• Speed\n• Individual motor speeds\n• Location (Lat/Lng)\n• Battery charge percentage\n• Camera statistics (like capture rate, etc.)\n• Camera images\n• An event when it comes online\n\nIt also allows for Teleop control.\n\n``````import sys\nimport time\nimport collections\nfrom statistics import mean, stdev\n\nfrom formant.sdk.agent.v1 import Client as FormantClient\nimport cv2\n\nfrom jetbot import Robot, INA219\n\nMAX_CHARGING_VOLTAGE = 12.6\nMIN_CHARGING_VOLTAGE = 11.0\nMAX_DISCHARGING_VOLTAGE = 12.1\nMIN_DISCHARGING_VOLTAGE = 10.0\nDEFAULT_MAX_SPEED = 0.7\nDEFAULT_MIN_SPEED = 0.1\nDEFAULT_START_SPEED = 0.1\nDEFAULT_SPEED_INCREMENT = 0.025\nDEFAULT_ANGULAR_REDUCTION = 0.50\nDEFAULT_LATITUDE = 41.322937 # The pyramid of Enver Hoxha\nDEFAULT_LONGITUDE = 19.820896\nDEFAULT_GST_STRING = (\n\"nvarguscamerasrc ! \"\n\"video/x-raw(memory:NVMM), width=(int)640, height=(int)480, format=(string)NV12, framerate=(fraction)30/1 ! \"\n\"nvvidconv ! \"\n\"video/x-raw, width=(int)640, height=(int)480, format=(string)BGRx ! \"\n\"videoconvert ! \"\n\"appsink \"\n)\n\ndef __init__(self):\n\n# Set global params\nself.max_speed = DEFAULT_MAX_SPEED\nself.min_speed = DEFAULT_MIN_SPEED\nself.speed_increment = DEFAULT_SPEED_INCREMENT\nself.angular_reduction = DEFAULT_ANGULAR_REDUCTION\nself.latitude = DEFAULT_LATITUDE\nself.longitude = DEFAULT_LONGITUDE\nself.gst_string = DEFAULT_GST_STRING\nself.start_speed = DEFAULT_START_SPEED\nself.speed = self.start_speed\nself.is_shutdown = False\n\n# Store frame rate information to publish\nself.camera_width = 0\nself.camera_height = 0\nself.camera_frame_timestamps = collections.deque([], maxlen=100)\nself.camera_frame_sizes = collections.deque([], maxlen=100)\n\n# Create clients\nself.robot = Robot()\nself.fclient = FormantClient(ignore_throttled=True, ignore_unavailable=True)\n\nself.update_from_app_config()\nself.publish_online_event()\n\nself.fclient.register_command_request_callback(self.handle_command_request)\n\nself.fclient.register_teleop_callback(\nself.handle_teleop, [\"Joystick\", \"Buttons\"]\n)\n\n# Start the camera feed\nself.publish_camera_feed()\n\ndef __del__(self):\nself.is_shutdown = True\n\ndef publish_speed(self):\nwhile not self.is_shutdown:\n# self.fclient.post_numeric(\"speed\", self.speed)\nself.fclient.post_numericset(\n\"Speed\", {\"speed\": (self.speed + self.speed_deadzone, \"m/s\")},\n)\ntime.sleep(1.0)\n\ndef publish_motor_states(self):\nwhile not self.is_shutdown:\nself.fclient.post_numeric(\n\"Motor Speed\", self.robot.left_motor.value, {\"value\": \"left\"}\n)\nself.fclient.post_numeric(\n\"Motor Speed\", self.robot.right_motor.value, {\"value\": \"right\"}\n)\ntime.sleep(0.5)\n\ndef publish_location(self):\nwhile not self.is_shutdown:\nself.fclient.post_geolocation(\"Location\", self.latitude, self.longitude)\ntime.sleep(10.0)\n\ndef publish_battery_state(self):\nwhile not self.is_shutdown:\nbus_voltage = self.ina219.getBusVoltage_V()\nshunt_voltage = self.ina219.getShuntVoltage_mV() / 1000\ncurrent = self.ina219.getCurrent_mA() / 1000\n\ncharging = False\nif shunt_voltage > 0.01 and current > 0.01:\ncharging = True\n\n# approximate battery charge percentage calibration\nnow = bus_voltage - MIN_DISCHARGING_VOLTAGE\nfull = MAX_DISCHARGING_VOLTAGE - MIN_DISCHARGING_VOLTAGE\ncharge_percentage = now / full * 100\nif charging:\nnow = bus_voltage - MIN_CHARGING_VOLTAGE\nfull = MAX_CHARGING_VOLTAGE - MIN_CHARGING_VOLTAGE\ncharge_percentage = now / full * 100\n\nif charge_percentage >= 100:\ncharge_percentage = 100\n\nself.fclient.post_battery(\n\"Battery State\", charge_percentage, voltage=bus_voltage, current=current\n)\n\nself.fclient.post_bitset(\n\"Battery Charging\", {\"charging\": charging, \"discharging\": not charging}\n)\n\ntime.sleep(1.0)\n\ndef publish_camera_stats(self):\nwhile not self.is_shutdown:\ntry:\ntimestamps = list(self.camera_frame_timestamps)\nsizes = list(self.camera_frame_sizes)\nexcept:\nprint(\"ERROR: deque mutated while iterating\")\npass\n\nlength = len(timestamps)\nif length > 2:\nsize_mean = mean(sizes)\nsize_stdev = stdev(sizes)\njitter = self.calculate_jitter(timestamps)\noldest = timestamps\nif diff > 0:\nhz = length / diff\nself.fclient.post_numericset(\n\"Camera Statistics\",\n{\n\"Rate\": (hz, \"Hz\"),\n\"Mean Size\": (size_mean, \"bytes\"),\n\"Std Dev\": (size_stdev, \"bytes\"),\n\"Mean Jitter\": (jitter, \"ms\"),\n\"Width\": (self.camera_width, \"pixels\"),\n\"Height\": (self.camera_height, \"pixels\"),\n},\n)\ntime.sleep(5.0)\n\ndef publish_camera_feed(self):\ncap = cv2.VideoCapture(self.gst_string, cv2.CAP_GSTREAMER)\nif cap is None:\nprint(\"ERROR: Could not read from video capture source.\")\nsys.exit()\n\nwhile not self.is_shutdown:\n\ntry:\nencoded = cv2.imencode(\".jpg\", image).tostring()\nself.fclient.post_image(\"Camera\", encoded)\n\n# Track stats for publishing\nself.camera_frame_timestamps.append(time.time())\nself.camera_frame_sizes.append(len(encoded) * 3 / 4)\nself.camera_width = image.shape\nself.camera_height = image.shape\nexcept:\nprint(\"ERROR: encoding failed\")\n\ndef publish_online_event(self):\ntry:\ncommit_hash_file = (\n)\nwith open(commit_hash_file) as f:\nexcept Exception:\nprint(\n\"ERROR: formant-jetbot-adapter repo must be installed at \"\n)\n\nself.fclient.create_event(\nnotify=False,\ntags={\"hash\": commit_hash.strip()},\n)\n\ndef update_from_app_config(self):\nprint(\"INFO: Updating configuration ...\")\nself.max_speed = float(\nself.fclient.get_app_config(\"max_speed\", DEFAULT_MAX_SPEED)\n)\nself.min_speed = float(\nself.fclient.get_app_config(\"min_speed\", DEFAULT_MIN_SPEED)\n)\n)\nself.speed_increment = float(\nself.fclient.get_app_config(\"speed_increment\", DEFAULT_SPEED_INCREMENT)\n)\nself.angular_reduction = float(\nself.fclient.get_app_config(\"angular_reduction\", DEFAULT_ANGULAR_REDUCTION)\n)\nself.latitude = float(\nself.fclient.get_app_config(\"latitude\", DEFAULT_LATITUDE)\n)\nself.longitude = float(\nself.fclient.get_app_config(\"longitude\", DEFAULT_LONGITUDE)\n)\nself.gst_string = self.fclient.get_app_config(\"gst_string\", DEFAULT_GST_STRING)\nself.start_speed = float(\nself.fclient.get_app_config(\"start_speed\", DEFAULT_START_SPEED)\n)\n\ndef handle_command_request(self, request):\nif request.command == \"jetbot.nudge_forward\":\nself._handle_nudge_forward()\nself.fclient.send_command_response(request.id, success=True)\nelif request.command == \"jetbot.nudge_backward\":\nself._handle_nudge_backward()\nself.fclient.send_command_response(request.id, success=True)\nelif request.command == \"jetbot.update_config\":\nself.update_from_app_config()\nself.fclient.send_command_response(request.id, success=True)\nelse:\nself.fclient.send_command_response(request.id, success=False)\n\ndef handle_teleop(self, control_datapoint):\nif control_datapoint.stream == \"Joystick\":\nself.handle_joystick(control_datapoint)\nelif control_datapoint.stream == \"Buttons\":\nself.handle_buttons(control_datapoint)\n\ndef handle_joystick(self, joystick):\nleft_motor_value = 0.0\nright_motor_value = 0.0\n\n# Add contributions from the joysticks\n# TODO: turn this into a circle, not a square\nleft_motor_value += (\nself.speed * joystick.twist.angular.z * self.angular_reduction\n)\nright_motor_value += (\n-self.speed * joystick.twist.angular.z * self.angular_reduction\n)\n\nleft_motor_value += self.speed * joystick.twist.linear.x\nright_motor_value += self.speed * joystick.twist.linear.x\n\nif left_motor_value > 0:\nelif left_motor_value < 0:\n\nif right_motor_value > 0:\nelif right_motor_value < 0:\n\n# Set the motor values\nself.robot.left_motor.value = left_motor_value\nself.robot.right_motor.value = right_motor_value\n\ndef handle_buttons(self, _):\nif _.bitset.bits.key == \"nudge forward\":\nself._handle_nudge_forward()\nelif _.bitset.bits.key == \"nudge backward\":\nself._handle_nudge_backward()\nelif _.bitset.bits.key == \"speed +\":\nself._handle_increase_speed()\nelif _.bitset.bits.key == \"speed -\":\nself._handle_decrease_speed()\n\ndef _handle_nudge_forward(self):\nself.fclient.post_text(\"Commands\", \"nudge forward\")\ntime.sleep(0.5)\nself.robot.stop()\n\ndef _handle_nudge_backward(self):\nself.fclient.post_text(\"Commands\", \"nudge backward\")\ntime.sleep(0.5)\nself.robot.stop()\n\ndef _handle_increase_speed(self):\nself.fclient.post_text(\"Commands\", \"increase speed\")\nif self.speed + self.speed_increment <= self.max_speed:\nself.speed += self.speed_increment\nelse:\nself.speed = self.max_speed\n\ndef _handle_decrease_speed(self):\nself.fclient.post_text(\"Commands\", \"decrease speed\")\nif self.speed - self.speed_increment >= self.min_speed:\nself.speed -= self.speed_increment\nelse:\nself.speed = self.min_speed\n\ndef calculate_jitter(self, timestamps):\nlength = len(self.camera_frame_timestamps)\noldest = self.camera_frame_timestamps\nstep_value = (newest - oldest) / length\n\n# Make a list of the difference between the expected and actual step sizes\njitters = []\nfor n in range(length - 1):\nif n > 0:\njitter = abs((timestamps[n] - timestamps[n - 1]) - step_value)\njitters.append(jitter)\n\nreturn mean(jitters)\n\nif __name__ == \"__main__\":" ]
[ null ]
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