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https://www.definify.com/word/Tangent | math | Webster 1913 Edition
-entis, p. pr. of
tangereto touch; akin to Gr. [GREEK] having seized: cf. F.
A tangent line curve, or surface; specifically, that portion of the straight line tangent to a curve that is between the point of tangency and a given line, the given line being, for example, the axis of abscissas, or a radius of a circle produced. See
Trigonometrical function, under
Artificial tangent, or
the logarithm of the natural tangent of an arc.–
a decimal expressing the length of the tangent of an arc, the radius being reckoned unity.–
a form of galvanometer having a circular coil and a short needle, in which the tangent of the angle of deflection of the needle is proportional to the strength of the current.–
Tangent of an angle,
the natural tangent of the arc subtending or measuring the angle.–
Tangent of an arc,
a right line, as ta, touching the arc of a circle at one extremity a, and terminated by a line ct, passing from the center through the other extremity o.
-entis, p. pr.]
Touching; touching at a single point; specifically
meeting a curve or surface at a point and having at that point the same direction as the curve or surface; – said of a straight line, curve, or surface;
as, a line
tangentto a curve; a curve
tangentto a surface;
a plane which touches a surface in a point or line.–
a kind of breech sight for a cannon.–
an endless screw; a worm.
Webster 1828 Edition
In geometry, a right line which touches a curve, but which when produced, does not cut it. In trigonometry, the tangent of an arc, is a right line touching the arc at one extremity, and terminated by a second passing through the other extremity. | s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320305288.57/warc/CC-MAIN-20220127193303-20220127223303-00083.warc.gz | CC-MAIN-2022-05 | 1,661 | 24 |
http://ieeexplore.ieee.org/xpl/articleDetails.jsp?reload=true&arnumber=5703202&contentType=Journals+%26+Magazines | math | Skip to Main Content
In this paper, we address the problem of decentralized parameter estimation via Wireless Sensor Networks (WSNs). We consider two different encoding strategies, namely, Quantize-and-Estimate (Q&E) and Compress-and-Estimate (C&E) and assume that sensor observations are conveyed to the Fusion Center (FC) over a number of orthogonal Gaussian or Rayleigh-fading channels. We constrain both power and bandwidth to be constant irrespectively of the network size and find approximate closed-form expressions of the optimal number of sensors for a number of cases of interest. Besides, we derive the optimal encoding rate for the Q&E scheme when, in the absence of Transmit Channel State Information (CSIT), sensors must encode their observations at a common and constant rate. For the (successive) C&E strategy, we also determine the encoding order that minimizes the resulting distortion in the FC estimates. We complement the analysis by deriving an expression of the asymptotic distortion when the number of sensors grows without bound, and the rate at which distortion decreases in the high-SNR regime. Finally, we close the paper by presenting some computer simulation results. | s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1397609539066.13/warc/CC-MAIN-20140416005219-00569-ip-10-147-4-33.ec2.internal.warc.gz | CC-MAIN-2014-15 | 1,197 | 2 |
http://nccr-swissmap.ch/research/publications/bootstrapping-massive-quantum-field-theories | math | We propose a new non-perturbative method for studying UV complete unitary quantum field theories (QFTs) with a mass gap in general number of spacetime dimensions. The method relies on unitarity formulated as positive semi-definiteness of the matrix of inner products between asymptotic states (in and out) and states created by the action of local operators on the vacuum. The corresponding matrix elements involve scattering amplitudes, form factors and spectral densities of local operators. We test this method in two-dimensional QFTs by setting up a linear optimization problem that gives a lower bound on the central charge of the UV CFT associated to a QFT with a given mass spectrum of stable particles (and couplings between them). Some of our numerical bounds are saturated by known form factors in integrable theories like the sine-Gordon, E 8 and O(N) models. | s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250594333.5/warc/CC-MAIN-20200119064802-20200119092802-00349.warc.gz | CC-MAIN-2020-05 | 870 | 1 |
https://apps.dtic.mil/sti/citations/ADA218220 | math | Optimization of Series Expressions: Part 1: User's Manual for the Series Macro Package
MASSACHUSETTS INST OF TECH CAMBRIDGE ARTIFICIAL INTELLIGENCE LAB
Pagination or Media Count:
The benefits of programming in a functional style are well known. In particular, algorithms that are expressed as compositions of functions operating on seriesvectorsstreams of data elements are much easier to understand and modify than equivalent algorithms expressed as loops. Unfortunately, many programmers hesitate to use series expressions. In part, this is due to the fact that series expressions are typically implemented very inefficiently. A Common Lisp macro package called Series has been implemented that can evaluate a wide class of series expressions very efficiently by transforming them into iterative loops. When using this class of series expressions, programmers can obtain the advantages of expressing computations as series expressions without incurring any run-time overhead. Keywords Programming manuals.
- Computer Programming and Software | s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487658814.62/warc/CC-MAIN-20210620054240-20210620084240-00596.warc.gz | CC-MAIN-2021-25 | 1,043 | 5 |
https://www.khanacademy.org/math/cc-fourth-grade-math/comparing-fractions-and-equivalent-fractions/imp-common-denominators/v/common-denominators-35-and-72 | math | Current time:0:00Total duration:4:15
- Rewrite each fraction with a denominator of 10. So we have two fractions, three fifths and seven halves and we wanna take their denominators of five and two and change them to be a common denominator of 10. Lets start with three fifths and we can look at this visually. Here we can use this rectangle to represent a whole, one whole. To show three fifths of that whole, we're gonna need to divide it into fifths or five equal pieces. Lets do that. Try to make these as equal as possible. We have three pieces, and then finally, there we go. So, these should represent five equal pieces, or fifths. To show three fifths, we need to shade three of those five pieces. So, one, two, three of those five pieces should be shaded in to show three fifths. We've decided we don't want fifths anymore. Now, we want tenths. We want a new denominator of 10. To change this fraction over here, to change this to be tenths, we need to split each of these fifths in half. We need to double the amount of pieces. We can do that here. Now, instead of fifths, or five equal size pieces, we have tenths. We have one, two, three, four, five, six, seven, eight, nine, ten. We found a way to have tenths without changing the amount that's represented. The same amount is still shaded, but now we have tenths. Our denominator doubled. We multiplied it be two, we have twice as many pieces. But look at what happened to our numerator, instead of three pieces, now we have one, two, three, four, five, six pieces. It also doubled. It also was multiplied by two, because if we double all of the pieces, well then the shaded ones will also double. Each of those pieces also split in two, so now there's twice as many shaded pieces. So, three fifths can be rewritten as six tenths. Three fifths is equal to six tenths, and again, we didn't change the fraction. We didn't change how much was shaded. Three fifths and six tenths represented the same amount. We just changed the denominator and wrote it a different way. So, three fifths can be rewritten in tenths as six tenths. Now, for seven halves, we again want a denominator of 10. So, we can draw it out, or we could try to use this pattern we just noticed up here to figure out how to make halves turn into tenths. To get from fifths to tenths we had to double, or multiply by two. To get from halves to tenths, we'd have to multiply each of our pieces times five. Each of our halves would be split into five pieces. So, we multiply two times five to get tenths. Like the pattern showed us up here, if the denominator is multiplied by a number, we multiply the numerator by the same number. Those shaded pieces would also be split five times. We multiply our seven times five also. You should match the numerator and denominator are multiplied by the same number. Seven times five is 35. So 35 tenths is equal to seven halves. To change these two fractions to have a common denominator of 10, three fifths will become six tenths, and seven halves will become 35 tenths. | s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337625.5/warc/CC-MAIN-20221005105356-20221005135356-00770.warc.gz | CC-MAIN-2022-40 | 3,035 | 2 |
https://witknowlearn.com/worksheet/view/1682/cracking-the-cbse-class-11-permutations-and-combinations-exam-learn-with-100-questions-with-detailed-solutions | math | permutations and combinations class 11 worksheet with solutions
Are you preparing for the CBSE Class 11 Permutations and Combinations exam and feeling overwhelmed by the vast syllabus? Look no further! In this comprehensive guide, we will help you crack the exam with confidence by providing you with 100 practice questions with detailed solutions. Permutations and combinations can be quite challenging for many students, but with the right guidance and practice, you can ace this subject.
Our carefully curated set of questions covers a wide range of concepts, ensuring that you are well-prepared for any type of question that may appear in the exam. Each question is accompanied by a step-by-step solution, allowing you to understand the logic and reasoning behind the answer. This not only helps you in finding the correct answer but also helps in building a strong foundation in permutations and combinations. Whether you are a visual learner, a kinesthetic learner, or an auditory learner, our variety of question types and detailed solutions cater to all learning styles. So, gear up, put your problem-solving skills to the test, and conquer the CBSE Class 11 Permutations and Combinations exam with ease.
When it comes to Class 11 Maths, the topic of permutations and combinations holds significant importance, especially in Chapter 6. This chapter introduces students to the fascinating world of arranging and selecting objects in a systematic way. Whether you're a student, a teacher, or a parent guiding your child, understanding permutations and combinations is crucial. For those diving into this topic, the permutations and combinations formula serves as the backbone. This formula helps to solve various kinds of problems and questions that often appear in exams and real-life situations.
Students aiming for a strong grasp on Class 11 Chapter 6 Maths topics should not just limit themselves to the textbook. It's beneficial to explore additional resources like permutations and combinations Class 11 notes, permutations and combinations Class 11 worksheet with answer, and permutations and combinations Class 11 MCQ sets. These supplementary materials provide a well-rounded understanding of the topic and offer practical practice to solidify concepts. Our permutations and combinations Class 11 extra questions can also serve as a challenging exercise to test your knowledge and preparation level.
One highly effective way to enhance understanding is by practicing permutations and combinations questions. Many students prefer using the permutation and combination Class 11 questions with answers as these come with detailed solutions, facilitating easy learning. Worksheets offer a hands-on approach, allowing you to apply the permutations and combinations formula and check your answers instantaneously. When you consistently practice, you get a firm understanding of the core concepts, and that's where the permutations and combinations Class 11 notes become handy. These notes are simplified, well-structured, and offer invaluable insights into the topic, making them an ideal resource for students and even helpful for teachers and parents.
Moreover, MCQs are not just for practice but also an excellent way to test understanding. The permutations and combinations Class 11 MCQ questions are carefully curated to cover all important aspects of the topic. Coupled with a robust question bank, they form an integral part of your study resources. Students preparing for Chapter 6 Class 11 Maths or even planning ahead for Chapter 7 Maths Class 11 can use these resources for a seamless learning experience.
For a complete study solution, you might want to look at permutation and combination Class 11 solutions PDF. These downloadable PDFs serve as a portable study resource that you can access anytime, offering the flexibility to study at your own pace. As you transition from Chapter 6 Class 11 Maths to other topics like Chapter 7, having a strong grounding in permutations and combinations will certainly prove beneficial. So, whether you refer to it as 11th Class Maths Chapter 6, Ch 6 Class 11 Maths, or any other term, this topic is essential for building a strong mathematical foundation. Make the most out of the available resources and master permutations and combinations in Class 11 Maths.
permutations and combinations definition
In permutations, the arrangement of objects is important, meaning the order in which you select or arrange items makes a difference. For example, if you have three letters , , and , you can arrange them in different ways like , , , etc. Each different arrangement is considered a separate permutation.
Combinations, on the other hand, focus on the selection of items without considering the order. For instance, if you're selecting two letters from , , and , combinations like and are considered the same because the order does not matter.
permutations and combinations formula for class 11
Permutations deal with the arrangement of objects in a specific order. The formula for permutations is given as:
where is the total number of items to choose from, and is the number of items to choose.
Combinations, on the other hand, deal with the selection of objects without considering the order. The formula for combinations is:
where is the total number of items, and is the number of items to choose.
Here, (n factorial) is the product of all positive integers from 1 to . For example, .
These formulas are the cornerstone for solving various types of permutations and combinations questions in Class 11. Once you understand these formulas, you can use them to solve problems found in your textbook, as well as those in the permutations and combinations Class 11 worksheet with answers, to get practical experience. Understanding these formulas also prepares you for more advanced topics in mathematics and helps you in solving real-world problems that involve arrangement and selection.
For more practice and to deepen your understanding, you can look into permutations and combinations Class 11 notes, MCQs, and extra questions. These resources often provide examples that apply these formulas in different contexts, making it easier for students, as well as parents and teachers, to grasp the topic thoroughly.
Understanding the Fundamental Principles
In Class 11 Maths, particularly in Chapter 6, understanding the fundamental principles of permutations and combinations is crucial. These principles lay the groundwork for solving various types of questions and real-world problems. Grasping the basics also helps when you're dealing with permutations and combinations Class 11 worksheet with answers or attempting Class 11 MCQs.
Permutations: Arranging Objects in a Specific Order
Permutations involve arranging objects in a particular sequence or order. This is essential in various fields like computer science, statistics, and even in everyday scenarios like arranging books on a shelf. Understanding permutations prepares you for more complex topics and helps in solving permutation problems in Class 11 Maths.
Combinations: Selecting Objects Without Considering the Order
Combinations are all about selecting items where the arrangement or order doesn't matter. This concept is widely used in statistics, probability, and daily life situations like forming a team from a group of people. When studying combinations, it's helpful to consult resources like permutations and combinations Class 11 notes and permutations and combinations Class 11 extra questions.
Solving Permutation Problems
Solving problems based on permutations usually involves the use of the permutation formula. Practice is key to mastering this, and the permutations and combinations Class 11 worksheet with answer serves as a useful resource. The more you practice, the better you get at identifying which problems require the use of permutations.
Solving Combination Problems
Similar to permutations, solving combination problems effectively requires understanding the combination formula. Resources like permutations and combinations Class 11 extra questions and Class 11 Maths Chapter 6 solutions can provide additional practice and insights into solving these types of problems.
Solving Problems Involving Both Permutations and Combinations
Some questions might require the use of both permutations and combinations. Understanding the fundamental principles and the differences between the two is crucial for solving such problems. Class 11 permutation and combination questions with answers often cover these complex scenarios.
Practice Questions for Permutations and Combinations
To master permutations and combinations in Class 11, practice is essential. Utilize the permutations and combinations Class 11 question bank to explore various types of questions and understand the application of formulas.
Detailed Solutions for Practice Questions
For effective learning, merely solving questions is not enough. One must also understand the solutions, which is where detailed solutions come in. These can be found in resources like permutation and combination Class 11 solutions PDF.
Conclusion: Tips to Excel in the CBSE Class 11 Permutations and Combinations Exam
To excel in this topic, make the best use of available resources like Class 11 Maths Chapter 6 solutions, practice consistently, and focus on understanding the core principles. Doing so will not only help you score well in exams but will also lay a strong foundation for future mathematical endeavours. | s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947475757.50/warc/CC-MAIN-20240302052634-20240302082634-00016.warc.gz | CC-MAIN-2024-10 | 9,513 | 37 |
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If you want to pass a basic set of classes, then you don't need this; just stick to the textbooks and you'll do fine. However, if you really want to understand what's going on in that math, and why it's going on, this is a great place to start. There's no place like to source for good information.
As for this particular translation, this edition has a surprising amount of explanatory notes and introductory material relating the circumstances under which this writing was made, and the interaction between the author and the other well known thinkers of the time. The first ~150 pages were explanations by Heath, including terminology of Archimedes, which was useful at times.
All in all, the works of Archimedes are definitely worth reading for anyone interested in learning the process of mathematical discovery.
Archimedes's determination of the volume (and secondarily the surface area) of a sphere may be considered the undisputed crown jewel of his works. Indeed, Archimedes himself seems to have thought so judging by the story that he requested it inscribed on his tombstone (xviii). Like an axiom needs no demonstration, this beautiful result needs no motivation.
But no sooner has Archimedes proved this result than he turns, in the same treatise, to matters of much less evident value. Thus he solves numerous baroque problems about areas and volumes of various sections of spheres such as "Given two segments of spheres, to find a third segment of a sphere similar to one of the given segments and having its surface equal to that of the other" (82) and other things along similar lines. What is the purpose of this? What use could one ever make of such a problem?
One might say: Archimedes is here working out the complete theory of spherical areas and volumes for future reference. The main result is beautiful in its own right, but these technical further propositions form a "toolbox" of results that subsequent mathematicians will find useful in technical contexts. If this is so (which I doubt) then it may be observed that previous mathematicians were apparently not inclined to do something similar when they worked out the theory of the cone. For Archimedes cites previous propositions on volumes of cones without proof (22), yet he has to work out the rather basic result of the surface area of frustum from scratch (21).
Another possible motivation for these technical propositions emerges from Archimedes's preface to another work, where he says of a list of problems along these lines that: "there are two included among them which are impossible of realisation [and which may serve as a warning] how those who claim to discover everything but produce no proofs of the same may be confuted as having actually pretended to discover the impossible" (151). Thus a sprinkling of technical propositions such as those mentioned above can serve a useful purpose even if they are of no actual use to any mathematician; the use being to expose poseur mathematicians by a kind of acid test. Indeed this seems to fit with Archimedes's preface to the original treatise where he appears to think that there is hardly anyone capable of judging his work: "these discoveries of mine ... ought to have been published while Conon was still alive, for I should conceive that he would best have been able to grasp them and to pronounce upon them the appropriate verdict" (2). (Incidentally, perhaps this lack of competent peers is also part of the reason why Archimedes chose to withdraw to a recluse life in Syracuse rather than remaining in Alexandria where he studied (xvi).)
In the Measurement of a Circle, Archimedes offers the two-dimensional analog of the above result: "The area of any circle is equal to a right-angled triangle in which one of the sides about the right angle is equal to the radius, and the other to the circumference of the circle" (91).
Why did Euclid not prove this rather basic theorem about the areas of circles? The answer is obvious: because the triangle in question cannot be constructed by ruler and compass. Thus the problem cannot be considered truly solved. Indeed, Archimedes himself seems to agree with this when he writes: "Some of the earlier geometers tried to prove it possible to find a rectilineal area equal to a given circle ..., assuming lemmas not easily conceded, so that it was recognised by most people that the problem was not solved" (233). It seems clear from this quotation that the mere result that the area of a circle is equal to such-and-such a triangle was well known, since people proved it by *some* means. The problem, rather, was with the method used in those proofs. In other words, the problem was, as Archimedes says, to *find* the rectilineal area in question, meaning to construct it, not to prove that it was in fact equal to the circle.
It seems clear that this is the reason Archimedes studies his spiral, for if it is admitted that the spiral and its tangents can be drawn then a construction of the triangle in question follows immediately (171), though probably Archimedes would have been the first to admit that these spiral constructions are just one more of those "lemmas not easily conceded" that he spoke of above. One indication that the spiral is meant to fit into the tradition of ruler-and-compass constructions is that Archimedes defines it in terms of motions and derives the locus-definition (essentially r=theta) as a theorem (155) even though it is the latter rather than the former that is needed in the subsequent proofs.
It is often assumed that the ruler-and-compass paradigm was favoured over a numerical conception of mathematics because things like the irrationality of square roots pose problems for the latter but not the former. Perhaps it is understandable then that when the ruler-and-compass paradigm proved poorly suited for dealing with the quadrature of the circle, the numerical conception of geometry was revived. This could perhaps explain why Archimedes takes pains to establish bounds for pi (93), and perhaps by extension and analogy his interest in determining how many grains of sand fit in the universe (221-232), and maybe by one more tenuous step of association his interest in numerical problems generally, as in the cattle-problem (318-326) and apparently another lost work (xxxvi).
Archimedes worked out axiomatic theories of statics and hydrostatics, showing that the geometrical method is remarkably and perhaps surprisingly well-suited to deal with these physical matters. In this it seems he had "no fore-runners" (xl). Some might look for his motivations in his work on warfare machines (xvi-xvii), but I would suggest that it actually followed quite naturally from his interest in volumes. As Archimedes says (2), his work on the volume of the sphere builds on Eudoxus's result that the volume of a cone is one third of the corresponding cylinder. Seeing as plane geometry is always "operationalised" in terms of ruler-and-compass constructions, one might look for a way to "operationalise" this result. Thus the use of a lever or balance suggests itself: a cylinder in one bowl balances with three cones in the other, or one cone at three times the distance. Alternatively, three cones or one cylinder dropped into a container of water make the surface rise by equal amounts. To put it another way, Greek results about volumes and areas are always comparative rather than absolute: they don't say it's equal to such-and-such a number or formula, but to such-and-such other figure. This comparative aspect goes hand in hand with the idea of a physical balance in equilibrium, again suggesting that Archimedes's work grew out of geometry.
Archimedes's work on statics is also the basis for his "Method" of finding areas and volumes by (hypothetically) balancing them on levers. As he says: "Certain things first became clear to me by a mechanical method, although they had to be demonstrated by geometry afterwards because their investigation by the said method did not furnish an actual demonstration. But it is of course easier, when we have previously acquired, by the method, some knowledge of the questions, to supply the proof than it is to find it without any previous knowledge." (Method appendix, 13)
Notably the volume of a sphere and the area of a parabolic segment are found in this way. Both are proved rigorously using the method of exhaustion in other works. In those works, the volume of the sphere is investigated by approximating a circle with a regular polygon and rotating it, so that the volume of the sphere is approximated by conical frustums; and the parabolic area is approximated by triangles stacked upon triangle fitted closer and closer to the perimeter. Both of these methods of approximation are natural and straightforward. It seems, therefore, that the only reason they were not feasible before the Method was that it was too difficult to brute-force sum these pieces (which basically amounts to simplifying intricate algebraic expressions) without knowing in advance what answer should be.
In reality, however, the "mechanical" aspect of the method has rather little to do with it. More importantly the Method consists in investigating the shapes slice by slice. True, each slice is then balanced with some suitable slice of a comparison figure with some suitable choice of lever arm, but this is little more than a convenient and flexible way of expressing an algebraic equality. The greater contrast with the rigorous proofs is the slicing of shapes in to "lines," which basically means investigating the figures by their algebraic equations, since the line in question has height y=f(x).
More generally, Archimedes seems to have taken a constant interest in conic sections simply for the fact that they are the most tractable "next" figures beyond circles. He constantly generalises all of his results about circles and spheres to conics, for example investigating their areas (in the parabolic case), rotational volumes, centers of gravity, and even the behaviour of a paraboloid submerged in water. None of these results seem particularly useful or natural except as a way of generating more mathematics from existing ideas. When they were first introduced conic sections surely had to be motivated and serve a purpose for solving established problems, but clearly at the time of Archimedes they were accepted as part of the standard repertoire of curves and it was seen as natural to "cut one's teeth" on the conics by generalising to them anything one did for circles. | s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267864740.48/warc/CC-MAIN-20180622162604-20180622182604-00141.warc.gz | CC-MAIN-2018-26 | 11,247 | 30 |
https://studylib.net/doc/18566769/unit-4--electromagnetic-induction-and-alternating-current | math | REVISION ASSIGNMENT PHYSICS (CLASS XII) UNIT 4 4-- ELECTROMAGNETIC INDUCTION AND ALTERNATING CURRENT 1. Predict the polarity of the capacitor C connected to coil, which is situated between two bar magnets moving as shown in figure. 2. If the number of turns in the solenoid is doubled, keeping other factors constant, how does the self-inductance of the coil change? 3. A plot of magnetic flux (Ф) versus current (I) for two inductors A and B is as shown in the figure below. Which of the two has large value of self-inductance? 4. A bar magnet falls through a ring of wire having a cut, so as not to form a closed loop. Will the acceleration of magnet be equal to the acceleration due to gravity? State the reason. 5. Graduations on scale in ac ammeter and voltmeter are not equally distant, why? 6. A bar magnet m is dropped so that it falls vertically through the coil C. The graph obtained for voltage produced across the coil versus time is showing in figure (b). 7. A radio can tune over the frequency range of a portion of medium wave (MW) broadcast band (800 kHz to 1200 kHz). If its LC circuit has an effective inductance of 200µH, what must be the range of variable capacitor? 8. A small piece of metal wire is dragged across the gap between the pole piece of a magnet in 0.5 s. The magnetic flux between the pole pieces is known to be 8 x 10-4 Wb. Estimate the induced emf in the wire. 9. A resistor of 200Ω and a capacitor of 15.0 µ F are connected in series to a 220 V, 50Hz ac source. Calculate the current in the circuit and the rms voltage across the resistor and the capacitor. Is the algebraic sum of these voltages more than the source voltage? If yes, resolve the paradox. 10. Current in a circuit falls steadily from 5.0 A to 0.0 A in 100ms. If an average emf of 200 V is induced, calculate the self inductance of the circuit. | s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233506481.17/warc/CC-MAIN-20230923130827-20230923160827-00121.warc.gz | CC-MAIN-2023-40 | 1,851 | 1 |
https://docslib.org/doc/9016929/radiometry-and-photometry-faq | math | James M. Palmer Research Professor Optical Sciences Center University of Arizona Tucson, AZ; 85721
Latest update 10/26/03
“When I use a word, it means just what I choose it to mean - neither more nor less.”
Lewis Carroll (Charles Lutwidge Dodgson)
Effective technical communication demands a system of symbols, units and nomenclature (SUN) that is reasonably consistent and that has widespread acceptance. Such a system is the International System of Units (SI). There is no area where words are more important than radiometry and photometry. This document is an attempt to provide necessary and correct information to become conversant.
1. What is the motivation for this FAQ? 2. What is radiometry? What is photometry? How do they differ? 3. What is projected area? What is solid angle? 4. What are the quantities and units used in radiometry? 5. How do I account for spectral quantities? 6. What are the quantities and units used in photometry? 7. What is the difference between lambertian and isotropic? 8. When do the properties of the eye get involved? 9. How do I convert between radiometric and photometric units? 10. Where can I learn more about this stuff?
RADIOMETRY &. PHOTOMETRY FAQ 1 1. What is the motivation for this FAQ?
There is so much misinformation and conceptual confusion regarding photometry and radiometry, particularly on the WWW by a host of “authorities”, it is high time someone got it straight. So here it is, with links to the responsible agencies.
Background: It all started over a century ago. An organization called the General Conference on Weights and Measures (CGPM) was formed by a diplomatic treaty called the Metre Convention. This treaty was signed in 1875 in Paris by representatives from 17 nations (including the USA). There are now 48 member nations. Also formed were the International Committee for Weights and Measures (CIPM) and the International Bureau of Weights and Measures (BIPM). The CIPM, along with a number of sub-committees, suggests modifications to the CGPM. In our arena, the subcommittee is the CCPR, Consultative Committee on Photometry and Radiometry. The BIPM is the physical facility responsible for dissemination of standards, the international metrology institute.
The SI was adopted by the CGPM in 1960. It currently consists of seven base units and a larger number of derived units. The base units are a choice of seven well- defined units that by convention are regarded as independent. The seven are: metre, kilogram, second, ampere, kelvin, mole and candela. The derived units are those formed by various combinations of the base units.
International organizations involved in the promulgation of SUN include the International Commission on Illumination (CIE), the International Union of Pure and Applied Physics (IUPAP), and the International Standards Organization (ISO). In the USA, the American National Standards Institute (ANSI) is the primary documentary (protocol) standards organization. Many other scientific and technical organizations publish recommendations concerning the use of SUN for their learned publications. Examples are the International Astronomical Union (IAU) and the American Institute of Physics (AIP).
Read all about the SI, its history and application, at physics.nist.gov/cuu/ or at www.bipm.fr.
2. What is radiometry? What is photometry? How do they differ?
Radiometry is the measurement of optical radiation, which is electromagnetic radiation within the frequency range between 3×1011 and 3×1016 Hz. This range corresponds to wavelengths between 0.01 and 1000 micrometres (µm), and includes the regions commonly called the ultraviolet, the visible and the infrared. Two out of many typical units encountered are watts/m2 and photons/s-steradian.
Photometry is the measurement of light, which is defined as electromagnetic radiation that is detectable by the human eye. It is thus restricted to the wavelength range from about 360 to 830 nanometers (nm; 1000 nm = 1 µm).
RADIOMETRY &. PHOTOMETRY FAQ 2 Photometry is just like radiometry except that everything is weighted by the spectral response of the eye. Visual photometry uses the eye as a comparison detector, while physical photometry uses either optical radiation detectors constructed to mimic the spectral response of the eye, or spectroradiometry coupled with appropriate calculations to do the eye response weighting. Typical photometric units include lumens, lux, candelas, and a host of other bizarre ones.
The only real difference between radiometry and photometry is that radiometry includes the entire optical radiation spectrum, while photometry is limited to the visible spectrum as defined by the response of the eye. In my forty years of experience, photometry is more difficult to understand, primarily because of the arcane terminology, but is fairly easy to do, because of the limited wavelength range. Radiometry, on the other hand, is conceptually somewhat simpler, but is far more difficult to actually do.
3. What is projected area? What is solid angle?
Projected area is defined as the rectilinear projection of a surface of any shape onto a plane normal to the unit vector. The differential form is dAproj = cos(β) dA where β is the angle between the local surface normal and the line of sight. We can integrate over the (perceptible) surface area to get
AA= cosβ d proj z A
Some common examples are shown in the table below:
SHAPE AREA PROJECTED AREA
Flat rectangle A = L×W Aproj= L×W cos β 2 2 2 2 Circular disc A = π r = π d / 4 Aproj = π r cos β = π d cos β / 4 2 2 2 Sphere A = 4 π r = π d Aproj = A/4 = π r
Plane angle and solid angle are two derived units on the SI system. The following definitions are from NIST l SP811. r
“The radian is the plane angle between θ two radii of a circle that cuts off on the l circumference an arc equal in length to θ = r the radius.”
RADIOMETRY &. PHOTOMETRY FAQ 3 The abbreviation for the radian is rad. Since there are 2π radians in a circle, the conversion between degrees and radians is 1 rad = (180/π) degrees.
A solid angle extends the concept to three dimensions.
“One steradian (sr) is the solid angle that, having its vertex in the center of a A sphere, cuts off an area on the surface of the sphere r equal to that of a square with sides of length equal A to the radius of the sphere.” ω = r2
The solid angle is thus ratio of the spherical area to the square of the radius. The spherical area is a projection of the object of interest onto a unit sphere, and the solid angle is the surface area of that projection. If we divide the surface area of a sphere by the square of its radius, we find that there are 4π steradians of solid angle in a sphere. One hemisphere has 2π steradians. Accepted symbols for solid angle are ω, the lowercase Greek letter omega, and Ω, the uppercase omega. I use ω exclusively for solid angle, reserving Ω for the advanced concept of projected solid angle (ω cosθ).
Both plane angles and solid angles are dimensionless quantities, and they can lead to confusion when attempting dimensional analysis.
4. What are the quantities and units used in radiometry?
Radiometric units can be divided into two conceptual areas: those having to do with power or energy, and those that are geometric in nature. The first two are:
Energy is an SI derived unit, measured in joules (J). The recommended symbol for energy is Q. An acceptable alternate is W.
Power (a.k.a. radiant flux) is another SI derived unit. It is the rate of flow (derivative) of energy with respect to time, dQ/dt, and the unit is the watt (W). The recommended symbol for power is Φ (the uppercase Greek letter phi). An acceptable alternate is P.
Energy is the integral over time of power, and is used for integrating detectors and pulsed sources. Power is used for non-integrating detectors and continuous (in a time sense) sources. Even though we patronize the power utility, what we are actually buying is energy in watt hours.
RADIOMETRY &. PHOTOMETRY FAQ 4 Now we become more specific and incorporate power with the geometric quantities area and solid angle.
Irradiance (a.k.a. flux density) is another SI derived unit and is measured in W/m2. Irradiance is power per unit area incident from all directions in a hemisphere onto a surface that coincides with the base of that hemisphere. A similar quantity is radiant exitance, which is power per unit area leaving a surface into a hemisphere whose base is that surface. The symbol for irradiance is E and the symbol for radiant exitance is M. Irradiance (or radiant exitance) is the derivative of power with respect to area, dΦ/dA. The integral of irradiance or radiant exitance over area is power.
Radiant intensity is another SI derived unit and is measured in W/sr. Intensity is power per unit solid angle. The symbol is I. Intensity is the derivative of power with respect to solid angle, dΦ/dω. The integral of radiant intensity over solid angle is power.
Radiance is the last SI derived unit we need and is measured in W/m2-sr. Radiance is power per unit projected area per unit solid angle. The symbol is L. Radiance is the derivative of power with respect to solid angle and projected area, dΦ/dω dA cos(θ) where θ is the angle between the surface normal and the specified direction. The integral of radiance over area and solid angle is power.
A great deal of confusion concerns the use and misuse of the term intensity. Some folks use it for W/sr, some use it for W/m2 and others use it for W/m2-sr. It is quite clearly defined in the SI system, in the definition of the base unit of luminous intensity, the candela. Some attempt to justify alternate uses by adding adjectives like optical (used for W/m2) or specific (used for W/m2-sr), but this practice only adds to the confusion. The underlying concept is (quantity per unit solid angle). For an extended discussion, see my paper entitled “Getting Intense on Intensity” for Metrologia (official journal of the BIPM) and a letter to OSA's “Optics and Photonics News”, with a modified version available on the web at www.optics.Arizona.EDU/Palmer/intenopn.html.
Photon quantities are also common. They are related to the radiometric quantities by the relationship Qp = hc/λ where Qp is the energy of a photon at wavelength λ, h is Planck's constant and c is the velocity of light. At a wavelength of 1 µm, there are approximately 5×1018 photons per second in a watt. Conversely, a single photon has an energy of 2×10–19 joules (W s) at 1 µm. Common units include s–1-m–2-sr–1 for photon radiance.
5. How should I represent spectral quantities?
Most sources of optical radiation are spectrally dependent, and the terms radiance, intensity, etc. give no information about the distribution of these quantities over wavelength. Spectral quantities, like spectral radiance, spectral power, etc. are
RADIOMETRY &. PHOTOMETRY FAQ 5 defined as the quotient of the quantity in an infinitesimal range of wavelength divided by that wavelength range. In other words, spectral quantities are derivative quantities, per unit wavelength, and have an additional (λ–1) in their units. When integrated over wavelength they yield the total quantity. These spectral quantities are denoted by using a subscript λ, e.g., Lλ, Eλ, Φλ,, and Iλ.
Some other quantities (examples include spectral transmittance, spectral reflectance, spectral responsivity, etc.) vary with wavelength but are not used as derivative quantities. These quantities should not be integrated over wavelength; they are only weighting functions, to be included with the above derivative quantities. To distinguish them from the derivative quantities, they are denoted by a parenthetical wavelength, i.e. ℜ(λ) or τ(λ).
6. What are the quantities and units used in photometry?
They are basically the same as the radiometric units except that they are weighted for the spectral response of the human eye and have funny names. A few additional units have been introduced to deal with the amount of light reflected from diffuse (matte) surfaces. The symbols used are identical to those radiometric units, except that a subscript “v “ is added to denote “visual. “The following chart compares them.
QUANTITY RADIOMETRIC PHOTOMETRIC power watt (W) lumen (lm) power per unit area W/m2 lm/m2 = lux (lx) power per unit solid angle W/sr lm/sr = candela (cd) power per unit area per unit solid angle W/m2-sr lm/m2-sr = cd/m2 = nit
Now we can get more specific about the details.
Candela (unit of luminous intensity). The candela is one of the seven base units of the SI system. It is defined as follows:
The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540×1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.
The candela is abbreviated as cd and its symbol is Iv. The above definition was adopted by the 16th CGPM in 1979.
The candela was formerly defined as the luminous intensity, in the perpendicular direction, of a surface of 1/600 000 square metre of a black body at the temperature of freezing platinum under a pressure of 101 325 newtons per square metre. This earlier definition was initially adopted in 1946 and later modified by the 13th CGPM (1967). It was abrogated in 1979 and replaced by the current definition.
RADIOMETRY &. PHOTOMETRY FAQ 6 The current definition was adopted because of several reasons. First, the freezing point of platinum (≈2042K) was tied to another base unit, the kelvin. If the best estimate of this point were changed, it would then impact the candela. The uncertainty of the thermodynamic temperature of this fixed point created an unacceptable uncertainty in the value of the candela. Second, the realization of the Pt blackbody was extraordinarily difficult; only a few were ever built. Third, if the temperature were slightly off, possibly because of temperature gradients or contamination, the freezing point might change or the temperature of the cavity might differ. The sensitivity of the candela to a slight change in temperature is significant. At a wavelength 555 nm, a change in temperature of only 1K results in a luminance change approaching 1%. Fourth, the relative spectral radiance of blackbody radiation changes drastically (some three orders of magnitude) over the visible range. Finally, recent advances in radiometry offered new possibilities for the realization of the candela.
The value 683 lm/W was selected based upon the best measurements with existing platinum freezing point blackbodies and the best estimates for the thermodynamic temperature of the platinum point. . It has varied over time from 620 to nearly 700 lm/W, depending largely upon the assigned value of the Pt freezing point on the best available temperature scale. The value of 1/600 000 square metre was chosen to maintain consistency with prior flame standards.
Also note that in the definition there is no specification for the spatial distribution of intensity. Luminous intensity, while often associated with an isotropic (see section 7 below) point source, is a valid specification for characterizing highly directional light sources such as automotive lighting, searchlights and LEDs.
One other issue before we press on. Since the candela is now defined in terms of other SI derived quantities, there is really no need to retain it as an SI base quantity. It remains so for reasons of history and continuity.
Lumen (unit of luminous flux). The lumen is an SI derived unit for luminous flux. The abbreviation is lm and the symbol is Φv. The lumen is derived from the candela and is the luminous flux emitted into unit solid angle (1 sr) by an isotropic (see section 7 below) point source having a luminous intensity of 1 candela. The lumen is the product of luminous intensity and solid angle, cd-sr. It is analogous to the unit of radiant flux (watt), differing only in the eye response weighting. If a light source is isotropic, the relationship between lumens and candelas is 1 cd = 4π lm. In other words, an isotropic source having a luminous intensity of 1 candela emits 4π lumens into space, which just happens to be 4π steradians. We can also state that 1 cd = 1 lm/sr, analogous to the equivalent radiometric definition.
If a source is not isotropic, the relationship between candelas and lumens is empirical. A fundamental method used to determine the total flux (lumens) is to measure the luminous intensity (candelas) in many directions using a goniophotometer, and then numerically integrate over the entire sphere. Later on,
RADIOMETRY &. PHOTOMETRY FAQ 7 we can use this “calibrated” lamp as a reference in an integrating sphere for routine measurements of luminous flux.
Lumens are what we get from the hardware store when we purchase a light bulb. We want a high number of lumens with a minimum of power consumption and a reasonable lifetime. Projection devices are also characterized by lumens to indicate how much luminous flux they can deliver to a screen. The ANSI standard delineates the method for determining average luminous flux; it is not a different lumen.
Recently, marketeers for digital projectors have introduced a new unit, the “market comparable lumen,’ which is somewhere between 1.1 and 1.25 ANSI lumens. This appears to be a ploy to jack up the numbers to compete with those who are not inclined to use ANSI lumens.
Lux (unit of luminous flux density, or illuminance). Illuminance is another SI derived unit which denotes luminous flux density . The unit has a special name, 2 the lux, which is lumens per square metre, or lm/m . The symbol is Ev. Most light meters measure this quantity, as it is of great importance in illuminating engineering. The IESNA Lighting Handbook has some sixteen pages of recommended illuminances for various activities and locales, ranging from morgues
to museums. Typical values range from 100 000 lx for direct sunlight to 20-50 lx for hospital corridors at night.
Nit (unit of luminance). Luminance should probably be included on the official list of derived SI units, but is not. It is analogous to radiance, differentiating the lumen with respect to both area and direction. This unit also has a special name, the nit, 2 2 which is cd/m or lm/m sr if you prefer. The symbol is Lv. It is most often used to characterize the “brightness “ of flat emitting or reflecting surfaces. A typical use would be the luminance of your laptop computer screen. They have between 100 and 250 nits, and the sunlight readable ones have more than 1000 nits. Typical CRT monitors have between 50 and 125 nits.
Other photometric units
We have other photometric units (boy, do we have some strange ones). Photometric quantities should be reported in SI units as given above. However, the literature is filled with now obsolete terminology and we must be able to interpret it. So here are a few terms that have been used in the past.
RADIOMETRY &. PHOTOMETRY FAQ 8 Illuminance:
1 metre-candle = 1 lux 1 phot = 1 lm/cm2 = 104 lux 1 foot-candle = 1 lumen/ft2 = 10.76 lux 1 milliphot = 10 lux
Luminance: Here we have two classes of units. The first is conventional, easily related to the SI unit, the cd/m2 (nit).
1 stilb = 1 cd/cm2 = 104 cd/m2 = 104 nit 1 cd/ft2 = 10.76 cd/m2 = 10.76 nit
The second class was designed to “simplify” characterization of light reflected from diffuse surfaces by including in the definitions the concept of a perfect (reflectance ρ = 1), diffuse reflector (lambertian, see section 7 below.) If one unit of illuminance falls upon this hypothetical reflector, then 1 unit of luminance is reflected. The perfect diffuse reflector emits 1/π units of luminance per unit illuminance. If the reflectance is ρ, then the luminance is ρ times the illuminance. Consequently, these units all have a factor of (1/π) built in.
Photometric quantities are already the result of integration over wavelength. It therefore makes no sense to speak of spectral luminance or the like.
7. What is the difference between lambertian and isotropic?
Both terms mean “the same in all directions” and are unfortunately sometimes used interchangeably.
Isotropic implies a spherical source that radiates the same in all directions, i.e., the intensity (W/sr) is the same in all directions. We often encounter the phrase “isotropic point source.” There can be no such thing; because the energy density would have to be infinite. But a small, uniform sphere comes very close. The best example is a globular tungsten lamp with a milky white diffuse envelope, as used in dressing room lighting. From our vantage point, a distant star can be considered an isotropic point source.
Lambertian refers to a flat radiating surface. It can be an active surface or a passive, reflective surface. Here the intensity falls off as the cosine of the observation angle with respect to the surface normal (Lambert's law). The radiance (W/m2-sr) is independent of direction. A good example is a surface painted with a
RADIOMETRY &. PHOTOMETRY FAQ 9 good “matte” or “flat” white paint. If it is uniformly illuminated, like from the sun, it appears equally bright from whatever direction you view it. Note that the flat radiating surface can be an elemental area of a curved surface.
The ratio of the radiant exitance (W/m2) to the radiance (W/m2-sr) of a lambertian surface is a factor of π and not 2π. We integrate radiance over a hemisphere, and find that the presence of the factor of cos(θ) in the definition of radiance gives us this interesting result. It is not intuitive, as we know that there are 2π steradians in a hemisphere.
A lambertian sphere illuminated by a distant point source will display the maximum radiance at the surface where the local normal coincides with the incoming beam. The radiance will fall off with a cosine dependence to zero at the edge of the lit area (terminator.) If the intensity (integrated radiance over area) is unity when viewing from the source, then the intensity when viewing from the side is 1/π. Think about this and consider whether or not our Moon is lambertian. Take a look at www.optics.Arizona.EDU/Palmer/moon/lunacy.htm.
8. Where do the properties of the eye get involved?
We know that the eye does not see all wavelengths equally. The eye has two general classes of photosensors, cones and rods.
Cones: The cones are responsible for light-adapted vision; they respond to color and have high resolution in the central foveal region. The light-adapted relative spectral response of the eye is called the spectral luminous efficiency function for photopic vision, V(λ). This empirical curve, first adopted by the International Commission on Illumination (CIE) in 1924, has a peak of unity at 555 nm, and decreases to levels below 10–5 at about 370 and 785 nm. The 50% points are near 510 nm and 610 nm, indicating that the curve is slightly skewed. The V(λ) curve looks very much like a Gaussian function; in fact a Gaussian curve can easily be fit and is a good representation under some circumstances. I used a non-linear regression technique to obtain the following equation: −−2854.(λ 0559 . )2 Vebλg ≅ 1019.
More recent measurements have shown that the 1924 curve may not best represent typical human vision. It appears to underestimate the response at wavelengths shorter than 460 nm. Judd (1951), Vos (1978) and Stockman and Sharpe (1999) have made incremental advances in our knowledge of the photopic response. Go to www.cvrl.org for details.
Rods: The rods are responsible for dark-adapted vision, with no color information and poor resolution when compared to the foveal cones. The dark-adapted relative spectral response of the eye is called the spectral luminous efficiency function for scotopic vision, V’(λ). This is another empirical curve, adopted by the CIE in 1951.
RADIOMETRY &. PHOTOMETRY FAQ 10 It is defined between 380 nm and 780 nm. The V’(λ) curve has a peak of unity at 507 nm, and decreases to levels below 10–3 at about 380 and 645 nm. The 50% points are near 455 nm and 550 nm. This scotopic curve can also be fit with a Gaussian, although the fit is not quite as good as the photopic curve. My best fit is −−321.( 9λ 0 . 503 )2 Ve'.bλg ≅ 0992
Photopic (light adapted cone) vision is active for luminances greater than 3 cd/m2. Scotopic (dark-adapted rod) vision is active for luminances lower than 0.01 cd/m2. In between, both rods and cones contribute in varying amounts, and in this range the vision is called mesopic. There are currently efforts under way to characterize the composite spectral response in the mesopic range for vision research at intermediate luminance levels.
The Color Vision Research Lab (www.cvrl.org) has an impressive collection of the data files, including V(λ) and V’(λ), that you need to do this kind of work.
9. How do I convert between radiometric and photometric units?
We know from the definition of the candela that there are 683 lumens per watt at a frequency of 540THz, which is 555 nm (in vacuum or air). This is the wavelength that corresponds to the maximum spectral responsivity of the human eye. The conversion from watts to lumens at any other wavelength involves the product of the power (watts) and the V(λ) value at the wavelength of interest. As an example, we can compare laser pointers at 670 nm and 635 nm. At 670 nm, V(λ) is 0.032 and
RADIOMETRY &. PHOTOMETRY FAQ 11 a 5 mW laser has 0.005W×0.032×683 lm/W = 0.11 lumens. At 635 nm, V(λ) is 0.217 and a 5 mW laser has 0.005W×0.217×683 lm/W = 0.74 lumens. The shorter wavelength (635 nm) laser pointer will create a spot that is almost 7 times as bright as the longer wavelength (670 nm) laser (assuming the same beam diameter).
In order to convert a source with non-monochromatic spectral distribution to a luminous quantity, the situation is decidedly more complex. We must know the spectral nature of the source, because it is used in an equation of the form: ∞ XKXVdvm= λ bλλg z0
where Xv is a luminous term, Xλ is the corresponding spectral radiant term, and V(λ) is the photopic spectral luminous efficiency function. For X, we can pair luminous flux (lm) and spectral power (W/nm), luminous intensity (cd) and spectral radiant intensity (W/sr-nm), illuminance (lx) and spectral irradiance (W/m2-nm), or luminance (cd/m2) and spectral radiance (W/m2-sr-nm). This equation represents a weighting, wavelength by wavelength, of the radiant spectral term by the visual response at that wavelength. The constant Km is a scaling factor, the maximum spectral luminous efficiency for photopic vision, 683 lm/W. The wavelength limits can be set to restrict the integration to only those wavelengths where the product of the spectral term Xλ and V(λ) is non-zero. Practically, this means we only need integrate from 360 to 830 nm, limits specified by the CIE V(λ) table. Since this V(λ) function is defined by a table of empirical values, it is best to do the integration numerically. Use of the Gaussian equation given above is only an approximation. I compared the Gaussian equation with the tabulated data using blackbody curves and found the differences to be less than 1% for temperatures between 1500K and 20000K. This result is acceptable for smooth curves, but don’t try it for narrow wavelength sources, like LEDs.
There is nothing in the SI definitions of the base or derived units concerning the eye response, so we have some flexibility in the choice of the weighting function. We can use a different spectral luminous efficacy curve, perhaps one of the newer ones. We can also make use of the equivalent curve for scotopic (dark-adapted) vision for studies at lower light levels. This V'(λ) curve has its own constant K'm, the maximum spectral luminous efficiency for scotopic vision. K'm is 1700 lm/W at the peak wavelength for scotopic vision (507 nm) and this value was deliberately chosen such that the absolute value of the scotopic curve at 555 nm coincides with the photopic curve, at the value 683 lm/W. Some workers are referring to “scotopic lumens”, a term which should be discouraged because of the potential for misunderstanding. In the future, we can also expect to see spectral weighting to represent the mesopic region.
The International Commission on Weights and Measures (CGPM) has approved the use of the CIE V(λ) and V'(λ) curves for determination of the value of photometric quantities of luminous sources.
RADIOMETRY &. PHOTOMETRY FAQ 12
Now about converting from lumens to watts. The conversion from watts to lumens that we saw just above required that the spectral function Xλ of the radiation be known over the spectral range from 360 to 830 nm, where V(λ) is non-zero. Attempts to go in the other direction, from lumens to watts, are far more difficult. Since we are trying to back out a quantity that was weighted and placed inside of an integral, we must know the spectral function Xλ of the radiation over the entire spectral range where the source emits, not just the visible region.
Also please note that there is no such thing as a spectral lumen, spectral lux, spectral nit, spectral candela, etc. The photometric terms are all the result of integration over wavelength; they are never subject to integration.
10. Where can I learn more about this stuff?
Books, significant journal articles:
DeCusatis, C., “Handbook of Applied Photometry” AIP Press (1997). Authoritative, with pertinent chapters written by technical experts at BIPM, CIE and NIST. Skip chapter 4!
Rea, M., ed. “Lighting Handbook: Reference and Application” 8th edition, Illuminating Engineering Society of North America (1993).
“Symbols, Units and Nomenclature in Physics” International Union of Pure and Applied Physics (1987).
“American National Standard Nomenclature and Definitions for Illuminating Engineering” ANSI Standard ANSI/IESNA RP-16 96.
“The Basis of Physical Photometry” CIE Technical Report 18.2 (1983)
Publications available on the World Wide Web
All you ever wanted to know about the SI is contained at BIPM and at NIST. Available publications (highly recommended) include:
“The International System of Units (SI)” 7th edition (1998), direct from BIPM. The official document is in French; this is the English translation). Available on-line at www.bipm.fr/pdf/si-brochure.pdf.
NIST Special Publication SP330 “The International System of Units (SI)” The US edition of the above BIPM publication. Available on-line at physics.nist.gov/Pubs/SP330/sp330.pdf.
NIST Special Publication SP811 “Guide for the Use of the International System of Units (SI)” Available on-line at physics.nist.gov/Document/sp811.pdf.
RADIOMETRY &. PHOTOMETRY FAQ 13 Papers published in recent issues of the NIST Journal of Research are also available on-line at nvl.nist.gov/pub/nistpubs/jres/jres.htm. Of particular relevance is “The NIST Detector-Based Luminous Intensity Scale,” Vol. 101, page 109 (1996).
Useful Web sites
BIPM International Bureau of Weights and Measures - www.bipm.fr/
NIST Nat'l Inst. of Standards and Technology - physics.nist.gov/cuu/
ISO International Standards Organization - www.iso.ch/
ANSI American Nat'l Standards Institute - www.ansi.org/
CIE International Commission on Illumination - www.cie.co.at/cie/
IESNA Illuminating Engineering Society of North America - www.iesna.org/
IUPAP International Union of Pure and Applied Physics - www.physics.umanitoba.ca/iupap/
Color Vision Research Lab – www.cvrl.org
AIP American Institute of Physics - www.aip.org
SPIE - International Society for Optical Engineering - www.spie.org
OSA Optical Society of America - www.osa.org
CORM Council of Optical Radiation Measurements - www.corm.org
RADIOMETRY &. PHOTOMETRY FAQ 14 | s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296815919.75/warc/CC-MAIN-20240412101354-20240412131354-00416.warc.gz | CC-MAIN-2024-18 | 31,880 | 125 |
https://deepblue.lib.umich.edu/handle/2027.42/58219/discover?filtertype=hlbsecondlevel&filter_relational_operator=equals&filter=Mathematics | math | Now showing items 1-10 of 17
On tactical configurations with no four-cycles
An improved lower bound is given for the band sizes of tactical configurations of rank exceeding two having no 4-cycles. This bound is applied to find an optimal configuration with certain specified parameters. A formula ...
The study of shape transformation after D'Arcy Thompson
On the number of unique subgraphs
Entringer and Erdos introduced the concept of a unique subgraph of a given graph G and obtained a lower bound for the maximum number of unique subgraphs in any n-point graph, which we now improve.
Boolean distance for graphs
The boolean distance between two points x and y of a connected graph G is defined as the set of all points on all paths joining x and y in G (O if X = y). It is determined in terms of the block-cutpoint graph of G, and ...
Embedding and characterization of quantum chemical reaction graphs on two-dimensional orientable surfaces
Quantum chemical reaction graphs defined on multidimensional potential energy hypersurfaces are embedded on two-dimensional orientable surfaces. Topological invariants of these graphs and those of the embedding two-dimensional ...
The number of caterpillars
A caterpillar is a tree which metamorphoses into a path when its cocoon of endpoints is removed. The number of nonisomorphic caterpillars with n+4 points is 2n + 2[n/2]. This neat formula is proved in two ways: first, as ...
The graphs with only self-dual signings
Given a graph G, it is possible to attach positive and negative signs to its lines only, to its points only, or to both. The resulting structures are called respectively signed graphs, marked graphs and nets. The dual of ...
The cutting center theorem for trees
We introduce the cutting number of a point of a connected graph as a natural measure of the extent to which the removal of that point disconnects the graph. The cutting center of the graph is the set of points of maximum ...
Graph theoretic models
Graph theory 1736-1936 : By N. L. Biggs, E. K. Lloyd, and R. J. Wilson. Oxford (Clarendon Press). 1976. 239 pp. $27.85 | s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500058.1/warc/CC-MAIN-20230203154140-20230203184140-00524.warc.gz | CC-MAIN-2023-06 | 2,096 | 18 |
https://cshlccb.wordpress.com/author/sajiyaj/ | math | I am listing the names we have on the record for the books that are out. One book has no name on the record. Please return the books as soon as possible or let me (Sajiya) know if you find the missing book. Thank you.
Nazilla: Random walks in biology (c.1), Learning Matlab, A guide to XPPAUT, Computational cell biology
Mariam: Calcium signaling, Nonlinear dynamics and chaos
Wei: A guide to XPPAUT, Mathematical foundation of neuroscience, Physical biology of the cell.
Niamh: Computational cell biology, A primer of mathematical models in biology.
Sepideh: Stability, instability and chaos; Systems modeling in cellular biology.
Illyce: Biochemical oscillations and cellular rhythms.
Bharat: Elements of applied bifurcation theory, Stochastic modeling for systems biology.
[unknown]: Computational modeling of gene regulatory networks – a primer. | s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676591296.46/warc/CC-MAIN-20180719203515-20180719223515-00107.warc.gz | CC-MAIN-2018-30 | 851 | 9 |
https://www.plantedtank.net/threads/1-per-gallon-heads-up.583697/ | math | It only applies above 10g, correct?
Yes, that is correct.....yayIt only applies above 10g, correct?
Okay, great...thanks for the heads up...my fiance and I want another, each...lol:bounce:aqualady i called the one of 41st
soothing i believe it is 10-55 gal. i have seen in some areas 75 gallons are included but not many places do that | s3://commoncrawl/crawl-data/CC-MAIN-2023-23/segments/1685224648000.54/warc/CC-MAIN-20230601175345-20230601205345-00193.warc.gz | CC-MAIN-2023-23 | 335 | 4 |
https://senseis.xmp.net/?TheBambooJointMayBeShortOfLiberties | math | The bamboo joint may be short of liberties
The bamboo joint is an effective shape, that cannot directly be cut. But because of its compactness and the shared liberties of the four stones, there are only 10 liberties in total, for an isolated bamboo joint.
To maintain a connection against a push involves losing two liberties in gote. (Don't take away your own liberties?) This implies that bamboo joints can be attacked using shortage of liberties: for example by setting up a connect and die.
Scartol: Bamboo joints are not invincible, as I found out. I played and felt incredibly proud of myself for breaking through to my formerly dead group.
Black to win the capturing race.
(Sebastian:) Does this prove that the bamboo joint is as strong as the linear joint (or whatever it's called), because whoever moves first wins?
DJ I'm afraid I do not quite understand your question.
A bamboo joint is as strong as the liberties it has, taking into account the inherent possibility of damezumari - see the examples.
If the bamboo joint has the same number of liberties as the group it is involved in a semeai with, whoever starts first wins...
(Sebastian:) Yes, you did understand and answer my question. It just wasn't obvious to me that they had the same number of liberties.
Ellbur: The bamboo joint may have fewer liberties than the linear joint. See Scartol's example at the top.
(Sebastian:) Scartol's example is great to illustrate the cautionary tale of this page, but I don't see an obvious way to compare the liberties with those of a pole connection. (1) There is no equivalent to the situation in the diagram since the threat of W's circled move wouldn't even be possible. (2) So, what would be the equivalent pole connection? We can choose a pole with any number of liberties >0; depending on that choice you get different answers. (3) What exactly do you mean by "liberty"?
symplicity: I too don't see an obvious way to compare the two. I mostly interpret this statement as a warning that even though a bamboo joint may "look" like it has a lot of liberties, because of the space in the center, it might not, for tactical purposes.
Basically, one should be aware that the liberties in the middle can vanish very suddenly when the opponent's threat to cut is sente. And as in problem 2, the opponent can also wait for the opportune time to do so. | s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947474686.54/warc/CC-MAIN-20240227184934-20240227214934-00461.warc.gz | CC-MAIN-2024-10 | 2,355 | 14 |
https://books.google.fr/books?id=lBwCfjLVP0AC&hl=fr&source=gbs_navlinks_s | math | Avis des internautes - Rédiger un commentaire
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Page 92 - H are called the electric and magnetic fields, D is the electric displacement. H is the magnetic induction, J the eleotrl^ ."urrnnt, p the electric charge density. "Curl" and "div" are the usual operations of three-dimensional Euclidean vector analysis. | s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500255.78/warc/CC-MAIN-20230205130241-20230205160241-00761.warc.gz | CC-MAIN-2023-06 | 1,454 | 4 |
https://books.google.no/books?id=LpdYAAAAMAAJ&pg=PA23&focus=viewport&vq=third&dq=editions:UOM39015067252117&lr=&hl=no&output=html_text | math | « ForrigeFortsett »
let BE be in the same straight line with it; therefore, be- Book I.
may be demonstrated, that no other can be in the same straight line with it but BD, which therefore is in the same straight line with CB. Wherefore, if at a point, &c. Q. E. D.
PROP. XV. THEOR. IF two straight lines cut one another, the vertical, 1 or opposite, angles shall be equal.
Let the two straight lines AB, CD cut one another in the
For the angles CEA,
B a 13. 1.
Therefore, if two straight lines, &c.
Cor. 1. From this it is manifest, that, if two straight lines
COR. 2. And hence, all the angles made by any number of straight lines, meeting in one point, are together equal to four right angles.
PROP. XVI. THEOR.
IF one side of a triangle be produced, the exterior angle is greater than either of the interior and oppo. site angles.
Let ABC be a triangle, and let its side BC be produced to D; the exterior angle ACD is greater than either of the interior opposite angles CBA, А.
Bisecta ĄC in E, join BE
Because AE is equal to EC,
D each; and the angle AEB is equal to the - angle CEF, because they are vertical angles; therefore the base AB is equal c to the base CF,
G and the triangle AEB to the triangle CEF, and the remaining angles to the remaining angles, each to each, to which the equal sides are opposite; wherefore the angle BAE is equal to the angle ECF; but the angle ECD is greater than the angle ECF; therefore the angle ECD, that is, ACD, is greater than BAE. In the same manner, if the side BC Be bisected, it may be demonstrated that the angle BCG, that is the angle ACD, is greater than the angle ABC. Therefore, if one side, &c. Q. E. D.
b 15. 1.
C 4. 1.
PROP. XVII. THEOR.
ANY two angles of a triangle are together less than two right angles,
Let ABC be any triangle ;
Produce BC to D; and
a 16. 1. interior and opposite angle ABC; to each of these add the angle ACB; therefore B
D the angles ACD, ACB are greater than the angles ABC, ACB; but ACD, ACB are together equal to two right b 13. 1. angles; therefore the angles ABC, BCA are less than two right angles. In like manner, it may be demonstrated, that BAC, ACB, as also CAB, ABC, are less than two right angles. Therefore, any two angles, &c. Q. E. D.
THE greater side of every triangle has the greater angle opposite to it.
Let ABC be a triangle, of A
Ċ a 3. 1.
PROP. XIX. THEOR.
ang gre BC
THE greater angle of every triangle is subtended by the greater side, or has the greater side opposite
ani iti tha sid
a 5. 1.
Let ABC be a triangle, of which the angle ABC is greater than the angle BCA; the side AC is likewise greater than the side AB.
For, if it be not greater, AC
b 18. 1.
PROP. XX. THEOR.
ANY-two sides of a triangle are together greater than the third side.
a 3. 1.
Let ABC be a triangle ; any two sides of it together are
Produce BA to the point
Because DA is equal to
b 5. 1.
cause the angle BCD of the triangle DCB is greater than its Book I. angle BDC, and that the greater side is opposite to the greater angle: therefore the side DB is greater than the side c 19. 1. BC; but DB is equal to BA and AC together; therefore BA and AC together are greater than BC. In the same manner it may be demonstrated, that the sides AB, BC are greater than CA, and BC, CA greater than AB. Therefore any two sides, &c. Q. E. D.
PROP. XXI. THEOR.
IF from the ends of one side of a triangle there N. be drawn 'two straight lines to a point within the triangle, these two lines shall be less than the other two sides of the triangle, but shall contain a greater angle.
Let the two straight lines BD, CD be drawn from B, C, the ends of the side BC of the triangle ABC, to the point D within it; BD and DC are less than the other two sides BA, AC of the triangle, but contain an angle BDC greater than the angle BAC.
Produce BD to E ; 'and because two sides of a trianglea are a 20. 1. greater than the third side, the two sides BA, AE of the triangle ABE are greater than BE. To each of these add EC; therefore the sides BA, AC are
А. greater than BE, EC. Again, because the two sides CE, ED, of the triangle CED, are greater than CD, add DB to each of these; therefore the sides CE, EB are greater than CD, DB; but it has been shown that BA, AC are greater than BE, EC; much more then are BA, AC greater than BD, DC.
C Again, because the exterior angle of a triangleb is greater b 16.1. than the interior and opposite angle, the exterior angle BDC of the triangle CDE is greater than CED; for the same reason, the exterior angle CEB of the triangle ABE is greater than BAC; and it has been demonstrated that the angle | s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487611320.18/warc/CC-MAIN-20210614013350-20210614043350-00513.warc.gz | CC-MAIN-2021-25 | 4,604 | 50 |
https://www.grossarchive.com/project/19121/scheduling-a-timetabling-problem-using-automated-genetic-algorith | math | Any problem has a set of valid results. It is said to form the solution space. In an
optimization problem, the main aim or goal is to find results that maximize or
minimize a set of criteria. If we look at the solution space as an
n-dimensional space then essentially we are searching for a global minima or
maxima in the solution space. The Genetic Algorithm is a type of algorithm for
searching the solution space and finding maxima or minima, though not
necessarily the global maxima or minima. Timetable scheduling is always said to
be a complex optimization problem which has shown to be related to the clique
of minimization problem which is called NP complete. In such kind of problem
where no efficient algorithm is known, it is ideal to apply genetic algorithm
to such kind which is used for search a solution space. It is necessary to
realize that such scheduling is a world problem that has an immediate
application in various forms of timetabling including, examinations, public
transport and roaster, though in no way limited to.
Scheduling is one of the important tasks that we encountered in our daily life situations.
There are various types of scheduling problems which includes personnel
scheduling, production scheduling, and educational timetable scheduling etc.In
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Educational timetable scheduling can be called a non-polynomial hard (NP hard)
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scheduling. Hence, evolutionary techniques have been used to solve the time
table scheduling problem. | s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882573623.4/warc/CC-MAIN-20220819035957-20220819065957-00422.warc.gz | CC-MAIN-2022-33 | 1,710 | 23 |
https://www.onlinemath4all.com/6th_grade_worksheet3.html | math | 6th Grade Worksheet3
Here, 6th grade worksheet3 on math is given. You can do the problems on this work sheet and also check whether the answer you have got is correct.
1.A cinema hall is to be constructed in which each row must have 36 seats.Determine the minimum number of rows required to seat 60 persons at one time.
2.Add -37 and -42
3.Two tankers contain 850 liters and 680 liters of petrol, respectively.Find the maximum capacity of the container which can measure the petrol of either tanker in exact number of times.
4.The traffic lights at three different road crossings change after every 48 seconds,72 and 108 seconds respectively. If they change simultaneously at 7 a.m after what time will they change again simultaneously?
5.A Plane flies 4000 km in 5 hours.How far does it fly in 3 hours?
6.Find the number of girl students in a school,if there are 28% girl student in the school and the total number of students in the school is 1000.
7.Peter obtained 285 marks out of the maximum of 500 marks.Find the percentage of marks obtained by peter.
8.Find the value of a 2 - 2(b 2 + c2) if a = 2,b = 3 and c = 1
9.An angle of measure 180° is called a _________________
10.Find the perimeter of a rectangle whose length and breadth are 16 cm and 8 cm respectively.
These are the questions on math prepared in 6th grade worksheet3 based on the curriculum of 6th grade.We hope that this will be very useful to you.
1. 17 rows
3. 170 L
4. 8 min 12 sec
5. 2400 km
9. Straight angle
10. 48 cm | s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250608295.52/warc/CC-MAIN-20200123041345-20200123070345-00362.warc.gz | CC-MAIN-2020-05 | 1,496 | 19 |
https://www.gvsu.edu/catalog/course/sta-415.htm | math | LAKERS TOGETHER: Find out how we're moving forward. Learn about campus safety measures including testing, face coverings and vaccines.
2020-2021 Undergraduate & Graduate Catalog
STA 415 - Mathematical Statistics II (Capstone)
A theoretical study of the following topics: the Law of Large Numbers, the Central Limit Theorem, the nature of statistical inference, tests of hypotheses, sampling theory, point and interval estimation, linear models, analysis of categorical data, and distribution-free methods. Offered winter semester. Prerequisites: STA 412 and MTH 204. | s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046150307.84/warc/CC-MAIN-20210724160723-20210724190723-00159.warc.gz | CC-MAIN-2021-31 | 566 | 4 |
https://mech.enacademic.com/429/frequency_rate | math | - frequency rate
- the ratio of exciting frequency to the natural frequency.
Mechanics glossary. 2013.
Look at other dictionaries:
frequency rate — noun : the number of disabling injuries of given types resulting from industrial accident per million man hours worked … Useful english dictionary
rate — of camber change rate of caster change rate of heat generation rate of track change amplitude rate critical cooling rate damping rate dynamic rate frequency rate overall steering rate ride rate … Mechanics glossary
Rate of fire — is the frequency at which a specific weapon can fire or launch its projectiles. It is usually measured in rounds per minute (RPM or round/min), or per second (RPS or round/s). Contents 1 Overview 2 Measurement 2.1 Cyclic rate … Wikipedia
Frequency Of Exclusion — refers to the rate of occurrences where a group is excluded from a sample or study. The frequency of exclusion would attempt to define the percentage or rate that a specified group is under represented in a sample or study. Statistical study… … Investment dictionary
rate — n 1: a fixed ratio between two things 2: a charge, payment, or price fixed according to a ratio, scale, or standard: as a: a charge per unit of a commodity provided by a public utility b: a charge per unit of freight or passenger service see also … Law dictionary
rate — Ⅰ. rate ► NOUN 1) a measure, quantity, or frequency measured against another quantity or measure: the crime rate. 2) the speed with which something moves, happens, or changes. 3) a fixed price paid or charged for something. 4) the amount of a … English terms dictionary
frequency — ► NOUN (pl. frequencies) 1) the rate at which something occurs over a particular period or in a given sample. 2) the fact or state of being frequent. 3) the rate per second of a vibration constituting a wave, e.g. sound, light, or radio waves. 4) … English terms dictionary
Rate of response — is a ratio between two measurements with different units. Rate of responding is the number of responses per minute, or some other time unit. It is usually written as R. Its first major exponent was B. F. Skinner (1939). It is used in the Matching … Wikipedia
frequency — 1640s, fact of occurring often, from L. frequentia a crowding, crowd, from frequentem (see FREQUENT (Cf. frequent)). Earlier it had been used in a now obsolete sense of state of being crowded (mid 16c.); sense in physics, rate of recurrence,… … Etymology dictionary
frequency — noun common occurrence, commonness, continuity, crebritas, cycle, frequence, frequentia, periodicity, prevalence, rate, recurrence, regularity, regularity of recurrence, repetition, repetitiveness, succession, usualness Burton s Legal Thesaurus.… … Law dictionary | s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540511946.30/warc/CC-MAIN-20191208150734-20191208174734-00434.warc.gz | CC-MAIN-2019-51 | 2,780 | 14 |
https://www.bartleby.com/questions-and-answers/x-12/07e6761e-d98b-4d91-9e4a-76dd5fc9bb89 | math | Refer to the given 3x3 coefficient matrix with initial conditions (see attached image). Find the particular solution to the initial value problem.
To solve we have to find eigen vectors for this we have to find eigen values.
To find eigen values,
Solving above equation we can get
Reducing to echelon form
Our solutions are written by experts, many with advanced degrees, and available 24/7See Solution
Q: Chapter 1 Section 1.2 19. A section of a gear is shown. Given the formulas below and the circular pi...
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A: Construct the truth table for p, q and r. use p and r to find the p →r.
Q: Pls explain to me step by step and dont skip any steps. Thanks
A: To locate and analyze the critical points of the given non-linear system
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A: It is known that,
Q: Subject: Elements of Set Theory Greetings,I am really having difficult time with these problems that...
A: (a)We have to prove:
Q: How many ways can you choose 5 out of 10 friends to invite to a dinner party?
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A: Let, S and T be a any set. also, P(S) be any power set of S and P(T) be any power set of T.x∈P(S∩T) ...
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Sorry about that. What wasn’t helpful? | s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986653216.3/warc/CC-MAIN-20191014101303-20191014124303-00423.warc.gz | CC-MAIN-2019-43 | 1,735 | 25 |
https://www.jagranjosh.com/articles/cbse-class-12-chemistry-practice-paper-2017-set-i-1480400833-1 | math | Get CBSE class 12 Chemistry practice paper 2017 for the coming CBSE board examination 2017. This practice paper is as per latest CBSE examination pattern of class 12 Chemistry. All the questions of this practice paper are based on latest CBSE syllabus.
CBSE board exams 2017 are about to start from 1st March 2017 and every student of CBSE class 12 want to score maximum marks in board examinations. CBSE result 2017 of class 12 students will depend on their score in core subjects. This practice paper is developed by subject experts after the brief analysis of CBSE class 12 Chemistry question paper 2016. Some important questions from previous year CBSE papers are also included in this practice paper.
The complete practice paper is given below:
Time allowed: 3 hours Maximum Marks: 70
(i) All questions are compulsory.
(ii) Questions number 1to 5 are very short answer questions and carry 1 mark each.
(iii) Questions number 6 to 10 are very short answer question and carry 2 marks each.
(iv) Questions number 11 to 22 are also short answer question and carry 3 marks each.
(v) Question number 23 is a value based question and carry 4 marks.
(vi) Questions number 24 to 26 are long answer question and carry 5 marks each.
(vii) Use log tables, if necessary. Use of calculators is not allowed.
Question1: Write the structure of an isomer of compound C4H9Br which is most reactive towards SN1 reaction.
Question2: Why CuSO4. 5H2O is blue in colour while CuSO4 is colourless?
Question3: NO2 group show its effect only at ortho- and para- positions and not at meta- position. Explain.
Question4: Write IUPAC name of the given compound:
Question5: Explain the causes of Brownian movement in a colloidal solution?
Question6: The formula of a coordination compound is CoCl3.4NH3. It does not liberate ammonia but precipitates chloride ions as silver chloride.
(i) Write the structural formula of the complex?
(ii) What is the IUPAC name of the complex?
Question7: Explain why alkylamine more basic than ammonia.
Question8: Write mathematical expression of Henry’s law correlating the pressure of a gas and its solubility in a solvent and mention one applications of the law.
Question9: Out of the following two coordination entities which is chiral (optically active)?
(a) cis-[CrCl2(ox)2]3‒ (b) trans-[CrCl2(ox)2]3‒
Question10: Draw the structures of the following molecules:
Question10: Complete the following equations:
(i) HgCl2 + PH3 →?
(ii) XeF4 + H2O →?
Question11: Name the reagents which are used in the following conversions:
(i) A primary alcohol to an aldehyde
(ii) Butan-2-one to butan-2-ol
(iii) Phenol to 2, 4, 6-tribromophenol
Question12: Account for the following observations:
(i) pKb for aniline is more than that for methylamine.
(ii) Methylamine solution in water reacts with ferric chloride solution to produce a precipitate of ferric hydroxide.
(iii) Aniline does not undergo Friedel-Crafts reaction.
Question13: Define the following in relation to proteins :
(i) Primary structure
(iii) Peptide linkage
Question14: What do you understand by flux? What is its role in the metallurgy of iron and copper?
Question15: Give reasons for the following:
(i) Nickel does not form low spin octahedral complexes.
(ii) The p-complexes are known for the transition metals only.
(iii) Co2+ is easily oxidised to Co3+ in the presence of a strong ligand.
Question16: An element has a body-centred cubic (bcc) structure with a cell edge of 288 pm. The density of the element is 7.2 g/cm3. How many atoms are present in 208 g of the element?
Question17: (a) What is the significance of number 6 and 6, 6 in the polymer names nylon-6 and nylon-6, 6?
(b) What is the difference between Buna-N and Buna-S?
(c) Arrange the following polymers in increasing order of their intermolecular forces
Neoprene, Nylon 6, Polyvinyl chloride
Question18: In a pseudo first order hydrolysis of an ester in water, the following results were observed
(i) Find the average rate of reaction between the time intervals 30 to 60 seconds.
(ii) Find the pseudo first order rate constant for the hydrolysis of ester.
Question19: (i) Why alkylamine is more basic than ammonia?
(ii) What are azo dyes?
(iii) What do you understand by coupling reaction?
Question20: What is Corrosion? What are the chemical reactions involved in the formation of corrosion?
Question21: Calculate the boiling point of a 1M aqueous solution (density 1.04 g mL) of Potassium chloride (Kb for water = 0.52 K kg mol−1. Atomic masses: K = 39 u. C1 = 39.9 u). Assume, Potassium chloride is completely dissociated in solution.
Question21: Find the depression in the freezing point of water when 10 g of CH3CH2CHClCOOH is added to 250 gram of water. Kα = 1.4 × 10 ‒ 3, Kf = 1.86 K kg mol‒1.
Question22: Define the following terms:
(b) Tyndall Effect
Question23: Observing the growing cases of diabetes and depression among young children, Mr. Amit, the principal of one reputed school organized a seminar in which he invited parents and principals. They all resolved this issue by strictly banning junk food in school s and introducing healthy snacks and drinks like soup, lassi, milk etc in school canteens. They also decided to make compulsory half an hour of daily physical activities for the students in the morning assembly. After six months, Mr. Amit conducted the health survey in most of the schools and discovered a tremendous improvement in the heath of students.
After reading the above passage answer the following question:
(i) What are the values displayed by Mr. Amit?
(ii) As a student, how can you spread awareness about this issue?
(iii) What are the anti-depressant drugs? Give an example.
(iv) Name the sweetening agent used in the preparation of sweets for a diabetic patient.
Question24: (a) Define molar conductivity of a substance and also write the relationship between molar conductivity and specific conductivity.
(b) A voltaic cell is set up at 25o C with the following half cells:
Ag+ (0.001 M) | Ag and Cu2+ (0.10 M) | Cu
What would be the voltage of this cell? (Eo cell = 0.46 V)
Question24: (a) Describe how for weak and strong electrolytes, molar conductivity changes with concentration of solute. How is such change explained?
(b) Conductivity of 0.00241 M acetic acid is 7.896 × 10‒5 S cm‒1. Find its molar conductivity and if Λo for acetic acid is 390.5 S cm2 mol‒1, what is the dissociation constant?
Question25: (a) How are the following obtained?
(i) Benzoic acid from ethyl benzene.
(ii) Benzaldehyde from toluene.
(b) Complete each synthesis by giving the missing material, reagent or products:
Question25: (a) Name two commonly used methods to convert >C=O group into >CH2 group
(b) Name the products formed when ethanal is heated with hydrogen iodide and red phosphorous under high pressure.
(c) Name the acid present is vinegar.
(d) Identify the compounds X, Y and Z in the following reaction.
Question26: (a) What may be the possible oxidation states of the transition metals with the following d electronic configurations in the ground state of their atoms: 3d 3 4s 2, 3d5 4s 2 & 3d 6 4s 2. Indicate relative stability of oxidation states in each case.
(b) Write steps involved in the preparation of (i) Na2CrO4 from chromite ore and (ii) K2MnO4 from pyrolusite ore.
Question26: Assign reasons for the following
(a) The transition metals and many of their compounds act as good catalysts.
(b) The enthalpies of atomisation of transition elements are high.
(c) From element to element the actinoid contraction is greater than the lanthanoid contraction.
(d) The Eo value for Mn3+/Mn2+ couple is much more positive than that of Cr3+/Cr2+
(e) Scandium (Z = 21) does not exhibit variable oxidation states and yet it is regarded as a transition element. | s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103917192.48/warc/CC-MAIN-20220701004112-20220701034112-00338.warc.gz | CC-MAIN-2022-27 | 7,769 | 87 |
https://armyordnance.tpub.com/Od16338/Od163380046.htm | math | BASIC ELECTRONICS - OD1633 - LESSON 1/TASK 2
R3 = 40 Ohms - 20 Ohms
R3 = 20 Ohms
(2) Current in a Series Circuit.
Since there is only one path for
current in a series circuit, the same current must flow through each
component of the circuit.
To determine the current in a series circuit,
only the current through one of the components need be known.
The fact that the same current flows through each component of a series
circuit can be verified by inserting meters into the circuit at various
points, as shown in figure 22 (on the following page). If this were done,
each meter would be found to indicate the same value of current.
CALCULATING THE VALUE OF ONE RESISTOR IN A SERIES CIRCUIT.
(3) Voltage in a Series Circuit.
The voltage dropped across the
resistor in a circuit consisting of a single resistor and a voltage source
is the total voltage across the circuit and is equal to the applied voltage.
The total voltage across a series circuit that consists of more than one
resistor is also equal to the applied voltage, but consists of the sum or
the individual resistor voltage drops.
In any series circuit, the sum of
the resistor voltage drops must equal the source | s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233510412.43/warc/CC-MAIN-20230928130936-20230928160936-00168.warc.gz | CC-MAIN-2023-40 | 1,176 | 23 |
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System substitution solver can be found online or in mathematical textbooks. Solve with steps is one of the most popular types of puzzles. In this type, you must solve each step in sequence to reach the final solution. Solving with steps puzzles are great for people who want a quick yet challenging brain workout while also providing a sense of accomplishment. If you’re new to solving with steps, start off by simply counting out each step and then visualize yourself making your way through the puzzle. Once you have all the steps down, it will only take a few extra seconds to complete the puzzle. People unfamiliar with solving with steps often end up trying to count out each and every step when they should be focusing on just one or two steps at a time. This can quickly lead to frustration and confusion if you have a lot of information to process at once. Instead, focus on just one or two key steps that you need to remember and try to encode them in your memory as quickly as possible so that you can easily recall them later on.
First determine the y intercept. The y intercept is the value where the line crosses the Y axis. It is sometimes referred to as the "zero" point, or reference point, along the line. The y intercept of an equation can be determined by drawing a vertical line down through the origin of each graph and placing a dot at the intersection of the two lines (Figure 1). When graphing a parabola, the y intercept is placed at the origin. When graphing a line with a slope 1, then both y-intercepts are placed at 0. When graphing a line with a slope >1, then both y-intercepts are moved to positive infinity. In order to solve for x intercept on an equation, first use substitution to solve for one of the variables in terms of another variable. Next substitute back into original equation to find x-intercept. In order to solve for y intercept on an equation, first use substitution to solve for one of the variables in terms of another variable. Next substitute back into original equation to find y-intercept. Example: Solve for x-intercept of y = 4x + 10 Solution: Substitute 4x + 5 = 0 into original problem: y = 4x + 10 => y = 4(x + 5) => y =
Solving math equations is a fundamental skill in mathematics. It’s also a great way to practice your critical thinking skills and develop your problem solving abilities. You can use a variety of resources to help you learn how to solve math equations. For example, you can read books, watch educational videos, take online courses, or enroll in math tutoring programs. And you can get extra practice whenever you have free time at school or at home. So don’t let your math skills slip! If you have any questions about solving math equations, please reach out to a teacher or tutor for help. They’re more than happy to lend a hand!
Elimination equations are a type of math problem in which you have to find the solution that leaves the least number of equations. They are often used when you have to find the minimum or maximum value for one variable after another variable has been changed. There are four types of elimination equations: Linear: One variable is raised to a power, and the other variables are multiplied by it. For example, if one variable is raised to the power 3 and another to the power 8, then the resulting equation would be (3x8) = 64. The solution would be 32. Square: Two variables are multiplied. For example, if one variable is squared (or raised to 4) and another is squared (or raised to 4), then their resulting product is 16. The solution would be 8. Cubed: Three variables are multiplied. For example, if one variable is cubed (i.e., raised to 8) and another is cubed (i.e., raised to 8), then their resulting product is 56. The solution would be 40. To solve an elimination equation, you first need to identify which equation needs solving. Then you need to identify all of the variables involved in that equation and their values at each step in your problem, such as x1 = 1, x2 = 2, x3 = 4, … . This will allow you to | s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500074.73/warc/CC-MAIN-20230203185547-20230203215547-00644.warc.gz | CC-MAIN-2023-06 | 4,222 | 7 |
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Oh I'm sorry<3 I don't know this one. Try @ParthKohli or @lgbasallote I'm really sorry.
yeah sure tag the poor lgba :(
It would be 180 - 60
120..but can you explain to me why? becuase I want to learn for next time!
@eyust707 ..is it 120? how?
if you have 4 parallel lines like this |dw:1339087707750:dw|
all the intersections are exactly the same
so those angles are exactly the same
so that angle is 60
and they told us its against a line
so from there to there is 180
all thats left is the difference
oh ok I see! terrific..there was another way I looked at it too! if you look at the picture angle K has one arc which measures 60 degrees, and angle M has two arcs! so I was thinking that I could multiply 60 times 2!
will that technique work on all equations?
the arc simply mean that they are different angles
they dont have to be different by a factor of 2 tho
oh ok I see! thanx ;) | s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463613780.89/warc/CC-MAIN-20170530031818-20170530051818-00418.warc.gz | CC-MAIN-2017-22 | 1,579 | 18 |
http://dickhats.com/northern-territory/how-to-find-the-pitch-of-a-screw.php | math | DESIGN AND SIZING OF SCREW FEEDERS Lehrstuhl fml an der
16/10/2011 · For instance, a screw with 5 mm of pitch will advance 5 mm for every complete turn when hit by the screwdriver. In fact, the "screw propeller" concept is literally making reference to that the propeller works exactly like a screw.... The propeller pitch, or prop pitch, depends on the diameter and the pitch of the boat or airplane. The diameter is determined by the revolutions per minute at which the propeller will be turning and the amount of power need to turn the propeller.
How To Read A Micrometer Screw Gauge Mini Physics
The following is a very simple pitch and lead calculator, given the number of starts and the number of threads or turns per inch of a lead screw.... The pitch of the screw is the distance moved by the spindle per revolution. To find this, the distance advanced by the head scale over the pitch scale for a definite number of complete rotation of the screw …
Screw Thread Calculators and Charts amesweb.info
The following is a very simple pitch and lead calculator, given the number of starts and the number of threads or turns per inch of a lead screw. how to get bleach out of your hair The following is a very simple pitch and lead calculator, given the number of starts and the number of threads or turns per inch of a lead screw.
How to find pitch diameter" Keyword Found Websites Listing
A screw is made of a head, where the screwdriver or drill bit is inserted, and a body, which is composed of threads that bore into a material. In construction and engineering settings, you might need to identify the size of the threads being used in the screw to properly find replacements. how to find the risk free rate in capm Pitch is the axial distance between two consecutive threads on a screw. Lead is the linear distance traveled by the nut or screw during one full rotation. Starts are the number of independent
How long can it take?
Screw Gauge (Theory) Class 11 Physics Amrita Online Lab
- Screw Conveyor Capacity Engineering Guide
- What are the different ways of measuring the pitch
- What is the difference between screw pitch and lead?
- What is the formula to find the pitch of a screw gauge
How To Find The Pitch Of A Screw
The following is a very simple pitch and lead calculator, given the number of starts and the number of threads or turns per inch of a lead screw.
- Product : Standard screw: JHS-200: Bulk density: kg/m3: Power factor : Product speed: m/s: Degree of filling % Rpm screw: omw/min: Capacity : ton/u
- a uniform pitch for the auger flighting and decreasing inside diameter. The other had a The other had a uniform inside diameter and a decreasing pitch of the flighting with distance from the …
- Refer ISO 261.ISO 261 specifies a detailed list of preferred combinations of outer diameter D and pitch P for ISO metric screw threads. You can also find data about standard threads online on various sites.Against a specific screw size usually you will find two pitch sizes, first COARSE pitch and FINE pitch.
- The screw’s lead also affects the linear actuators thrust capacity. To calculate linear thrust of a screw assembly, use the following equation: Torque = Thrust required × Screw lead/(2 | s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195525699.51/warc/CC-MAIN-20190718170249-20190718192249-00052.warc.gz | CC-MAIN-2019-30 | 3,232 | 20 |
http://sysreview.com/fuser-error/hp-4350-50-5-fuser-error.html | math | If you think you have received a fake HP Support message, please report it to us by clicking on the blue “Report Inappropriate Content” button above the message. Brand new OEM would define it as coming from HP. This is an international forum, after all. Re-install the plastic rear output bin. check over here
Push the fuser firmly--listen for the sound of both blue levers clicking into place. Push the fuser firmly--listen for the sound of both blue levers clicking into place. Some pictures derived from HP User and Service guides. No more fusion problems. http://www.printertechs.com/printer-troubleshooting/367-50-5-error-on-laserjet-4200-4240-4250-4300-4350
Please try the request again. by dmzcompute on Jan 2, 2007 at 3:28pm Add comment Please sign in to comment 0 thank you, i will order the parts and report back. The only other explanation might be that the connectors aren't mating properly.
The new fuser specifically has a "4200" sticker on it along with the part number: PM1-0013 / 110V. by rottielover on Nov 12, 2007 at 2:44pm Add comment Please sign in to comment 0 A 4300 fuser will work in a 4345, so you should be able to check the 4345 heating element using this diagram: http://www.partsnow.com/service_today/4300.asp by Stephen on Nov 13, 2007 at 5:30pm Add comment Please sign in to comment 0 Brand new always confuses me. Join the community of 500,000 technology professionals and ask your questions. Hp 4250 Fuser So I took off the top cover and then left side cover to expose the cooling fan.
Glad I could help. 50.4 Fuser Error by unknown on May 29, 2009 at 7:29am Add comment Please sign in to comment 0 There is no fuser reset. Clean or straighten the pins if necessary. This problem was (and remains) notorious with LJ 4200/ 4300/ 4250 / 4350 printers where the fusers look the same but are different in detail. by moe on Jun 1, 2009 at 10:18am Add comment Please sign in to comment 0 Thank you, I appricate it.
I had this problem with a 4200 changed the fuser it's now working ok. - Anonymous 0 Next item would be the dc controller, followed by the power supply. 50.2 Fuser Error Laserjet Pro 400 printertechs Just the Index page again. If you have another 4200 fuser even if the teflon is bad just try anyway to see if the message goes away. - dmzcompute Am still having the same error,so what else can I do to resolve the problem? - Anonymous can you send vido that you maintain this fuser error or to change this fuser.thanks - Anonymous 0 Ohm out the fusers.http://www.partsnow.com/service_today/4200.aspLikely you have two bad ones. Since the error is a low fuser temp, you could try to jack up the fuser temp from normal to high 1 for all types of paper and see if maybe it will stay hot enough.
by unknown on Mar 19, 2008 at 8:13am Add comment Please sign in to comment 0 Since we have no idea what you did before, we can't advise you.
PrinterTechs.com 608-831-2396 or 866-352-7108 About Us Contact Us Search Products Search Support All Products PrintersHewlett PackardLexmarkCables and Misc.JetDirect CardsBrotherKyoceraDell Toner Maintenance Kits Printers Parts Tech Support Account Login Shopping Cart My Account Checkout Home Troubleshooting 50.5 Fuser Error on LaserJet 4200 4240 4250 4300 4350 Email 50.5 Fuser Error on LaserJet 4200 4240 4250 4300 4350 If you see this error code 50.5 on an HP LaserJet 4200, 4240, 4250, 4300, or 4350 series printer, the fuser installed in the printer is registering as an incorrect fuser for that model printer. Hp Laserjet 50.2 Fuser Error We do try to help; but there is a substantial cost to us in dealing with the problem so there will be a re-stocking charge. 50.5 Fuser Error Hp 4015 If you have any questions give us a call toll-free 866-352-7108 or local 608-831-2396, we can help you get the right fuser for your specific model.
by Anonymous on Nov 12, 2007 at 10:09am Add comment Please sign in to comment 0 Anonymous asked: "We are trying to help you solve your issue. check my blog part# RM1-0013 purchase HP 4200 fuser/maintenance kit here for use in HP LaserJet 4200, HP LaserJet 4200N, HP LaserJet 4200TN, HP LaserJet 4200DTN, HP LaserJet 4200DTNs, HP LaserJet 4200DTNsl part# RM1-1082 purchase HP 4240, 4250, 4350 fuser/maintenance kit here for use in HP LaserJet 4240, HP LaserJet 4240N, HP LaserJet 4250, HP LaserJet 4250N, HP LaserJet 4250DN, HP LaserJet 4250TN, HP LaserJet 4250DTN, HP LaserJet 4250DTNsl part# RM1-0101 purchase HP 4300 fuser/maintenance kit here for use in HP LaserJet 4300, HP LaserJet 4300N, HP LaserJet 4300DN, HP LaserJet 4300TN, HP LaserJet 4300DTN, HP LaserJet 4300DTNs, HP LaserJet 4300DTNsl Removal instructions: How to remove the fuser: Turn the printer off and unplug the power cord. Replace power supply 50.5 Fuser Error Description: incorrect fuser is installe Solution: 1. I'm hoping it's just a manufacturing defect on the "new" fuser I ordered from before. Hp 4200 Fuser
Unit has been sitting un-plugged. I found on the powerboard a burnt fuse - the larger of the two (125v 15A). by unknown on May 31, 2009 at 6:53pm Add comment Please sign in to comment 0 My bad, I just naturally assumed that since you said it was a 220V fuser, that you were from out of the country. this content Replace power supply 50.2 Fuser Error Description: fuser warm up service,- Fusing Assembly is taking too long to reach proper temperature. Solution: 1.
This is how video conferencing should work! Hp 4240 Maintenance Kit While grasping onto both sides of the fuser, push the blue levers upward and pull the fuser straight out. by moe on Nov 8, 2007 at 9:24am Add comment Please sign in to comment 0 wow great trouble shooting advice turns out my 50.2 fuser error was due to having the wrong input voltage.
Otherwise you may actually have a defective new fuser. There are probably very few 5SI and CLJ-4500 printers left in service - you cant get the parts. by nivek on Jun 1, 2009 at 10:31am Add comment Please sign in to comment 0 I tore apart a 4250 after having a 50.2 fuser error. Fuser Error Hp Printer Bookmark the permalink.
Wird geladen... by sstuart on Dec 26, 2006 at 11:29am Add comment Please sign in to comment I have seen alreasy about a dozen printers where the wrong fuser has been installed. If the part number on the fuser is the exact same as the one you removed, try powering off the printer and unplugging it from the power source for a few minutes. http://sysreview.com/fuser-error/hp-50-4-fuser-error.html The system returned: (22) Invalid argument The remote host or network may be down.
backpage.com completely irrelevant - it must be triggered by an ad that used to be on the page. Leave a Reply Cancel reply Your email address will not be published. Learn How to Post and More Community News Best of the Community Blog Notebooks Notebook Operating System and Recovery Notebook Boot and Lockup Notebook Wireless and Networking Notebook Audio Notebook Video, Display and Touch Notebook Hardware and Upgrade Questions Notebook Software and How To Questions Business Notebooks Printers sprocket Inkjet Printing LaserJet Printing Printer Software and Drivers DesignJet, Large Format Printers and Digital Press HP Connected, Mobile Printing and Cloud Printing Scanning, Faxing, and Copying JetAdvantage, Printing Applications and Services Desktops Desktop Operating Systems and Recovery Desktop Boot and Lockup Desktop Wireless and Networking Desktop Audio Desktop Video, Display and Touch Desktop Hardware and Upgrade Questions Desktop Software and How To Questions Sprout by HP Business PCs, Workstations and Point of Sale Systems Gaming Gaming Notebooks Gaming Desktops Gaming Accessories Tablets and Mobile Devices Elite x3 Android Windows Calculators Palm and WebOS Software HP Workspace HP Touchpoint Manager HP Collaboration Commercial PC Software Archived Topics (Read Only) Notebooks Archive (Read Only) Printers Archive (Read Only) Desktops Archive (Read Only) Tablets and Mobile Devices Archive (Read Only) Software Archive (Ready Only) Windows Beta and Previews Archive (Read Only) Miscellaneous Topics (Read Only) Your Voice Forum Feedback & Suggestions HP Expert Portal Welcome to the HP Expert Program Meet the Experts News and Events Blogs Open Menu Blogs Open Menu Best of the Community BlogMeet the ExpertsNews and EventsWelcome to the HP Expert Program Beware of fake HP Support Open Menu Beware of fake HP Support Open Menu Be alert for scammers who may be posing as HP representatives and only call numbers from people who have a label next to their screen name. Get 1:1 Help Now Advertise Here Enjoyed your answer?
Autoplay Wenn Autoplay aktiviert ist, wird die Wiedergabe automatisch mit einem der aktuellen Videovorschläge fortgesetzt. The argument that "Marks and Spencers just take things back" isn't helpful, they make a huge margin on clothes and anyway that policy has changed. Replace power supply 50.3 Fuser Error Description: Fuser over temperature - Fusing Assembly is exceeding proper temperature. (Too Hot) Solution: 1. Wird verarbeitet... | s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891814393.4/warc/CC-MAIN-20180223035527-20180223055527-00158.warc.gz | CC-MAIN-2018-09 | 9,119 | 15 |
https://www.hackmath.net/en/math-problem/373 | math | In the pool is numbers from 1 to 115. What is the probability that a randomly selected number is not a prime number?
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How many 4 digit numbers that are divisible by 10 can be formed from the numbers 3, 5, 7, 8, 9, 0 such that no number repeats? | s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107904039.84/warc/CC-MAIN-20201029095029-20201029125029-00672.warc.gz | CC-MAIN-2020-45 | 3,493 | 36 |
http://slideplayer.com/slide/6541132/ | math | Presentation on theme: "EMF. E.m.f and p.d - Learning Outcomes You should all be able to: define potential difference (p.d.); select and use the equation W = VQ; define the volt;"— Presentation transcript:
E.m.f and p.d - Learning Outcomes You should all be able to: define potential difference (p.d.); select and use the equation W = VQ; define the volt; describe how a voltmeter may be used to determine the p.d. across a component; define electromotive force (e.m.f.) of a source such as a cell or a power supply; describe the difference between e.m.f. and p.d. in terms of energy transfer
Electric Potential (a bit like Gravitational Potential) To give the ball more gravitational ‘potential’ energy work must be done on it. Now it is ‘higher’ it has more ‘potential’. This is a bit like electrical ‘potential’. The position of a charge (rather than in a ball) in an electric field (rather than a gravitational field) determines its potential.
Electric Potential (a bit like Gravitational Potential) The direction of current flow is conventionally taken to be from points of higher potential (i.e. the top of a hill) to a point of lower potential. Note: Conventional current flows from +ve to –ve, but the electrons (that are –ve) flow to the positive terminal.
If the work done in causing one coulomb of electric charge to flow between two points is one joule, then the PD between the points is one volt (i.e. 1V = 1 JC -1 ) It follows that W = QV Where W = the work done (J) Q = the charge (C) V = the potential difference (V)
e.m.f is the energy transferred per unit charge when one type of energy is converted into electrical energy. Potential difference is the energy transferred per unit charge when electrical energy is transferred into another form of energy. Key Definitions
Potential difference 12V What is the voltage across each resistor? 6V What happens to the charge as it flows through the resistor? Electrical energy is transformed into another energy (heat in this case)
Resistance - Learning Outcomes You should all be able to: define resistance; select and use the equation for resistance (V = I.R) define the ohm; state and use Ohm’s law; describe the I–V characteristics of a resistor at constant temperature, filament lamp and light-emitting diode (LED); describe an experiment to obtain the I–V characteristics of a resistor at constant temperature, filament lamp and light-emitting diode (LED); describe the uses and benefits of using light emitting diodes (LEDs).
AV bit of wire http://phet.colorado.edu/en/simulation/circuit-construction-kit-dc How to measure resistance
Ohm’s Law Resistance = Potential Difference (volts) (ohms) Current (amperes) V is Potential Difference measured in voltage, V I is current measured in Amps, A R is resistance measured in Ohms, Ω R = V I V = I R
Ohm’s Law The current through a resistor at a constant temperature is directly proportional to the potential difference across the resistor. This means if you double the current you double the voltage over a component. It also means that the resistance of the component does not change when you put more current through it.
Candidates should be able to: define resistivity of a material; select and use the resistivity equation ; describe how the resistivities of metals and semiconductors are affected by temperature; describe how the resistance of a pure metal wire and of a negative temperature coefficient (NTC) thermistor is affected by temperature.
Resistivity The resistivity ρ of a wire of length l, resistance R and cross sectional area A is given by: ρ = RA l
Candidates should be able to: describe power as the rate of energy transfer; select and use power equations P = VI, P = I 2 R and P = V 2 / R explain how a fuse works as a safety device determine the correct fuse for an electrical device; select and use the equation W = IVt; define the kilowatt-hour (kW h) as a unit of energy; calculate energy in kW h and the cost of this energy when solving problems.
Power Power (watts) = Energy Transformed (joules) Time (seconds) This means the more powerful something is, the more energy is transferred every second.
Power Power (watts) = Energy Transformed (joules) Time (seconds) For example: If a bulb transforms 300 J of electrical energy into light in 3 second, the power is: P = Energy Transformed ÷Time P = 300 (J) ÷ 3 (s) P = 100 W
Power in a circuit Power = Current x Potential Difference (watts, W) = (ampere, A) x (volts, V) P = I x V For example: If a bulb has a p.d. across it of 3.0V, and a current flowing through it of 2.0A then the power is: P = I x V P = 2.0 (A) x 3.0 (V) P = 6.0 W
Charge in a circuit Charge = Current x Time (coulomb, C) = (ampere, A) x (seconds, s) For example: How much charge flows if a current of 2.0 A flows for 60 seconds? Charge = Current x Time Charge = 2.0 (A) x 60 (s) Charge = 120 C
Energy in a circuit E nergy Transformed = Potential Difference × Charge (joules, J) = (volts, V) x (coulomb, C) For example: How much energy is transformed when the p.d. is 30V and the charge is 2.0 C? Energy = Potential Difference × Charge Energy = 30 (V) x 2.0 (C) Energy = 60 J
SOUND WAVES Why do car headlights dim when you turn on the ignition? What has this got to do with internal resistance?
Lesson Objectives To understand a method by which internal resistance may be calculated. To analyse and evaluate quantitative data. To develop your scientific approach to carrying out practical work.
Task – To calculate the internal resistance of a power source Physics by Robert Hutchings (the white book) pages 250 – 251 may help. Use the sheet to help you get started. Think about your practical skills.
Candidates should be able to: (a) state Kirchhoff’s second law and appreciate that this is a consequence of conservation of energy; (b) apply Kirchhoff’s first and second laws to circuits; (c) select and use the equation for the total resistance of two or more resistors in series; (d) select and use the equation for the total resistance of two or more resistors in parallel; (e) solve circuit problems involving series and parallel circuits with one or more sources of e.m.f.; (f) explain that all sources of e.m.f. have an internal resistance; (g) explain the meaning of the term terminal p.d.; (h) select and use the equations e.m.f. = I (R + r) = V + Ir.
Kichhoff’s Second Law In any closed loop in a circuit the sum of the e.m.f.s is equal to the sum of the p.d.s. | s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627997501.61/warc/CC-MAIN-20190615222657-20190616004608-00020.warc.gz | CC-MAIN-2019-26 | 6,480 | 24 |
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Ordinary Differential Equations: A Systems Approach - Temple
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https://primes.utm.edu/curios/page.php?number_id=185&submitter=Capelle | math | This number is a prime.
Just showing those entries submitted by 'Capelle': (Click here to show all)
263 is the smallest prime number which is sum of primes beginning and ending with the digit 1. Note that the digit sum of each prime is prime and that the digit sum of 263 is beginning and ending with the digit 1: 263 = 11 + 101 + 151. [Capelle] | s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030334620.49/warc/CC-MAIN-20220925225000-20220926015000-00723.warc.gz | CC-MAIN-2022-40 | 345 | 3 |
https://lnipe.net/questions/1134405-you-and-your-friend-are-splitting-a-restaurant-bill-and-leaving-a-tip-you-pay-half-of-the-bill-plus.html | math | You and your friend are splitting a restaurant bill and leaving a tip. You pay half of the bill plus $5. Your friend pays half of the bill plus 25% of the bill. you and your friend pay the same total amount. How much is half the bill? (a) Write an equation. Let x be the cost of half the bill (b) Solve the equation. Show your work. (c) Check your solution. Show your work. (d) State the solution in complete sentences.
A (pls give me brainliest)
it think the answer is A | s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038066981.0/warc/CC-MAIN-20210416130611-20210416160611-00085.warc.gz | CC-MAIN-2021-17 | 471 | 3 |
https://www.brainpop.com/math/algebra/equationswithvariables/qanda.weml | math | How do you solve an equation that contains a variable?
What is an expression?
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I got a math question like this: N is greater then or equal to 5 but less than 12. How do I solve this question?
What does x equal if x + y = 25?
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https://numbersworksheet.com/dot-to-dot-numbers-1-20-worksheets/ | math | Dot To Dot Numbers 1-20 Worksheets – A Reasonable Figures Worksheet will help your kids become a little more knowledgeable about the ideas powering this rate of integers. With this worksheet, individuals will be able to resolve 12 various issues associated with rational expressions. They will figure out how to multiply several amounts, class them in sets, and figure out their products. They may also exercise simplifying rational expressions. When they have mastered these concepts, this worksheet will certainly be a useful resource for furthering their studies. Dot To Dot Numbers 1-20 Worksheets.
Rational Figures can be a percentage of integers
The two main forms of amounts: irrational and rational. Logical phone numbers are considered whole figures, while irrational figures will not recurring, and get an limitless quantity of numbers. Irrational figures are no-absolutely no, no-terminating decimals, and sq . origins which are not perfect squares. They are often used in math applications, even though these types of numbers are not used often in everyday life.
To establish a logical number, you must understand such a realistic quantity is. An integer is really a whole number, plus a logical variety is a ratio of two integers. The ratio of two integers is the variety on the top divided up through the number at the base. If two integers are two and five, this would be an integer, for example. However, there are also many floating point numbers, such as pi, which cannot be expressed as a fraction.
They may be created in to a portion
A reasonable quantity has a denominator and numerator which are not absolutely nothing. This means that they may be depicted as being a small percentage. Along with their integer numerators and denominators, realistic figures can in addition have a adverse importance. The bad benefit ought to be located to the left of as well as its absolute value is its range from no. To easily simplify this example, we will claim that .0333333 is actually a small fraction which can be written as being a 1/3.
As well as bad integers, a logical variety may also be created in to a small fraction. By way of example, /18,572 is a realistic number, although -1/ is not. Any small percentage composed of integers is rational, given that the denominator fails to include a and might be created as an integer. Likewise, a decimal that ends in a level is yet another rational amount.
They create sense
Despite their name, reasonable numbers don’t make much perception. In math, they may be individual organizations with a exclusive duration around the quantity series. Which means that once we count some thing, we could order the dimensions by its proportion to its unique quantity. This holds correct even though you can find endless realistic phone numbers between two specific figures. If they are ordered, in other words, numbers should make sense only. So, if you’re counting the length of an ant’s tail, a square root of pi is an integer.
In real life, if we want to know the length of a string of pearls, we can use a rational number. To obtain the length of a pearl, as an example, we could matter its size. An individual pearl weighs in at ten kilos, that is a logical number. Furthermore, a pound’s body weight equates to 15 kilograms. Thus, we should be able to break down a lb by ten, without concern yourself with the size of one particular pearl.
They are often expressed being a decimal
If you’ve ever tried to convert a number to its decimal form, you’ve most likely seen a problem that involves a repeated fraction. A decimal amount could be composed as a numerous of two integers, so four times 5 is equal to seven. An identical difficulty necessitates the recurring fraction 2/1, and both sides should be split by 99 to find the correct respond to. But how will you make your conversion process? Below are a few good examples.
A logical number can also be developed in various forms, which include fractions as well as a decimal. A great way to represent a reasonable amount within a decimal is usually to break down it into its fractional comparable. There are three ways to split a rational variety, and each one of these methods brings its decimal equal. One of these brilliant approaches is to split it into its fractional equal, and that’s what’s known as a terminating decimal. | s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947474688.78/warc/CC-MAIN-20240227220707-20240228010707-00724.warc.gz | CC-MAIN-2024-10 | 4,358 | 13 |
https://etc.usf.edu/clipart/43100/43192/pent5_43192.htm | math | Similar Pentagonal Pyramids
Illustration of 2 similar right pentagonal pyramids with hidden edges shown. The height of the pyramid and length of the side of the pentagon (base) on the smaller pentagonal pyramid are one half that of the larger.
Keywordspyramid, double, volume, height, pentagon, triangles, proportion, Polyhedron, Regular, isosceles triangle, solids, triangular faces, one half, proportionate, geometric solid, polyhedrons, proportional, right similar pentagonal pyramids
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http://mathhelpforum.com/algebra/102490-table.html | math | i have a table of numbers, x is from 0 to 10 going up by increments of 1, y is from to 10 to 100 going up in increments of 10.
what is an equation to represent this?
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Try to find a rule that takes the x-value and gives out the y-value. What do you see?
Use this rule to create your equation.
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https://www.hackmath.net/en/math-problem/6753 | math | Find the volume and the surface area of the cube if the area of one of its walls is 40 cm2.
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Solve system of equations: 5x+3y=5 5x+7y=25 | s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986659097.10/warc/CC-MAIN-20191015131723-20191015155223-00302.warc.gz | CC-MAIN-2019-43 | 2,108 | 36 |
https://metaglossary.com/define/multiple+regression+analysis | math | A statistical technique for analyzing the mathematical relationship between two or more variables. One of the variables is called the dependent variable as its values are assumed to depend on changes in the values of the other (one or more) independent (or, explanatory) variables.
Multiple regression analysis (MRA) is a generally accepted statistical technique commonly used in the mass appraisal of property. MRA is used to determine the relationship that exists between property characteristics in determining the anticipated sale price of a property.
a statistical method used with one dependent variable and more than one independent variable. | s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057416.67/warc/CC-MAIN-20210923013955-20210923043955-00646.warc.gz | CC-MAIN-2021-39 | 649 | 3 |
https://repositorioslatinoamericanos.uchile.cl/discover?query=Algebraic+topology&filtertype=type&filter_relational_operator=equals&filter=Art%C3%ADculos+de+revistas | math | Now showing items 1-10 of 134
NATURAL TOPOLOGIES ON COLOMBEAU ALGEBRAS
(JULIUSZ SCHAUDER CTR NONLINEAR STUDIES, 2009)
We define intrinsic, natural and metrizable topologies T(Omega), T, T(s,Omega) and T(s) in G(Omega), (K) over bar, G(s)(Omega) and (K) over bar (s) respectively. The topology T(Omega) induces T, T(s,Omega) and T(s). The ...
Hilbert algebras with a necessity modal operator
(Jagiellonian University, 2014-10)
We introduce the variety of Hilbert algebras with a modal operator , called H -algebras. The variety of H -algebras is the algebraic counterpart of the f!; g-fragment of the intuitionitic modal logic IntK . We will study ...
Spectral-like duality for distributive Hilbert algebras with infimum
Distributive Hilbert algebras with infimum, or DH^-algebras for short, are algebras with implication and conjunction, in which the implication and the conjunction do not necessarily satisfy the residuation law. These ...
ALGEBRAIC AND GEOMETRIC THEORY OF THE TOPOLOGICAL RING OF COLOMBEAU GENERALIZED FUNCTIONS
(CAMBRIDGE UNIV PRESS, 2008)
We continue the investigation of the algebraic and topological structure of the algebra of Colombeau generalized functions with the aim of building up the algebraic basis for the theory of these functions. This was started ...
Tempered generalized functions and Hermite expansions
(Pergamon-elsevier Science LtdOxfordInglaterra, 2011)
Evolution of probability measures by cellular automata on algebraic topological Markov chains
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MV-closures of Wajsberg hoops and applications
In this paper we construct, given a Wajsberg hoop A, an MV-algebra MV(A) such that the underlying set A of A is a maximal filter of MV(A) and the quotient MV(A)/A is the two element chain. As an application we provide a ...
ON TWO-DIMENSIONAL QUASITOPOLOGICAL FIELD THEORIES
(WORLD SCIENTIFIC PUBL CO PTE LTDSingapura, 2009)
We study a class of lattice field theories in two dimensions that includes gauge theories. We show that in these theories it is possible to implement a broader notion of local symmetry, based on semisimple Hopf algebras. ...
Algebra and topology on the Dedekind completion of a totally ordered abelian group
(ELSEVIER SCIENCE BV, 2013)
Algebraic geometry of topological spaces I
(Institut Mittag-Leffler, 2012-09)
We use techniques from both real and complex algebraic geometry to study K-theoretic and related invariants of the algebra C(X) of continuous complex-valued functions on a compact Hausdorff topological space X. For example, ... | s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030338001.99/warc/CC-MAIN-20221007080917-20221007110917-00145.warc.gz | CC-MAIN-2022-40 | 2,541 | 26 |
https://www.doubtnut.com/question-answer/if-int0xxdxint0x-xdxx-in-integer-where-and-denotes-the-greatest-integer-and-fractional-parts-respect-644012157 | math | Updated On: 6-5-2021
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|00:00 - 00:59||hello students today aur question is if integration 0 2 X greatest integer function of X into DX is equal to zero to greatest integer function of X Into X into DX where are you doesn't belong 20 where this and this is not the greatest integer function and fractional part of the respectively then the value of 4 into fractional part of X is equals to so we have to find this so we can write a integration 0 2x and greatest integer function of X is equals to we can write here this is 0 to 10 X + 12 2nd year arts and here we have taken x0x one and their access to 23 so be taken to into DX and this is|
|01:00 - 01:59||new aap to x minus 1 and here is X so we get x minus 1 year so we get x minus 1 into DX so now we can write we can write integration of integration of x to DX is equal to zero 2 by taking right and this side of by taking this is our elders this is Rs so this will zero to greatest integer function X Into X into DX so this will = 2 x square x square divided by x divided by 2|
|02:00 - 02:59||and here is greatest integer function X and Y = 2 dismil = 2 greatest integer function of x power 2 and this is divided by 2 minus zero from here we get greatest integer function square divided by these all times are equal so from here we can write one plus DL 20 plus one plus into minus 1 into 2 - 1 + 2 into 3 - 2 + 3 into 4 - 3 and this is continue up to|
|03:00 - 03:59||greatest integer function X here is greatest integer function x minus greatest integer function of X is equals to greatest integer function of x square - 2 year is greatest integer function and this is my plus one here as in all terms we added so that this is + 8 so we can write it as X + 1 - greatest integer function of X is equals to greatest integer function of x square divided by 2 from here we can ride 123 this is information 123 and this is up to x minus 1 equals to greatest integer function of x square|
|04:00 - 04:59||Tu so from here we know that some of the natural numbers is equals to and into an + 1 divided by 2 from here we can write X this is our hand and hour access the greatest integer function of 2 - + greatest integer function of X into fractional part of X and this will cause 2 x square divided by 2 from here by taking this function greatest integer function common so we get X + 1 + X and this is divided by 2 this is fractional part and this is equals to greatest integer function square - / to so this will cancel out here so we left will greatest integer function this is minus 9 plus so we can|
|05:00 - 05:59||corrected so this is my Naseer from here we get -6 greatest integer function of 1 -2 and fractional part of x = 2 X this is a greatest integer function so this will / to so on solving this we get by taking to as LCM so we get greatest integer function - 2 + 2 time of fractional part and this will cause 2x and two and two will be cancel out here now we get greatest integer function is also cancel out so we get -1 this will cancel out so fractional X is equals to zero from here to time of X is equals to 1|
|06:00 - 06:59||so from here we can ride for time of the time of greatest integer function is equals to 2 into 1 2 decimal = 22 so this is our answer thank you|
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Bihar UGEAC 2021: Register for Mop-up counselling online. Candidates will be able to apply till 7th December in online mode. Check complete details here. | s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964363520.30/warc/CC-MAIN-20211208175210-20211208205210-00181.warc.gz | CC-MAIN-2021-49 | 4,258 | 19 |
https://justaaa.com/physics/565769-a-bright-star-20-light-years-away-emits-violet | math | A bright star 20 light-years away emits violet light with wavelength of 380 nm as seen from the earth. A spaceship is covered with tinanium on its surface, whose work function is 4.3 eV.
a) When the spaceship is stationed on earth, determine whether photoelectrons are ejected from the spaceship due to the violet starlight. If so, compute their maximum kinetic energy.
b) The spaceship has just departed earth (with negligible travel distance so far) and is flying towards the star at a speed of 0.8 c. Calculate the maximum kinetic energy of the photoelectrons ejected from the spaceship as measured by the pilot of the spaceship.
c) If the pilot performs an experiment with these photoelectrons during a spacewalk near her spaceship, what is the probability for the most energetic photoelectrons to penetrate a 10 eV energy barrier that is 1 nm thick?
d) One of the most energetic photoelectrons is shooting precisely towards the star. In the reference frame of this electron, how long does it take (for the electron itself) to reach the star?
e) When this electron is arriving on the star, an alien there performs the same experiment as in part (c), using his 10 eV energy barrier that is 1 nm thick, what is the probability for the electron to penetrate that barrier?
1eV = 1.6×10−19 J
h = 6.626×10^−34 J· s = 4.135×10^−15 eV·s
h ̄ = 1.05×10^−34 J·s = 6.6×10^−16 eV·s
hc = 1240 nm · eV
me = 0.511 MeV – mass of the electron
KT = 1/40 eV at room temperature
E1 = −13.6 eV – ground state of the Hydrogen atom
a0 = 0.053 nm – radius of the Hydrogen atom in its ground state
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https://calculators.io/permutation/ | math | A permutation calculator is a handy tool which helps you find out how many permutations a given set has. Permutation is often symbolized as nPr which we will also use in this article. Let’s cover how to use this permutation formula calculator, how to calculate permutation without an nPr calculator, and more.
How to use the permutation calculator?
This permutation calculator is simple, easy to understand, and extremely easy to use too. All you have to do is input 2 values and it will do the calculation for you.
This online tool is just as useful as a permutations and combinations calculator which provides you with both the permutations and the combinations of a given set. Here are the steps to follow for this calculator:
- First, enter the value of the Number of Objects (n) in the appropriate field.
- Then enter the value of the Sample Size (r) in the appropriate field.
- After entering both values, the permutation formula calculator automatically generates the value of the Permutations of the set for you.
How do you calculate a permutation?
Permutation or nPr refers to the number of ways by which you can select r elements out of any given set containing n distinct objects. Unlike combinations, when it comes to permutations, the order of selecting the elements has relevance.
For instance, let’s assume that you have a whole deck of cards which have numbers from 1-9. Select 3 cards from the deck randomly then place them on a table in a line to create a number with 3-digits. For these three cards, how many different numbers can you come up with?
The good news is that you don’t have to list down all of the possible 3-digit numbers in such a case. You can either use the nPr calculator or the permutation formula if you want to perform the calculation manually. Either of these allows you to calculate the number of permutations easily. Here is the formula:
P(n,r) = n!/(n-r)!
p refers to the number of permutations
n refers to the total number of elements in a given set
r refers to the number of elements you select from the given set
The exclamation point in the equation represents a factorial. If you need to learn more about factorials or you need to perform factorial calculations, check out the factorial calculator.
As you can see in the permutation formula, the number of permutations for when you select a single element is n. On the other hand, if you need to select all of the elements, you must modify the formula slightly. Therefore, the formula becomes:
To help you understand this better, let’s go back to our earlier example. Let’s apply the formula to our situation with the deck of cards. In this case, you must solve for the number of ways to select 3 cards out of the total 9. Replace the numbers in the equation:
P(9,3) = 9!/(9-3!) = 9!/6! = 504
After performing the calculation, you can check the accuracy using the permutation calculator. Then keep using this formula every time you need to calculate permutations manually in any given situation.
What is the formula for nPr?
As aforementioned, permutation and nPr mean the same thing. nPr is the symbolic representation of permutation. This means that the formula for nPr is the same as the formula for permutations which is:
P(n,r)=n!(n−r)! for n ≥ r ≥ 0
By definition, permutations refer to how many ways you can get n ordered subsets of elements r from a set of elements n. Permutations differ from combinations because of the significance of the order of the elements. The permutation of n elements taken r at a time also means the number of ways that you can order r objects you selected from distinct n objects in a set.
In mathematics, it’s denoted as the r at the bottom-right corner and n at the top-left corner of P. This is why another common form of notation of permutation is P(n,r) as seen in the permutation formula. When you use the basic principle of counting, you will be more familiar with the symbol P(n,r) which is a closed expression.
Let’s have another example to help you understand the nPr formula further. Let’s assume that you have r places. For the first place, you can fill it by selecting any of the n elements and putting them in this place. For these elements in the first place, you can arrange them in n ways.
Since you’ve already filled the first place, you now have n-1 elements remaining. Now you can select elements from any of the n-1 elements left for the second place. Again, you can arrange the elements in the second place in n number of ways.
Keep going until you’ve filled the nth place or until you run out of elements. In doing this, you will observe something interesting:
For the first place, n=n−(1–1) ways
For the second place, n−1=n−(2–1) ways
For the third place: n−2=n−(3–1) ways, and so on
As you can see, this progression suggests that you can fill up the rth place in n−(r−1)=n−r+1 ways.
Since these events occur all at the same time or simultaneously, the total number of arrangements possible is the product of how many ways there are to fill each individual r place. To close this expression, multiply then divide it by (n-r)!. Obviously, the numerator then becomes n!. This is why the equation for permutation is:
What is the difference between nCr and nPr?
While both nCr and nPr are quantities in statistics which refer to possible subsets of a given set of objects, they aren’t totally identical. First, they have different formulas which are:
When you use sets to define these statistical quantities, nPr refers to the formula to solve for permutations of n elements which you take r at a time. Here, the arrangement or order of the elements matters. For nCr, this refers to combinations wherein you don’t take into consideration the arrangement or order of the elements. | s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100525.55/warc/CC-MAIN-20231204052342-20231204082342-00749.warc.gz | CC-MAIN-2023-50 | 5,786 | 36 |
https://intlpress.com/site/pub/pages/journals/items/ajm/content/vols/0012/0003/a005/index.php | math | Asian Journal of Mathematics
Volume 12 (2008)
Dissipative Hyperbolic Geometric Flow
Pages: 345 – 364
In this paper we introduce a new kind of hyperbolic geometric flows - dissipative hyperbolic geometric flow. This kind of flow is defined by a system of quasilinear wave equations with dissipative terms. Some interesting exact solutions are given, in particular, a new concept - hyperbolic Ricci soliton is introduced and some of its geometric properties are described. We also establish the short-time existence and uniqueness theorem for the dissipative hyperbolic geometric flow, and prove the nonlinear stability of the flow defined on the Euclidean space of dimension larger than 2. Wave character of the evolving metrics and curvatures is illustrated and the nonlinear wave equations satisfied by the curvatures are derived.
Dissipative hyperbolic geometric flow, quasilinear wave equation, hyperbolic Ricci soliton, short-time existence, nonlinear stability
2010 Mathematics Subject Classification
Published 1 January 2008 | s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947474569.64/warc/CC-MAIN-20240224212113-20240225002113-00634.warc.gz | CC-MAIN-2024-10 | 1,032 | 8 |
https://stream.syscoi.com/2020/10/08/what-is-ergodicity-lars-p-syll/ | math | What is ergodicity?
Why are election polls often inaccurate? Why is racism wrong? Why are your assumptions often mistaken? The answers to all these questions and to many others have a lot to do with the non-ergodicity of human ensembles. Many scientists agree that ergodicity is one of the most important concepts in statistics. So, what is it?
Suppose you are concerned with determining what the most visited parks in a city are. One idea is to take a momentary snapshot: to see how many people are this moment in park A, how many are in park B and so on. Another idea is to look at one individual (or few of them) and to follow him for a certain period of time, e.g. a year. Then, you observe how often the individual is going to park A, how often he is going to park B and so on.
Thus, you obtain two different results: one statistical analysis over the entire ensemble of people at a certain moment in time, and one statistical analysis for one person over a certain period of time. The first one may not be representative for a longer period of time, while the second one may not be representative for all the people.
The idea is that an ensemble is ergodic if the two types of statistics give the same result. Many ensembles, like the human populations, are not ergodic.
continues in source:What is ergodicity? | LARS P. SYLL | s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057274.97/warc/CC-MAIN-20210921221605-20210922011605-00391.warc.gz | CC-MAIN-2021-39 | 1,331 | 6 |
https://www.physicsforums.com/threads/multiplying-polynomials-to-find-values-of-k.607913/ | math | 1. The problem statement, all variables and given/known data Find the value or values of k that make the equation true. 2. Relevant equations Starting Equation: (2x + k)(x - 2k) = 2x2 + 9x - 18 3. The attempt at a solution (2x + k)(x - 2k) = 2x2 + 9x - 18 2x2 - 3xk - 2k2 = 2x2 + 9x - 18 <- I just foiled the left side Sadly enough, this is where I got stuck. I'm currently reviewing for my final, and this is what we went over at the very beginning of the quarter, so these types of problems aren't very fresh in my mind. The book isn't helpful at all because all it explains how to do is multiply binomials, and doesn't elaborate on anything beyond that. My teacher, who was short on time when I asked, said that I either needed to factor the right side to get both sides to be similar, or FOIL the left side to get both sides similar, but either he didn't explain it well enough or it didn't click for me on what to do next to solve for k. Any help would be appreciated, thanks. | s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267160400.74/warc/CC-MAIN-20180924110050-20180924130450-00068.warc.gz | CC-MAIN-2018-39 | 981 | 1 |
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Feel free to contact me via deviantart note or profile comment and send me your ideas. Feel free to attach whatever you need. I will answer as soon as possible! | s3://commoncrawl/crawl-data/CC-MAIN-2017-26/segments/1498128321309.25/warc/CC-MAIN-20170627101436-20170627121436-00344.warc.gz | CC-MAIN-2017-26 | 1,765 | 38 |
http://www.semanarioangolense.net/course-1-chapter-10-volume-and-surface-area-chapter-quiz/ | math | Vocabulary Words and Definitions List. Olivia is placing a gift inside a box that measures 15 centimeters by 8 centimeters by 3 centimeters.
Find the volumes of non-rectangular shapes including cylinders pyramids cones.
Course 1 chapter 10 volume and surface area chapter quiz. Syllabus reference MS522 MS531 WM. Chapter 10 Quiz 1 Review and Reflection. Course 1 Chapter 10 Volume and Surface Area 235.
A prism that has rectangular bases. 9 cm 11 cm Round to the nearest tenth. In this chapter you will learn.
A special box designed to hold an antique artifact is shaped like a triangular prism. Check your level of practice and understand where you stand in your preparation. Learn vocabulary terms and more with flashcards games and other study tools.
These sheets will certainly maintain preschoolers active as well as involved for a long period of time. What is the slant height of the pyramid. Surface Area and Volume.
Find the volume of the triangular prism. The surface area of the pyramid below is 175 square meters. 3768 m 2 12.
A pyramid has all sides that are equilateral triangles. Surface Area and Volume. Lesson 2 – Volume of Triangular prisms.
118692 cm 2 9. Use 314 for π. Surface Area and Volume Chapter 10 Summary and Practice Problems.
102 Lesson and Opener. Volume and Surface Area. Course 1 Chapter 10 Volume and Surface Area Chapter 10 Extra Practice Answers Lesson 10-1 1.
628 cm 2 11. SLO 101 I can find the volume of 3D shapes including cylinders cones pyramids and spheres. The height of the ramp is 12 meters.
One of the two parallel congruent faces of a prism. 8 mm Lesson 10-2 1. Lesson 5 – Surface Area of Pyramids.
What is the volume of the prism in cubic inches. Volume and Surface Area. Lesson 3 – Surface Area of Rectangular prisms.
2512 in 2 5. Here are extra practice problems by section including examples. Triangle and Trapezoid Area.
Start studying Course 1 Chapter 10 Vocabulary – Volume and Surface Area. 101 Lesson and Opener. 10362 in 2 13.
A rectangular prism has a length of 2 feet a width of 4 feet and a height of 6 inches. What is the volume of the cylinder. A prism that has triangular bases.
_____ 238 Course 1 Chapter 10 Volume and Surface Area Boxes of Popcorn Box Length in Width in Height in A 8 1 2. The Volume Surface Area chapter of this Glencoe Math Companion Course helps students learn the essential lessons associated with volume and surface area. 101 Classwork and Closer.
Then fill in the correct answer on the answer sheet provided by your teacher or on a sheet of paper. Start studying Course 1 – Chapter 10. Volume Surface Area 6G2 6G4.
FREE Course 1 Chapter 10 Volume And Surface Area Answer Key 6Th Grade. 135648 m 2 15. Course 1 Chapter 10 Volume And Surface Area Answer Key DOWNLOAD Course 1 Chapter 10 Volume And Surface Area Answer Key.
Found 5440 results for. The surface area of the box is 4392 square inches. A figure with length width and height.
On this page you will find additional support and information relating to this chapter in Math 8. Used to measure volume. Surface Area of Triangular Prisms.
Course 1 Volume and Surface Area Write the letter for the correct answer in the blank at the right of each question. Lesson 4 – Surface Area of Triangular prisms. Course 1 Chapter 10 Vocabulary – Volume and Surface Area 12 Terms.
Course 1 – Ch10 – Volume Surface Area. NAME DATE Test Form 2B continued 6. 2512 m 2 2.
Tell how many cubes of a certain size it will take to fill a three-dimensional figure. Cylinders Volume and Surface. McGraw-Hill Math Course 1Chapter 10 vocabulary.
Area of Triangles and Trapezoids. Online Textbook Lesson 1. Volume of Rectangular Prisms.
70336 ft 2 7. 60288 cm 2 14. Course 1 Chapter 10 Volume And Surface Area Worksheet Answers Comply with these steps to create free printable worksheets for your youngsters.
Learn vocabulary terms and more with flashcards games and other study tools. Pat has four rectangular baking pans. The point where three or more faces meet.
52752 m 2 10. Flashcards vocabulary wordsdefinitions practice Comments. Find the volume and surface area of the prism.
Lesson 1 – Volume of Rectangular prisms. What is the surface area of the box. The sum of the areas of all the surfaces of a 3D figure.
102 Classwork and Closer. Terms in this set 12. What is the surface area of a cylinder with a radius of 2 feet and a.
After completing this chapter you should be able to. Lesson 1 Homework. Chapter 10 Chapter 10 This chapter deals with surface area and volume of right solids and pyramids.
Math Connects Coarse two Chapter 10 Vocab 14 Terms. S521S525 S531S535 Surface Area and Volume Surface Area and Volume find the surface area of right cylinders calculate the volume of composite solids use the fact. Find surface areas of cylinders and pyramids.
Chapter 10 Surface Area and Volume Answer Key CK-12 Middle School Math Concepts – Grade 7 3 106 Surface Area of Cylinders Answers 1. 115 5 16 m 3 4. Course 1 – Chapter 10.
Chapter Test Study Guide. Course 1 Chapter 10 Volume and Surface Area 236 11. 60288 in 2 4.
RECREATION The base of a skateboard ramp has an area of 23 square meters. Find the cube root of a number. Chapter 10 – Volume Surface Area.
7536 cm 2 3. Volume Surface Area 6G2 6G4 12 Terms. 471 in 2 6.
1570 m 2 8. Which of the pans has the eatest volume. Step by Step Solutions is provided so that you can get to know the concepts better.
222 Course 1 Chapter 10 Volume and Surface Area Chapter Quiz. 224 Course 1 Chapter 10 Volume and Surface Area Standardized Test Practice Read each question. Lesson 3 Extra Practice. | s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662561747.42/warc/CC-MAIN-20220523194013-20220523224013-00190.warc.gz | CC-MAIN-2022-21 | 5,597 | 38 |
https://homework.cpm.org/category/ACC/textbook/acc6/chapter/3%20Unit%203/lesson/CC1:%203.1.6/problem/3-88 | math | Find the area and perimeter of the shape.
The area is the space inside the drawing.The perimeter is the length around the edges.
Draw a Base Ten Block shape with a value of
using the fewest number of blocks possible. Find the perimeter of the shape that you drew.
blocks if you use the fewest blocks possible. | s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947474541.96/warc/CC-MAIN-20240224144416-20240224174416-00894.warc.gz | CC-MAIN-2024-10 | 309 | 5 |
https://educatorpages.com/site/nierer/pages/67612 | math | ------Second Marking Period (10/21/10-)Homework------
HW# 23: Complete "Create-a-Sonnet" handout (grey)
HW# 22: Read "This Quiet Dust" by Emily Dickinson and "The Dead" by Rupert Brooke. In your notebook compare and contrast the images, themes, structure, etc. in 1-2 paragraphs or in a Venn Diagram or in pictures.
HW# 21: Choose a character from the play you feel would benefit from therapy. Write a dialogue between that character and the therapist. It must be at least 2 sides of looseleaf. If you choose a character that died by the end of the play be sure to use onl information up to the person's demise...no ghosts in the therapist's office!
Use Acts 1-4 only. Imagine you are either Othello or Desdemona. Write a letter to a newspaper advice columnist about the problems in his/her marriage and then ask for help. EC--write the advice columnist's response.
Create a poem or draw a picture that you feel appropriately depicts the feelings of Othello, Desdemona or both at the end of Act 4. EC--write a poem and draw a pic.
HW# 19: Read "Death the Leveller" by James Shirley. In your notebook answer the following questions.
1. What is meant by the term leveller?
2. Explain in detail and use direct reference to the poem to show how each stanza of the poem (there are three octets) proves the validity of the title.
HW# 18: Read "Death Be Not Proud" by John Donne. In your notebook, create a paragraph that explains how the poem shows the poet's belief that Death is not the ultimate power in the universe.
HW# 17: In your notebook create a Venn Diagram or write 2-3 paragraphs to completely compare and contrast poetry, plays and novels.
HW# 16: Complete biopoem handout (pink)
HW# 15: In your notebook, list the description for each of the following types of poems:
HW# 14: Complete poetric terms worksheet (yellow)
------First Marking Period (9/8/10-10/20/10) Homework------
HW# 13: Define vocabulary words for Acts 4 & 5 on loose-leaf (or typed on typing paper)
HW# 12: Read Act 5 of Othello. In your notebook, answer the following questions completely and use specicif references to the text (Act, scene line(s))
- Which characters die? How does each die?
- Ultimately, how is Iago responsible for all the deaths?
- Do you think the | s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320302715.38/warc/CC-MAIN-20220121010736-20220121040736-00430.warc.gz | CC-MAIN-2022-05 | 2,245 | 20 |
http://www.chegg.com/homework-help/college-physics-a-strategic-approach-with-masteringphysics-2nd-edition-chapter-9-problem-71gp-solution-9780321595485 | math | Let puck circulating with velocity v in a path of radius r
Centrifugal force acting on the puck of mass m is given by,
Weight of the hanging objects is
The centrifugal force acting on the puck will support the hanging weight at the center of the table.
Solve for v | s3://commoncrawl/crawl-data/CC-MAIN-2016-07/segments/1454701164289.84/warc/CC-MAIN-20160205193924-00217-ip-10-236-182-209.ec2.internal.warc.gz | CC-MAIN-2016-07 | 264 | 5 |
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Login/register with FaceBook! | s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917118552.28/warc/CC-MAIN-20170423031158-00280-ip-10-145-167-34.ec2.internal.warc.gz | CC-MAIN-2017-17 | 507 | 15 |
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http://nrich.maths.org/public/leg.php?code=5039&cl=2&cldcmpid=2914 | math | It's easy to work out the areas of most squares that we meet, but
what if they were tilted?
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?
This rectangle is cut into five pieces which fit exactly into a triangular outline and also into a square outline where the triangle, the rectangle and the square have equal areas.
A tilted square is a square with no horizontal sides. Can you
devise a general instruction for the construction of a square when
you are given just one of its sides?
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
Can you make a right-angled triangle on this peg-board by joining up three points round the edge?
Can you locate the lost giraffe? Input coordinates to help you
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Interactive game. Set your own level of challenge, practise your table skills and beat your previous best score.
The number of plants in Mr McGregor's magic potting shed increases
overnight. He'd like to put the same number of plants in each of
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Can you create a story that would describe the movement of the man
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Use the interactivity to move Mr Pearson and his dog. Can you move
him so that the graph shows a curve?
Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects the distance it travels at each stage.
Experiment with the interactivity of "rolling" regular polygons,
and explore how the different positions of the red dot affects its
vertical and horizontal movement at each stage.
You can move the 4 pieces of the jigsaw and fit them into both
outlines. Explain what has happened to the missing one unit of
What shaped overlaps can you make with two circles which are the
same size? What shapes are 'left over'? What shapes can you make
when the circles are different sizes?
Two engines, at opposite ends of a single track railway line, set
off towards one another just as a fly, sitting on the front of one
of the engines, sets off flying along the railway line...
Can you find a relationship between the number of dots on the
circle and the number of steps that will ensure that all points are
Can you explain the strategy for winning this game with any target?
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
7 balls are shaken in a container. You win if the two blue balls
touch. What is the probability of winning?
Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.
We can show that (x + 1)² = x² + 2x + 1 by considering
the area of an (x + 1) by (x + 1) square. Show in a similar way
that (x + 2)² = x² + 4x + 4
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
A game for two or more players that uses a knowledge of measuring
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Do you know how to find the area of a triangle? You can count the
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Six balls of various colours are randomly shaken into a trianglular
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Carry out some time trials and gather some data to help you decide
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An interactive game to be played on your own or with friends.
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Two circles of equal radius touch at P. One circle is fixed whilst the other moves, rolling without slipping, all the way round. How many times does the moving coin revolve before returning to P?
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Use the interactivity to make this Islamic star and cross design.
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Hover your mouse over the counters to see which ones will be
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Mo has left, but Meg is still experimenting. Use the interactivity
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Show how this pentagonal tile can be used to tile the plane and
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Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
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Start by putting one million (1 000 000) into the display of your
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Can you beat the computer in the challenging strategy game?
Can you find all the 4-ball shuffles?
Cut four triangles from a square as shown in the picture. How many
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Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Can you put the numbers 1 to 8 into the circles so that the four
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Use the blue spot to help you move the yellow spot from one star to
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Can you make the green spot travel through the tube by moving the
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A simulation of target archery practice | s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463609598.5/warc/CC-MAIN-20170528043426-20170528063426-00472.warc.gz | CC-MAIN-2017-22 | 6,844 | 93 |
https://www.lessonplanet.com/teachers/part-3-of-the-fundamental-theorem-of-calculus | math | Part 3 of the Fundamental Theorem of Calculus
In this Fundamental Theorem of Calculus worksheet, students find the solution of given functions. This one-page worksheet contains five problems.
3 Views 0 Downloads
Nine Definite Integrals and Fundamental Theorem Of Calculus Problems
In this definite integral instructional activity, student find the value of five definite integrals. Student then explain why a definite integral inequality holds true. Finally, students are given the graph of a functions and asked to...
11th - Higher Ed Math
Introduction to Calculus
This heady calculus text covers the subjects of differential and integral calculus with rigorous detail, culminating in a chapter of physics and engineering applications. A particular emphasis on classic proof meshes with modern graphs,...
11th - Higher Ed Math CCSS: Adaptable
Calculus - Early Transcendentals
This textbook takes the learner from the basic definition of slope through derivatives, integrals, and vector multivariable calculus. Each section is composed primarily of examples, with theoretical introductions and explanations in...
9th - Higher Ed Math CCSS: Adaptable
The Second Fundamental Theorem of Calculus
How many fundamental theorems are there? The Second Fundamental Theorem of Calculus is also known as the second part of the Fundamental Theorem of Calculus. Here's a video that introduces the theorem as the method to evaluate a definite...
2 mins 11th - Higher Ed Math | s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463608642.30/warc/CC-MAIN-20170526051657-20170526071657-00208.warc.gz | CC-MAIN-2017-22 | 1,461 | 15 |
http://www.brighthubeducation.com/homework-math-help/99982-factor-trees-in-math/ | math | Building the Factor Tree
So let's go through the process of creating the factor tree for the number 24. To start, write down 24 on a piece of paper (leave plenty of room on either side) and circle it. The circle shows that this is actually the node of a tree; lines between nodes will are called edges of the tree.
The first prime number is two. Two divides evenly into 24 (that is, 24 divided by 2 has no remainder), so write two underneath 24 and to the left. 24 divided by 2 is 12, so write 12 to the right of the two. Circle both numbers and draw an edge from each new circle up to the circle containing the 24. Your drawing should look like the top section of the picture at right.
Now, we go down to the 12. Twelve is also divisible by two, so we put another two underneath it, along with a six, which is the quotient of twelve and two. Six is also divisible by two, so underneath the six we put a two and a three.
Three is not divisible by two, which means we need to try the next prime number. The smallest prime number after two is three; in other words, the current value is already prime, so we're done. Since the current node (each circled number is called a node of the tree) is prime, every leaf (a node with no children, that is, no nodes hanging from it) of the tree is prime, and we are done. By reading off all the leaves, we can see that 24 = 2 x 2 x 2 x 3. | s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560280587.1/warc/CC-MAIN-20170116095120-00478-ip-10-171-10-70.ec2.internal.warc.gz | CC-MAIN-2017-04 | 1,376 | 5 |
https://www.clubdeski.it/science-books/mathematics/13635-elementary-linear-algebra-and-its-applications-james-w-daniel-ebook.html | math | Fb2 Elementary Linear Algebra and Its Applications ePub
by James W. Daniel
|Author:||James W. Daniel|
|Publisher:||Prentice Hall (June 1, 1981)|
|Fb2 eBook:||1516 kb|
|ePub eBook:||1855 kb|
|Digital formats:||lit lrf doc txt|
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Elementary Linear Algebra with Applications. Linear Algebra and Its Applications. 05 MB·8,997 Downloads. Student solutions manual. Elementary Linear Algebra with Applications. 66 MB·45,269 Downloads. 04 MB·3,794 Downloads. Department of Mathematics and Computer Science. La Salle University Elementary Linear.
Elementary Linear Alge. by James W. Daniels and James W. Daniel. More by James W. Computation and Theory in Ordinary Differential Equations (A Series of books in mathematics). Ramon E. Moore, James W.
James W Daniel (Daniel, James W). used books, rare books and new books. Elementary Linear Algebra and Its Applications: ISBN 9780132582933 (978-0-13-258293-3) Hardcover, Prentice Hall, 1981. Masonic Networks and Connections. Find all books by 'James W Daniel' and compare prices Find signed collectible books by 'James W Daniel'. Applied linear algebra. ISBN 9780130412607 (978-0-13-041260-7) Softcover, Pearson, 1987. ISBN 9780955843709 (978-558437-) Softcover, The Library and Museum of Freemasonry, 2007.
Linear Systems and Invertible Matrices 61 . Diagonal, Triangular, and Symmetric Matrices 67 . Matrix Transformations 75 . Applications of Linear Systems 84, Network Analysis (Traffic Flow) 84, Electrical Circuits. Applications of Linear Systems 84, Network Analysis (Traffic Flow) 84, Electrical Circuits 86, Balancing Chemical Equations 88, Polynomial Interpolation 91 . 0 Application: Leontief Input-Output Models 96 C HA PT E R 2 Determinants 105 . Determinants by Cofactor Expansion.
Applications of Linear Systems. Shed the societal and cultural narratives holding you back and let free step-by-step Elementary Linear Algebra textbook solutions reorient your old paradigms. NOW is the time to make today the first day of the rest of your life. Unlock your Elementary Linear Algebra PDF (Profound Dynamic Fulfillment) today. YOU are the protagonist of your own life. Let Slader cultivate you that you are meant to be!
For courses in linear algebra
For courses in linear algebra. With traditional linear algebra texts, the course is relatively easy for students during the early stages as material is presented in a familiar, concrete setting. However, when abstract concepts are introduced, students often hit a wall. Instructors seem to agree that certain concepts (such as linear independence, spanning, subspace, vector space, and linear transformations) are not easily understood and require time to assimilate
Elementary linear algebra: solutions to problems. Applied numerical linear algebra. Numerical Linear Algebra and Applications in Data Mining. Elden L. Download (PDF).
Elementary linear algebra: solutions to problems. Download (DJVU). Читать.
The aim is to present the fundamentals of linear algebra in the clearest possible way; pedagogy is the main consideration. There are now more than 150 versions of his books in print, including translations into Spanish, Arabic, Portuguese, French, German, Chinese, Japanese, Hebrew, Italian, and Indonesian. He was awarded a Textbook Excellence Award in 1994 by the Textbook Authors Association, and in 2011 that organization awarded his Elementary Linear Algebra text its McGuffey Award. | s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662521041.0/warc/CC-MAIN-20220518021247-20220518051247-00478.warc.gz | CC-MAIN-2022-21 | 3,458 | 18 |
https://www.physicsforums.com/threads/natural-convection-question.225587/ | math | 1. The problem statement, all variables and given/known data What is the heat transfer from a 60W electric light bulb at 127C to the stagnant air in a room at 27C. Approximate the bulb to a 50mm diameter sphere. What percentage of the power is lost by free convection? 2. Relevant equations Nu=2 + 0.6(Gr^1/4)(Pr^1/3) Gr=(g[tex]\beta[/tex][tex]\theta[/tex]d^3)/[tex]\nu[/tex]^2 Nu=hd/k 3. The attempt at a solution I started by working out the Grasshof no. with [tex]\nu[/tex] at 27C= 1.568x10^-5m^2/s, [tex]\beta[/tex]=1/T = 1/27, [tex]\theta[/tex] = 100 to be Gr = 1.8x10^7. Pr = 0.707 therefore Nu = 21.702, using the relationship above. substitute this into Nu = hd/k and h= 1.139x10^-5kW/m^2K the area of a sphere = 4(pi)r^2= 7.854x10^-3 so finally Q=hAdT left me with 8.945x10^-3W which is 0.014% of the power being lost by free convection. this appears to be out by a factor of 100, but that could just be a coincidence, meaning that im totally wrong. Can anyone assist? | s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257647600.49/warc/CC-MAIN-20180321082653-20180321102653-00187.warc.gz | CC-MAIN-2018-13 | 977 | 1 |
https://vivo.library.tamu.edu/vivo/display/n177449SE | math | On approximate stochastic control in genetic regulatory networks.
- Additional Document Info
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The control of probabilistic Boolean networks as a model of genetic regulatory networks is formulated as an optimal stochastic control problem and has been solved using dynamic programming; however, the proposed methods fail when the number of genes in the network goes beyond a small number. There are two dimensionality problems. First, the complexity of optimal stochastic control exponentially increases with the number of genes. Second, the complexity of estimating the probability distributions specifying the model increases exponentially with the number of genes. We propose an approximate stochastic control method based on reinforcement learning that mitigates the curses of dimensionality and provides polynomial time complexity. Using a simulator, the proposed method eliminates the complexity of estimating the probability distributions and, because the method is a model-free method, it eliminates the impediment of model estimation. The method can be applied on networks for which dynamic programming cannot be used owing to computational limitations. Experimental results demonstrate that the performance of the method is close to optimal stochastic control.
author list (cited authors)
Faryabi, B., Datta, A., & Dougherty, E. R.
complete list of authors
Faryabi, B||Datta, A||Dougherty, ER | s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100508.23/warc/CC-MAIN-20231203125921-20231203155921-00397.warc.gz | CC-MAIN-2023-50 | 1,410 | 8 |
http://tex.stackexchange.com/questions/tagged/cards+poetry | math | TeX - LaTeX
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cc by-sa 3.0 | s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1394011278661/warc/CC-MAIN-20140305092118-00009-ip-10-183-142-35.ec2.internal.warc.gz | CC-MAIN-2014-10 | 2,328 | 55 |
https://opiatalk.com/what-is-the-graeco-latin-square-design/ | math | What is the Graeco-Latin square design?
A Graeco-Latin square design is a design of experiment in which the experimental units are grouped in three different ways. It is obtained by superposing two Latin squares of the same size. If every Latin letter coincides exactly once with a Greek letter, the two Latin square designs are orthogonal.
How do you randomize Latin square designs?
The ideal randomization would be to select a square from the set of all possible Latin squares of the specified size. However, a more practical randomization scheme would be to select a standardized Latin square at random (these are tabulated) and then: randomly permute the columns, randomly permute the rows, and then.
Why we use Graeco-Latin square design?
Graeco-Latin squares, as described on the previous page, are efficient designs to study the effect of one treatment factor in the presence of 3 nuisance factors. They are restricted, however, to the case in which all the factors have the same number of levels.
How do you solve a Latin square?
How to solve a latin square? The resolution algorithm consists in noting, for each unfilled cell, the list of possible symbols respecting the rules (prohibition of 2 identical symbols on the same line or the same column), if only one symbol among the N is possible then fill in the cell with this symbol.
What are the disadvantages of a latin square design?
Disadvantages of latin square designs 1. Number of treatments is limited to the number of replicates which seldom exceeds 10. 2. If have less than 5 treatments, the df for controlling random variation is relatively large and the df for error is small.
What are the advantages of latin square design?
The advantages of Latin square designs are:
- They handle the case when we have several nuisance factors and we either cannot combine them into a single factor or we wish to keep them separate.
- They allow experiments with a relatively small number of runs.
What are the disadvantages of latin square design?
What is a balanced Latin square?
Balanced Latin Squares (the ones generated above) are special cases of Latin Squares which remove immediate carry-over effects: A condition will precede another exactly once (or twice, if the number of conditions is odd).
Is latin square a factorial design?
The latin square design only permits three main effects to be estimated because the design is incom- plete. It is an “incomplete” factorial design because not all cells are represented. The signature of a latin square design is that a given treatment of interest appears only once in a given row and a given column.
What are the disadvantages of a Latin square design?
On what basis Latin square design is selected?
A Latin square design is the arrangement of t treatments, each one repeated t times, in such a way that each treatment appears exactly one time in each row and each column in the design. We denote by Roman characters the treatments. Therefore the design is called a Latin square design.
How to choose a Graeco-Latin square design?
For example, one recommendation is that a Graeco-Latin square design be randomly selected from those available, then randomize the run order. Graeco-Latin Square Designs for 3-, 4-, and 5-Level Factors
How to create graeco latin squares using genetic algorithms?
Graeco Latin squares have a wide number to facilitate calculations and performing genetic variety of applications in many areas of science. operators. This number consists of 2 sections. Section 1 is the ordinal number of Latin square, for example A=1, B=2, etc, %u0011u0003 *HQHWLFu0003$OJRULWKPu0003 multiplied by 100.
Is the Latin square design easy to analyze?
A Latin Square design is actually easy to analyze. Because of the restricted layout, one observation per treatment in each row and column, the model is orthogonal. If the row, ρ i, and column, β j, effects are random with expectations zero, the expected value of Y i j k is μ + τ k.
When was the 10×10 Graeco Latin square discovered?
The 10×10 Graeco-Latin square below is one of those discovered by R. C. Bose, S. S. Shrikhande, and E. T. Parker. It was published in numerical form in the Canadian Journal of Mathematics in 1960. Many of the 10×10 squares they discovered include a 3×3 square, which you can see in the bottom right corner. | s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233510100.47/warc/CC-MAIN-20230925215547-20230926005547-00787.warc.gz | CC-MAIN-2023-40 | 4,324 | 30 |
https://quant.stackexchange.com/questions/48776/what-mips-municipal-inflation-protected-securities-are-out-there-besides-the-t | math | Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
Quantitative Finance Stack Exchange is a question and answer site for finance professionals and academics. It only takes a minute to sign up.
DFA has DMREX AND DCARX. Are there others? I'm specially looking for high quality, medium or long duration MIPS but a list of anything would help.
Required, but never shown | s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585371858664.82/warc/CC-MAIN-20200409122719-20200409153219-00465.warc.gz | CC-MAIN-2020-16 | 511 | 4 |
https://www.shearwell.co.nz/applicators | math | We'll supply the applicator FREE on your first order of 200 or more SET tags. Please add it to your basket so we know you'd like one.
• Tags come preloaded in cartridges
• Takes 10 SET Tags at a time
• Fast method of tagging sheep
• Easy to use and robust | s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578526807.5/warc/CC-MAIN-20190418201429-20190418222514-00065.warc.gz | CC-MAIN-2019-18 | 263 | 5 |
http://www.foltyn.net/ | math | Why would you want to do that? IMHO, by now the question is rather why you would want to continue using Kontact for your email/calendar/contact management needs given all the bugs and regressions. For example, after upgrading to KDE 4.8 on my Gentoo machine recently, once again address completion when composing emails ceased to work (it worked some time with 4.7.x, but not before that). Also, every now and then the virtuoso process consumed 100% CPU on login.
I had problems with KDEPIM2 ever since it was released (version 4.6.x), but was reluctant to ditch it since I had been a happy user for more than 5 years. Furthermore, KDEPIM is more powerful than Thunderbird. Nevertheless, this is 2012 and I am no longer willing to invest considerable time to have a working email and calendar solution. Maybe it works if you clean everything akondadi-, nepomuk- and kontact-related on each upgrade, but this is just not a viable option.
Anyway, to replace Kontact with Thunderbird there are several tweaks to make Thunderbird resemble the behavior of Kontact:
- Kmail, Akregator and KNode can be replaced by Thunderbird’s Email, Blogs & News Feeds and Newsgroup accounts, respectively. They may not be as powerful as the original programs, but they do their job.
- The KDE calendar is best replaced by the Lightning add-on. For remote synchronization, you will need something like the Provider for Google Calendar add-on. This works reasonably well.
Some additional useful add-ons that make Thunderbird behave like Kmail:
- SendWithoutSubject, otherwise there is a confirmation popup every time you try to send an email without a subject (you need an add-on for this, seriously?)
- Subject cleaner to eliminate repeated Re: Re:, etc. from subjects when replying (KMail does this automatically)
- Sieve to manage sieve scripts on your IMAP server, if you use those.
- ThunderPlunger is a useful add-on if you happen to delete accounts, because Thunderbird does not actually remove the data from disk, potentially leaving you with hundreds of megabytes of junk.
- LookOut is required to deal with those infamous winmail.dat files brought to you by MS Outlook’s proprietary handling of attachments.
- StartupMaster is a useful addon to eliminate multiple password prompts if you have a master password for the builtin password manager. This happens because the Google Calendar provider prompts for a password for each account.
Update: For KDE users, the kwalltet password integration addon seems to be the way to go.
KMail also automatically checks all folders on your IMAP server, while Thunderbird does this only for the currently open folder. To mimic KMail’s behaviour you have to set
to true in the config editor.
Of course Thunderbird is not as nicely integrated into your desktop as Kontact. For example, I have yet to find a solution to display a systray icon with the number of unread mails, since solutions such as the Gnome integration add-on do not seem to work with the current version of TB. Also your calendar events are not displayed in the KDE Plasma calender if you decide to get rid of Akonadi completely.
It took some time, but today I finally managed to proofread my diploma thesis in economics (which is similar to a master’s thesis) titled “Endogenous growth in heterogeneous-firm trade models.”
Abstract: This thesis aims to demonstrate how a heterogeneous-firm trade and growth model can be used to analyze productivity and welfare effects of trade liberalization. To this end, I first discuss the evolution of trade and growth theories that culminated in a class of comprehensive models capable of accounting for phenomena that are deemed important by both trade and growth theorists. Focusing on one of these models, Gustafsson and Segerstrom (2010), I extend their comparative static analysis to out-of-steady-state dynamics and show that the presence of heterogeneous firms introduces nontrivial complications absent from homogeneous-firm models. Lastly, I present Gustafsson and Segerstrom’s main finding that knowledge spillovers play a pivotal role in determining whether trade liberalization is welfare increasing.
You can download the complete thesis here (PDF, 2.1 MB).
Another Mathematica demonstration: this one visualizes the comparative statics as well as the adjustment dynamics resulting from a parameter change in the Solow-Swan growth model.
I took professor Sorger‘s advanced macro class on growth and business cycle theories last semester, so I noticed that some textbooks (such as Barro/Sala-i-Martin) don’t show the adjustment process of capital, per-capita output, consumption, etc. I think it helps intuition to visualize these variables, which is why I created this demonstration.
You can download the Mathematica notebook (you’ll need either Mathematica or the free Mathematica player to view this), or look at the online version here. (Unfortunately Wolfram changed the demo so only one graph is visible at a time.)
Melitz, again. I took a Mathematica class this semester where we had to build a demonstration that could be uploaded to Wolfram’s demonstration project site. I created an animated version of figure 2 from Melitz’ paper (based on the calculations done in one of the Mathematica notebooks presented below), which IMO is well suited to do a comparative statics analysis of autarky and the open economy.
The online demonstration is available here.
The Melitz (2003) trade model is one of the central models of my diploma thesis, so I’ve spent (wasted?) some time derived a closed-form solution for Pareto-distributed firm productivity levels (Melitz himself does not use a particular distribution). I’ve been able to replicate most of paper’s results, while a few do not hold for the Pareto distribution (using other distributions, though, will generally not produce closed-form solutions). With the Mathematica notebook it is easy to manipulate model parameters and see the effects on equilibrium values.
Download links: PDF, Mathematica Notebook (ZIP archive)
Update (Dec. 8, 2009): minor changes and error corrections in PDF and Mathematica notebook.
Update (Dec. 14, 2009): Helpman/Melitz/Yeaple (2004) present a similar model with heterogeneous firms and Pareto-distributed firm productivity. It is less complex than Melitz (2003) as it omits the stochastic firm entry and exit process. However, it allows to model firm decisions concerning production for the domestic market and export / FDI in foreign markets depending on firm productivity. The Mathematica notebook below derives this model in greater detail than the original paper.
Download links: PDF, Mathematica notebook/package
- Helpman, Elhanan/ Melitz, Marc J. and Yeaple, Stephen R. (2004): Export versus FDI with Heterogeneous Firms . In: American Economic Review 94(1), 300 316.
- Melitz, Marc J. (2003): “The Impact of Trade on Intra-Industry Reallocations and Aggregate Industry Productivity”. In: Econometrica 71(6), 1695.
While researching for my current diploma thesis on “new new” trade theory I realized that fully understanding (or rather: knowing by heart) the Dixit/Stiglitz (1977) model is a necessary precondition to be able to read most of the relevant papers. Unfortunately, the original Dixit/Stiglitz is not written for undergraduate students (intermediate steps are mostly omitted), and the obsolete Chamberlinian terminology does not exactly promote understanding (obsolete by Austrian university standards, that is).
Consequently I’ve compiled this step-by-step walkthrough of the first and most widely used model (the CES case) covered in Dixit/Stiglitz (1977). This should be sufficient for most of the “new” and “new new” trade theory models. You can download it here.
Please let me know if you find any mistakes.
Update (Dec. 21, 2009): Minor corrections.
- Dixit, Avinash K. and Stiglitz, Joseph E. (1977): “Monopolistic Competition and Optimum Product Diversity”. In: American Economic Review 67(3), 297–308.
I guess this looks like a blog, but I won’t be using it as one. I see little value in further polluting the internet by sharing my thoughts on this or that. After all, I am not Paul Krugman or Brad DeLong, so why should anyone care? 😉 However, I will occasionally post stuff concerning my studies which other economics students might find useful. | s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583658702.9/warc/CC-MAIN-20190117041621-20190117063621-00466.warc.gz | CC-MAIN-2019-04 | 8,370 | 37 |
https://www.calculators.live/impulse-time | math | Impulse Time Calculator
Use our simple online calculator to calculate Impulse (I), Force (F) or Time Change (ΔT). Impulse is the change in momentum. In this impulse time calculator, select the one you wish to calculate and enter the remaining values. This online Impulse with Time calculator works based on the impulse of force, which states that the change in momentum is a fixed quantity.
This online Impulse with time calculator helps you to calculate the three values of Impulse, Force, Time Change. The process of minimizing an impact force can be approached from the definition of the impulse of force: If an impact stops a moving object, then the change in momentum is a fixed quantity, and extending the time of the collision will decrease the time average of the impact force by the same factor. | s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296949025.18/warc/CC-MAIN-20230329182643-20230329212643-00260.warc.gz | CC-MAIN-2023-14 | 805 | 3 |
https://www.jiskha.com/display.cgi?id=1187193859 | math | posted by Mack .
A video store sells a certain video for $32, which is 60 percent more than it costs the store to purchase this video. During an inventory sale, employees are invited to purchase remaining videos at 25 percent off the store's cost. If an employee purchases this video during the sale, the employee's purchase price would be what percent of the price the store originally charged for the video?
Here's the book answer: First your told that a store sells a certain video for $32, which is 60 percent more than it costs the store. So to figure out the store's cost, translate the English into math: 32=1.6x, where x is the cost to the store. x=32/1.6=20, so the store's cost is $20. During a sale it's offered to employees at 25 percent off the store's cost, or .75*$20=$15, so $15 is the final price to the employee. But wait! the question asks what percent of the original price the employee pays, so divide 15 by 32. You should get .46875, or 46.875 percent, which you can grid as either 46.8 or 46.9.
My question is: Where did they get 1.6x from and how did they get .75*$20 from? And I really don't understand the answer so help me.
1.6 is the decimal equivalent of 160%. The store charged customers 160% of its wholesale price. 1.6x is 160% of an unknown number (the store's wholesale price).
.75*$20 is 75% of the store's cost of $20. 100% - 25% = 75%
explain how they got the whole answer. Because what you just explained to me is'nt enough. | s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934804610.37/warc/CC-MAIN-20171118040756-20171118060756-00231.warc.gz | CC-MAIN-2017-47 | 1,462 | 7 |
https://www.ftm.by/en/risk-reward/ | math | Search for the optimal «risk-profit» ratio
Almost all professional Forex clients in the Republic of Belarus use the profit-risk ratio to compare potential gains from investment positions with possible losses. The most popular parameters of this coefficient are the following numbers: 2:1, 3:1, 4:1 and they depend on many aspects, including the investment system, as well as the psychological stability of the client. Of course, the performance of transactions with non-deliverable financial instruments is influenced not only by this ratio, but also by other factors: managing the size of positions, market volatility, etc., but nevertheless, the ratio of profit and risk plays an important role in the development of the client as a professional.
Example of using the «profit-risk» ratio
Let’s say you decide to open a purchase on ABC shares, which are currently worth $20 apiece. You buy 100 shares, which is equivalent to the position size of $ 2,000. The order to fix the price of the underlying asset, you put the take profit at $30, and the stop loss at $15 per share. In other words, you are willing to risk five dollars per share in the hope of earning $10 per share after closing your position. This is the 2:1 ratio. If your potential earnings were $15 per share, you could talk about a 3:1 ratio and so on.
At the same time, it is important to remember that a good profit-risk ratio does not give you any additional probability of success of the transaction, rather it is a technical point of over-the-counter investment.
The importance of the «risk-profit» ratio
Most clients tend to set the ratio between orders to fix the price of the underlying asset Stop Loss and Take Profit no worse than 1:1 because otherwise, we can talk about transactions with non-deliverable financial instruments with a high degree of risk. A positive ratio, such as 2:1, guarantees that your potential income will be higher than your potential losses in any case. And even if you get a loss on one of the positions, you will only need one good trade to return some of the margin collateral and get a net profit.
Below you will see a table where there are various options for the ratio of profit and risk, and also calculated the impact of these coefficients on the result of transactions with no-deliverable financial instruments.
We took 10 conditional trades, of which 5 are closed with a profit, and 5-with a loss. The unit in the ratio is equal to $100 (that is, the 2:1 entry indicates that we want to earn$200 with a risk of $ 100).
|Profit: risk||Probability of winning||Total profit||Total loss||Total return|
From the results of the table, you can clearly see the potential advantages that a high profit-risk ratio has. Even if you reduce the probability of winning trades to 40% or even 35%, in the last two ratios, you will still make a profit in the long run. | s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233506320.28/warc/CC-MAIN-20230922002008-20230922032008-00030.warc.gz | CC-MAIN-2023-40 | 2,871 | 11 |
https://confit.atlas.jp/guide/event/jpgu2015/subject/03980/date | math | 4:40 PM - 5:05 PM
★ [ACG08-04] Uncertainty Estimate in Runoff Analysis Based on Theory of Stochastic Process
In this paper, therefore, the uncertainty of discharge on the uncertainty of rainfall is explained theoretically and mathematically by introduction of theory of stochastic process. The rainfall data is generally used as input data for rainfall-runoff analysis. The lumped rainfall-runoff model is represented by SDE (stochastic differential equation) due to describe it as difference formula, because the temporal variation of rainfall is expressed by its average plus deviation, which is approximated by Gaussian distribution. This is attributed to the observed rainfall by rain-gauge station and radar rain-gauge system. Moreover, we obtained the time evolution of PDF (probability density function) of water level or discharge from correspondence relationship of SDE (stochastic differential equation) and Fokker-Planck equation.
As a result, this paper has shown that it is possible to evaluate the uncertainty of discharge by using the relationship between SDE (stochastic differential equation) and Fokker-Planck equation. Moreover, the results of this study show that the uncertainty of discharge increases as rainfall intensity rises and non-linearity about resistance grows strong. These results are clarified by PDFs (probability density function) that satisfy Fokker-Planck equation about discharge. It means the reasonable discharge can be estimated based on the theory of stochastic processes, and it can be applied to the probabilistic risk of flood management. | s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487637721.34/warc/CC-MAIN-20210618134943-20210618164943-00524.warc.gz | CC-MAIN-2021-25 | 1,586 | 4 |
https://www.mysciencework.com/publication/show/0241fb7a274cac4b9b1588764fd583ce | math | Abstract In this paper, we have investigated the dynamic behavior of an SEI model with acute and chronic stages. Firstly by using Theorem 4.1 of Busenberg and van den Driessche [S. Busenberg, P. van den Driessche, Analysis of a disease transmission model in a population with varying size, J. Math. Biol., 28 (1990), 257–270], we have shown that if the basic reproduction number R 0 > 1, the unique endemic equilibrium is global asymptotically stable. The results obtained here improved the main results of Yuan and Yang [J. Yuan, Z. Yang, Global dynamics of an SEI model with acute and chronic stages, J. Comput. Appl. Math. (2007), doi: 10.1016/j.cam.2007.01.042]. Then the criterion for robustness of the system is established under stochastic perturbations. Finally, numerical simulations are performed to illustrate the analytical results. | s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917121752.57/warc/CC-MAIN-20170423031201-00125-ip-10-145-167-34.ec2.internal.warc.gz | CC-MAIN-2017-17 | 846 | 1 |
https://www.researchgate.net/publication/224362048_Optimal_Periodic_Controls_for_Linear_Impulsive_Periodic_System | math | Optimal Periodic Controls for Linear Impulsive Periodic System
In this paper, the optimal periodic controls problem for linear impulsive periodic system is discussed. Utilizing the geometric theory of Banach space and regarding quadratic function as the optimal index of measuring impulsive periodic system, the existence of optimal periodic controls for optimal control problems arising in systems governed by the linear impulsive periodic system on Banach space is presented. An example is given for demonstration.
Data provided are for informational purposes only. Although carefully collected, accuracy cannot be guaranteed. The impact factor represents a rough estimation of the journal's impact factor and does not reflect the actual current impact factor. Publisher conditions are provided by RoMEO. Differing provisions from the publisher's actual policy or licence agreement may be applicable. | s3://commoncrawl/crawl-data/CC-MAIN-2016-07/segments/1454701168998.49/warc/CC-MAIN-20160205193928-00187-ip-10-236-182-209.ec2.internal.warc.gz | CC-MAIN-2016-07 | 902 | 3 |
https://definition.org/define/non-empty/ | math | Of a set, containing at least one element; not the empty set.(adjective)
Wiktionary.org : Text is available under the Creative Commons Attribution-ShareAlike License
Use "non-empty" in a sentence
"If we can equate nothing with the empty set and something with a non-empty set, (not a trivial assumption, given that mathematics extends beyond set theory), then it is significant to note that whilst every set contains the empty set as a subset, the converse certainly isn't true."
"Clearly the intersections of sex with both toothpaste and orange juice should be non-empty."
"The ones who get hosed by the present system are those with no bargaining power and non-empty pockets." | s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780058456.86/warc/CC-MAIN-20210927151238-20210927181238-00560.warc.gz | CC-MAIN-2021-39 | 678 | 6 |
http://oai.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=AD0714615 | math | Accession Number : AD0714615
Title : Comparison of Optimal and Suboptimal Controllers.
Descriptive Note : Technical rept.,
Corporate Author : LOUISIANA STATE UNIV BATON ROUGE COLL OF ENGINEERING
Personal Author(s) : Miller,John A. ; Smith,Cecil L. ; Murrill,Paul W.
Report Date : MAR 1970
Pagination or Media Count : 22
Abstract : Basically there are two approaches to the design of control systems. One approach is to propose a given form of the control algorithm or strategy, and then determine the numerical values of the parameters that give the 'best' control according to some performance criterion. This is a parameter optimization problem which yields what is commonly called a suboptimal controller. The second approach is to determine the optimal function to be used as the control algorithm or strategy. This is a functional optimization problem which yields an optimal controller. The purpose of this article is to compare the performance of linear optimal and suboptimal controllers on four different formulations of the control problems for a given linear system. (Author)
Descriptors : (*CONTROL SYSTEMS, MATHEMATICAL MODELS), (*LINEAR SYSTEMS, OPTIMIZATION), ADAPTIVE CONTROL SYSTEMS, FEEDBACK, TRANSFER FUNCTIONS, CORRELATION TECHNIQUES
Subject Categories : Statistics and Probability
Distribution Statement : APPROVED FOR PUBLIC RELEASE | s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891817999.51/warc/CC-MAIN-20180226025358-20180226045358-00154.warc.gz | CC-MAIN-2018-09 | 1,354 | 11 |
https://www.physicsforums.com/threads/norton-equivalent-circuit-find-i-sc-and-r-t.675981/ | math | 1. The problem statement, all variables and given/known data The (b) circuit shown in the attached image is the Norton equivalent circuit of the (a) circuit. Find the value of the short-circuit current, isc, and Thévenin resistance, Rt. isc being the current that would flow through the two open nodes if they were shorted. 3. The attempt at a solution Right now I'm stuck on the current. I used mesh current analysis to find the current. Here are my equations. KVLa: -10v + 3ia - 2ia + 6(ia - isc) = 0 KVLsc: 6(isc - ia) + 5isc = 0 I reduced and ordered the equations as follows: KVLa: 7ia - 6isc = 10 KVLsc: -6ia + 11isc = 0 Which I solved as: ia = 2.68A isc = 1.46A However the book has the isc equaling 1.13A Where have I messed up? | s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794866276.61/warc/CC-MAIN-20180524112244-20180524132244-00437.warc.gz | CC-MAIN-2018-22 | 737 | 1 |
http://outdoors.stackexchange.com/questions/tagged/trekking-poles+walking | math | The Great Outdoors
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cc by-sa 3.0 | s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1405997873839.53/warc/CC-MAIN-20140722025753-00157-ip-10-33-131-23.ec2.internal.warc.gz | CC-MAIN-2014-23 | 2,287 | 55 |
http://gluedideas.com/content-collection/Cyclopedia-of-Architecture-Carpentry-and-Building-a-General-Reference-V-09/Cm-X.html | math | CM X V D— 4 Formulæ are frequently given for calculating sizes of conductors, etc., where the load, instead of being given in amperes, is stated in lamps or in horse-power. It is usually advisable, however, to reduce the load to amperes, as the efficiency of lamps and motors is a variable quantity, and the current varies correspondingly.
It is sometimes convenient, however, to make the calculation in terms of watts. It will readily be seen that we can obtain a formula expressed in watts from Formula 1. To do this, it is advisable to express the loss in volts in percentage, instead of actual volts lost. It must be remembered that, in the above formulae, V represents the volts lost in the circuit, or, in other words, the difference in potential between the beginning and the end of the circuit, and is not the applied E. M. F. The loss in percentage, in any circuit, is equal to the actual loss expressed in volts, divided by the line voltage, multiplied by 100; or, P — E X 100.
From this equation, we have: V= PE 100 If, for example, the calculation is to be made on a loss of 5 per cent, with an applied voltage of 250, using this last equation, we would have: V = 5 = 12.5 volts. Substituting the equation V= 100 in Formula 1, we have: This equation, it should be remembered, is expressed in terms of applied voltage. Now, since the power in watts is equal to the applied voltage multiplied by the current (W = EC), it follows that By substituting this value of C in the equation even above (C M= D X 2,160` , the formula is expressed in terms of watts instead PE J of current, thus: in which W = Power in watts transmitted; D = Length of the circuit (one way)—that is, the length of one conductor; P = Figure representing the percentage loss; E*= Applied voltage.
All the above formulae are for calculations of two-wire circuits. In making calculations for three-wire circuits, it is usual to make the calculation on the basis of the two outside conductors; and in three wire calculations, the above formulae can be used with a slight modifi cation, as will be shown.
In a three-wire circuit, it is usually assumed in making the cal culation, that the load is equally balanced on the two sides of the neutral conductor; and, as the potential across the outside conductors is double that of the corresponding potential across a two-wire circuit, it is evident that for the same size of conductor the total loss in volts could be doubled without increasing the percentage of loss in lamps.
Furthermore, as the load on one side of the neutral conductor, when the system is balanced, is .virtually in series with the load on the third side, the current in amperes is usually one-half the sum of the current required by all the lamps. If C be still taken as the total current in amperes (that is, the sum of the current required by all of the lamps) in Formula I, we shall have to divide this current by 2, to use the formula for calculating the two outside conductors for a three-wire system. Furthermore, we shall have to multiply the voltage lost in the lamps by 2, to obtain the voltage lost in the two out side conductors, for the reason that the potential of the outside con. ductors is double the potential required by the lamps themselves. In other words, Formula I will become: in which C = Sum of current required by all of the lamps on both sides of the neutral conductor; D = Length of is, of any one of the three conductors; V = Loss allowed in the lamps, i. e., one-half the total loss in the two outside conductors.
In the same manner, all of the other formulae may be adapted for making calculations for three-wire systems. Of course the calcula tion of a three-wire system could be made as if it were a two-wire system, by taking one-half the total number of lamps supplied, at one-half the voltage between the outside conductors.
It is understood, of course, that the size of the conductor in Formula 6 is the size of each of the two outs de ones; but, inasmuch as the Rules of the National Electric Code require that for interior wiring the neutral conductor shall be at least equal in size to the outside conductors, it is not necessary to calculate the size of the neutral conductor. It must be remembered, however, that, in a three-wire system where the neutral conductor is made equal in capacity to the combined size of the two outside conductors, and where the two outside conductors are joined together, we have virtually a two-wire system arranged so that it can be converted into a three-wire system later. In this case the calculation is exactly the same as in the case of the two-wire circuits, except that one of the two conductors is split into two smaller wires of the same capacity. This is frequently done where isolated plants are installed, and where the generators are wound for 125 volts and it may be desired at times to take current from an outside three-wire 125-250-volt system. | s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320302723.60/warc/CC-MAIN-20220121040956-20220121070956-00025.warc.gz | CC-MAIN-2022-05 | 4,936 | 8 |
https://mathiex.blogspot.com/2016/07/cubic-formula-analysis.html | math | Twenty-four hours later, I had the math parody ready to go for February 29th. It was posted directly to my math comic blog, rather than being placed into the music parody archive, because I hadn’t had time to actually verify the maths yet. I wanted to run the formula on an equation, to make sure it actually produced all three roots as I advertised. I figured I’d do that over the March Break, and maybe produce a video.
Instead, I fell down this rabbit hole. To see my conclusions, skip to “Actual Analysis” below. To follow the journey, keep reading.
THE FORMULA FAILED
Given y = ax^3 + bx^2 + cx + d, I wanted different values for each coefficient, and ideally some nice whole number roots. Expanding (x+1)(x-1)(x-2) felt like it would work, and indeed it means a=1, b=-2, c=-1, d=2 (all different but small). I plugged them into the formula... and I did not get -1, 1, and 2. Rather, I got -1/3, 2/3 and 7/3.
That wasn’t supposed to happen.
After poking at the maths, I decided my problem was the negative square roots that had turned up. I’d actually had to turn to ‘wolfram alpha’ to take the cube roots of those complex numbers; maybe I’d entered it wrong. This would probably be easier if I kept that nested square root ‘positive’. After swapping all the signs (multiplying by -1) and seeing that wouldn’t fix it, I moved my calculations off of a paper bag and onto actual lined paper.
I focussed on what was under the square root. I would later call this the “root discriminant” of the cubic formula. One piece of it is already squared, no problem, that’s positive, ignore it. To get a positive result overall, I needed c/(3a) to be larger than b^2/(3a)^2. Except with the latter also being squared (always positive), this meant “a” and “c” HAD to be the same sign. Huh.
I played around with some other expansions of factored form. At first those signs were wrong, or some coefficients were zero, or they weren’t unique numbers. Then I found one that worked: (x+2)(x+3)(x+4) But it still produced a negative root result. At this point in my notes I’ve scribbled “a can’t be +-1”, which is kind of silly in retrospect.
I kept going, further scribbles being “need smaller abs(b) vs. (c)” and “3ac>b^2”. To my horror, I began to suspect that the root would always be negative, so long as I was feeding in three real solutions. I played with some sliders in Desmos, then decided I should contrast with cubic formulas which had only one functional root instead (also verified in Desmos).
Working with y1 = 2x^3 - 3x^2 - x - 2, which is solved when x=2, produced a positive square root overall. But it led to doing cube roots of nasty fractions, and the decimal approximations were NOT giving me the answer x=2 (closer to x=1.68). I started to think maybe the formula ITSELF was wrong. (The internet, unreliable? What?!)
The previous work wasn’t done all in one sitting. I’d already given up on having this done through March Break. One weekend, while heading into school for a play rehearsal, I stopped in a food court and started tackling other formula variations I’d discovered online. For instance, one that separated out the three x1, x2 and x3 solutions, and another that used expressions for q, p and r to simplify the formula overall.
None of them worked with my y1 equation (above). Worse, they were giving me different solutions. Depending on which formula variation I used, I either got x=1.68 or x=2.13 or x=2.29. But the solution is TWO, dammit! I checked my math, found a mistake, it didn’t fix the problem. Surely the issue was the “cube root of fractions” step, which I was approximating on my calculator (to 8 decimal places).
This was going to take more time than I had. Easter Break, at the end of March, wouldn’t help. I had to use it to bank a bunch of my math comics, in anticipation of being at school for 25 days straight due to the play. While still writing 2,000 words/week on my serial. Yeah. So after downloading some plausible “cube” footage on March 26th for that later video, I shelved the whole project.
It resurfaced briefly in May, when I put together a Cubic Formula Song Powerpoint for my MCT class. (We were finishing our Polynomials unit at the time.) This despite my unfounded reservations about the formula. The performance went fine; as a student remarked, “It just kept growing!”.
The project resurfaced again in June, when John Golden tweeted out something about the cubic formula - except his formula image looked DIFFERENT from any of the others. Time to get back into actual research. As motivation, I decided I would do a presentation of the song on the last day of my MCR class, if it felt right.
I’d realized that “a” only ever appears in the denominator. This is different from the quadratic formula, where we have -4ac. But from the research, it makes total sense. The first step in developing the cubic formula is to divide everything by “a”, creating a simpler problem, namely x^3 + Bx^2 + Cx + D = 0. (As noted, it makes my “a can’t be 1” remark above rather silly.)
The next step in creating the formula seemed to be developing a depressed cubic, by substituting in a different value for “x” to get rid of the squared term, effectively giving you m^3 + Jm + K = 0, where once you have the “m” you can reverse determine “x” from there. That made sense, but didn’t really help me grab numbers for an example.
This was when I discovered the “cubic discriminant”. It seems to have it's own definition that synchs with the quadratic, but had me consider the piece under the square root - a "root discriminant", if you will. And I had been correct - for there to be 3 real solutions, that "root discriminant" had to be NEGATIVE. Conversely, if it was POSITIVE, that meant there would be only one real solution (the other two solutions would be imaginary). Again, this made some sense to me. If you picture cube roots equidistant from each other on the polar plane, only one root can land where b*i=0.
But there’s a third case. If my "root discriminant" is ZERO, this means you get at least a double root. That’s honestly *the only way* to avoid either doing cube roots of imaginary numbers, or having imaginary answers as solutions. Wonderful. (It also meant Golden’s found formula was invalid, as the cubic discriminant, which appears twice, had an invalid sign one of those times.)
There was even this “wikihow” website showing how to do the steps by hand. With renewed faith, I sang the song for the few 3Us who were there the last day of class, then shelved this project AGAIN until after exams - I was SO behind in my marking.
July 2016. The website “SOSMath” offered a cubic formula with x=3 as the only solution. I tried the formula, and it worked, despite ugly radicals. (I don’t know why I was having such trouble before.) The last hurdle was a formula with a “cubic discriminant” of zero that would work nicely. I created one... for some reason, it didn’t work?! ... Damn sign error. Okay. Good to go!
And that's the story. The final video will premiere within the next 3-4 days; I’ve linked to it here. I’m still maintaining weekly posts on three blogs (including here), that’s holding me back a bit. Thanks for reading, feel free to check out some of my fiction writing too! | s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337490.6/warc/CC-MAIN-20221004085909-20221004115909-00393.warc.gz | CC-MAIN-2022-40 | 7,379 | 22 |
https://ead.fiar.com.br/blog/b98a3b-bond-enthalpy-of-graphite | math | >> The enthalpy difference between graphite and diamond is too large for both to have a standard enthalpy of formation of zero. /F6 10 0 R Not in this one. Example #9: The ΔH for the following reaction equals −89 kJ: In addition, these two standard enthalpies of formation are known: 2) Inserting values into the above, we find: 1) Here are all three data reactions written out in equation form: 2) What we need to do is add the three data equations together in such a way as to recover the target equation: 4) However, this is not the enthalpy of formation, since that value is always for one mole of the product. 11 0 obj 2) Adding the following equations will yield the equation needed: 3) Add the three equations and their enthalpies: The heat of formation of CH4(g) is −79 kJ/mole, The Chemistry Webbook gives the value as being a bit less than −75 kJ/mol. = [ (4136) ] − [ (6) (−393.5) + (7) (−285.8) ]. Introducing Textbook Solutions. /Encoding 3 0 R = −1367 kJ/mol of ethyl alcohol. For example, I have a link several problems above to a table of bond enthalpy values. Therefore. /Type /Font The standard enthalpy of formation is defined as the change in enthalpy when one mole of a substance in the standard state (1 atm of pressure and 298.15 K) is formed from its pure elements under the same conditions. 1) Write the equation for the formation of hexane: ΔH rxno endobj << 2 0 obj Example #5: The standard enthalpy of formation of hexane can be determined indirectly. The ChemTeam does not know for sure. The bond enthalpy values are each associated with a specific chemical equation. Problem #3: Determine the enthalpy of reaction for the following: Using the following bond enthalpies (in kJ/mol): H−H (432); O=O (496); H−O (463). Average Bond Enthalpy- Is the average enthalpy change that takes place when breaking by homolytic fission 1 mol of a given type of bond in the molecules of … Solution The bond energy involves breaking HCl into H and Cl atoms. >> The general equation for the standard enthalpy change of formation is given below: Plugging in the equation for the formation of CO2 gives the following: ΔHreactiono= ΔHfo[CO2(g)] - (ΔHfo[O2(g)] + ΔHfo[C(graphite)]. The conversion of graphite into diamond is an endothermic reaction (ΔH = +3 kJ mol–1). Since we are discussing formation equations, let's go look up their formation enthalpies: 1⁄2H2(g) + 1⁄2Br2(ℓ) ---> HBr(g) ΔH fo Be prepared. This is not the usual way in which bond enthalpy values are used. Between Br2(l) and Br2(g) at 298.15 K, which substance has a nonzero standard enthalpy of formation? Unless otherwise noted, LibreTexts content is licensed by CC BY-NC-SA 3.0. The reaction will always form one mole of the target substance (glucose in the example) in its standard state. Consequently, enthalpy calculations using bond enthalpies are only a rough guide to the enthalpy of a given reaction. The −393.5 value is the enthalpy for the combustion of carbon. The enthalpy of formation involves making HCl from H 2 and Cl 2 molecules. >> The former parameter tends to be favored in theoretical and computational work, while the latter is more convenient for thermochemical studies. goes on the left-hand side. Completing the CAPTCHA proves you are a human and gives you temporary access to the web property. 1) The balanced equation for the combustion of C2H6 (ethane) is: [(2 moles CO2) (−393.5 kJ/mole) + (6 moles H2O) (−241.8 kJ/mole)] − [(2 moles C2H6) (−84.68 kJ/mole) + (7 moles O2) (0 kJ/mole)]. In addition, the chemical environment changes as you remove a given bond. >> Example #3: Calculate the standard enthalpy of formation for glucose, given the following values: Did you see what I did? Note the approach to the solution. I'll explain the above equation using an example problem. 2) Let's write the formation equation for AgNO2(s): 3) Determine the unknown value by adding the two equations listed in step 1: When the two equations are added together, the AgNO3(s) cancels out as does 1⁄2O2(g) and we are left with the formation equation for AgNO2(s), the equation given in step 2. Using the standard enthalpy of formation data in Appendix G, calculate the bond energy of, 7.5: Strengths of Ionic and Covalent Bonds, 71. Given the standard enthalpy of combustions of: methane gas (-890.5 kJ/mol), hydrogen gas (-285.9 kJ/mol), C graphite (-393.5 kJ/mol), the bond dissociation enthalpy of hydrogen gas (435.8 kJ/mol), and the latent heat of sublimation of graphite (718.4 kJ/mol) Evaluate the bond enthalpy of the C-H bond … (ii) C (diamond) + O2 (g) → CO2 (g) ; … /Type /Encoding Make sure you find it and figure out how to use it. The moral of the story? >> Now I examine each statement: 1. The enthalpy of formation involves making HCl from H 2 and Cl 2 molecules. /F3 6 0 R 1) First of all, this is the reaction we want an answer for: We know this because the problem asks for the standard enthalpy of formation for glucose. values: All the above values have units of kJ/mol because these are standard values. Bond energies of H − − H, C − − H, and C − − C bonds are 1 0 4. Sometimes terms overlap. The differences between Cl and Br are slight, but they do make for a difference that can be measured experimentally. | s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662636717.74/warc/CC-MAIN-20220527050925-20220527080925-00561.warc.gz | CC-MAIN-2022-21 | 5,293 | 1 |
http://www.glassmessages.com/index.php/topic,42677.msg237325.html | math | DUH to me :ho:
I thought the Z looked like a 2. The initials of CG, I did think of Caithness -- but when I goolgled CGZ I would get nothing. So Gee, this is Caithness too :thup: . That is good right? It still looks well made, and being a second makes it rarer, or not -- or what. I am new to this as with these purchases -- they are my very First Caithness PW here.............totally.
Never had handled one before..
** Also, I asked a question in the one PW that has the *bubble Circle* in it too. See that post.
Wow...this is interesting!! | s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917123172.42/warc/CC-MAIN-20170423031203-00519-ip-10-145-167-34.ec2.internal.warc.gz | CC-MAIN-2017-17 | 541 | 5 |
https://flylib.com/books/en/2.729.1/computing_the_inverse_fft_using_the_forward_fft.html | math | There are many signal processing applications where the capability to perform the inverse FFT is necessary. This can be a problem if available hardware, or software routines, have only the capability to perform the forward FFT. Fortunately, there are two slick ways to perform the inverse FFT using the forward FFT algorithm.
13.6.1 Inverse FFT Method 1
The first inverse FFT calculation scheme is implemented following the processes shown in Figure 13-14.
Figure 13-14. Processing for first inverse FFT calculation method.
To see how this works, consider the expressions for the forward and inverse DFTs. They are
To reiterate our goal, we want to use the process in Eq. (13-51) to implement Eq. (13-52). The first step of our approach is to use complex conjugation. Remember, conjugation (represented by the superscript * symbol) is the reversal of the sign of a complex number's imaginary exponent—if x = ejø, then x* = e–jø. So, as a first step we take the complex conjugate of both sides of Eq. (13-52) to give us
One of the properties of complex numbers, discussed in Appendix A, is that the conjugate of a product is equal to the product of the conjugates. That is, if c = ab, then c* = (ab)* = a*b*. Using this, we can show the conjugate of the right side of Eq. (13-53) to be
Hold on; we're almost there. Notice the similarity of Eq. (13-54) to our original forward DFT expression Eq. (13-51). If we perform a forward DFT on the conjugate of the X(m) in Eq. (13-54), and divide the results by N, we get the conjugate of our desired time samples x(n). Taking the conjugate of both sides of Eq. (13-54), we get a more straightforward expression for x(n):
13.6.2 Inverse FFT Method 2
The second inverse FFT calculation technique is implemented following the interesting data flow shown in Figure 13-15.
Figure 13-15. Processing for second inverse FFT calculation method.
In this clever inverse FFT scheme we don't bother with conjugation. Instead, we merely swap the real and imaginary parts of sequences of complex data. To see why this process works, let's look at the inverse DFT equation again while separating the input X(m) term into its real and imaginary parts and remembering that ejø = cos(ø) + jsin(ø).
Multiplying the complex terms in Eq. (13-56) gives us
Equation (13-57) is the general expression for the inverse DFT and we'll now quickly show that the process in Figure 13-15 implements this equation. With X(m) = Xreal(m) + jXimag(m), then swapping these terms gives us
The forward DFT of our Xswap(m) is
Multiplying the complex terms in Eq. (13-59) gives us
Swapping the real and imaginary parts of the results of this forward DFT gives us what we're after:
If we divided Eq. (13-61) by N, it would be exactly equal to the inverse DFT expression in Eq. (13-57), and that's what we set out to show. | s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499646.23/warc/CC-MAIN-20230128153513-20230128183513-00156.warc.gz | CC-MAIN-2023-06 | 2,829 | 18 |
http://lifeng.lamost.org/courses/astrotoday/CHAISSON/AT308/HTML/AT30803.HTM | math | As just mentioned, the Moon's rotation period is precisely equal to its period of revolution about Earth27.3 days sothe Moon keeps the same side facing Earth at all times (see Figure 8.10). To an astronaut standing on the Moon's near-side surface, Earth would appear almost stationary in the sky (although its daily rotation would be clearly evident). This condition, in which the spin of one body is precisely equal to (or synchronized with) its revolution around another body, is known as a synchronous orbit. The fact that the Moon is in a synchronous orbit around Earth is no accident. It is an inevitable consequence of the gravitational interaction between those two bodies.
Figure 8.10 The Moon is slightly elongated in shape, with its long axis perpetually pointing toward Earth. (The elongation is highly exaggerated in this diagram.)
Just as the Moon raises tides on Earth, Earth also produces a tidal bulge in the Moon. Because Earth is so much more massive, the tidal force on the Moon is about 20 times greater than that on Earth, and the Moon's tidal bulge is correspondingly larger. In Chapter 7 we saw how lunar tidal forces are causing Earth's spin to slow and how, as a result, Earth will eventually rotate on its axis at the same rate as the Moon revolves around Earth. (Sec. 7.6) Earth's rotation will not become synchronous with the EarthMoon orbital period for hundreds of billions of years. In the case of the Moon, however, the process has already gone to completion. The Moon's much larger tidal deformation caused it to evolve into a synchronous orbit long ago, and the Moon is said to have become tidally locked to Earth. Most of the moons in the solar system are similarly locked by the tidal fields of their parent planets.
In fact, the size of the lunar bulge is too great to be produced by Earth's present-day tidal influence. The explanation seems to be that, long ago, the distance from Earth to the Moon may have been as little as two-thirds of its current value, or about 250,000 km. Earth's tidal force on the Moon would then have been more than three times greater than it is today and could have accounted for the Moon's elongated shape. The resulting distortion could have "set" when the Moon solidified, thus surviving to the present day, while at the same time accelerating the synchronization of the Moon's orbit.
In principle, the ability to discern surface features on Mercury should allow us to measure its rotation rate simply by watching the motion of a particular region around the planet. In the mid-nineteenth century, an Italian astronomer named Giovanni Schiaparelli did just that. He concluded that Mercury always keeps one side facing the Sun, much as our Moon perpetually presents only one face to Earth. The explanation suggested for this synchronous rotation was the same as for the Moonthe tidal bulge raised in Mercury by the Sun had modified the planet's rotation rate until the bulge always pointed directly at the Sun. Although the surface features could not be seen clearly, the combination of Schiaparelli's observations and a plausible physical explanation was enough to convince most astronomers, and the belief that Mercury rotates synchronously with its revolution about the Sun (that is, once every 88 Earth days) persisted for almost half a century.
In 1965, astronomers making radar observations of Mercury from the Arecibo radio telescope in Puerto Rico (see Figure 5.21) discovered that this long-held view was in error. The technique they used is illustrated in Figure 8.11, which shows a radar signal reflecting from the surface of a hypothetical planet. Let's imagine, for the purpose of this discussion, that the pulse of outgoing radiation is of a single frequency.
Figure 8.11 A radar beam reflected from a rotating planet yields information about both the planet's overall motion and its rotation rate.
The returning pulse bounced off the planet is very much weaker than the outgoing signal. Beyond this change, the reflected signal can be modified in two important ways. First, the signal as a whole may be redshifted or blueshifted as a consequence of the Doppler effect, depending on the overall radial velocity of the planet with respect to Earth. (Sec. 3.5) Let's assume for simplicity that this velocity is zero, so that, on average, the frequency of the reflected signal is the same as the outgoing beam. Second, if the planet is rotating, the radiation reflected from the side of the planet moving toward us returns at a slightly higher frequency than the radiation reflected from the receding side. (Think of the two hemispheres as being separate sources of radiation and moving at slightly different velocities, one toward us and one away.) The effect is very similar to the rotational line broadening discussed in Chapter 4 (see Figure 4.18), except that in this case the radiation we are measuring was not emitted by the planet but only reflected from its surface. (Sec. 4.4) What we see in the reflected signal is a spread of frequencies on either side of the original frequency. By measuring the extent of that spread, we can determine the planet's rotational speed.
In this way, the Arecibo researchers found that the rotation period of Mercury is not 88 days, as had previously been believed, but 59 days, exactly two-thirds of the planet's orbital period. Because there are exactly three rotations for every two revolutions, we say that there is a 3:2 spin-orbit resonance in Mercury's motion. In this context, the term resonance just means that two characteristic timeshere Mercury's day and yearare related to each other in a simple way. An even simpler example of a spinorbit resonance is the Moon's orbit around Earth. In that case, the rotation is synchronous with the revolution, so the resonance is said to be 1:1.
Figure 8.12 illustrates some implications of Mercury's curious rotation for a hypothetical inhabitant of the planet. Mercury's solar daythe time from noon to noon, sayis actually 2 Mercury years long! The Sun stays "up" in the black Mercury sky for almost 3 Earth months at a time, after which follows nearly 3 months of darkness. At any given point in its orbit, Mercury presents the same face to the Sun not every time it revolves, but every other time.
Figure 8.12 Mercury's orbital and rotational motions combine to produce a day that is 2 years long. The arrow represents an observer standing on the surface of the planet. At day 0, it is noon for our observer, and the Sun is directly overhead. By the time Mercury has completed one full orbit around the Sun and moved from day 0 to day 88, it has rotated on its axis exactly 1.5 times, so that it is now midnight at the observer's location. After another complete orbit, it is noon once again. The eccentricity of Mercury's orbit is not shown in this simplified diagram.
The Orbit of Mercury
Mercury's 3:2 spinorbit resonance did not occur by chance. What mechanism establishes and maintains it? In the case of the Moon orbiting Earth, the 1:1 resonance is explained as the result of tidal forces. In essence, the lunar rotation period, which probably started off much shorter than its present value, has lengthened so that the tidal bulge created by Earth is fixed relative to the body of the Moon. Tidal forces (this time due to the Sun) are also responsible for Mercury's 3:2 resonance, but in a much more subtle way.
Mercury cannot settle into a 1:1 resonance because its orbit around the Sun is quite eccentric. By Kepler's second law, Mercury's orbital speed is greatest at perihelion (closest approach to the Sun) and least at aphelion (greatest distance from the Sun). (Sec. 2.3) A moment's thought shows that because of these variations in the planet's orbital speed, there is no way that the planet (rotating at a constant rate) can remain in a synchronous orbit. If its rotation were synchronous near perihelion, it would be too rapid at aphelion, while synchronism at aphelion would be too slow at perihelion.
Tidal forces always act to try to synchronize the rotation rate with the instantaneous orbital speed, but such synchronization cannot be maintained over Mercury's entire orbit. What happens? The answer is found when we realize that tidal effects diminish very rapidly with increasing distance. The tidal forces acting on Mercury at perihelion are much greater than those at aphelion, and perihelion "won" the struggle to determine the rotation rate. In the 3:2 resonance, Mercury's orbital and rotational motion are almost exactly synchronous at perihelion, so that particular rotation rate was naturally "picked out" by the Sun's tidal influence on the planet. Notice that even though Mercury rotates through only 180° between one perihelion and the next (see Figure 8.12), the appearance of the tidal bulge is the same each time around.
The motion of Mercury is one of the simplest nonsynchronous resonances known in the solar system. Astronomers now believe that these intricate dynamical interactions are responsible for much of the fine detail observed in the motion of the solar system. Examples of resonances can be found in the orbits of many of the planets, their moons, their rings, and in the asteroid belt.
The Sun's tidal influence also causes Mercury's rotation axis to be exactly perpendicular to its orbit plane. As a result, and because of Mercury's eccentric orbit and the spinorbit resonance, some points on the surface get much hotter than others. In particular, the two (diametrically opposite) points on the surface where the Sun is directly overhead at perihelion get hottest of all. They are called the hot longitudes. The peak temperature of 700 K mentioned earlier occurs at noon at those two locations. At the warm longitudes, where the Sun is directly overhead at aphelion, the peak temperature is about 150 K coolera mere 550 K! By contrast, the Sun is always on the horizon as seen from the planet's poles. Recent Earth-based radar studies suggest that Mercury's polar temperatures may be as low as 125 K and that, despite the planet's scorched equator, the poles may be covered with extensive sheets of water ice. (See Interlude 8-1 for similar findings regarding the Moon.) | s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571959.66/warc/CC-MAIN-20220813142020-20220813172020-00615.warc.gz | CC-MAIN-2022-33 | 10,204 | 17 |
https://www.tutoreye.com/homework-help/math/basic-operations | math | 5.I’m scheduling appointments. If I answered 31 phone calls and I got 11 people scheduled and did not schedule 3 ...
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Basic operations in mathematics contain addition,subtractions,multiplications,and division. In basic operations we use the BODMAS rule.
Question 1: Which of the following is/are true?
I 13^2 = 169
II 2^8 = 82
III 27^1/3 = 3
(a) II only
(b) I and II only
(c) I and III only
Explanation: Simplify and check.
Question 2: The average age of 20 students is A and the average age of 15 students is B. What is the average of the two numbers?
Explanation: Let the sum of ages of 20 students be S^1 and the sum of ages of 15 students be S^2.
Question 3: Ishika creates the base of a picture frame of dimension 4.5m × 6.5m of red fabric. If the cost of fabric is $5 per m2. Calculate the total money spent on making a frame?
Explanation: Area of picture frame = 4.5m × 6.5m = 29.25m^2
Question 4: John draws a rectangle with a length of 8cm. He draws a second rectangle with a length of 11cm. John continued drawing more rectangles, where for each rectangle drawn he used a length of 5cm more than the previous rectangle. If these patterns continue, what will be the length of the 12th rectangle?
Explanation: Since the length of the first rectangle is 8cm and the length of the second rectangle is 11cm. Now, the length of the third rectangle is 11+5=16cm, and continues adding 5cm to the previous one.
Question 5: Tina ran 12 laps everyday. In how many days does she complete 300 laps?
(a) 20 days
(b) 30 days
(c) 25 days
(d) 15 days
Explanation: Number of days to complete 12 laps = 1days
Therefore, number of days to complete 300 laps = 1/12 x 300
Question 6: Simplify:
Question 7: A man walks at the speed of 12 km per hour. How much time does he take to cover 78 km?
(a) 6 hours
(b) 7 hours
(c) 8 hours
(d) 6.5 hours
Explanation: Use the formula Time = Distance/Speed
Question 8: If ‘÷’ means ‘×’, ‘+’ means ‘÷’, ‘-’ means ‘+’, ‘×’ means ‘-’, then solve 8+4÷3-5×6 =?
Explanation: Change the sign accordingly and simplify.
Question 9: Simplify:
Explanation: Use the BODMAS.
Question 10: In a farm, there are some cows and hens. If there are a total 35 heads and 110 legs, how many cows and hens are there?
(a) 20 cows & 15 hens
(b) 15 cows & 20 hens
(c) 25 cows & 10 hens
(d) 10 cows & 25 hens
Explanation: Let the number of cows be x.
And, the number of hens will be y.
Number of legs of cow = 4x
Number of legs of hen = 2y
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https://aviation.stackexchange.com/questions/16525/can-an-airplane-lift-off-the-ground-when-lift-is-equal-to-weight | math | Stack Exchange Network
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Can a plane lift off the ground at the point when there is the same amount of lift as weight? Or does lift have to be greater?
Jul 2, 2015 at 8:37
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Yes they can, in fact aircraft regularly lift off the ground when lift is less than weight. They achieve this by rotating the nose, which provides a vertical component of the thrust vector. See the excellent answers to
this question for a detailed explanation.
Jul 2, 2015 at 9:21
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http://uzbpmany.cf/news7429-annual-dividend-yield-calculation.html | math | annual dividend yield calculation
Dividend Yield Calculator. Annual Dividend per Share ()You chose the Basic version of the Dividend Yield Calculator. The Basic version is non-editable, calculations are limited to 100/month, and the CalculatorPro.com link must be included. Saturday, September 18, 2010. How to Calculate Dividend Yield? Not all of the tools of fundamental analysis work for every investor on every stock.You calculate the Dividend Yield by taking the annual dividend per share and divide by the stocks price. Dividend yield, or annual dividend yield, refers to the amount of money a stock pays out as dividends relative to its current share price, expressed as aThe dividend yield is a financial calculation that tells you how much money you will earn for every dollar invested in Dividends Yield . Age Calculator Calculator Download App.Dividend Yield (DY) (Annual Dividends / Current Share Price) Rate of DY DY x 100. Example. A companys annual dividend is 5 and the current share price is 30. We divide the annual dividend per share by the market value per share. It is often used by investors who are looking for continuous dividend income.You can easily calculate the dividend yield ratio by using the following formula Calculations. Acid Test Ratio or Quick Ratio or Liquid Ratio Calculator.It tell what percentage of purchase price the company return in dividend. Formula. Dividend Yield Annual Dividend Per Share / Stock Price.
Dividend yield calculator ultimatecalculators. 10 per share in annual dividends.Definition calculation video lesson yield ratio explanation, formula, example and what Stocks glossary moneycontrol. It is calculated by dividend yield to price ratio. Dividend Yield Calculator. The calculator asks for: Annual Dividends per Share, which is found via company announcements or the financial media and is the sum of all dividends throughout the year Stock Price, which is found in the financial media or via your broker. Our free dividend yield calculator will calculate the dividend yield ratio for you. Dividend Yield Calculator. Annual Dividend per Share (): Market Price of the Stock () Below are the calculations to calculate the current dividend yield. Step 1: Annualized the dividend payment. Number of Dividend Payments: 4 Dividend Paid Per Share: 0.52 Annual Dividend Payment: 2.08. Dividend yield is considered as ROI for income investors who are not interested in capital gains or long-term earnings. It is calculated as Annual Dividend Per Share divided by Current Market Value Per Share.
Calculation (formula). Dividend Yield is used to determine the current annual yield of a security that pays dividends. The dividend yield is used to calculate the income produced and returned to shareholders and does not include capital gains. Use the dividend yield calculator below to solve the formula. Dividend yield ratio shows what percentage of the market price of a share a company annually pays to its stockholders in the form of dividends. It is calculated by dividing the annual dividend per share by market value per share. Dividend Yield Calculator (Click Here or Scroll Down).An example of the dividend yield formula would be a stock that has paid total annual dividends per share of 1.12. The original stock price for the year was 28. You can calculate dividend yield by annual dividend per share. And it divides by stock price.And Dividend per share is paid out by business including interim dividend. Calculation of Dividends per Share. Dividend Yield Calculator. Enter Annual Dividend Value Per Share in USD.In fact, when you divide the annual dividend per share, by its current stock price, what you are left with, is the dividend yield. Here is the formula used for dividend yield calculation. This article will explain the various financial calculations related to dividend investing like how to calculate dividend yield, dividend yield formula.Dividend yield, or annual dividend yield, refers to the amount of money a stock pays out as dividends relative to its current share price, expressed You calculate the dividend yield ratio for the business as follows: 1.50 annual cash dividend per share 70 current market price of stock 2.1 dividend yield. An income statement example for a business. Dividend Yield Calculation.The following equation can be used to calculate a stocks current yield . Yield Annual Dividends / Current Share Price. In this article, you will find a clear explanation of dividend yield calculation, from the knowledge of dividends per share and current share price.Dividend Yield Calculator. Enter Annual Dividend Value Per Share in USD. The formula for dividend yield is annual dividend divided by the share price. ROE or Return On Equity (as used in the DuPont formula) is defined as Net Income divided by Equity. In other words, the net profit that a company has generated during a year Dividend yield is calculated by dividing the total annual dividend amount by the companys share price.Therefore, the yield for Verizon is: Are all dividend distributions included in the dividend yield calculation? Dividend Yield annual dividend per share / stocks price per share.Heres a dividend yield example to explain the concept from Investopedia: Suppose company XYZs stock is trading at 20 and pays yearly dividends of 1 per share to its shareholders. Dividend Yield Formula:Dividend Yield Annual Dividend per Share / Market Price of the Stock. Dividend Yield DefinitionUsing the free online Dividend Yield Calculator is a quick way to calculate the dividend yield of any dividend paying stock. What would be a formula for calculating the annualized continuous dividend yield of a stock? Given the quarterly or annual dividend.Calculation of dividend yield from index returns. 0. This calculator can be used for calculating Dividend Yield in percentage. Dividend yield shows the pay out of dividend in relative to share price. Annual Dividend Per Share. Market Price of Stock. Dividend Yield (). Notes. Annual Dividend is the sum of dividends given in the financial year. How to Calculate Dividends. Three Methods:Dividends Calculator Finding Total Dividends from DPS Finding Dividend Yield Community QA.Thus, if youre using past dividend values to estimate what youll be paid in the future, theres a chance that your calculation may not be accurate. The dividend yield is calculated by dividing the dividend by the share price, and then expressing it as a percentage.However in the interim Loadsamoney has revealed its annual results and increased its dividend payment by 10 for the year, to 11p. Current yield relates the annual Since the reported distribution yield includes monthly dividend It is generally calculated using a financial calculatorDividend yield - calculation Find the annual Calculate Dividend Yield Dividend Yield What is the Dividend Yield A financial ratio that indicates how much a company pays out in dividends each year relative to its share price.Dividend Yield Annual Dividend / Current Stock Price. Dividend Calculator. Investment Type. Portfolio Individual Stock.New Annual Dividend Income. Dividend Paid out through Years. Yield On Cost. Year. Principal. Annual Dividend. The formula for calculating dividend yield may be represented as followsTo better explain the concept, refer to the following dividend yield example. Suppose company ABCs stock is trading at 20 and pays annual dividends of 1 per share to its shareholders. How to Calculate Dividend Yield. To calculate dividend yield, use the dividend yield formula. This can be done by dividing the annual dividend by the current stock price The dividend yield or dividend-price ratio of a share is the dividend per share, divided by the price per share. It is also a companys total annual dividend payments divided by its market capitalization, assuming the number of shares is constant. It is often expressed as a percentage. Calculation of Dividends per Share. denominator than the dividend per share calculation prior annual report.Using the free online Dividend Yield Calculator is a quick way to calculate the dividend yield of any dividend paying stock. How did Investingcalculator calculate the Dividend Yield? The dividend yield is calculated by taking the annual dividend payments and divide it by the current stock price.
Investing Calculator. The website for every Financial or Investment calculation! Dividend Yield: The dividend yield of the stock. Dividend Growth RateThe calculated compounded total return for dividends only. Annual Dividend Return The yield on cost is a simple, but effective calculation investors can use to track their return for shares in their portfolio.The second piece of information you will need is the annual dividend for the stock. To find its indicated dividend yield, just multiply the current quarterly rate by four and use the result (3.08 per share) in the calculation.Dividend Yield: Expected-Annual-Dividend divided by Price, expressed as a percentage. The dividend yield formula is calculated by dividing the cash dividends per share by the market value per share.Analysis. Investors use the dividend yield formula to compute the cash flow they are getting from their investment in stocks. Dividend yield is the annual dividend per share of a company compared to the price of the stock expressed as a percentage. In other words it tells you the percentage dividend return the stock owner receives based on the current price of a stock. Dividend Yield Calculation. Dividend yield ratio is expressed as a percentage and indicates the shares a company pays out on an annual basis relative to its share price.As youve seen, there is a lot involved in these calculations, and sometimes students tend to make mistakes or mix up formulas when they carry them out. Dividend Yield annual dividend per share / stocks price22/02/2017 This article will explain the various financial calculations related to dividend investing like how to calculate dividend yield, dividend yield formula. Calculate the dividend yield for the previous year by dividing the dividends paid by the price at the start of the year.In this example, divide 17 percent by 5 to find the average annual dividend yield is 3.4 percent. If your stock pays varying amounts, total up the payments youve received throughout the whole year and enter it as an annual dividend.In these examples the stock was purchased 50 years previously in 1966, and heres how their dividend yield calculations look, using the purchase price paid taking Current dividend yield is calculated by dividing the annual dividend by the current stock price.Any calculation of a future value must therefore be based on certain assumptions.Difficulty:ModerateInstructions Select the time frame. Annual dividend yield calculator - Page 1 of about 55,100,000 results.Subcategories. Advertisement. How dividend yield is calculated. I am not sure I can understand your question. Your reference to a closing price of 8282 in November leads me to think you are asking what the dividend yield of the Dow is. Stock Price Annual Dividend / Dividend Yield. Lets play with some numbers: Wal Marts (NYSE:WMT) annual dividend is 2.04 and its price March 4, 2017 is 70.03. Calculate the dividend yield for an actual example of stock. Dividend yield equals dividend per share divided by share price.The total yield is the capital gain plus the annual dividend divided by the initial investment. | s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794864572.13/warc/CC-MAIN-20180521235548-20180522015548-00533.warc.gz | CC-MAIN-2018-22 | 11,435 | 5 |
http://mxtermpapersymd.frenchiedavis.info/economics-price-elasticities.html | math | Economics price elasticities
Managerial economics management elasticities of demand | price elasticity | income elasticity introduction to elasticities of demand - 00:00:00- 00:00:58. In economics, elasticity is the measurement of how an economic variable responds to a change in another it gives answers to questions such as: if i lower the price of a product, how much more will sell. Key takeaways key points complementary goods have a negative cross- price elasticity: as the price of one good increases, the demand for the second good decreases. Video created by university of virginia, bcg for the course cost and economics in pricing strategy this week we'll dive deep into the world of demand modeling we'll start with a brief overview of regressions--what they are, why they're useful. Price elasticity of supply in contrast the supply of milk is price elastic because of a short time span from subscribe to email updates from tutor2u economics.
Price elasticity of demand however demand for any one filling station’s petrol is likely to more price elastic than petrol as a whole. Price optimization considering demand basic economics to make better pricing calculate three types of price elasticities to determine the impact. Ib economics - elasticities in ib economics we define elasticity as a measure of how responsive one variable is to changes in price or any of the variable's determinants.
Here's a common-sense and easy to understand explanation of what price elasticity of demand is and how to calculate it. Price elasticity of demand is a measure used in economics to show the various research methods are used to calculate price elasticities in real. Defining elasticities • when price elasticity is between zero and -1 we say demand is inelastic • when price elasticity is between -1 and - infinity.
Economics and finance qs q, s, and the corresponding percent change in price the price elasticity of demand is the price elasticities of demand are always. Definition of price elasticity of supply examples and diagrams explaining the difference between elastic and inelastic supply factors that affect elasticty.
Elasticities of substitution of production economics, vol 1 (theory) price elasticity of demand4 blackorby and russell.
Ib economics notes on 21 price elasticity of demand (ped). Mastering managerial economics involves calculating values, with the ultimate goal of determining how to maximize profit the usefulness of the price elasticity of demand depends upon calculating a specific value that measures how responsive quantity demanded is to a price change in this formula.
Elasticity measures the sensitivity of demand (quantity demanded) to changes in variables such as its own price if the supply curve shifts because of government subsidies, it is useful to know the impact on the price and the quantity demanded a subsidy leads to an outward shift in supply, prices. Start studying economics: elasticity learn vocabulary, terms, and more with flashcards, games, and other study tools. Investopedia explains: what elasticity is, how to calculate elasticity, the difference between elastic and inelastic curves, and the various factors that impact elasticity. For better understanding the concepts of elastic and inelastic demand, the price elasticity of demand has been divided into five types, which are shown in figure-1:.Get file | s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583511175.9/warc/CC-MAIN-20181017132258-20181017153758-00124.warc.gz | CC-MAIN-2018-43 | 3,379 | 8 |
http://www.chegg.com/homework-help/questions-and-answers/1find-estimated-standard-error-sample-mean-following-samples-use-one-decimal-place-1-n-7-s-q3803125 | math | 1.Find the estimated standard error for the sample mean for each of the following samples. (Use one decimal place.) 1. n=7 with SS=1132: ____ 2. n=36 with SS=2365: ____ 3. n=34 with SS=1260: ____ ***** Can you please show steps for I can fully understand how to solve this problem. Thank you. 2. A sample of n=25 scores has a mean of M=83 and a standard deviation of s=15. Explain what is measured by the sample standard deviation. The sample standard devaition decribes the ______________ of the ____________. In this case, the standard distance between _________ and _________ is 15 points. Compute the estimated standard error for the sample mean, and explain what is measured by the standard error. The standard error provides a measure of __________ a_______________-and _____________. In this case, the estimated standard error is ______ points. | s3://commoncrawl/crawl-data/CC-MAIN-2016-30/segments/1469257826773.17/warc/CC-MAIN-20160723071026-00180-ip-10-185-27-174.ec2.internal.warc.gz | CC-MAIN-2016-30 | 851 | 1 |
http://www.physicsforums.com/showthread.php?t=564614 | math | |Jan3-12, 01:57 AM||#1|
the basic concept of branching process
I have a question on the basic concept of branching process.
Say, in such a process, different objects of a generation don't
interfere with each other.
Consider an email forwarding analogy where one node forwards an email
to some other users. And those users will continue forwarding
the email to others....thus forming a cascade. However, it's
possible that different nodes may forward the email to one same node.
In this sense, is the process a branching process?
Thank you a lot.
|Jan5-12, 11:53 AM||#2|
The mathematical definitions of stochastic processes say that these processes have certain parts such as "states", "individuals", "descendants" etc. Until you say what things in the real world correspond these parts, then it is impossible to evaluate whether the situation in the real world satisfies the required mathematical assumptions of the process.
You didn't specify such definitions. When you say "in this sense", the phrase is ambiguous. If we ask a general question like "Is this, in some sense" a branching process?" or "Is this, in some sense, a Markov process?" then we allow the answerer complete freedom as to how he defines parts of the process such as "individuals" and "descendants". For example, in the case of email forwarding, you might be thinking of an "individual" as an email message forwarded from person A to person B. However, there is no law of mathematics that says that we must define an "individual" in this manner, so perhaps clever and devious people looking at the same situation might come up with different and more complicated definitions of "individual".
If we take "individual" to mean an email message forwarded from person A to person B then we still have the problem of defining a "descendant". For example, we could assume a simple model where no two emails arrive at the same time and person A always does his forwarding of messages in response to the first copy of a message he recieves. Then we could define the copy he forwards is a "descendant" of the first copy he got and not of the subsequent copies.
In my opinion, in the way the average person would define things, the example of email forwarding is not a branching process. However, I wouldn't put limits on human ingenuity by saying that no way exists to look at it as a branching process.
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http://www.wxsfdp.com/news/shownews.php?lang=cn&id=799 | math | Epoxy floor paint construction is a direct impact on its use value, so it is very important in the construction, but one thing we are more concerned about, is this kind of floor from the surface is very difficult to see whether it is flat? Then, how should the construction of epoxy floor be judged? Let Xiaobian tell you.
There are two ways to detect the evenness of epoxy floor. One is our regular method of measuring the smoothness of the floor by using a ruler. It is generally 2 meters in length and within 2 meters, the difference is not more than 5mm.
Lay on the ground, take the highest and lowest point, and see the difference.
However, there will be some defects in measuring the flatness of the ground by using the ruler. Figure:
When it comes to a lot of falls, the ruler method can not be expressed, and if many falls are less than 5 mm, then the ruler method is used to detect, but the actual ground flatness is not (wavy).
Another test method for the flatness of epoxy floors in Chongqing is the F value jointly developed by the American Concrete Association and the Canadian Scale Association. This detection method has two values, FF is flatness and FL is high difference value.
F数值一般的写法是 FF / FL 。如：FF 25 /FL 20 。
The F value is generally written in FF / FL. For example, FF 25 /FL 20.
Because the F value can express the evenness of the floor more accurately, it is often used in the super flat floor. But because the F value detection method is more complex than the rule method, and the epoxy floor is basically smooth, there are not too many flatness disputes, so the current most widely used still depends on the rule method.
标签: 环氧地坪 地坪 环氧地坪漆 环氧地坪施工 | s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400202686.56/warc/CC-MAIN-20200922000730-20200922030730-00222.warc.gz | CC-MAIN-2020-40 | 1,743 | 10 |
https://www.springerprofessional.de/metric-foliations-in-space-forms/4435392 | math | We have so far focused our attention mostly on the base space
of a Riemannian submersion
, in particular when searching for new metrics of nonnegative curvature on
It is also interesting to look at the total space of the fibration. The very fact that there exists a Riemannian submersion from
(or more generally, that
admits a metric foliation) is a sign that the space possesses a fair amount of symmetry. One therefore expects those Riemannian manifolds with the largest amount of symmetry — namely, space forms — to be the ones that display the most variety as far as these foliations are concerned. Surprisingly, a complete classification of metric foliations on spaces of constant curvature is not yet available. There does, however, exist a classification of metric
, at least in nonnegative curvature, which will be described in this chapter. | s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232256040.41/warc/CC-MAIN-20190520142005-20190520164005-00255.warc.gz | CC-MAIN-2019-22 | 853 | 7 |
http://mathforum.org/kb/message.jspa?messageID=7101576 | math | On Jun 17, 2:49 am, WM <mueck...@rz.fh-augsburg.de> wrote: > On 16 Jun., 23:43, MoeBlee <jazzm...@hotmail.com> wrote: > > > > Look simply at the results. > > > If a theory says that there is an uncountable set of real numbers such > > > each number can be identified as a computable or definable or > > > constructable one, or in other ways, then this theory is provably > > > wrong. > > > Please tell me which EXACT, SPECIFIC theorem of ZFC "says" that "each > > real number can be identified as a computable or definable or > > constructable one, or in other ways". > > If you start with Cantor's list, then the diagonal can be identified. > Do you mean that in ZFC Cantor's argument is wrong?
In this particular conversation, my interest is in Cantor's argument as it is formalized in Z set theory. And of course it's not "wrong". It is simply first order logic applied to axioms. You may wish to have any feeling or conviction you like about first order logic and the axioms, but that Cantor's argument can be formalized as proof in Z set theory is not controvertible. (As I alluded, a proof being a certain kind of finite sequence of finite sequences of symbols.)
> Further: A number that cannot be put in trichotomy with others is not > a number. Is such an unknown entity called a number in ZFC?
I make no use of a predicate 'is a number' where 'number' is STAND- ALONE nor does an ordinary formalization of Cantor's argument.
And I don't know what failure of trichotomy (in ZFC) you might have in mind.
> > > Reason: Cantor either proves that a countable set is uncountable or > > > that a constructible/computable/definable number is not constructible/ > > > computable/definable. > > > Whatever Cantor proves, my question is specifically as to ZFC. > > I consider results only. If ZFC allows the conclusion that Cantor's > diagonal argument is wrong, then ZFC may be right. Is it right?
"right", "wrong" are your terminology. I've stated already now my most basic view of Cantor's argument as formalized in Z set theory. Whether this or that is, in some other sense, "right" or "wrong" is another discussion, but not needed to address the mere question of the theoremhood of a certain formula in the language of ZFC.
> > > What the theory internally may be able to prove or not to prove is, at > > > least for my person, completely uninteresting. > > > What interests you is entirely up to you, of course. But you've not > > shown that ZFC is inconsistent (where 'inconsistent' is defined as > > "having as a theorem some formula and its negation"). > > I have been told that ZFC yields this result: There are uncountable > many real numbers. And by number I understand something that can be > put in trichotomy with other numbers.
ZFC doesn't make use in this context of a predicate "is a number" where 'number' is STAND-ALONE. As to 'real number" we may regard that as single predicate. In light of the formal itself itself, we could as well write 'realnumber' or 'realschmumber' or 'schmeal schmumber' so that 'number' has no component meaning onto itself. You should understand that names of predicates in formal mathematics are not always compositional, particular with adjectives. I can define "is a slooper spockle" without committing that 'slooper' and 'spockle' have independent meaning. This is because English is only an INFORMAL rendering of certain formal predicates. So, as to the FORMAL theory, for example, where we say "x is a real number", the actual formula would be "Rx" where 'R' (or whatever other typographic shape) has been chosen as the formal predicate symbol ordinarily rendered in English as 'is a real number'.
Please tell me whether you understand this. If you find fault in it, then so be it. I'm not interested in arguing with you about it. But at least you know now how I regard such matters in terminology.
> If this is not the case, ZFC may > be right. > Others have told me that ZFC does not prove any uncountability at all > and that the "standard model" is not a model of ZFC at all. If this is > the case, ZFC may be right.
ZFC proves a FORMULA that we READ or RENDER in ENGLISH as "there exists an x such that x is uncountable".
As to models, there are different senses of the word 'model' depending on context of discussion. | s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794864186.38/warc/CC-MAIN-20180521122245-20180521142245-00167.warc.gz | CC-MAIN-2018-22 | 4,275 | 13 |
https://www.gordonbrush.com/products/ostrich-feather-duster-m550260 | math | Item sold in packages of 12 for $240.96 pkg
$20.08 each (price per package $240.96)
$19.08 each (price per package $228.96)
$17.94 each (price per package $215.28)
$16.86 each (price per package $202.32)
This Ostrich Feather Duster is made with genuine ostrich feathers to attract and hold dust. The brush is designed with a retractable plastic handle, to make it quick and easy to reach hard to clean areas. | s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662552994.41/warc/CC-MAIN-20220523011006-20220523041006-00431.warc.gz | CC-MAIN-2022-21 | 408 | 6 |
https://techcrazee.com/calculus-in-engineering/ | math | Application of Differential Calculus in Engineering
Differential calculus has developed, and its application is for multiple modern purposes. It is useful in almost all sciences like engineering and physics. Most of the contemporary developments like aviation, building methods, and other technologies use differential calculus.
The success is on the application of differential equations. Other uses are in calculus variation, vector calculus, differential topology, and complex analysis. In general, calculus means the mathematical study of change; on the other hand, engineering is the knowledge you possess of natural sciences and mathematical from any research, practice, and experience. It brings about ways to develop different approaches to use all the materials and forces to benefit all humankind. Most engineers utilize differential engineering in their daily life and some in their computer programs. Some of the programs help in simplifying engineering designs.
There are two main applications; differentiation and integration. They are all beneficial in engineering practice for optimization and summation.
Most of the applications use differential calculus. They help in the derivation of fundamental fluid mechanics where you need calculus. The entire hydraulic analysis program helps in designing and opening channel systems using numerical approaches. It is the area measurable as the area located on the plot curve and the time applicable using calculus.
In this type of engineering, differential calculus helps know the forces of any complex configurations in structural elements. It is all about structural analysis concerning seismic designs applied using calculus. When there is a need to know about soil structure, it is possible to know about the soil strength using calculus. It will determine the lateral earth pressure and slope stability for complicated situations.
Most of differential calculus and calculus, in general, is in mechanical engineering. It has helped calculate the surface area of complicated objects to know about the friction forces, pump designing as per head, and flow rate. The calculating power is from the battery system. The Newton law of cooling uses differential equations in HVAC design to solve any integration.
Multiple application of differential calculus is in aerospace engineering. It helps in calculating the ideal rocket equation for calculus application. Itis beneficial in rockets analysis and gravitational modelling over space and time. Most physics models use calculus, especially in astronomy and complex systems.
They use integration to know the number of materials required for curved shape construction,mostly when done on a sports arena. It helps in measuring the structure’s weight and improving buildings and infrastructures like bridges.
Integration in calculus helps to know the exact power cable length needed for any substations apart from each other.
Space flight engineering
Differential calculus helps in planning for extended missions. It helps in launching exploratory probes before orbiting velocities on earth and the planet. It helps with other gravitational influences such as the moon and sun.
When in college, differential calculus is complex hence affect your grades. In case you need support from experts, you can view this resource to help you understand the concepts and when handling your assignments. Most engineers apply calculus in their daily work, while others use computer-based programs to incorporate calculus, irrespective of calculus application, used in daily duties. The number of times you apply differential calculus will depend on the job and responsibilities. You will need to know about workflow and the ways to deliver all the work assigned. Differential calculus is a vital application in engineering. | s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296817249.26/warc/CC-MAIN-20240418222029-20240419012029-00891.warc.gz | CC-MAIN-2024-18 | 3,817 | 13 |
https://www.kopykitab.com/Basic-Engineering-Mathematics-Volume-II-For-3rd-Semester-of-RGPV-Bhopal-by-H-K-Dass-Verma-Rama | math | This book is revised according to the new syllabus of mathematics of second semester for all Engineering colleges affiliated to Rajiv Gandhi Proudyogiki Vishwavidyalaya, Bhopal (M.P.).
This book also covers the B. Tech., (B.E.) B. Arch. II semester course of other Indian Engineering colleges.
This book is divided into 12 chapters on the topics of the syllabus so that the students can easily understand the subject.
This book Useful for Engineering Students.
1. Rank Of Matrix
2. Solution Of Simultaneous Equation
3. Eigen Values, Eigen Vector, Cayley Hamilton Theorem
4. First Order Differential Equations
5. Linear Differential Equation Which Constant Co-efficients
6. Homogeneous Linear Differential-equations
7. Simultaneous Linear Differential-equations
8. Second Order Linear Differential Equations With Variable Co-efficients
9. Linear Partial Differential Equation Of First Order
10. Non-linear Partial Differential Equation Of First Order
11. Partial Differential Equations With Constant Coefficients
12. The Method Of Separable Variables
12. Working Capital Management—Inventory Management
13. Working Capital Management—Cash Management
14. Sources of Finance
15. Ratio Analysis
16. Cash Flow Statement
17. Funds Flow Statement | s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103033925.2/warc/CC-MAIN-20220625004242-20220625034242-00293.warc.gz | CC-MAIN-2022-27 | 1,243 | 22 |
https://attic.city/item/JL5j/1960s-does-1920s-white-mary-jane-strap-style-heels-/cackling-caps | math | 1960s does 1920s white Mary Jane strap style heels
60s/70s white Mary Janes with 2.5” heels, and cutest button strap. These measure at 10.24”, so these would best suit a modern 7.5 or 8. These are in ...
$$$$$ · Indexed on January 18, 2022
ATTIC Availability Predictor beta
San Diego, CA | s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662526009.35/warc/CC-MAIN-20220519074217-20220519104217-00694.warc.gz | CC-MAIN-2022-21 | 292 | 5 |
https://www.gocomics.com/nancy/2017/01/09 | math | Nancy: I've done this problem OVER and OVER, and the math notes tell me I keep getting the WRONG ANSWER!! Hello? Math homework? We're going to have to agree to disagree and just move on!
August 01, 2018
June 28, 2018
And a certain popular doll years ago got backlash for saying “Math is hard!”
September 24, 2018 | s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104189587.61/warc/CC-MAIN-20220702162147-20220702192147-00639.warc.gz | CC-MAIN-2022-27 | 316 | 5 |
https://www.rasmusen.org/rasmapedia/index.php?title=Test_Scores | math | The most recently available figures shows that the 75th percentile at Hillsdale is 33 for the ACT overall, and, I think, 31 for Math, 35 for Verbal. But Hillsdale's application pool soared from 2019 to 2020.
"How to estimate your IQ based on your GRE or SAT scores" says a GRE of 1430 corresponds to a 15-SD IQ score (Wechsler test) of 145 (99.9th percentile of the general population). A GRE of 1390 corresponds to a 16-SD IQ score (Stanford-Binet test) of 145 (99.8th percentile of the general population).
"Old and New GRE Comparison Tool" says a GRE of 1440 from equal verbal (new test 168) and math (new test 156) is 98th percentile verbal, 74th percentile math. A GRE of 1400 from equal verbal and math is 97th percentile verbal, 69th percentile math. A score of 1440 from top 800 for math (new test 166) and 640 for verbal (new test 162) is 90th percentile verbal, 94th percentile math.
Average GRE scores by graduate field 2015-2018 are:
- Biology 153 verbal, 154 math (75,000)
- Math 153, 163 (24,000)
- Physics 156, 162 (14,000)
- Electrical Engineering 148, 159 (49,000)
- Materials Engineering 153, 162 (5,000)
- Mechanical Engineering 149, 159 (35,000)
- Economics 154, 160 (19,000)
- History 156, 149 (8,000)
- Philosophy 159, 154 (3,000)
- Education 151, 148 (38,000)
What shocks me here are the numbers of test takers in differen fields. So few economists! So many engineers! So few in Education! I think this must include M.S. programs, and Education must have some other test it uses too. Still, how is it there are almost double the number of Math test takers as Economics? | s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585916.29/warc/CC-MAIN-20211024081003-20211024111003-00216.warc.gz | CC-MAIN-2021-43 | 1,592 | 15 |
https://www.gradesaver.com/textbooks/math/algebra/college-algebra-6th-edition/chapter-1-equations-and-inequalities-exercise-set-1-2-page-121/107 | math | $y=2x+5$; This is a linear equation (straight line on graph) including one variable, which is $x$.
Work Step by Step
A linear equation has the form $y=mx+b$, and so there are countless ways to express this.
You can help us out by revising, improving and updating this answer.Update this answer
After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback. | s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376824822.41/warc/CC-MAIN-20181213123823-20181213145323-00462.warc.gz | CC-MAIN-2018-51 | 455 | 5 |
https://www.homeworkmarket.com/content/i-need-help-physics-homework-its-about-project-motion-and-newtons-second-law | math | i need help with physics homework......... its about project motion and newton's second lawq8_rim
i need help with physics homework......... its about project motion and newton's second law
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https://puzzling.stackexchange.com/questions/105210/stacking-word-bouncer | math | Am I (3<) a singer in a temple (3,5v) or in a a sun-starved (5^) metric conflict area (3,5>)?
A disfiguring motherly animal(2,3,4v) with a not discrete behind (4,6<) has a flirty drink(3,5>) with an all-right animal (2,5^).
Wearable fish (3,4^) are more normal (4,5>) than coin kissers at Chinese distance(2,3,4<) getting a next life (2,5v)
You cannot win (5<) an already finished test (2,4v) with low prices (5>) or your fundamental qualities(6^).
1/ The clues refer to words of with the length and direction from one of the colored cells is given. e.g. "a singer in a temple" contains the hints for two words, which both can be read downward starting directly below the blue tile. The 3 letter word thus coincides with the first three letters of the 5 letter word.
2/ The grey diagonal lines change the direction of the words using the cell 90 degrees (as if they were mirrors).
3/ It does not matter what is behind a word. The longest word will always overlap with the longest word from the other side. eg the last 2 letters of green-up and green-right will overlap.
Note: I hope you like the concept. This is my first 'crossword' so some descriptions may be weird, vague or refer to obscure words. Still I think there are enough clues that are easy enough. Constructive criticism is appreciated. | s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964362923.11/warc/CC-MAIN-20211204003045-20211204033045-00252.warc.gz | CC-MAIN-2021-49 | 1,299 | 8 |
http://www.jiskha.com/display.cgi?id=1305997312 | math | Posted by clarissa on Saturday, May 21, 2011 at 1:01pm.
Your assignment is to define and explain in your own words.
We'll be glad to check your answers.
Ms. Sue, Will you be able to help me?
I'll be glad to help you.
You start, and I'll help you from there.
An equation is a statement of equality containing one or more variables.
To solve an equation means, find the value of the variable for which the equation satisfy
An example of an equation is x + 5 12.
x + 5 = 12
x = 12 - 5
x = 7
7 is a solution of the equation x + 5 = 12.
x + 5 = 12
7 + 5 = 12
12 = 12
Since both sides are, 7 satisfy to equation.
I just post can you check to see if I answer it correct?
This looks good -- as long as the definition is in your own words.
One minor correction -- you forgot the equal sign in this line.
An example of an equation is x + 5 12
Oh yea that's right thanks!
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For Further Reading | s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368706153698/warc/CC-MAIN-20130516120913-00016-ip-10-60-113-184.ec2.internal.warc.gz | CC-MAIN-2013-20 | 1,747 | 34 |
https://www.hackmath.net/en/math-problem/11541 | math | Boys and girls
There are 20 boys and 10 girls in the class. How many different dance pairs can we make of them?
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http://tauntgamers.com/forums/index.php?/topic/4289-thank-you/ | math | On the sticky topic, I had asked you how to use this forum. Now, after carefully reflecting on your response, do I finally realize the horrible truth that I have been hiding from myself:
The one who does not know how to use the forum... is MYSELF!
This must also be why so few people use it as well, because I do not know how to use it to truly see them! If I could only learn the correct way of forum viewing, surely the hidden paths of this website would spill open to me and reveal the secret that they hide. You must help me Dicky! | s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370510352.43/warc/CC-MAIN-20200403061648-20200403091648-00326.warc.gz | CC-MAIN-2020-16 | 535 | 3 |
http://ieeexplore.ieee.org/xpl/articleDetails.jsp?reload=true&arnumber=1142935&contentType=Journals+%26+Magazines | math | Skip to Main Content
An exact alternative approach to the diagrammatic technique for treating scattering from rough surfaces is developed. The magnetic field integral equation for the current induced on the rough perfectly conducting surface is multiplied by a Fourier kernel involving all orders of surface height derivatives and their associated transform variables. Averages of this weighted equation are converted to convolations in the transform domain. The result of this operation is a singular integral equation of the first kind of infinite dimensions (because of the infinite number of height derivatives) for the stochastic Fourier transform of the current. A procedure is developed for estimating the effects of ignoring one or more surface height derivatives in terms of the range of validity of the resulting approximate solution. Special limiting cases of very gently undulating surfaces and uniformly rough surfaces are examined. New and illuminating results are obtained for the latter case. | s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1394010557169/warc/CC-MAIN-20140305090917-00091-ip-10-183-142-35.ec2.internal.warc.gz | CC-MAIN-2014-10 | 1,008 | 2 |
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