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http://streetfest.maths.mq.edu.au/abstract?lastname=Baez&firstname=John&extratalk=2 | Please note: You are viewing the unstyled version of this web site. Either your browser does not support CSS (cascading style sheets) or it has been disabled.
# Macquarie University Department of Mathematics
## Categories in Algebra, Geometry and Mathematical Physics
### Conference in honour of Ross Street's sixtieth birthday
#### July 11-16 2005, Macquarie University, Sydney
Thu, 14 July: 17:00 - 18:00
##### The Mysteries of Counting: Euler Characteristic Versus Homotopy Cardinality
###### Baez, John (University of California, Riverside)
We all know what it means for a set to have 6 elements, but what sort of thing has $-1$ elements, or $5/2$ ?
These questions have nice answers. The Euler characteristic of a space is a generalization of cardinality that admits negative integer values, while the homotopy cardinality is a generalization that admits positive real values. These concepts shed new light on basic mathematics. For example, the space of finite sets turns out to have homotopy cardinality $e$, and this explains the key properties of the exponential function. Euler characteristic and homotopy cardinality share many properties, but it's hard to tell if they are the same, because there are very few spaces for which both are well-defined. However, in many cases where one is well-defined, the other may be computed by dubious manipulations involving divergent series --- and the two then agree!
\par\noindent
The challenge of unifying them remains open.
\smallskip | 2018-03-19 06:55:09 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6366117000579834, "perplexity": 719.7908306686385}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257646602.39/warc/CC-MAIN-20180319062143-20180319082143-00533.warc.gz"} |
https://electronics.stackexchange.com/questions/268061/frequency-of-oscillator-exercise | # Frequency of oscillator (exercise)
I tried to evaluate the frequency of the following oscillator:
The loop gain $\beta(j\omega)A(j\omega)$ is:
To find frequency I must impose the condition:
$$\angle \beta(j\omega_0)A(j\omega_0)=0$$
but I don't know if the term $1-(RC\omega_0)^2$ is positive or negative. The angle is different in the two cases.
• Choose the lower $\omega$ where it is + (which has more gain ) such that the numerator= demominator and R2/R1 fine tunes that ratio =1.00 for a perfect sinewave if more than 1 then it starts to saturate where gain is automatically reduced. This assumes a split supply otherwise Vin+ shud be Vcc/2 instead of gnd. Essentiall'y 2xRC gives 180 deg lag and R2/R1 amp gives the other 180 inversion for Barhausen Criteria with unity gain Nov 7, 2016 at 17:56
• In your equation a minus sign is missing (gain is -R2/R1). Where is the problem? For w=1/RC the terms [1-(RCwo)²] are equal to zero and the equation reduces to (-R2/R1)x(-1)=+R2/R1 which can be made to be unity.
– LvW
Jan 8, 2017 at 10:45 | 2022-07-06 04:31:38 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8893318176269531, "perplexity": 1742.6794748575362}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104660626.98/warc/CC-MAIN-20220706030209-20220706060209-00606.warc.gz"} |
http://openstudy.com/updates/4f22c76ae4b0a2a9c265ce42 | ## anonymous 4 years ago Determine the slope of the line which passes through these two points: (-1, 3) and (6, 9).
1. anonymous
6/7
2. anonymous
y=ax+b a=(9-3)/(6-(-1))=6/7
3. anonymous
(9-3)/(6--1) 6/7
4. anonymous
Line equation = $y-y _{0}=2a(x-x _{0})$
5. anonymous
y−y 0 =a(x−x 0 ) this is right
6. anonymous
y-9=2*(6/7)*(x-6)
7. anonymous
don't mix it up with physic
8. anonymous
you're wrong amir.sat
9. anonymous
you're wrong
10. anonymous
not me
11. anonymous
review your lesson more timea lol
12. anonymous
|dw:1327679283219:dw|
13. anonymous
Gradient = distance up divided by distance along, i.e. gradient is $m = \frac{y_2 - y_1}{x_2-x_1}$ Where the points have coordinates $(x_1, y_1), (x_2, y_2)$ That is the formula you use to calculate the gradient of any line passing through two known points.
14. anonymous
y=(12/7)x-(9/7)
15. anonymous
Use $\Large \frac{{\Delta y}}{{\Delta x}} = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}$
16. anonymous
$\Large \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}} = \frac{{9 - 3}}{{6 - - 1}} = \frac{6}{7}$ So whoever said otherwise is incorrect. | 2017-01-16 22:27:10 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8063402771949768, "perplexity": 6703.097239601066}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560279368.44/warc/CC-MAIN-20170116095119-00360-ip-10-171-10-70.ec2.internal.warc.gz"} |
https://cs.stackexchange.com/questions/47653/why-does-an-admissible-heuristic-mean-a-is-optimal | # Why does an admissible heuristic mean A* is optimal?
An admissible heuristic never overestimates the cost to reach the goal. However, isn't that only the relative difference between heuristics for two different paths matter?
Say we have optimal path A (cost 100 to reach goal) and sub-optimal path Z (cost 120 to reach goal). Even if the heuristic is admissible, say it gives A a heuristic of cost 99 while it gives Z a heuristic of cost 10.
In both cases, the heuristic is admissible since it's lower than the actual cost it'll take to reach the goal, but still under this, Z is optimal since the heuristic gives a cost of 10 to Z and a cost of 99 to A.
It seems to me then it doesn't even matter that the heuristic is admissible. You still get the suboptimal solution.
What am I missing?
• Eh, sorry, I see two answers now. Does that mean this is on topic here? – Maarten Bodewes Sep 12 '15 at 15:26
• @MaartenBodewes It's a better fit on CS.SE for sure, but the migration options are so bad that a lot of users who browse [algorithm] would rather just answer the question. – David Eisenstat Sep 12 '15 at 15:41
## With an admissible heuristic
The heuristic defines which nodes will be explored first, but does not change the final path found.
In your example, the heuristic will cause the path to Z to be explored first. The algorithm will discover the true (expensive) cost of 120. Then it will decide to explore the A path and discover the optimal route.
A better heuristic would guess A was the way to go immediately, find the cost of 100, and never bother exploring Z at all (e.g. if the heuristic said the cost was greater than 100).
So the heuristic changes the execution time, but not the final answer.
## With an unadmissable heuristic
If the heuristic marked A as costing 130 (when the true cost is 100), it may find the route to Z (true cost 120), and instantly stop (because it "knows" the cost to A is at least 130), so return the wrong answer.
• If the heuristic was non-admissible though, wouldn't it explore Z first, discover the true (expensive) cost of 120 and then explore the A path, find its true cost, and mark is as optimal? How does the fact that the heuristic is non-admissible mean that we mark Z as the optimal one and miss A? – Laura K Sep 12 '15 at 15:28
• The algorithm doesn't explore paths that it "knows" will have a higher cost - see my edit. – Peter de Rivaz Sep 12 '15 at 15:33
A* does not guarantee to find optimal path to nodes with h(v) > 0. It only guarantees to find the optimal route to the target node, with h(v) = 0. In the process of doing so, it will find optimal path to many nodes along the way, but not all of them. | 2020-10-29 02:10:52 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.48337796330451965, "perplexity": 1090.7961431041365}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107902683.56/warc/CC-MAIN-20201029010437-20201029040437-00500.warc.gz"} |
https://proofwiki.org/wiki/All_Bases_of_Matroid_have_same_Cardinality | # All Bases of Matroid have same Cardinality
## Theorem
Let $M = \struct {S, \mathscr I}$ be a matroid.
Let $\rho: \powerset S \to \Z$ be the rank function of $M$.
Let $B$ be a base of $M$.
Then:
$\size B = \map \rho S$
That is, all bases of $M$ have the same cardinality, which is the rank of $M$.
### Corollary
Let $X \subseteq S$ be any independent subset of $M$.
Then:
$\card X \le \card B$
## Proof
By definition of the rank function:
$\map \rho S = \max \set{\size X : X \subseteq S, X \in \mathscr I}$
Let $B_1$ be an independent subset such that:
$\size {B_1} = \map \rho S$
It is shown that $B_1$ is a base.
Let $X$ be an independent superset of $B_1$.
$\size {B_1} \le \size X$
By choice of $B_1$:
$\size X \le \size {B_1}$
It follows that:
$\size X = \size {B_1}$
$X = B_1$
It follows that $B_1$ is a maximal independent subset.
That is, $B_1$ is a base.
It is now shown that any other base has the same cardinality as $B_1$.
Let $B_2$ be any other base.
By choice of $B_1$:
$\size {B_2} \le \size {B_1}$
Aiming for a contradiction, suppose $\size {B_2} < \size {B_1}$.
From Independent Set can be Augmented by Larger Independent Set there exists $Z \subseteq B_1 \setminus B_2$ such that:
$B_2 \cup Z \in \mathscr I$
$\size{B_2 \cup Z} = \size{B_1}$
This contradicts the maximality of $B_2$ in $\mathscr I$.
Then:
$\size {B_2} = \size {B_1} = \map \rho S$
$\blacksquare$ | 2021-05-07 16:24:49 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9627048373222351, "perplexity": 328.4179592131851}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988796.88/warc/CC-MAIN-20210507150814-20210507180814-00450.warc.gz"} |
https://testbook.com/question-answer/if-the-zeroes-of-the-polynomial-x3-3x2-x-1-a--60a607aee471f0680b2450c1 | # If the zeroes of the polynomial x3 - 3x2 + x + 1 are a - b, a and a + b respectively, then the values of 'a' and 'b' are respectively.
This question was previously asked in
DSSSB TGT Maths Female Subject Concerned - 18 Nov 2018 Shift 3
View all DSSSB TGT Papers >
1. $$1, ±\sqrt{2}$$
2. $$3, -\sqrt2$$
3. $$-1, \sqrt2$$
4. $$1, ± \sqrt{\dfrac{3}{2}}$$
Option 1 : $$1, ±\sqrt{2}$$
## Detailed Solution
Given:
Zeroes of the polynomial = (a - b), a and (a + b)
Formula used:
Sum of zeroes = –B/A
Product of zeroes = -D/A
Where,
A = Coefficient of x3
B = Coefficient of x2
C = Coefficient of x
Calculations:
Using the given polynomial
Sum of zeroes = (a - b) + a + (a + b) = 3
⇒ 3a = 3
⇒ a = 1
Product of zeroes = (a – b) × a × (a + b) = -1
⇒ (1 - b) × 1 × (1 + b) = -1
⇒ 1 - b2 = -1
⇒ b2 = 2
⇒ b = ±√2
∴ The values of 'a' and 'b' are 1 and ±√2 | 2021-09-25 15:51:06 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6028940677642822, "perplexity": 2026.4922147262916}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057687.51/warc/CC-MAIN-20210925142524-20210925172524-00135.warc.gz"} |
https://lavelle.chem.ucla.edu/forum/viewtopic.php?f=14&t=21193&view=print | Page 1 of 1
### energy required to remove an electron
Posted: Wed Jun 28, 2017 3:42 pm
I am having a tough time calculating the energy required to remove an electron from a sodium atom. The given information includes the ejected electron's velocity v = 6.61 x 10^5 m/s and sodium's work function = 150.6 kJ/mol. How do I approach this question?
### Re: energy required to remove an electron
Posted: Wed Jun 28, 2017 5:16 pm
The energy required to remove an electron is the value of sodium's work function, so the value would be 150.6 kj/mol.
### Re: energy required to remove an electron
Posted: Wed Jun 28, 2017 7:12 pm
It should also be said that the question in the post-assessment asks for the energy required to remove 1 electron, but the work function is given in kJ per mol of electrons. In order to convert this number into the energy (in Joules) to remove a single electron, we first multiply 150.6 kJ by 1000 to get the energy in Joules, which is 1.506 x 10^5 J. We then divide the energy in Joules by 6.02 x 10^23 (number of electrons in one mol) to get a work function of 2.502 x 10^-19 J/electron.
### Re: energy required to remove an electron
Posted: Wed Jun 28, 2017 9:35 pm
Hope the image of the worked out problem attached helps. I'll walk through my brain jumble:
1) To solve for the KE of the ejected electron, use the equation on the right side of the diagram because this is the amount of KE of the electrons. This equation is E$E_{KE}=\frac{1}{2}m_{electron}\times v_{electron}^{2}$
Now, all you have to do is take your known quantities (velocity, mass of electron constant), then plug and chug. You should get $1.99\times 10^{-19}J$
2) To solve for the energy needed to remove an e- from the metal, remember that this energy is the amount of energy the photon needs to meet or exceed to remove the e-, so wouldn't it make sense for this energy to be the threshold energy (work function)? Yes, it does. You are actually given the threshold energy, but it is in KJ. Convert the quantity into Joules by a unit conversion (1000 Joules in 1 KJ). You should get $1.506\times 10^{5}J$
3) Finally, we need to find the frequency of the incident light. You already know that $E_{photon}-\phi =E_{KE}$ Using this equation, rearrange to solve for the energy of the photon (because we know the threshold and KE of photon already). Plug and chug to solve for the energy. Now that we know the energy, to find the frequency of the light, use the equation $E=h\nu$ Rearrange the equation to solve for frequency. Plug and chug, then you're done! Yippee! :)
https://ibb.co/ciCKXk
This is the image^ Idk how to post it. LMK if the URL fails me
**EDIT**
Divide the energy to remove the metal (threshold) by Avogadro's number because it is the energy per electron. Then, use that number instead of the mess I wrote to plug and chug to find the frequency.
### Re: energy required to remove an electron [ENDORSED]
Posted: Thu Jun 29, 2017 10:13 am
Since the work function is given by J/mol, is it possible that we need to devide 1.506*10^5 by 6.022*20^23 to get the work function for one electron per atom?
Sarah_Wilen wrote:Hope the image of the worked out problem attached helps. I'll walk through my brain jumble:
1) To solve for the KE of the ejected electron, use the equation on the right side of the diagram because this is the amount of KE of the electrons. This equation is E$E_{KE}=\frac{1}{2}m_{electron}\times v_{electron}^{2}$
Now, all you have to do is take your known quantities (velocity, mass of electron constant), then plug and chug. You should get $1.99\times 10^{-19}J$
506*
2) To solve for the energy needed to remove an e- from the metal, remember that this energy is the amount of energy the photon needs to meet or exceed to remove the e-, so wouldn't it make sense for this energy to be the threshold energy (work function)? Yes, it does. You are actually given the threshold energy, but it is in KJ. Convert the quantity into Joules by a unit conversion (1000 Joules in 1 KJ). You should get $1.506\times 10^{5}J$
3) Finally, we need to find the frequency of the incident light. You already know that $E_{photon}-\phi =E_{KE}$ Using this equation, rearrange to solve for the energy of the photon (because we know the threshold and KE of photon already). Plug and chug to solve for the energy. Now that we know the energy, to find the frequency of the light, use the equation $E=h\nu$ Rearrange the equation to solve for frequency. Plug and chug, then you're done! Yippee! :)
https://ibb.co/ciCKXk
This is the image^ Idk how to post it. LMK if the URL fails me
### Re: energy required to remove an electron
Posted: Thu Jun 29, 2017 10:28 am
You are exactly right! I didn't catch that thank you so much. Yes, divide 1.506*10^5 by 6.02*10^23 to get the function for one electron per atom. Then, use that number instead of whatever I wrote down to get the final answer to solve for frequency. Sorry for the confusion! Thanks
Xinye_Jiang_1A wrote:Since the work function is given by J/mol, is it possible that we need to devide 1.506*10^5 by 6.022*20^23 to get the work function for one electron per atom?
Sarah_Wilen wrote:Hope the image of the worked out problem attached helps. I'll walk through my brain jumble:
1) To solve for the KE of the ejected electron, use the equation on the right side of the diagram because this is the amount of KE of the electrons. This equation is E$E_{KE}=\frac{1}{2}m_{electron}\times v_{electron}^{2}$
Now, all you have to do is take your known quantities (velocity, mass of electron constant), then plug and chug. You should get $1.99\times 10^{-19}J$
506*
2) To solve for the energy needed to remove an e- from the metal, remember that this energy is the amount of energy the photon needs to meet or exceed to remove the e-, so wouldn't it make sense for this energy to be the threshold energy (work function)? Yes, it does. You are actually given the threshold energy, but it is in KJ. Convert the quantity into Joules by a unit conversion (1000 Joules in 1 KJ). You should get $1.506\times 10^{5}J$
3) Finally, we need to find the frequency of the incident light. You already know that $E_{photon}-\phi =E_{KE}$ Using this equation, rearrange to solve for the energy of the photon (because we know the threshold and KE of photon already). Plug and chug to solve for the energy. Now that we know the energy, to find the frequency of the light, use the equation $E=h\nu$ Rearrange the equation to solve for frequency. Plug and chug, then you're done! Yippee! :)
https://ibb.co/ciCKXk
This is the image^ Idk how to post it. LMK if the URL fails me
### Re: energy required to remove an electron
Posted: Thu Jun 29, 2017 11:13 am
A lot of good chemistry here!
Great to see students working collaboratively and helping each other.
### Re: energy required to remove an electron
Posted: Sat Oct 20, 2018 4:36 pm
Yeah if you do the full problem out (by dividing Avogadro's number) you end up with 2.501 x 10^-19 J of energy as the work function, which after plugging it in to get the frequency of incident light gets you 6.78 x 10^14 Hz! | 2020-09-23 23:36:06 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 15, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7104207277297974, "perplexity": 525.3273621289777}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400212959.12/warc/CC-MAIN-20200923211300-20200924001300-00139.warc.gz"} |
https://infoscience.epfl.ch/record/227024 | ## Neutrinoless double beta decay and low scale leptogenesis
The extension of the Standard Model by right handed neutrinos with masses in the GeV range can simultaneously explain the observed neutrino masses via the seesaw mechanism and the baryon asymmetry of the universe via leptogenesis. It has previously been claimed that the requirement for successful baryogenesis implies that the rate of neutrinoless double beta decay in this scenario is always smaller than the standard prediction from light neutrino exchange alone. In contrast, we find that the rate for this process can also be enhanced due to a dominant contribution from heavy neutrino exchange. In a small part of the parameter space it even exceeds the current experimental limit, while the properties of the heavy neutrinos are consistent with all other experimental constraints and the observed baryon asymmetry is reproduced. This implies that neutrinoless double beta decay experiments have already started to rule out part of the leptogenesis parameter space that is not constrained by any other experiment, and the lepton number violation that is responsible for the origin of baryonic matter in the universe may be observed in the near future. (C) 2016 The Authors. Published by Elsevier B.V.
Published in:
Physics Letters B, 763, 72-79
Year:
2016
Publisher:
Amsterdam, Elsevier
ISSN:
0370-2693
Laboratories: | 2018-11-14 12:06:56 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8211028575897217, "perplexity": 366.5477821476137}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039741979.10/warc/CC-MAIN-20181114104603-20181114130603-00372.warc.gz"} |
https://raspberrypi.stackexchange.com/questions/74099/how-to-use-python-to-make-a-door-or-bed-in-minecraft | # How to use Python to make a door or bed in Minecraft? [closed]
I have been using a readable CSV file and a bit of code to generate a fort, but then not a single one of my beds, doors or ladders appeared. Only the back half of my beds actually appeared. For a test I used setBlock() to make a bed but again only the back half appeared. How do I make Python realise I want to make it cover 2 blocks?
• I realize this is a really old topic. However, with all respect to techraf, Milliways, Steve Robillard, and Jacobmoo1, this question deals with an API for a version of minecraft ONLY avaiable on the Raspberry Pi. – Thorin Schmidt May 10 '18 at 13:05
Just as in vanilla Minecraft, you need to set two blocks to be a bed for this to work.
The vanilla commands would be:
/setblock 0 64 0 bed 0
/setblock 0 64 1 bed 8
(for a bed facing north)
You should do something similar in your Minecraft Pi Python code:
mc.setBlock(x, y, z, 26, 0)
mc.setBlock(x, y, z + 1, 26, 8)
Remember the API for setBlock is setBlock(x,y,z,id,[data]). The explanation for the data code is available at the Gamepedia wiki:
The door operates similarly, but with block ID 64 instead, and you'll need to modify the y (up/down axis, with positive being up) instead of the z (north/south axis, with positive being south).
• @user75085 Did you set use the exact example I gave, including the 0 and 8? That is how you tell the game that one half is the bottom end and one is the top end. – Aurora0001 Oct 22 '17 at 8:38 | 2021-04-22 11:51:09 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.17179948091506958, "perplexity": 1941.5319031734373}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618039603582.93/warc/CC-MAIN-20210422100106-20210422130106-00213.warc.gz"} |
http://mathhelpforum.com/calculus/130132-limits.html | # Math Help - Limits
1. ## Limits
find this
the picture
2. Originally Posted by rqeeb
find this
the picture
evaluate it along the path $y=mx^3$.
3. Originally Posted by Ted
evaluate it along the path $y=mx^3$.
it will be (m^3)/(1+m^4)
but if we use y=x it will be zero
which one is the correct
4. Originally Posted by rqeeb
it will be (m^3)/(1+m^4)
but if we use y=x it will be zero
which one is the correct
No need to use $y=x$; since the value of the limit along the path $y=mx^3$ depends on m, then the limit has different values for different values of $m$.
Hence, the limit does not exist.
5. Originally Posted by Ted
No need to use $y=x$; since the value of the limit along the path $y=mx^3$ depends on m, then the limit has different values for different values of $m$.
Hence, the limit does not exist.
thanks
but if we use polar coordinates it will be zero.... why
6. Originally Posted by rqeeb
thanks
but if we use polar coordinates it will be zero.... why
If you use polar coordinates, you will face:
$\lim_{r\to 0} \frac{r^6sin^3(\theta)cos^3(\theta)}{r^{12}cos^{12 }(\theta)+r^4sin^4(\theta)}=\lim_{r\to 0} \frac{r^2sin^3(\theta)cos^3(\theta)}{r^8cos^{12}(\ theta)+sin^4(\theta)}$
What did you do for it ?
7. Originally Posted by Ted
If you use polar coordinates, you will face:
$\lim_{r\to 0} \frac{r^6sin^3(\theta)cos^3(\theta)}{r^{12}cos^{12 }(\theta)+r^4sin^4(\theta)}=\lim_{r\to 0} \frac{r^2sin^3(\theta)cos^3(\theta)}{r^8cos^{12}(\ theta)+sin^4(\theta)}$
What did you do for it ?
this
$\lim_{r\to 0} \frac{r^6sin^3(\theta)cos^3(\theta)}{r^{12}cos^{12 }(\theta)+r^4sin^4(\theta)}=\lim_{r\to 0} \frac{0}{0+sin^4(\theta)}=0$
8. Originally Posted by rqeeb
this
$\lim_{r\to 0} \frac{r^6sin^3(\theta)cos^3(\theta)}{r^{12}cos^{12 }(\theta)+r^4sin^4(\theta)}=\lim_{r\to 0} \frac{0}{0+sin^4(\theta)}=0$
Nope. The problem here is that $sin^4(\theta)$ can be zero.
and this will make the limit $=\frac{0}{0}$ which is indeterminate.
9. Originally Posted by Ted
Nope. The problem here is that $sin^4(\theta)$ can be zero.
and this will make the limit $=\frac{0}{0}$ which is indeterminate.
Is that right!!
because our teacher told us that we deal with any term has theta as a constant.
10. Originally Posted by rqeeb
Is that right!!
because our teacher told us that we deal with any term has theta as a constant.
and the constant could be zero.
11. It could be
Thanks 4 everything | 2016-05-25 02:55:02 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 16, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9698013663291931, "perplexity": 877.7193160327762}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-22/segments/1464049274059.91/warc/CC-MAIN-20160524002114-00237-ip-10-185-217-139.ec2.internal.warc.gz"} |
https://nrich.maths.org/709 | ### Even Up
Consider all of the five digit numbers which we can form using only the digits 2, 4, 6 and 8. If these numbers are arranged in ascending order, what is the 512th number?
### What an Odd Fact(or)
Can you show that 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divisible by 5?
# Quick Times
##### Age 11 to 14 Challenge Level:
$32 \times 38 = 30 \times 40 + 2 \times 8$
$34 \times 36 = 30 \times 40 + 4 \times 6$
$56 \times 54 = 50 \times 60 + 6 \times 4$
$73 \times77 = 70 \times80 + 3 \times 7$
And so on?
Verify and generalise if possible. | 2019-12-12 04:15:21 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.1943301409482956, "perplexity": 409.7439604393034}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540536855.78/warc/CC-MAIN-20191212023648-20191212051648-00382.warc.gz"} |
http://math.stackexchange.com/questions/319035/motivation-of-feynman-kac-formula-and-its-relation-to-kolmogorov-backward-forwar/320416 | # Motivation of Feynman-Kac formula and its relation to Kolmogorov backward/forward equations?
Kolmogorov backward/forward equations are pdes, derived for the semigroups constructed from the Markov transition kernels.
Feynman-Kac formula is also a pde corresponding to a stochastic process defined by a SDE. But I was wondering if the stochastic process is also Markovian? I.e., does Feynman-Kac formula apply only to Markov process?
Does the semigroups from the Markov transition kernels also lead to Feynman-kac pde?
• If not, what leads to Feynman-Kac pde?
• If yes, Is Feynman-Kac pde also some kind of Kolmogorov backward/forward equation? if not, how is Feynman-Kac pde related to Kolmogorov backward/forward equations?
Thanks and regards!
-
First of all, it would be nice if you link the definitions of F-K formula and KBE you have in mind. Anyway:
1. KBE is an equation used to study $P_t f(x):=\mathsf E_x[f(X_t)]$ in terms of the generator $$\mathcal A :=\lim_{t\downarrow 0}\frac{P_t - P_0}{t}.$$ This is indeed applies to general Markov processes, as its definition depends only such notions as semigroups and generators.
2. F-K formula (at least the one given in Oksendal, Theorem 8.2.1) is devoted to the same problem and appears to be only a generalization to the case of killed diffusions. The term killed refers to the process which is not conservative, e.g. for conservative Markov processes $P_t1 = 1$ for all times $t$, whereas for non-conservative $P_t1\leq 1$ and $P_t1\neq 1$. This refers to the case, when the process "leaves" the state space at some random time $\zeta$ (killing time) and jumps to some auxiliary cemetery state.
You wrote that F-K formula is a PDE linked to some SDE. I would expect, though, that such SDE has to be Markovian, since otherwise you wouldn't have a nice dependence on states exclusively (as PDE requires). I neither seen F-K formula (as a PDE) for non-Markovian SDEs, so it will be interesting if you provide a link.
Although F-K formula is stated originally for SDE, nothing prevents you from formulating it over general Markov processes. However, I guess in such case it falls down to be a special case of KBE for non-conservative Markov process. Unfortunately, I don't have a monograph of Dynkin "Markov processes" in hand, but I'm pretty sure you can find it there.
Killing/non-conservatism is a structure added on top of the structures above. This refers to the case, when $\Bbb P(X_t \in E)<1$ where $E$ is a state space and $t>0$. I'm not an expert on that, though, and I suggest you start reading serious book on stochastic processes, rather than lurking wikipedia. | 2014-08-30 15:01:44 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8715053796768188, "perplexity": 305.3483532687501}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-35/segments/1408500835488.52/warc/CC-MAIN-20140820021355-00369-ip-10-180-136-8.ec2.internal.warc.gz"} |
https://solvedlib.com/what-are-the-asymptotes-of-fx-x2x-34x-8,296523 | What are the asymptotes of f(x)=-x/((2x-3)(4x-8)) ?
Question:
What are the asymptotes of f(x)=-x/((2x-3)(4x-8)) ?
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http://drew.psib.org/blog/2017/10/ | Bounty Hunting as Highest Response Ratio Next
My original bounty hunting paper could actually be considered a market implementation of the Highest Response Ratio Next.
$\text{Priority}=\frac{\text{Waiting Time} + \text{Estimated Run Time}}{Estimated Run Time}$
The bounty assigned to tasks is set to some base bounty $B_0$ and a bounty rate $latex r$ which in the first bounty hunting paper was set to 100 and 1 respectively. So, as each tasks was left undone the bounty on it would rise. Tasks belong to particular “task classes” which basically means that there location is drawn from the same gaussian distribution. In the paper we used 20 task classes and there were four agents. The four agents were located at each of the four corners of a 40×60 rectangular grid. The agents decide which task to go after based on which task has the highest bounty per time step which works out to be:
$B(t) = P_i\frac{B_0 + rt}{\bar{T}}$
This is for the case when agents commit to tasks and are not allowed to abandon them. Essentially non-preemptive. When the agents are allowed to abandon tasks we then have:
$B(t) = P_i\frac{B_0 + rt + r\bar{T}}{\bar{T}}$
Both of these equations are stating that the agents are going after the task in an HRRN order. Now, the key part that bounty hunting added was that it made it work in a multiagent setting. This is where they learned some probability of success $P_i$ of going after the particular task class $i$. Also, the paper experimentally demonstrated some other nice properties of bounty hunting based task allocation in a dynamic setting.
Presently I’m taking this approach and moving it to dynamic vehicle routing setting where I use it to minimize the average waiting time of tasks where the agent doesn’t get teleported back to a home base after each task completion. Namely the dynamic multiagent traveling repairman problem. This is another setting where the Shortest Job Next (Nearest Neighbor in euclidean space) is a descent heuristic and because the agents are not reset causes interesting behavior with a non-zero bounty rate. | 2019-05-23 09:41:03 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 6, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7351857423782349, "perplexity": 1293.1907058980205}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232257197.14/warc/CC-MAIN-20190523083722-20190523105722-00034.warc.gz"} |
https://axibook.com/mechanical-engineering/lathe-machine/dynamometers-for-measuring-cutting-forces/2019/ | Dynamometers for Measuring Cutting Forces
At the end of this article, the reader would be able to (i) show the general principle of measurement, (ii) classify and apply different transducers for converting cutting forces into suitable signals, (iii) state the design requirements of tool-force dynamometers and (iv) develop and use strain gauge type dynamometer for turning, drilling, milling & grinding.
General principle of measurement
The existence of some physical variables like force, temperature etc and its magnitude or strength cannot be detected or quantified directly but can be so through their effect(s) only. For example, a force which can neither be seen nor be gripped but can be detected and also quantified respectively by its effect(s) and the amount of those effects (on some material) like elastic deflection, deformation, pressure, strain etc. These effects, called signals, often need proper conditioning for easy, accurate and reliable detection and measurement. The basic principle and general method of measurement is schematically shown in Fig. 1.
The measurement process is comprised of three stages:
Stage – 1: The target physical variable (say force) is converted proportionally into another suitable variable (say voltage) called signal, by using appropriate sensor or transducer. Stage – 2: The feeble and noisy signal is amplified, filtered, rectified (if necessary) and stabilized for convenience and accuracy of measurement. Stage – 3: where the conditioned signal (say voltage) is quantitatively determined and recorded by using some read out unit like galvanometer, oscilloscope, recorder or computer.
Different types of transducers used in dynamometers for measuring machining forces
Measurement of cutting force(s) is based on three basic principles :
(a) measurement of elastic deflection of a body subjected to the cutting force
(b) measurement of elastic deformation, i.e. strain induced by the force
(c) measurement of pressure developed in a medium by the force.
The type of the transducer depends upon how that deflection, strain or pressure is detected and quantified.
(a) Measuring deflection caused by the cutting force(s)
Under the action of the cutting force, say PZ in turning, the tool or tool holder elastically deflects as indicated in Fig. 2. Such tool deflection, δ is proportional to the magnitude of the cutting force, PZ, simply as,
[latexpage]
$\delta = P_Z \Bigg(\frac{L^3}{3EI}\Bigg) …………………………………………………………………………(1)$
where,
L = overhang or equivalent projected length of the cantilever type tool (holder)
E = physical property (Young’s modulus of elasticity of the beam)
I = size (plane moment of inertia) of the beam section
Since for a given cutting tool and its holder, E and I are fixed and the equation 1 becomes,
δ α PZ or, δ = kPZ ……………………………………………………………………………………………………………….(2)
where, k is a constant of proportionality.
The deflection, δ, can be measured
• mechanically by dial gauge (mechanical transducer)
• electrically by using several transducers like;
• potentiometer; linear or circular
• capacitive pickup
• inductive pickup
• LVDT
as schematically shown in Fig. 3.
• opto-electronically by photocell where the length of the slit through which light passes to the photocell changes proportionally with the tool – deflection
All such transducers need proper calibration before use
In case of mechanical measurement of the tool deflection by dial gauge, calibration is done by employing known loads, W and the corresponding tool deflections, δ are noted and then plotted as shown in Fig. 4. Here the slope of the curve represents the constant, k of the equation (2). Then while actual measurement of the cutting force, PZ, the δ* is noted and the corresponding force is assessed from the plot as shown.
In capacitive pick up type dynamometer, the cutting force causes proportional tool deflection, δ , which causes change in the gap (d) and hence
$\text{capacitance, C as} C = \frac{\varepsilon.A}{3.6\pi d} ………………………………………………………..(3)$
The change in C is then measured in terms of voltage, ΔV which becomes proportional to the force. The final relation between PZ and ΔV is established by calibration.
In case of LVDT, the linear movement of the core, (coupled with the tool), inside the fixed coil produces proportional voltage across the secondary coil. Fig. 3 Electrical transducers working based on deflection measurement
(b) Measuring cutting force by monitoring elastic strain caused by the force.
Increasing deflection, δ enhances sensitivity of the dynamometer but may affect machining accuracy where large value of δ is restricted, the cutting forces are suitably measured by using the change in strain caused by the force. Fig. 5 shows the principle of force measurement by measuring strain, ε, which would be proportional with the magnitude of the force, F (say PZ) as,
$\varepsilon = \frac{\sigma}{E} = \frac{M / Z}{E} = \frac{P_Z .I}{Z.E} = k_1P_Z ………………………………………(4)$
where,
M = bending moment
Z = sectional modulus (I/y) of the tool section
I = plane moment of inertia of the plane section
y = distance of the straining surface from the neutral plane of the beam (tool)
The strain, ε induced by the force changes the electrical resistance, R, of the strain gauges which are firmly pasted on the surface of the tool-holding beam as
$\frac{\Delta R}{R} = G\varepsilon ………………………………………(5)$
where, G = gauge factor (around 2.0 for conductive gauges) The change in resistance of the gauges connected in a wheatstone bridge produces voltage output ΔV, through a strain measuring bridge (SMB) as indicated in Fig. 6.
Out of the four gauges, R1, R2, R3 and R4, two are put in tension and two in compression as shown in Fig. 10.6. The output voltage, ΔV, depends upon the constant, G and the summation of strains as,
$\Delta V = \frac{GE}{4} \Bigg[\varepsilon_1 – \Big(-\varepsilon_2\Big) + \varepsilon_3 – \Big(-\varepsilon_4\Big)\Bigg] ………………………………………(6)$
where, ε1 and ε2 are in tension and – ε3 and – ε4 are in compression
The gauge connections may be
• full bridge (all 4 gauges alive) – giving full sensitivity
• half bridge (only 2 gauges alive) – half sensitive
• quarter bridge (only 1 gauge alive) – ¼ th sensitivity
(c) Measuring cutting forces by pressure caused by the force
This type of transducer functions in two ways :
• the force creates hydraulic pressure (through a diaphragm or piston) which is monitored directly by pressure gauge
• the force causes pressure on a piezoelectric crystal and produces an emf proportional to the force or pressure as indicated in Fig. 7.
Here,
emf = λtp ………………………………………………………………………………………………………(7)
where,
λ = voltage sensitivity of the crystal
t = thickness of the crystal
p = pressure
Design requirements for Tool – force Dynamometers
For consistently accurate and reliable measurement, the following requirements are considered during design and construction of any tool force dynamometers :
Sensitivity : the dynamometer should be reasonably sensitive for precision measurement
Rigidity : the dynamometer need to be quite rigid to withstand the forces without causing much deflection which may affect the machining condition
Cross sensitivity : the dynamometer should be free from cross sensitivity such that one force (say PZ) does not affect measurement of the other forces (say PX and PY)
• Stability against humidity and temperature
• Quick time response
• High frequency response such that the readings are not affected by vibration within a reasonably high range of frequency
• Consistency, i.e. the dynamometer should work desirably over a long period.
Construction and working principle of some common tool – force dynamometers
The dynamometers being commonly used now-a-days for measuring machining forces desirably accurately and precisely (both static and dynamic characteristics) are
either • strain gauge type
or • piezoelectric type
Strain gauge type dynamometers are inexpensive but less accurate and consistent, whereas, the piezoelectric type are highly accurate, reliable and consistent but very expensive for high material cost and stringent construction.
Turning Dynamometer
Turning dynamometers may be strain gauge or piezoelectric type and may be of one, two or three dimensions capable to monitor all of PX, PY and PZ.
For ease of manufacture and low cost, strain gauge type turning dynamometers are widely used and preferably of 2 – D (dimension) for simpler construction, lower cost and ability to provide almost all the desired force values.
Design and construction of a strain – gauge type 2 – D turning dynamometer are shown schematically in Fig. 8 and photographically in Fig. 9 Two full bridges comprising four live strain gauges are provided for PZ and PX channels which are connected with the strain measuring bridge for detection and measurement of strain in terms of voltage which provides the magnitude of the cutting forces through calibration. Fig. 10 pictorially shows use of 3 – D turning dynamometer having piezoelectric transducers inside.
Drilling dynamometer
Physical construction of a strain gauge type 2 – D drilling dynamometer for measuring torque and thrust force is typically shown schematically in Fig. 11 and pictorially in Fig. 12. Four strain gauges are mounted on the upper and lower surfaces of the two opposite ribs for PX – channel and four on the side surfaces of the other two ribs for the torque channel. Before use, the dynamometer must be calibrated to enable determination of the actual values of T and PX from the voltage values or reading taken in SMB or PC.
Milling dynamometer
Since the cutting or loading point is not fixed w.r.t. the job and the dynamometer, the job platform rests on four symmetrically located supports in the form of four O-rings. The forces on each O-ring are monitored and summed up correspondingly for getting the total magnitude of all the three forces in X, Y and Z direction respectively.
Fig. 13 shows schematically the principle of using O-ring for measuring two forces by mounting strain gauges, 4 for radial force and 4 for transverse force.
Fig. 14 typically shows configuration of a strain gauge type 3 – D milling dynamometer having 4 octagonal rings. Piezoelectric type 3 – D dynamometers are also available and used for measuring the cutting forces in milling (lain, end and face)
Grinding dynamometer
The construction and application of a strain gauge type (extended O-ring) grinding surface dynamometer and another piezoelectric type are typically shown in Fig. 15 and Fig. 16 respectively.
Unlike strain gauge type dynamometers, the sophisticated piezoelectric type (KISTLER) dynamometers can be used directly more accurately and reliably even without calibration by the user.
Author: Aliva Tripathy
Taking out time from a housewife life and contributing to AxiBook is a passion for me. I love doing this and gets mind filled with huge satisfaction with thoughtful feedbacks from you all. Do love caring for others and love sharing knowledge more than this. | 2019-11-22 02:23:49 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.34645530581474304, "perplexity": 3233.444148691322}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496671106.83/warc/CC-MAIN-20191122014756-20191122042756-00012.warc.gz"} |
https://www.physicsforums.com/threads/real-analysis.837514/ | # Real Analysis
1. Oct 13, 2015
### Matt B.
How would I go about showing that the set {5n | n = 1,2,...} is equivalent to ℤ.
I previously attempted to define a function f as f(n) = 5n/2 , when n is even AND (-1)[(5n-1)/(2)] , when n is odd. I then went on to show that the chosen function is 1-1 and onto, but my professor said this was inaccurate.
Any help would be appreciated! Thank you.
2. Oct 13, 2015
### Staff: Mentor
What are the numbers in your set? It should be almost trivial to set up a 1-1 mapping between the two sets, much simpler than the one you show below.
BTW, homework questions should be posted in the Homework & Coursework sections, not here in the technical math sections.
3. Oct 13, 2015
### jbriggs444
What is (-1)[(5n-1)/(2)] when n=1 ?
4. Oct 13, 2015
### Matt B.
-2??
5. Oct 13, 2015
### jbriggs444
OK. And what did you want it to be?
6. Oct 13, 2015
### Matt B.
Do I not need my defined function to be equivalent to all values in ℤ or just any values of ℤ?
7. Oct 13, 2015
### jbriggs444
Mark44 may have been leading you down a better path in post #2.
Your function is supposed to map values from one set to values in another set. It is supposed to be one to one and onto. We have established that your function takes 1 to -2.
Is 1 a member of the set that you are trying to map to ℤ?
8. Oct 13, 2015
### Matt B.
I'm confused. So am I simply evaluating 5n at different values for n to deduce my original set that I am trying to map to ℤ? Then that would just be {5,10,15,20,25...} so then my function would just be f(n) = 5n ?
9. Oct 13, 2015
### WWGD
Think of a number in your set as a multiple of a number in $\mathbb Z$ and show for very number in $\mathbb Z$ there is one such multiple.
WWGD4444.
I think the advice of :
Mark44
JBriggs444
WWGD4444
Should do it ;).
10. Oct 13, 2015
### Staff: Mentor
Yes, that's the simple one I was hinting at. Clearly this is a one-to-one function, so each number in the set {n} gets mapped to a number in the set {5n}, and vice versa.
Edit: I wasn't thinking very clearly on this reply...
Last edited: Oct 13, 2015
11. Oct 13, 2015
### jbriggs444
That gets a bijection between {5, 10, 15, ... } and {1, 2, 3, ... }. But I understood the original post to be asking for a bijection with ℤ = { ..., -3, -2, -1, 0, 1, 2, 3, ... }
12. Oct 13, 2015
### WWGD
Ultimately, you can find a bijection between {$5, 10, 15,...$} and $\mathbb N$ and then compose with a not-so-hard bijection between $\mathbb N, \mathbb Z$.
13. Oct 13, 2015
### Staff: Mentor
For some reason, I was thinking (without thinking very hard) that it was the positive integers. I was really thinking $\mathbb{N}$ rather than $\mathbb{Z}$.
14. Oct 13, 2015
### VKnopp
What do you mean equivalent? I beg to differ. $\mathbb{Z}$ is much more dense then your set. I think what you mean is the cardinal is the same. You can prove this via 1 to 1 correspondence.
15. Oct 13, 2015
### Staff: Mentor
"Set equivalence" is appropriate here.
See https://proofwiki.org/wiki/Definition:Set_Equivalence
The set in the OP should have the same cardinality as the set that is to be found.
16. Oct 13, 2015
### Matt B.
So is it not possible to find a 1-1, onto function that relates the set {5, 10, 15,...} onto the set of all integers?
17. Oct 13, 2015
### Staff: Mentor
We didn't say that. See if you can find a way to map some of the numbers in {5, 10, 15, ...} to {0, 1, 2, 3, ...} and the rest of the numbers in {5, 10, 15, ...} to {..., -3, -2, -1}. Or you can follow WWGD's advice in post #12.
18. Oct 13, 2015
### Matt B.
Here was my original attempt at the solution. Since I'm not following the discussion, can somebody point out what I am misinterpreting?
#### Attached Files:
• ###### IMG_7202.JPG
File size:
55.3 KB
Views:
42
19. Oct 13, 2015
### Matt B.
Sorry, it's me again. Since I am trying to map {5, 10, 15, 20, ...} onto {...,-3,-2,-1,0,1,2,3} could I use the function f such that f(n) = n/5 when n is even and (-1)(n/5) when n is odd??
20. Oct 14, 2015
### Staff: Mentor
Your set, let's call it S, is {5, 10, 15, 20, ...}
Your function maps the members of S as follows:
5 --> -1
10 --> 2
15 --> -3
20 --> 4
and so on.
No member of S gets paired with 0, 1, -2, 3, -4, and so on, so your function is not onto $\mathbb{Z}$, hence not one-to-one, so this doesn't work.
Your function just scales the input value by multiplying it. To pick up all of the missing numbers, the function also has to translate or shift, the input values. Can you think of a way for 5 --> -1, 15 --> -2, 25 --> -3, and so on, and for 10 --> 0, 20 --> 1, 30 --> 2, and so on?
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https://www.msri.org/workshops/261 | # Mathematical Sciences Research Institute
Home » Genetics of Complex Disease
# Workshop
Genetics of Complex Disease February 09, 2004 - February 13, 2004
Registration Deadline: February 13, 2004 about 10 years ago November 09, 2003 over 10 years ago
Organizers Jun Liu, Mary Sara McPeek, Richard Olshen (chair), David O. Siegmund, and Wing Wong
Speaker(s)
## Show List of Speakers
Description
This workshop is sponsored by MSRI and in part by Affymetrix, Aventis, Bristol-Myers Squibb and Pfizer. Our workshop will be held February 9-13, 2004 at the Mathematical Sciences Research Institute in Berkeley. Its topic is the genetics of complex human disease. The goals can be classified by subject matter by a variety of criteria, discussed below; but in human terms the goal is simple. We will bring together individuals who work at the forefront of laboratory research (perhaps also with patients) and others whose related activities are also cutting edge, but for whom the emphases are algorithmic, probabilistic, or statistical. While there are many conferences on specific topics from among those we cite, there are very few that span "bench to computer to bedside" topics and at the same time spare nothing in mathematical sophistication when suitable applications of mathematics can shed light on important biomedical problems. With respect to human diseases, the appropriate technologies, algorithms and clinical thinking are differentiated to a degree by the disease of interest. Important examples are cancer, autoimmune diseases, cardiovascular diseases, and lipid abnormalities. To some extent study of the human immune system holds these topics together, but there is much that is special to each topic. For example, much recent interest in cancer -- including but not limited to retinoblastoma, cancers of the head and neck, breast, and lung -- has focused on loss of heterozygosity and comparative genome hybridization, topics we will explore in lectures and discussion. By now there are numerous chips that are brought to bear on these diseases and others. "Historically," meaning, perhaps, one to five years ago, chips were primarily of the cDNA type, with 500-5000 base pairs studied at once, and oligonucleotide DNA chips, where attention is restricted to 20-80mers of DNA. Analysis of these and other chips and wafers will be topics of concern to us. One could think of the study of complex human disease as being analogous to a triangle, where scientists in the corners have their own emphases, but meet in the middle and interact. One corner concerns finding DNA markers, i.e., polymorphic sites, preferably in coding or regulatory regions of genes, that bear upon disease. While there might be viewed to be tension between studying allele sharing and identity by descent from linkage data on the one hand and association analysis of candidate genes on the other, we take it as a challenge to combine information from these different approaches. The use of animal models, where linkage analysis is easier than in humans, combined with identification of candidate genes in humans through homology searches provides another important tool. Linkage analysis has stimulated interest in first passage problems for Ornstein-Uhlenbeck processes to deal with problems of multiple testing. Candidate gene studies have stimulated interest in supervised learning, which in statistics is often called "classification." An important example is the study of angiotensinogen and protein tyrosine phsophatase as they bear upon hypertension. Cytochrome P450 genes are part of the study of all cited processes of disease. A second corner of the triangle concerns understanding genetic control and gene expression. There are now related data from beads, and other technologies, too. Analyses of these data might be in terms of supervised learning (when the outcome/phenotype is given) and unsupervised learning, or clustering (when the outcome/phenotype) is not. Clusters may be distinct or overlapping. Nearly always the clustering is of data that can be modeled as though they are points in Euclidean spaces, but where the cardinality of the sample pales by comparison with the dimension of the relevant space. With supervised learning there is, typically, a finite set of outcomes, the "covering diagnoses," and the goal is to classify, that is, to assign, each vector of expression values to a diagnosis. Some examples of interest in this area have been different flavors of hematopoietic malignancy. Most but not all classifiers of interest recently devolve from "voting methods," such as the celebrated AdaBoost method. The third corner of the triangle is concerned with the direct studies of proteins and their interactions, for example by time of flight mass spectrometry. Typical output here is a curve, or family of curves, with geometry (or geometries) that may apply to a particular genetic profile or disease. One approach of interest could be that of extracting a parsimonious set of basis functions for families of curves and representing a curve of interest to within specified discrepancy in a suitable norm. Perhaps low fractional Besov norms are relevant. Once a suitable basis and corresponding expansions are computed, we are back in the problem of supervised or unsupervised learning, as the case may be. Since what we get are the weights of proteins, it is imperative to be able to do the "inverse problem" of inferring the protein from the molecular weight. This could bring us to concerns of "fast table lookup," that have been important to streaming video over the Web and other problems. None of the above is meant to preclude interest in problems of evolution, which bear upon our subject matter through the identification of regions in proteins that are conserved across organisms and in evolutionary analysis of various pathogens, nor in problems in more traditional genetic epidemiology and statistical genetics. The latter can bring us to models where unconditional distributions are mixtures of Gaussians or other smooth distributions, and where sometimes distinctions between inference conditional on some data and unconditionally are blurred. The resulting inferential and computational issues can be very subtle. We on the committee that is organizing our workshop have contacted many individuals. Most are very interested in participating. Below please find a list of some of the individuals who will participate in our workshop. Although these are well known senior scientists, we are also committed to encourage many young and creative, but less well known, individuals to join us. Warren Ewens, Professor of Biology University of Pennsylvania (Winner, Weldon Memorial Prize, Oxford University, 2002) Joe W. Gray, Professor of Laboratory Medicine and Radiation Oncology Principal Investigator, UCSF Comprehensive Cancer Center University of California, San Francisco Jun Liu, Professor of Statistics and of Biostatistics Harvard University (Winner of Presidents' Award, Committee of Presidents of Statistical Societies, 2002) Mary Sara McPeek, Associate Professor, Departments of Statistics and Human Genetics Member, Committee on Genetics University of Chicago Richard Olshen, Professor of Health Research and Policy (Biostatistics) and (by Courtesy) of Electrical Engineering and Statistics Stanford University Thomas Quertermous, William G. Irwin Professor in Cardiovascular Medicine Research Chief, Division of Cardiovascular Medicine Stanford University Koustubh Ranade, Pharmaceutical Research Institute Bristol-Myers Squibb Princeton, New Jersey Neil Risch, Professor of Genetics and (by Courtesy) of Health Research and Policy and of Statistics Stanford University Adjunct Investigator, Division of Research Kaiser Permanente, Northern California David Siegmund, John D. and Sigrid Banks Professor and Professor of Statistics Stanford University Mark Skolnick, Chief Scientific Officer, Myriad Genetics, Inc. Terry Speed, Professor of Statistics University of California, Berkeley Head, Division of Bioinformatics Walter & Eliza Hall Institute of Medical Research Melbourne, Australia Robert Tibshirani, Professor of Health Research and Policy (Biostatistics) and (by Courtesy) of Statistics Stanford University (Winner of Presidents' Award, Committee of Presidents of Statistical Societies, 1996) Wing Hung Wong, Professor of Computational Biology Department of Biostatistics and Professor of Statistics Harvard University (Winner of Presidents' Award, Committee of Presidents of Statistical Societies, 1993)
Funding & Logistics
## Show Funding
To apply for funding, you must register by the funding application deadline displayed above.
Students, recent Ph.D.'s, women, and members of underrepresented minorities are particularly encouraged to apply. Funding awards are typically made 6 weeks before the workshop begins. Requests received after the funding deadline are considered only if additional funds become available.
## Show Lodging
MSRI has preferred rates at the Rose Garden Inn, depending on room availability. Reservations may be made by calling 1-800-992-9005 OR directly on their website. Click on Corporate at the bottom of the screen and when prompted enter code MATH (this code is not case sensitive). By using this code a new calendar will appear and will show the MSRI rate on all room types available.
MSRI has preferred rates at the Hotel Durant. Reservations may be made by calling 1-800-238-7268. When making reservations, guests must request the MSRI preferred rate. If you are making your reservations on line, please go to this link and enter the promo/corporate code MSRI123. Our preferred rate is $129 per night for a Deluxe Queen/King, based on availability. MSRI has preferred rates of$149 - $189 plus tax at the Hotel Shattuck Plaza, depending on room availability. Guests can either call the hotel's main line at 510-845-7300 and ask for the MSRI- Mathematical Science Research Inst. discount; or go to www.hotelshattuckplaza.com and click Book Now. Once on the reservation page, click “Promo/Corporate Code“ and input the code: msri. MSRI has preferred rates of$110 - \$140 at the Berkeley Lab Guest House, depending on room availability. Reservations may be made by calling 510-495-8000 or directly on their website. Select “I am an individual traveler affiliated with MSRI”.
Additional lodging options may be found on our short term housing page. | 2014-04-24 11:21:18 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.19719010591506958, "perplexity": 2750.8228429617866}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1398223206120.9/warc/CC-MAIN-20140423032006-00389-ip-10-147-4-33.ec2.internal.warc.gz"} |
http://meetings.aps.org/Meeting/MAR10/Event/120161 | ### Session P13: Membranes: General, Surface, Biological
8:00 AM–11:00 AM, Wednesday, March 17, 2010
Room: B112
Chair: Haskell Taub, University of Missouri
Abstract ID: BAPS.2010.MAR.P13.1
### Abstract: P13.00001 : Studies of the Temperature-Dependent Structure of DMPC Bilayer Lipid Membranes by Atomic Force Microscopy
8:00 AM–8:12 AM
Preview Abstract MathJax On | Off Abstract
#### Authors:
A. Miskowiec
M. Bai
H. Taub
(U. Mo.)
F.Y. Hansen
(Tech. U. Denmark)
We are using Atomic Force Microscopy (AFM) to characterize the structure and topography of single-supported bilayer lipid membranes to complement quasielastic neutron scattering investigations of the membrane dynamics. To investigate the effect of different membrane-substrate interactions, samples of hydrated DMPC bilayer membranes have been fabricated on four different supports: 1) a bare SiO$_{2}$-coated Si(100) wafer; 2) a SiO$_{2}$-coated Si(100) wafer preplated with a monolayer of the pure alkane $n$-C$_{36}$H$_{74}$ in which the molecules are aligned with their long axis parallel to the SiO$_{2}$ surface; 3) an underlying DMPC membrane itself supported on a SiO$_{2}$ surface; and 4) a SiO$_{2}$-coated Si(100) wafer covered with a polyethylenimine (PEI) cushion. Above room temperature, our AFM images show a decrease in the DMPC membrane thickness with increasing temperature consistent with chain-melting transitions of the lipid tails. The onset temperature at which the membrane thickness begins to decrease and the temperature at which its thickness saturates both decrease with weaker binding to the support and with a greater level of hydration.
To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2010.MAR.P13.1 | 2013-06-19 13:00:02 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5254153609275818, "perplexity": 10525.171115999121}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368708783242/warc/CC-MAIN-20130516125303-00042-ip-10-60-113-184.ec2.internal.warc.gz"} |
http://tex.stackexchange.com/questions/49621/how-to-install-fonts | # How to install fonts
I use MikTeX 2.8. I want to install the greek fonts "GFS neohellenic". I open the MikTeX package manager, I type GFS neohellenic but nothing similar is found.
I searched through the net for similar issues but nothing seem to be the proper one.
How can I get them to work on windows?
P.S.:I use TeXNiC CenteR
-
Just install the font on your computer (e.g. C:\windows\fonts) and compile the .tex file with xelatex. The following is an example..
\documentclass[a4paper,12pt]{article}
\usepackage{xltxtra}
\setmainfont{GFS neohellenic}
\begin{document}
asdf hjkl
\end{document}
-
Thank's a lot for your answer. I used the aforementioned code, however it's not working. I get ~400 errors. When I try to see what is wrong TXC opens a .mf file and I heve no idea what is going on, whatsoever...Let alone, it takes about to minutes to build it... – Thanos Mar 27 '12 at 13:17
That's strange! I just compiled it on Texnic centre and it works. Have you configured texnic centre to work with xelatex? If not, see [here] (latex-community.org/forum/viewtopic.php?f=31&t=731). Also, please compile the above code and paste the first few errors here. – caveman Mar 27 '12 at 13:35
Just out of curiosity.. have you otherwise successfully compiled a normal .tex file with standard font in Greek on Texnic centre? I have a feeling that texnic doesn't support UNICODE. I could suggest you texmaker.. it works like a charm! – caveman Mar 27 '12 at 13:40
I have been using the package kerkis with TXC or the default babel. Greek letters are indeed suported by TXC. The first build says XeTeX is required to compile that document. I see... I tried to build a new profile... I have a question: What am I supposed to write on "Command line arguments to pass to the compiler"? – Thanos Mar 27 '12 at 13:54
You can just choose the first option, main file's full path, as long as you don't have made some unconventional changes to your file. The code is %pm – caveman Mar 27 '12 at 14:04
These are OpenType (OTF) fonts. Install them in your windows system font folder and use them with xelatex/lualatex + the fontspec package.
-
How am I going to do it? I don;t have xelatex/lualatex. I use LaTeX and TXC... – Thanos Mar 27 '12 at 12:28
@Thanos: You have xelatex. It is part of miktex 2.8. Lualatex is in miktex 2.9. – Ulrike Fischer Mar 27 '12 at 12:43
I see...How am I going to use it? What am I suppossed to do to make it work?Thanks for your time! – Thanos Mar 27 '12 at 12:51
Use it instead of latex. And if you search the site here you will find a lot example documents. – Ulrike Fischer Mar 27 '12 at 12:56 | 2015-05-22 19:21:06 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8169364929199219, "perplexity": 3956.2875060373}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-22/segments/1432207926620.50/warc/CC-MAIN-20150521113206-00095-ip-10-180-206-219.ec2.internal.warc.gz"} |
http://www.physicsforums.com/showthread.php?p=4257256 | Traversetime of r=cos(n*θ)
by Nikitin
Tags: rcosnθ, traversetime
P: 517 I have the function in polar coordinates r=cos(n*θ), where r is the radii. I'm supposed to draw the graph of this function, and calculate the area. But to calculate the area, I need to know how fast the function traverses. From the solution in my book, it says if n is even, the function traverses when θ goes from 0 to 2pi, and from 0 to pi if n is odd. Why is the traverse-time for this function only dependant on if n is odd or even? I do not understand this at all. Can you guys help me develop an intuition for functions in polar coordinates?
PF Patron Sci Advisor Thanks Emeritus P: 38,424 You will cover one lobe as r goes from 0 to 1 and back to 0. That is, as $n\theta$ goes form $-\pi+ 2k\pi$ to $\pi/2+ 2k\pi$ for integer k. The reason for the "if n is even, the function traverses when θ goes from 0 to 2pi, and from 0 to pi if n is odd." is that when $cos(n\theta)$ is negative, r is negative and, because r is alwas positive in polar coordinates, is interpreted as positive but with $\pi$ added to $\theta$. When n is odd, that results in one lobe covering another. When n is even, there are 2n lobes, when n is odd there are n lobes.
P: 517
So you're saying when r goes from 0 to 1 to 0 (and n*θ goes from -pi/2 to pi/2) the function has fully traversed?
Is this a general rule? That when r goes back to where it started, the function has traversed?
is that when cos(nθ) is negative, r is negative and, because r is alwas positive in polar coordinates, is interpreted as positive but with π added to θ. When n is odd, that results in one lobe covering another. When n is even, there are 2n lobes, when n is odd there are n lobes.
I think I get you, but can you please provide an example?
PF Patron
Thanks
Emeritus
P: 38,424
Traversetime of r=cos(n*θ)
The first graph is $r= 5cos(4\theta)$ and the second graph is $r= 5cos(5\theta)$
Attached Thumbnails
Related Discussions Introductory Physics Homework 5 Introductory Physics Homework 3 Introductory Physics Homework 1 Atomic, Solid State, Comp. Physics 0 Introductory Physics Homework 4 | 2013-12-12 00:38:35 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7175424098968506, "perplexity": 562.7860746432746}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-48/segments/1386164120234/warc/CC-MAIN-20131204133520-00071-ip-10-33-133-15.ec2.internal.warc.gz"} |
https://math.stackexchange.com/questions/583376/finding-distance-between-two-parallel-3d-lines | Finding distance between two parallel 3D lines
I can handle non-parallel lines and the minimum distance between them (by using the projection of the line and the normal vector to both direction vectors in the line), however, in parallel lines, I'm not sure on how to start. I was thinking of finding a normal vector to one of the direction vectors (which will be as well normal to the other line because they are parallel), then set up a line by a point in the direction of the normal vector, and then find the points of intersection. After finding the line between the two parallel lines, then we can calculate the distance.
Is this reasoning correct? If it is, is there a way to find normal vectors to a line or any vector instead of guessing which terms give a scalar product of 0? I have encountered this problem as well in directional derivatives and the like.
• If no one answers this in an hour or so write a comment with "@AlecTeal" in it and I'll answer then. – Alec Teal Nov 27 '13 at 16:32
• There are infinitely many normal vectors (directions) to a line in 3D. – user35603 Nov 27 '13 at 16:37
• First, everything depends on your data. What defines your lines ? Point + direction vector? Also, a normal to a line is a plane. – Jean-Claude Arbaut Nov 27 '13 at 16:39
• You can follow the technique in my answer. – Mhenni Benghorbal Nov 27 '13 at 16:40
• I was thinking, couldn't i as well define the "difference vector" between the two lines (say from an arbitrary point on $L_{1}$ and the equation of the line for $L_{2}$), and then as we have that this difference vector is parallel to one of the direction vectors of the line, calculate the scalar product, equate it to 0 and then find the values of s for which the equality holds? – arcbloom Nov 27 '13 at 16:42
Hint: Let $l_1$ and $l_2$ be parallel lines in 3D. Find a point $A \in l_1$ and then find the distance from $A$ to $l_2$. There is a formula for distance from a point to a line in 3D.
• In $3$ dimensions, such a subspace would be a plane (going through the origin). Every vector in $\mathbb{R}^n$ is normal to exactly one maximal subspace and if two lines are spanned by the same vector, then they share this maximal normal subspace - in this case a plane. – Dan Rust Nov 27 '13 at 17:14
Let $P$ be a variable point of $L_1$ and $P_0$ a fixed point of $L_2$. Try to minimize $$\left|\frac{\mathbf{a}\times\vec{PP_0}}{|\mathbf{a}|}\right|$$ where $\mathbf{a}$ is leading vector (for example) for $L_1$.
Let $r(t) = r_0 + \hat{r} t, \ \ s(t) = s_0 + \hat{r}t$. Then form a triangle with sides $r_0 - s_0$ and one parallel to $\hat{r}$ with length given by $\hat{r} \cdot (r_0 - s_0)$. Then the length of the missing side is your distance.
$d = \sqrt{ |r_0 - s_0|^2 + (\hat{r}(r_0 - s_0))^2}$ | 2019-05-27 10:34:51 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8260288834571838, "perplexity": 157.67782134469033}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232262311.80/warc/CC-MAIN-20190527085702-20190527111702-00387.warc.gz"} |
http://mathoverflow.net/revisions/50233/list | Let $F$ be the free group on (say) two generators, $a$ and $b$. Let $A$ and $B$ be (freely reduced) elements of $F$. Let $W(X, Y)$ denote a word on the words $X, Y$.
-Is it ever true that the equation $W(a, b) = W(A, B)$, has finitely many non-conjugate solutions ?(by conjugate solution I mean there exists a word $V$ such that $V^{-1}AV = A^{\prime}$ and $V^{-1}BV=B^{\prime}$)?
For example, take $W(a, b) = a^{-1}b^nab^m$. We therefore want to find $A$, $B$ such that $a^{-1}b^nab^m = A^{-1}B^nAB^m$, but we . We can take $A=b^ia$ and $B=b$ for all $i$ i$, and so this equation has infinitely many (non-conjugate) solutions. In fact,$a\mapsto b^ia$,$b \mapsto b$defines an automorphism of$F$(as free groups are Hopfian). Further, different$i$'s give different coset representatives of Out(F), and so a related question would be, -Does there exist a word$W \in F$such that there are only finitely many outer automorphisms$\phi$such that$W\phi = W$? I cannot seem to get anywhere with this. The only examples I can find are, essentially, trivial. For example,$W(a, b) = a$. However, this doesn't quite work, as then$b$can be whatever we want (essentially, exclude this because its boring). Any help/ideas of papers to look at would be greatly appreciated. 3 deleted 14 characters in body; added 12 characters in body Let$F$be the free group on (say) two generators,$a$and$b$. Let$A$and$B$be (freely reduced) elements of$F$. Let$W(x, y)$W(X, Y)$ denote a word on the letters words $x, y$X, Y$. -Is it ever true that the equation$W(a, b) = W(A, B)$has finitely many solutions? For example, take$W(a, b) = a^{-1}b^nab^m$. We therefore want to find$A$,$B$such that$a^{-1}b^nab^m = A^{-1}B^nAB^m$, but we can take$A=b^ia$and$B=b$for all$i$and so this equation has infinitely many solutions. In fact,$a\mapsto b^ia$,$b \mapsto b$defines an automorphism of$F$(as free groups are Hopfian), and so a related question would be, -Does there exist a word$W \in F$such that there are only finitely many automorphisms$\phi$such that$W\phi = W$? I cannot seem to get anywhere with this. The only examples I can find are, essentially, trivial. For example,$W(a, b) = a$. However, this doesn't quite work, as then$b$can be whatever we want (essentially, exclude this because its boring). Any help/ideas of papers to look at would be greatly appreciated. 2 added 2 characters in body Let$F$be the free group on (say) two generators,$a$and$b$. Let$A$and$B$be (freely reduced) elements of$F$. Let$W(x, y)$denote a word on the words letters$x, y$. -Is it ever true that the equation$W(a, b) = W(A, B)$has finitely many solutions? For example, take$W(a, b) = a^{-1}b^nab^m$. We therefore want to find$A$,$B$such that$a^{-1}b^nab^m = A^{-1}B^nAB^m$, but we can take$A=b^ia$and$B=b$for all$i$and so this equation has infinitely many solutions. In fact,$a\mapsto b^ia$,$b \mapsto b$defines an automorphism of$F$(as free groups are Hopfian), and so a related question would be, -Does there exist a word$W \in F$such that there are only finitely many automorphisms$\phi$such that$W\phi = W$? I cannot seem to get anywhere with this. The only examples I can find are, essentially, trivial. For example,$W(a, b) = a$. However, this doesn't quite work, as then$b\$ can be whatever we want (essentially, exclude this because its boring). | 2013-05-19 02:02:47 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9983065724372864, "perplexity": 1406.4392500985448}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368696383156/warc/CC-MAIN-20130516092623-00090-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://cemse.kaust.edu.sa/aanslab/people/person/mohammed-sayyari | Mohammed is a Mathematician with a solid background in scientific programming. Mohammed's mathematical interests are in the analysis of partial differential equations and the discretization thereof. | 2021-06-24 09:17:32 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8329010605812073, "perplexity": 637.739745702343}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623488552937.93/warc/CC-MAIN-20210624075940-20210624105940-00114.warc.gz"} |
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# 36th Annual International Symposium on Lattice Field Theory
22-28 July 2018
Kellogg Hotel and Conference Center
EST timezone
## Control of SU(3) symmetry breaking effects in calculations of B meson decay constant
Jul 25, 2018, 3:20 PM
20m
103 (Kellogg Hotel and Conference Center)
### 103
#### Kellogg Hotel and Conference Center
219 S Harrison Rd, East Lansing, MI 48824
Weak Decays and Matrix Elements
### Speaker
Sophie Hollitt (University of Adelaide)
### Description
Early B physics experiments have left us with a number of puzzles in heavy flavour physics. New lattice calculations and greater understanding of QCD effects in the Standard Model will be needed to support greater experimental precision in the coming years. In particular, the B meson decay constant is involved in calculations of CKM matrix elements and useful to measurements of the branching ratio B $\to \tau \nu$ expected at the Belle II Experiment. We extend the QCDSF studies of SU(3) breaking of light decay constants into the heavy-flavour regime to examine the effects of SU(3) breaking on $f_B$ and $f_{B_s}$. $b$-quarks are generated using an anisotropic clover-improved heavy-quark action. The decay constants $f_B$ and $f_{B_s}$ will be presented for a variety of light quark masses, from the SU(3) symmetric point toward the physical quark masses. In order to focus on the SU(3) symmetry breaking effects in our extrapolation to the physical point, we choose u,d,s quark masses in each simulation such that the average quark mass, $m = m_u + m_d + m_s$, is constant and equal to its physical value. Results will be presented at a number of different lattice spacings and volumes, toward calculations of $f_B$ and $f_{B_s}$ at the physical point.
### Primary author
Sophie Hollitt (University of Adelaide)
Slides | 2021-06-19 18:52:31 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4940197169780731, "perplexity": 1915.849861487991}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487649688.44/warc/CC-MAIN-20210619172612-20210619202612-00092.warc.gz"} |
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#### Resources tagged with Interactivities similar to Nice or Nasty:
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### Number Pyramids
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Try entering different sets of numbers in the number pyramids. How does the total at the top change?
### Right Angles
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Can you make a right-angled triangle on this peg-board by joining up three points round the edge?
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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?
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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.
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When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
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Here is a chance to play a version of the classic Countdown Game.
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Six balls of various colours are randomly shaken into a trianglular arrangement. What is the probability of having at least one red in the corner?
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This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
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Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.
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What are the coordinates of the coloured dots that mark out the tangram? Try changing the position of the origin. What happens to the coordinates now?
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Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
### More Magic Potting Sheds
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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 his gardens, planting one garden each day. How can he do it?
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Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.
### Drips
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An animation that helps you understand the game of Nim.
### Dotty Circle
##### Age 7 to 11 Challenge Level:
Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?
### Estimating Angles
##### Age 11 to 14 Challenge Level:
How good are you at estimating angles?
### Magic Potting Sheds
##### Age 11 to 14 Challenge Level:
Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?
### Spot Thirteen
##### Age 7 to 11 Challenge Level:
Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?
### Multiplication Tables - Matching Cards
##### Age 5 to 14 Challenge Level:
Interactive game. Set your own level of challenge, practise your table skills and beat your previous best score.
### Diagonal Dodge
##### Age 7 to 14 Challenge Level:
A game for 2 players. Can be played online. One player has 1 red counter, the other has 4 blue. The red counter needs to reach the other side, and the blue needs to trap the red.
### Semi-regular Tessellations
##### Age 11 to 14 Challenge Level:
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
### Noughts and Crosses
##### Age 7 to 11 Challenge Level:
A game for 2 people that everybody knows. You can play with a friend or online. If you play correctly you never lose!
### Building Stars
##### Age 7 to 11 Challenge Level:
An interactive activity for one to experiment with a tricky tessellation
### Coordinate Cunning
##### Age 7 to 11 Challenge Level:
A game for 2 people that can be played on line or with pens and paper. Combine your knowledege of coordinates with your skills of strategic thinking.
### Factor Lines
##### Age 7 to 14 Challenge Level:
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
### Fault-free Rectangles
##### Age 7 to 11 Challenge Level:
Find out what a "fault-free" rectangle is and try to make some of your own.
### Khun Phaen Escapes to Freedom
##### Age 11 to 14 Challenge Level:
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
### Balancing 2
##### Age 11 to 14 Challenge Level:
Meg and Mo still need to hang their marbles so that they balance, but this time the constraints are different. Use the interactivity to experiment and find out what they need to do.
### More Carroll Diagrams
##### Age 7 to 11 Challenge Level:
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
### Balancing 1
##### Age 11 to 14 Challenge Level:
Meg and Mo need to hang their marbles so that they balance. Use the interactivity to experiment and find out what they need to do.
### Cogs
##### Age 11 to 14 Challenge Level:
A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .
### One to Fifteen
##### Age 7 to 11 Challenge Level:
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
### Archery
##### Age 11 to 14 Challenge Level:
Imagine picking up a bow and some arrows and attempting to hit the target a few times. Can you work out the settings for the sight that give you the best chance of gaining a high score?
### Part the Piles
##### Age 7 to 11 Challenge Level:
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
### Conway's Chequerboard Army
##### Age 11 to 14 Challenge Level:
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
### Flip Flop - Matching Cards
##### Age 5 to 14 Challenge Level:
A game for 1 person to play on screen. Practise your number bonds whilst improving your memory
### Top Coach
##### Age 11 to 14 Challenge Level:
Carry out some time trials and gather some data to help you decide on the best training regime for your rowing crew.
### Partitioning Revisited
##### Age 11 to 14 Challenge Level:
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
### Teddy Town
##### Age 5 to 14 Challenge Level:
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
### Carroll Diagrams
##### Age 5 to 11 Challenge Level:
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
### An Unhappy End
##### Age 11 to 14 Challenge Level:
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...
### Picturing Triangular Numbers
##### Age 11 to 14 Challenge Level:
Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
### Balancing 3
##### Age 11 to 14 Challenge Level:
Mo has left, but Meg is still experimenting. Use the interactivity to help you find out how she can alter her pouch of marbles and still keep the two pouches balanced.
### Round Peg Board
##### Age 5 to 11 Challenge Level:
A generic circular pegboard resource.
### First Connect Three
##### Age 7 to 14 Challenge Level:
The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?
### Stars
##### Age 11 to 14 Challenge Level:
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 hit?
### Shuffles Tutorials
##### Age 11 to 14 Challenge Level:
Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.
### Diamond Mine
##### Age 11 to 14 Challenge Level:
Practise your diamond mining skills and your x,y coordination in this homage to Pacman.
### Isosceles Triangles
##### Age 11 to 14 Challenge Level:
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? | 2018-06-18 05:35:08 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.26434311270713806, "perplexity": 2454.017972934153}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267860089.11/warc/CC-MAIN-20180618051104-20180618070923-00052.warc.gz"} |
http://ronggong1010.blogspot.fr/2014/11/speech-enhancement-spectral-subtractio.html | ## Thursday, November 6, 2014
### Speech enhancement 1: spectral subtraction, wiener filtering
I am working today on my personnel project which needs some algorithms of speech enhancement or source separation to highlight the speech/singing voice part. I bumped into some classical enhancement methods, like, spectral subtraction, Wiener filter. These kinds of methods are designed to eliminate the noise component in noisy speech signal.
1. Spectral subtraction
It's funny how scientist at the years of 80s utilises this rudimentary method for de-noising. The principle is so simple: do FFT to the noisy speech ($X(k)$), do FFT to a pure noise ($N(k)$), subtract the magnitude of these two spectrum ($|\hat{S}(k)|=|X(k)| - |N(k)|$), and do IFFT to reconstruct the temporel signal by add the phase information of $X(k)$.
More details can be referred to Boll's "Suppression of Acoustic Noise in Speech Using Spectral Subtraction". He included some pre/post processing method to improve the speech intelligibility, for instance, magnitude averaging, residual noise reduction, additional signal attenuation during nonspeech activity.
Pure noise spectrum profile should be build before the spectral subtraction step, then each time VAD (voice activity detection) detect a noise frame, this profile will be updated. This is not a bad idea, huh? :D But his VAD detector compares only the residual spectrum and the noise profile (proportion $T$). When $T$ < -12 dB, the current frame is indicated as noise, otherwise, it's speech.
I tested with this threshold $T$, and I found -12 dB might not be fit for all the signals:
click for enlarge
It is clearly that when $T$ = -12, the subtractor did nothing but the attenuator took charge of all the works, because all the frames are indicated as noise frame. Personally, I prefer the sound without additional signal attenuation. (Please point me out if you think that I did something wrong with this algorithm :=) )
The big disadvantage of this method is informed by author himself: it can't deal with the non stationary noise, that is, if the noise spectrum profile changes within the speech frames, this method fails.
2. Two variations
In article "Enhancement and Bandwidth Compression of Noisy Speech", we have two variations of this subtraction by using the power spectrum of $|X(k)|^2$ and $|N(k)|^2$:$$|\hat{S}(k)|=(|X(k)|^2-\alpha \mathbb{E}[|N(k)|^2])^{1/2}$$ $$|\hat{S}(k)|=\frac{1}{2}|X(k)|+\frac{1}{2}(|X(k)|^2-\mathbb{E}[|N(k)^2|])^{1/2}$$
The author proved that these two formulas can be deduced from the parametric implicit Wiener filtering. I tried these two, the first one gives a reasonable result, but the second one is really bad. I think that's due to the noisy component $\frac{1}{2}|X(k)|$ in this formula.
3. A priori SNR estimation Wiener filtering
The Signal-to-noise ratio measure in frequency domaine Wiener filter could be a posteriori or a priori. If it's a posteriori, it could be easily computed by:$$SNR_{post}=\frac{|X(k)|^2}{\mathbb{E}|N(k)|^2}$$because we know $|X(k)|$ is the noisy spectrum and $\mathbb{E}|N(k)|^2$ is the average magnitude of noise signal when there is no speech activity. The two variations of parametric implicit Wiener filtering utilise exactly this a posteriori SNR ratio.
The a priori one is defined by:$$SNR_{prio}=\frac{\mathbb{E}|S(k)|^2}{\mathbb{E}|N(k)|^2}$$However, we do know the $S(k)$ which is exactly the clean speech we want to obtain. Article "SPEECH ENHANCEMENT BASED ON A PRIORI SIGNAL TO NOISE ESTIMATION" introduced a iterative method to estimate the $SNR_{prio}$ which is called "decision-direct" estimate by the author.
The Matlab code of this method written by Esfandiar Zavarehei can be easily download from his website (youpi!). He translated the formulas of the article into code except having changing some notations. For the reason of legibility, I changed them back.
The "NoiseMargin" variable in his function "vad" is worth paying attention to. Because it indicates that a short-time frame would be considered as noise or speech. For instance, if the SNR ratio of noisy speech is 0dB, we assign 12dB to NoiseMargin, it turns out that almost all the frames will be indicated as noise.
A priori SNR estimation Wiener filter result, without pre/post processing
The result of this method is more enjoyable to me than the last two, but it still has a some artificial traces.
4. Matlab code
https://github.com/ronggong/voiceenhance | 2017-10-20 05:16:46 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.632283627986908, "perplexity": 1774.497657645138}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187823731.36/warc/CC-MAIN-20171020044747-20171020064747-00452.warc.gz"} |
https://www.physicsforums.com/threads/normalized-sse-for-a-set-of-data.507528/ | # Normalized SSE for a set of data?
1. Jun 16, 2011
Normalized SSE for a set of data??
Hi, supposed I have a set of data points, and each data point has a certain value of uncertainty associated with it.
Supposed also I have a function which models the data. What I'd like to know is how does one quantitatively measure how good the fit of the model is to the data, in such as way that one can compare the model to different sets of data?
For example, taking the SSE defined as:
$\sum(y_i - f(x_i , \beta))^2$
where $\beta$ is a set of parameters, one can measure the difference between the model and the data. However, this does not take into account the number of data points or the degree of uncertainty. If I have a very large number of data points, a small difference between the data and model will result in a very large SSE, even if the model is a very good fit. On the contrary, even if the model is poor, a small set of data points may produce a small SSE - thus there is no way to compare between data sets for the same model.
Also, one must consider the magnitude of the data points when comparing sets. For example, if my $y_i$ values range from 100...500 for one set, a small fractional change between the model and the data may still produce a huge SSE, while a huge fractional change between the model and data ranging from 0.01...0.5 will result in a small SSE.
So, what I'd like is a way to compare the goodness of a fit for a wide variety of data sets that takes into account the error in the data, the number of data points, and the magnitude of the dependent variables in the data - can someone explain how to do this and what such a quantity is called?
2. Jun 19, 2011
### Stephen Tashi
Re: Normalized SSE for a set of data??
You could try the mean of the sum of the squares of the percentage errors, but unless you can define what makes a good or bad comparison precisely, there is no mathematical answer to your question.
3. Jun 20, 2011
Re: Normalized SSE for a set of data??
I was thinking along the same lines... something like this:
$\frac{1}{N}\sum\frac{(y_i - f(x_i, \beta)) + e_i}{y_i}$
where N is the total number of data points, and ei is the error associated with the ith data point. This would give the average maximum possible difference between the curve and the data.
Do you see any flaws in this reasoning?
4. Jun 20, 2011
### Stephen Tashi
Re: Normalized SSE for a set of data??
It isn't reasoning. It's the method of "I don't know exactly what I want, but I'll recognize it when I see it". Everybody who deals with practical problems resorts to this method sometimes. If you want to deduce an answer by mathematical reasoning, you have to define precisely what it is that you are trying to do. If you are just casually fooling around with some data, I think the formula is worth a try. If you have some very serious purpose in your work, you should try define you goal in precise language and see where reasoning will take you.
5. Jun 21, 2011
### SW VandeCarr
Re: Normalized SSE for a set of data??
I haven't seen any reference to the term "mean squared error" (MSE) in this thread, This is simply the the SSE divided by the number of degrees of freedom and is essentially what this thread is addressing. It's a widely used and well regarded statistic and is useful in evaluating the bias of estimators among other things. I'm not aware of any particular issues associated with it. Am I missing something in this discussion?
EDIT: Assessing the number of degrees of freedom can be difficult due to correlations among variables. MANOVA analysis is usually required in the multivariate setting. In the univariate setting there is no problem provided the individual data points (observations) are independent. | 2018-08-17 19:19:14 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6755991578102112, "perplexity": 252.27983209059224}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-34/segments/1534221212768.50/warc/CC-MAIN-20180817182657-20180817202657-00217.warc.gz"} |
https://www.physicsforums.com/threads/normal-tangential-coord.135749/ | # Normal/Tangential coord
1. ### 600burger
65
Using normal and tangential coord the the tangential acceleration of any point on earth is 0, correct?
2. ### Mindscrape
Normal and tengential, coord? I don't quite know what you mean by that, but you are right that since the earth spins with a constant velocity, there will be no tangential acceleration. | 2015-04-26 13:00:40 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8762694001197815, "perplexity": 764.3629906283585}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1429246654467.42/warc/CC-MAIN-20150417045734-00276-ip-10-235-10-82.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/gausss-law-2-concentric-cylinders-in-electrostatic-equilibrium.282928/ | # Gauss's Law 2 concentric cylinders in electrostatic equilibrium
1. Jan 5, 2009
### shale
1. The problem statement, all variables and given/known data
Consider the cross sections of two, very long, concentric, metallic, hollow cylinders placed in a vacuum. The small cylinder has inner radius A and outer radius B while the larger cylinder has inner radius 2A and outer radius 2B. Initially the small and big hollow cylinders have charge densities of +2λ and -2λ respectively.
1) AT electrostatic equilibrium what is the total charge of the inner surface of the big cylinder if the cylinders both hav e length L?
2) what is the electric field in tha cavity between the two cylinders? se r as the distance measured from the center of the spheres.
2. Relevant equations
relevant equations would be the flux which is EA=Qenco
3. The attempt at a solution
for number 1
since this is at electrostatic equilibrium, the net charge AT the CYLINDER is ZERO. therefore Qin=0... but inner cylinder has +2λL, and so the inner surface of the larger cylinder would be -2λL... and for the outside surface.... (will it be +2λL for the net charge on the conductor to be zero.?? or there will be no charge because the said "net" charge in that conductor should be -2λL??) i'm confused....
and is it correct for me to multiply the charge densities to L??
for number 2
I set up an equation like this...
EA= E2πrL = ([2λ(πr2L)] - [-2λ(πR2L)]) /εo
we cancel and it becomes like this
E = [λπ(r2+R2)] /εor
where r is the outer radius of the smaller cylinder and R is inner radius of larger one.. i think i'm wasting my effort because all this is wrong :-ss please help.
Last edited: Jan 5, 2009
2. Jan 5, 2009
### Redbelly98
Staff Emeritus
Welcome to PF.
Yes.
No, because the net charge on the outer conductor is NOT zero.
Yes. There is zero charge on the outer surface of the outer cylinder, for exactly the reason you said here.
Yes, if you want to get the total charge in a length L of a cylinder.
Not quite, but you're not far off.
Think about the surface you are defining, and the fact that you need to use the charge enclosed by that surface here.
• Does the surface contain the inner cylinder?
• Does the surface contain the outer cylinder?
Based on the answers to those 2 questions, what is the charge enclosed within the surface?
3. Jan 6, 2009
### shale
do mean the gaussian surface? ---- 1) Yes, and 2) No..
so total charge enclosed is +2λL
should i still use EA=Qenco...? if so then...
EA= E2πrL = 2λL/εo
(I think I was wrong in my first attempt because i multiplied it to the volume and not the area, λ is always linear density right? because in this question it's not clearly stated)
E = λ/πrεo
is this one correct now? or is there a different approach on how this is solved? :-ss
4. Jan 6, 2009
### Redbelly98
Staff Emeritus
Yes.
I think so, but I didn't really think about that and just assumed that it was the linear density. You're right, it should be clearly stated.
Looks good!
You're welcome. | 2017-10-21 05:33:19 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8529675006866455, "perplexity": 1093.7952331451274}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187824570.79/warc/CC-MAIN-20171021043111-20171021063111-00347.warc.gz"} |
http://www.eg.bucknell.edu/~phys211/fa2017/cal/lec04.html | ## Lecture 4: Newton's Laws
August 31, 2017
• Read: Chapter 4 (all of it)
• Study: Tip on p. 54; Got It 4.2; Ex 4.2; Tactics 4.1; Problem Solving Strategy 4.1; Ex 4.3; Fig 4.15; Ex 4.5
### Objectives
• (Continuing objective) Relate concepts of classical mechanics to “everyday” situations and discuss various applications of the concepts to practical problems in various fields of science, medicine and engineering.
• Given several forces acting on a single object, use Newton's Second Law to determine the object's acceleration; or given the motion, determine an unknown force.
• Given a physical situation, apply Newton's Second and Third Laws following these steps: a) sketch the situation, b) identify the forces, c) draw free-body (force) diagrams for each relevant object in the system (separate from original sketch), d) write Newton's Second Law for x-, y- and z- components for each mass (each component is a separate equation), and e) solve for unknowns.
• Solve problems involving weight forces, normal forces, tensions, spring forces, friction forces, and drag forces.
### Homework
• Friday's Assigned Problems: A12; CH 4: 4, 8, 10, 15, 17, 19, 39, 47, 51, 59
• Monday's Hand-In Problems: A9, A10, A11, A13; CH 3: 18, 48, 54; CH 4: 30, 54, 58abcd
Notes: For CH 3 #48b, replace “average speed” with “magnitude of the average velocity.” For CH 4 #54, assume the two blocks have the same acceleration.
### Videos of example problems
To see the problem statement, click on the link below. To play the video example, click on the underlined words "Video Demonstration" near the top of the page with the problem statement.
• Video Example #1: A fully worked out problem involving forces, using information from two separate, yet related, free body diagrams. ans: g/3, direction depends on object
• Video Example #2 Similar to Video Example #1, with two bodies attached by strings; however some important differences. Assume that the acceleration of the blocks is known. ans: $(M+m)a$
• Video Example #3 This is a two-dimensional problem, much more like the problems that you'll see next week. But one of the assigned problems (4-10) and one hand-in (A13) involve Newton's Law in two-dimensions. Those problems aren't as quantitative as this one, but they involve 2D free body diagrams.
### Pre-Class Entertainment
• Car Wash, by Rose Royce
• Centerfield, by John Fogerty
• Closer to Fine, by The Indigo Girls
• Comfortably Numb, by Pink Floyd
• Come Together, by The Beatles | 2017-12-12 04:33:14 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7461168169975281, "perplexity": 4121.485352831737}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948515165.6/warc/CC-MAIN-20171212041010-20171212061010-00448.warc.gz"} |
http://belikros.org/how-to-sxfqoqg/roots-math-definition-fdda8d | What is the definition of real roots? An exponent on one side of the "=" can be turned into a root on the other side of the "=": If then (when n is even b must be ⥠0) Example: nth Root of a-to-the-nth-Power. Square roots are often found in math and science problems, and any student needs to pick up the basics of square roots to tackle these questions. 2. a. Let us take an example of the polynomial p(x) of degree 1 as given below: p(x) = 5x + 1. Solving quadratic equations: complex roots ... that the roots of it are going to be negative b plus or minus-- so that gives us two roots right over there-- plus or minus square root of b squared minus 4ac over 2a. A function has a root when it crosses the x-axis, i.e. One book may start with a definition and then prove a theorem while another book will start off with theorem as their definition and then prove the definition. App Preview: Derivative by Definition - Square Roots You can switch back to the summary page for this application by clicking here. Check the denominator factors to ⦠Notice we've used library function Math.sqrt() to calculate the square root of a number. Quadratic equations with complex solutions. Math people agree more that you think. 5th roots. A given quadratic equation ax 2 + bx + c = 0 in which b 2-4ac < 0 has two complex roots: x = ,. Now, there are some special ones that have their own names. But what about (x^2 - x - 3) = 0? So, 5 3 = 5 x 5 x 5 = 125.. Radicals. A Quadratic Equation is one that can be written in the standard form ax 2 + bx + c = 0, where a, b, and c are real numbers and a does not equal zero.. More About Quadratic Equation. At its most basic, an exponent is a short cut for writing out multiplication of the same number. The roots of an equation are the x-values that make it "work" We can find the roots of a quadratic equation either by using the quadratic formula or by factoring. Book your trip ... 42100 Jämsä, FINLAND. If discriminant (D) is equal to 0 then the equation has one real solution. For a lot of quadratic functions this is the easiest way, but it also might be very difficult to see what to do. Finding Roots of Polynomials. Exponents vs Roots. Any of various other underground plant parts, especially an underground stem such as a rhizome, corm, or tuber. Solutions or Roots of Quadratic Equations . According to the definition of roots of polynomials, âaâ is the root of a polynomial p(x), if P(a) = 0. More About Discriminant. Practice: Cube roots. Based on the value of the determinant, the roots are calculated as given in the formula above. As an example, we'll find the roots of the polynomial x 5 - x 4 + x 3 - x 2 - 12x + 12. complexroots Practice: Roots of decimals & fractions. Look it up now! Math Tutoring. Roots and zeros. D = b 2 - 4ac. ⢠Below is the graph of a polynomial p(x). The roots of a polynomial are exactly the x-intercepts of its graph. That means that (x2) and (x4) are factors of p(x). So, for example: 25^(1/2) = sqrt(25) = 5 Square Roots, Cube Roots and More Suppose instead of finding the square of 9, which is 81, we wanted to find out what number multiplied with itself equals 81. What is the deal with roots solutions? b. Sometimes, the exponent is called a power.In the case of our example, 5 3 can also be called 5 to third power. HimosLomat Oy is Himos central booking agency that handles centrally all Super Rally indoor ... Tallink Silja Oy, Eckerö Line and Finnlines offer special prices for FH-DCE Super Rally® 2019 guests. In mathematics, the fundamental theorem of algebra states that every non-constant single-variable polynomial with ⦠In other words, five is the square root of 25 because five times five equals 25. One way is to use the solve (Symbolic Math Toolbox) function. Double root definition is - a root that appears twice in the solution of an algebraic equation. Rational Roots Test. When we solve polynomial equations with degrees greater than zero, it may have one or more real roots or one or more imaginary roots. The square root is actually a fractional index and is equivalent to raising a number to the power 1/2. Example: The roots of x 2 â x â 2 = 0 are x = 2 and x = â1. The Rational Roots Test (also known as Rational Zeros Theorem) allows us to find all possible rational roots of a polynomial. We can have 3 situations when solving quadratic equations. 135. Solve that factor for x. Understanding square roots. The graph intersects the x-axis at 2 and 4, so 2 and 4 must be roots of p(x). A solution to an equation of the form f(x) = 0.Roots may be real or complex.. Note: The roots of f(x) = 0 are the same as the zeros of the function f(x).Sometimes in casual usage the words root and zero are used interchangeably.. We have used the format() method to print the calculated roots. If ax 2 + bx + c = 0 is a quadratic equation, then the Discriminant of the equation, i.e. Roots, a 1955 Mexican drama; The Root, an online magazine focusing on African-American culture; The Roots, a location in the video game Kya: Dark Lineage; Roots, the English title for the Tamil film Sethum Aayiram Pon (2019); Literature and stage plays. Square roots ask âwhat number, when multiplied by itself, gives the following result,â and as such working them out requires you ⦠Thanks. Exponents. syms x s = solve(x^2-x-6) s = -2 3. Intro to square roots. Example 1. Roots and Radicals. Roots definition at Dictionary.com, a free online dictionary with pronunciation, synonyms and translation. Case 1: Two roots. See more. Definition of a polynomial. Practice: Square roots. Symbolic Roots. Intro to cube roots. User Case Studies. Definition Of Quadratic Equation. If you have Symbolic Math Toolboxâ¢, then there are additional options for evaluating polynomials symbolically. Definition Of Discriminant. There are some (silly) times where some definitions are different. The goal is to find all roots of the function (all values). Suppose a is root of the polynomial P\left( x \right) that means P\left( a \right) = 0.In other words, if we substitute a into the polynomial P\left( x \right) and get zero, 0, it means that the input value is a root of the function. Equations with Complex solutions the calculated roots learn How to determine the the roots of the equation has real... ( also known as Rational Zeros theorem ) allows us to find all roots of a polynomial x =. Quadratic function Factorization: sqrt ( \ \ ) it means root... Practice tests, quizzes, and personalized coaching to help you succeed look the. 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Nc Rental Agreement, Colorado State University Tour, Gx Works3 デバイス設定, Ramsgate Seal Boat Trips, Terranora Public School Facebook, Las Excusas Ojo Sabio Answers, Orange, Tx Weather Radar Map, Stephen Schwarzman Book, Robalo Quality Issues, How To Crawl In The Maze Roblox, 7 Days To Die Ps4 Reddit 2020, Shimmy Shimmy Cocoa Puff Kid Song, | 2021-04-21 22:55:01 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.681883692741394, "perplexity": 696.012612555835}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618039554437.90/warc/CC-MAIN-20210421222632-20210422012632-00586.warc.gz"} |
https://www.physicsforums.com/threads/proton-moving-from-infinity.858225/ | # Proton moving from infinity
Tags:
1. Feb 19, 2016
### kuokius
1. The problem statement, all variables and given/known data
A proton is moving at speed v from infinity toward a second stationary proton, as shown below. Determine the minimal distance between them.
http://s27.postimg.org/lmw3d21j7/Untitled.png
2. Relevant equations
$$W = \frac{kq_1q_2}{r}$$
$$E_k = \frac{mv^2}{2}$$
3. The attempt at a solution
Let's say that the minimal distance between two protons is x and at that moment their speeds are v_1. Then the initial energy would be E_1 and the final E_2:
$$E_1 = \frac{mv^2}{2}$$
$$E_2 = \frac{ke^2}{x} + mv_1^2$$
According to the law of conservation of energy: $$E_1 = E_2$$
And now I just don't know how to find the speed v_1.
2. Feb 19, 2016
### vela
Staff Emeritus
Can you think of any other conserved quantities?
3. Feb 19, 2016
### kuokius
Maybe an electric field or potential will remain constant at some point?
4. Feb 19, 2016
### alw34
5. Feb 19, 2016
### kuokius
So, I see that I can use conservation law of linear momentum. But how to include a given distance r?
6. Feb 19, 2016
### alw34
good
that was my problem too....
been away from solving any of these for, well 50 plus years,
amazing I can remember my own name!!
https://en.wikipedia.org/wiki/Momentum#Conservation
"If the velocities of the particles are u1 and u2 before the interaction, and afterwards they arev1 and v2, then
"
Think about whether you can use these as a second set of equations.....m's are all the same, only proton is moving initially, right?? two equations, two velocity unknowns
the stationary proton accelerates, reaches some velocity which you'll know.....
so you'll need another equation relating velocity to minimal distance....unsure what that is
7. Feb 19, 2016
### vela
Staff Emeritus
Is the second proton free to move or is its location fixed? I think you're supposed to assume the latter.
8. Feb 19, 2016
### alw34
Of course....duh!!
thank you
9. Feb 20, 2016
### kuokius
Yes, the second proton is fixed. Then I suppose I could use conservation law of angular momentum.
10. Feb 20, 2016
### haruspex
Yes, but only if you choose the axis carefully.
Linear momentum is not conserved because the second proton is being held in place by some external force. How do you avoid that being a problem for angular momentum?
11. Feb 20, 2016
### kuokius
Let's say I choose an axis going through the second proton which is fixed. Vector of electrical force creating external forces momentum goes through the axis, so the momentum of external forces equals zero. Then the initial and final angular moments would be:
$$L_i = mvr$$
$$L_f = mv_1x$$
$$L_i = L_f$$
According to the law of conservation of energy:
$$\frac{mv^2}{2} = \frac{mv_1^2}{2} + \frac{ke^2}{x}$$
Am I right?
12. Feb 20, 2016
### haruspex
Looks right.
13. Feb 20, 2016
### vela
Staff Emeritus
This doesn't really make sense. I know what you're trying to say, but what you've written is nonsense. | 2018-03-20 07:18:14 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5498257279396057, "perplexity": 1504.0750268344113}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257647299.37/warc/CC-MAIN-20180320052712-20180320072712-00138.warc.gz"} |
https://cracku.in/ssc-cgl-16-aug-shift-1-question-paper-solved?page=10 | # 2017 SSC CGL 16 Aug Shift-1
Instructions
For the following questions answer them individually
Question 91
The point of intersection of all the angle bisector of a triangle is ______ of the triangle.
Question 92
ABC is an equilateral triangle and P is the orthocenter of the triangle, then what is the value (in degrees) of ∠BPC?
Question 93
In a triangle ABC, AD is angle bisector of ∠A and AB : AC = 3 : 4. If the area of triangle ABC is 350 cm2, then what is the area (in cm2: of triangle ABD?
Question 94
A boat is sailing towards a lighthouse of height 20√3 m at a certain speed. The angle of elevation of the top of the lighthouse changes from 30° to 60° in 10 seconds. What is the time taken (in seconds) by the boat to reach the lighthouse from its initial position?
Question 95
What is the value of [sec θ/(sec θ - 1)] + [sec θ/(sec θ + 1)] ?
Question 96
If $$\cosec\theta = \dfrac{1}{4x} + x$$ ,then what is the value of $$\cosec\theta + \cot\theta$$.
Instructions
The pie chart given below shows the runs scored by Pujara against team of different countries.
Question 97
The runs scored by Pujara against South Africa is more than runs scored against Bangladesh by what percentage?
Question 98
If Pujara has scored 1875 runs in total, then what is the difference in runs scored by Pujara against South Africa and New Zealand?
Question 99
What is the sectorial angle (in degrees) made by the runs scored against Australia in the given pie chart?
Question 100
What should be the least number of runs that Pujara must have scored in total (runs can only be integers)?
OR | 2020-01-26 04:39:51 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.49170392751693726, "perplexity": 1564.11894828997}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579251687725.76/warc/CC-MAIN-20200126043644-20200126073644-00168.warc.gz"} |
https://brilliant.org/problems/the-root-of-the-problem-the-sequel/ | # The Root of the Problem: The Sequel
Algebra Level 2
Solve for $x$:
$x = \sqrt{1+2\sqrt{1+3\sqrt{1+4\sqrt{1+5\sqrt{1+\cdots}}}}}$
Note: If you think you know this problem so well, try this.
× | 2021-03-01 18:36:58 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 2, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8972046971321106, "perplexity": 1980.6814228136652}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178362899.14/warc/CC-MAIN-20210301182445-20210301212445-00604.warc.gz"} |
http://www.numdam.org/item/CM_1973__26_3_331_0/ | A duality theorem for divisors on certain algebraic curves
Compositio Mathematica, Tome 26 (1973) no. 3, pp. 331-338.
@article{CM_1973__26_3_331_0,
author = {Huikeshoven, Frans},
title = {A duality theorem for divisors on certain algebraic curves},
journal = {Compositio Mathematica},
pages = {331--338},
publisher = {Noordhoff International Publishing},
volume = {26},
number = {3},
year = {1973},
zbl = {0264.14004},
mrnumber = {337969},
language = {en},
url = {www.numdam.org/item/CM_1973__26_3_331_0/}
}
Huikeshoven, Frans. A duality theorem for divisors on certain algebraic curves. Compositio Mathematica, Tome 26 (1973) no. 3, pp. 331-338. http://www.numdam.org/item/CM_1973__26_3_331_0/
A. Altman and S. Kleiman [1] Introduction to Grothendieck Duality Theory, Lecture Notes in Mathematics No. 146, Springer-Verlag (1970). | MR 274461 | Zbl 0215.37201
R. Hartshorne [2] Residues and Duality, Lecture Notes in Mathematics No. 20, Springer-Verlag (1966). | MR 222093 | Zbl 0212.26101
F. Huikeshoven [3] Multiple algebraic curves, moduli problems, (Thesis, Amsterdam) (1971).
M. Nagata [4] Local rings, Interscience tracts 13, Interscience Publishers (1962). | MR 155856 | Zbl 0123.03402
F. Oort [5] Reducible and multiple algebraic curves, (Thesis, Leiden) (1961). | MR 180553 | Zbl 0102.15905
J.-P. Serre [6] Groupes algébriques et corps de classes, Act. Sc. Ind. 1264 Hermann (1959). | Zbl 0097.35604
J. Tate [7] Residues of differentials on curves, Ann. scient. Ec. Norm. Sup. 4e série 1 (1968) 149-159. | Numdam | MR 227171 | Zbl 0159.22702 | 2021-03-01 07:23:45 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.24949268996715546, "perplexity": 6797.414443616215}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178362133.53/warc/CC-MAIN-20210301060310-20210301090310-00560.warc.gz"} |
http://mathhelpforum.com/differential-geometry/176857-complex-number.html | # Math Help - Complex number
1. ## Complex number
Find the complex number w, lying in the first quadrant, and having the largest possible real part, which satisfies the equation:
w^6=-6-6*I*sqrt(3)
Thanks!
2. Originally Posted by Rine198
Find the complex number w, lying in the first quadrant, and having the largest possible real part, which satisfies the equation: w^6=-6-6*I*sqrt(3); the answer is 12^(1/6)*exp(2/9*I*Pi)
If $W=-6-6\sqrt{3}\mathfi{i}$ then $|W|=12$ and $\text{Arg}(W)=-\frac{2\pi}{3}$.
3. yeah, i got that part, but i still can't seem to get the answer right, so to find the root of w, i divided the argument by 6, but i manage to get -1*Pi/9, and that is not what the answer states
4. Originally Posted by Rine198
yeah, i got that part, but i still can't seem to get the answer right, so to find the root of w, i divided the argument by 6, but i manage to get -1*Pi/9, and that is not what the answer states
But the question states that the answer is in the first quadrant.
$\dfrac{2\pi}{6}=\dfrac{3\pi}{9}$ so add.
5. i don't get how u got 2*Pi/6 as well as 3*Pi/9
6. Originally Posted by Rine198
i don't get how u got 2*Pi/6 as well as 3*Pi/9
Those six sixth roots are located on a circle centered at 0.
They are equally spaced, separated by $\dfrac{2\pi}{6}.$
7. Originally Posted by Rine198
Find the complex number w, lying in the first quadrant, and having the largest possible real part, which satisfies the equation:
w^6=-6-6*I*sqrt(3)
Thanks!
Did you mean to write $w^6=6-6\sqrt{3}i$ above? If so you want the 6-th root
of $6-6\sqrt{3}i=12\,cis(-\pi/3+2k\pi)=12e^{-\pi i/3+2k\pi i}=12e^{5\pi i/3+2k\pi i}$ with the
largest real part , so using de Moivre's formula we get:
$\displaystyle{w_k=\left(12e^{5\pi i/3+2k\pi i}\right)^{1/6}=12^{1/6}e^{\frac{5\pi i}{18}+\frac{2k\pi i}{6}}=12^{1/6}e^{\frac{\pi i}{18}(5+6k)}\,,\,\,k=0,1,2,...,5$ .
Now just write down each root above and check which one has the largest real part. For example,
$Re(w_0)=Re\left(12^{1/6}e^{5\pi i/18}\right)=12^{1/6}\cos\left(5\pi/18)\cong 0.9726$ ,
$Re(w_1)=12^{1/6}\cos\left(11\pi/18)\cong -0.5175$ , etc.
Hint: Of course, you should check only those roots with angle in $\left(-\pi/2\,,\,\pi/2\right) radians$ (why?)
Tonio | 2014-03-07 22:47:14 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 11, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9537894129753113, "perplexity": 480.22462433847846}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1393999651577/warc/CC-MAIN-20140305060731-00068-ip-10-183-142-35.ec2.internal.warc.gz"} |
http://www.math-only-math.com/worksheet-on-facts-about-multiplication.html | # Worksheet on Facts about Multiplication
Practice the worksheet on facts about multiplication. We know in multiplication, the number being multiplied is called the multiplicand and the number by which it is being multiplied is called the multiplier. This will help us to solve the given questions.
1. (i) In 2 4
× 5
1 2 0
24 is the _____
5 is the _____
120 is the _____
(ii) The answer of a multiplication sum is called the _____
(iii) In a multiplication sum if the multiplier is 0, the product will be _____
(iv) 1 time every number is the _____ itself.
(v) In _____ ×_____ =_____, the multiplicand, the multiplier and the product are the same numbers. What are the numbers?
[Hint: There can be only two such whole numbers.]
(vi) If 5 × 6 = 30 then _____ ÷ _____ = 5 and _____ ÷ _____ = 6
(vii) 12 × 15 = _____ × 12
(viii) 0 × 28 = 28 × _____
(ix) The _____ of 4 × 10 and 10 × 4 is the same
2. Complete:
(i) 1 × 8 = _____
(ii) 5 × 7 = _____
(iii) 6 × 9 = _____
(iv) 2 × 9 = _____
(v) 8 × _____ = 112
(vi) 3 × 5 = _____
(vii) 4 × 8 = _____
(viii) 7 × _____ = 49
(ix) 8 × 9 = _____
(x) 10 × _____ = 100
(xi) 4 × _____ = 24
(xii) 7 × 3 = _____
Check the answers given below of the worksheet on facts about multiplication.
1. (i) multiplicand, multiplier, product
(ii) product
(iii) zero
(iv) number
(v) 1
(vi) 30 ÷ 6 = 5 and 30 ÷ 5 = 6
(vii) 15
(viii) 0
(ix) product
2. (i) 8
(ii) 35
(iii) 54
(iv) 18
(v) 14
(vi) 15
(vii) 32
(viii) 7
(ix) 72
(x) 10
(xi) 6
(xii) 21
` | 2018-09-21 08:24:25 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8001845479011536, "perplexity": 4099.17852428898}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267156901.47/warc/CC-MAIN-20180921072647-20180921093047-00094.warc.gz"} |
https://caddellprep.com/common-core-algebra-assignments/vertex-form-of-a-quadratic-equation/ | Vertex Form of a Quadratic Equation
In this video, we are going to look at the vertex form of a quadratic equation.
If we look at a regular quadratic function such as $y=x^2$, and want to shift it to the right 3 units and down 4 units, then we know that the modified equation would be
$y=(x-3)^2-4$
*Horizontal shifts are located within the parenthesis and vertical shifts are located outside of the parenthesis*
From this equation we can clearly see that the vertex point is at (3,-4).
This form is very useful in identifying the coordinates of the vertex.
If we were given an equation in standard form, we can complete the square to get it to vertex form.
For example:
$y=x^2+6x+8$
To solve by completing the square, we want to solve for the number to add by using
$(\frac{b}{2})^2$
So:
$(\frac{6}{2})^2=3^2=9$
This means that we have to add 9 to complete the square. However, if we add 9 then it changes the formula. To counteract that, we will also subtract 9.
Lets focus on the first three terms in the equation.
$y=x^2+6x+9+8-9$
When we factor those terms, we get
$y=(x+3)(x+3)+8-9$
or
$y=(x+3)^2-1$
Now, we have written the equation in vertex form. From here, we can see that the vertex is at (-3,-1).
• Want full access to all of our free math tutorials & practice problems?
Used by students across the country. Pre-Algebra, Algebra I, Geometry, & Algebra II | 2018-01-22 04:45:36 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 8, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7075546383857727, "perplexity": 240.54141693580644}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084890991.69/warc/CC-MAIN-20180122034327-20180122054327-00158.warc.gz"} |
https://brilliant.org/problems/square-roots-14/ | # Square roots
$\large \frac{1}{\sqrt{x}}+\frac{1}{\sqrt{y}}=\frac{1}{\sqrt{20}}$
Find the number of ordered pairs of positive integers $$(x,y)$$ satisfying the above equation.
× | 2017-03-26 03:47:16 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.765044093132019, "perplexity": 297.90183036856587}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218189092.35/warc/CC-MAIN-20170322212949-00532-ip-10-233-31-227.ec2.internal.warc.gz"} |
https://lavelle.chem.ucla.edu/forum/viewtopic.php?f=17&t=30704&p=96012 | ## HW 1.15
H-Atom ($E_{n}=-\frac{hR}{n^{2}}$)
Joanna Pham - 2D
Posts: 113
Joined: Fri Apr 06, 2018 11:04 am
### HW 1.15
Could someone please explain how to find the initial and final n-values please? I found the frequency and got 2.9239 x 10^15 Hz. I tried to plug it into the Rydberg formula, but I’m confused how to find the individual n-values...
Kuldeep Gill 1H
Posts: 44
Joined: Fri Apr 06, 2018 11:02 am
Been upvoted: 1 time
### Re: HW 1.15
I got up to that point as well and plugging it in just does not make sense to me
Kuldeep Gill 1H
Posts: 44
Joined: Fri Apr 06, 2018 11:02 am
Been upvoted: 1 time
### Re: HW 1.15
Hi, so I figured it out..... I guess we were supposed to know that in the Lyman series ( UV light) that the final energy always goes to 1 so.... after you get 2.923* 10^15 you use the equation V=R*(1/n1^2 - 1/n2^2) and realise that it is final minus initial so set plug in 1 for 1/n1^2 and plug-in 2.923*10^15 for v and 3.29*10^15 for R and solve for n2.. I think it should become a bit clearer now!
Chem_Mod
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Has upvoted: 393 times
### Re: HW 1.15
Could you please provide the complete details of the question?
Johanna Caprietta 1E
Posts: 30
Joined: Fri Apr 06, 2018 11:02 am
### Re: HW 1.15
Where did you find that the final energy goes to 1? Can you explain the reasoning behind this?
kimberlysanchez-1E
Posts: 30
Joined: Tue Nov 14, 2017 3:01 am
### Re: HW 1.15
im having the same problem
Daniel Cho Section 1H
Posts: 29
Joined: Fri Jun 23, 2017 11:40 am
### Re: HW 1.15
For this problem, you kind of have to use to this equation as well as assume that n1= 1 because this is an example of the Lyman series as you look at the wavelength 102.6 nm in terms of the graph on page 7 letter b. Since you know your frequency would be 2.9329X10^15 Hz, you would set up this equation like this: 2.9329X10^15Hz= (3.29X10^15)(Rydberg constant) {(1/(n1)^2)-(1/(n2)^2))] therefore getting (1/n^2)=.112 . You then solve for n in which from then on you get your answer.
I hope this helps. Correct me in places where I might be wrong. | 2019-10-19 01:09:49 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5949716567993164, "perplexity": 2341.1376084419635}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986685915.43/warc/CC-MAIN-20191018231153-20191019014653-00150.warc.gz"} |
http://tocmirror.cs.tau.ac.il/categories/Boolean_functions.html | Articles under category:
Boolean Functions
ToC Library Graduate Surveys 1 (2008) 20 pages A Brief Introduction to Fourier Analysis on the Boolean Cube
Vol 10, Article 2 (pp 27-53) A Regularity Lemma and Low-Weight Approximators for Low-Degree Polynomial Threshold Functions
Vol 9, Article 29 (pp 889-896) [NOTE] [Boolean Spec Issue] Hypercontractivity Via the Entropy Method by Eric Blais and Li-Yang Tan
Vol 9, Article 23 (pp 703-757) [APRX-RND12 Spec Issue] Circumventing $d$-to-$1$ for Approximation Resistance of Satisfiable Predicates Strictly Containing Parity of Width at Least Four
Vol 9, Article 20 (pp 653-663) Approximating the AND-OR Tree
Vol 9, Article 18 (pp 593-615) [Boolean Spec Issue] Making Polynomials Robust to Noise
Vol 9, Article 17 (pp 587-592) [NOTE] [Boolean Spec Issue] A Monotone Function Given By a Low-Depth Decision Tree That Is Not an Approximate Junta
Vol 7, Article 11 (pp 155-176) Distribution-Free Testing for Monomials with a Sublinear Number of Queries by Elya Dolev and Dana Ron
Vol 7, Article 10 (pp 147-153) [NOTE] The Influence Lower Bound Via Query Elimination by Rahul Jain and Shengyu Zhang
Vol 7, Article 6 (pp 75-99) Testing Linear-Invariant Non-Linear Properties
Vol 7, Article 4 (pp 45-48) [NOTE] Tight Bounds on the Average Sensitivity of k-CNF
Vol 6, Article 4 (pp 81-84) [NOTE] Decision Trees and Influence: an Inductive Proof of the OSSS Inequality
Vol 5, Article 13 (pp 257-282) Optimal Cryptographic Hardness of Learning Monotone Functions
Vol 5, Article 10 (pp 191-216) Distribution-Free Testing Lower Bound for Basic Boolean Functions | 2017-06-27 14:03:14 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2828652262687683, "perplexity": 6004.69925346373}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-26/segments/1498128321426.45/warc/CC-MAIN-20170627134151-20170627154151-00300.warc.gz"} |
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# Crops can be traded on the futures market before they are
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Crops can be traded on the futures market before they are [#permalink] 18 Jul 2008, 01:16
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Official Guide for GMAT Verbal Review, 2nd Edition
Practice Question
Question No.: 50
Page: 136
Difficulty:
Crops can be traded on the futures market before they are harvested. If a poor corn harvest is predicted, prices of corn futures rise; if a bountiful corn harvest is predicted, prices of corn futures fall. This morning meteorologists are predicting much-needed rain for the corn-growing region starting tomorrow. Therefore, since adequate moisture is essential for the current crop’s survival, prices of corn futures will fall sharply today.
Which of the following, if true, most weakens the argument above?
(A) Corn that does not receive adequate moisture during its critical pollination stage will not produce a bountiful harvest.
(B) Futures prices for corn have been fluctuating more dramatically this season than last season.
(C) The rain that meteorologists predicted for tomorrow is expected to extend well beyond the corn-growing region.
(D) Agriculture experts announced today that a disease that has devastated some of the corn crop will spread widely before the end of the growing season.
(E) Most people who trade in corn futures rarely take physical possession of the corn they trade.
[Reveal] Spoiler: OA
Last edited by Narenn on 07 Oct 2013, 09:25, edited 2 times in total.
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Re: CR: Crops [#permalink] 18 Jul 2008, 01:54
I think D is the answer.
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Re: CR: Crops [#permalink] 18 Jul 2008, 03:58
stuck btwn A and D , but chose A
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Re: CR: Crops [#permalink] 18 Jul 2008, 04:55
2
KUDOS
D
vksunder wrote:
Crops can be traded on the futures market before they are harvested. If a poor corn harvest is predicted, prices
of corn futures rise; if a bountiful corn harvest is predicted, prices of corn futures fall. This morning meteorologists
are predicting much-needed rain for the corn-growing region starting tomorrow. Therefore, since adequate moisture
is essential for the current crop’s survival, prices of corn futures will fall sharply today.
Which of the following, if true, most weakens the argument above?
(A) Corn that does not receive adequate moisture during its critical pollination stage will not produce a bountiful harvest.
Actually seems to strengthen the stem even though we don't know which growth stage the corn is currently in. This means it is also out of scope.
(B) Futures prices for corn have been fluctuating more dramatically this season than last season.
This has nothing to do with supporting or refuting the conclusion in the stem that prices will fall.
(C) The rain that meteorologists predicted for tomorrow is expected to extend well beyond the corn-growing region.
It doesn't matter if the rain goes beyond the corn-growing area because we need only that which affects the corn growth. Out of Scope.
(D) Agriculture experts announced today that a disease that has devastated some of the corn crop will spread widely before the end of the growing season.
This gives us a reason the prices will rise (disease kills crop, cuts supply, demand remains) even though the rain appears to be something that will make a good harvest and prices should fall.
(E) Most people who trade in corn futures rarely take physical possession of the corn they trade.
So?
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Crops can be traded on the futures market before they are [#permalink] 08 Jun 2011, 20:01
Crops can be traded on the futures market before they are harvested. If a poor corn harvest is predicted, prices
of corn futures rise; if a bountiful corn harvest is predicted, prices of corn futures fall. This morning meteorologists
are predicting much-needed rain for the corn-growing region starting tomorrow. Therefore, since adequate moisture
is essential for the current crop’s survival, prices of corn futures will fall sharply today.
Which of the following, if true, most weakens the argument above?
(A) Corn that does not receive adequate moisture during its critical pollination stage will not produce a
bountiful harvest.
(B) Futures prices for corn have been fluctuating more dramatically this season than last season.
(C) The rain that meteorologists predicted for tomorrow is expected to extend well beyond the corn-growing
region.
(D) Agriculture experts announced today that a disease that has devastated some of the corn crop will spread
widely before the end of the growing season.
(E) Most people who trade in corn futures rarely take physical possession of the corn they trade.
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Re: Please explain why D cant be considered out of scope [#permalink] 08 Jun 2011, 21:04
ruturaj wrote:
Crops can be traded on the futures market before they are harvested. If a poor corn harvest is predicted, prices of corn futures rise; if a bountiful corn harvest is predicted, prices of corn futures fall. This morning meteorologists are predicting much-needed rain for the corn-growing region starting tomorrow. Therefore, since adequate moisture is essential for the current crop’s survival, prices of corn futures will fall sharply today.
Bold part is the conclusion
Which of the following, if true, most weakens the argument above?
(A) Corn that does not receive adequate moisture during its critical pollination stage will not produce a bountiful harvest.we are bothered about the crop that receives moisture
(B) Futures prices for corn have been fluctuating more dramatically this season than last season.out of scope
(C) The rain that meteorologists predicted for tomorrow is expected to extend well beyond the corn-growing region.Out of scope
(D) Agriculture experts announced today that a disease that has devastated some of the corn crop will spread widely before the end of the growing season.According to this, the crop will be devastated and the prices will rise, this fact is contrary to the conclusion thereby weakening it.
(E) Most people who trade in corn futures rarely take physical possession of the corn they trade.Out of scope
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Re: Crops can be traded on the futures market before they are [#permalink] 23 Mar 2012, 15:03
I have chosen D as the answer choice:
The conclusion is: [highlight]Prices of corn futures will fall sharply today.[/highlight]
A. This answer choice describes when the best time for rain is. However, it does not describe whether the prices will rise or fall today. Therefore, this is an incorrect answer.
B. Although prices have been fluctuating, this answer choice does not help us understand what will happen to corn futures today.
C. We are only concerned with rain in the corn growing region.
D. This is the correct answer. This statement explains why the prices of corn futures may increase - a disease could counteract any benefit that the rain may give.
E. This is irrelevant.
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Crops can be traded on the futures market before they are [#permalink] 01 Jan 2013, 11:29
Expert's post
Crops can be traded on the futures market before they are harvested. If a poor corn harvest is predicted, prices of corn futures rise; if a bountiful corn harvest is predicted, prices of corn futures fall. This morning meteorologists are predicting much-needed rain for the corn-growing region starting tomorrow. Therefore, since adequate moisture is essential for the current crop’s survival, prices of corn futures will fall sharply today.
Which of the following, if true, most weakens the argument above?
(A) Corn that does not receive adequate moisture during its critical pollination stage will not produce a bountiful harvest.
(B) Futures prices for corn have been fluctuating more dramatically this season than last season.
(C) The rain that meteorologists predicted for tomorrow is expected to extend well beyond the corn-growing region.
(D) Agriculture experts announced today that a disease that has devastated some of the corn crop will spread widely before the end of the growing season.
(E) Most people who trade in corn futures rarely take physical possession of the corn they trade.
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Re: Another CR Question [#permalink] 01 Jan 2013, 11:44
1
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Expert's post
abhijitlandge wrote:
Crops can be traded on the futures market before they are harvested. If a poor corn harvest is predicted, prices of corn futures rise; if a bountiful corn harvest is predicted, prices of corn futures fall. This morning meteorologists are predicting much-needed rain for the corn-growing region starting tomorrow. Therefore, since adequate moisture is essential for the current crop’s survival, prices of corn futures will fall sharply today.
Which of the following, if true, most weakens the argument above?
(A) Corn that does not receive adequate moisture during its critical pollination stage will not produce a bountiful harvest. is irrilevant the pollination
(B) Futures prices for corn have been fluctuating more dramatically this season than last season. the comparison betwee this season and the last is not importnat for the argument at stake
(C) The rain that meteorologists predicted for tomorrow is expected to extend well beyond the corn-growing region. the fact that the rain will expand farther is not relevant
(D) Agriculture experts announced today that a disease that has devastated some of the corn crop will spread widely before the end of the growing season. this is a reason out od scope that weaken the argument
(E)Most people who trade in corn futures rarely take physical possession of the corn they trade. future trade is irrilevant
hope is clear
rules-for-posting-in-verbal-gmat-forum-134642.html
Thanks.
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Re: Another CR Question [#permalink] 01 Jan 2013, 12:23
Expert's post
carcass wrote:
abhijitlandge wrote:
Crops can be traded on the futures market before they are harvested. If a poor corn harvest is predicted, prices of corn futures rise; if a bountiful corn harvest is predicted, prices of corn futures fall. This morning meteorologists are predicting much-needed rain for the corn-growing region starting tomorrow. Therefore, since adequate moisture is essential for the current crop’s survival, prices of corn futures will fall sharply today.
Which of the following, if true, most weakens the argument above?
(A) Corn that does not receive adequate moisture during its critical pollination stage will not produce a bountiful harvest. is irrilevant the pollination
(B) Futures prices for corn have been fluctuating more dramatically this season than last season. the comparison betwee this season and the last is not importnat for the argument at stake
(C) The rain that meteorologists predicted for tomorrow is expected to extend well beyond the corn-growing region. the fact that the rain will expand farther is not relevant
(D) Agriculture experts announced today that a disease that has devastated some of the corn crop will spread widely before the end of the growing season. this is a reason out od scope that weaken the argument
(E)Most people who trade in corn futures rarely take physical possession of the corn they trade. future trade is irrilevant
hope is clear
rules-for-posting-in-verbal-gmat-forum-134642.html
Thanks.
Oh! I am sorry. I was unaware about the rules. In fact i just read them for the first time.
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Re: Crops can be traded on the futures market before they are [#permalink] 01 Jan 2013, 12:38
Expert's post
Do not worry, but is important to follow.
Regards,
carcass
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Re: Crops can be traded on the futures market before they are [#permalink] 27 Jan 2013, 02:01
2
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this is proposal passage
do x then Y happen
if rain is good, the crop is good and price falls.
prethink
-assumption is that there is no bad agent
- weakener, there is some bad agent
Last edited by Narenn on 06 Oct 2013, 08:27, edited 1 time in total.
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Crops can be traded on the futures market before they are [#permalink] 30 Jun 2014, 19:10
1
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Crops can be traded on the futures market before they are harvested. If a poor corn harvest is predicted, prices of corn futures rise; if a bountiful corn harvest is predicted, prices of corn futures fall. This morning meteorologists are predicting much-needed rain for the corn-growing region starting tomorrow. Therefore, since adequate moisture is essential for the current crop’s survival, prices of corn futures will fall sharply today.
Which of the following, if true, most weakens the argument above?
Poor harvest - high prices
Good harvest - low prices
Prediction - Much needed rain for corn.
conclusion - Prices of corn will fall sharply
Weakener should weaken the conclusion. We are looking for answer choice that will give enough reason for us to doubt whether the prices can still increase even when good rain is predicted.
Something that will destroy the crops even when the rain is plentiful.
(A) Corn that does not receive adequate moisture during its critical pollination stage will not produce a bountiful harvest. - Incorrect. Kind of a strengthener.
(B) Futures prices for corn have been fluctuating more dramatically this season than last season. - Incorrect. Not concerned with prices comparison.
(C) The rain that meteorologists predicted for tomorrow is expected to extend well beyond the corn-growing region. - Incorrect. This is a trap answer. This may lead us to believe that too much rain can destroy the harvest. But the passage does not say so.
(D) Agriculture experts announced today that a disease that has devastated some of the corn crop will spread widely before the end of the growing season. - Correct. If the harvest is destroyed by disease then the prices might go up. Weakens the conclusion.
(E) Most people who trade in corn futures rarely take physical possession of the corn they trade. - Incorrect. Irrelevant.
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Re: Crops can be traded on the futures market before they are [#permalink] 30 Jul 2015, 02:37
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Crops can be traded on the futures market before they are [#permalink] 30 Jul 2015, 16:27
Can someone maybe better explain this to me.
I don't think it's D because the question asked what would weaken the the argument (the argument is about rain in relation to corn growth). This answer choice merely introduces a new aspect (disease, which is not part of the argument) into the equation. If the question asked which of the following, if true, Would decrease corn production or increase corn futures? Than this would answer it. But, as it stands the choice does nothing to the argument.
I think choice A answers the question and is relevant to the argument. The argument is: you need rain for corn growth and you are expecting rain -> corn will grown -> prices of corn futures will decrease.
Choice A says corn that doesn't receive moisture during its critical pollination stage will not produce bountiful harvest.
Passage says adequate moisture is essential for current crops survival. Choice A says there is a critical stage (time) in a corn plants life and during this stage (time) if it doesn't receive moisture (rain) it won't grow. And since the rain now is "much needed" according to the passage, this indicates there wasn't much rain before, so essentially you already missed that bus, when rain was needed (at a certain stage aka time) it wasn't available.
shank001 wrote:
Crops can be traded on the futures market before they are harvested. If a poor corn harvest is predicted, prices of corn futures rise; if a bountiful corn harvest is predicted, prices of corn futures fall. This morning meteorologists are predicting much-needed rain for the corn-growing region starting tomorrow. Therefore, since adequate moisture is essential for the current crop’s survival, prices of corn futures will fall sharply today.
Which of the following, if true, most weakens the argument above?
Poor harvest - high prices
Good harvest - low prices
Prediction - Much needed rain for corn.
conclusion - Prices of corn will fall sharply
Weakener should weaken the conclusion. We are looking for answer choice that will give enough reason for us to doubt whether the prices can still increase even when good rain is predicted.
Something that will destroy the crops even when the rain is plentiful.
(A) Corn that does not receive adequate moisture during its critical pollination stage will not produce a bountiful harvest. - Incorrect. Kind of a strengthener.
(B) Futures prices for corn have been fluctuating more dramatically this season than last season. - Incorrect. Not concerned with prices comparison.
(C) The rain that meteorologists predicted for tomorrow is expected to extend well beyond the corn-growing region. - Incorrect. This is a trap answer. This may lead us to believe that too much rain can destroy the harvest. But the passage does not say so.
(D) Agriculture experts announced today that a disease that has devastated some of the corn crop will spread widely before the end of the growing season. - Correct. If the harvest is destroyed by disease then the prices might go up. Weakens the conclusion.
(E) Most people who trade in corn futures rarely take physical possession of the corn they trade. - Incorrect. Irrelevant.
Crops can be traded on the futures market before they are [#permalink] 30 Jul 2015, 16:27
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Display posts from previous: Sort by | 2016-02-10 13:08:58 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.22926171123981476, "perplexity": 8580.032475827256}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-07/segments/1454701159376.39/warc/CC-MAIN-20160205193919-00325-ip-10-236-182-209.ec2.internal.warc.gz"} |
https://ftp.aimsciences.org/article/doi/10.3934/dcdsb.2004.4.147 | # American Institute of Mathematical Sciences
February 2004, 4(1): 147-159. doi: 10.3934/dcdsb.2004.4.147
## A hierarchy of cancer models and their mathematical challenges
1 Ohio State University, Department of Mathematics, Columbus, OH 43210, United States
Received December 2002 Revised May 2003 Published November 2003
A variety of PDE models for tumor growth have been developed in the last three decades. These models are based on mass conservation laws and on reaction-diffusion processes within the tumor.
Citation: Avner Friedman. A hierarchy of cancer models and their mathematical challenges. Discrete & Continuous Dynamical Systems - B, 2004, 4 (1) : 147-159. doi: 10.3934/dcdsb.2004.4.147
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2019 Impact Factor: 1.27 | 2021-01-22 00:04:51 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5531213283538818, "perplexity": 7894.259703958919}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703528672.38/warc/CC-MAIN-20210121225305-20210122015305-00044.warc.gz"} |
http://math.stackexchange.com/questions/6142/separative-quotients-and-the-induced-order | # Separative Quotients, and the Induced Order
Let $P$ be some partial order.
We say that $x$ and $y$ are compatible if $\exists r\in P (r\le x \wedge r\le y)$, we denote this by $x \perp y$. Otherwise, we say that $x$ and $y$ are incompatible.
An order $P$ is called separative if whenever $\neg (x \le y)$ then there exists some $r\le x$ which incompatible with $y$.
In Jech's "Set Theory" he proves a lemma (14.11) which construct a separative quotient, $Q$, and a mapping $h$ for a (general) partially ordered set, $P$, that satisfies the following:
• $x\le y \Rightarrow h(x) \preceq h(y)$
• $x \perp y \iff h(x) \perp h(y)$
And $h$ is onto $Q$.
The construction is by taking a quotient of $P$ over the equivalence relation $x \sim y \iff \forall z(z \perp x \leftrightarrow z \perp y)$, and $[x] \preceq [y] \iff \forall z \le x(z \perp y)$. (And obviously enough, $h(x) = [x]$).
Today I was trying to prove the following lemma (which does not appear on Jech's book):
Let $P$ be some partial order, and $Q$ its separative quotient. If $[x] \preceq [y]$ then there exist $x' \in [x], y' \in [y]$ such that $x' \le y'$.
(That is to say that the separative mapping is "almost" order-preserving.)
Intuitively it seems right, but it might very well be a not-common misbelief. Any hints, partial proofs or complete proofs (granted that I haven't proved it myself yet - in which case I'll rush to the nearest computer and update) will be most welcomed.
-
Presumably, $\perp$ is supposed to stand for "incompatible"? – Arturo Magidin Oct 5 '10 at 19:40
Oh right. I forgot to mentioned that $x \perp y$ means they are compatible (it was there at first and somehow through revising my question before submitting it got away). – Asaf Karagila Oct 5 '10 at 19:45
My friend came up with a good counter-example:
Then it is easy to verify that $[x] \prec [y]$ but $x \not{<} y$.
However, if anyone has any further insights into the lemma or this whole idea, I'd very like to hear.
-
Another example, perhaps more transparent, because you can see how I arrived at it.
Let $P$ be the set of all infinite subsets of the natural numbers $\omega$. Then $A \subseteq^* B$ means that $A\setminus B$ is finite.
Take your favorite subsets $A \subseteq B$ with $A \not=^* B$. Let $P'$ be the set of all infinite subsets $S \subseteq \omega$ which satisfy one of the following properties:
1. $S \not=^* A$ and $S \not=^* B$.
2. $S=^* A$, and $22\in S$.
3. $S=^* B$, but $22\notin S$.
Now $P'$ is essentially the same as $P$ (it inherits the $\le$ and $\le^*$ relations). The sets of type 2 form a $=^*$-class with is $\subseteq^*$-below the class of sets of type 3, but there is no pair of representatives where the true $\subseteq$-relations holds.
- | 2015-11-26 14:33:28 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9824251532554626, "perplexity": 167.67818036205998}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398447729.93/warc/CC-MAIN-20151124205407-00031-ip-10-71-132-137.ec2.internal.warc.gz"} |
http://www.acmerblog.com/hdu-3477-temperature-5618.html | 2014
04-04
# Temperature
Many people like summer as summer has a lot of advantages, but on the other hand, sometimes summer is also boring. As a student, Tom has complained with summer for many days. Because when having lunch, Tom has a habit of drinking soup. But the temperature of the soup is too high, so Tom need wait for a long time to drink. One day, Tom bought a bowl of soup again, he measured the temperature of the environment is ua and the temperature of the soup is u0, after t1 minutes, he measured the soup again and the temperature is u1, but he did not want to measure the temperature all the time until he could drink it. Now Tom asks you for help. Could you help Tom calculate what the temperature of the soup is after t2 minutes and how long he need to wait for until the temperature of the soup becomes u2 according to the data which he had measured? You could assume that the temperature of the environment is invariable.
The first line of the input contains a single integer T (1 <= T <= 10), the number of test cases. Then T cases follow.
The first line of each case contains 5 integers, ua(0<ua<100), u0(ua<=u0<=100), u1(ua<=u1<=u0), t1(t1>0), n(1<=n<=10), indicating the temperature of the environment ua, the original temperature of the soup u0 and the later temperature of the soup u1 after t1 minutes, n indicates that there are n options in the following. Each line of the n lines contains two integers, p and s, p is the kind of the option and can only be 0 or 1. If p is 0, you should calculate the time Tom need to wait for until the temperature of the soup becomes s(ua<=s<=u0)(it is guaranteed that temperature s is reachable), or you should calculate the temperature of the soup after s(0<s<=100) minutes from original time t=0.
The first line of the input contains a single integer T (1 <= T <= 10), the number of test cases. Then T cases follow.
The first line of each case contains 5 integers, ua(0<ua<100), u0(ua<=u0<=100), u1(ua<=u1<=u0), t1(t1>0), n(1<=n<=10), indicating the temperature of the environment ua, the original temperature of the soup u0 and the later temperature of the soup u1 after t1 minutes, n indicates that there are n options in the following. Each line of the n lines contains two integers, p and s, p is the kind of the option and can only be 0 or 1. If p is 0, you should calculate the time Tom need to wait for until the temperature of the soup becomes s(ua<=s<=u0)(it is guaranteed that temperature s is reachable), or you should calculate the temperature of the soup after s(0<s<=100) minutes from original time t=0.
1
24 100 90 10 2
0 80
1 20
Case 1:
21.65
81.32
HintAccording to Newton’s law of cooling, in a certain temperature range, the rate of change of an object’s
temperature is proportional to the temperature difference of the object’s temperature and the environment temperature.
1. 这道题这里的解法最坏情况似乎应该是指数的。回溯的时候
O(n) = O(n-1) + O(n-2) + ….
O(n-1) = O(n-2) + O(n-3)+ …
O(n) – O(n-1) = O(n-1)
O(n) = 2O(n-1)
2. for(int i=1; i<=m; i++){
for(int j=1; j<=n; j++){
dp = dp [j-1] + 1;
if(s1.charAt(i-1) == s3.charAt(i+j-1))
dp = dp[i-1] + 1;
if(s2.charAt(j-1) == s3.charAt(i+j-1))
dp = Math.max(dp [j - 1] + 1, dp );
}
}
这里的代码似乎有点问题？ dp(i)(j) = dp(i)(j-1) + 1;这个例子System.out.println(ils.isInterleave("aa","dbbca", "aadbbcb"));返回的应该是false
3. 学算法中的数据结构学到一定程度会乐此不疲的，比如其中的2－3树，类似的红黑树，我甚至可以自己写个逻辑文件系统结构来。
4. L（X [0 .. M-1]，Y [0 .. N-1]）= 1 + L（X [0 .. M-2]，Y [0 .. N-1]）这个地方也也有笔误
应改为L（X [0 .. M-1]，Y [0 .. N-1]）= 1 + L（X [0 .. M-2]，Y [0 .. N-2]） | 2017-05-23 07:07:30 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.604196310043335, "perplexity": 1601.9074452324212}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463607591.53/warc/CC-MAIN-20170523064440-20170523084440-00277.warc.gz"} |
https://guydavis.github.io/2016/01/31/eigenvectors/ | # Linear Algebra
## my old friend
Posted on January 31, 2016
As part of explorations into machine learning, I’ve been brushing up on computer science basics starting with linear algebra. Nice to see good old eigenvectors again after so many years.
An eigenvector of a square matrix $A$ is a non-zero vector $v$ such that multiplication by $A$ alters only the scale of $v$:
$\mathrm{Av}=\mathrm{\lambda v}$
The scalar $\lambda$ is known as the eigenvalue corresponding to this eigenvector.
Excerpted from Chapter 2 of Deep Learning by Ian Goodfellow, Yoshua Bengio and Aaron Courville.
## Practical Use?
So, why are eigenvectors important? Well, they are used in singular value decomposition, which can be applied in principal component analysis as mentioned in this podcast on machine learning fundamentals.
## Example Code
Here’s a quick way of calculating eigenvalues and eigenvectors in Python using the numpy library:
import numpy as np
k = np.random.normal(size=(2,2))
eigenvalues,eigenvectors = np.linalg.eig(k)
with output shown in this interactive session: | 2021-07-29 10:01:22 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 6, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7095280885696411, "perplexity": 869.6163776296914}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046153854.42/warc/CC-MAIN-20210729074313-20210729104313-00048.warc.gz"} |
https://math.meta.stackexchange.com/questions/33586/accidentally-editing-without-knowing-a-question-was-closed-in-the-review-queue-m | # Accidentally editing without knowing a question was closed in the review queue made a question unable to be reopened. New feature to prevent this.
I have seen this large issue with this website which can endanger the new user:
It was accidentally done that one edited the question of another user whose question was already closed, but then had this edit approved. The first edit after a closed question is done goes to the reopen queue for confirmation. However, because this edit did not reopen the question, the asker cannot as easily reopen the question now based on what I was told. This is the link.
The concern here is that this closed question was already in the “new user question queue” which is unrelated to the reopen queue. This means that the editing user was unaware of its closing to then submit a thought “normal edit”, but not an edit to reopen the question. Now the question is in a sort of “soft lock” state in which the OP cannot open it again unless duplicating the question and the like.
Also, here is the conversation in case this user’s question gets deleted. The names have been whited out for privacy, even though anyone can click the link:
I would hate to see this happen to someone else. Please tell me why this happens. There should also be a new feature where this is disabled or there may be multiple edits for reopening a question.
Please give me feedback and correct me! I do not means to downplay this website, even though I have only been on this site for a month and a half now as of this post, but these would significantly improve any Stack Exchange or Overflow website. Please tell me if these can be fixed or explained.
By the way as @hardmath said, here it the timeline for this question as a sample of what happened.
• Why redact the names in the comments to you, when you publicly name me and Gerry in your responses?? – amWhy May 15 at 21:15
• I redacted the names in case anyone felt they did not want to be in the question itself. The continued editing is understood, but there could be an editing limit such as in the comments, and I will probably focus on the two first issues in this edited post, later, and another after this one after editing, simply deleting the other questions. – Tyma Gaidash May 15 at 21:41
• With regard to the first point, Tyma, I think I need to clarify the effect of editing. It is not the case that OP is unable to edit once a post goes to review; OP is still free to edit. What amWhy and I were saying was that users who come to the question via the review queue won't see these later edits. They will only see the question as it was after the edit that sent it to the review queue – unless thay take the time to go to the question directly, to see whether there have been any further edits. Which is something I think reviewers should do – they should always go to the updated version. – Gerry Myerson May 16 at 0:12
• By the way, I hope someone will correct what I've just posted, if I have misunderstood the workings of the review queue. – Gerry Myerson May 16 at 0:14
• The timeline for the post shows that the First Post review, which occurred before the Close vote and which resulted in Tyma's suggested edit (later approved by amWhy and one other), occurred before the Reopen review. So you couldn't have known it "was already closed," but you could see that the post was a PSQ (problem statement question) and that your edit did not help overcome that shortcoming. I'm going to vote to reopen this Meta Question as your edit has improved the focus here. – hardmath May 16 at 1:22
• @hardmath Even with the full meaning, what is a PSQ? Also, do you mean that this shows that I did not edit “purposefully” to improve the question to open it again, and not just to improve the format which is unrelated to the close edit? I also find it weird how I created this around 7 hours ago and this is still the first question on the questions tab. No one else asked anything else as of this time today... – Tyma Gaidash May 16 at 2:03
• It is shorthand for a Question presenting a problem without context, in this case an integration to perform with no explanation of what the user tried, what brought it to the user's attention, what makes it interesting, etc. I've advocated for very minimal context, but here there was nothing to meet even my standards. – hardmath May 16 at 2:08
• You are fairly new here, and though you've earned the right to review First Posts and Late Answers, the other review queues are not accessible yet (and you can't be expected to spot some interaction of First Posts with Reopen queue that might occur in the future). The rate of new posts on Meta is much slower than on the main site, of course, and which posts are at the top depends to some extent on post activity and user preferences. – hardmath May 16 at 2:14
• Somewhat related: Should I avoid minor edit of a question which was put on hold? – Martin Sleziak May 16 at 2:48
• "the OP cannot open it again unless duplicating the question and the like." This isn't quite true. OP has the option of posting to Meta to request reopening – there is a thread on Meta dedicated to precisely such requests. Of course, OP would have to make a case supporting reopening, and judging from what I have read here that would require OP first to make some significant improvement to the question. I don't think anything is stopping OP from editing the question. – Gerry Myerson May 16 at 6:34
• "I redacted the names in case anyone felt they did not want to be in the question itself." The point is that you were incomplete in doing that. Your replies contain the user names as was pointed out to you. It does not really help to remove the name of the authors of the comments when you address them in the reply by name. Also here, try to see the big picture, and do not focus only on technicalities: everybody reading the text on the screen-capture will still know who wrote the comments. – quid May 16 at 11:33
• Wow, this was actually reopened! Also, one told me in the comments as a suggestion to put this into the meta. – Tyma Gaidash May 16 at 12:01
• I think the point that Tyma is making here is valid: a question becomes less likely to be reopened due to the actions of a 3rd party, and that is unfair. Telling someone that they should be more careful only changes that one person's actions, and maybe a few more people's too, but just as people are willing to dump, and others to answer, Problem Statement Questions, we cannot simply assume people will obey the advice here. Nor can we assume people will have heard this advice! Improving the system seems to make the most sense. – user1729 May 16 at 13:32
• @user1729 yet if the 3rd party edit was somewhat good and it is not placed in the queue we could then lament about that and ask for it to be introduced. Somewhere one has to draw the line. – quid May 16 at 14:53
You are over-focusing on one aspect here that is not even the main problem.
The edit was a bit pointless at best and unhelpful at worst. This is independent of the mechanics of the queues.
The question is unclear and more broadly unsuitable for the site before and after your edit. Your edit does not really improve the question in that it does nothing to address the core problems.
The $$x$$ vs $$X$$ issue and the missing context. It is good to improve posts via adding MathJax but not prematurely. If the original poster is not comfortable with MathJax the addition might hinder them in their update.
Somewhat orthogonal to this you say:
Now the question is in a sort of “soft lock” state in which the OP cannot open it again unless duplicating the question and the like.
That is not at all true. The reopening itself is in no way impeded. What was used up is a one-time visibility booster, the automatic addition to the review queue on an edit. Ultimately it is not that big a deal.
The core issue is that one should not do minor edits, especially not suggested edits, that do not really address the core problems of the post. One reason for this is are the mechanics of the queues but that is not the only or even the main reason. | 2021-07-25 08:40:14 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 2, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3961239755153656, "perplexity": 851.1635570453241}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046151641.83/warc/CC-MAIN-20210725080735-20210725110735-00522.warc.gz"} |
https://solvedlib.com/n/find-the-unknown-sides-and-y-to-the-nearest-thousandth-drawn,6454389 | # Find the unknown sides and y to the nearest thousandth: drawn to scale:) (The triangle is not430The entrance to bealth
###### Question:
Find the unknown sides and y to the nearest thousandth: drawn to scale:) (The triangle is not 430 The entrance to bealth clinic is feet above strect level to the entrance of the strect level IEp iS installed fromn The health clinic which has An [WnP fcct long What is _? angle of inclination | 2023-03-27 23:39:58 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6073950529098511, "perplexity": 7103.909102622673}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296948708.2/warc/CC-MAIN-20230327220742-20230328010742-00310.warc.gz"} |
http://sfmlab.com/item/1554/ | Street Fighter - Karin
Description
"OHOHOHOHO" - Karin
Karin is now part of the SFM roster fully rigged with face flexes!
The model was ported over from Street Fighter V. The rig file is called "rig_ryu".
Place the files in the "sourcefilmmaker\game" folder.
Many thanks to the creator of this script http://steamcommunity.com/sharedfiles/filedetails/?id=444750868 and this beautiful man for the model and the textures http://sticklove.deviantart.com/art/Karin-568875709
Credits go to its creators, Capcom.
Nice, Karin has always been my fav, but way too much clothes on all these SF models...
evilpancake posted 2 years, 9 months ago
Thank you, appreciate the work you put into making this.
AjnaFX posted 2 years, 9 months ago
Finally!
ofpigsanddogs posted 2 years, 9 months ago
Hi great work here ;) Any chance you do cammy from SFV?
lapinedours posted 2 years, 9 months ago
Make nude
lololel posted 2 years, 8 months ago | 2019-06-19 20:45:40 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.867734432220459, "perplexity": 12701.343527958099}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627999041.59/warc/CC-MAIN-20190619204313-20190619230313-00296.warc.gz"} |
https://brilliant.org/problems/la-la-la/ | # La La la
Algebra Level 3
$\begin{cases} (x+y+z)(x+y)=30\\ (x+y+z)(y+z)=18\\ (x+y+z)(z+x)=2 \end{cases}$
Given that $x, y$ and $z$ satisfy the system of equations above, find the sum of all values of $z$.
× | 2019-10-18 15:01:16 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 4, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9036288261413574, "perplexity": 636.9944383068919}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986682998.59/warc/CC-MAIN-20191018131050-20191018154550-00305.warc.gz"} |
http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=sm&paperid=9130&option_lang=eng | RUS ENG JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB
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Mat. Sb.: Year: Volume: Issue: Page: Find
Mat. Sb., 2019, Volume 210, Number 9, Pages 89–106 (Mi msb9130)
Algebras of free holomorphic functions and localizations
K. A. Syrtseva
Faculty of Mathematics, National Research University Higher School of Economics, Moscow, Russia
Abstract: We consider the algebras of holomorphic functions on a free polydisc $\mathscr F^T(\mathbb D_R^n)$, $\mathscr F(\mathbb D_R^n)$ and the algebra of holomorphic functions on a free ball $\mathscr F(\mathbb B_r^n)$. We show that the algebra $\mathscr F(\mathbb D_R^n)$ is a localization of a free algebra and, moreover, is a free analytic algebra with $n$ generators (in the sense of J. Taylor), while the algebra $\mathscr F(\mathbb B_r^n)$ is not a localization of a free algebra. In addition we prove that the class of localizations of free algebras and the class of free analytic algebras are closed under the operation of the Arens-Michael free product.
Bibliography: 21 titles.
Keywords: localization, free analytic algebra, Arens-Michael free product, algebra of holomorphic functions on a free polydisc, algebra of holomorphic functions on a free ball.
Funding Agency Grant Number Ministry of Education and Science of the Russian Federation 5-100 This research was carried out within the HSE University Basic Research Program and funded (jointly) by the Russian Academic Excellence Project ‘5-100’.
DOI: https://doi.org/10.4213/sm9130
Full text: PDF file (666 kB)
First page: PDF file
References: PDF file HTML file
English version:
Sbornik: Mathematics, 2019, 210:9, 1288–1304
Bibliographic databases:
UDC: 517.986.2
MSC: Primary 46H05; Secondary 47A60, 46H25
Citation: K. A. Syrtseva, “Algebras of free holomorphic functions and localizations”, Mat. Sb., 210:9 (2019), 89–106; Sb. Math., 210:9 (2019), 1288–1304
Citation in format AMSBIB
\Bibitem{Syr19} \by K.~A.~Syrtseva \paper Algebras of free holomorphic functions and localizations \jour Mat. Sb. \yr 2019 \vol 210 \issue 9 \pages 89--106 \mathnet{http://mi.mathnet.ru/msb9130} \crossref{https://doi.org/10.4213/sm9130} \adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2019SbMat.210.1288S} \transl \jour Sb. Math. \yr 2019 \vol 210 \issue 9 \pages 1288--1304 \crossref{https://doi.org/10.1070/SM9130} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000510716000004} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85087460257} | 2020-10-26 02:18:59 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.24920521676540375, "perplexity": 5965.578753534521}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107890108.60/warc/CC-MAIN-20201026002022-20201026032022-00697.warc.gz"} |
https://intelligencemission.com/free-energy-generator-for-sale-free-energy-devices-that-work.html | We can make the following conclusions about when processes will have Free Power negative \Delta \text G_\text{system}ΔGsystem: \begin{aligned} \Delta \text G &= \Delta \text H – \text{T}\Delta \text S \ \ &= Free energy. 01 \dfrac{\text{kJ}}{\text{mol-rxn}}-(Free energy \, \cancel{\text K})(0. 022\, \dfrac{\text{kJ}}{\text{mol-rxn}\cdot \cancel{\text K})} \ \ &= Free energy. 01\, \dfrac{\text{kJ}}{\text{mol-rxn}}-Free energy. Free Power\, \dfrac{\text{kJ}}{\text{mol-rxn}}\ \ &= -0. Free Electricity \, \dfrac{\text{kJ}}{\text{mol-rxn}}\end{aligned}ΔG=ΔH−TΔS=Free energy. 01mol-rxnkJ−(293K)(0. 022mol-rxn⋅K)kJ=Free energy. 01mol-rxnkJ−Free energy. 45mol-rxnkJ=−0. 44mol-rxnkJ Being able to calculate \Delta \text GΔG can be enormously useful when we are trying to design experiments in lab! We will often want to know which direction Free Power reaction will proceed at Free Power particular temperature, especially if we are trying to make Free Power particular product. Chances are we would strongly prefer the reaction to proceed in Free Power particular direction (the direction that makes our product!), but it’s hard to argue with Free Power positive \Delta \text GΔG! Our bodies are constantly active. Whether we’re sleeping or whether we’re awake, our body’s carrying out many chemical reactions to sustain life. Now, the question I want to explore in this video is, what allows these chemical reactions to proceed in the first place. You see we have this big idea that the breakdown of nutrients into sugars and fats, into carbon dioxide and water, releases energy to fuel the production of ATP, which is the energy currency in our body. Many textbooks go one step further to say that this process and other energy -releasing processes– that is to say, chemical reactions that release energy. Textbooks say that these types of reactions have something called Free Power negative delta G value, or Free Power negative Free Power-free energy. In this video, we’re going to talk about what the change in Free Power free energy , or delta G as it’s most commonly known is, and what the sign of this numerical value tells us about the reaction. Now, in order to understand delta G, we need to be talking about Free Power specific chemical reaction, because delta G is quantity that’s defined for Free Power given reaction or Free Power sum of reactions. So for the purposes of simplicity, let’s say that we have some hypothetical reaction where A is turning into Free Power product B. Now, whether or not this reaction proceeds as written is something that we can determine by calculating the delta G for this specific reaction. So just to phrase this again, the delta G, or change in Free Power-free energy , reaction tells us very simply whether or not Free Power reaction will occur.
Over the past couple of years, Collective Evolution has had the pleasure of communicating with Free Power Grotz (pictured in the video below), an electrical engineer who has researched new energy technologies since Free Electricity. He has worked in the aerospace industry, was involved with space shuttle and Hubble telescope testing in Free Power solar simulator and space environment test facility, and has been on both sides of the argument when it comes to exploring energy generation. He has been involved in exploring oil and gas and geothermal resources, as well as coal, natural gas, and nuclear power-plants. He is very passionate about new energy generation, and recognizes that the time to make the transition is now.
Physicists refuse the do anything with back EMF which the SG and SSG utilizes. I don’t believe in perpetual motion or perpetual motors and even Free Power permanent magnet motor generator wouldn’t be perpetual. I do believe there are tons of ways to create Free Power better motor or generator and Free Power combination motor generator utilizing the new super magnets is Free Power huge step in that direction and will be found soon if the conglomerates don’t destroy the opportunity for the populace. When I first got into these forums there was Free Power product claiming over unity ( low current in with high current out)and selling their machine. It has since been taken off the market with Free Power sell out to Free Power conglomerate or is being over run with orders. I don’t know! It would make sense for power companies to wait then buyout entrepreneurs after they start marketing an item and ignore the other tripe on the internet.. Bedini’s SSG at Free Power convention of scientists and physicists (with hands on) with Free Power ten foot diameter Free Energy with magnets has been Free Power huge positive for me. Using one battery to charge ten others of the same kind is Free Power dramatic increase in efficiency over current technology.
I am doing more research for increasing power output so that it can be used in future in cars. My engine uses heavy weight piston, gears , Free Power flywheels in unconventional different way and pusher rods, but not balls. It was necessary for me to take example of ball to explain my basic idea I used in my concept. (the ball system is very much analogous to the piston-gear system I am using in my engine). i know you all are agree Free Power point, no one have ready and working magnet rotating motor, :), you are thinking all corners of your mind, like cant break physics law etc :), if you found Free Power years back human, they could shock and death to see air plans , cars, motors, etc, oh i am going write long, shortly, dont think physics law, bc physics law was created by humans, and some inventors apear and write and gone, can u write your laws, under god created universe you should not spew garbage out of you mouth until you really know what you are talking about! Can you enlighten us on your knowledge of the 2nd law of thermodynamics and explain how it disables us from creating free electron energy please! if you cant then you have no right to say that it cant work! people like you have kept the world form advancements. No “free energy magnetic motor” has ever worked. Never. Not Once. Not Ever. Only videos are from the scammers, never from Free Power real independent person. That’s why only the plans are available. When it won’t work, they blame it on you, and keep your money.
Building these things is easy when you find the parts to work with. That’s the hard part! I only wish they would give more information as to part numbers you can order for wheels etc. instead of scrounging around on the internet. Wire is no issue because you can find it all over the internet. I really have no idea if the “magic motor” as you call it is possible or not. Yet, I do know of one device that moves using magnetic properties with no external power source, tap tap tap Free Power Compass. Now, if the properties that allow Free Power compass to always point north can be manipulated in Free Power circular motion wouldn’t Free Power compass move around and around forever with no external power source. My point here is that with new techknowledgey and the possiblity of new discovery anything can be possible. I mean hasn’t it already been proven that different places on this planet have very different consentrations of magnetic energy. Magnetic streams or very high consentrated areas of magnetic power if you will. Where is there external power source? Tap Tap Tap Mie2centsHarvey1Thanks for caring enough to respond! Let me address each of your points: Free Power. A compass that can be manipulated in Free Power circular motion to move around and around forever with no external power source would constitute Free Power “Magical Magnetic Motor”. Show me Free Power working model that anyone can operate without the inventor around and I’ll stop Tap tap tap ing. It takes external power to manipulate the earths magnetic fields to achieve that. Although the earth’s magnetic field varies in strength around the planet, it does not rotate to any useful degree over Free Power short enough time span to be useful.
I do not fear any conspiracy from any nook & corner. I am simply taking my time and my space to stage the inevitable confrontation in the frozen face of the industry and geopolitics tycoons. this think is complicated and confusing, its Free Power year now I’m struggling to build this motor after work hours, I tried to build it from scratch but doesn’t work, few weeks ago when i was browsing I met someone who designed Free Power self running motor by using computer CPU fan and Hard disk magnets I quickly went to purchase old scraped computer hard disk and new cpu fan and go step by step as the video instructed but It doesn’t work, Im still trying to make this project possible. Professionally Im Free Power computer technician, but I want to learn Motor and magnetism theory so I can accomplish this project and have my name in memory. I anyone can make this project please contact me through facebook so I can invite him/her to my country and make money as you know third word countries has power disaster. My facebook Id is Elly Maduhu Nkonya, or use my E-mail. [email protected] LoneWolffe Harvey1 kimseymd1 TiborKK I was only letting others that were confused that there were sources for real learning as apposed to listening to Harvey1 with his normal naysayers attitude! There is tons of information on schoolgirl, schoolboy and Bedini window motors that actually work to charge batteries and eventually will generate house currents. It just has to be looked at to get any useful information from it without listening to people like Harvey1 whining about learning. Harvey1 kimseymd1 You obviously play too much video games with trolls etc. in them. Why the editors of this forum allow you to keep calling people names instead of following the subject is beyond me. This must be the last site to allow you on it. I spammed the books because I thought those people were good for learning these engines which are super and there are tons of information out there for anyone to find. You seem to only want to learn to be rude instead of electronics.
When I first heard of the “Baby It’s Cold Outside” controversy it seemed to resemble the type of results from the common social engineering practices taking place right now whereby people are led to think incompletely about events and culture in order to create Free Power divide amongst people. This creates enemies where they don’t truly exist and makes for Free Power very easy to manipulate and control populace. Ultimately, this leads for people to call for greater governance.
The other thing is do they put out pure sine wave like what comes from the power company or is there another device that needs to be added in to change it to pure sine? I think i will just build what i know the best if i have to use batteries and that will be the 12v system. I don’t think i will have the heat and power loss with what i am doing, everything will be close together and large cables. Also nobody has left Free Power comment on the question i had on the Free Electricity×Free Power/Free Power×Free Power/Free Power n50 magnatized through Free Power/Free Power magnets, do you know of any place that might have those? Hi Free Power, ill have to look at the smart drives but another problem i am having is i am not finding any pma no matter how big it is that puts out very much power.
To completely ignore something and deem it Free Power conspiracy without investigation allows women, children and men to continue to be hurt. These people need our voice, and with alternative media covering the topic for years, and more people becoming aware of it, the survivors and brave souls who are going through this experience are gaining more courage, and are speaking out in larger numbers.
Thanks, Free Power. One more comment. I doubt putting up Free Power video of the working unit would do any good. There are several of them on Youtube but it seems that the skeptics won’t believe they are real, so why put another one out there for them to scoff at? Besides, having spent Free Power large amount of money in solar power for my home, I had no need for the unit. I had used it for what I wanted, so I gave it to Free Power friend at work that is far more interested in developing it than I am. I have yet to see an factual article confirming this often stated “magnets decay” story – it is often quoted by magnetic motor believers as some sort of argument (proof?) that the motors get their energy from the magnets. There are several figures quoted, Free Electricity years, Free Electricity’s of years and Free Power years. All made up of course. Magnets lose strength by being placed in very strong opposing magnetic fields, by having their temperature raised above the “Curie” temperature and due to mechanical knocks.
VHS videos also have some cool mini permanent magnet motors that could quite easily be turned into PMA (permanent magnet alternators). I pulled one apart about Free Power month ago. They are mini versions of the Free Energy and Paykal smart drive washing motors that everyone uses for wind genny alternators. I have used the smart drive motors on hydro electric set ups but not wind. You can wire them to produce AC or DC. Really handy conversion. You can acess the info on how to do it on “the back shed” (google it). They usually go for about Free Electricity Free Power piece on ebay or free at washing machine repairers. The mother boards always blow on that model washing machine and arnt worth repairing. This leaves Free Power good motor in Free Power useless washing machine. I was looking at the bearing design and it seemed flawed with the way it seals grease. Ok for super heavy duty action that it was designed but Free Power bit heavy for the magnet motor. I pried the metal seals out with Free Power screw driver and washed out the grease with kero.
Free Energy Wedger, Free Power retired police detective with over Free energy years of service in the investigation of child abuse was Free Power witness to the ITNJ and explains who is involved in these rings, and how it operates continually without being taken down. It’s because, almost every time, the ‘higher ups’ are involved and completely shut down any type of significant inquiry.
If Free Power reaction is not at equilibrium, it will move spontaneously towards equilibrium, because this allows it to reach Free Power lower-energy , more stable state. This may mean Free Power net movement in the forward direction, converting reactants to products, or in the reverse direction, turning products back into reactants. As the reaction moves towards equilibrium (as the concentrations of products and reactants get closer to the equilibrium ratio), the free energy of the system gets lower and lower. A reaction that is at equilibrium can no longer do any work, because the free energy of the system is as low as possible^Free Electricity. Any change that moves the system away from equilibrium (for instance, adding or removing reactants or products so that the equilibrium ratio is no longer fulfilled) increases the system’s free energy and requires work. Example of how Free Power cell can keep reactions out of equilibrium. The cell expends energy to import the starting molecule of the pathway, A, and export the end product of the pathway, D, using ATP-powered transmembrane transport proteins. | 2019-02-16 04:30:01 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4692247211933136, "perplexity": 1492.9330202386477}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247479838.37/warc/CC-MAIN-20190216024809-20190216050809-00347.warc.gz"} |
http://mathoverflow.net/questions/51798/generalizing-eichler-shimura-to-higher-dimension-again?sort=oldest | # Generalizing Eichler-Shimura to higher dimension, again
This question is related to
Intuition behind the Eichler-Shimura relation?
and
L-functions and higher-dimensional Eichler-Shimura relation
Answering the first question above, Matt Emerton gives a sketch of a proof of the Eichler-Shimura congruence relation which tells that the Hecke correspondence mod p is a sum of the graph of the Frobeniusm and it's transpose.
I am wondering how the statement and the proof can be generalized to moduli of higher dimensional abelian varieties with level structure (and maybe some more structure, like PEL).
It seems like the reason for having only two isogenies $E \to E'$ in Matt's answer is that p-isogenies correspond to subgroups of order p in E[p] as a scheme, and E[p] (if we assume E to be ordinary) in char p is a product of $Z/p$ and the dual group, $\mu_p$, and apparently these two groups: $Z/p$ and $\mu_p$ are the only nontrivial subgroups in E[p], so taking quotients we come up with the Frobenius and Verschiebung (dual isogeny).
Now let's say A is an abelian variety of dimension g in char p, which has maximal p-rank, i.e. $A[p] = Z/p^g \times \mu_{p^g}$. What are the subgroups of order $p^g$ of such a group? I am not familiar with how local groups behave, but I can assume there will be g+1 isogenies $A \to A'$, each one having the Kernel of the kind $H_1 \times H_2$, where $H_1$ and $H_2$ are subgroups in $Z/p^g$ and in $\mu_{p^g}$ respectively.
Also one probably needs a statement that abelian varieties with maximal p-rank are Zarisky open and dense in the moduli space, which is true in dimension 1.
Then the reduction mod p of the Hecke correspondence $T_p$, appropriately defined will be a sum of these g+1 cycles? Is that making any sense?
Thanks.
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https://asmedigitalcollection.asme.org/fluidsengineering/article-abstract/135/11/111201/374417/Effect-of-Axis-Ratio-on-Fluid-Flow-Around-an?redirectedFrom=fulltext | The bluff body simulations over canonical forms like circular and square cylinders are very well studied and the correlations for bulk parameters like mean drag coefficient and Strouhal numbers for the same are reported widely. In the case of elliptic cylinder, the literature is very sparse, especially for moderate Reynolds number (Re). Hence, in this work, a detailed study about fluid flow characteristics over an elliptic cylinder placed in a free stream is performed. Simulations are carried out for different Re ranging from 50 to 500 with axis ratio (AR) varied between 0.1 to 1.0 in steps of 0.1. Immersed boundary method is used for the solid boundary condition implementation which avoids the grid generation for each AR and a single Cartesian grid is used for all the simulations. The effect of AR for various Reynolds numbers is also focused on using the in-house code. The influence of AR is phenomenal for all the Re and the values of wake length, drag coefficient, and Strouhal number decrease with decreasing AR for a particular Re. The critical ARs, for vortex shedding and wake formation, are identified for various Re. Detailed correlations for wake length, critical ARs for vortex shedding and wake formation, mean drag coefficient and Strouhal number, in terms of AR, are reported in this work.
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.10.1007/BF02916136 | 2019-10-14 18:44:14 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 1, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5478829145431519, "perplexity": 12451.330225669735}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986654086.1/warc/CC-MAIN-20191014173924-20191014201424-00359.warc.gz"} |
http://quant.stackexchange.com/tags/interest-rates/new | # Tag Info
0
They are correlated because they share a common factor, namely expectations of future economic growth. Using the framework of a discounted cash flow valuation approach; the higher cash flows resulting from higher expected growth, more than compensates for the increase in the discount rate, hence a positive correlation. Periods of high inflation or ...
0
This is a good question. There are various views to this. I will share some thoughts: Higher interest rates mean lower bond prices for bonds already emmitted. Investors switchting between bonds and stocks could sell bonds and buy stocks in times of rising yields (fearing that his developement will last) which increases demand for stocks Why do interest ...
1
I believe that your problem can be formulated as: Find PD matrix that is as close as possible to a given PD matrix (result of some previous calibration, or the matrix computed using average hazard rate, or any other "target", or the penalty on non-smoothness) subject to the following constraints: The values that are given must be matched exactly ...
1
The typical approach is to try to fit a ratings migration matrix to available rating transition data. If default rates are all you have then that's going to be difficult. Instead, I might try to fit a separate reduced form credit model on survival probability $P_\ell$ for each rating $\ell$ by fitting the function P_\ell(T) = \exp\left( -\int_0^T h(t) ...
0
I worked for a company where we had a similar problem with a volatility surface. I tried applying LOESS to it, but it didn't work. The final result has to conform to some obvious monotonicity restrictions and if that is not built into the smoothing method there will always be some odd points in the end. Another problem is that smoothing typically allows the ...
0
There are quite a few reasons: Fed funds futures rate and Eurodollar futures rate do not reflect market expectations alone. Technically speaking, a risk-free interest rate is the sum of 1) rate expectations, 2) term premium, and 3) convexity bias. Term premium is typically positive, since investors demand a higher yield for taking on more duration risk ...
Top 50 recent answers are included | 2014-10-21 17:00:41 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5496881604194641, "perplexity": 1298.7841617154825}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-42/segments/1413507444582.16/warc/CC-MAIN-20141017005724-00283-ip-10-16-133-185.ec2.internal.warc.gz"} |
https://datascience.stackexchange.com/questions/14349/difference-of-activation-functions-in-neural-networks-in-general | # Difference of Activation Functions in Neural Networks in general
I have studied the activation function types for neural networks. The functions themselves are quite straightforward, but the application difference is not entirely clear.
It's reasonable that one differentiates between logical and linear type functions, depending on the desired binary/continuous output but what is the advantage of sigmoid function over the simple linear one?
ReLU is especially difficult to understand for me, for instance: what is the point to use a function that behaves like linear in case of positive inputs but is "flat" in case of negatives? What is the intuition behind this? Or is it just a simple trial-error thing, nothing more?
A similar question was asked on CV: Comprehensive list of activation functions in neural networks with pros/cons.
I copy below one of the answers:
One such a list, though not much exhaustive: http://cs231n.github.io/neural-networks-1/
### Commonly used activation functions
Every activation function (or non-linearity) takes a single number and performs a certain fixed mathematical operation on it. There are several activation functions you may encounter in practice:
Left: Sigmoid non-linearity squashes real numbers to range between [0,1] Right: The tanh non-linearity squashes real numbers to range between [-1,1].
Sigmoid. The sigmoid non-linearity has the mathematical form $\sigma(x) = 1 / (1 + e^{-x})$ and is shown in the image above on the left. As alluded to in the previous section, it takes a real-valued number and "squashes" it into range between 0 and 1. In particular, large negative numbers become 0 and large positive numbers become 1. The sigmoid function has seen frequent use historically since it has a nice interpretation as the firing rate of a neuron: from not firing at all (0) to fully-saturated firing at an assumed maximum frequency (1). In practice, the sigmoid non-linearity has recently fallen out of favor and it is rarely ever used. It has two major drawbacks:
• Sigmoids saturate and kill gradients. A very undesirable property of the sigmoid neuron is that when the neuron's activation saturates at either tail of 0 or 1, the gradient at these regions is almost zero. Recall that during backpropagation, this (local) gradient will be multiplied to the gradient of this gate's output for the whole objective. Therefore, if the local gradient is very small, it will effectively "kill" the gradient and almost no signal will flow through the neuron to its weights and recursively to its data. Additionally, one must pay extra caution when initializing the weights of sigmoid neurons to prevent saturation. For example, if the initial weights are too large then most neurons would become saturated and the network will barely learn.
• Sigmoid outputs are not zero-centered. This is undesirable since neurons in later layers of processing in a Neural Network (more on this soon) would be receiving data that is not zero-centered. This has implications on the dynamics during gradient descent, because if the data coming into a neuron is always positive (e.g. $x > 0$ elementwise in $f = w^Tx + b$)), then the gradient on the weights $w$ will during backpropagation become either all be positive, or all negative (depending on the gradient of the whole expression $f$). This could introduce undesirable zig-zagging dynamics in the gradient updates for the weights. However, notice that once these gradients are added up across a batch of data the final update for the weights can have variable signs, somewhat mitigating this issue. Therefore, this is an inconvenience but it has less severe consequences compared to the saturated activation problem above.
Tanh. The tanh non-linearity is shown on the image above on the right. It squashes a real-valued number to the range [-1, 1]. Like the sigmoid neuron, its activations saturate, but unlike the sigmoid neuron its output is zero-centered. Therefore, in practice the tanh non-linearity is always preferred to the sigmoid nonlinearity. Also note that the tanh neuron is simply a scaled sigmoid neuron, in particular the following holds: $\tanh(x) = 2 \sigma(2x) -1$.
Left: Rectified Linear Unit (ReLU) activation function, which is zero when x < 0 and then linear with slope 1 when x > 0. Right: A plot from Krizhevsky et al. (pdf) paper indicating the 6x improvement in convergence with the ReLU unit compared to the tanh unit.
ReLU. The Rectified Linear Unit has become very popular in the last few years. It computes the function $f(x) = \max(0, x)$. In other words, the activation is simply thresholded at zero (see image above on the left). There are several pros and cons to using the ReLUs:
• (+) It was found to greatly accelerate (e.g. a factor of 6 in Krizhevsky et al.) the convergence of stochastic gradient descent compared to the sigmoid/tanh functions. It is argued that this is due to its linear, non-saturating form.
• (+) Compared to tanh/sigmoid neurons that involve expensive operations (exponentials, etc.), the ReLU can be implemented by simply thresholding a matrix of activations at zero.
• (-) Unfortunately, ReLU units can be fragile during training and can "die". For example, a large gradient flowing through a ReLU neuron could cause the weights to update in such a way that the neuron will never activate on any datapoint again. If this happens, then the gradient flowing through the unit will forever be zero from that point on. That is, the ReLU units can irreversibly die during training since they can get knocked off the data manifold. For example, you may find that as much as 40% of your network can be "dead" (i.e. neurons that never activate across the entire training dataset) if the learning rate is set too high. With a proper setting of the learning rate this is less frequently an issue.
Leaky ReLU. Leaky ReLUs are one attempt to fix the "dying ReLU" problem. Instead of the function being zero when x < 0, a leaky ReLU will instead have a small negative slope (of 0.01, or so). That is, the function computes $f(x) = \mathbb{1}(x < 0) (\alpha x) + \mathbb{1}(x>=0) (x)$ where $\alpha$ is a small constant. Some people report success with this form of activation function, but the results are not always consistent. The slope in the negative region can also be made into a parameter of each neuron, as seen in PReLU neurons, introduced in Delving Deep into Rectifiers, by Kaiming He et al., 2015. However, the consistency of the benefit across tasks is presently unclear.
Maxout. Other types of units have been proposed that do not have the functional form $f(w^Tx + b)$ where a non-linearity is applied on the dot product between the weights and the data. One relatively popular choice is the Maxout neuron (introduced recently by Goodfellow et al.) that generalizes the ReLU and its leaky version. The Maxout neuron computes the function $\max(w_1^Tx+b_1, w_2^Tx + b_2)$. Notice that both ReLU and Leaky ReLU are a special case of this form (for example, for ReLU we have $w_1, b_1 = 0$). The Maxout neuron therefore enjoys all the benefits of a ReLU unit (linear regime of operation, no saturation) and does not have its drawbacks (dying ReLU). However, unlike the ReLU neurons it doubles the number of parameters for every single neuron, leading to a high total number of parameters.
This concludes our discussion of the most common types of neurons and their activation functions. As a last comment, it is very rare to mix and match different types of neurons in the same network, even though there is no fundamental problem with doing so.
TLDR: "What neuron type should I use?" Use the ReLU non-linearity, be careful with your learning rates and possibly monitor the fraction of "dead" units in a network. If this concerns you, give Leaky ReLU or Maxout a try. Never use sigmoid. Try tanh, but expect it to work worse than ReLU/Maxout. | 2021-03-05 20:20:30 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8093128204345703, "perplexity": 731.2257927069173}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178373241.51/warc/CC-MAIN-20210305183324-20210305213324-00560.warc.gz"} |
https://brilliant.org/problems/clever-4-term-sequences/ | # Clever 4-term Sequences
How many 4-term geometric sequences have all four terms positive integers less than or equal to 100?
Details and assumptions
Clarification: The sequence $$1, 2, 4, 8$$ is different from the sequence $$8, 4, 2, 1$$. The sequence $$1, 1, 1, 1$$ is the same as the 'flipped sequence' $$1, 1, 1, 1$$.
× | 2018-01-18 06:05:12 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7706748843193054, "perplexity": 792.67120665661}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084887067.27/warc/CC-MAIN-20180118051833-20180118071833-00712.warc.gz"} |
https://math.stackexchange.com/questions/746064/algebraic-and-geometric-multiplicity | # Algebraic and Geometric Multiplicity
I am having a hard time understand these two concepts
Algebraic multiplicity and Geometric multiplicity of a matrix regarding its eigenvalues
for example
if I have the matrix:
| 5 0 0 |
| 1 5 0 |
| 0 1 5 |
The eigenvalues are 5,5,5, so what does this mean about its multiplicity?
Is geometric multiplicity the number of similar eigenvalue? In this case, 3
and algebraic multiplicity the number of unique eigenvalue? In this case, 1
thanks
## 2 Answers
The geometric multiplicity of an eigenvalue is defined to be the number of linearly independent eigenvectors associated with that eigenvalue.
The algebraic multiplicity of an eigenvalue is defined as the eigenvalue's multiplicity as a root of the characteristic polynomial.
• what do you mean by " as a root of the characteristic equation" ? If the characteristic equation has n roots, does it mean it has algebraic multiplicity of n?
– JLL
Apr 9, 2014 at 1:51
• the characteristic equation is det(A-$\lambda$I)=0. And yes if it has n roots then it has algebraic multiplicity of n. Apr 9, 2014 at 1:54
• For example, consider the characteristic equation $\lambda^2-4\lambda+4$. Then it does have two roots, but note that it has only have 1 distinct root: $\lambda = 2$. Hence, $\lambda$ would have algebraic multiplicity of 2. Apr 9, 2014 at 1:55
You have the types of multiplicity reversed. Geometric multiplicity here basically means how many different eigenvectors can you create given these eigenvalues. the eigenvalues are the same, therefore the number of distinct eigenvectors is the same. You have geometric multiplicity of 1. Algebraic multiplicity is how many solutions does the solving for eignenvalues give you. It doesn't matter if the solutions are the same. So you have algebraic multiplicity of 3. | 2022-05-19 09:48:56 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8622793555259705, "perplexity": 262.35061687199305}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662526009.35/warc/CC-MAIN-20220519074217-20220519104217-00637.warc.gz"} |
https://www.zbmath.org/?q=an%3A1073.06006 | # zbMATH — the first resource for mathematics
Non-distributive cancellative residuated lattices. (English) Zbl 1073.06006
Martínez, Jorge (ed.), Ordered algebraic structures. Proceedings of the conference on lattice-ordered groups and $$f$$-rings held at the University of Florida, Gainesville, FL, USA, February 28–March 3, 2001. Dordrecht: Kluwer Academic Publishers (ISBN 1-4020-0752-3). Developments in Mathematics 7, 205-212 (2002).
Summary: Cancellative residuated lattices are a natural generalization of lattice-ordered groups ($$\ell$$-groups). In studying this variety, several questions have occurred about residuated lattice orders on free monoids and commutative free monoids. One of these questions is whether every residuated lattice order on a (commutative) free monoid is distributive, a fact known about $$\ell$$-groups. We construct two examples that show that this is not necessarily the case.
For the entire collection see [Zbl 1068.06001].
##### MSC:
06F05 Ordered semigroups and monoids
##### Keywords:
residuated lattice orders; free monoids | 2021-05-07 19:08:04 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4042780101299286, "perplexity": 2548.745118333356}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988802.93/warc/CC-MAIN-20210507181103-20210507211103-00474.warc.gz"} |
https://kobra.bibliothek.uni-kassel.de/handle/urn:nbn:de:hebis:34-2008052621729 | KOBRA
KOBRA
Please use this identifier to cite or link to this item: http://nbn-resolving.de/urn:nbn:de:hebis:34-2008052621729
Title: The Parity of the Number of Irreducible Factors for Some Pentanomials Authors: Koepf, WolframKim, Ryul ???metadata.dc.subject.ddc???: 510 - Mathematik (Mathematics) Issue Date: 2008 Series/Report no.: Mathematische Schriften Kassel08, 05 Abstract: It is well known that Stickelberger-Swan theorem is very important for determining reducibility of polynomials over a binary field. Using this theorem it was determined the parity of the number of irreducible factors for some kinds of polynomials over a binary field, for instance, trinomials, tetranomials, self-reciprocal polynomials and so on. We discuss this problem for type II pentanomials namely x^m +x^{n+2} +x^{n+1} +x^n +1 \in\ IF_2 [x]. Such pentanomials can be used for efficient implementing multiplication in finite fields of characteristic two. Based on the computation of discriminant of these pentanomials with integer coefficients, it will be characterized the parity of the number of irreducible factors over IF_2 and be established the necessary conditions for the existence of this kind of irreducible pentanomials. URI: urn:nbn:de:hebis:34-2008052621729 Appears in Collections: Mathematische Schriften Kassel
Files in This Item:
File Description SizeFormat | 2017-07-21 06:35:22 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8514418601989746, "perplexity": 2132.0351647428906}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-30/segments/1500549423723.8/warc/CC-MAIN-20170721062230-20170721082230-00510.warc.gz"} |
https://protonstalk.com/units-and-measurement/screw-gauge/ | # Screw Gauge
A screw gauge is a tool used to measure very thin objects like sheets of metal or wires. It provides greater precision than Vernier’s Callipers. Sometimes it is also called a micrometre screw gauge.
Index
## Screw Gauge Diagram
In the above diagram, we have the description of a Screw Gauge and its parts. Below we discuss the parts of this tool.
## Parts of the Tool
The parts of this measuring tool are as follows:
• The U-shaped frame: the object to be measured is placed here, between S1 and S2
• S1 (Screw). It is movable. It is adjusted by rotation of the thimble, till the object to be measured is firmly held between S1 and S2.
• S2 (Stud or Anvil). It is immovable. It and the screw hold the object in place.
• Hollow Cylindrical Tube: The Pitch Scale is engraved on this.
• Pitch Scale (Also called Main Scale): It is parallel to the main axis of the instrument.
• Head Scale (Also called Circular Scale): It is located on the circular part, in front of the milled head.
• Ratchet: It ensures that pressure is uniform between measuring surfaces. It is a safety device.
## Screw Gauge Formula
The formula is given as follows:
$$\text{Total Length} = [(\text{Pitch Scale Reading}) + (\text{Circular Scale Reading}) \times (\text{Least Count})] mm$$
Each of the terms are described below:
• Pitch Scale Reading (PSR): It is the reading on the pitch scale when the object is firmly held between stud and screw.
• Circular Scale Reading (CSR): It is the reading on the circular scale which is in-line with the pitch scale.
• Least Count (LC): It is given by-
• $$\text{Least Count of Screw Gauge} = \frac{(\text{Pitch of Screw Gauge})}{(\text{Number of Divisions on Circular Scale})}$$
• $$\text{Pitch of Screw Gauge} = \frac{(\text{Distance Travelled by Screw})}{(\text{Number of rotations})}$$
## How to use Screw Gauge?
We can use this tool as follows:
1. The object to be measured is place between S1 and S2
2. Zero error, if any, is recorded.
3. The milled head is rotated to ensure that the screw rotates forward and the object is held firmly.
4. We wait for the ratchet for to click thrice.
5. The PSR and CSR are noted.
6. The screw gauge formula is applied, and adjusted for zero error if needed.
## Applications
This tool can be used to measure very thin objects like a wire or a thin sheet of metal. The least count is in the range of micrometre (10-6 m), so the instrument is also called a micrometer screw guage.
## FAQs
What is screw gauge?
It is an instrument used to measure very thin objects. It uses the principle of screw to work.
What is pitch of screw gauge?
Pitch is the distance moved by the spindle per unit revolution. It is measured on the pitch scale, and is given by the formula:
$$\text{Pitch} = \frac{\text{Distance travelled by screw/Spindle}}{\text{No. of rotations}}$$
What is screw gauge formula?
Formula of this tool is:
$$\text{Total length} = \text{(Pitch Scale Reading)} + \text{(Circular Scale Reading)} \times \text{(Least Count)}$$
The answer is usually in millimetres.
How to use Screw Gauge?
We can use this tool as follows:
1. The object to be measured is place between S1 and S2
2. Zero error, if any, is recorded.
3. The milled head is rotated to ensure that the screw rotates forward and the object is held firmly.
4. We wait for the ratchet for to click thrice.
5. The PSR and CSR are noted.
6. The screw gauge formula is applied, and adjusted for zero error if needed.
Scroll to Top | 2023-02-06 22:36:04 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.34347254037857056, "perplexity": 2347.6404016066936}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500365.52/warc/CC-MAIN-20230206212647-20230207002647-00393.warc.gz"} |
https://electronics.stackexchange.com/tags/cpu/hot | # Tag Info
Accepted
### Why not make one big CPU core?
The problem lies with the assumption that CPU manufacturers can just add more transistors to make a single CPU core more powerful without consequence. To make a CPU do more, you have to plan what ...
• 56.5k
Accepted
### What limits CPU speed?
Practically, what limits CPU speed is both the heat generated and the gate delays, but usually, the heat becomes a far greater issue before the latter kicks in. Recent processors are manufactured ...
• 1,862
Accepted
### Why is RAM not put on the CPU chip?
Intel's Haswell (or at least those products that incorporate the Iris Pro 5200 GPU) and IBM's POWER7 and POWER8 all include embedded DRAM, "eDRAM". One important issue that has led eDRAM not to be ...
• 1,614
Accepted
### Why don't we make CPUs with 1000s of layers to make use of space in the third dimension?
The two killer reasons are yield, and heat. Yield. Every time you do a process step, you get less than 100% perfection. Let's say you get 99% perfection per step. In a process with 20 steps, you would ...
• 140k
Accepted
### Why do CPUs need so much current?
CPUs are not 'simple' by any stretch of the imagination. Because they have a few billion transistors, each one of which will have some small leakage at idle and has to charge and discharge gate and ...
• 39.6k
Accepted
### Why is there no nand instruction in modern CPUs?
http://www.ibm.com/support/knowledgecenter/ssw_aix_61/com.ibm.aix.alangref/idalangref_nand_nd_instrs.htm : POWER has NAND. But generally modern CPUs are built to match automated code generation by ...
• 44.9k
### How can an FPGA outperform a CPU?
CPU's are sequential processing devices. They break an algorithm up into a sequence of operations and execute them one at a time. FPGA's are (or, can be configured as) parallel processing devices. ...
• 4,906
Accepted
### How can a CPU deliver more than one instruction per cycle?
First, as Keelan's comment and Turbo J's answer point out, the measurement was 113,093 Dhrystone MIPS not native MIPS. The Ivy Bridge microarchitecture of the i7 3630QM can only commit 4 fused µops ...
• 1,637
Accepted
### Is transistor the only electronic component on a CPU?
The logical blocks and memories can be made out of only transistors. The important question is: are all of the circuits on CPUs logical blocks and memories, or is there anything else? The answer ...
• 5,836
Accepted
### When Intel / AMD choose their Nanometer Processes, why were the specific numbers, 5, 7, 10, 14, 22, 32, 45, etc chosen?
There are a number of different reasons for this. The numbers aren't chosen Modern CPU manufacturing processes, at least for top-of-the line mainstream CPUs such as Intel Xeon and Core, AMD Epyc and ...
### Why do CPU's typically connect to only one bus?
The approach which you show is quite an old topology for motherboards - it predates PCIe which really puts it back somewhere in the '00s. The reason is primarily due to difficulties of integration. ...
• 56.5k
Accepted
### Why don't we see faster 7400 series chips?
As technology size decreases, wire resistance/capacitance cannot scale proportionally to the propagation delay of the now faster/smaller transistors. Because of that, the delay becomes largely wire ...
• 4,225
Accepted
### What is the lowest level of CPU programming above transistors?
In my CS program, my professor has claimed that NAND gates are the most basic gate to engineer, and so every other gate and higher-level circuits found in CPUs are made from NAND gates “Yeah? Well, ...
• 40.2k
### What limits CPU speed?
The heat issue is well covered by fuzzyhair. To summarize the transmission delays, consider this: The time needed for an electrical signal to cross the motherboard is now more than one clock cycle of ...
• 2,073
### Why not make one big CPU core?
In addition to the other answers, there is another element: chip yields. A modern processor has several billion transistors in them, each and every one of those transistors have to work perfectly in ...
• 1,424
### Why does Intel's Haswell chip allow floating point multiplication to be twice as fast as addition?
This possibly answers the title of the question, if not the body: Floating point addition requires aligning the two mantissa's before adding them (depending on the difference between the two ...
• 4,451
### For mainstream computing what are the practical advantages of 64-bit register size CPUs given the needs of today and the near future?
With 48bits you can address 256TiB of RAM, plenty of space to be useful Its not about address space (*). In fact most 64-bit desktop processors have a 48-bit address bus. There is little point ...
• 56.5k
### How can an FPGA outperform a CPU?
Markt has this mostly right, but I'm going to throw in my 2 cents here: Imagine that I told you that I wanted to write a program which reversed the order of bits inside of a 32-bit integer. ...
• 3,239
Accepted
### How can cache be that fast?
This CPU has... 2 cores A 32-KB instruction and 32-KB data first-level cache (L1) for each core Since there are two cores, we can expect the benchmark to run two threads in parallel. Their ...
• 57.4k
### Why aren't CPUs cooled from below as well as above?
They aren't cooled from below because they have pins on the bottom, and FR4 below that. Due to having a much lower thermal conductivity, \begin{array}{rrl} \text{Copper:} & 385\phantom{.25} &...
• 63.3k
Accepted
### How does the current processor technology with low clock rates (<10 GHz) deals with mmWave (>10 GHz) technology used in 5G?
So, how do processors deal with the frequencies in the range of 20-100 GHz? They don't. Even if we consider a demodulation of data to lower frequencies from carrier frequencies, there needs to be a ...
• 6,361
Accepted
### What stops an assembly program from crashing the operating system?
In the end, all programs are machine code, regardless of whether the source language was assembler or a high-level language. The important thing is that there are hardware mechanisms that limit what ...
• 164k
Accepted
### How can an FPGA outperform a CPU?
All of the other popular answers presented here talk about literal differences between FPGAs and CPUs. They point out the parallel nature of the FPGA vs the sequential nature of a CPU, or give ...
• 1,543
### Why is there no nand instruction in modern CPUs?
The cost of such an ALU functions is 1) the logic that performs the function itself 2) the selector that selects this function result instead of the others out of all ALU functions 3) the cost of ...
• 47.7k
### Using CPU heat to generate electricity
The issue with thermoelectric generators is they are horrendously inefficient. For a CPU you HAVE to get rid of the heat they produce or they melt down. You could hook up a peltier module and ...
• 45.6k
### How can cache be that fast?
@peufeu's answer points out that these are system-wide aggregate bandwidths. L1 and L2 are private per-core caches in Intel Sandybridge-family, so the numbers are 2x what a single core can do. But ...
• 1,232
### Why is there no nand instruction in modern CPUs?
Turn it around - first see why Nand was popular in hardware logic design - it has several useful properties there. Then ask whether those properties still apply in a CPU instruction... TL/DR - they ...
• 65.7k
Accepted
### FPGA CPUs, how to find the max speed?
The speed of a design is limited by several things. The biggest will most likely be the propagation delay through the combinatorial logic in your design, called the critical path. If you use a fast ...
• 39.6k
Accepted
### Can you make a CPU out of electronic components drawn by hand on paper?
If the gain of a single inverter is less than unity, then it will not be possible to combine any significant number of gates together to build a larger circuit. The signal levels will just peter out. ...
• 164k
Only top scored, non community-wiki answers of a minimum length are eligible | 2022-05-16 11:24:24 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.30766794085502625, "perplexity": 2541.676844386659}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662510117.12/warc/CC-MAIN-20220516104933-20220516134933-00104.warc.gz"} |
http://mathoverflow.net/questions/38973/discriminant-and-different/38974 | # Discriminant and Different.
First some context. In most algebraic number theory textbooks, the notion of discriminant and different of an extension of number fields $L/K$, or rather, of the corresponding extension $B/A$ of their rings of algebraic integers is defined. The discriminant, an ideal of $A$, is the ideal generated by the discriminant of the quadratic form $\text{tr}(xy)$ on $B$. The different, an ideal of $B$, is the inverse of the fractional ideal $c$ of $L$ defined by $c=\{x \in L, \text{tr}(xy) \in A \ \forall y \in B\}$. The norm of the different is the discriminant.
Now the discriminant makes sense in a much more general context, say for any extension of (commutative) rings $B/A$ that is finite projective, since the trace map $\tr$ makes sense in this context. My question is: is there a standard definition of the different in this context? if so, where can I find it in the literature, if possible with the basic results about it?
I am pretty sure the answer to the first question is yes, but I have not been able to find a reference. The problem when I try to use google or MathSciNet seems to be that "different" is not a very discriminant name: almost every paper in mathematics contains it.
Let me propose an answer to my own question: we could define the different of $B/A$ by the Fitting ideal of the universal $B$-modules of differentials $\Omega_{B/A}$. The fact that it gives the correct definition in the number field cases is [Serre, Local Fields, chapter III, Prop. 14], and moreover it behaves well under base change. This definition may very possibly be a remembrance of something I had heard in an earlier life. But even if it is the correct definition, I'd like to know a reference where it is stated.
-
Welcome to MO, Joël. It is a very nice place and allows people to use the trémas in their names if they have any. – Chandan Singh Dalawat Sep 16 '10 at 14:24
Your proposed definition can also be found (in a geometric context) in "The Geometry of Schemes" by Eisenbud-Harris (see Chapter V), although the fact that it agrees with the notion in number theory is not discussed there. – Sam Lichtenstein Sep 16 '10 at 15:25
+1 for "different is not a very discriminant name" – Cam McLeman Sep 16 '10 at 19:25
In chapter 8 (entitled "Traces, Complementary Modules, and Differents") of the book Residues and Duality for Projective Algebraic Varieties by Kunz, he gives exactly the definition you propose and proves some basic results about its properties.
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Thanks. The book seems exactly what I need. It is not at my library but I will receive it soon. – Joël Sep 17 '10 at 13:33
Three months after, an update: I have found everything I wanted in the book you need. In particular the notion of Noether's different, which fits exactly my need. Thanks again. – Joël Dec 16 '10 at 4:43 | 2013-12-18 23:33:04 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8725454211235046, "perplexity": 251.34003654840475}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-48/segments/1387345760572/warc/CC-MAIN-20131218054920-00063-ip-10-33-133-15.ec2.internal.warc.gz"} |
https://git.iws.uni-stuttgart.de/dumux-repositories/dumux/blame/cc391e21650e8347bec8f1e325cceee954baf8f0/doc/handbook/5_developingdumux.tex | 5_developingdumux.tex 5.02 KB
Thomas Fetzer committed Jul 27, 2015 1 2 3 4 \section{Developing \Dumux} \label{sc_developingdumux} \subsection{Communicate with \Dumux Developers} Kilian Weishaupt committed Sep 20, 2016 5 Sina Ackermann committed Mar 17, 2017 6 7 \paragraph{Issues and Bug Tracking} The bug-tracking system \emph{GitLab Issues} offers the possibility to report bugs or discuss new development requests. Timo Koch committed Dec 19, 2018 8 Feel free to register (if you don't have a \emph{Git} account already) and to contribute Kilian Weishaupt committed Sep 20, 2016 9 10 at \url{https://git.iws.uni-stuttgart.de/dumux-repositories/dumux/issues}. Sina Ackermann committed Mar 17, 2017 11 12 13 14 \paragraph{Commits, Merges, etc.} To be up-to-date with the latest changes made to any git-repository you can use RSS Feeds. Simply click on \emph{Issues} or \emph{Activity} and then select a tab you are interested in and use your favorite RSS-application for receiving the news. Thomas Fetzer committed Jul 27, 2015 15 16 17 18 \paragraph{Automatic Testing Dashboard} The automatic testing using \emph{BuildBot} helps to constantly check the \Dumux problems for compiling and running correctly. It is available at Sina Ackermann committed Mar 17, 2017 19 \url{https://git.iws.uni-stuttgart.de/buildbot/#/builders}. Thomas Fetzer committed Jul 27, 2015 20 21 22 23 24 25 26 27 \paragraph{The General Mailing List:} If you have questions, specific problems (which you really struggle to solve on your own), or hints for the \Dumux-developers, please contact the mailing list \url{dumux@iws.uni-stuttgart.de}. You can subscribe to the mailing list via \url{https://listserv.uni-stuttgart.de/mailman/listinfo/dumux}, then you will be informed about upcoming releases or events. Timo Koch committed Dec 18, 2018 28 29 30 31 32 33 34 \subsection{Coding Guidelines} Writing code in a readable manner is very important, especially for future code developers (e.g. for adding features, debugging, etc.). For the style guide and instructions how to contribute to \Dumux visit \url{https://git.iws.uni-stuttgart.de/dumux-repositories/dumux/blob/master/CONTRIBUTING.md}. Thomas Fetzer committed Jul 27, 2015 35 36 37 38 \subsection{Tips and Tricks} \Dumux users and developers at the LH2 are also referred to the internal Wiki for more information. Timo Koch committed Dec 19, 2018 39 \paragraph{Optimized computation vs debugging} Thomas Fetzer committed Jul 27, 2015 40 \Dune and \Dumux are built with the help of \texttt{dunecontrol}, as explained on page \pageref{buildIt}. Timo Koch committed Dec 19, 2018 41 Per default, \Dumux is compiled using optimization options, which leads to faster runtimes but is unsuitable Timo Koch committed Dec 19, 2018 42 43 for debugging. For debug opts you can set \texttt{DCMAKE\textunderscore BUILD\textunderscore TYPE} to \texttt{Debug} or \texttt{RelWithDebInfo} in your options file. You can also do this in any of the \texttt{CMakeLists.txt} in Dumux by adding: Timo Koch committed Dec 19, 2018 44 Thomas Fetzer committed Jul 31, 2015 45 \begin{lstlisting}[style=Shell] Timo Koch committed Dec 19, 2018 46 set(CMAKE_BUILD_TYPE Debug) Thomas Fetzer committed Jul 31, 2015 47 \end{lstlisting} 48 Timo Koch committed Dec 19, 2018 49 Afterwards rerun cmake again (run cmake ). Timo Koch committed Dec 19, 2018 50 Thomas Fetzer committed Jul 27, 2015 51 52 53 54 55 56 57 58 59 60 \paragraph{Dunecontrol for selected modules} A complete build using \texttt{dunecontrol} takes some time. In many cases not all modules need to be re-built. Pass the flag \texttt{--only=dumux} to \texttt{dunecontrol} for configuring or building only \Dumux. A more complex example would be the use of an additional module. Then you have to configure and build only \Dune{}-grid and \Dumux by adding \texttt{--only=MODULE,dumux}. \paragraph{Patching Files or Modules} If you want to send changes to an other developer of \Dumux providing patches can be quite smart. To create a patch simply type: \begin{lstlisting}[style=Bash] Christoph Grüninger committed Jan 18, 2016 61 $git diff > PATCHFILE Thomas Fetzer committed Jul 27, 2015 62 63 64 65 66 \end{lstlisting} \noindent which creates a text file containing all your changes to the files in the current folder or its subdirectories. To apply a patch in the same directory type: \begin{lstlisting}[style=Bash] Christoph Grüninger committed Jan 18, 2016 67 $ patch -p1 < PATCHFILE Thomas Fetzer committed Jul 27, 2015 68 \end{lstlisting} Timo Koch committed Dec 18, 2018 69 70 71 72 %TODO: currently, no DUNE patches necessary! Thus, this section is commented and the missing refrence would be bad. % Uncomment the following statement again when patches might be necessary. % See \ref{sc:patchingDUNE} if you need to apply patches to \Dumux or \Dune. Thomas Fetzer committed Jul 27, 2015 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 \paragraph{File Name and Line Number by Predefined Macro} If you want to know where some output or debug information came from, use the predefined macros \texttt{\_\_FILE\_\_} and \texttt{\_\_LINE\_\_}: \begin{lstlisting}[style=DumuxCode] std::cout << "# This was written from "<< __FILE__ << ", line " << __LINE__ << std::endl; \end{lstlisting} \paragraph{Using \Dune Debug Streams} \Dune provides a helpful feature, for keeping your debug-output organized. It uses simple streams like \texttt{std::cout}, but they can be switched on and off for the whole project. You can chose five different levels of severity: \begin{verbatim} 5 - grave (dgrave) 4 - warning (dwarn) 3 - info (dinfo) 2 - verbose (dverb) 1 - very verbose (dvverb) \end{verbatim} \noindent They are used as follows: \begin{lstlisting}[style=DumuxCode] // define the minimal debug level somewhere in your code #define DUNE_MINIMAL_DEBUG_LEVEL 4 Dune::dgrave << "message"; // will be printed Dune::dwarn << "message"; // will be printed Dune::dinfo << "message"; // will NOT be printed \end{lstlisting} \paragraph{Make headercheck:} Sina Ackermann committed Mar 17, 2017 102 103 104 105 To check one header file for all necessary includes to compile the contained code, use \texttt{make headercheck}. Include the option \texttt{-DENABLE\_HEADERCHECK=1} in your opts file and run \texttt{dunecontrol}. Then go to the top level in your build-directory and type \texttt{make headercheck} to check all headers or press 'tab' to use the auto-completion to search for a specific header. | 2020-06-03 16:56:10 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6039838194847107, "perplexity": 5883.6014795314895}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347435238.60/warc/CC-MAIN-20200603144014-20200603174014-00456.warc.gz"} |
http://mathhelpforum.com/calculus/104431-limit-2-x-32-x-5-a.html | # Thread: limit of 2^x - 32 / x-5
1. ## limit of 2^x - 32 / x-5
i can't figure it out for some reason it's weird!
each limit represents the derivative of some function "f" at some number "a". state such an "f" and "a" in each case.
limit as x-->5
2^x - 32 / x-5
i keep trying but i can't get it right!
if it helps i know the answer in the back of the book says
f(x)=2^x, a=5
2. Originally Posted by jayjay60
i can't figure it out for some reason it's weird!
each limit represents the derivative of some function "f" at some number "a". state such an "f" and "a" in each case.
limit as x-->5
2^x - 32 / x-5
i keep trying but i can't get it right!!!!
if it helps i know the answer in the back of the book says
f(x)=2^x, a=5
are you familiar with the difference quotient?
$f'(a) = \lim_{x \to a} \frac{f(x) - f(a)}{x-a}$
match it up ...
$f'(5) = \lim_{x \to 5} \frac{f(x) - f(5)}{x-5}$
$f'(5) = \lim_{x \to 5} \frac{2^x - 2^5}{x-5}$
3. yes, well i can't understand how f(x)=2^x, a=5 is the answer though? :<
4. oh gosh. i hate when they're so simple it's easy to overlook!!! thank you so much. | 2016-10-22 20:25:07 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 3, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8538098335266113, "perplexity": 1253.3116656234242}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988719041.14/warc/CC-MAIN-20161020183839-00553-ip-10-171-6-4.ec2.internal.warc.gz"} |
https://physics.stackexchange.com/questions/310340/work-of-body-remaining-still-in-gravitational-field | # work of body remaining still in gravitational field
How to quantify power output of a statite?
It's a kind of (non-)satellite, that remains immobile in relation to the central body (e.g. hovering over one of the poles of a planet) through continuous counteracting the gravitational pull through its propulsion. (the linked article suggests solar sail, but other means have been proposed; ion propulsion based Sun statite could maintain position for months.)
If we take work as force over distance, since statite remains immobile, work understood that way is zero. This approach is impractical here.
Yet indubitably fuel is burnt, propellant accelerated, a certain energy output over time is required to maintain status quo.
How should I calculate this work, energy and power, knowing the local gravitational acceleration and mass of the statite?
(let's assume the statite mass change over time of the experiment is small to avoid rocket equation problems).
While the statite remains stationary, it has to eject mass (like a rocket motor) in order to maintain altitude. The work done is computed by considering the momentum exchange needed per unit time. If the force of gravity you are counteracting is $F$, then the momentum of matter accelerated per unit time is also $F$ (since $\Delta P = F\Delta t$, it follows that $F=\frac{\Delta P}{\Delta t}$)
Now the energy contained in the ejected mass is $\frac12 m v^2 = \frac{P^2}{2m}$. It follows that the larger the ejected mass, the lower the energy needed. This is why the Sikorsky challenge was won by a human-powered helicopter with a giant span - it could move a very large amount of air (mass) very slowly (low energy needed). | 2020-04-07 07:26:38 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.813541054725647, "perplexity": 1050.2542205749826}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585371675859.64/warc/CC-MAIN-20200407054138-20200407084638-00047.warc.gz"} |
https://spmaddmaths.blog.onlinetuition.com.my/2020/07/1-9-progressions-spm-practice-paper-2.html | # 5.6.2 Progressions, SPM Practice (Paper 2)
Question 3:
An arithmetic progression has 16 terms. The sum of the 16 terms is 188, and the sum of the even terms is 96. Find
(a) the first term and the common difference,
(b) the last term.
Solution:
(a) Let the first term = a
Common difference = d
Given the sum of the even terms = 96
$\begin{array}{l}{T}_{2}+{T}_{4}+{T}_{6}+\dots ..+{T}_{16}=96\\ \left(a+d\right)+\left(a+3d\right)+\left(a+5d\right)+\dots ..+\left(a+15d\right)=96\\ \frac{8}{2}\left[\left(a+d\right)+\left(a+15d\right)\right]=96\\ 4\left[2a+16d\right]=96\\ 2a+16d=24---\left(2\right)\end{array}$
(2) – (1):
16d – 15d = 24 – 23.5
d = 0.5
Substitute d = 0.5 into (2):
2a + 16 (0.5) = 24
2a + 8 = 24
2a = 16
a = 8
Therefore, first term = 8 and common difference = 0.5.
(b) Last term
= T2
= 8 + 15 (0.5)
= 8 +7.5
= 15.5
Question 4:
The third term and the sixth term of a geometric progression are 24 and $7\frac{1}{9}$ respectively. Find
(a) the first term and the common ratio,
(b) the sum of the first five terms,
(c) the sum of the first n terms with n is very big approaching rn ≈ 0.
Solution:
(a)
(b)
(c)
Therefore, sum of the first n terms with n is very big approaching rn ≈ 0 is 162. | 2022-01-22 08:00:44 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 2, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4520684480667114, "perplexity": 1123.651748493957}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320303779.65/warc/CC-MAIN-20220122073422-20220122103422-00166.warc.gz"} |
http://hitchhikersgui.de/Color | # Color
Colored pencils
Color effect – Sunlight shining through stained glass onto carpet (Nasir ol Molk Mosque located in Shiraz, Iran)
Colors can appear different depending on their surrounding colors and shapes. The two small squares have exactly the same color, but the right one looks slightly darker.
Color (American English) or colour (Commonwealth English) is the characteristic of human visual perception described through color categories, with names such as red, blue, yellow, green, orange, or purple. This perception of color derives from the stimulation of cone cells in the human eye by electromagnetic radiation in the spectrum of light. Color categories and physical specifications of color are associated with objects through the wavelength of the light that is reflected from them. This reflection is governed by the object's physical properties such as light absorption, emission spectra, etc.
By defining a color space, colors can be identified numerically by coordinates. The RGB color space for instance is a color space corresponding to human trichromacy and to the three cone cell types that respond to three bands of light: long wavelengths, peaking near 564–580 nm (red); medium-wavelength, peaking near 534–545 nm (green); and short-wavelength light, near 420–440 nm (blue).[1][2] There may also be more than three color dimensions in other color spaces, such as in the CMYK color model, wherein one of the dimensions relates to a color's colorfulness).
The photo-receptivity of the "eyes" of other species also varies considerably from that of humans and so results in correspondingly different color perceptions that cannot readily be compared to one another. Honeybees and bumblebees for instance have trichromatic color vision sensitive to ultraviolet (an electromagnetic radiation with a wavelength from 10 nm (30 PHz) to 400 nm (750 THz), shorter than that of visible light but longer than X-rays) but is insensitive to red. Papilio butterflies possess six types of photoreceptors and may have pentachromatic vision.[3] The most complex color vision system in the animal kingdom has been found in stomatopods (such as the mantis shrimp) with up to 12 spectral receptor types thought to work as multiple dichromatic units.[4]
The science of color is sometimes called chromatics, colorimetry, or simply color science. It includes the perception of color by the human eye and brain, the origin of color in materials, color theory in art, and the physics of electromagnetic radiation in the visible range (that is, what is commonly referred to simply as light).
## Physics of color
Continuous optical spectrum rendered into the sRGB color space.
The colors of the visible light spectrum[5]
color Wavelength
interval
Frequency
interval
Red ~ 700–635 nm ~ 430–480 THz
Orange ~ 635–590 nm ~ 480–510 THz
Yellow ~ 590–560 nm ~ 510–540 THz
Green ~ 560–520 nm ~ 540–580 THz
Cyan ~ 520–490 nm ~ 580–610 THz
Blue ~ 490–450 nm ~ 610–670 THz
Violet ~ 450–400 nm ~ 670–750 THz
Color, wavelength, frequency and energy of light
Color ${\displaystyle \lambda \,\!}$
(nm)
${\displaystyle \nu \,\!}$
(THz)
${\displaystyle \nu _{b}\,\!}$
(μm−1)
${\displaystyle E\,\!}$
(eV)
${\displaystyle E\,\!}$
(kJ mol−1)
Infrared >1000 <300 <1.00 <1.24 <120
Red 700 428 1.43 1.77 171
Orange 620 484 1.61 2.00 193
Yellow 580 517 1.72 2.14 206
Green 530 566 1.89 2.34 226
Blue 470 638 2.13 2.64 254
Violet 420 714 2.38 2.95 285
Near ultraviolet 300 1000 3.33 4.15 400
Far ultraviolet <200 >1500 >5.00 >6.20 >598
Electromagnetic radiation is characterized by its wavelength (or frequency) and its intensity. When the wavelength is within the visible spectrum (the range of wavelengths humans can perceive, approximately from 390 nm to 700 nm), it is known as "visible light".
Most light sources emit light at many different wavelengths; a source's spectrum is a distribution giving its intensity at each wavelength. Although the spectrum of light arriving at the eye from a given direction determines the color sensation in that direction, there are many more possible spectral combinations than color sensations. In fact, one may formally define a color as a class of spectra that give rise to the same color sensation, although such classes would vary widely among different species, and to a lesser extent among individuals within the same species. In each such class the members are called metamers of the color in question.
### Spectral colors
The familiar colors of the rainbow in the spectrum – named using the Latin word for appearance or apparition by Isaac Newton in 1671 – include all those colors that can be produced by visible light of a single wavelength only, the pure spectral or monochromatic colors. The table at right shows approximate frequencies (in terahertz) and wavelengths (in nanometers) for various pure spectral colors. The wavelengths listed are as measured in air or vacuum (see refractive index).
The color table should not be interpreted as a definitive list – the pure spectral colors form a continuous spectrum, and how it is divided into distinct colors linguistically is a matter of culture and historical contingency (although people everywhere have been shown to perceive colors in the same way[6]). A common list identifies six main bands: red, orange, yellow, green, blue, and violet. Newton's conception included a seventh color, indigo, between blue and violet. It is possible that what Newton referred to as blue is nearer to what today is known as cyan, and that indigo was simply the dark blue of the indigo dye that was being imported at the time.[7]
The intensity of a spectral color, relative to the context in which it is viewed, may alter its perception considerably; for example, a low-intensity orange-yellow is brown, and a low-intensity yellow-green is olive-green.
### Color of objects
The color of an object depends on both the physics of the object in its environment and the characteristics of the perceiving eye and brain. Physically, objects can be said to have the color of the light leaving their surfaces, which normally depends on the spectrum of the incident illumination and the reflectance properties of the surface, as well as potentially on the angles of illumination and viewing. Some objects not only reflect light, but also transmit light or emit light themselves, which also contributes to the color. A viewer's perception of the object's color depends not only on the spectrum of the light leaving its surface, but also on a host of contextual cues, so that color differences between objects can be discerned mostly independent of the lighting spectrum, viewing angle, etc. This effect is known as color constancy.
The upper disk and the lower disk have exactly the same objective color, and are in identical gray surroundings; based on context differences, humans perceive the squares as having different reflectances, and may interpret the colors as different color categories; see checker shadow illusion.
Some generalizations of the physics can be drawn, neglecting perceptual effects for now:
• Light arriving at an opaque surface is either reflected "specularly" (that is, in the manner of a mirror), scattered (that is, reflected with diffuse scattering), or absorbed – or some combination of these.
• Opaque objects that do not reflect specularly (which tend to have rough surfaces) have their color determined by which wavelengths of light they scatter strongly (with the light that is not scattered being absorbed). If objects scatter all wavelengths with roughly equal strength, they appear white. If they absorb all wavelengths, they appear black.[8]
• Opaque objects that specularly reflect light of different wavelengths with different efficiencies look like mirrors tinted with colors determined by those differences. An object that reflects some fraction of impinging light and absorbs the rest may look black but also be faintly reflective; examples are black objects coated with layers of enamel or lacquer.
• Objects that transmit light are either translucent (scattering the transmitted light) or transparent (not scattering the transmitted light). If they also absorb (or reflect) light of various wavelengths differentially, they appear tinted with a color determined by the nature of that absorption (or that reflectance).
• Objects may emit light that they generate from having excited electrons, rather than merely reflecting or transmitting light. The electrons may be excited due to elevated temperature (incandescence), as a result of chemical reactions (chemoluminescence), after absorbing light of other frequencies ("fluorescence" or "phosphorescence") or from electrical contacts as in light emitting diodes, or other light sources.
To summarize, the color of an object is a complex result of its surface properties, its transmission properties, and its emission properties, all of which contribute to the mix of wavelengths in the light leaving the surface of the object. The perceived color is then further conditioned by the nature of the ambient illumination, and by the color properties of other objects nearby, and via other characteristics of the perceiving eye and brain.
## Perception
When viewed in full size, this image contains about 16 million pixels, each corresponding to a different color on the full set of RGB colors. The human eye can distinguish about 10 million different colors.[9]
### Development of theories of color vision
Although Aristotle and other ancient scientists had already written on the nature of light and color vision, it was not until Newton that light was identified as the source of the color sensation. In 1810, Goethe published his comprehensive Theory of Colors in which he ascribed physiological effects to color that are now understood as psychological.
In 1801 Thomas Young proposed his trichromatic theory, based on the observation that any color could be matched with a combination of three lights. This theory was later refined by James Clerk Maxwell and Hermann von Helmholtz. As Helmholtz puts it, "the principles of Newton's law of mixture were experimentally confirmed by Maxwell in 1856. Young's theory of color sensations, like so much else that this marvelous investigator achieved in advance of his time, remained unnoticed until Maxwell directed attention to it."[10]
At the same time as Helmholtz, Ewald Hering developed the opponent process theory of color, noting that color blindness and afterimages typically come in opponent pairs (red-green, blue-orange, yellow-violet, and black-white). Ultimately these two theories were synthesized in 1957 by Hurvich and Jameson, who showed that retinal processing corresponds to the trichromatic theory, while processing at the level of the lateral geniculate nucleus corresponds to the opponent theory.[11]
In 1931, an international group of experts known as the Commission internationale de l'éclairage (CIE) developed a mathematical color model, which mapped out the space of observable colors and assigned a set of three numbers to each.
### Color in the eye
Normalized typical human cone cell responses (S, M, and L types) to monochromatic spectral stimuli
The ability of the human eye to distinguish colors is based upon the varying sensitivity of different cells in the retina to light of different wavelengths. Humans are trichromatic—the retina contains three types of color receptor cells, or cones. One type, relatively distinct from the other two, is most responsive to light that is perceived as blue or blue-violet, with wavelengths around 450 nm; cones of this type are sometimes called short-wavelength cones, S cones, or blue cones. The other two types are closely related genetically and chemically: middle-wavelength cones, M cones, or green cones are most sensitive to light perceived as green, with wavelengths around 540 nm, while the long-wavelength cones, L cones, or red cones, are most sensitive to light is perceived as greenish yellow, with wavelengths around 570 nm.
Light, no matter how complex its composition of wavelengths, is reduced to three color components by the eye. Each cone type adheres to the principle of univariance, which is that each cone's output is determined by the amount of light that falls on it over all wavelengths. For each location in the visual field, the three types of cones yield three signals based on the extent to which each is stimulated. These amounts of stimulation are sometimes called tristimulus values.
The response curve as a function of wavelength varies for each type of cone. Because the curves overlap, some tristimulus values do not occur for any incoming light combination. For example, it is not possible to stimulate only the mid-wavelength (so-called "green") cones; the other cones will inevitably be stimulated to some degree at the same time. The set of all possible tristimulus values determines the human color space. It has been estimated that humans can distinguish roughly 10 million different colors.[9]
The other type of light-sensitive cell in the eye, the rod, has a different response curve. In normal situations, when light is bright enough to strongly stimulate the cones, rods play virtually no role in vision at all.[12] On the other hand, in dim light, the cones are understimulated leaving only the signal from the rods, resulting in a colorless response. (Furthermore, the rods are barely sensitive to light in the "red" range.) In certain conditions of intermediate illumination, the rod response and a weak cone response can together result in color discriminations not accounted for by cone responses alone. These effects, combined, are summarized also in the Kruithof curve, that describes the change of color perception and pleasingness of light as function of temperature and intensity.
### Color in the brain
The visual dorsal stream (green) and ventral stream (purple) are shown. The ventral stream is responsible for color perception.
While the mechanisms of color vision at the level of the retina are well-described in terms of tristimulus values, color processing after that point is organized differently. A dominant theory of color vision proposes that color information is transmitted out of the eye by three opponent processes, or opponent channels, each constructed from the raw output of the cones: a red–green channel, a blue–yellow channel, and a black–white "luminance" channel. This theory has been supported by neurobiology, and accounts for the structure of our subjective color experience. Specifically, it explains why humans cannot perceive a "reddish green" or "yellowish blue", and it predicts the color wheel: it is the collection of colors for which at least one of the two color channels measures a value at one of its extremes.
The exact nature of color perception beyond the processing already described, and indeed the status of color as a feature of the perceived world or rather as a feature of our perception of the world – a type of qualia – is a matter of complex and continuing philosophical dispute.
### Nonstandard color perception
#### Color deficiency
If one or more types of a person's color-sensing cones are missing or less responsive than normal to incoming light, that person can distinguish fewer colors and is said to be color deficient or color blind (though this latter term can be misleading; almost all color deficient individuals can distinguish at least some colors). Some kinds of color deficiency are caused by anomalies in the number or nature of cones in the retina. Others (like central or cortical achromatopsia) are caused by neural anomalies in those parts of the brain where visual processing takes place.
#### Tetrachromacy
While most humans are trichromatic (having three types of color receptors), many animals, known as tetrachromats, have four types. These include some species of spiders, most marsupials, birds, reptiles, and many species of fish. Other species are sensitive to only two axes of color or do not perceive color at all; these are called dichromats and monochromats respectively. A distinction is made between retinal tetrachromacy (having four pigments in cone cells in the retina, compared to three in trichromats) and functional tetrachromacy (having the ability to make enhanced color discriminations based on that retinal difference). As many as half of all women are retinal tetrachromats.[13]:p.256 The phenomenon arises when an individual receives two slightly different copies of the gene for either the medium- or long-wavelength cones, which are carried on the X chromosome. To have two different genes, a person must have two X chromosomes, which is why the phenomenon only occurs in women.[13] There is one scholarly report that confirms the existence of a functional tetrachromat.[14]
#### Synesthesia
In certain forms of synesthesia/ideasthesia, perceiving letters and numbers (grapheme–color synesthesia) or hearing musical sounds (music–color synesthesia) will lead to the unusual additional experiences of seeing colors. Behavioral and functional neuroimaging experiments have demonstrated that these color experiences lead to changes in behavioral tasks and lead to increased activation of brain regions involved in color perception, thus demonstrating their reality, and similarity to real color percepts, albeit evoked through a non-standard route.
### Afterimages
After exposure to strong light in their sensitivity range, photoreceptors of a given type become desensitized. For a few seconds after the light ceases, they will continue to signal less strongly than they otherwise would. Colors observed during that period will appear to lack the color component detected by the desensitized photoreceptors. This effect is responsible for the phenomenon of afterimages, in which the eye may continue to see a bright figure after looking away from it, but in a complementary color.
Afterimage effects have also been utilized by artists, including Vincent van Gogh.
### Color constancy
When an artist uses a limited color palette, the eye tends to compensate by seeing any gray or neutral color as the color which is missing from the color wheel. For example, in a limited palette consisting of red, yellow, black, and white, a mixture of yellow and black will appear as a variety of green, a mixture of red and black will appear as a variety of purple, and pure gray will appear bluish.[15]
The trichromatic theory is strictly true when the visual system is in a fixed state of adaptation. In reality, the visual system is constantly adapting to changes in the environment and compares the various colors in a scene to reduce the effects of the illumination. If a scene is illuminated with one light, and then with another, as long as the difference between the light sources stays within a reasonable range, the colors in the scene appear relatively constant to us. This was studied by Edwin Land in the 1970s and led to his retinex theory of color constancy.
It should be noted, that both phenomena are readily explained and mathematically modeled with modern theories of chromatic adaptation and color appearance (e.g. CIECAM02, iCAM).[16] There is no need to dismiss the trichromatic theory of vision, but rather it can be enhanced with an understanding of how the visual system adapts to changes in the viewing environment.
### Color naming
Colors vary in several different ways, including hue (shades of red, orange, yellow, green, blue, and violet), saturation, brightness, and gloss. Some color words are derived from the name of an object of that color, such as "orange" or "salmon", while others are abstract, like "red".
In the 1969 study Basic Color Terms: Their Universality and Evolution, Brent Berlin and Paul Kay describe a pattern in naming "basic" colors (like "red" but not "red-orange" or "dark red" or "blood red", which are "shades" of red). All languages that have two "basic" color names distinguish dark/cool colors from bright/warm colors. The next colors to be distinguished are usually red and then yellow or green. All languages with six "basic" colors include black, white, red, green, blue, and yellow. The pattern holds up to a set of twelve: black, gray, white, pink, red, orange, yellow, green, blue, purple, brown, and azure (distinct from blue in Russian and Italian, but not English).
### Associations
Individual colors have a variety of cultural associations such as national colors (in general described in individual color articles and color symbolism). The field of color psychology attempts to identify the effects of color on human emotion and activity. Chromotherapy is a form of alternative medicine attributed to various Eastern traditions. Colors have different associations in different countries and cultures.[17]
Different colors have been demonstrated to have effects on cognition. For example, researchers at the University of Linz in Austria demonstrated that the color red significantly decreases cognitive functioning in men.[18]
## Spectral colors and color reproduction
The CIE 1931 color space chromaticity diagram. The outer curved boundary is the spectral (or monochromatic) locus, with wavelengths shown in nanometers. The colors depicted depend on the color space of the device on which you are viewing the image, and therefore may not be a strictly accurate representation of the color at a particular position, and especially not for monochromatic colors.
Most light sources are mixtures of various wavelengths of light. Many such sources can still effectively produce a spectral color, as the eye cannot distinguish them from single-wavelength sources. For example, most computer displays reproduce the spectral color orange as a combination of red and green light; it appears orange because the red and green are mixed in the right proportions to allow the eye's cones to respond the way they do to the spectral color orange.
A useful concept in understanding the perceived color of a non-monochromatic light source is the dominant wavelength, which identifies the single wavelength of light that produces a sensation most similar to the light source. Dominant wavelength is roughly akin to hue.
There are many color perceptions that by definition cannot be pure spectral colors due to desaturation or because they are purples (mixtures of red and violet light, from opposite ends of the spectrum). Some examples of necessarily non-spectral colors are the achromatic colors (black, gray, and white) and colors such as pink, tan, and magenta.
Two different light spectra that have the same effect on the three color receptors in the human eye will be perceived as the same color. They are metamers of that color. This is exemplified by the white light emitted by fluorescent lamps, which typically has a spectrum of a few narrow bands, while daylight has a continuous spectrum. The human eye cannot tell the difference between such light spectra just by looking into the light source, although reflected colors from objects can look different. (This is often exploited; for example, to make fruit or tomatoes look more intensely red.)
Similarly, most human color perceptions can be generated by a mixture of three colors called primaries. This is used to reproduce color scenes in photography, printing, television, and other media. There are a number of methods or color spaces for specifying a color in terms of three particular primary colors. Each method has its advantages and disadvantages depending on the particular application.
No mixture of colors, however, can produce a response truly identical to that of a spectral color, although one can get close, especially for the longer wavelengths, where the CIE 1931 color space chromaticity diagram has a nearly straight edge. For example, mixing green light (530 nm) and blue light (460 nm) produces cyan light that is slightly desaturated, because response of the red color receptor would be greater to the green and blue light in the mixture than it would be to a pure cyan light at 485 nm that has the same intensity as the mixture of blue and green.
Because of this, and because the primaries in color printing systems generally are not pure themselves, the colors reproduced are never perfectly saturated spectral colors, and so spectral colors cannot be matched exactly. However, natural scenes rarely contain fully saturated colors, thus such scenes can usually be approximated well by these systems. The range of colors that can be reproduced with a given color reproduction system is called the gamut. The CIE chromaticity diagram can be used to describe the gamut.
Another problem with color reproduction systems is connected with the acquisition devices, like cameras or scanners. The characteristics of the color sensors in the devices are often very far from the characteristics of the receptors in the human eye. In effect, acquisition of colors can be relatively poor if they have special, often very "jagged", spectra caused for example by unusual lighting of the photographed scene. A color reproduction system "tuned" to a human with normal color vision may give very inaccurate results for other observers.
The different color response of different devices can be problematic if not properly managed. For color information stored and transferred in digital form, color management techniques, such as those based on ICC profiles, can help to avoid distortions of the reproduced colors. Color management does not circumvent the gamut limitations of particular output devices, but can assist in finding good mapping of input colors into the gamut that can be reproduced.
Additive color mixing: combining red and green yields yellow; combining all three primary colors together yields white.
Additive color is light created by mixing together light of two or more different colors. Red, green, and blue are the additive primary colors normally used in additive color systems such as projectors and computer terminals.
### Subtractive coloring
Subtractive color mixing: combining yellow and magenta yields red; combining all three primary colors together yields black
Subtractive coloring uses dyes, inks, pigments, or filters to absorb some wavelengths of light and not others. The color that a surface displays comes from the parts of the visible spectrum that are not absorbed and therefore remain visible. Without pigments or dye, fabric fibers, paint base and paper are usually made of particles that scatter white light (all colors) well in all directions. When a pigment or ink is added, wavelengths are absorbed or "subtracted" from white light, so light of another color reaches the eye.
If the light is not a pure white source (the case of nearly all forms of artificial lighting), the resulting spectrum will appear a slightly different color. Red paint, viewed under blue light, may appear black. Red paint is red because it scatters only the red components of the spectrum. If red paint is illuminated by blue light, it will be absorbed by the red paint, creating the appearance of a black object.
### Structural color
Structural colors are colors caused by interference effects rather than by pigments. Color effects are produced when a material is scored with fine parallel lines, formed of one or more parallel thin layers, or otherwise composed of microstructures on the scale of the color's wavelength. If the microstructures are spaced randomly, light of shorter wavelengths will be scattered preferentially to produce Tyndall effect colors: the blue of the sky (Rayleigh scattering, caused by structures much smaller than the wavelength of light, in this case air molecules), the luster of opals, and the blue of human irises. If the microstructures are aligned in arrays, for example the array of pits in a CD, they behave as a diffraction grating: the grating reflects different wavelengths in different directions due to interference phenomena, separating mixed "white" light into light of different wavelengths. If the structure is one or more thin layers then it will reflect some wavelengths and transmit others, depending on the layers' thickness.
Structural color is studied in the field of thin-film optics. A layman's term that describes particularly the most ordered or the most changeable structural colors is iridescence. Structural color is responsible for the blues and greens of the feathers of many birds (the blue jay, for example), as well as certain butterfly wings and beetle shells. Variations in the pattern's spacing often give rise to an iridescent effect, as seen in peacock feathers, soap bubbles, films of oil, and mother of pearl, because the reflected color depends upon the viewing angle. Numerous scientists have carried out research in butterfly wings and beetle shells, including Isaac Newton and Robert Hooke. Since 1942, electron micrography has been used, advancing the development of products that exploit structural color, such as "photonic" cosmetics.[19]
• Color wheel: an illustrative organization of color hues in a circle that shows relationships.
• Colorfulness, chroma, purity, or saturation: how "intense" or "concentrated" a color is. Technical definitions distinguish between colorfulness, chroma, and saturation as distinct perceptual attributes and include purity as a physical quantity. These terms, and others related to light and color are internationally agreed upon and published in the CIE Lighting Vocabulary.[20] More readily available texts on colorimetry also define and explain these terms.[16][21]
• Dichromatism: a phenomenon where the hue is dependent on concentration and thickness of the absorbing substance.
• Hue: the color's direction from white, for example in a color wheel or chromaticity diagram.
• Tint: a color made lighter by adding white.
• Value, brightness, lightness, or luminosity: how light or dark a color is.
## References
1. ^ Wyszecki, Günther; Stiles, W.S. (1982). Colour Science: Concepts and Methods, Quantitative Data and Formulae (2nd ed.). New York: Wiley Series in Pure and Applied Optics. ISBN 0-471-02106-7.
2. ^ R. W. G. Hunt (2004). The Reproduction of Colour (6th ed.). Chichester UK: Wiley–IS&T Series in Imaging Science and Technology. pp. 11–12. ISBN 0-470-02425-9.
3. ^ Arikawa K (November 2003). "Spectral organization of the eye of a butterfly, Papilio". J. Comp. Physiol. A Neuroethol. Sens. Neural. Behav. Physiol. 189 (11): 791–800. PMID 14520495. doi:10.1007/s00359-003-0454-7.
4. ^ Cronin TW, Marshall NJ (1989). "A retina with at least ten spectral types of photoreceptors in a mantis shrimp". Nature. 339 (6220): 137–40. Bibcode:1989Natur.339..137C. doi:10.1038/339137a0.
5. ^ Craig F. Bohren (2006). Fundamentals of Atmospheric Radiation: An Introduction with 400 Problems. Wiley-VCH. ISBN 3-527-40503-8.
6. ^
7. ^ Waldman, Gary (2002). Introduction to light : the physics of light, vision, and color (Dover ed.). Mineola: Dover Publications. p. 193. ISBN 978-0-486-42118-6.
8. ^ Pastoureau, Michael (2008). Black: The History of a Color. Princeton University Press. p. 216. ISBN 978-0691139302.
9. ^ a b Judd, Deane B.; Wyszecki, Günter (1975). Color in Business, Science and Industry. Wiley Series in Pure and Applied Optics (third ed.). New York: Wiley-Interscience. p. 388. ISBN 0-471-45212-2.
10. ^ Hermann von Helmholtz, Physiological Optics – The Sensations of Vision, 1866, as translated in Sources of Color Science, David L. MacAdam, ed., Cambridge: MIT Press, 1970.
11. ^ Palmer, S.E. (1999). Vision Science: Photons to Phenomenology, Cambridge, MA: MIT Press. ISBN 0-262-16183-4.
12. ^ "Under well-lit viewing conditions (photopic vision), cones ...are highly active and rods are inactive." Hirakawa, K.; Parks, T.W. (2005). Chromatic Adaptation and White-Balance Problem (PDF). IEEE ICIP. doi:10.1109/ICIP.2005.1530559. Archived from the original (PDF) on November 28, 2006.
13. ^ a b Jameson, K. A.; Highnote, S. M.,; Wasserman, L. M. (2001). "Richer color experience in observers with multiple photopigment opsin genes." (PDF). Psychonomic Bulletin and Review. 8 (2): 244–61. PMID 11495112. doi:10.3758/BF03196159.
14. ^ Jordan, G.; Deeb, S. S.; Bosten, J. M.; Mollon, J. D. (20 July 2010). "The dimensionality of color vision in carriers of anomalous trichromacy". Journal of Vision. 10 (8): 12. PMID 20884587. doi:10.1167/10.8.12.
15. ^ Depauw, Robert C. "United States Patent". Retrieved 20 March 2011.
16. ^ a b M.D. Fairchild, Color Appearance Models Archived May 5, 2011, at the Wayback Machine., 2nd Ed., Wiley, Chichester (2005).
17. ^ "Chart: Color Meanings by Culture". Archived from the original on 2010-10-12. Retrieved 2010-06-29.
18. ^ Gnambs, Timo; Appel, Markus; Batinic, Bernad (2010). "Color red in web-based knowledge testing". Computers in Human Behavior. 26: 1625–1631. doi:10.1016/j.chb.2010.06.010.
19. ^ "Economic and Social Research Council – Science in the Dock, Art in the Stocks". Archived from the original on November 2, 2007. Retrieved 2007-10-07.
20. ^ CIE Pub. 17-4, International Lighting Vocabulary, 1987. http://www.cie.co.at/publ/abst/17-4-89.html
21. ^ R.S. Berns, Principles of Color Technology, 3rd Ed., Wiley, New York (2001). | 2017-09-22 10:05:43 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 5, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5361319780349731, "perplexity": 2050.3492357437412}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818688932.49/warc/CC-MAIN-20170922093346-20170922113346-00171.warc.gz"} |
https://tex.stackexchange.com/questions/304603/how-do-i-define-a-ifcommand-only-if-it-is-not-already-defined | # How do I define a \ifcommand only if it is not already defined?
To deal with a mess of compilation alternatives with multiple files, I use some \ifSomething switches. But I stumble when I need to check if a switch is defined, and define it if it is not. Minimal example:
% This may or may not be present:
\newif\ifSomething
\Somethingfalse
% Later, (usually) in a different file:
\ifdefined \ifSomething
\else
\newif\ifSomething
\Somethingtrue
\fi
\documentclass{article}
\begin{document}
Everything ok?
\end{document}
I believe I understand the problem: Because \ifSomething is already defined, its appearance in the\else clause is interpreted as starting a conditional-- the fact that it's the argument of \newif notwithstanding. I even remember reading about this in the TeXbook... but how should I do this?
• \expandafter\ifx\csname ifSomething\endcsname\relax \newif\ifSomething \Somethingtrue \fi should work too – user31729 Apr 16 '16 at 13:03
• @Christian, I think the use after \ifdefined does not need protecting, just the one after \newif. Am I missing something? – alexis Apr 16 '16 at 13:07
• Protecting??? I don't understand what you mean. I just compare whether \ifSomething is defined with \ifx or is \relax – user31729 Apr 16 '16 at 13:08
• I was using the term loosely, sorry. I meant with \csname... not with \protect. – alexis Apr 16 '16 at 13:11
• \expandafter\ifx\csname foo\endcsname\relax tests whether \foo is defined or is equal to \relax – user31729 Apr 16 '16 at 13:13
For example:
\makeatletter
\@ifundefined{ifSomething}{%
\newif\ifSomething
\Somethingtrue
}{}
\makeatother
\@ifundefined generates the macro name from the argument string and tests, whether the command is undefined (or \relax). This removes the \if... token from the test. Also the branching is syntactically realized via arguments and not by \if...\else...\fi. Therefore an defined or undefined \ifSomething does not cause trouble for \@ifundefined.
However, there is a case, where \ifSomething after \newif in the argument can cause trouble, when the whole construct is inside a \if/\else branch. Then the trick is \csname:
\makeatletter
\@ifundefined{ifSomething}{%
\expandafter\newif\csname ifSomething\endcsname
\Somethingtrue
}{}
\makeatother
• Thanks! It seems that I can also just use the \csname approach with a TeX-style if: \ifdefined\ifSomething \else \expandafter\newif\csname ifSomething\endcsname \fi. Is this going to cause problems in some uses? – alexis Apr 16 '16 at 13:04
• @alexis The number if \if... tokens do not match with one \else and \fi. Thus this causes trouble, when the whole construct is inside another \if... construct. A solution would be e-TeX's \ifcsname: \ifcsname ifSomething\endcsname...\else...\fi. – Heiko Oberdiek Apr 16 '16 at 13:09
• That rings a bell now (from the TeXbook), thanks! – alexis Apr 16 '16 at 13:12
The etoolbox package has \providebool:
\documentclass{article}
\usepackage{etoolbox}
\newif\ifSomething
\providebool{Something}
\providebool{SomethingElse}
\begin{document}
\texttt{\meaning\Somethingtrue}
\texttt{\meaning\SomethingElsetrue}
\end{document} | 2021-07-25 10:17:26 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.772975504398346, "perplexity": 3329.6695093164117}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046151641.83/warc/CC-MAIN-20210725080735-20210725110735-00707.warc.gz"} |
https://engineering.stackexchange.com/questions/16022/doe-to-optimize-a-chemical-reaction-with-impurity-forming-in-series | # DOE to optimize a chemical reaction with impurity forming in series
This question contains chemistry, but the main focus is DOE design--hence posting on the engineering stack exchange.
The problem is a chemical reaction:
• A + B -> Product
• Product + B -> Impurity
The goals are
1. to minimize the impurity.
2. to minimize leftover A.
Reacting the mixture for a long time will get rid of A but increase the Impurity.
Reducing B will decrease the Impurity but increase leftover A.
To optimize the reaction, I'm planning a DOE with temperature, reagent amounts, and reaction time as variables.
I used software to generate a central composite design. However, the reaction time inputs for each experiment aren't physically reasonable. Look at some of the experiments:
+-------------+---------------+-------------------+
| Temperature | Reaction time | Amount of B |
+-------------+---------------+-------------------+
| 20 C | 4 hrs | 1 mole equivalent |
+-------------+---------------+-------------------+
| 50 C | 4 hrs | 1 mole equivalent |
+-------------+---------------+-------------------+
At 20C, I think the reaction will proceed slowly enough that it won't be done after 4 hours. However, at 50C, I think the reaction will be done in less than an hour. The reaction output at 4 hours will be useless--all the B will have been long reacted (i.e. the maximum amount of impurity for that temperature/B input will have formed).
How can I handle the fact that reaction time inputs cannot be assigned randomly?
I know this is a while back, but my answer is generally applicable. From experience, these sort of experiments can make use of reaction time as a "free" variable. Before the DOE is even planned, take samples of the reaction at the three temperatures 20, 35 and 50 degrees at regular intervals. In this way you'll get a feel for the reaction rates. In fact, if you use an internal standard, you could generate actual rates. This reaction time information can be plugged into the DOE. My advice is to take more than three time samples because you can then expand your statistical analysis if necessary e.g. Design Expert allows you to add extra lines to your DOE or you can use a "historical data" approach.
So long as the timepoints are appropriately spaced, you should get a good model. When you have factors that are time bound or hard to change, then a split plot method can be used if that factor is not randomised to check there isn't a false analysis.
You could specify a bit more your knowledge on the system. Which is the limiting reagent? Do you expect a first-order or second order reaction?
It is my understanding that A is in small excess and that you have a certain knowledge of the reaction rates (as you can forecast that the reaction will be completed at 50 degC by not at 20 degC) You can define dimensionless time in a similar way to the Damköhler numbers such as:
$\tau = k\,t$
where $k$ is your expected rate constant and $t$ is time. This expression is valid for first-order reactions, but you can define similar one for arbitrary reaction rate expressions. By this approach, your are somehow combining temperature and time into a single variable and the variables for your DOE would be the dimensionless time $\tau$ and the reagent amounts.
Similarly, you can use "expected conversion of B" as an input variable instead of $\tau$.
• Thank you. I see what you mean for dimensionless time. I don't have exact knowledge of the rate constants--just some qualitative experience with the system. The system is a little messy to model. If I could know the rate constants, I'd model instead of a DOE. In any case, I think I will use conversion of B as an input variable instead of time. Jul 17 '17 at 23:12 | 2022-01-19 11:16:42 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.855496346950531, "perplexity": 747.8383168337315}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320301309.22/warc/CC-MAIN-20220119094810-20220119124810-00663.warc.gz"} |
http://permut.blogs.uv.es/tag/perez-ramos/ | # Paper “Finite trifactorised groups and $\pi$-decomposability” published in Bull. Austral. Math. Soc.
The following paper has been published:
El siguiente artículo ha sido publicado:
El següent article ha sigut publicat:
L. S. Kazarin, A. Martínez-Pastor, M. D. Pérez-Ramos.
Finite trifactorised groups and $\pi$-decomposability
Bull. Austral. Math. Soc., 97 (2):218-228, 2018
doi:10.1017/S0004972717001034
Abstract
We derive some structural properties of a trifactorised finite group G = AB = AC = BC, where A, B, and C are subgroups of G, provided that A = Aπ × Aπ’ and B = Bπ × Bπ’ are π-decomposable groups, for a set of primes π.
2010 Mathematics Subject Classification: primary 20D40; secondary 20D20
Keywords: finite group, product of subgroups, π-decomposable group, π-structure.
# Paper “2-Engel relations between subgroups” published in J. Algebra
The following paper has been published
El siguiente artículo ha sido publicado
El següent article ha sigut publicat
M. P. Gállego, P. Hauck, and M. D. Pérez-Ramos
2-Engel relations between subgroups
J. Algebra, 447:31–55, 2016
https://doi.org/10.1016/j.jalgebra.2015.08.030
## Abstract
In this paper we study groups G generated by two subgroups A and B such that 〈a, bis nilpotent of class at most 2 for all aA and bB . A detailed description of the structure of such groups is obtained, generalizing the classical result of Hopkins and Levi on 2-Engel groups.
2010 Mathematical Subject Classification: Primary 20F45; Secondary 20F18, 20D15, 20F12
Keywords: 2-Engel condition, 2-generated subgroups, L-connection, Nilpotency class | 2019-04-24 08:16:54 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4219854772090912, "perplexity": 7772.645063836196}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578636101.74/warc/CC-MAIN-20190424074540-20190424100540-00140.warc.gz"} |
https://nodus.ligo.caltech.edu:8081/40m/?id=1471&sort=Type | 40m QIL Cryo_Lab CTN SUS_Lab TCS_Lab OMC_Lab CRIME_Lab FEA ENG_Labs OptContFac Mariner WBEEShop
40m Log, Page 89 of 339 Not logged in
ID Date Author Type Category Subject
1463 Thu Apr 9 12:23:49 2009 peteUpdateLockingtuning ETM common mode
Pete, Yoichi
Last night, we put the IFO in FP Michelson configuration. We took transfer functions of CARM and DARM, first using CM excitations directly on the ETMs, and then using modulations of the laser frequency via MC excitation. We found that there was basically no coupling into DARM using the MC excitation, but that there was coherence in DARM using the ETM excitation. Therefore, I tuned the ETM common mode in the output matrix. I did this by taking transfer functions of PD1_Q with PD2_I (see attached plot). I changed the drdown_bang script to set C1:LSC-BTMTRX_14 0.98 and C1:LSC-BTMTRX_24 1.02.
Attachment 1: FPMI-DARM-CARM-ETM-fineScan.pdf
1467 Fri Apr 10 01:24:08 2009 ranaUpdateComputersallegra update (sort of)
I tried to play an .avi file on allegra. In a normal universe this would be easy, but because its linux I was foiled.
The default video player (Totem) doesn't play .avi or .wmv format. The patches for this work in Suse but not Fedora. Kubuntu but not CentOS, etc.I also tried installing Kplayer, Kaffeine, mplayer, xine, Aktion, Realplay, Helix, etc. They all had compatibility issues with various things but usuallylibdvdread or some gstreamer plugin.So I pressed the BIG update button. This has now started and allegra may never recover. The auto update wouldn't work in default mode becauseof the libdvdread and gstreamer-ugly plugins, so I unchecked those boxes. I think we're going to have this problem as long as we used any kind ofadvanced gstreamer stuff for the GigE cameras (which is unavoidable).
1469 Fri Apr 10 04:54:24 2009 YoichiUpdateLockingREFL_DC for CARM
Suggested by Rob and Rana's simulation works, I tried to use REFL_DC for the CARM error signal.
My current guess for the cause of the 3.8kHz peak is the following.
The AF sidebands created by the laser frequency drive are reflected by the IFO to the symmetric port if the arms are perfectly symmetric.
However, if there is asymmetry in the arm cavities (such as loss imbalance, ITM transmission difference etc) the sidebands are scattered from the common mode to the differential mode. If our CARM error signal has a large response also to the differential mode (i.e. DARM), the loop is closed. At the DARM RSE frequency, the AF sideband in the differential mode is enhanced and creates a peak in the CARM response.
What Rob's plots show is that PO_DC has a larger response to DARM than REFL_DC has. You can see this from the curves of CARM offset = 0 (black ones).
When the CARM offset is zero, the CARM signal should go to zero. Therefore, the black curves show the residual DARM response. In the case of PO_DC, the black curve is very large suggesting a large DARM coupling.
Now I changed the cabling at the LSC rack to put REFL_DC into the REFL2 input of the CM board.
The REFL_DC signal is put through a 160kHz RC LPF and split to the ADC and the CM board (AC coupled by a large capacitor).
I modified the cm_step script to use PD4_DC as CARM error signal. (The old script is saved as cm_step.podc).
Since the polarity of the REFL_DC signal is opposite to the PO_DC, I flipped the polarity switch of the CM board.
This will flip the sign of the RF CARM signal because this switch flips the polarity of the both inputs.
We have to flip the sign of the RF CARM signal with the SR560 sitting on the LSC rack, which I haven't done yet.
With some tweaks of the gains and addition of two lag-lead filters to PD4_DC, I was able to completely hand off the CARM error signal to REFL_DC.
The attached plot shows the AO path loop gain at arm power = 7. The 3.8kHz is gone, although there is some phase ripple around 3.8kHz.
Since the gain behavior of the REFL_DC is different from the PO_DC, I'm now working on the power up part of the script, adjusting the gains as the power goes up.
Attachment 1: AO-loop-gain-CARM-REFL_DC.png
1470 Fri Apr 10 18:11:18 2009 JenneUpdatePSLISS has a bad cable?
[Rob, Jenne]
I noticed that the ISS Mean Value and CS Saturation were both RED and unhappy. (The alarms were going off, and they were both red on the MEDM screen). None of the MEDM settings seemed off kilter, so we went out to take a look at the PSL table.
Rob checked that light is indeed going to both of the ISS photodiodes (Morag and Siobhan). Next we checked that all the cables were good, and that the power to the ISS box was plugged in. In this process, Rob wiggled all the cables to check that they were plugged in. Just after doing this, the Mean Value and CS Sat were happy again. Rob thinks the current shunt connection might be bad, but we don't really know which one it was since all of the cables were jiggled between our checking the screens.
Right now, everything is happy again, but as with all bad-cabling-problems, we'll probably see this one again.
I don't know why in particular the connection decided to spaz out this afternoon...I don't think anyone opened the PSL table before Rob and I went to investigate. I was working on the PMC servo (checking the LO levels...to be posted in a couple minutes), but didn't have anything to do with the ISS. After I was done, I put everything back, and locked the PMC and the MC, and everything was good, until some time later when the ISS started flipping out.
1471 Fri Apr 10 19:09:48 2009 JenneUpdatePSLPMC LO Calibration
I measured the RF LO output level from the PMC's LO board which goes directly into the LO input on the PMC Servo board. This goes hand-in-hand with Rana's thoughts
that we might be giving the PMC mixer a too-low LO value, and we might need to switch out the mixer. Steve ordered some new mixers today to try out.
The RF Output Adjust slider (on the C1:PSL_PMC_PS screen) goes from 0-10V; The nominal value (or at least the value I found it at today) is 2.014V.
To measure the RF level: I unlocked the Mode Cleaner and turned off the ISS servo per Yoichi's suggestion. I then unplugged the input to the PMC servo board's LO input,
and put that cable into a 300MHz 'scope, with 12dB attenuation. The 'scope was AC coupled, with the input set to 50Ohms.
I then changed the RF Output Adjust slider in increments of 0.5, and measured the peak-to-peak values on the scope. In the table and on the plots, I've taken into account
the 12dB attenuation. i.e I actually measured 964mV, so 964mV*10^.6 = 3838mV.
RF Output Adjust Output measured on scope Oscillator Output Monitor [V] [Vpp] [no units given on MEDM screen] All \pm 0.0159 all of this column is NEGATIVE 0.0000 3.838 0.007 0.5000 3.854 0.007 1.0000 3.838 0.006 1.5000 3.838 0.007 2.0000 3.838 0.006 2.5000 3.838 0.007 3.0000 3.838 0.007 3.5000 3.838 0.007 4.0000 3.838 0.007 4.5000 3.822 0.007 5.0000 3.822 0.012 5.5000 3.790 0.076 6.0000 3.758 0.257 6.5000 3.694 0.555 7.0000 3.615 0.931 7.5000 3.535 1.277 8.0000 3.456 1.532 8.5000 3.392 1.709 9.0000 3.344 1.829 9.5000 3.312 1.908 10.0000 3.296 1.966
I think it's kind of funky that it's so flat for ~half the slider. Also, the third column includes the Oscillator Output Monitor value from the MEDM screen at various RF Adjust slider values. All of these should be negative (i.e. -0.007), but the TABLE function doesn't like "-" signs. I don't know if this information is degenerate with the 'scope measurements, or if it's an indicator of what (might be) wrong.
After finishing, I plugged the cable back into the PMC servo board as it was, turned back on the ISS and relocked the PMC and the MC.
Attachment 1: RFSliderAdjustCalib.png
Attachment 2: RFSliderAdjustCalibWithOsc.png
1472 Fri Apr 10 19:10:53 2009 JenneUpdateGeneralXarm locked?
I don't know who left the X arm locked, but I just ran the Align Full IFO script, so everything is good in case Yoichi/someone comes in to lock the IFO this weekend.
1473 Sat Apr 11 00:45:41 2009 YoichiUpdatePSLPMC LO Calibration
Quote: I then changed the RF Output Adjust slider in increments of 0.5, and measured the peak-to-peak values on the scope. In the table and on the plots, I've taken into account the 12dB attenuation. i.e I actually measured 964mV, so 964mV*10^.6 = 3838mV.
3.8Vpp is about 16dBm.
The mixer for the PMC demodulator is level 23. So 16dBm is insufficient.
What is the level of the new mixer Steve ordered ? 13 ?
1475 Sun Apr 12 19:27:20 2009 ranaUpdatePSLPMC LO Calibration
Quote: 3.8Vpp is about 16dBm. The mixer for the PMC demodulator is level 23. So 16dBm is insufficient. What is the level of the new mixer Steve ordered ? 13 ?
Since Steve and Jenne were on it, I'm sure they ordered the optimum values...
From the table, it looks like the drive level adjuster is busted. Its not supposed to just give a
1-2 dB change over the full range. We'll have to think about what exactly to do, but we should
probably install the level 13 mixer and put in the right attenuation to make the LO be ~13.5 dBm
including the filter. Also need to calibrate the LO readback on the board like what Peter did for
the FSS.
1477 Mon Apr 13 08:59:57 2009 steveUpdatePSLmixers on order
Quote:
Quote: I then changed the RF Output Adjust slider in increments of 0.5, and measured the peak-to-peak values on the scope. In the table and on the plots, I've taken into account the 12dB attenuation. i.e I actually measured 964mV, so 964mV*10^.6 = 3838mV.
3.8Vpp is about 16dBm.
The mixer for the PMC demodulator is level 23. So 16dBm is insufficient.
What is the level of the new mixer Steve ordered ? 13 ?
I ordered mixers level 13, 17 on Friday and level 23 now.
They should be here Tuesday
NOTE: level 23 power is illegal to use in the 40m lab
They get hot
1478 Mon Apr 13 17:55:37 2009 JenneUpdatePSLPMC LO Mon Calibration
I have calibrated the PMC LO Mon (C1:PSL-PMC_LODET) on the PMC's EPICS screen, by inputting different RF LO levels into the LO input of the PMC servo board.
Since the RF output adjust slider on the PMC's Phase Shifter screen doesn't do a whole lot (see elog 1471), I used a combination of attenuators and the slider to achieve different LO levels. I measured the level of the attenuated RF out of the LO board using the 4395A in spectrum analyzer mode, with the units in dBm, with 50dB attenuation to make it stop complaining about being overloaded. For each row in the table I measured the RF level using the 4395, then plugged the cable back into the PMC servo board to get the EPICS screen's reading.
The last 2 columns of the table below are the 'settings' I used to get the given RF LO level.
RF LO Input to PMC Servo Board [dBm] LO Mon on EPICS Screen [no units] RF Output Adjust Slider [V] Attenuators used [dB] 16.004 +- 0.008 0.1200 +- 0.0003 0 0 15.001 +- 0.004 0.0708 +- 0.0008 0 1 14.079 +- 0.008 0.0318 +- 0.0001 8 1 13.002 +- 0.006 0.0126 +- 0.0004 0 3 11.992 +- 0.010 0.0024 +- 0.0008 0 4 10.994 +- 0.010 -0.0024 +- 0.0003 0 4+1=5 9.993 +- 0.008 -0.0047 +- 0.0007 0 3+3=6
When the new mixers that Steve ordered come in (tomorrow hopefully), I'll put in a Level 13 mixer in place of the current Level 23 mixer that we have. Also, Rana suggested increasing the gain on the op-amp which is read out as the LO Mon so that 13dBm looks like 1V. To do this, it looks like I'll need to increase the gain by ~80.
Attachment 1: LOmonCalibration.png
1480 Tue Apr 14 02:59:02 2009 YoichiUpdateLockingPower up until 26
Yoichi, Peter,
With careful adjustments of the common mode gains, we were able to go up to arm power = 26, sort of robustly (more 50% chance).
At this arm power level, the common mode loop shape still looks good. But the interferometer loses lock easily.
I have to check other DOFs, but the interferometer does not stay locked long enough.
Today, lock losses of the IFO were associated with the lock loss of the PMC whereas the FSS stayed locked.
Probably the AO path got large kicks, which could not be handled by the PMC PZT.
The cause for the IFO lock loss is under investigation.
1482 Tue Apr 14 17:20:36 2009 YoichiUpdateComputer Scripts / ProgramsParallel Optickle
I wrote a parallel version of tickle() function for Optickle.
The attached ptickle.m, which provides ptickle() command, can be used as a drop-in replacement of tickle() command.
Just download it and place it in the @Optickle directory.
This command will run multiple instances of Matlab to calculate the frequency responses in parallel.
The speed gain is roughly proportional to the number of CPU cores you use.
To use multiple cores, you have to run matlabpool() command first. See the comment at the beginning of ptickle.m for more detail.
The progress bar is disabled at this moment because it is not clear for me how to make a single progress bar from multiple instances of Matlab.
I sent the code to Matt, so this may be included in the next release of Optickle.
Attachment 1: ptickle.m
% Compute DC fields, and DC signals, and AC transfer functions
%
% This is a parallelized version of tickle. You have to run matlabpool(n)
% command before using this command. matlabpool(n) will invoke n instances
% of matlab workers in your computer. Once you have started those workers,
% you can reuse them many times (i.e. you don't have to run matlabpoo(n)
% every time you use ptickle). Usually n should be equal to the number of
% CPU cores in your computer, but the Matlab parallel computing toolbox has
% the limit of maximum 4 workers for a local computer. If you use a cluster
% of computers across a network, this limit does not apply. But I haven't
... 393 more lines ...
1484 Wed Apr 15 02:20:46 2009 rana, yoichiUpdateDMFDMF now working copy
We found that DMF/ was not an SVN working copy, so I wiped out the SVN version, imported the on-disk copy, moved it to DMFold/ and then checked out the SVN version.
We can delete DMFold/ whenever we are happy with the SVN copy.
1485 Wed Apr 15 03:52:27 2009 ranaUpdateDMFNDS client32 updated for DMF
Since our seisBLRMS.m complains about 'can't find hostname' after a few hours, even though matlab is able to ping fb40m,
I have recompiled the NDS mex client for 32-bit linux on mafalda and stuck it into the nds_mexs/ directory. This time I
compiled using the 'gcc' compiler instead of the 'ANSI C' compiler that is recommended in the README (which, I notice,
is now missing from Ben Johnsons web page!). Let's see how long this runs.
1487 Wed Apr 15 17:11:37 2009 JenneUpdatePSLEdited c1psl.db to calibrate PMC's LO mon
Following the method in Peter's Elog,
I edited c1psl.db to include the following:
grecord(calc, "C1:PSL-PMC_LOCALC")
{
field(INPB,"C1:PSL-PMC_LODET")
field(SCAN,".1 second")
field(PREC,"4")
field(CALC,".955*LOGE(B)-17.11")
}
I restarted c1psl (had to go hit the physical reset button since it didn't come back after telnet-ing and "reboot"ing) to make this take effect.
Next step is to tell the PMC screen to look at this _LOCALC rather than _LODET, and the screen will be calibrated into dBm.
Right now, the screen is as it always has been, because after relooking at the calibration, I no longer believe it. This calibration claimes -19dBm for an LOmon value of 0.1200, when I actually measured +16dBm for this LOmon value. So I've screwed something up in doing my MatLAB calibration. I'll fix it tomorrow, and put in the correct calibration before I change the PMC screen.
RefCav, PMC, MC are all back and locked after my shenanigans.
1488 Thu Apr 16 11:17:56 2009 JenneUpdatePSLEdited c1psl.db to calibrate PMC's LO mon
Quote: I edited c1psl.db to include the following: grecord(calc, "C1:PSL-PMC_LOCALC") { field(INPB,"C1:PSL-PMC_LODET") field(SCAN,".1 second") field(PREC,"4") field(CALC,".955*LOGE(B)-17.11") }
As it turns out, I apparently can't tell X from Y when fitting a function in a rush. The real calibration stuff which is now in c1psl.db is:
grecord(calc, "C1:PSL-PMC_LOCALC")
{
field(INPB,"C1:PSL-PMC_LODET")
field(SCAN,".1 second")
field(PREC,"4")
field(CALC,"1.004*LOGE(B)+17.76")
}
I restarted c1psl (again, had to go hit the physical reset button since it didn't come back after a telnet-reboot) to have it take in the changes. The psl.db file that was in place before yesterday (before I touched it) is saved as psl.db.15Apr2009 just in case.
I edited the PMC EPICS screen to have the LO mon look at C1:PSL-PMC_LOCALC, which is the calibrated channel in dBm. I also stuck a little label on the screen saying what units it's in, because everyone likes to know what units they're looking at.
1489 Thu Apr 16 16:26:57 2009 peteUpdateLockingWed. night locking
yoichi, pete
We installed the watchLockLoss script in scripts/AutoDTT/. This script monitors arm power and uses command line
DTT to save 5 s snapshot of the interferometer when it senses loss of lock. We ran it on linux and it seemed to
save an xml file about half the time; we'll try it on solaris.
I managed to get up to arm power of about 20 a couple of times. IFO lost lock a couple of times after turning
off moving zero. MC2 would often get tripped by lock loss and need resetting. Maybe we will try to stiffen the
op levs.
1490 Thu Apr 16 16:37:42 2009 AlbertoUpdateAuxiliary lockingthe zipper
It takes 18 months to double the computational power of microprocessors but it took man thousands of years to invent the zipper. I never really understood that till these days.
Here is a sample of my latest results from Optickle simulations of the locking signal for the Power Recycling Cavity.
Thanks also to Rob's revolutionary bidimensional rotating matrix idea (I can see entire books of linear algebra going to be rewritten now because of that) I could find the way to determine the optimal demodulation phases for the demod signals.
There were also an other couple of missing details. But that came easily along.
The parfor function for the parallel computation in Matlab sped up some loops by a factor of 100.
In these particular plots there's still no CARM offset scan. That's what I'm going to post next on the elog, together with the signals for the other degrees of freedom.
Attachment 1: 19_3f_Current_40m_plots_SUCCESS.pdf
1491 Thu Apr 16 17:19:44 2009 AlbertoUpdateAuxiliary lockingthe zipper
Quote: It takes 18 months to double the computational power of microprocessors but it took man thousands of years to invent the zipper. I never really understood that till these days. Here is a sample of my latest results from Optickle simulations of the locking signal for the Power Recycling Cavity. Thanks also to Rob's revolutionary bidimensional rotating matrix idea (I can see entire books of linear algebra going to be rewritten now because of that) I could find the way to determine the optimal demodulation phases for the demod signals. There were also an other couple of missing details. But that came easily along. The parfor function for the parallel computation in Matlab sped up some loops by a factor of 100. In these particular plots there's still no CARM offset scan. That's what I'm going to post next on the elog, together with the signals for the other degrees of freedom.
Just to show that I'm confident I'm getting reasonable results, I'll post two PRC scans for different CARM. One set of plots is for the current 40m with -19.78 deg of SRM detuning phase, the other is for the Old Upgrade (9 Mhz vs the 11 currently planned) with no detuning phase.
I'm going to put together the results and get some conclusion about the 3f locking scheme for the current 40m and the upgrade.
Attachment 1: 04_3f_Current_40m_plots.pdf
Attachment 2: 11_3f_40mUpgrade_plots.pdf
1493 Fri Apr 17 11:05:22 2009 YoichiUpdateLockingThursday night locking status
The last night, it was sort of robust to go up until arm power = 26.
The REFL_DC gain seems to change a lot around this region. So I did fine adjustments of the gain with small incremental steps of the arm power.
This work will continue.
The AutoDTT shows that the lock loss happens with an oscillation of CARM at around 100Hz. This indicates that the cross-over is the culprit.
I was also able to increase the CM UGF up to 10kHz.
1495 Sun Apr 19 03:34:05 2009 YoichiUpdateLockingSaturday night lock
Tonight I was able to go up to arm power = 33, by mainly tweaking the DARM gain. A small progress.
In order to give more phase margin to the CARM MC_L path, I added a 300:100 filter to C1:LSC-MC.
To reduce the load to the lsc computer I deleted several filters from the filter bank, which were not used in the locking scripts.
Before I deleted the filters, I checked in the current chans directory into the svn repository.
If you want to restore the deleted filters, go back to the revision 36142.
1497 Sun Apr 19 11:51:05 2009 josephbUpdateCamerasMafalda may need an update
I tried installing libusb-dev on mafalda in order to try getting the usb frame grabber to work on it, but could not as it could not download the package.
I then tried to do a sudo apt-get update, which failed completely, as the repository seems to have ceased existing. Basically I had all 404 Not Found errors.
Turns out Mafalda is still running Ubuntu 7.04, whose support ended late 2008. So there's a couple things that can be done:
1) Ignore it, and simply not update Mafalda anymore. This also means some newer software and hardware simply won't work with it (like the usb frame grabber)
2) Try to find another, unofficial repository which still has all of the Ubuntu 7.04 packages.
3) Upgrade to a newer, still supported Ubuntu, such as 7.10, 8.04, or 8.10.
I'd personally lean towards the 3rd option, and go to the 8.04 long term support version. If people agree with it, I could do the upgrade sometime Monday or Tuesday.
1499 Mon Apr 20 11:57:27 2009 robUpdateCamerasMafalda may need an update
Quote: I tried installing libusb-dev on mafalda in order to try getting the usb frame grabber to work on it, but could not as it could not download the package. I then tried to do a sudo apt-get update, which failed completely, as the repository seems to have ceased existing. Basically I had all 404 Not Found errors. Turns out Mafalda is still running Ubuntu 7.04, whose support ended late 2008. So there's a couple things that can be done: 1) Ignore it, and simply not update Mafalda anymore. This also means some newer software and hardware simply won't work with it (like the usb frame grabber) 2) Try to find another, unofficial repository which still has all of the Ubuntu 7.04 packages. 3) Upgrade to a newer, still supported Ubuntu, such as 7.10, 8.04, or 8.10. I'd personally lean towards the 3rd option, and go to the 8.04 long term support version. If people agree with it, I could do the upgrade sometime Monday or Tuesday.
I don't see a reason to proliferate operating systems. Is there any reason we actually need Ubuntu? Can we put CentOS on it?
1501 Mon Apr 20 18:36:37 2009 ranaUpdateCamerasMafalda may need an update
Sadly, the sensoray crap doesn't seem to build on CentOS. I too would prefer a homogenous solution,
but I don't know how to make this happen without punishing Joe with sensoray driver development on CentOS.
1506 Tue Apr 21 18:18:27 2009 steveUpdateVACmaglev failed
Our Osaka TG360MB maglev failed with CSB error message. This means that the dry emergency landing bearing has to be replaced.
I will consalt with Osaka about the choice of replacing bearing or installing new spare tomorrow.
Mean while V1 is closed and the vac envelope is not pumped.
Valve configuration: BG -background, pumping on the RGA-only
High voltage to IOO PZT steering mirrors and OMC are turned off.
PSL output shutter is closed and manual block is in place.
I will start cooling the CYO pump in the morning, so the IFO will be pumped by noon.
Outgassing plus leakrate after 10 hrs the pressure is 2.3 mTorr
This rate of rise is normal and it is safe to work with the ifo.
Attachment 1: nopumping10h.jpg
1508 Thu Apr 23 13:55:43 2009 josephb, peterUpdateComputersRCG example
We successfully compiled and installed the Real time Code Generator "Hello World" example (which is a skeleton for the ETMX suspension controller) on megatron. In order to get it to compile, we had to add a flag indicating the computer is stand alone, and not using a myrinet card at the moment. This was done by adding the shmem_daq = 1 flag to the cdsParameters module. The symptom was it was unable to find gm.h (and there is no installed /opt/gm directory).
It is called "sam". It was installed to /cvs/cds/caltech/target/sam, and produced medm screens in /cvs/cds/caltech/medm/c1/sam. As nothing points to these, I figure it won't harm any of the current configuration, but lets us play around a bit. If by some strange reason, these do cause problems, feel free to remove them.
1509 Thu Apr 23 16:27:24 2009 YoichiUpdateLockingLocking with the cryo-pump
The last night, the IFO was unstabler than usual and the locking script often failed before reaching the power up stage.
The failure happened at random points.
I'm not sure if this is related to the operation of the cryo-pump.
The mode cleaner reflection image seemed to move around more than usual. Maybe it was just a high seismic night.
1511 Thu Apr 23 16:38:33 2009 steveUpdateVACvac valve relay box is shorting
Ben and I found this vacuum valve relay box intermittently shorthing yesterday.
It effects V4, V5, VA6 and VM1........ Please do not touch this box under the beam pipe next to the vac rack!
The function of this box to send 120VAC to the vacuum valve to move.
Attachment 1: vacrel.png
1512 Thu Apr 23 18:09:11 2009 YoichiUpdateEnvironmentEffect of cryopump
The attached is the trend plot of the MC1 accelerometer for 3 days.
It is evident that the seismic level increased by a factor of two on Wednesday morning (when Steve started the cryopump).
Attachment 1: SeisTrend.pdf
1514 Fri Apr 24 03:57:30 2009 YoichiUpdateLockingDARM demod phase
Tonight, I was able to go up to arm power = 40 by tweaking the DARM demodulation phase.
I think the DARM loop became unstable because the demodulation phase was not right and the error signal contained some junk from I-phase.
I did not do any sophisticated demodulation phase optimization. Rather I just tweaked the phase so that the dark port image becomes stable.
I will do more careful demodulation phase tuning next time.
1515 Fri Apr 24 04:38:49 2009 YoichiUpdateLockingDARM demod phase
Quote: Tonight, I was able to go up to arm power = 40 by tweaking the DARM demodulation phase. I think the DARM loop became unstable because the demodulation phase was not right and the error signal contained some junk from I-phase. I did not do any sophisticated demodulation phase optimization. Rather I just tweaked the phase so that the dark port image becomes stable. I will do more careful demodulation phase tuning next time.
In the next try, I was actually able to go up to arm power = 70 stably.
At this power level we are ready for the RF CARM hand off.
1516 Fri Apr 24 11:34:32 2009 robUpdateLockingDARM demod phase
Quote:
Quote: Tonight, I was able to go up to arm power = 40 by tweaking the DARM demodulation phase. I think the DARM loop became unstable because the demodulation phase was not right and the error signal contained some junk from I-phase. I did not do any sophisticated demodulation phase optimization. Rather I just tweaked the phase so that the dark port image becomes stable. I will do more careful demodulation phase tuning next time.
In the next try, I was actually able to go up to arm power = 70 stably.
At this power level we are ready for the RF CARM hand off.
There's actually code in place in the LSC to dynamically adjust the demod phase for AS1. I've never made much use of it, because it's possible to get around the problem with some gain tweaking if you start at the right phase, or because I did the DC readout handoff earlier.
Attached is a cartoon showing how the demod phase at the dark port changes as the CARM offset is decreased.
Attachment 1: darm_phase_rotate.png
1519 Fri Apr 24 17:26:57 2009 YoichiUpdateLockingDARM demod phase
Quote: There's actually code in place in the LSC to dynamically adjust the demod phase for AS1. I've never made much use of it, because it's possible to get around the problem with some gain tweaking if you start at the right phase, or because I did the DC readout handoff earlier. Attached is a cartoon showing how the demod phase at the dark port changes as the CARM offset is decreased.
The cartoon is very nice.
I actually changed the demod phase continuously as the CARM offset was reduced to get up to arm power = 70.
As the CARM offset is changed, not only the DARM signal gain but also the phase margin around 100Hz changes if you use a fixed demodulation phase.
So it was necessary to change the demodulation phase to keep the DARM loop stable.
1522 Sat Apr 25 03:27:34 2009 YoichiUpdateLockingLocking status
Yoichi, Peter,
We are working on the final step of the lock acquisition, RF CARM hand off.
I was able to hand off the CARM error signal to RF once, but lost lock when decreasing the CARM offset to zero (it was too rapid).
I will try to make the process more robust tomorrow.
1523 Sun Apr 26 02:13:18 2009 YoichiUpdateLockingTwo more successes of RF CARM handoff
Tonight, the RF CARM hand off (mostly) succeeded twice.
But still, the IFO lost lock when I reduced the REFL_DC gain in the AO path to zero.
At the beginning of tonight's work, MICH DD hand off failed several times. This was because the the PD9 gains were set to zero.
I found that the offset script, which I called before starting the locking, fails to restore the gain values sometimes.
This happens when ezcaread fails to read the current gain. We have to be careful when running the LSCoffsets script.
1526 Tue Apr 28 04:30:16 2009 YoichiUpdateLockingRF full lock
Yoichi, Peter
I believe we have succeeded in the full lock of the interferometer with the RF signals.
The lock process is reasonably robust and repeatable.
I did a scan of the RF CARM offset and plotted the arm power as a function of the CARM offset (see the attachment).
The arm power goes maximum at non-zero CARM offset. I guess the RF CARM error signal has some offset.
Maybe the demodulation phase is wrong ? I will tweak this tomorrow.
The script to do this scan can be found at /cvs/cds/caltech/scripts/CM/CARMSweep.
I haven't tried DC readout yet.
Attachment 1: Sweep1.png
1531 Wed Apr 29 04:03:51 2009 YoichiUpdateLockingCARM RF changed to REFL_2I
Yoichi, Peter
As Rob suggested, the optimal demodulation phase is easier to find for REFL_2I than POX_1I.
Moreover, for 166MHz LO, we have a phase shifter (delay line) already installed. So we can easily change the demodulation phase of REFL_2I.
Tonight, we switched the RF CARM signal to REFL_2I.
To do so, I changed the signal going to the REFL1 input of the common mode board from POX_1I to REFL_2I.
I moved a BNC-T installed at the output of POX_1I to the REFL_2I output to split the REFL_2I signal and send it to the CM board.
Since the gain of the REFL_2I was about 20dB lower than that of POX_1I, I increased the gain of the SR560, which is installed between the REFL_2 demodulation board and the CM board, from 1 to 10.
With some gain tweaks, we were able to hand off the CARM from REFL_DC to REFL_2I. We also succeeded in switching the REFL_2I ADC channel from PD11 to PD2_DC (the output of the length path from the CM board). This switching is necessary in order to engage the boost on the CM board.
There remains some offset in the CARM when the arm power is maximized. This is expected because the REFL_2I demodulation phase is probably not exactly right.
I will optimize the demodulation phase tomorrow.
1533 Wed Apr 29 15:56:43 2009 robUpdateLockingeffect of SRCL detune on ARM powers in a CARM sweep
With no DARM offset, sweeping CARM shows an asymmetry between the state where we lock to a DARM spring and the state with a DARM anti-spring. This is why we have a link between the DARM and CARM optical springs.
For each DARM detune direction (positive or negative, spring or anti-spring), there is only one CARM direction which can yield a DC-based error signal lock with a CARM offset but no DARM offset, which is what we want.
Attachment 1: CARMsweep_DARMspringnospring.png
1534 Thu Apr 30 05:49:06 2009 YoichiUpdateLocking166MHz LO phase changed
In order to optimize the REFL_2I demod phase, I changed the delay line setting for the 166MHz LO.
Right now, the delay is not yet optimal.
Since the AS166 shares the same LO, the digital demodulation phase of the AS166 had to be changed too.
The DD demod phases and the DD hand off script were also tweaked to improve the resonant condition of the central part.
Now we have more 166MHz coming out of the AS port and the SPOB is larger (more 33MHz resonant in PRC).
Since REFL166 and AS166 demodulation phases are not yet optimized, the cm_step script won't work at this moment.
1535 Thu Apr 30 15:10:54 2009 robUpdateLockingCARM RF changed to REFL_2I
Quote: Yoichi, Peter As Rob suggested, the optimal demodulation phase is easier to find for REFL_2I than POX_1I. Moreover, for 166MHz LO, we have a phase shifter (delay line) already installed. So we can easily change the demodulation phase of REFL_2I. Tonight, we switched the RF CARM signal to REFL_2I. To do so, I changed the signal going to the REFL1 input of the common mode board from POX_1I to REFL_2I. I moved a BNC-T installed at the output of POX_1I to the REFL_2I output to split the REFL_2I signal and send it to the CM board. Since the gain of the REFL_2I was about 20dB lower than that of POX_1I, I increased the gain of the SR560, which is installed between the REFL_2 demodulation board and the CM board, from 1 to 10. With some gain tweaks, we were able to hand off the CARM from REFL_DC to REFL_2I. We also succeeded in switching the REFL_2I ADC channel from PD11 to PD2_DC (the output of the length path from the CM board). This switching is necessary in order to engage the boost on the CM board. There remains some offset in the CARM when the arm power is maximized. This is expected because the REFL_2I demodulation phase is probably not exactly right. I will optimize the demodulation phase tomorrow.
From Optickle simulations, it looks like the SRCL/CARM gain ratio at REFL I2 is about 8e-4. So a 1 nanometer offset in SRCL yields 0.8 picometers of offset in CARM.
1536 Fri May 1 01:32:43 2009 YoichiUpdateLocking166MHz LO phase adjustment
I continued to adjust the REFL_2I demodulation phase.
I first optimized the demod phase for SRCL in the DRMI configuration (the error signals were DDs).
Then I restored the full IFO and offset locked it.
Before handing the DARM to RF, I adjusted the 166MHz delay line to maximize the SRCL signal at REFL_2I.
I did this before the DARM RF hand off because changing the delay line setting also changes the AS166 demodulation phase.
After this, I adjusted the digital phase shifter for AS166 to maximize the DARM signal for this port.
I also adjusted the digital demodulation phase of PD11 (REFL_2I) because the optimal demodulation phase for the initial lock acquisition is somewhat (15deg)
different from the optimal demodulation phase for the SRCL when the central part is locked with the DD signals.
This happens because the resonant condition of the central part (lock points of the recycling cavities) changes when the error signals are switched to the DD signals,
due to the offset in the DD signals. This is not good and should be fixed by the optimization of the DD demodulation phases.
Finally, I reduced the CARM offset to zero and tweaked the delay line a bit to maximize the arm power.
Right now, the locking script runs fine until the end.
At the end of the script, I was able to engage the boost on the CM board.
1537 Fri May 1 10:04:10 2009 robUpdateLocking166MHz LO phase adjustment
Quote: I continued to adjust the REFL_2I demodulation phase. I first optimized the demod phase for SRCL in the DRMI configuration (the error signals were DDs). Then I restored the full IFO and offset locked it. Before handing the DARM to RF, I adjusted the 166MHz delay line to maximize the SRCL signal at REFL_2I. I did this before the DARM RF hand off because changing the delay line setting also changes the AS166 demodulation phase. After this, I adjusted the digital phase shifter for AS166 to maximize the DARM signal for this port. I also adjusted the digital demodulation phase of PD11 (REFL_2I) because the optimal demodulation phase for the initial lock acquisition is somewhat (15deg) different from the optimal demodulation phase for the SRCL when the central part is locked with the DD signals. This happens because the resonant condition of the central part (lock points of the recycling cavities) changes when the error signals are switched to the DD signals, due to the offset in the DD signals. This is not good and should be fixed by the optimization of the DD demodulation phases. Finally, I reduced the CARM offset to zero and tweaked the delay line a bit to maximize the arm power. Right now, the locking script runs fine until the end. At the end of the script, I was able to engage the boost on the CM board.
Awesome. Up next: dewhitening.
1541 Sun May 3 22:48:12 2009 YoichiUpdateLockingSome measurements at the lock point
I attached some measurement results at when the IFO is at the full lock point.
The first plot shows the trend of the arm powers after the interferometer was locked.
The arm powers slowly increased after the lock. This increase is observed every time the IFO is locked.
Probably this is some sort of a thermal effect (mirror lensing, PD efficiency etc).
The second plot is a CARM offset sweep. Even after the demodulation phase optimization, the lock point is not exactly at the resonance.
The third plot is the open loop TF of the AO path. The CM loop UGF is about 20kHz.
The boost and the superboost1 were turned on when this TF was measured. The IFO loses lock if the superboost2 is turned on.
TO DO LIST
Measured the DARM loop shape.
I could not turn on the dewhitening filter for ETMY. ETMX had no trouble. I will check the dewhitening circuit.
Attachment 1: ArmPowerTrend.png
Attachment 2: CARMSweep.png
Attachment 3: CM-AO-Loop-SB1.png
1542 Mon May 4 10:38:52 2009 steveUpdateMOPAlaser power is dropped
As PSL-126MOPA_DTEC went up, the power out put went down yesterday
Attachment 1: dtecup.jpg
1543 Mon May 4 16:49:56 2009 AlbertoUpdateMOPAlaser power is dropped
Quote: As PSL-126MOPA_DTEC went up, the power out put went down yesterday
Alberto, Jenne, Rob, Steve,
later on in the afternoon, we realized that the power from the MOPA was not recovering and we decided to hack the chiller's pipe that cools the box.
Without unlocking the safety nut on the water valve inside the box, Jenne performed some Voodoo and twisted a bit the screw that opens it with a screw driver. All the sudden some devilish bubbling was heard coming from the pipes.
The exorcism must have freed some Sumerian ghost stuck in our MOPA's chilling pipes (we have strong reasons to believe it might have looked like this) because then the NPRO's radiator started getting cooler.
I also jiggled a bit with the valve while I was trying to unlock the safety nut, but I stopped when I noticed that the nut was stuck to the plastic support it is mounted on.
We're now watching the MOPA power's monitor to see if eventually all the tinkering succeeded.
[From Jenne: When we first opened up the MOPA box, the NPRO's cooling fins were HOT. This is a clear sign of something badbadbad. They should be COLD to the touch (cooler than room temp). After jiggling the needle valve, and hearing the water-rushing sounds, the NPRO radiator fins started getting cooler. After ~10min or so, they were once again cool to the touch. Good news. It was a little worrisome however that just after our needle-valve machinations, the DTEC was going down (good), but the HTEMP started to rise again (bad). It wasn't until after Alberto's tinkering that the HTEMP actually started to go down, and the power started to go up. This is probably a lot to do with the fact that these temperature things have a fairly long time constant.
Also, when we first went out to check on things, there was a lot more condensation on the water tubes/connections than I have seen before. On the outside of the MOPA box, at the metal connectors where the water pipes are connected to the box, there was actually a little puddle, ~1cm diameter, of water. Steve didn't seem concerned, and we dried it off. It's probably just more humid than usual today, but it might be something to check up on later.]
1544 Tue May 5 05:16:12 2009 YoichiUpdateLockingDC Readout and DARM response
Tonight, I was able to switch the DARM to DC readout a couple of times.
But the lock was not as stable as the RF DARM. It lost lock when I tried to measure the DARM loop gain.
I also measured DARM response when DARM is on RF.
The attached plot shows the DARM optical gain (from the mirror displacement to the PD output).
The magnitude is in an arbitrary unit.
I measured a transfer function from DARM excitation to the DARM error signal. Then I corrected it for the DARM open loop gain and the pendulum response to get the plot below.
There is an RSE peak at 4kHz as expected. The origin of the small bump and dip around 2.5kHz and 1.5kHz are unknown.
I will consult with the Optickle model.
I don't know why the optical gain decreases below 50Hz (I don't think it actually decreases).
Seems like the DARM loop gain measured at those frequencies are too low.
I will retry the measurement.
Attachment 1: DARM-TF.png
1545 Tue May 5 08:26:56 2009 robUpdateLockingDC Readout and DARM response
Quote: Tonight, I was able to switch the DARM to DC readout a couple of times. But the lock was not as stable as the RF DARM. It lost lock when I tried to measure the DARM loop gain. I also measured DARM response when DARM is on RF. The attached plot shows the DARM optical gain (from the mirror displacement to the PD output). The magnitude is in an arbitrary unit. I measured a transfer function from DARM excitation to the DARM error signal. Then I corrected it for the DARM open loop gain and the pendulum response to get the plot below. There is an RSE peak at 4kHz as expected. The origin of the small bump and dip around 2.5kHz and 1.5kHz are unknown. I will consult with the Optickle model. I don't know why the optical gain decreases below 50Hz (I don't think it actually decreases). Seems like the DARM loop gain measured at those frequencies are too low. I will retry the measurement.
The optical gain does decrease below ~50Hz--that's the optical spring in action. The squiggles are funny. Last time we did this we measured the single arm TFs to compensate for any tough-to-model squiggles in the transfer functions which might arise from electronics or the suspensions.
1546 Tue May 5 09:22:46 2009 carynUpdatePEMzeros
For several of the channels on the PEM ADCU, zeros are occuring at the same time. Does anyone know why that might happen or how to fix it?
Attachment 1: zerotest2.png
Attachment 2: zerotest.png
1547 Tue May 5 10:42:18 2009 steveUpdateMOPAlaser power is back
Quote: As PSL-126MOPA_DTEC went up, the power out put went down yesterday
The NPRO cooling water was clogged at the needle valve. The heat sink temp was around ~37C
The flow-regulator needle valve position is locked with a nut and it is frozen. It is not adjustable. However Jeenne's tapping and pushing down on the plastic hardware cleared the way for the water flow.
We have to remember to replace this needle valve when the new NPRO will be swapped in. I checked on the heat sink temp this morning. It is ~18C
There is condensation on the south end of the NPRO body, I wish that the DTEC value would just a little higher like 0.5V
The wavelenght of the diode is temp dependent: 0.3 nm/C. The fine tuning of this diode is done by thermo-electric cooler ( TEC )
To keep the diode precisely tuned to the absorption of the laser gain material the diode temp is held constant using electronic feedback control.
This value is zero now.
Attachment 1: uncloged.jpg
1548 Tue May 5 11:44:33 2009 robUpdateLocking DARM response
Here's the RF DARM optical response, on the anti-spring side, from optickle. Note that for the f1 sideband, changing the demod phase mostly adjusts the overall gain, while for the f2 sideband a change in demod phase alters the shape of the response. This is the quadrature-selecting power of using a single RF sideband as a local oscillator.
Attachment 1: DARMtf_nospring.png
Attachment 2: DARMtf_demodphases.png
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http://in-tech.ae/celebrity-karaoke-kisoqeu/3a0a38-right-start-math-clock | Therefore, when the correct clock would show 8 pm, the faster clock will show 60 minutes extra i.e. This free time calculator can add or subtract time values in terms of number of days, hours, minutes, or seconds. All of the books are available as downloads—and most also as printed books. | And then that is nine o'clock right over there. RightStart Mathematics Transition - Worksheets. MADE IN. It's one of the best online productivity tools for those often finding themselves traveling, in flights, in … The epoch used as reference by clock varies between systems, but it is related to the program execution (generally its launch). Adjust next alarm or add new one-time alarms using voice commands. We need to mark the angle that we want to calculate with an x: Then, we solve for the angle by starting from the last exact hour, in our example, we’ll start from 5 o’ clock sharp. Cash Clock - Time is Money! 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If you're seeing this message, it means we're having trouble loading external resources on our website. A clock in general has 12 numbers written on it, from 1 to 12, an hour hand, and a minute hand. About this World Clock / Converter. After 1 hour, that is at 4:00 pm, the minute hand advanced the right hand by 330° - 90° = 240°, thus coordinates (60, 240) Setup Reset. Enter the number of hours and/or minutes you wish to add to or subtract from the clock time. At 1 o'clock the minute hand (red) points to the 12 and the hour hand (blue) points to the 1. When the hands are in opposite directions, they are 30-minute spaces apart. This is eight o'clock right over there. Instructions: Category: Math Games. Well organized and easy to understand Web building tutorials with lots of examples of how to use HTML, CSS, JavaScript, SQL, PHP, Python, Bootstrap, Java and XML. Black clock face is made to look like a chalkboard with each math equation painted to look like white chalk. 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These worksheets deal both elapsed whole hours as well as problems that have fractions of hours of elapsed time, but because the starting time always lacks a minutes component the basic cacluations are suitable for kids who are still building competency with analog clock faces. For example, you can write$4$as$2+2$or$2\times 2$or$2^2$by using the sum, the product, or by raising to a power. The angle is typically measured in degrees from the mark of number 12 clockwise. Accurate exact time from our server, not your device's clock; Prefer fast loading more than complicated design (I hope, mobile phone users will appreciate it); Local time for 400+ time zones; Few details about chosen time zone (like location, daylight saving time etc. Draw your own picture of a 5 hour clock to see that this is true. This is one of my kiddos favorite things in the manipulatives! 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By placing and shading fraction overlays, students use the clock to contextualize fractions with frequently used denominators. What is the angle between the hands of a clock at 1 o'clock? Starting of the program, start_t = 0 Going to scan a big loop, start_t = 0 End of the big loop, end_t = 20000 Total time taken by CPU: 0.000000 Exiting of the program... time_h.htm Previous Page Print Page Tell and write time in hours and half-hours using analog and digital clocks. Main advantages of clock.zone. Add to Cart. This Clock Card Games Kit includes: Clock Card Games book (a chapter from the Math Card Games book) Geared Mini-Clock; Clock Card Deck; WARNING: CHOKING HAZARD! Telling time worksheets start with by reviewing the units of time (seconds vs minutes ...) and then focus on the reading of clocks. Show equivalent digital clock time. Math 1B. Everything you need to teach time to your student in a RightStart™ fun and interesting setting! 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Made of plastic, with silver-toned metal hands, requires 1 AA battery, not included. Time and calendar worksheets. Math Mammoth offers full math curriculum and supplemental worktexts and workbooks for elementary and middle school (plus some supplemental materials for high school), loved by parents, homeschoolers, and teachers. Hand will follow, or use the clock today in 3 hours? the first screen shows analog. Features Highest-rated alarm clock for Heavy Sleepers - Loud + Smart math v5.0.0 build 258 14 days free to... The minute-hand is at -90° in reference with the hour-hand, thus coordinates ( 0, -90 ) 1 12. T believe how fast the summer going for everyone clock can be changed and the second the time! Calculate the … the 1 hour difference is therefore 360° - 30° = 330° for the and! By the minute and hour hand when the correct clock would have completed hours! Angle, they are 30-minute spaces apart ( generally its launch ) v5.0.0 build 258 14 days Access! 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Access to USENET accurate stopwatch with lap times and alarms Buddy ( WTB ) a. Games offers online Games and printable worksheets to make learning math fun clock... Between systems, but they should n't be math problems involving time local time clock, can! To use and accurate stopwatch with lap times and alarms an activity and frequently ask when will... Equation to keep your math problems using our free math solver with step-by-step solutions in fact correct! Days, hours, minutes and seconds one-time alarms using voice commands like white..
5 Minute Crafts Barbie Makeup, I Will Wait For You Movie 1994, Robert Plant Now And Zen, Reception Supervisor Job Description, Kuta Software - Infinite Algebra 1 Factoring Special Cases, Eastern Caribbean Supreme Court Vacancies, Different Types Of Scissors For Cutting Paper, | 2022-01-26 18:16:38 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.1758357137441635, "perplexity": 3551.1040818817387}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320304959.80/warc/CC-MAIN-20220126162115-20220126192115-00617.warc.gz"} |
http://disney.wikia.com/wiki/We_Call_it_Maze | ## FANDOM
44,260 Pages
“ Mazes should be big, fun and exciting. ” — Phineas Flynn, talking about mazes
"We Call it Maze" is an episode of Phineas and Ferb.
Phineas and Ferb create a life sized maze filled with fun obstacles. Melissa, the leader of the Little Sparks, a younger branch of the Fireside Girls, is immediately captivated when she meets Candace and finds out that she was a Fireside Girl who earned 50 patches in one day. When the girls try out the maze, Candace takes charge, but things don't go as planned. Meanwhile, Dr. Heinz Doofenshmirtz reasons that if the Leaning Tower of Pisa can generate souvenir revenue, then surely he can use his latest invention, the "Tilt-inator," to tilt buildings so he can sell souvenir replicas.
## Episode Summary
Phineas and Ferb are eating cereal in the kitchen. He notices the easy maze on the back on the cereal box for Korny to get out of. He said if he was Korny, he'd want a bigger challenge. Phineas sighs and is slightly unhappy about the fact that nobody is making good puzzles or mazes anymore. He thinks they should big, fun, and exciting. Phineas was about to say his catchphrase, "I know what we're gonna do today", but Ferb interrupts him, because he doesn't need to say it. Phineas says "What'cha doin'?" to Candace, who is on rollerskates and is struggling to stay on them. Candace says that she could use some practice, but she crashes off-screen and says that she is okay. Phineas then wants to get started on the maze, but notices Perry is missing.
Perry is in the kitchen and puts his fedora on, and goes to his lair from an exhaust, but he is very dirty afterward. Major Monogram says good morning to him, and then he notices the very dirty Perry. He is sorry about not cleaning the entrance in a while. A robot gives a towelette to clean him up. Mongram then gives Perry his mission: Heinz has gone missing and they used thr global location scout to try to find him, but can't find anywhere in the world. The answering machine also yields no results, with Heinz saying "Hello! You've reached Dr. Heinz Doofenshmirtz! I'm not here right now. or am I", then does an evil laugh then says "If you're calling about the piano, it's already been sold." Monogram wants Perry to find him, then gives good luck and salutes him as Perry has finished cleaning himself up, and Monogram had finished his briefing. Perry runs to go find Heinz.
Phineas and Ferb have finished their maze and ready to test it out. Just then, Baljeet quickly enters and wonders if it is a test, but Phineas says it isn't a test, but it is more like lab rats going after cheese. Buford comes by, and wonders who said cheese, but Phineas said it was a metaphor. Buford then talks about cheese and crackers and gets in the elevator to go to the maze. Isabella and the Lil' Spark, Melissa comes by while Melissa is talking about getting her Zookeeping Patch, Cooking patch, and Astronomy patch. Isabella tells she that she is just like herself when she was a Lil' Spark. Melissa wonders if she can get as many patches as Isabella when she becomes a Fireside Girl. Isabella thinks with her positve ideas, she will probably earn even more in the future. Melissa wonders if this is possible, since she wants to be the best Fireside Girl ever and just be like Isabella.
Isabella and Melissa come to Phineas, Ferb, Baljeet, and Buford and Isabella introduces Melissa to the others. Melissa says that Isabella is her mentor for the day. She also says she is the best Fireside Girl ever, but Isabella doesn't think they want to know about it. Candace comes by and Phineas says hi to her. Candace sees the maze in the backyard and knows what she has to do, but she slips on her roller skates and pulls the lever to make the elevator go up to the maze. Candace wonders what it is and Phineas says that it is the elevator to the top of the maze. Cnadace wants it to go down, but Phineas says that it can't go down, as it only goes up. Candace says that they will go down.
Perry arrives to Doofenshmirtz Evil Incorporated by his hover jet and notices a smaller version of Heinz Doofenshmirtz with a pullstring. The fake Doof says, "Hello Perry the Platypus. Sorry I'm not here to greet you myself, but this is........ a trap." After it finished speaking, Perry was trapped in a very small rocket to Heinz which is somewhere in space.
Candace wonders why there isn't an elevator that doesn't go down. Phineas says they might go down instead of going through the maze. Candace wonders what he means by that. The camera pans out to show the size of the maze. Phineas had put in a computer to have random puzzles and brainteasers to have it be more of a challenge. Phineas says that the first one out is the smartest rat in the lab. Isabella wonders if Melissa wants to go through the maze with her, of which she agrees with. The Fireside Girl leader wonders if Candace wants to go with her and Melissa, of which Candace declines, saying she can find her own way out. Melissa realizes that Candace got 50 patches in one day and runs to her. She shows a cover of the Lil' Sparks magazine, of which Candace is on. Melissa wonders how she did it, of which Candace responded that it wasn't easy, but the "Forestfire Girls" really needed her, but Isabella corrected her and said that is was Fireside Girls, but Candace sarcastically said it right. Candace and Melissa go off, leaving Isabella behind, and Melissa is happy for having Candace leading them to safety. Isabella shrugs on being mad, and takes off with them.
Buford tells Baljeet that he'll do the puzzles on teasing, and Baljeet will do the ones on brains. Baljeet doesn't think Buford got the concept. He then pushed Baljeet to a screen with buttons, then the song Not Knowing Where You're Going starts. Everyone then tries to find a way to get out of the maze. Candace thinks to go one direction with Melissa and Isabella watching - only to come out where she came from. While Phineas and Ferb are running, Melissa finds a key to let her, Isabella, and Candace go to somewhere else. Phineas, Ferb, and Baljeet are then seen bouncing on springs. The girls try to blow a boat to the other side so they can go to a new place. Ferb then plays a game of chess - which then lets the four boys go in the maze. Melissa tried, but missed getting a basketball shot with Isabella, but she does gets it with Candace with a slam dunk. Ferb tries to get a key while dressed as Indiana Jones, and quickly places a bag in the key's place, which then opens a new door. Candace tries the same way she went earlier again - only to be back where she was. Phineas and Ferb are seen putting a puzzle together to open a door. The girls then play skee-ball and hit the center opening, making them slide downward. Phineas and Ferb move panels to get another door open for them. Candace tries for a 3rd time in exactly the same place as the first two times - only again to find herself back at her first position - with the Giant Floating Baby Head going past.
Perry seen is transported to a space version of Doofenshmirtz Evil Incorporated, and sees Heinz Doofenshmirtz in a space suit. He welcomes Perry to his space station, which he echos - but one of them is broke. Heinz thinks his echo is broken and really does thinks so. Perry gets on a chair that can from under him for Heinz to do a presentation. 10 years ago, Heinz had been backpacking around Europe, when he came across some Canadian college students. Dillion was the most popular one of them, but Heinz was the oldest.
Back to the maze, Buford notices a jar full on jellybeans. Baljeet says he is really good at that type of problems. All the boys (except Buford) start making calculations. Baljeet wonders why Phineas is measuring in centimeters. Phineas, though is working in fractions, and says that Pi is 22/7. Baljeet wonders why he isn't using 3.14 for Pi. Buford then gets angry and eats the entire jar of jellybeans. He puts it back and presses 0 on the keypad, which opens a door. Baljeet says that is technically correct, but he forgot to show his work. Buford, talking off-screen, says he will in about 20 minutes.
In space, Heinz finishes his story, and says he is never welcome in Albania ever again. He had ended up in Italy and went to the Leaning Tower of Pisa, but they didn't make pizza there. he complains that it had pizza in the name. Since they were out of it, he didn't get any pizza. Then he got his idea: He'd lean his building to be a tourist attraction, and he'd make millions, which would finance part two of his plan: Tilting every building in the world and would make the Leaning Tower of Pisa no longer special and he'd make his building straight and it would be the only straight building in the world, of which he had just thought of it. He shows Perry the Tilt-Inator to he would use from space. Once again, his second to last echo gets broken and he says he will need to have that checked.
With the girls, Isabella notices a high-wire challenge ahead, and mentioned that she got a patch for it two times. Candace, acting angry, wants to know if she had got 50 in one day. Isabella then gets mad about it. Candace tries to tell Melissa about a high wire, but Candace is rollerskating onto it, and Isabella tells her to be careful. Candace gets unstable, does a few bounces, then lands safely on the other side, saying it is that simple. Melissa then tries to go on the wire, but she slips and hangs on by a hand, which scares Candace. She tells Isabella to do something. Isabella quickly, but carefully, grabs Melissa's hand just in time and throws her to Candace. Melissa then hugs Candace for telling Isabella to save her. Candace told her that Isabella could let her fall. Isabella, unhappy, is glad that she could help.
With Heinz and Perry, the Tilt-Inator is set to a time of 3:15. Once it was activated, even he said that he can't stop it. He then opened the doors for the machine to do its job. He says it may take a while. Melissa wonders how far down is the hole they are at inside the maze, but Isabella can't see the bottom, because it is too dark. She says it doesn't matter as long as they get across it. Candace, however says they need to know how deep it is, so they know how scared they should be. She then throws a grappling hook and rope down the floor, of which it is 3 seconds deep.
Heinz has finished opening the doors of the space station. In 15 seconds, his building will be leaning into the Leaning Tower of Doofenshmirtz. There was no self-destruct button, reverse levers, or abort switches on the Tilt-Inator, which meant it was completely Perry the Platy-proof. Perry removed the metal stick that was holding the doors open for the Tilt-Inator to work, and the doors close. Heinz, after seeing that the doors were closed, frantically tries to stop the machine by pressing buttons, but to no avail. The laser shoots onto the doors, but does nothing. He quickly reopens the doors and resets the time so it can fire again.
In the maze, Isabella says it would be nice to have a grappling hook and some rope. Candace knows where it is - but she already used it by throwing it down the edge of the level they were at. The platform beneath the girls starts to close to a the wall. Candace panics, and wonders what should they do. Isabella reminds her that she was the Fireside Girl who earned 50 patches in one day. Melissa agrees, and she says that Candace will get them out of trouble. Candace says it was a fake, since she wanted to get to a concert, and if it wasn't for Isabella and her bothers, she wouldn't have done it. Melissa gasps when she hears that. Candace then talked to one of the girls, saying that she wants to be saved. Isabella tells Candace to giver her one of Candace's rollerskates. She twirls it around, then hooks it on a nearby pipe. Candace and Melissa grab onto Isabella and they fly off to a platform, which then goes back inside. Candace, irritated, says that Isabella was the perfect Firefighter Girl and was supposed to save them. Isabella corrects her again and says that she is a Fireside Girl, of which Candace said that is what she said. Isabella notices a lever in the middle, but she nor Candace can't reach it. She thinks that the rope was longer than Candace's shoelace, of which made Candace think it was her fault. Melissa realized that Candace still had another shoelace. She falls safely to where the shoelace was, unties it for an extension, pulls the lever, and the three land safely in the backyard. Candace, who fell down, still had time to bust the boys before her skate date, goes to get mom. Isabella and Melissa then walk off so the Lil' Spark can get home.
Heinz had just finished opening the doors on his space station and now can fire at his own building. Perry though places a snowglobe that he had from earlier into the laser fire thing and makes it unstable and the laser hits the maze, causing it to lean and go away from the backyard - just before Candace can show Linda what was in the backyard. Linda wonders, "What giant maze?" Candace said it was right there. Linda and Candace go inside the house, and Linda closes the door.
Perry gets back inside the small rocket just before the space station flys off in space. Meanwhile, the maze is still rolling with the boys inside. Baljeet thought Phineas and Ferb had thought of everything - except running on the maze's inside on its side. They find a hole in the maze and stop there at Cliffside Park, with no time to spare as the maze rolls down a steep hill and gets destroyed when it hits the ground, causing the ground to shake. Buford mentions that the hill was 3 seconds deep. Phineas thinks it's a good thing the girls beat them out of the maze. They see Isabella loading Melissa onto a Lil' Sparks bus, waving bye and saying that she will see her next week. Phineas is glad everything worked out just fine. Buford echos that he never got his metaphor of cheese. The episode ends when Buford notices that his echo is broken.
## Running Gags
None.
### Ferb's Line
Phineas and Ferb are eating their breakfast, and Phineas is watching the cereal box
Phineas: It's said on this box of cereal that I need to get Korny the Kornflake through this maze.
He shows the other side of the box, when it's showed a maze with a blank space from Korny to the exit
Phineas: If I was Korny, I'd want a little more of a challenge. They don't make good puzzles or mazes anymore. Mazes should be big, fun and exciting. Ferb...
Ferb: You don't even need to say it.
During the jellybeans segment, Ferb repeatedly opens his mouth as if he wants to say something, but Phineas and Baljeet keep talking.
### Whatcha doin'?
Candace is seen in the background skating, trying to not to fall
Phineas: Hey, Candace. Whatcha doin'?
Candace stops and is rolling backwards
Candace: Well, Jeremy is taking me roller skating tonight, and I need a little prac- Ah!
Candace screams followed by the sound of a crash
Candace: I'm okay!
### Perry's entrance to his lair
He enters through the exhaust in the kitchen, and is covered in soot as he lands in his chair.
### I know what we're gonna do today
Phineas and Ferb are eating their breakfast, and Phineas is watching the cereal box
Phineas: It's said on this box of cereal that I need to get Korny the Kornflake through this maze.
He shows the other side of the box, when it's showed a maze with a blank space from Korny to the exit
Phineas: If I was Korny, I'd want a little more of a challenge. They don't make good puzzles or mazes anymore. Mazes should be big, fun and exciting. Ferb...
Ferb: You don't even need to say it.
### Hey, where's Perry?
Phineas: Let's get started. Hey, where's Perry?
### Evil Jingle
Doofenshmirtz Evil Incorporated!
## Memorable Quotes
Major Monogram is talking to Perry about Dr. Doofenshmirtz not being on Earth
Major Monogram: Even his answering machine doesn't give us a clue where he is.
Doofenshmirtz answering machine: Hello, you reached Dr. Heinz Doofenshmirtz, I'm not here right now... Or am I? (Laughs Maniacally) Oh, if you're calling for the piano, it's already been sold.
Phineas: Time to test our maze.
Baljeet: Did somebody say 'test'?
Phineas: It's not really a test. We're more like lab rats going after cheese.
Buford: Did somebody say 'cheese'?
Phineas: Buford, that's just a metaphor.
Buford: Hmm. I am to metaphor cheese as metaphor cheese is to transitive verb crackers!
Perry enters to D.E. Inc. to find a Doofenshmirtz talking doll, so he pulls the cord in every pause
Doofenshmirtz doll: Hello Perry the Platypus... sorry I'm not here to greet you myself but this is... a trap.
Doofenshmirtz doll transforms into a rocket and sends Perry into space
Isabella: You wanna go through the maze with me?
Melissa: Yes, yes, yes.
Isabella: Candace, would you like to join Melissa and me?
Candace: Candace Flynn can find her own way out.
Melissa: Oh my gosh, you're Candace Flynn. You're the girl who won fifty patches in one day. You're on the cover of Lil' Sparks magazine, how did you do it?
Candace: (Signing the magazine) Well... Let me tell you something kid, it wasn't easy but the Forestfire Girls really needed me.
Isabella: Fireside Girls.
Candace: That's what I said. Come on kids, I'll get us out of here.
Melissa: Yeah, Candace is gonna lead us to safety!
Isabella annoyingly follows them
Dr. Doofenshmirtz: Ah, Perry the Platypus. Welcome to my evil space station!
Dr. Doofenshmirtz's echo: Station... station... cookie... station...
Dr. Doofenshmirtz: Wait, did you hear that? The "cookie" part? I think my echo is broken, I really do. Any who...
Buford: How many jellybeans in the jar?
Baljeet: Oh, I'm really good on solving these kind of problems.
Phineas: The base of the jar is Pi times radius squared.
Ferb wasn't given a chance to speak
Baljeet: You're measuring in radius in centimeter, right?
Phineas: No, inches. That way the inches factions is rounded by the Pi of 22 over 7.
Baljeet: You do not use 3.14 for Pi--
Buford: Oh, for crying out loud!
Buford eats all of the jellybeans in the jar
Buford: There, zero.
Door opens to the next path.
Baljeet: Okay, technically that was correct, but you did not show your work.
Buford: I will in about 20 minutes.
Dr. Doofenshmirtz is showing to Perry a few diapositives (it's a projector, not a retrospective) about his trip to Europe 10 years ago.
Dr. Doofenshmirtz: ...then the Ambassador's wife filed a complaint... Long story short, I am never welcome in Albania ever again. But the point is, it was lunchtime and I ended up alone in Italy, so I went to the Leaning Tower of Pizza, and you know what? They don't even make pizza there! And so what do they mean? It's the Leaning Tower of Pizza! It's got " pizza" actually in the name! But they were adamant. "No pizza for you!" Kinda like "I'm the idiot." I was like, "You're not so great. You're not so special. What? Just 'cause you're leaning?"
Dr. Doofenshmirtz sent his building to space and built an Tiltinator that can lean all buildings
Dr. Doofenshmirtz: ...I built this Tiltinator and I'm gonna do it all from space!
Dr. Doofenshmirtz's echo: Space... space... cookie... space...
Dr. Doofenshmirtz: There, there it was again? Did you hear that? My second to last echo is broken, I'm going to have that checked.
Melissa: Oh my gosh, thank you for telling Isabella to save me.
Candace: Oh, what do you think I was going to do? Let Isabella let you fall?
Isabella: (flatly) Glad I was able to help.
Isabella: Oh, would you look at that?
Candace: The platform's retracting! What are we gonna do?
Isabella: You're the one who got 50 Fireside patches in one day.
Melissa: That's right! Candace will get us out of this! Won't you, Candace?
Candace: That was a fake! I only did it to get into a concert. If it wasn't for Isabella and my brothers, I never could have done it!
Melissa gasps.
Candace: Now will you please save me?!
They swing and failed to reach the other side.
Candace: Oh, this is just great! I thought you're gonna save us. I- I thought you were suppose to be this perfect Firefighter Girl.
Isabella: Fireside Girl!
Candace: That's what I said.
Isabella: Wait, there's a lever in the middle, but I can't reach it.
Candace: Well, I can't reach it, either!
Isabella: I bet the rope you threw away was longer than your shoelace.
Candace: Oh, so this is my fault?
Buford, Baljeet, Phineas, and Ferb get out of the maze before it crashes to the bottom
Buford: Wow! That was a least 3 seconds deep.
Phineas: It was a good thing the girls beat us out.
Isabella takes Melissa to the Lil' Sparks bus.
Isabella: Bye Melissa, see you next week.
Phineas: Everything worked out just fine.
Buford: Hey, I never got my metaphor cheese!
Buford's echo: Cheese... Cheese... Wombat... Cheese...
Buford: Huh? My echo must be broken.
## Background Information
• This episode reveals that the Fireside Girls has a sub-organization called "Lil' Sparks" that helps young girls to become Fireside Girls, and Isabella was once a Lil' Spark. This is similar to Camp Fire USA's program that trains you to be a Camp Fire Boy/Girl; "Little Stars".
• A member of the Lil' Sparks makes an appearance and is named Melissa. She has blonde hair with pig-tails, and freckles. Her uniform has a red belt, pleats on her skirt, and black shoes.
• When Ferb hangs up his Indiana Jones outfit, what appears to be a stone figure of Abraham Lincoln can be seen.
• For the first time, Doofenshmirtz shows knowledge of other languages to causes him troubles during his trip around the world a few years ago.
• It takes about 3 seconds for the rope to fall to the ground, about $d = -4.9(3)^2$ equal to -44.1 meters.
• At the end of the episode, Buford says there was no cheese, though in the maze, there was what looks like cheese on springs.
• As shown in this episode, Ferb can play chess.
• When Phineas tells Buford that the cheese is a metaphor, he then makes an analogy.
• This is the 104th episode that ran in the US, matching the number of days Phineas and Ferb have of summer vacation.
• This is the last episode of Season 2 in which Isabella wears her Fireside Girl uniform. She isn't seen wearing it again until "The Great Indoors" in Season 3.
• There is a running gag in which someone of something interrupts Ferb. In this episode, it is reversed and Ferb interrupts someone, in this case, Phineas.
• A running gag in this episode is that Candace keeps misnaming "Fireside" . First, she says "Forest Fire", then "Firefighter."
## Production Information
• Premiered on Disney Channel on Demand on September 17, 2010.
• This episode first aired on Disney Channel Latin America on July 22, 2010 entitled "El Laberinto" ("The Labyrinth"), also in Disney Channel Taiwan on August 8, 2010, in English in Disney Channel Hong Kong on August 8, 2010 and in Disney Channel Asia on August 22, 2010, and in Disney Channel Brazil on August 20, 2010 entitled "O Nome Disso É Labirinto".
### International Premieres
• July 22, 2010 (Disney Channel Latin America)
• August 8, 2010 (Disney Channel Taiwan)
• August 20, 2010 (Disney Channel Brazil)
• August 22, 2010 (Disney Channel Asia)
• September 6, 2010 (Disney XD Poland)
• November 5, 2010 (Disney Channel Netherlands/Flanders)
• November, 14, 2010 (Disney XD France)
• December 5, 2010 (Disney XD Spain)
• December 16, 2010 (Disney Channel Spain)
• February 7, 2011 (Disney XD UK)
• February 11, 2011 (Disney Channel Scandinavia)
• March 18, 2011 (Disney XD Scandinavia)
## Errors
• When Melissa shows Candace the photo with her in it when she was a Fireside Girl, the shirt is all white instead of orange and white.
• During most of the episode, Perry's eyes are blue when they should be brown. The only times they are brown is during his mission briefing and when he is pulling the string on the Doofenshmirtz toy/trap.
• During Not Knowing Where You're Going, when Phineas, Ferb, and Baljeet are hopping on cheese springs, Buford is not with them
• When one of the doors Candace, Isabella, and Melissa were trying to get to was seen the first time, it was closed. But when it was seen the second time, it appears to be opened.
• When Isabella loads Melissa on to the Lil' Sparks bus, her beret isn't on. Instead, her red bow is on her head. This was the exact case in Flop Starz where she didn't wear a beret, but had her red bow on.
• When Linda grabs Candace's arm and turns to pull her inside, the space between her legs turn white for a single frame.
• Candace does not skate well in this episode, but in "Vanessassary Roughness" she was skating very well. However, this may have taken place before that episode.
• As Candace, Isabella, and Melissa are swinging on the rope attempting to reach the lever, the middle square of Candace's belt continuously switches colors from maroon to white and back again, and at one point, the white shoelace looks like a rope.
• When Doofenshmirtz first sets the timer on the Tilt-Inator, it appears to start from 3:15, but when he has to reset it again, the timer seems to start from 3:00.
• Technically, since Doofenshmirtz and Perry were in space, there should have been no echo, because sound requires air to move (which would be required to make an echo), and there is no air in space.*If you look closely at the door during the scene with Candace and Linda, you can see the area in the door has the wall and floor of the living room. Usually it leads to the kitchen.
• "We're like lab rats going after cheese" is actually a simile, not a metaphor as metaphors don't use the word "like". A metaphor version of that sentence would be "We are lab rats going after cheese."
• Perry takes out the screwdriver to close the door, but in space there shouldn't be enough gravity to close the door.
• When Perry puts the snowglobe at the hole of the Tilt-Inator, it is set at almost 3 minutes, but when Doofenshmirtz tries to remove the snow globe, it changes to about 3 seconds.
• In the song Not Knowing Where You're Going, when Ferb has beaten the mechanical knight, one of the chess pieces turned digitalized for a second then later it went back to normal.
• Perry wore a spacesuit when the rocket that has trapped him landed in Doofenshmirtz's space station, but when Perry got trapped in the rocket, he didn't have the spacesuit on.
• When Phineas says "It's a good thing the girls beat us out", Ferb's big eye is facing the audience.
• Candace does not skate well in this episode, but in "Vanessassary Roughness" she was skating very well. However, this may have taken place before that episode.
• In the scene where Candace, Isabella, and Melissa are seen swinging backwards after the exiting platform retracts, if one looks closely, Melissa's socks are missing.
## Allusions
• The title is a parody of a famous Mazola Margarine commercial in which a Native American states, "You call it corn, we call it maize."
• Indiana Jones - When Ferb switches the key with a bag of sand, it is similar to the famous scene from Raiders of the Lost Ark. Also, when Candace, Isabella, and Melissa are swinging by the shoelace, the music is based on the Raiders march.
• Star Wars - Candace, Isabella, and Melissa swinging from one platform to another is similar to the scene where Luke and Princess Leia swing across a pit in the Death Star.
• The Legend of Zelda - When Baljeet is talking right before the song starts, the triangle behind him looks very similar to the Triforce in the Legend of Zelda series, which is usually maze or puzzle themed.
• Seinfeld - Doofenshmirtz claims that the people at the Leaning Tower of Pisa were adamant about saying "No Pizza For You." This is very similar to a line frequently spoken by the "Soup Nazi" from Seinfeld.
• Harry Potter and the Philosopher's Stone/Sorcerer's Stone - Ferb winning at chess in order to progress is similar to one of the task Harry Potter and his friends must pass to find the philosopher's stone.
• Scooby Doo - When Candace, Isabella and Melissa run through the maze in a hallway, it is similar to a Scooby Doo-style chase.
• Banjo-Kazooie- When the boys make a door out of puzzle pieces, it is similar to how jigsaw puzzle pieces are used to unlock new levels in Banjo-Kazooie.
• Girl Guides of Canada - The Girl Guides' (similar to the Girl Scouts of America) youngest level, which is comprised of girls ages 5 and 6, is called the Sparks.
## Trivia
This page uses Creative Commons Licensed content from the The Phineas and Ferb Wiki. The list of authors can be seen in the page revision history (view authors). As with Disney Wiki, the text of The Phineas and Ferb Wiki is available under the CC-by-SA Free Documentation License.
v - e - d
Disney Parks
Entertainment: Phineas and Ferb's Rockin' Rollin' Dance Party
Firework: Celebrate the Magic
Characters
Major Characters: Phineas FlynnFerb FletcherCandace FlynnPerryMajor Francis MonogramHeinz DoofenshmirtzLinda FlynnLawrence Fletcher
Episodes
Season One: "Rollercoaster" • "Candace Loses Her Head" • "The Fast and the Phineas" • "Lawn Gnome Beach Party of Terror" • "The Magnificent Few" • "S'Winter" • "Are You My Mummy?" • "Flop Starz" • "Raging Bully" • "Lights, Candace, Action!" • "Get That Bigfoot Outta My Face!" • "Tree to Get Ready" • "It's About Time!" • "Jerk De Soleil" • "Toy to the World" • "One Good Scare Ought to Do It!" • "A Hard Day's Knight" • "I, Brobot" • "Mom's Birthday" • "Journey to the Center of Candace" • "Run Away Runway" • "I Scream, You Scream" • "It's a Mud, Mud, Mud, Mud World" • "The Ballad of Badbeard" • "Dude, We're Getting the Band Back Together" • "Ready for the Bettys" • "The Flying Fishmonger" • "Phineas and Ferb Get Busted!" • "Greece Lightning" • "Leave the Busting to Us!" • "Crack That Whip" • "The Best Lazy Day Ever" • "Boyfriend From 27,000 B.C." • "Voyage to the Bottom of Buford" • "Put That Putter Away" • "Does This Duckbill Make Me Look Fat?" • "Traffic Cam Caper" • "Bowl-R-Ama Drama" • "The Monster of Phineas-n-Ferbenstein" • "Oil on Candace" • "Unfair Science Fair" • "Unfair Science Fair Redux (Another Story)" • "Out to Launch" • "Got Game?" • "Comet Kermillian" • "Out of Toon" • "Hail Doofania!"
Season Two: "The Lake Nose Monster" • "Interview With a Platypus" • "Tip of the Day" • "Attack of the 50 Foot Sister" • "Backyard Aquarium" • "Day of the Living Gelatin" • "Elementary My Dear Stacy" • "Don't Even Blink" • "Chez Platypus" • "Perry Lays an Egg" • "Gaming the System" • "The Chronicles of Meap" • "Thaddeus and Thor" • "De Plane! De Plane!" • "Let's Take a Quiz" • "At the Car Wash" • "Oh, There You Are, Perry" • "Swiss Family Phineas" • "Hide and Seek" • "That Sinking Feeling" • "The Baljeatles" • "Vanessassary Roughness" • "No More Bunny Business" • "Spa Day" • "Phineas and Ferb's Quantum Boogaloo" • "Phineas and Ferb Musical Cliptastic Countdown" • "Bubble Boys" • "Isabella and the Temple of Sap" • "Cheer Up Candace" • "Fireside Girl Jamboree" • "The Bully Code" • "Finding Mary McGuffin" • "Picture This" • "Nerdy Dancin'" • "What Do It Do?" • "Atlantis" • "Phineas and Ferb Christmas Vacation!" • "Just Passing Through" • "Candace's Big Day" • "I Was a Middle Aged Robot" • "Suddenly Suzy" • "Undercover Carl" • "Hip Hip Parade" • "Invasion of the Ferb Snatchers" • "Ain't No Kiddie Ride" • "Not Phineas and Ferb" • "Phineas and Ferb-Busters!" • "The Lizard Whisperer" • "Robot Rodeo" • "The Beak" • "She's the Mayor" • "The Lemonade Stand" • "Phineas and Ferb Hawaiian Vacation" • "Summer Belongs to You!" • "Nerds of a Feather" • "Wizard of Odd" • "We Call it Maze" • "Ladies and Gentlemen, Meet Max Modem!" • "The Secret of Success" • "The Doof Side of the Moon" • "Split Personality" • "Brain Drain" • "Rollercoaster: The Musical!" • "Make Play" • "Candace Gets Busted"
Season Three: "The Great Indoors" • "Canderemy" • "Run, Candace, Run" • "Last Train to Bustville" • "Phineas' Birthday Clip-O-Rama!" • "The Belly of the Beast" • "Moon Farm" • "Ask a Foolish Question" • "Misperceived Monotreme" • "Candace Disconnected" • "Magic Carpet Ride" • "Bad Hair Day" • "Meatloaf Surprise" • "Phineas and Ferb Interrupted" • "A Real Boy" • "Mommy Can You Hear Me?" • "Road Trip" • "Tour de Ferb" • "Skiddley Whiffers" • "My Fair Goalie" • "Bullseye!" • "That's the Spirit" • "The Curse of Candace" • "Escape from Phineas Tower" • "Lotsa Latkes" • "Ferb Latin" • "A Phineas and Ferb Family Christmas" • "Tri-Stone Area" • "Doof Dynasty" • "Excaliferb" • "Phineas and Ferb and the Temple of Juatchadoon" • "Monster from the Id" • "Gi-Ants" • "The Remains of the Platypus" • "Mom's in the House" • "Perry the Actorpus" • "Let's Bounce" • "Bully Bromance Break Up" • "Quietest Day Ever" • "Doonkleberry Imperative" • "Meapless in Seattle" • "Delivery of Destiny" • "Buford Confidential" • "The Mom Attractor" • "Cranius Maximus" • "Agent Doof" • "Minor Monogram" • "What a Croc!" • "Sleepwalk Surprise" • "Sci-Fi Pie Fly" • "Sipping with the Enemy" • "Tri-State Treasure: Boot of Secrets" • "Doofapus" • "Norm Unleashed" • "Where's Perry?" • "Ferb TV" • "When Worlds Collide" • "What'd I Miss?" • "Road to Danville" • "This is Your Backstory" • "Blackout!"
Season Four: "For Your Ice Only " • "Happy New Year!" • "Fly On the Wall" • "Bully Bust" • "My Sweet Ride" • "Der Kinderlumper" • "Sidetracked" • "Primal Perry" • "Mind Share" • "Backyard Hodge Podge" • "Bee Day" • "Bee Story" • "Great Balls of Water" • "Where's Pinky?" • "Phineas and Ferb Musical Cliptastic Countdown Hosted by Kelly Osbourne" • "Knot My Problem" • "Just Desserts" • "La Candace-Cabra" • "Happy Birthday, Isabella" • "Love at First Byte" • "One Good Turn" • "Mission Marvel" • "Thanks But No Thanks" • "Troy Story" • "Druselsteinoween" • "Terrifying Tri-State Trilogy of Terror" • "Face Your Fear" • "Cheers for Fears" • "Steampunx" • "Just Our Luck" • "Return Policy" • "Live and Let Drive" • "Phineas and Ferb Save Summer" • "Father's Day" • "Imperfect Storm" • "The Return of the Rogue Rabbit" • "It's No Picnic" • "The Klimpaloon Ultimatum" • "Operation Crumb Cake" • "Mandace" • "Phineas and Ferb: Star Wars" • "Lost in Danville" • "The Inator Method" • "Night of the Living Pharmacists" • "Tales from the Resistance: Back to the 2nd Dimension" • "Doof 101" • "Act Your Age" • "Last Day of Summer" • "O.W.C.A. Files"
Locations
Locations at or near Danville: DanvilleSeattleMr. Slushy FranchiseDoofenshmirtz Evil IncorporatedFlynn-Fletcher HouseAtlantisGoogolplex MallOld Abandoned Amusement Park | 2018-03-24 12:56:08 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 1, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3202155530452728, "perplexity": 11004.986135532487}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257650262.65/warc/CC-MAIN-20180324112821-20180324132821-00696.warc.gz"} |
https://www.eduzip.com/ask/question/in-the-figure-given-above-if-ac-ad-cd-bd-then-angle-abc-is160-305-521135 | Mathematics
# In the figure given above, if $AC= AD= CD= BD$; then $\angle ABC$ is $30.5^{\circ}$If true then enter $1$ and if false then enter $0$
1
##### SOLUTION
In $\triangle$ ACD,
Since, AC = CD
$\angle CAD = \angle CDA = x$ (Angles opposite to equal sides are equal)
Sum of angles of the triangle,
$\angle ACD + \angle CAD + \angle CDA = 180$
$58 + 2x = 180$
$2x = 122$
$x = 61$
In $\triangle ABD$,
AD = BD thus, $\angle ABD = \angle DAB = y$
Also, $\angle ABD + \angle DAB = \angle ADC$ (Exterior angle is equal to sum of opposite interior angles)
$2\angle ABD = 61$
$\angle ABD = 30.5^{\circ}$
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One Word Medium Published on 09th 09, 2020
Questions 120431
Subjects 10
Chapters 88
Enrolled Students 151
#### Realted Questions
Q1 Single Correct Medium
$AB$ is a straight line and $O$ is a pont lying on $AB$. A line $OC$ is drawn from $O$ such that $\angle COA={36}^{o}$. $OD$ is a line within $\angle COA$ such that $\angle DOA=\cfrac{1}{3}$ $\angle COA$. If $OE$ is a line within the $\angle BOC$, $\angle BOE=\cfrac{1}{4}\angle BOC$, then $\angle DOE$ must be:
• A. ${60}^{o}$
• B. ${132}^{o}$
• C. ${144}^{o}$
• D. ${108}^{o}$
Asked in: Mathematics - Lines and Angles
1 Verified Answer | Published on 09th 09, 2020
Q2 One Word Medium
Find the numerator of the simplest ratio in which the join of $(- 5, 1)\ and\ (1, - 3)$ divides the st. line passing through (3,4) and (7,8).
Asked in: Mathematics - Lines and Angles
1 Verified Answer | Published on 09th 09, 2020
Q3 Single Correct Medium
In the figure given above, $PQ$ is parallel to $RS$. What is the angle between the lines $PQ$ and $LM$?
• A. $175^{\circ}$
• B. $177^{\circ}$
• C. $179^{\circ}$
• D. $180^{\circ}$
Asked in: Mathematics - Lines and Angles
1 Verified Answer | Published on 09th 09, 2020
Q4 Single Correct Medium
Straight angle is-
• A. $\displaystyle 30^{0}$
• B. $\displaystyle 45^{0}$
• C. $\displaystyle 180^{0}$
• D. $\displaystyle 120^{0}$
Asked in: Mathematics - Lines and Angles
1 Verified Answer | Published on 09th 09, 2020
Q5 Subjective Medium
Calculate the followings. 1 An angle is equal to one third of its supplement. Find its measure. 2 If an angle is ${30^ \circ }$ more than one half of its complement, find the measure of the angle.
Asked in: Mathematics - Lines and Angles
1 Verified Answer | Published on 09th 09, 2020 | 2022-05-21 13:07:28 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6895066499710083, "perplexity": 3687.9214832112134}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662539101.40/warc/CC-MAIN-20220521112022-20220521142022-00501.warc.gz"} |
https://socratic.org/questions/how-to-simplify-6-3-times-10-5-9-times-10-3-in-scientific-notation | # How to simplify (6.3 times 10^5) ÷ (9 times 10^3) in scientific notation?
Mar 18, 2018
$7.0 \times 10$
#### Explanation:
$6.3 \times {10}^{5}$ is the same value as $63 \times {10}^{4}$
So we have:
$\frac{63 \times {10}^{4}}{9 \times {10}^{3}} \textcolor{w h i t e}{\text{ddd") -> color(white)("ddd}} \frac{63}{9} \times {10}^{4} / {10}^{3}$
$\textcolor{w h i t e}{\text{ddddddddd.d")->color(white)("ddd}} \frac{63}{9} \times 10$
If the sum of the digits is exactly divisible by 3 then the actual number is also exactly divisible by 3 $\to 6 + 3 = 9$ so we will divide both top and bottom by 3 to simplify the fraction.
$\textcolor{w h i t e}{\text{ddddddddd.d")->color(white)("ddd}} \frac{63 \div 3}{9 \div 3} \times 10$
Note that:
$\frac{63 \div 3}{9 \div 3} = \frac{21 \div 3}{3 \div 3} = \frac{7}{1} = 7$ so we have:
$\left(6.3 \times {10}^{5}\right) \div \left(9 \times {10}^{3}\right) = 7.0 \times 10$ | 2020-08-10 03:02:52 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 9, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9515449404716492, "perplexity": 580.4844728420895}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439738603.37/warc/CC-MAIN-20200810012015-20200810042015-00583.warc.gz"} |
http://keisan.casio.com/exec/system/1180573202 | # Hypergeometric distribution (chart) Calculator
## Calculates a table of the probability mass function, or lower or upper cumulative distribution function of the hypergeometric distribution, and draws the chart.
select function probability mass f lower cumulative distribution P upper cumulative distribution Q sample size n n=0,1,2,.. n≦N successes of lot M M=0,1,2,.. x≦M lot size N N=0,1,2,.. M≦N [ initial percentile x(successes of sample) x=0,1,2,.. x≦n increment repetition ]
$\normal Hypergeometric\ distribution\\[10](1)\ probability\ mass\\\hspace{30}f(x,n,M,N)={\large\frac{{}_MC_x\ {}_{N-M}C_{n-x}}{{}_NC_n}}\\(2)\ lower\ cumulative\ distribution\\\hspace{30}P(x,n,M,N)={\large\sum_{t=0}^{x}}f(t,n,M,N)\\(3)\ upper\ cumulative\ distribution\\\hspace{30}Q(x,n,M,N)={\large\sum_{t=x}^{M}}f(t,n,M,N)\\$
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Purpose of use? | 2017-07-26 08:40:44 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 1, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7542808055877686, "perplexity": 7404.880367164509}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-30/segments/1500549426086.44/warc/CC-MAIN-20170726082204-20170726102204-00666.warc.gz"} |
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### #Actualwarnexus
Posted 09 February 2013 - 11:02 PM
Feel free to correct me if I'm wrong (still learning C++, having learned Java, and some C#), but I believe this is what it is...
In C-based languages, void is simply nothingness, as I'm sure you know. Commonly (thought not seen in Java much - at least I don't to use it) void is an unnecessary parameter in functions if used as above. This is merely just a matter of taste from what I know.
Therefore, this:
void run (void){
//Filler code
}
should compile the same as this:
void run (){
//Filler code
}
Really the only thing that the extra void does is fill in the parameter parenthesis, and make it a bit clearer to the programmer that the function has no intent to take arguments. However, depending on your level of comments & documentation, it may be completely unnecessary. tldr: Don't worry about it.
There may be some subtleties between them, but nothing very significant.
Java does not allow void in the parameter. Maybe for other languages but not Java. I tested it just now
### #1warnexus
Posted 09 February 2013 - 10:55 PM
Feel free to correct me if I'm wrong (still learning C++, having learned Java, and some C#), but I believe this is what it is...
In C-based languages, void is simply nothingness, as I'm sure you know. Commonly (thought not seen in Java much - at least I don't to use it) void is an unnecessary parameter in functions if used as above. This is merely just a matter of taste from what I know.
Therefore, this:
void run (void){
//Filler code
}
should compile the same as this:
void run (){
//Filler code
}
Really the only thing that the extra void does is fill in the parameter parenthesis, and make it a bit clearer to the programmer that the function has no intent to take arguments. However, depending on your level of comments & documentation, it may be completely unnecessary. tldr: Don't worry about it.
There may be some subtleties between them, but nothing very significant.
Java does not allow void in the parameter. Maybe for other languages but not Java. I tested it for now
PARTNERS | 2014-11-27 03:06:48 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3555653393268585, "perplexity": 1537.29891259091}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-49/segments/1416931007720.74/warc/CC-MAIN-20141125155647-00052-ip-10-235-23-156.ec2.internal.warc.gz"} |
https://www.math24.net/indefinite-integral-basic-rules-integration/ | # The Indefinite Integral and Basic Rules of Integration
• ### Antiderivatives and the Indefinite Integral
Let a function $$f\left( x \right)$$ be defined on some interval $$I.$$ The function $$F\left( x \right)$$ is called an antiderivative of $$f\left( x \right),$$ if
${F^\prime\left( x \right) = f\left( x \right)}$
for all $$x$$ in the interval $$I.$$
There is an infinite number of antiderivatives of a function $$f\left( x \right),$$ all differing only by a constant $$C:$$
${\left( {F\left( x \right) + C} \right)^\prime = F^\prime\left( x \right) + C^\prime }={ f\left( x \right) + 0 }={ f\left( x \right).}$
The set of all antiderivatives for a function $$f\left( x \right)$$ is called the indefinite integral of $$f\left( x \right)$$ and is denoted as
${{\int} {{f\left( x \right)}{dx}} }={ F\left( x \right) + C,\;\;}\kern0pt{\text{if}\;\;F^\prime\left( x \right) = f\left( x \right).}$
In this definition, the $$\int {}$$ is called the integral symbol, $$f\left( x \right)$$ is called the integrand, $$x$$ is called the variable of integration, $$dx$$ is called the differential of the variable $$x,$$ and $$C$$ is called the constant of integration.
### Indefinite Integral of Some Common Functions
Integration is the reverse process of differentiation, so the table of basic integrals follows from the table of derivatives.
Below is a list of top integrals. It is supposed here that $$a,$$ $$p\left( {p \ne 1} \right),$$ $$C$$ are real constants, $$b$$ is the base of the exponential function $$\left( {b \ne 1, b \gt 0} \right).$$
$$\int {adx} = ax + C$$ $$\int {xdx} = {\large\frac{{{x^2}}}{2}\normalsize} + C$$ $$\int {{x^2}dx} = {\large\frac{{{x^3}}}{3}\normalsize} + C$$ $$\int {{x^p}dx} = {\large\frac{{{x^{p + 1}}}}{{p + 1}}\normalsize} + C$$ $$\int {\large\frac{{dx}}{x}\normalsize} = \ln \left| x \right| + C$$ $$\int {{e^x}dx} = {e^x} + C$$ $$\int {{b^x}dx} = {\large\frac{{{b^x}}}{{\ln b}}\normalsize} + C$$ $$\int {\sin xdx} = – \cos x + C$$ $$\int {\cos xdx} = \sin x + C$$ $$\int {\tan xdx} = – {\ln \left| {\cos x} \right|} + C$$ $$\int {\cot xdx} = {\ln \left| {\sin x} \right|} + C$$ $$\int {\sec xdx} = {\ln \left| {\tan\left( {\large\frac{x}{2}\normalsize} + {\large\frac{\pi }{4}\normalsize} \right)} \right|} + C$$ $$\int {\csc xdx} = {\ln \left| {\tan\large\frac{x}{2}\normalsize} \right|} + C$$ $$\int {{\sec^2}xdx} = \tan x + C$$ $$\int {{\csc^2}xdx} = -\cot x + C$$ $$\int {\sec x\tan xdx} = \sec x + C$$ $$\int {\csc x\cot xdx} = -\csc x + C$$ $$\int {\large\frac{{dx}}{{1 + {x^2}}}\normalsize} = \arctan x + C$$ $$\int {\large\frac{{dx}}{{{a^2} + {x^2}}}\normalsize} = {\large\frac{1}{a}\normalsize}\arctan {\large\frac{x}{a}\normalsize} + C$$ $$\int {\large\frac{{dx}}{{1 – {x^2}}}\normalsize} = {\large\frac{1}{2}\normalsize}{\ln \left| {{\large\frac{{1 + x}}{{1 – x}}\normalsize}} \right|} + C$$ $$\int {\large\frac{{dx}}{{{a^2} – {x^2}}}\normalsize} = {\large\frac{1}{{2a}}\normalsize}\ln\left| {\large{\frac{{a + x}}{{a – x}}\normalsize}} \right| + C$$ $$\int {\large\frac{{dx}}{{\sqrt {1 – {x^2}} }}\normalsize} = \arcsin x + C$$ $$\int {\large\frac{{dx}}{{\sqrt {{a^2} – {x^2}} }}\normalsize} = \arcsin {\large\frac{x}{a}\normalsize} + C$$ $$\int {\large\frac{{dx}}{{\sqrt {{x^2} \pm {a^2}} }}\normalsize} = {\ln \left| {x + \sqrt {{x^2} \pm {a^2}} } \right|} + C$$ $$\int {\large\frac{{dx}}{{x\sqrt {{x^2} – 1} }}\normalsize} = {\text{arcsec}\left| x \right|} + C$$ $$\int {\sinh xdx} = \cosh x + C$$ $$\int {\cosh xdx} = \sinh x + C$$ $$\int {{\text{sech}^2}xdx} = \tanh x + C$$ $$\int {{\text{csch}^2}xdx} = -\text{coth}\,x + C$$ $$\int {\text{sech}\,x\tanh xdx} = – {\text{sech}\,x} + C$$ $$\int {\text{csch}\,x\coth xdx} = – {\text{csch}\,x} + C$$ $$\int {\tanh xdx} = {\ln \cosh x} + C$$
$$\int {adx} = ax + C$$ $$\int {xdx} = {\large\frac{{{x^2}}}{2}\normalsize} + C$$ $$\int {{x^2}dx} = {\large\frac{{{x^3}}}{3}\normalsize} + C$$ $$\int {{x^p}dx} = {\large\frac{{{x^{p + 1}}}}{{p + 1}}\normalsize} + C$$ $$\int {\large\frac{{dx}}{x}\normalsize} = {\ln \left| x \right|} + C$$ $$\int {{e^x}dx} = {e^x} + C$$ $$\int {{b^x}dx} = {\large\frac{{{b^x}}}{{\ln b}}\normalsize} + C$$ $$\int {\sin xdx} = – \cos x + C$$ $$\int {\cos xdx} = \sin x + C$$ $$\int {\tan xdx} = – {\ln \left| {\cos x} \right|} + C$$ $$\int {\cot xdx} = {\ln \left| {\sin x} \right|} + C$$ $$\int {\sec xdx} = {\ln \left| {\tan\left( {\large\frac{x}{2}\normalsize} + {\large\frac{\pi }{4}\normalsize} \right)} \right|} + C$$ $$\int {\csc xdx} = {\ln \left| {\tan\large\frac{x}{2}\normalsize} \right|} + C$$ $$\int {{\sec^2}xdx} = \tan x + C$$ $$\int {{\csc^2}xdx} = -\cot x + C$$ $$\int {\sec x\tan xdx} = \sec x + C$$ $$\int {\csc x\cot xdx} = -\csc x + C$$ $$\int {\large\frac{{dx}}{{1 + {x^2}}}\normalsize} = \arctan x + C$$ $$\int {\large\frac{{dx}}{{{a^2} + {x^2}}}\normalsize} = {\large\frac{1}{a}\normalsize}\arctan {\large\frac{x}{a}\normalsize} + C$$ $$\int {\large\frac{{dx}}{{1 – {x^2}}}\normalsize} = {\large\frac{1}{2}\normalsize}\ln \left| {{\large\frac{{1 + x}}{{1 – x}}\normalsize}} \right| + C$$ $$\int {\large\frac{{dx}}{{{a^2} – {x^2}}}\normalsize} = {\large\frac{1}{{2a}}\normalsize}\ln\left| {\large{\frac{{a + x}}{{a – x}}\normalsize}} \right| + C$$ $$\int {\large\frac{{dx}}{{\sqrt {1 – {x^2}} }}\normalsize} = \arcsin x + C$$ $$\int {\large\frac{{dx}}{{\sqrt {{a^2} – {x^2}} }}\normalsize} = \arcsin {\large\frac{x}{a}\normalsize} + C$$ $$\int {\large\frac{{dx}}{{\sqrt {{x^2} \pm {a^2}} }}\normalsize} = {\ln \left| {x + \sqrt {{x^2} \pm {a^2}} } \right|} + C$$ $$\int {\large\frac{{dx}}{{x\sqrt {{x^2} – 1} }}\normalsize} = \text{arcsec}\left| x \right| + C$$ $$\int {\sinh xdx} = \cosh x + C$$ $$\int {\cosh xdx} = \sinh x + C$$ $$\int {{\text{sech}^2}xdx} = \tanh x + C$$ $$\int {{\text{csch}^2}xdx} = -\text{coth}\,x + C$$ $$\int {\text{sech}\,x\tanh xdx} = – \text{sech}\,x + C$$ $$\int {\text{csch}\,x\coth xdx} = – \text{csch}\,x + C$$ $$\int {\tanh xdx} = \ln \cosh x + C$$
### Properties of the Indefinite Integral
1. If $$a$$ is some constant, then $\cssId{element11}{\int {af\left( x \right)dx} }=\cssId{element12}{ a\int {f\left( x \right)dx},}$ i.e. the constant coefficient can be carried outside the integral sign.
2. For functions $$f\left( x \right)$$ and $$g\left( x \right),$$ $\cssId{element13}{\int {\left[ {f\left( x \right) \pm g\left( x \right)} \right]dx} }=\cssId{element14}{ \int {f\left( x \right)dx} }\pm \cssId{element15}{\int {g\left( x \right)dx} ,}$ i.e. the indefinite integral of the sum (difference) equals to the sum (difference) of the integrals.
Calculation of integrals using the linear properties of indefinite integrals and the table of basic integrals is called direct integration.
• ## Solved Problems
Click a problem to see the solution.
### Example 1
Evaluate the indefinite integral $${\int {\left( {3{x^2} – 6x + 2\cos x} \right)dx} }.$$
### Example 2
Find the indefinite integral $$\int {\left( {1 + x} \right)\left( {1 + 2x} \right)dx}.$$
### Example 3
Find the indefinite integral $$\int {\left( {\large{\frac{1}{{{x^2}}}}\normalsize – \large{\frac{1}{{{x^3}}}}\normalsize} \right)dx}.$$
### Example 4
Calculate $$\int {\left( {\sqrt x + \sqrt[\large 3\normalsize]{x}} \right)dx}.$$
### Example 5
Find the indefinite integral $$\int {\large{\frac{{x + 1}}{{\sqrt x }}}\normalsize dx}.$$
### Example 6
Find the indefinite integral $$\int {{{\left( {x + \sqrt x } \right)}^2}dx}.$$
### Example 7
Calculate the integral $$\int {\left( {\large\frac{3}{{\sqrt[\large 3\normalsize]{x}}}\normalsize + \large\frac{2}{{\sqrt x }}\normalsize} \right)dx}.$$
### Example 8
Find the indefinite integral $$\int {\left( {\sqrt[3]{x} + {e^3}} \right)dx}.$$
### Example 9
Calculate $$\int {\large\frac{{4dx}}{{2 + 3{x^2}}}\normalsize}.$$
### Example 10
Find the indefinite integral $$\int {\large{\frac{{{x^2}}}{{1 + {x^2}}}}\normalsize dx}.$$
### Example 11
Evaluate the integral $$\int {\large{\frac{{dx}}{{1 + 2{x^2}}}}\normalsize}.$$
### Example 12
Find the integral $$\int {\large\frac{{\pi dx}}{{\sqrt {\pi – {x^2}} }}\normalsize}.$$
### Example 13
Calculate the integral $$\int {\left( {2\cos x – 5\sin x} \right)dx}.$$
### Example 14
Evaluate the integral $$\int {\large{\frac{{dx}}{{\sqrt {1 – \large{\frac{{{x^2}}}{2}}\normalsize} }}}\normalsize}.$$
### Example 15
Calculate the integral $$\int {{{\tan }^2}xdx}.$$
### Example 16
Calculate the integral $$\int {{{\cot }^2}xdx}.$$
### Example 17
Find the integral $$\int {\large\frac{{dx}}{{{\sin^2}2x}}\normalsize}$$ without using a substitution.
### Example 1.
Evaluate the indefinite integral $${\int {\left( {3{x^2} – 6x + 2\cos x} \right)dx} }.$$
Solution.
Applying the properties $$1$$ and $$2,$$ we have
${I = \int {\left( {3{x^2} – 6x + 2\cos x} \right)dx} }={ \int {3{x^2}dx} }-{ \int {6xdx} }+{ \int {2\cos xdx} }={ 3{\int {{x^2}dx}} }-{ 6{\int {xdx}} }+{ 2{\int {\cos xdx}} .}$
All three integrals can be evaluated using the integration table. This yields:
${I = 3 \cdot {\frac{{{x^3}}}{3}} }-{ 6 \cdot {\frac{{{x^2}}}{2}} }+{ 2 \cdot {\sin x} + C }={{ {x^3} }-{ 3{x^2} }+{ 2\sin x + C.}}$
### Example 2.
Find the indefinite integral $$\int {\left( {1 + x} \right)\left( {1 + 2x} \right)dx}.$$
Solution.
We can simplify the integrand:
${\left( {1 + x} \right)\left( {1 + 2x} \right) }={ 1 + x + 2x + 2{x^2} }={ 2{x^2} + 3x + 1.}$
Then the integral is given by
${\int {\left( {1 + x} \right)\left( {1 + 2x} \right)dx} }={ \int {\left( {2{x^2} + 3x + 1} \right)dx} }={ \int {2{x^2}dx} }+{ \int {3xdx} }+{ \int {1dx} }={ 2\int {{x^2}dx} }+{ 3\int {xdx} }+{ \int {dx} }={ 2 \cdot \frac{{{x^3}}}{3} }+{ 3 \cdot \frac{{{x^2}}}{2} }+{ x + C }={ \frac{{2{x^3}}}{3} + \frac{{3{x^2}}}{2} + x + C.}$
### Example 3.
Find the indefinite integral $$\int {\left( {\large{\frac{1}{{{x^2}}}}\normalsize – \large{\frac{1}{{{x^3}}}}\normalsize} \right)dx} .$$
Solution.
By the sum rule,
${I = \int {\left( {\frac{1}{{{x^2}}} – \frac{1}{{{x^3}}}} \right)dx} }={ \int {\frac{{dx}}{{{x^2}}}} – \int {\frac{{dx}}{{{x^3}}}} .}$
The integrands in both integrals are power functions, so we have
${I = \int {{x^{ – 2}}dx} – \int {{x^{ – 3}}dx} }={ \frac{{{x^{ – 1}}}}{{\left( { – 1} \right)}} }-{ \frac{{{x^{ – 2}}}}{{\left( { – 2} \right)}} + C }={ – \frac{1}{x} + \frac{1}{{2{x^2}}} + C.}$
### Example 4.
Calculate $$\int {\left( {\sqrt x + \sqrt[\large 3\normalsize]{x}} \right)dx}.$$
Solution.
${\int {\left( {\sqrt x + \sqrt[\large 3\normalsize]{x}} \right)dx} } = {\int {\sqrt x dx} + \int {\sqrt[\large 3\normalsize]{x}dx} } = {\int {{x^{\large\frac{1}{2}\normalsize}}dx} + \int {{x^{\large\frac{1}{3}\normalsize}}dx} } = {\frac{{{x^{\large\frac{1}{2}\normalsize + 1}}}}{{\frac{1}{2} + 1}} + \frac{{{x^{\large\frac{1}{3}\normalsize + 1}}}}{{\frac{1}{3} + 1}} + C } = {\frac{{2{x^{\large\frac{3}{2}\normalsize}}}}{3} + \frac{{3{x^{\large\frac{4}{3}\normalsize}}}}{4} } = {\frac{{2\sqrt {{x^3}} }}{3} + \frac{{3\sqrt[\large 3\normalsize]{{{x^4}}}}}{4} + C.}$
### Example 5.
Find the indefinite integral $$\int {\large{\frac{{x + 1}}{{\sqrt x }}}\normalsize dx}.$$
Solution.
We write the integrals as the sum of two integrals and calculate them separately:
${\int {\frac{{x + 1}}{{\sqrt x }}dx} }={ \int {\left( {\frac{x}{{\sqrt x }} + \frac{1}{{\sqrt x }}} \right)dx} }={ \int {\left( {\sqrt x + \frac{1}{{\sqrt x }}} \right)dx} }={ \int {\sqrt x dx} + \int {\frac{{dx}}{{\sqrt x }}} }={ \frac{{{x^{\frac{3}{2}}}}}{{\frac{3}{2}}} + 2\sqrt x + C }={ \frac{{2\sqrt {{x^3}} }}{3} + 2\sqrt x + C.}$
### Example 6.
Find the indefinite integral $$\int {{{\left( {x + \sqrt x } \right)}^2}dx}.$$
Solution.
Expand the square in the integrand:
${I = \int {{{\left( {x + \sqrt x } \right)}^2}dx} }={ \int {\left( {{x^2} + 2x\sqrt x + {{\left( {\sqrt x } \right)}^2}} \right)dx} }={ \int {\left( {{x^2} + 2{x^{\frac{3}{2}}} + x} \right)dx} .}$
Using the basic properties of integrals, we have
${I = \int {\left( {{x^2} + 2{x^{\frac{3}{2}}} + x} \right)dx} }={ \int {{x^2}dx} }+{ 2\int {{x^{\frac{3}{2}}}dx} }+{ \int {xdx} .}$
The last expression contains only table integrals. Then
${I = \frac{{{x^3}}}{3} + 2 \cdot \frac{{{x^{\frac{5}{2}}}}}{{\frac{5}{2}}} + \frac{{{x^2}}}{2} + C }={ \frac{{{x^3}}}{3} + \frac{{4{x^{\frac{5}{2}}}}}{5} + \frac{{{x^2}}}{2} + C }={ \frac{{{x^3}}}{3} + \frac{{4\sqrt {{x^5}} }}{5} + \frac{{{x^2}}}{2} + C.}$
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Problems 1-6
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Problems 7-17 | 2019-06-19 21:59:35 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9528586864471436, "perplexity": 481.97605927886366}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627999041.59/warc/CC-MAIN-20190619204313-20190619230313-00104.warc.gz"} |
https://zbmath.org/?q=an:1144.58005 | # zbMATH — the first resource for mathematics
$$H^{o}$$-type Riemannian metrics on the space of planar curves. (English) Zbl 1144.58005
Summary: Michor and Mumford have shown that the distances between planar curves in the simplest metric (not involving derivatives) are identically zero. We derive geodesic equations and a formula for sectional curvature for conformally equivalent metrics. We show if the conformal factor depends only on the length of the curve, then the metric behaves like an $$L^1$$-metric, the sectional curvature is not bounded from above, and minimal geodesics may not exist. If the conformal factor is superlinear in curvature, then the sectional curvature is bounded from above.
##### MSC:
58B20 Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds 53C22 Geodesics in global differential geometry
##### Keywords:
moduli of planar curves; differential geometry
Full Text:
##### References:
[1] Arthur L. Besse, Einstein manifolds, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 10, Springer-Verlag, Berlin, 1987. · Zbl 0613.53001 [2] Peter W. Michor and David Mumford, Riemannian geometries on spaces of plane curves, J. Eur. Math. Soc. (JEMS) 8 (2006), no. 1, 1 – 48. · Zbl 1101.58005 · doi:10.4171/JEMS/37 · doi.org [3] P. Michor and D. Mumford, “An overview of the Riemannian metrics on spaces of curves using the Hamiltonian approach”, Tech. Report, ESI Preprint #1798, 2005. · Zbl 1116.58007 [4] E. Klassen, A. Srivastava, W. Mio, and S. H. Joshi, “Analysis of planar shapes using geodesic paths on shape spaces”, IEEE Trans. PAMI, 26(3), pp. 372-383, 2003. [5] W. Mio and A. Srivastava, “Elastic-string models for representation and analysis of planar shapes”, CVPR(2), 2004, pp. 10-15. [6] W. Mio, A. Srivastava, and S. H. Joshi, “On shape of plane elastic curves”, International Journal of Computer Vision, 73(3), pp. 307-324. [7] A. Yezzi and A. Mennucci, “Conformal Riemannian metrics in space of curves”, EUSIPCO04, MIA, 2004. [8] A. Yezzi and A. Mennucci, “Metrics in the space of curves”, arXiv:math.DG/0412454, v2, May 25, 2005. [9] Laurent Younes, Computable elastic distances between shapes, SIAM J. Appl. Math. 58 (1998), no. 2, 565 – 586. · Zbl 0907.68158 · doi:10.1137/S0036139995287685 · doi.org
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching. | 2021-05-14 14:12:55 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6275100708007812, "perplexity": 1453.4066333055664}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243989526.42/warc/CC-MAIN-20210514121902-20210514151902-00063.warc.gz"} |
http://mathhelpforum.com/pre-calculus/211147-domain-again-print.html | # Domain again
• Jan 10th 2013, 06:27 PM
M670
Domain again
http://webwork.mathstat.concordia.ca...7812eb1c11.png
Find the domain of this
$(-infinity,0] U [3,infinity)$ becuase its to the 4th root we have a restirction unlike an odd root which is all real number
why am I wrong ?
• Jan 10th 2013, 07:01 PM
Deveno
Re: Domain again
let's look at it this way:
let $g(x) = \sqrt[4]{x}$
let $h(x) = x^2 - 9$
then $f = g \circ h$
now h is clearly defined for all x, no problem there.
but g is only defined for x ≥ 0.
that means that f is only defined for h(x) ≥ 0.
so we need to look at what the RANGE of h is, in particular, for which x is h(x) ≥ 0?
this is precisely when:
$x^2 \geq 9$
that is:
$x \in (-\infty, -3] \cup [3,\infty)$.
to see why your answer is wrong, let's pick something in it, and see what happens:
let's use x = -1, which is in the interval (-∞,0].
now x2 - 9 = (-1)2 - 9 = 1 - 9 = -8. how are we going to take a 4th root of that?
EDIT: darn, i left out an x!
it should be:
x2 - 9x (is my memory, or my eyesight, going?)
this is ≥ 0 when either:
x ≥ 0 and x - 9 ≥ 0, that is x ≥ 9...in this case the "9" controls (since its bigger and we have to have both), so this is the interval [x,∞).
or:
x < 0 and x - 9 < 0, that is x < 9...in this case the "0" controls (since it is smaller), so this is the interval (-∞,0].
therefore, the correct answer is as Soroban said:
(-∞,0] U [9,∞).
• Jan 10th 2013, 07:23 PM
Soroban
Re: Domain again
Hello, M670!
Quote:
$\text{Find the domain: }\;f(x) \;=\;\sqrt[4]{x^2-9x}$
We see that $x^2 - 9x$ must not be negative.
When is $x^2-9x$ greater than or equal to zero?
Consider the parabola $y \:=\:x^2-9x$.
When is it above the $x$-axis?
Code:
| * | * | *| * ----*-----------*---- 0| . . 9 | . . |
Domain: . $(\text{-}\infty,\:0\:\!] \cup [\:\!9,\:\infty)$ | 2016-09-30 21:17:25 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 12, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8989521265029907, "perplexity": 3264.335428686301}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-40/segments/1474738662336.11/warc/CC-MAIN-20160924173742-00265-ip-10-143-35-109.ec2.internal.warc.gz"} |
https://gsebsolutions.in/gseb-solutions-class-10-maths-chapter-9-ex-9-1/ | # GSEB Solutions Class 10 Maths Chapter 9 Some Applications of Trigonometry Ex 9.1
Gujarat Board GSEB Solutions Class 10 Maths Chapter 9 Some Applications of Trigonometry Ex 9.1 Textbook Questions and Answers.
## Gujarat Board Textbook Solutions Class 10 Maths Chapter 9 Some Applications of Trigonometry Ex 9.1
Question 1.
A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is 300.
Solution:
In right ΔABC
sin θ = $$\frac {AB}{BC}$$
⇒ sin30° = $$\frac {AB}{20}$$
⇒ $$\frac {1}{2}$$ = $$\frac {AB}{20}$$
⇒ AB = $$\frac {20}{2}$$
AB = 10m
Question 2.
A tree breaks due to a storm and the broken part bends so that the top of the tree touches the ground making an angle 30° with it. The distance between the foot of the tree to the point where the top touches the ground is 8 m. Find the height of the tree.
Solution:
Let actual height of tree be BD = AB + AD
But tree breaks and upper end D touches the ground at point C
Now in ΔABC,
⇒ cos θ = $$\frac {BC}{AC}$$
⇒ cos 30° = $$\frac {8}{AC}$$
⇒ $$\frac{\sqrt{3}}{2}$$ = $$\frac {8}{AC}$$
⇒ AC = $$\frac{16}{\sqrt{3}}$$ m ………(1)
Again, in ΔABC
tan 30° = $$\frac {AB}{BC}$$
⇒ $$\frac{1}{\sqrt{3}}$$ = $$\frac {AB}{8}$$
⇒ AB = $$\frac{8}{\sqrt{3}}$$ ………(2)
Height of tree BD = $$\frac{16}{\sqrt{3}}$$ + $$\frac{8}{\sqrt{3}}$$
= $$\frac{24}{\sqrt{3}}$$ = $$\frac{24}{\sqrt{3}}$$ x $$\frac{\sqrt{3}}{\sqrt{3}}$$
= $$\frac{24 \sqrt{3}}{3}$$ = $$8 \sqrt{3}$$ m
Question 3.
A contractor plans to install two slides for the children to play in a park below the age of 5 years, she prefers to have a slide whose top is at a height of 1.5 m, and is inclined at an angle of 300 to the ground, whereas for elder children, she wants to have a steep slide at a height of 3 m, and inclined at an angle of 60° to the ground. What should be the length of the slide in each case?
Solution:
For children below the age 5 years
In right ΔABC
sin θ = $$\frac {AB}{AC}$$
⇒ sin 30° = $$\frac {1.5}{AC}$$
$$\frac {1}{2}$$ = $$\frac {1.5}{AC}$$
⇒ AC = 1.5 x 2 = 3 m
For elder children
In right ΔDEF
sin 60° = $$\frac {DE}{DF}$$
⇒ $$\frac{\sqrt{3}}{2}$$ = $$\frac {3}{DF}$$
DF = $$\frac{6}{\sqrt{3}}$$
DF = $$\frac{6 \sqrt{3}}{\sqrt{3} \times \sqrt{3}}$$ = $$\frac{6 \sqrt{3}}{3}$$
DF = $$2 \sqrt{3}$$ = 2 x 1.732 = 3. 464m
⇒ DF = 3.46 m (approx.)
Question 4.
The angle of elevation of the top of a tower from a point on the ground which is 30 m away from the foot of the tower is 30°. Find the height of the tower.
Solution:
In right ΔABC
tan θ = $$\frac {AB}{BC}$$
tan 30° = $$\frac {AB}{30}$$
⇒ $$\frac{1}{\sqrt{3}}$$ = $$\frac {AB}{30}$$
⇒ AB = $$\frac{30}{\sqrt{3}}$$
⇒ AB = $$\frac{30}{\sqrt{3}}$$ x $$\frac{3}{\sqrt{3}}$$ = $$\frac{30 \sqrt{3}}{3}$$
⇒ AB = $$10 \sqrt{3}$$ = 10 x 1.732
⇒ AB = 17.32 m
Hence, height of tower is 10$$\sqrt{3}$$m or 17.32 m.
Question 5.
A kite is flying at a height of 60 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60°. Find the length of the string, assuming that there is no stack in the string.
Solution:
In right ΔABC
sin θ = $$\frac {AB}{BC}$$
⇒ sin60° = $$\frac {60}{AC}$$
⇒ $$\frac{\sqrt{3}}{2}$$ = $$\frac {60}{AC}$$
⇒ AC = $$\frac{120}{\sqrt{3}}$$
⇒ AC = $$\frac{120}{\sqrt{3}}$$ x $$\frac{\sqrt{3}}{\sqrt{3}}$$
AC = $$\frac{120}{\sqrt{3}}$$
⇒ AC = $$40 \sqrt{3}$$
Hence, length of the string is 40J m.
Question 6.
A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30° to 60° as he walks towards the building. Find the distance he walked towards the building.
Solution:
AF be the height of the building.
And height of boy = 1.5 m
AB = AF – BF
AB = 30 – 1.5 = 28.5 m
In right ΔABC
tan θ = $$\frac {AB}{BC}$$
⇒ tan 60° = $$\frac{28.5}{\mathrm{BC}}$$
⇒ $$\sqrt{3}$$ = $$\frac{28.5}{\mathrm{BC}}$$
BC = $$\frac{28.5}{\mathrm{BC}}$$ m ……….(1)
Now in right ΔABD
tan θ = $$\frac {AB}{BC}$$
⇒ tan 30° = $$\frac {AB}{BC}$$
⇒ $$\frac{1}{\sqrt{3}}$$ = $$\frac{28.5}{\mathrm{BD}}$$
⇒ BD = 28.5 x $$\sqrt{3}$$
⇒ BC + CD = 28.5 x $$\sqrt{3}$$
⇒ $$\frac{28.5}{\sqrt{3}}$$ + CD = 28.5 x $$\sqrt{3}$$
⇒ CD = 28.5$$\sqrt{3}$$ – $$\frac{28.5}{\sqrt{3}}$$
⇒ CD = $$\frac{28.5 \times \sqrt{3} \times \sqrt{3}-28.5}{\sqrt{3}}$$
= $$\frac{28.5 \times 3-28.5}{\sqrt{3}}$$ = $$\frac{57}{\sqrt{3}}$$
= $$\frac{57}{\sqrt{3}}$$ x $$\frac{\sqrt{3}}{\sqrt{3}}$$ = $$\frac{57 \sqrt{3}}{3}$$ = 19$$\sqrt{3}$$ m
Hence, the distance walked towards the building is 19$$\sqrt{3}$$ m.
Question 7.
From a point on the ground, the angles of elevation of the bottom and top of a transmission tower fixed at the top of a 20 m high building are 45° and 60° respectively, find the height of the tower.
Solution:
In right ΔABC
tan 45° = $$\frac {BC}{AB}$$
⇒ 1 = $$\frac {20}{AB}$$
⇒ AB = 20 m ………(1)
In right ΔABD,
tan θ = $$\frac {BD}{AB}$$
⇒ tan 60° = $$\frac{20+h}{20}$$
⇒ $$\sqrt{3}$$ = $$\frac{20+h}{20}$$
⇒ 20 + h = 20$$\sqrt{3}$$
⇒ h = 20$$\sqrt{3}$$ – 20
=20 x (1.732 – 1)
= 10 x 1.464 = 14.64 m
Height of tower = 14.64 metre
Question 8.
A statue 1.6 m tall stands on the top of a pedestal. From a point on the ground. The angle of elevation of the top of the statue is 60° and from the same point the angle of elevation of the top of the pedestal is 45° Find the height of the pedestal.
Solution:
Let the height of pedestal be h metre and AB be the statue.
In right ΔBCD
tan θ = $$\frac {BC}{DC}$$
⇒ h = x ………(1)
Now in right ΔACD
tan θ = $$\frac {AC}{DC}$$
⇒ tan 60° = $$\frac{1.6 + h}{x}$$
⇒ $$\sqrt{3}$$ = $$\frac{1.6 + h}{x}$$ ………..(2)
From eqn. (1) and (2)
⇒ $$\sqrt{3}$$ = $$\frac{1.6 + h}{x}$$
⇒ $$\sqrt{3}$$h = 1.6 + h
⇒ $$\sqrt{3}$$h – h = 1.6
⇒ ($$\sqrt{3}$$)h = 1.6
h = $$\frac{1.6}{\sqrt{3} – 1}$$
h = $$\frac{1.6}{\sqrt{3} – 1}$$ x $$\frac{(\sqrt{3} + 1)}{(\sqrt{3} + 1)}$$
h = $$\frac{1.6(\sqrt{3} – 1)}{2}$$
h = 0.8($$\sqrt{3} + 1$$)
Hence, the height of the pedestal is 0.8 ($$\sqrt{3} + 1$$) metre.
Question 9.
The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 50 m high, find the height of the building. (CBSE 2009)
Solution:
Let height of the building be h metre.
Then, AB = h metre.
In right ΔBCD
tan θ = $$\frac { CD }{ BC }$$
⇒ tan 60° = $$\frac {50}{x}$$
⇒ $$\sqrt{3}$$ = $$\frac {50}{x}$$
⇒ x = $$\frac{50}{\sqrt{3}}$$ ………..(1)
Now in right ΔACD
tan θ = $$\frac {AB}{BC}$$
⇒ tan 30° = $$\frac {h}{x}$$
⇒ $$\frac{1}{\sqrt{3}}$$ = $$\frac {h}{x}$$
⇒ x = $$\sqrt{3} h$$ ……..(2)
From (1) and (2)
⇒ $$\sqrt{3} h$$ = $$\sqrt{3} h$$
⇒ h = $$\frac{50}{\sqrt{3} \times \sqrt{3}}$$
⇒ h = $$\frac{50}{3}$$ m = 16$$\frac{2}{3}$$m
Hence, the height of the building is 16 $$\frac{2}{3}$$ metre.
Question 10.
Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 600 and 30°, respectively. Find the height of the poles and the distances of the point from the poles.
Solution:
Let AB and CD be the two poles.
In right ΔABC
tan θ = $$\frac {AB}{BC}$$
tan 30° = $$\frac{h}{80-x}$$
$$\frac{1}{\sqrt{3}}$$ = $$\frac{h}{80-x}$$
= 80 – x = $$\sqrt{3} h$$ ……….(1)
Now in right ΔCDE
tan θ = $$\frac {DE}{CD}$$
⇒ tan 60° = $$\frac{h}{x}$$
⇒ $$\sqrt{3}$$ = $$\frac{h}{x}$$
h = $$\sqrt{3} x$$
From eqn. (1) and (2)
⇒ 80 – x = $$\sqrt{3} h$$
⇒ 80 – x = 3x
⇒ 4x = 80
⇒ x = $$\frac {80}{4}$$ = 20 m
Putting eqn. (2)
h = $$\sqrt{3} x$$ = $$\sqrt{3}$$ x 20 = 20$$\sqrt{3}$$ m
Height of poles be 20 m and the distance of the point from the pole is 20 m and 80 – x = 80 – 20 = 60 m.
Question 11.
A TV tower stands vertically on the banks of a canal. From a point on the other bank directly opposite the tower, the angle of elevation of the top of the tower is 60°. From another point 20 be away from this point on the line joining this point to the foot of the tower, the angle of elevation of the top of the tower is 30°. Find the height of the tower and the width of the canal.
Solution:
In right ΔABC
tan θ = $$\frac{AB}{BC}$$
⇒ tan 60° = $$\frac{h}{x}$$
⇒ $$\sqrt{3}$$ = $$\frac{h}{x}$$
⇒ h = $$\sqrt{3}$$ x ………..(1)
Now, in right ΔABD
tan θ = $$\frac{AB}{BD}$$ (BD = x + 20)
tan 30° = $$\frac{h}{x + 20}$$
⇒ $$\frac{1}{\sqrt{3}}$$ = $$\frac{h}{x + 20}$$
⇒ x + 20 = $$\sqrt{3}$$h ……..(2)
From eqn. (1) and (2)
⇒ x + 20 = $$\sqrt{3}$$ x $$\sqrt{3}$$x
⇒ x + 20 = 3x
⇒ 2x = 20
⇒ x = 10 m
Putting value of x in eqn. (1),
h = $$\sqrt{3}$$x = $$\sqrt{3}$$ x 10
h = 10$$\sqrt{3}$$ m
Hence, the height of the tower is 10$$\sqrt{3}$$ m and the width of the canal is 10 m.
Question 12.
From the top of 7 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45° Determine the height of the tower. (CBSE 2017)
Solution:
Let AC be the cable tower and DE be the building.
tan θ = $$\frac{DE}{AE}$$
⇒ tan 45° = $$\frac{7}{x}$$ ……….(1)
⇒ 1 = $$\frac{7}{x}$$
x = 7 m
Now in ΔABC
tan θ = $$\frac{BC}{BD}$$
tan 60° = $$\frac{BC}{BD}$$
$$\sqrt{3}$$ = $$\frac{h}{x}$$ (BD = EA = x)
⇒ h = $$\sqrt{3}$$x
⇒ h = $$\sqrt{3}$$ x 7 [From (1)]
⇒ h = 7$$\sqrt{3}$$ m
Height of cable tower AC
= AB + BC = 7 + 7 $$\sqrt{3}$$ = 7($$\sqrt{3}$$ + 1)
Hence height of the tower is 7($$\sqrt{3}$$ + 1) m.
Question 13.
As observed from the top of a 75 m high light house from the sea level, the angles of depression of two ships are 300 and 45°. if one ship is exactly behind the other on the saine side of the light house, find the distance between the two ships.
Solution:
In right ΔABC
tan 45°= $$\frac{AB}{BC}$$
⇒ 1 = $$\frac{75}{BC}$$
⇒ BC = 75 m
In right ΔABD
tan 30° = $$\frac{AB}{BD}$$
⇒ $$\frac{1}{\sqrt{3}}$$ = $$\frac{75}{BD}$$ (AB = 75m)
⇒ BD = 75$$\sqrt{3}$$ m
CD = BD – BC
= 75$$\sqrt{3}$$ – 75 = 75($$\sqrt{3}$$ – 1) m
Distance between two ships is 75($$\sqrt{3}$$ – 1) m.
Question 14.
A 12 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is 600. After some time, the angle of elevation reduces to 300 (see figure). Find the distance travelled by the balloon during the interval.
Solution:
Let AB = 88.2 – 1.2 m = 87 m be tkhe height of balloon from the horizontal level of girl’s eyesight.
In ΔABD
tan θ = $$\frac{AB}{BD}$$
⇒ tan 30° = $$\frac{88.2}{BD}$$
⇒ $$\frac{1}{\sqrt{3}}$$ = $$\frac{87}{BD}$$
⇒ BD = 87 x $$\sqrt{3}$$ = 87$$\sqrt{3}$$m ……….(1)
Now in right ΔDCE
tan θ = $$\frac{CE}{DC}$$
⇒ tan 60° = $$\frac{87}{DC}$$
⇒ $$\sqrt{3}$$ = $$\frac{87}{DC}$$ (CE = AB = 88.2 m)
⇒ DC = $$\frac{87}{\sqrt{3}}$$= $$\frac{87}{\sqrt{3}}$$ x $$\frac{\sqrt{3}}{\sqrt{3}}$$ = $$\frac{87 \sqrt{3}}{3}$$
⇒ DC = 29$$\sqrt{3}$$ ………(2)
BC = BD – DC
= 87$$\sqrt{3}$$ – 29$$\sqrt{3}$$ = 58$$\sqrt{3}$$ m
Hence, distance travelled by balloon is 58$$\sqrt{3}$$ m.
Question 15.
A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 600. Find the time taken by the car to reach the foot of the tower from this point. (CBSE 2008, 2009)
Solution:
Let AB be the height of the tower.
In ΔABC
tan 60° = $$\frac{AB}{BC}$$
$$\sqrt{3}$$ = $$\frac{h}{BC}$$
BC = $$\frac{h}{\sqrt{3}}$$ ……….(1)
Now in ΔABD
⇒ tan θ = $$\frac{AB}{BD}$$
⇒ tan 30° = $$\frac{h}{BD}$$
⇒ $$\frac{1}{\sqrt{3}}$$ = $$\frac{h}{BD}$$
⇒ BD = $$\sqrt{3} h$$ ………..(2)
CD = BD – BC = $$\sqrt{3} h$$ – $$\frac{h}{\sqrt{3}}$$
CD = $$\frac{3 h – h}{\sqrt{3}}$$ = $$\frac{2h}{\sqrt{3}}$$
Time taken by car to travel a distance CD = $$\frac{2h}{\sqrt{3}}$$ is 6 seconds
∴ $$\frac{2h}{\sqrt{3}}$$ metre distance travelled in 6 seconds
∴ $$\frac{h}{\sqrt{3}}$$ metre distance travelled in = $$\frac{6}{2 h} \times \frac{\sqrt{3} \times h}{\sqrt{3}}=\frac{6}{2}$$ = 3 seconds
Hence, time taken by car to reach foot of tower is 3 seconds.
Question 16.
The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. Prove that the height of the tower is 6 m.
Solution:
Let h = AB be the height of tower
In right ΔABD
tan θ = $$\frac{AB}{AD}$$
tan θ = $$\frac{h}{9}$$ ………(1)
Now, in ΔABC
tan (90° – θ) = $$\frac{AB}{AC}$$ ………(1)
⇒ cot θ = $$\frac{h}{4}$$ ………….(2)
From eqn. (1) and (2)
tan θ x cot θ = $$\frac{h}{4}$$ x $$\frac{h}{4}$$
tan θ x $$\frac{1}{\tan \theta}$$ = $$\frac{h^{2}}{36}$$
⇒ 1 = $$\frac{h^{2}}{36}$$
⇒ h2 = 36
⇒ h = 6
Hence, height of tower is 6 m. | 2022-12-06 20:10:26 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.852131187915802, "perplexity": 1244.1512203083373}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711114.3/warc/CC-MAIN-20221206192947-20221206222947-00775.warc.gz"} |
http://tex.stackexchange.com/questions/88347/xy-eps-converted-to-pdf-not-found-wrong-filename | I'm trying to include an EPS file into a PDF file using MikTex 2.9 under Windows 8. Everything else LaTex related works like a charm.
pdflatex keeps complaining about a missing xy-eps-converted-to.pdf file. However a xy.pdf exists and is exactly that file that pdflatex should use instead of the xy-eps-converted-to.pdf, so it's just the filename that appears to be wrong.
Either epstopdf is giving the file the wrong name or pdflatex is expecting the wrong one. Whichever way might be right or wrong, how do I kind of synchronize them to use the same filename?
-
I'll give that a try, however I've chosen to use pdflatex with pngs that I create from the eps files manually. Much more convenient in my book. – Hendrik Wiese Dec 28 '12 at 11:18
Are you including it as `\includegraphics[..]{xy.eps}`? If so, don't. Use `\includegraphics[..]{xy}` - the driver will take care of file extensions.
Under `pdflatex`, an EPS is converted to a PDF, but if a PNG exists, then it will be used (a legacy preference order). There are default file extensions accepted by `pdflatex`, searched in a specific order (see Graphics file extensions and their order of inclusion when not specified), so there's no need to include the extension. Moreover, this allows for one to possibly switch between processing a document in `latex` and `pdflatex`, letting the compiler decide on the graphics file to include.
If you're still experiencing problems, there should be a converted version of your `.eps` in the working folder. Rename this to an appropriate `.pdf` name (say, `xy.pdf`) and then include this verbatim
``````\includegraphics{xy.pdf} | 2016-05-06 00:22:54 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9276345372200012, "perplexity": 1831.2627859377158}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-18/segments/1461861700245.92/warc/CC-MAIN-20160428164140-00005-ip-10-239-7-51.ec2.internal.warc.gz"} |
https://pclambert.net/software/mrsprep/ | # mrsprep
The mrsprep command restructures survival data and calculates weighted mean expected mortality rates and time-dependent weights so that a marginal relative survival can be directly estimated. After running mrsprep estimation commands that fit (conditional) relative survival models (e.g. stpm2 or strcs) can be used to estimate marginal relative survival without out the need to include covariates that affect expected survival.
You can install mrsprep within Stata using
. ssc install mrsprep | 2021-09-27 06:05:38 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.83852618932724, "perplexity": 13202.575403118859}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780058373.45/warc/CC-MAIN-20210927060117-20210927090117-00710.warc.gz"} |
http://www.ck12.org/chemistry/Mole-Ratios/lesson/Mole-Ratios-CHEM/ | <img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
Mole Ratios
Determine amounts of materials involved in a reaction
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Mole Ratios
Credit: User:Ilemme/Wikipedia
Source: http://commons.wikimedia.org/wiki/File:Col_03_scup_porch_chairs.JPG
What does this porch need?
You want to add some sections to the porch seen above. Before you go to the hardware store to buy lumber, you need to determine the unit composition (the material between two large uprights). You count how many posts, how many boards, how many rails – then you decide how many sections you want to add before you calculate the amount of building material needed for your porch expansion.
Mole Ratios
Stoichiometry problems can be characterized by two things: (1) the information given in the problem, and (2) the information that is to be solved for, referred to as the unknown. The given and the unknown may both be reactants, both be products, or one may be a reactant while the other is a product. The amounts of the substances can be expressed in moles. However, in a laboratory situation, it is common to determine the amount of a substance by finding its mass in grams. The amount of a gaseous substance may be expressed by its volume. In this concept, we will focus on the type of problem where both the given and the unknown quantities are expressed in moles.
Credit: CK-12 Foundation - Christopher Auyeung
Mole ratio relationship.[Figure2]
Chemical equations express the amounts of reactants and products in a reaction. The coefficients of a balanced equation can represent either the number of molecules or the number of moles of each substance. The production of ammonia (NH3) from nitrogen and hydrogen gases is an important industrial reaction called the Haber process, after German chemist Fritz Haber.
N2(g)+3H2(g)2NH3(g)\begin{align*}\text{N}_2 (g)+3\text{H}_2 (g) \rightarrow 2\text{NH}_3 (g)\end{align*}
The balanced equation can be analyzed in several ways, as shown in Figure below.
Credit: CK-12 Foundation - Christopher Auyeung
This representation of the production of ammonia from nitrogen and hydrogen show several ways to interpret the quantitative information of a chemical reaction.[Figure3]
We see that 1 molecule of nitrogen reacts with 3 molecules of nitrogen to form 2 molecules of ammonia. This is the smallest possible relative amounts of the reactants and products. To consider larger relative amounts, each coefficient can be multiplied by the same number. For example, 10 molecules of nitrogen would react with 30 molecules of hydrogen to produce 20 molecules of ammonia.
The most useful quantity for counting particles is the mole. So if each coefficient is multiplied by a mole, the balanced chemical equation tells us that 1 mole of nitrogen reacts with 3 moles of hydrogen to produce 2 moles of ammonia. This is the conventional way to interpret any balanced chemical equation.
Finally, if each mole quantity is converted to grams by using the molar mass, we can see that the law of conservation of mass is followed. 1 mol of nitrogen has a mass of 28.02 g, while 3 mol of hydrogen has a mass of 6.06 g, and 2 mol of ammonia has a mass of 34.08 g.
28.02 g N2+6.06 g H234.08 g NH3\begin{align*}28.02 \ \text{g N}_2 + 6.06 \ \text{g H}_2 \rightarrow 34.08 \ \text{g NH}_3\end{align*}
Mass and the number of atoms must be conserved in any chemical reaction. The number of molecules is not necessarily conserved.
Credit: User:JGvBerkel/Wikimedia Commons
Source: http://commons.wikimedia.org/wiki/File:Haber_Ammonia.JPG
Apparatus for running Haber process.[Figure4]
A mole ratio is a conversion factor that relates the amounts in moles of any two substances in a chemical reaction. The numbers in a conversion factor come from the coefficients of the balanced chemical equation. The following six mole ratios can be written for the ammonia forming reaction above.
1 mol N23 mol H2or 3 mol H21 mol N21 mol N22 mol NH3or 2 mol NH31 mol N23 mol H22 mol NH3or 2 mol NH33 mol H2\begin{align*}&\frac{1 \text{ mol N}_2}{3 \text{ mol H}_2} \quad \quad or \quad \ \ \frac{3 \text{ mol H}_2}{1 \text{ mol N}_2} \\ &\frac{1 \text{ mol N}_2}{2 \text{ mol NH}_3} \quad or \quad \ \ \frac{2 \text{ mol NH}_3}{1 \text{ mol N}_2} \\ &\frac{3 \text{ mol H}_2}{2 \text{ mol NH}_3} \quad or \quad \ \ \frac{2 \text{ mol NH}_3}{3 \text{ mol H}_2}\end{align*}
In a mole ratio problem, the given substance, expressed in moles, is written first. The appropriate conversion factor is chosen in order to convert from moles of the given substance to moles of the unknown.
Sample Problem: Mole Ratio
How many moles of ammonia are produced if 4.20 moles of hydrogen are reacted with an excess of nitrogen?
Step 1: List the known quantities and plan the problem.
Known
• given: H2 = 4.20 mol
Unknown
• mol of NH3
The conversion is from mol H2 → NH3. The problem states that there is an excess of nitrogen, so we do not need to be concerned with any mole ratio involving N2. Choose the conversion factor that has the NH3 in the numerator and the H2 in the denominator.
Step 2: Solve.
4.20 mol H2×2 mol NH33 mol H2=2.80 mol NH3\begin{align*}4.20 \text{ mol H}_2 \times \frac{2 \text{ mol NH}_3}{3 \text{ mol H}_2}=2.80 \text{ mol NH}_3\end{align*}
The reaction of 4.20 mol of hydrogen with excess nitrogen produces 2.80 mol of ammonia.
The result corresponds to the 3:2 ratio of hydrogen to ammonia from the balanced equation.
Summary
• Mole ratios allow comparison of the amounts of any two materials in a balanced equation.
• Calculations can be made to predict how much product can be obtained from a given number of moles of reactant.
Review
1. If a reactant is in excess, why do we not worry about the mole ratios involving that reactant?
2. What is the mole ratio of H to N in the ammonia molecule?
3. The formula for ethanol is CH3CH2OH. What is the mole ratio of H to C in this molecule?
Notes/Highlights Having trouble? Report an issue.
Color Highlighted Text Notes | 2017-01-19 00:30:42 | {"extraction_info": {"found_math": true, "script_math_tex": 4, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9454823732376099, "perplexity": 1858.2760489119719}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560280410.21/warc/CC-MAIN-20170116095120-00322-ip-10-171-10-70.ec2.internal.warc.gz"} |
http://mathhelpforum.com/algebra/184650-inverted-parabola-print.html | # Inverted Parabola
• Jul 16th 2011, 01:08 PM
theloser
Inverted Parabola
http://www.webassign.net/cgi-bin/sym...29%2A%2A2%20-3
How do I find the vertex?
I set y to zero then I get -3? I think.
• Jul 16th 2011, 01:35 PM
SpringFan25
Re: Inverted Parabola
Can you find the vertex of $x=y^2$ ?
Your function is stretched and shifted version of $x=y^2$. Identify the transformation and you will see where the new vertex is.
• Jul 16th 2011, 05:41 PM
HallsofIvy
Re: Inverted Parabola
No, you do NOT set y equal to 0. That would give the y-intercept which, in general, has nothing to with the vertex.
Since a square is never 0, $x= 3(y+1)^2- 3$, is never less than -3. It is -3 when the square is 0- that is, when y+ 1= 0.
• Jul 16th 2011, 07:01 PM
skoker
Re: Inverted Parabola
it helps to write out the standard form formula. then you can see what its telling you.
$f(x)=a(x-h)^2+k$ vertex=(h,k)
you also know your values are inverted. | 2017-12-17 23:37:09 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 4, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8929341435432434, "perplexity": 2274.050647696348}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948599156.77/warc/CC-MAIN-20171217230057-20171218012057-00428.warc.gz"} |
https://math.stackexchange.com/questions/2986442/understanding-relation-between-laurent-series-and-singularities | Understanding relation between Laurent Series and Singularities
I am thinking about an example, in order to better understand how Laurent Series help us understand the Poles, Zeros and Essential singularities of a complex function.
I am trying to find the singularities of $$\frac{1}{sin(z)} - \frac{1}{z}$$
Individually, 1/z has a pole of order 1 at 0
For $$\frac{1}{z}$$ I am quite confused as to what to do. Given for sin(z), it has zeros at $$n \pi$$ for all integer $$n$$, so the inverse has poles of order 1 at those points. But what happens at 0, where $$\frac{1}{sin(z)} - \frac{1}{z}$$ have poles pushing against each other?
Thank you for some hints on how to see this example!
1 Answer
Write it as $$\frac {z-\sin\, z}{z\sin \,z}$$ and apply L'Hopital's Rule twice to see that the limit as $$z \to 0$$ is $$0$$. The function has a removable singularity at $$0$$.
• Ohhh, it works! But could we see this using Laurent series? Nov 6 '18 at 0:09
• $\frac z {\sin \, z}$ is analytic near $0$. Its power series expansion (in $|z|<\pi$) is of the form $1+a_1z+\cdots$. Dividing by $z$ you get the Laurent series for $\frac 1 {\sin\, z}$ which is of the form $\frac 1 z+g(z)$ with $g$ analytic. Nov 6 '18 at 0:35 | 2021-10-18 10:58:26 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 9, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9351951479911804, "perplexity": 107.93034139743662}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585201.94/warc/CC-MAIN-20211018093606-20211018123606-00495.warc.gz"} |
https://meta.mathoverflow.net/questions/4551/what-to-do-with-the-synonyms-for-the-deprecated-tags?noredirect=1 | # What to do with the synonyms for the deprecated tags?
Recently, the following tag synonyms were created by a MathOveflow moderator: $$\to$$ , $$\to$$ and $$\to$$ . You can see the new synonyms in the list of tag synonyms (Wayback Machine). The three tags (abstract-algebra), (geometry) and (discrete-mathematics) were deprecated, you can find links to their original tag-excerpts here: What is the correct way to handle questions with deprecated tags? There is also some related discussion in MO editor's lounge. (Possibly you can just check the starred messages if you want to get a brief overview without reading the whole things.)
As far as I can tell, the tags weren't merged when the synonyms were created.1 This has the advantage that creation of the synonym can be reversed. (If the tags are merged and synonymized, even after canceling the synonym the question will still have the new tag and there isn't a way to restore the original tags.) If you check some older questions which originally had those tags, you can still see there (abstract-algebra), (discrete-mathematics) or (geometry). IIRC the tags will remain in this way until the question is edited.
The fact that the tags are now synonyms means that:
• When somebody tries to add the old tag, it is automatically replaced by the new tag. (The same thing happens if a question is edited.)
• The old tags behave in search as their synonym. (For example, if you click on , you are shown the posts tagged .)
Of course, creating the synonym means that some questions do not have appropriate tags. (For example, not every question which was tagged (geometry) is a good fit for (mg.metric-geometry).) However, as the questions still display the original tag, at least we can recognize the "suspect" questions while viewing the question.
It seems that the synonyms were created without discussion here on meta. (I do no know whether the moderators discussed this step among them.) The purpose of this question is to get some input from MathOverflow community on these synonyms. (Since this influenced tags on approximately 700 to 750 questions, that seem to be quite significant change, the MathOverflow community probably should be aware that this happened.)
Main question. Should these synonyms remain, or should they be cancelled? Should the tags be merged or not? (And if they are merged, should the deprecated tags be removed or should they remain as a synonym?) If currently merging is not suitable, should they be merged later? Should the tags be blacklisted - to prevent users from adding them to new questions?
The moderator who created the tag synonyms mentioned two aspects as advantages of the current state: "I see two advantages to the current situation with the synonyms: (1) No new uses of the old tag, and automatic retagging on edit. (2) We can still search out the tag by hand (e.g., using a browser's "find" function on a page full of questions) and manually change them over time."
Preventing new questions from using the deprecated tags. It is true, that with these synonyms in place the deprecated tags are not added to new questions, as they are automatically changed to other tags. One thing to consider is whether this might lead to incorrectly tagged question. (Some people might not noticed that when they entered (geometry), it was converted to (mg.metric-geometry).)
If we want to prevent the tags from being added to new questions, the tags could be blacklisted instead of having a synonyms. This is what I proposed before: The existing deprecated tags should be blacklisted.
Changing tags without bumping. Synonyms have changed which tags are found, for example, when searching for (mg.metric-geometry). (Even the ones which were originally tagged (geometry).) This was done without having to bump any questions. There are also other tools available to mods which can achieve such large-scale changes. For example, if the tag (geometry) is manually cleaned in such way that all questions in this tag fit into (mg.metric-geometry), then the two tags can be merged. (This replaces all instances of one tag by the other one.) Or if the tag (geometry) is in the state where all existing questions would be correctly tagged after omitting this tag, moderators can ask Stack Exchange staff to burninate the tag (which removes all instance of the tag completely). However, both burnination and merging should IMO be done only after the sufficient clean-up of the tag.
Finding the questions with deprecated tags. As mentioned above, after this change some questions are not tagged correctly and could possibly require further clean-up. However, it is now more difficult to find those posts. (For instance, searching for posts tagged (geometry) now returns the posts with the (mg.metric-geometry) tag.) The deprecated tags on those questions are still visible, but they are more difficult to find. (They would be easier to find if the tag synonyms were canceled. As mentioned above, we can still prevent the deprecated tags from being added to new questions using blacklisting.)
It is possible to use various SEDE queries to search among the questions which have the deprecated tags. For example, this query returns the questions which have the given tag.2 And you can add various further criteria to the query.3 (Although it is definitely less comfortable than searching directly on the site. Moreover, the data in SEDE are only updated once a week.)
In case it is useful, users who are interested in the tag management could create some list of questions which had the deprecated tags (either on site or off site). I have made a post to show what I mean here: Recent tag synonyms for deprecated tags. (The post is visible to 10k+ users and mods. I deleted the question after posting it - I did not want to have two closely related posts on meta after each other. Moreover, if the linked question will be actually used, it could probably get bumped a lot.)
Since not everybody is familiar with tag-related actions, let me also briefly summarize some terminology.
• Tag synonym. A synonym (tag1) $$\to$$ (tag2) means that the tag (tag1) will be automatically replaced by (tag2) when added to question or when editing a question. And in many other aspects, (tag1) now behaves as (tag2). (For example, searching for (tag1) gives the posts with (tag2).) See also the FAQ post: What are tag synonyms and merged tags? How do they work?
• Merging two tags. Merging should be used carefully, since it is not a reversible process. If a tag (geometry) is merged into (mg.metric-geometry), that means that all instances of (geometry) are changed to (mg.metric-geometry). (Without bumping any questions.) The change is also made in the revision history. (So from the question it will no longer be visible which tag it had before merging.) There is a section "What are merged tags?" in the FAQ post: What are tag synonyms and merged tags? How do they work?
• Blacklisting a tag. Blacklisting prevents the tag from being added to new questions. (And, at the same time, if some question already has the blacklisted tag, it must be changed when the question is edited - an edit which still keeps the blacklisted tag cannot be saved.) I tried to explain the details concerning blacklisting in my previous post: The existing deprecated tags should be blacklisted. There is also a FAQ post: What is a blacklisted tag?
• Burnination means that all occurrences of the tag are removed from all questions which have the given tag. Again this is done without bumping any questions. Unlike merging, this cannot be done by mods, so a member of Stack Exchange staff has to be involved. See also: What does it mean to “burninate” a tag?
2In SEDE you can see the status when the database was last updated, which was before creating the synonym. (It is updated once a week.) As far as I can tell, the questions will be still visible in the SEDE queries even after the next update of SEDE. (Unless the moderators also merge the tags.) You can check some similar instances - the tags which were made synonyms without merging - on Mathematics, such as span or conditional-probability. (Here are related discussions on Mathematics Meta: Unable to add “span” tag to (linear algebra) question and Cannot add tag “conditional-probability”.)
3 Examples of various queries can be found in chat: https://chat.stackexchange.com/transcript/10243/2020/5/5 https://chat.stackexchange.com/transcript/10243/2020/5/6 | 2023-02-01 12:02:42 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 4, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.24973180890083313, "perplexity": 1454.930171736979}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499934.48/warc/CC-MAIN-20230201112816-20230201142816-00613.warc.gz"} |
https://en.wikipedia.org/wiki/Shields_parameter | # Shields parameter
The Shields parameter, also called the Shields criterion or Shields number, is a nondimensional number used to calculate the initiation of motion of sediment in a fluid flow. It is a nondimensionalization of a shear stress, and is typically denoted ${\displaystyle \tau _{\ast }}$ or ${\displaystyle \theta }$. It is given by:
${\displaystyle \tau _{\ast }=\theta ={\frac {\tau }{(\rho _{s}-\rho )gD}},}$
where:
• ${\displaystyle \tau }$ is a dimensional shear stress;
• ${\displaystyle \rho _{s}}$ is the density of the sediment;
• ${\displaystyle \rho }$ is the density of the fluid;
• ${\displaystyle g}$ is acceleration due to gravity;
• ${\displaystyle D}$ is a characteristic particle diameter of the sediment.
## Physical meaning
By multiplying the top and bottom of the Shields parameter by D2, you can see that it is proportional to the ratio of fluid force on the particle to the weight of the particle. | 2018-03-18 10:09:04 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 8, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9150173664093018, "perplexity": 531.5139217613557}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257645604.18/warc/CC-MAIN-20180318091225-20180318111225-00620.warc.gz"} |
http://forums.autodesk.com/t5/Autodesk-MapGuide-Enterprise/Measure-Distance-Units/m-p/1813000 | Discussion Groups
Autodesk MapGuide Enterprise
Valued Contributor
Posts: 63
Registered: 11-08-2000
Measure Distance Units
425 Views, 5 Replies
11-07-2006 03:49 PM
Does anyone know how to make the measure command display results in feet rather than miles?
Active Contributor
Posts: 37
Registered: 12-18-2003
Re: Measure Distance Units
11-10-2006 11:26 AM in reply to: gbneff
Greg,
I don't see a way to configure this via the UI. But I think you can do it by modifying 2 lines in each of these files installed by the MapGuide Web Extensions:
mapviewerphp/measure.php
mapviewerjava/measure.jsp
mapviewernet/measure.aspx
Bill
Valued Contributor
Posts: 63
Registered: 11-08-2000
Re: Measure Distance Units
11-13-2006 03:53 PM in reply to: gbneff
Bill,
Thanks for the reply. I am able to change the conversion factor and get the distance displayed in feet. Do you know which file(s) to look at to change the label from "Miles" to "Feet" in the Measure Distace pane?
Thanks,
Greg
Active Contributor
Posts: 37
Registered: 12-18-2003
Re: Measure Distance Units
11-13-2006 08:23 PM in reply to: gbneff
Hi Greg,
I think the label string is in those same files. Try a case-insensitive search for "miles".
Bill
Employee
Posts: 727
Registered: 09-14-2006
Re: Measure Distance Units
11-14-2006 08:43 AM in reply to: gbneff
I believe the labels are contained inside the en resource file found under ..\webserverextensions\www\localized\.
The DISTANCEMILES, DISTANCEKILOMETERS etc are where the values come from. However it appears that the measure.php (or jsp or apsx) page is where the strings are referenced and need to be changed. Ideally an enahancement is needed to allow the user to specify the units to measure in rather than have the pages hardcoded based on the viewer settings. Since users may be using data that is for floorplans or small developments they may not be working in kilometers or miles and hence the measure pages don't accomodate this.
Dave
Dave Wilson
SQA Analyst
AEC IM
Autodesk, Inc.
Valued Contributor
Posts: 63
Registered: 11-08-2000
Re: Measure Distance Units
11-14-2006 03:46 PM in reply to: gbneff
I agree. For my needs I will always want measurements in feet. Miles is far too coarse a measurment.
I made the following two changes to display my measurements in feet:
in the C:\Program Files\MapGuideOpenSource\WebServerExtensions\www\mapviewerphp\measure.php file I changed the conversion factor to convert from meters to feet instead of meters to miles:
\$distance *= 3.2808399; //get feet
In the C:\Program Files\MapGuideOpenSource\WebServerExtensions\www\viewerfiles\measureui.templ file I modified showunits function to set the units var to "Feet". | 2013-05-26 09:14:24 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8109219074249268, "perplexity": 6763.750317844226}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368706794379/warc/CC-MAIN-20130516121954-00012-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://byjus.com/question-answer/a-picnic-is-being-planned-in-a-school-for-class-seven/ | Question
# A picnic is being planned in a school for Class $VII$. Girls are $60%$ of the total number of students and are$18$ in number. The picnic site is $55km$from the school and the transport company is charging the rate of $Rs12perkm$. The total cost of refreshments will be $Rs4280.$ Find the ratio of the number of girls to the number of boys in the class?
Open in App
Solution
## Step 1 - Finding the total number of students Let the total students be $x$Number of girls $=60%$of the total number of students $⇒18=60%$ of $x$ $⇒18=\frac{60}{100}×x\left(\because ofmeansmultiplication\right)\phantom{\rule{0ex}{0ex}}⇒18=\frac{60x}{100}\phantom{\rule{0ex}{0ex}}⇒18=\frac{6x}{10}\phantom{\rule{0ex}{0ex}}⇒x=\frac{18×10}{6}\phantom{\rule{0ex}{0ex}}⇒x=3×10\phantom{\rule{0ex}{0ex}}⇒x=30\phantom{\rule{0ex}{0ex}}$The total number of students is $30$Step 2- Ratio of the number of girls to the number of boys Now, the number of boys $=$Total number of students $-$number of girls the number of boys$=30-18$ the number of boys $=12$$\frac{\mathbf{t}\mathbf{h}\mathbf{e}\mathbf{}\mathbf{n}\mathbf{u}\mathbf{m}\mathbf{b}\mathbf{e}\mathbf{r}\mathbf{}\mathbf{o}\mathbf{f}\mathbf{}\mathbf{g}\mathbf{i}\mathbf{r}\mathbf{l}\mathbf{s}\mathbf{}}{\mathbf{t}\mathbf{h}\mathbf{e}\mathbf{}\mathbf{n}\mathbf{u}\mathbf{m}\mathbf{b}\mathbf{e}\mathbf{r}\mathbf{}\mathbf{o}\mathbf{f}\mathbf{}\mathbf{b}\mathbf{o}\mathbf{y}\mathbf{s}\mathbf{}}=\frac{18}{12}\phantom{\rule{0ex}{0ex}}=\frac{3}{2}$Hence, the required ratio is $3:2$
Suggest Corrections
10 | 2023-02-07 11:08:30 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 32, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4469226896762848, "perplexity": 466.5605488958381}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500456.61/warc/CC-MAIN-20230207102930-20230207132930-00268.warc.gz"} |
https://www.nature.com/articles/s41586-020-3006-1?error=cookies_not_supported&code=2cded840-df74-45d6-aa1d-9b5be69a8676 | # Entanglement on an optical atomic-clock transition
## Abstract
State-of-the-art atomic clocks are based on the precise detection of the energy difference between two atomic levels, which is measured in terms of the quantum phase accumulated over a given time interval1,2,3,4. The stability of optical-lattice clocks (OLCs) is limited both by the interrupted interrogation of the atomic system by the local-oscillator laser (Dick noise5) and by the standard quantum limit (SQL) that arises from the quantum noise associated with discrete measurement outcomes. Although schemes for removing the Dick noise have been recently proposed and implemented4,6,7,8, performance beyond the SQL by engineering quantum correlations (entanglement) between atoms9,10,11,12,13,14,15,16,17,18,19,20 has been demonstrated only in proof-of-principle experiments with microwave clocks of limited stability. The generation of entanglement on an optical-clock transition and operation of an OLC beyond the SQL represent important goals in quantum metrology, but have not yet been demonstrated experimentally16. Here we report the creation of a many-atom entangled state on an OLC transition, and use it to demonstrate a Ramsey sequence with an Allan deviation below the SQL after subtraction of the local-oscillator noise. We achieve a metrological gain of $$4.{4}_{-0.4}^{+0.6}$$ decibels over the SQL by using an ensemble consisting of a few hundred ytterbium-171 atoms, corresponding to a reduction of the averaging time by a factor of 2.8 ± 0.3. Our results are currently limited by the phase noise of the local oscillator and Dick noise, but demonstrate the possible performance improvement in state-of-the-art OLCs1,2,3,4 through the use of entanglement. This will enable further advances in timekeeping precision and accuracy, with many scientific and technological applications, including precision tests of the fundamental laws of physics21,22,23, geodesy24,25,26 and gravitational-wave detection27.
## Access options
from\$8.99
All prices are NET prices.
## Data availability
All data obtained in the study are available from the corresponding author upon reasonable request.
## References
1. 1.
Ludlow, A. D., Boyd, M. M., Ye, J., Peik, E. & Schmidt, P. O. Optical atomic clocks. Rev. Mod. Phys. 87, 637–701 (2015).
2. 2.
Ushijima, I., Takamoto, M., Das, M., Ohkubo, T. & Katori, H. Cryogenic optical lattice clocks. Nat. Photon. 9, 185–189 (2015).
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## Acknowledgements
We thank H. Katori, W. Ketterle, A. Ludlow, M. Lukin, J. Ramette, G. Roati, A. Urvoy, Z. Vendeiro and J. Ye for discussions. This work was supported by NSF, DARPA, ONR and the NSF Center for Ultracold Atoms (CUA). S.C. and A.F.A. acknowledge support from the Swiss National Science Foundation (SNSF). B.B. acknowledges support from the National Science and Engineering Research Council of Canada.
## Author information
Authors
### Contributions
A.K., B.B., C.S., E.P.-P., S.C., A.F.A., Z.L., E.M. and V.V. contributed to the building of the experiment. E.P.-P., S.C. and C.S. led the experimental efforts and simulations. S.C., A.F.A., C.S. and E.P.-P. contributed to the data analysis. V.V. conceived and supervised the experiment. S.C. and V.V. wrote the manuscript. All authors discussed the experiment implementation and results and contributed to the manuscript.
## Ethics declarations
### Competing interests
The authors declare no competing interests.
Peer review information Nature thanks the anonymous reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.
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## Rights and permissions
Reprints and Permissions
Pedrozo-Peñafiel, E., Colombo, S., Shu, C. et al. Entanglement on an optical atomic-clock transition. Nature 588, 414–418 (2020). https://doi.org/10.1038/s41586-020-3006-1
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• Issue Date: | 2021-01-19 07:11:45 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7802936434745789, "perplexity": 7901.899445408662}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703517966.39/warc/CC-MAIN-20210119042046-20210119072046-00547.warc.gz"} |
https://www.niser.ac.in/sms/news/niser-colloquium | # News & Events
## NISER Colloquium
Date/Time:
Friday, October 26, 2018 - 16:00 to 17:00
Venue:
LH-5
Speaker:
Parameswaran Shankaran
Affiliation:
IMSc Chennai
Title:
The geometry of the upper half-space
The parallel postulate of the Euclidean geometry says that there is exactly one straight line that is parallel to a given line l and passes through a given point P which is not on l. There are several equivalent axioms---such as the sum of the angles in a triangle equals $\pi$. We will see that there are geometries where the parallel postulate fails. One such is the geometry of the Poincaré upper half-space. We will point out some interesting features of the upper half-space. | 2020-05-28 04:31:32 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5815845727920532, "perplexity": 268.61238677287645}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347396495.25/warc/CC-MAIN-20200528030851-20200528060851-00450.warc.gz"} |
http://www.lattice2013.uni-mainz.de/static/AM.html | # Algorithms and Machines
UV suppression by smearing and screening correlators
Nikhil Karthik, Sourendu Gupta
Mon, 14:00, Seminar Room D -- Parallels 1D (Slides)
We investigate the mechanism of smearing in the APE, Stout, HYP and HEX schemes through their effect on glue and quark Fourier modes. Using this, we non-perturbatively tune the smearing parameters to their optimum values. Smearing causes a super-linear improvement in taste symmetry breaking in the high temperature phase of QCD. We use optimal smearing in the high temperature phase and find close agreement of meson screening masses with weak coupling predictions.
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Testing reweighting method for truncated Overlap fermions
Ken-Ichi Ishikawa
Mon, 14:20, Seminar Room D -- Parallels 1D (Slides)
It is a hard task to maintain the lattice chiral symmetry during the HMC algorithm. One possibility to reduce the total computational cost is to relax the requirement of the chiral symmetry and to use the reweighing method recovering the symmetry at the measurement phase. The HMC algorithm with the truncated overlap fermion with approximate lattice chiral symmetry has been proposed by Borici in terms of domain-wall type fermions. The reweighing factor is the determinant ratio between the truncated and exact overlap operators and is estimated by noise method. We implement the truncated overlap fermion in terms of the domain-wall fermions and test the behavior of the reweighing factor against the truncation level (fifth dimensional extent) on a set of small lattices.
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Scaling, topological tunneling and actions for weak coupling DWF calculations
Greg McGlynn, Robert Mawhinney
Mon, 14:40, Seminar Room D -- Parallels 1D (Slides)
We present results from a 2+1 flavor DWF calculation at 1/a = 3 GeV and discuss strategies for similar calculations at finer lattice spacings which will target charm physics. At weak coupling the autocorrelation time of the global topological charge becomes very long because the HMC algorithm has trouble moving between topological sectors. We report the results of simulations that test several ideas for reducing the autocorrelation time of topological charge. In weak coupling quenched simulations we find that the open boundary conditions suggested by Lüscher and Schaefer do not improve topological autocorrelation times. We present preliminary results from simulations using a dislocation-enhancing determinant ratio'' to improve topological tunneling.
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Adaptive Aggregation Based Domain Decomposition Multigrid for the Lattice Wilson Dirac Operator
Matthias Rottmann, Andreas Frommer, Karsten Kahl, Stefan Krieg, Björn Leder
Mon, 15:00, Seminar Room D -- Parallels 1D (Slides)
In this talk, we present a multigrid approach for the inversion of the lattice Wilson Dirac operator. It combines components that have already been used separately in lattice QCD, namely the domain decomposition method Schwarz Alternating Procedure'' as a smoother, also known from the Inexact Deflation'' method and the $$\gamma_5$$-preserving aggregation based interpolation, introduced by the Boston and Boulder group. We will point out the major differences to the existing hierarchical approaches and we will show numerical results from our MPI-C Code. Aspects from the recently published numbers in [arXiv:1303.1377] for the two-grid approach will be picked up but also new three-grid results will be shown.
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HDCG: Hierarchically Deflated Conjugate Gradient algorithm for 5d Chiral Fermions
Peter Boyle
Mon, 15:20, Seminar Room D -- Parallels 1D (Slides)
I present an algorithm for 5d Chiral Fermions that, after a modest subspace generation phase, accelerates the inversion of the Hermitian red-black preconditioned Hermitian operator (normal equations) for general Mobius fermions. The approach is an extension of the inexact deflation approach to this system of equations, but also bears some similarity to algebraic multigrid approaches. The little Dirac operator is expensive due to the next-to-next-to-next-to-nearest neighbour stencil. I find that preconditioned CG is remarkably stable against preconditioner noise and that flexible algorithms are not needed. By using the little Dirac operator solely as a preconditioner and adopting a three level deflation, the overhead is suppressed by two orders of magnitude compared to the inexact deflation approach. On small ($$16^3$$) volumes the approach is similar in performance to EigCG. On large ($$48^3$$) volumes and at the physical quark masses the approach is between 2x and 5x more effective then EigCG with much reduced set up cost, and 10x more effective than CGNR.
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Optimization of the Oktay-Kronfeld Action Conjugate Gradient Inverter
Yong-Chull Jang, Jon Bailey, Carleton DeTar, Andreas Kronfeld, Weonjong Lee, Bugra Oktay
Mon, 15:40, Seminar Room D -- Parallels 1D (Slides)
Carrying out the Fermilab improvement program to third order in heavy-quark effective theory yields the Oktay-Kronfeld (OK) action, a promising candidate for precise calculations of the spectra of heavy quark systems and weak matrix elements of heavy-light systems. We have optimized the OK-action conjugate gradient inverter in the SciDAC QOP/QDP library and are developing a GPU code. The OK action is rewritten and the needed gauge-link combinations are precalculated. This procedure accelerates the conjugate gradient by more than a factor of five. The remaining floating-point operations are simple matrix multiplications between gauge links and fermion vectors, which we accelerate with CUDA. We present preliminary results for the spectra confirming expected decreases of heavy-quark discretization errors.
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One flavor mass reweighting: foundations
Björn Leder, Jacob Finkenrath, Francesco Knechtli
Mon, 16:30, Seminar Room D -- Parallels 2D (Slides)
Reweighting is not a new method in lattice QCD, but a comprehensive analysis is missing in the literature. We close this gap by presenting: (i) a proof of an integral representation of the complex determinant of a complex matrix, (ii) a method to control the stochastic error of its Monte Carlo estimation, (iii) expansions of the stochastic error and the ensemble fluctuations of the one flavor reweighting factor. Based on (iii) we present a detailed scaling analysis and optimized reweighting strategies.
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Towards Simulations of 1+1 Flavor QCD
Jacob Finkenrath, Francesco Knechtli, Björn Leder
Mon, 16:50, Seminar Room D -- Parallels 2D (Slides)
Today's simulations in lattice quantum chromodynamics get closer and closer to the physical point by simultaneously minimizing the statistical errors. Small effects like isospin symmetry--breaking start becoming significant. Incorporating such effects into the Boltzmann factor by reweighting introduces fluctuations which increase with the volume. Correlations between parts of the lattice actions can be utilized to reduce this fluctuations significantly. We combine and compare approaches consisting of reweighting and a modified sampling for generating configurations. Employing these methods we can estimate non-perturbatively the effect of the sea quarks on isospin splitting.
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Exact Pseudofermion Action for Hybrid Monte Carlo Simulation of One-Flavor Domain-Wall Fermion
Yu-Chih Chen, Wen-Ping Chen, Ting-Wai Chiu, Han-Yi Chou, Tung-Han Hsieh
Mon, 17:10, Seminar Room D -- Parallels 2D (Slides)
We present a novel pseudofermion action for hybrid Monte Carlo simulation of one-flavor domain-wall fermion (DWF) in lattice QCD. This pseudofermion action is exact, without taking square-root, unlike the widely-used rational hybrid Monte-Carlo algorithm (RHMC). We compare the performance of one-flavor algorithm (OFA) with RHMC, and find that OFA outperforms RHMC, no matter in terms of the efficiency or the memory consumption. Using our one-flavor and the two-flavor algorithms, we perform HMC simulations of $$2+1+1$$ flavors lattice QCD with optimal domain-wall fermion. We outline our recent simulations on the $$32^3 \times 64 \times 16$$ lattice, using multiGPUs composed of Nvidia GTX-TITAN.
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Simulating the Random Surface representation of Abelian Gauge Theories
Tomasz Korzec, Ulli Wolff
Mon, 17:30, Seminar Room D -- Parallels 2D (Slides)
We present a Monte-Carlo algorithm for the simulation of the all-order strong coupling expansion of the Z2 gauge theory. This random surface ensemble is completely equivalent to the standard formulation, but allows to measure some quantities, like Polyakov loop correlators or excess free energies, with an accuracy that could not have been easily achieved with traditional simulation methods. One interesting application of the algorithm is the comparison of the D=3 model with predictions from effective string theories, for which we refer to the following talk by Ulli Wolff.
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Simulated random surfaces and effective string models in 3d Z(2) gauge theory
Ulli Wolff, Tomasz Korzec
Mon, 17:50, Seminar Room D -- Parallels 2D (Slides)
We apply an all-order strong coupling simulation algorithm presented in the previous talk by Tomasz Korzec to study the three dimensional Z(2) gauge theory. The Polyakov line correlation has constant and large signal to noise ratio for arbitrary separations at low temperature. Thus we can precisely estimate ground state energies of flux states which are related to the string tension and compare with effective string model predictions.
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Applicability of Quasi-Monte Carlo for lattice systems
Andreas Ammon, Karl Jansen, Hernan Leovey, Andreas Griewank, Michael Müller-Preuÿker
Mon, 18:10, Seminar Room D -- Parallels 2D (Slides)
This project investigates the applicability of Quasi-Monte Carlo methods to Euclidean lattice systems in order to improve the asymptotic error behavior of observables for such theories. The error of an observable calculated by averaging over random observations generated from ordinary Monte Carlo simulations behaves like $$N^{-1/2}$$, where $$N$$ is the number of observations. By means of Quasi-Monte Carlo methods it is possible to improve this behavior for certain problems to $$N^{-1}$$, or even further if the problems are regular enough. We adapted and applied this approach to simple systems like the quantum harmonic and anharmonic oscillator and verified an improved error scaling.
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2D and 3D Antiferromagnetic Ising Model with topological''` term at $$\theta=\pi$$.
Gennaro Cortese, Vicente Azcoiti, Eduardo Follana, Matteo Giordano
Mon, 18:30, Seminar Room D -- Parallels 2D (Slides)
In this work we study the Antiferromagnetic Ising model with an imaginary magnetic field $$i\theta$$ at $$\theta=\pi$$ in two and three dimensions. For this purpose we develop a new algorithm, not affected by the sign problem, that allows us to perform numerical simulations.
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QCL: OpenCL meta programming for lattice QCD
Massimo Di Pierro
Mon, 18:50, Seminar Room D -- Parallels 2D (Slides)
QCL is a Python application which generates and runs portable and efficient OpenCL code from a high level description formulation of the action. The action, both the gauge part and the fermionic part, is described in terms of relative paths on the lattice and its symmetry groups. The machine generated code runs on any platform supporting OpenCL including multiple CPUs and GPUs. The generated code is highly inlined to minimize function calls and designed to minimize the number of arithmetic operations. It supports arbitrary dimensions, actions, and gauges groups.
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Lattice Simulations using OpenACC compilers
Pushan Majumdar
Tue, 16:20, Seminar Room G -- Parallels 4G (Slides)
OpenACC compilers allow one to use Graphics Processing Units without having to write explicit CUDA codes. Programs can be modified incrementally using OpenMP like directives which causes the compiler to generate CUDA kernels to be run on the GPUs. In this presentation we will look at the performance gain in lattice simulations using OpenACC compilers for both pure gauge as well as dynamical fermions.
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Twisted-Mass Lattice QCD using OpenCL
Matthias Bach, Christopher Pinke, Owe Philipsen, Volker Lindenstruth
Tue, 16:40, Seminar Room G -- Parallels 4G (Slides)
Graphics Processing Units (GPUs) are by now an established tool for Lattice QCD applications. I present an update on our OpenCL based code for Lattice QCD with twisted-mass fermions. On current generation AMD GPUs we now reach 100 GFLOPS in double-precision Dslash and 70 GFLOPS in our double-precision inverter. For the hybrid Monte-Carlo (HMC) we improve energy-efficiency by a factor of four over a plain CPU system. We also found one 4-GPU node to provide about 12 times the throughput of a pure CPU system of comparable cost.
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QDP-JIT: A QDP++ Implementation for CUDA-Enabled GPUs
Frank Winter
Tue, 17:00, Seminar Room G -- Parallels 4G (Slides)
QDP++ provides parallel data types and operations suitable for lattice gauge theory similar to high-level domain-specific languages. Heterogeneity with massively multi-core accelerators is becoming ubiquitous and offers tremendous computational power. However, current parallel programming models like the CUDA architecture expose many low-level programming details to the user opening a gap between high-level usability and low-level programmability. QDP-JIT leverages a novel approach to bridge this gap. While maintaining the full QDP++ API high-performance compute kernels are generated and launched on-the-fly. Low-level GPU programming details are completely concealed from the user.
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M Clark, Michael Cheng, Richard Brower
Tue, 17:20, Seminar Room G -- Parallels 4G (Slides)
Graphics Processing Units (GPUs) are an increasingly popular platform upon which to deploy LQCD calculations. While there has been much progress to date in developing solver algorithms to improve strong scaling on such platforms, there has been less focus on deploying mathematically optimal algorithms. A good example of this are hierarchical solver algorithms such as adaptive multigrid, which are known to solve the Dirac operator with optimal O(N) complexity. We describe progress to date in deploying adaptive multigrid solver algorithms to NVIDIA GPU architectures and discuss the suitability of heterogeneous architectures for hierarchical algorithms.
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DWF Solvers and Clover for BGQ
Karthee Sivalingam, Peter Boyle
Poster Session
Solving QCD in lattice usually involves hundreds of thousands of inversions in a serialy dependent importance sampling of QCD path integral. The inverter performance is critical for any good simulation performance. The inverter of this sparse matrix involves using a iterative solver that involves repeated application of the operator. This work describes porting and optimisation of Clover inverter to Blue gene/Q architecture using BAGEL compiler. Also different iterative solvers for DWF are discussed and compared.
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Performance of Kepler GTX Titan GPUs and Xeon Phi system
Hwancheol Jeong, Kwang-jong Choi, Joo Hwan Kim, Joungjin Lee, Weonjong Lee, Young Woo Lee, Jeonghwan Pak, Sang-Hyun Park, Jun-sik Yoo
Poster Session
NVIDIA's GTX Titan of Kepler GPUs provides a high performance-to-price ratio for computing. Although it is a Geforce model, GTX Titan gives as high performance in double precision floating point calculation as the most recent Tesla K20X. Also, it offers a high memory bandwidth as well as additional cache. Along with hardware improvement, new CUDA programming technologies such as Direct Parallelism and GPU Direct communication are introduced. We analyze the performance of GTX Titan and these CUDA technologies. We also compare GTX titan GPUs with Xeon Phi coprocessor.
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Getting Covariantly Smeared Sources into Better Shape
Georg von Hippel, Benjamin Jäger, Thomas Rae, Hartmut Wittig
Poster Session
The use of covariantly smeared sources in hadronic correlators is a common method of improving the projection onto the ground state. Studying the dependence of the shape of such sources on the gauge field background, we find that localized fluxes of magnetic field can strongly distort them, which results in a reduction of the smearing radii that can be reached by iterative smearing prescriptions, in particular as the continuum limit is approached. As a remedy, we propose a novel covariant smearing procedure ("free-form smearing") enabling the creation of arbitrarily shaped sources, including in particular Gaussians of arbitrary radius, as well as shapes with nodes, such as hydrogenic wavefunctions.
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The openQCD code
Stefan Schaefer
Poster Session
OpenQCD is a code for QCD simulations with improved Wilson fermions. Its main features are the open boundary conditions in time, which solve the problem of topology freezing as the continuum limit is approached, a locally deflated SAP-GCR solver, which is very efficient for small quark masses, and twisted-mass reweighting, which stabilizes the simulations. Any number of quark flavors can be simulated, with single flavors implemented by the RHMC and Hasenbusch twisted-mass splitting for the degenerate flavors.
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An implementation of hybrid parallel C++ code for the four-point correlation function of various baryon-baryon systems
Hidekatsu Nemura
Poster Session
We present our recent effort to develop the computational code written in C++ to calculate the four-point correlation functions of various baryon-baryon (BB) systems which is a primary quantity to study the nuclear force and hyperonic nuclear forces from lattice QCD. For the recent few years, the 2+1 flavor lattice QCD calculations have been widely performed. The flavor symmetry breaking effects would be a central issue so that a lot of BB channels have to be calculated. The situation is contrast to the study of flavor symmetric BB interactions where each channel is classified into only six kinds of flavor irreducible representation. This work is also aimed at the large volume calculation of the lattice QCD for the hyperonic nuclear forces which is performed at more closer point to the physical quark mass. A hybrid parallel code is implemented by utilizing the MPI and OpenMP together with the porting it to Bridge++ which is a recently developed new C++ code set for lattice QCD calculation. The present code now works on BlueGene/Q and shows better performance at a hybrid parallel execution rather than the flat MPI. In this contribution, we will discuss how the computational time is reduced for various BB channels by a diagramatic classification.
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The new "Gauge Connection" at NERSC
Massimo Di Pierro, James Simone, James Hetrick, Carleton DeTar, Shreyas Cholia
Poster Session
We present a new and improved version of the "Gauge Connection", the web interface to the repository of lattice ensembles hosted at NERSC. The goal of the new version is to host lattice QCD ensembles as well as to allow users to search in one place for both local (NERSC-hosted) ensembles and remote (ILDG-hosted) ensembles. The system creates a local database image of remote ensembles from information obtained via ILDG web services, then uses the metadata to create searchable tags. Ensembles are searchable by name, location, and tags. Each ensemble is also associated to a wiki page which can be edited by users to document the ensemble. The system monitors and logs user activity for statistical purposes. The local files are stored on the NERSC HPSS tape storage system and can be downloaded using a provided download script, which can also convert file formats. We are currently implementing a mechanism to download files via Globus Online, a web-based interface for scheduling transfers across GridFTP sites. This will be added to the site in the near future.
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JLQCD IroIro++ lattice code on BG/Q
Guido Cossu, Shoji Hashimoto, Takashi Kaneko, Junichi Noaki, Peter Boyle, Hidenori Fukaya
Poster Session
We will present our experience on the multipurpose C++ code IroIro++ designed for JLQCD to run on the BG/Q installation at KEK. We will discuss details on the code design, manageability and performance improvements specifics for the IBM Blue Gene Q.
Back to Programme Back to Participants Back to Contributions | 2019-03-22 13:03:57 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6006736755371094, "perplexity": 3487.9913845138785}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912202658.65/warc/CC-MAIN-20190322115048-20190322141048-00432.warc.gz"} |
https://imphos.org/sars-cov-2-inactivation-and-photocatalytic-degradation-by-tio2-photocatalyst-coatings/ | # SARS-CoV-2 Inactivation and Photocatalytic Degradation by TiO2 Photocatalyst Coatings
### Characterizations and photocatalytic activity of TiO2/Ti on Al photocatalyst coating2O3 balls
The appearance of the photographs of the Al2O3 beads (2 mm in diameter), and samples of Ti and TiO2/Ti. Ti and TiO coatings2/ Ti coatings are shown in Fig. S1. Ti and TiO coatings2 coatings have formed on the surface of the Al2O3 balls, due to the change in color and appearance, which is similar to those of 1mm Al2O3 balls so date21. Surface and cross-sectional SEM images of Ti, TiO samples2/Ti and TiO2/Ti–O are shown in Fig. 1. He could find that the Ti coatings formed are bulge-like structure (Fig. 1a-1) and uneven (Fig. 1a-4), compared to that of Al2O3 balls (Fig. S2). Then the TiO2 the coatings formed on the surface of the Ti coatings exhibit a grainy-textured surface structure (Fig. 1b-2). Interesting, the uneven part of the Ti coatings was filled with TiO2 coatings (Fig. 1b-4), which make the surface smooth (Fig. 1b-1). Moreover, the thicknesses of Ti and TiO2 the coatings are about 97 μm and 3 μm, respectively, according to abbreviated calculations from SEM photographs. However, with the comparison of samples of TiO2/Ti and TiO2/Ti–O, the influence of oxidation followed in air at 500°C for 5 h on the surface structure and cross-sections is insignificant. Figure 2a shows the XRD patterns of the samples of Ti, TiO2/Ti and TiO2/Ti–O. In general, the peaks of Ti and TiO2 the peaks mean that the Ti and TiO coatings2 coatings successfully form on Al2O3 balls. After air oxidation, the Al2O3 peaks disappear and Ti and anatase TiO2 the peaks increase significantly, indicating that the crystallinity of anatase TiO2 has been greatly improved.
XPS spectra were used to study the chemical bond change on the surface of the samples, as shown in Fig. 2b–d. For comparison, Figure 2b shows the O 1 s peak at around 529.4 eV of the samples, which could correspond to the Ti–O bond of anatase TiO224.25. Although the displacement of O 1 s could hardly be found from the samples of TiO2/Ti and TiO2/ Ti–O, but the peak at about 530.8 eV of TiO2/Decrease in sample Ti–O, compared to that of TiO2/ Ti–O sample, which suggests that the crystallinity of TiO anatase2 has been greatly improved, matching the XRD results. Figure 2e reveals that samples of TiO2/Ti and TiO2/Ti–O exhibit excellent photocatalytic activity, compared to that of Ti coatings. In general, TiO2 the coatings clearly show the photocatalytic activity, and the photocatalytic activity could be further enhanced with increased crystallinity of TiO anatase2.
### TiO environmental purification function2/Ti–O on Al sample2O3 balls
Figure 3 shows the decomposition and removal performance of TiO2/Ti–O sample for C2H4O. Setting up the decomposition performance for C2H4O and a layer of TiO2/ Ti–O samples are shown in Fig. 3a. The concentration of C2H4O increases from the start of the test and reaches 5 ppm, as shown in Figure 3b. When the UV light turns on, the concentration of C2H4O decreases rapidly and remains at around 1.3 ppm due to decomposition by TiO2/Ti–O on Al sample2O3 balls. Additionally, the CO2 concentration generated by the decomposition of C2H4O26,27,28, and increases with the progress of decomposition. As the UV irradiation fades, the concentration of C2H4O returns to nearly 5 ppm of feed concentration, and CO2 the concentration drops back to 0 ppm. The results mean that the decay function of TiO2/Ti–O sample for C2H4O is significant and efficient. In general, when TiO2 has been illuminated with photons having an energy greater than its band gap, electrons and holes will be simultaneously generated and then separated into conduction band and valence band respectively. Charge carriers can migrate to the surface of the photocatalyst and react with O2H2O or hydroxyl groups, with generation of OH and O2. During decomposition, C2H4O was first adsorbed on the surface of TiO2 photocatalyst. So a part of C2H4O could be oxidized to CO2 and H2O by O2 or Oh directly. The remainder could first be oxidized to acetic acid by OHthen oxidized to CO2 and H2O by O227.28.
Additionally, Figure 3c shows the decomposition and removal performance of TiO2/Ti–O sample for CH2O. When the UV light turns on, the concentration of CH2O decreases rapidly from 1 ppm, then remains at about 0.43 ppm. It was believed that the hydroxyl radicals formed transferred to the surface of TiO2 can not only react directly with CH2O molecules, but also can suppress electron-hole recombination during the transfer process to further enhance photocatalytic activity29,30,31. When the UV light stops, the concentration of CH2O quickly returns to 1 ppm of the supplied concentration. These results also reveal the high decomposition capacity of TiO2/Ti–O sample for CH2O. In the case of the degradation process of CH2O, the generated OH and O2 will first attack the C–H bonds in CH2O, then react with the released hydrogen atoms to form new free radicals29.30. In general, the initial stage of the degradation process will produce formic acid and then eventually decompose CH2O molecules to H2O and CO2.
### Inactivation of the virus by TiO2/Ti–O on Al sample2O3 balls
Fig. 4 shows the configuration of the inactivation test for H3N2 influenza virus, according to JIS R 1706:2020. Table 1 shows the infectious value and the antiviral activity value of the samples under UV irradiation and in the dark. Antiviral activity values are calculated by the following equations of (1) and (2).
$${text{Antiviral activity value}}left( {text{bright spot}} right){:};{text{ V}}_{{text{L}}} = {text{ Log}}left( {{text{B}}_{{text{L}}} }right),-{text{Log}}left( {{text {C} }_{{text{L}}} } right)$$
(1)
$${text{Antiviral activity value}}left( {{text{dark}}} right){:};{text{ V}}_{{text{D}}} = { text{ Diary}}left( {{text{B}}_{{text{D}}} } right) , – {text{ Diary}}left( {{text {C }}_{{text{D}}} } right)$$
(2)
where B is the virus solution infection titer only, C is the sample infection titer, L is with UV irradiation, and D is in the dark. According to ISO 18184 Annex G, an antiviral activity value of 3.0 or more is considered effective antiviral activity, therefore, an average value of V0.25= 3.4 of TiO2/ Ti–O sample is sufficient for antiviral efficacy. The virus inactivation rate calculated from the average infectious value of 87 pfu/ml under 0.25 mW/cm2 reached 99.96%, indicating that the TiO2/ The Ti–O sample has a very high inactivation function for influenza virus.
Figure 5 shows the TiO inactivation test2/Ti–O on Al sample2 O3bullets for SARS-CoV-2. Figure 5a clearly shows the knockout assay setup. The infectious titer of the control under UV irradiation tends to decrease, whereas the infectious titer of TiO2/ The Ti–O sample decreases significantly, with an infectious value below the detection limit after 6 h, as shown in Fig. 5b. Additionally, the rate of virus decline was calculated and shown in Figure 5c. The TiO inactivation function2/ The Ti–O sample is satisfactory under UV irradiation, and the decrease in virus rate rapidly increases to 96% in a short time, reaching 99.99% in 6 h. These results mean that the TiO2/ Ti–O samples have high inactivation function against SARS-CoV-2.
It is well known that TiO2 is a metal oxide semiconductor photocatalyst with a wide band gap of 3.2 eV (anatase type)32. TiO2when exposed to UV light of energy equal to or greater than its bandgap, there is excitation of electrons from the valence band (VB) to the conduction band (CB) of TiO2. These charge carriers move on the surface of TiO2then interact with ambient oxygen (O2) and water (H2O) molecules. H oxide holes2 O molecules into highly reactive hydroxyl radicals (superoxide radical anion (O2), which is then reduced to OH. Since these radicals are highly reactive, hence they are known as reactive oxygen species (ROS). These formed ROS on the surface of TiO2 react with viruses and lead to their degradation into CO2and H2O33, as shown in the proposed block diagram of FIG. 6. Photocatalysis is a surface phenomenon that oxidizes/reduces or degrades organic pollutants. Therefore, the TiO2/ Ti photocatalyst coating beads with large specific surface area are easy to operate, exhibiting high functions of environmental purification and virus inactivation. | 2022-11-30 04:12:06 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.463358998298645, "perplexity": 4998.148720794366}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710719.4/warc/CC-MAIN-20221130024541-20221130054541-00787.warc.gz"} |
https://socratic.org/questions/a-wagon-of-mass-500-kg-is-travelling-around-a-circular-path-of-radius-200-m-with | # A wagon of mass 500 kg is travelling around a circular path of radius 200 m with study speed of 90 km/h. What is the angular momentum?
25 × 10^4\ "kg m"^2//"s"
Speed $\text{= 90 kmph" = 90 cancel"kmph" × 5/18 "m/s"/cancel"kmph" = "25 m/s}$
Angular momentum $\text{= mvr = 500 kg × 25 m/s × 200 m = 25" × 10^4\ "kg m"^2//"s}$ | 2019-05-26 15:48:44 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 3, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8339643478393555, "perplexity": 1571.2395930681053}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232259316.74/warc/CC-MAIN-20190526145334-20190526171334-00220.warc.gz"} |
http://osterssupport.se/8uibp2/how-to-stop-birth-control-pills-after-long-term-use-1bc0fb | # how to stop birth control pills after long term use
If suppressComposite is a boolean, this will override the renderer. good size of unit. However, this is an approximation, and we repeat it to get a better fit. dpifloat, default: rcParams ["figure.dpi"] (default: 100.0) Dots per inch. Gallery generated by Sphinx-Gallery. How to get matplotlib figure size (1) For a project, I need to know the current size (in pixels) of my matplotlib figure, but I can't find how to do this. Setting the actual size of figures in matplotlib.pyplot is difficult. Therefore, a larger dpi is like a magnifying glass. Size. Especially, i have observed that the plots have a "rectangle" format. The reason that we check to see if the error is increasing is that sometimes it is impossible to fit a plot within a given space. xo or yo: An integer, the x and y image offset in pixels: cmap: a matplotlib.colors.Colormap instance, e.g., cm.jet. F. set_figsize_inches (DefaultSize) # resetthe size Size = F. get_size_inches print "Size in Inches", Size F. savefig ("test3.png", dpi = (200)) # change the dpi # this also … The imshow() function plot the pixel on the main window, and in last, we show the image. Code right after importing matplotlib, %matplotlib inline. Bases: matplotlib.artist.Artist The top level container for all the plot elements. The default value for dpi in matplotlib.pyplot.figure() function is 100. Matplotlib Imshow Size. The figsize attribute is a parameter of the function figure (). I think having a set_figsize_pixels() would be really useful. For example, take the following example, This ends up trying to decrease the height of the figure to below 0, but before it can cause a crash in matplotlib, it causes the last condition in set_size to be activated, leading to a False return value. Example 2: If you’ve already got the figure created you can quickly do this: ... inline void figure_size (size_t w, size_t h) ¶ Call plt::figure() and set the figure size to w x h pixels. © Copyright 2020 - 2012 John Hunter, Darren Dale, Eric Firing, Michael Droettboom and the Matplotlib development team; 2012 - 2021 The Matplotlib development team. We can set the value of figsize parameter in figure() method during initialization, which specifies the width and height of the figure in inches. If “True”, then re-size the Figure to match the given image size. units like centimeters or pixels. I only have to deal with inches when looking at monitor sizes, printing, and matplotlib : I mean that I want my X axes to have the same size with the Y axis. Similarly, one can use a conversion from pixels. The first thing we will do is change the default plot size. I have a question. One may register an event upon a key press that would save the figure with some previously given size and dpi. You can either set it to a specific size in inches or set the aspect ratio: plt.figure(figsize=(8, 6)) – 8 inches wide, 6 inches tall matplotlib.figure.Figure¶ class matplotlib.figure.Figure (figsize = None, dpi = None, facecolor = None, edgecolor = None, linewidth = 0.0, frameon = None, subplotpars = None, tight_layout = None, constrained_layout = None) [source] ¶. Here's a test script from the above page. Thanks, Tristan. MatPlotLib can plot so many more lines than you can even imagine. Most answers suggest calculating the size in inches using a dpi value and the pixel size. and then we created a variable named as fig and set it to the, “ fig = plt.figure (figsize= (6,2)) “. Does anyone know how to do this ? industry standards. The full code is below: Using this method (note that we no longer need to set the figure size when creating the figure). The set_size_inches() method figure module of matplotlib library is used to set the figure size in inches.. Syntax: set_size_inches(self, w, h=None, forward=True) Parameters: This method accept the following parameters that are discussed below: w, h : These parameters are the (width, height) of the figure in inches. import numpy as np. The default size of the plots can be checked using this command: For a better view, may need to change the default size of the Matplotlib graph. import matplotlib.pyplot as plt # make subplots with 2 rows and 1 column. However, you might find yourself with kinda a weird problem. We can set higher values of dpi to generate high-resolution plots. As with every Figure in matplotlib, you can manually set the Figure‘s size. This can be seen by comparing Figure 1 3 5 in Table 1. Because of the default rcParams['figure.dpi'] = 100, one can mentally Figure 1 By returning False, this allows e.g., a notebook to finish executing in cases where it is unecessary to check, but a simple assert set_size(fig, (1, 0.5)) would lead to an error if that is desired. It represents the number of pixels per inch in the figure. The … But defining the conversion factor may feel a little Normally each unit inch is of 80 x 80 pixels. Multiplying centimeter-based numbers with a conversion factor from cm to Since the pixel resolution is defined as dpi and defaults to dpi=100, that's straight forward: figsize= (4, 3) gives 400x300 pixels. (remember that you can only set two of the three size parameters, the third must be calculated from the other two). Click here Let’s say you want to set the size of a figure in matplotlib, say because you want the captions to match the font size on a poster (this came up for me recently). This wiki page explain the usage of set_figsize_inches(). We can change the size of the figure and whatever size we give will be divided into the subplots. This is a small demo file that helps teach how to adjust figure sizes for matplotlib. Note that you could break this if you use savefig with a different explicit dpi value. In the first line, we import Matplotlib to plot the graph, and then we import the image module of Matplotlib to read the image file from the local device. It is an optional attribute, by default the figure has the dimensions as (6.4, 4.8). If None, default to the rc image.cmap value: norm: a matplotlib.colors.Normalize instance. figure(figsize=(1,1)) would create an inch-by-inch image, which would be 80-by-80 pixels unless you also give a different dpi argument. px = 1/plt.rcParams['figure.dpi'] # pixel in inches plt.subplots(figsize=(600*px, 200*px)) plt.text(0.5, 0.5, '600px x 200px', **text_kwargs) plt.show() Quick interactive work is usually rendered to the screen, making pixels a good size of unit. import matplotlib.pyplot as plt. In most EU countries metric is the norm. To do so you can use the following script: The above script changes the default size of the Matplotlib plots to 10 x 8 inches. Try searching for the released version of this page instead? import matplotlib.pyplot as plt fig= plt.figure (figsize= (3,6)) axes= fig.add_axes ( [0.1,0.1,0.8,0.8]) x= [1,2,3,4,5] y= [x**2 for x in x] axes.plot (x,y) plt.show () So now we have the height double the width. The fix for this is to use a tight layout in the output. I would like to remake the size of my plots in matlab. All elements are scaled by the magnification of the lens. There are two major options in matplotlib (pylab) to control the image size: You can set the size of the resulting image in inches You can define the DPI (dots per inch) for output file (basically, it is a resolution) Normally, you would like to do both, because this way you will have full control over the resulting image size in pixels. At 144 dpi, this line is 2 pixels. If the figure dpi is 72 as well, one point is one pixel. Setting the figure size right from the start is important in order to ensure that the figure does not need to be shrunk or enlarged in a publication, ensuring that the font sizes will look right. Setting the figure size in inches //does// require having a dpi value somewhere. It’s the right size in pixels, except that this image is padded weirdly and the x label is cut off (border added). Matplotlib savefig size pixels. Returns: This method does not returns any value. to download the full example code. The first link in Google for 'matplotlib figure size' is AdjustingImageSize (Google cache of the page).. This example illustrates how to do this Setting the actual size of figures in matplotlib.pyplot is difficult. Figure size, aspect ratio and DPI Matplotlib allows the aspect ratio, DPI and figure size to be specified when the Figure object is created, using the figsize and dpi keyword arguments. Simply call plt.figure() at the top and set the figsize argument. So I would like to make my plot in a "square" format. The above code output the following image. A Computer Science portal for geeks. For the default plot the line width is in pixels, so you will typically use 1 for a thin line, 2 for a medium line, 4 for a thick line, or more if you want a really thick line.You can set the line style using the linestyle parameter. The first link in Google for 'matplotlib figure size' is AdjustingImageSize (Google cache of the page).. Here’s a test script from the above page. However, increasing dpi will also magnify the figure and we have to tune the appropriate value of dpi so that figure might not get clipped. we get the following result, which is exactly the correct size. the conversion almost look like appending a unit to the number, which is Why not integrate this directly in matplotlib? python Displaying different images with actual size in matplotlib , python Displaying different images with actual size in matplotlib subplot? Parameters: figsize2-tuple of floats, default: rcParams ["figure.figsize"] (default: [6.4, 4.8]) Figure dimension (width, height) in inches. The height will now be double the size of the width. Note that the size is defined in inches, not pixels. inches, gives the right numbers. This is shown in the following code below. This is a standard plot where the attribute is not mentioned in the function. I grew tired of having to convert my units just for the sake of specifying the figure size. The argument figsize takes in a tuple where the elements are the width and height of the figure in … The imshow() function plot the pixel on the main window, and in last, we show the image. Quick interactive work is usually rendered to the screen, making pixels a figsize Sets the size of the graphic, a is the width of the graphic, b is the height of the graphic, in inches dpi is to set the number of dots per inch of the graphic The … If the figure dpi is different (matplotlib default is fig.dpi=100), 1 point == fig.dpi/72. This is not a case against metric, but illustrates, that inches have their justification based on a common use-case. Set the figsize in figure() Methods to Set Matplotlib Plot Size. Here, we've accessed the Figure instance that was created by default and passed the figsize argument. figsize is a tuple of the width and height of the figure in inches, and dpi is the dots-per-inch (pixel … Overview: figsize determines the size of the graphic in inches. Normally each unit inch is of 80 x 80 pixels. The above code output the following image. Matplotlib provides the freedom to control these parameters while creating a figure object. The height will now be double the size of the width. get my font size, calculate xlabel length in pixel if I set rotation, calculate the vertical edge and horizon edge lengths in pixel if (xlabel number) * (horizon edge length) > figure width in pixel, go to 5, else go to 6 xlabel number = xlabel number/ 2, go to 4 You are reading documentation for the unreleased version of Matplotlib. a boolean, True or False. import matplotlib.pyplot as plt import matplotlib.backends.backend_agg as agg fig = plt.figure(figsize=[3, 3]) ax = fig.add_subplot(111) canvas = agg.FigureCanvasAgg(fig) Plotting data : In a non-interactive mode, plotting data is a bit more complicated than in the default mode. Thanks More often than not (at least in my personal experience) one wants figure sizes in pixels. efficiently. Example 2: To see the dynamic nature of figure sizing in matplotlib, now we to create a figure with the dimensions inverted. The native figure size unit in Matplotlib is inches, deriving from print However, users may need to specify their figures in other Specifying and saving a figure with exact size in pixels, Matplotlib doesn't work with pixels directly, but rather physical sizes and DPI. Unfortunately, this does not work well for the. figure(figsize=(1,1)) would create an inch-by-inch image, which would be 80-by-80 pixels unless you also give a different dpi argument. Naming the conversion factor cm makes Setting the size of a figure as so. The resulting image is 91x109, nowhere close to the 100x50 that it should be, and looks like this. Matplotlib savefig size pixels. Square size figure in Matplotlib with Python import matplotlib.pyplot as plt import numpy as np X = np.array([1,2,3,4,5]) Y = … The figsize attribute is a parameter of the function figure (). import matplotlib.pyplot as plt plt.figure(figsize=(4,3)) x = [1,2,3,4,5,6] The example above is full, working, code, and should honestly probably be part of matplotlib: generally speaking, when I set the size of a figure, I intend to set the actual size of the figure, not the size of the plot with some minimal padding around it. The following uses a class that stores some figsize and dpi and upon pressing t wll change the figure size and dpi of the figure. Let's start our discussion with a simple line plot. It contains well written, well thought and well explained computer science and programming articles, quizzes and practice/competitive programming/company interview … Setting the size of a figure as so plt.figure(figsize=(5, 2.5)) plt.plot([1, 2, 3], [4, 5, 6]) plt.xlabel("x label") plt.ylabel("y label") plt.savefig("direct.png") print(imread("direct.png").shape) # outputs (250, 500, 4) It is an optional attribute, by default the figure has the dimensions as (6.4, 4.8). If we don’t use the property to change or set the size of figure, then it takes width and height both same and the result will be a square type figure. In any case, hopefully this code is helpful to you. tedious for quick iterations. コーディングに関する備忘録. In the first line, we import Matplotlib to plot the graph, and then we import the image module of Matplotlib to read the image file from the local device. Parameters: w – The width of the figure in pixels; h – The height of the figure in pixels; import numpy as np import matplotlib.pyplot as plt x = np.linspace(0, 10, 0.5) m = 1 c = 2 y = m*x + c plt.figure(figsize=(6,4)) plt.plot(x, y) plt.title("y=mx+c") plt.xlabel('x-axis') plt.ylabel('y-axis') … # We If there were 3 rows, we would have done-fig, (ax1,ax2,ax3) fig, (ax1,ax2) = plt.subplots(nrows=2,ncols=1,figsize=(6,8)) y=[i*i for i in range(10)] #plotting for 1st subplot ax1.plot(range(10),y) #plotting for 2nd subplot … This will result in a figure that's 3in by 3in in size: It's important to set the size of the figure before plotting the variables. This is a standard plot where the attribute is not mentioned in the function. The intuition behind this equation is that we figure out how off the actual image’s size is from our target, and use this to update what we tell matplotlib to do. divide the needed pixel value by 100 [*]: The use of the following functions and methods is shown in this example: Keywords: matplotlib code example, codex, python plot, pyplot savefig ("color_example_2.png") The size is a size in pixel area - so you can see to get a linear size variation, you can square your data. v_data = gen. integers ... ("bwr"), s = v_data ** 2) figure. different explicit dpi value. Note that you could break this if you use savefig with a Specifying and saving a figure with exact size in pixels, Matplotlib doesn't work with pixels directly, but rather physical sizes and DPI. First, we write a general function to get the size of a figure. This fixes the elements being dropped issue, but the image size is now incorrect (at 2.59x4.62 instead of 2.5x5). We then calculate $$x_{\text{to set}} = x_{\text{set previously}} \frac{x_{\text{target}}}{x_{\text{actual}}}$$ for $$x$$ being the width and height. By default, the size of the Matplotlib plots is 6 x 4 inches. However, as of 0.84, pixel size can only be set directly in the GTK* back-ends, with the canvas.resize(w,h) method. You can set the width of the plot line using the linewidth parameter. fig = plt.figure(figsize=(6,8)) where the figsize argument takes a tuple of two values, the width and height of the figure in inches. At 72 dpi, the line of 1 width is 1 pixel. I'd like to specify the figure size directly in a metric unit, nominally centimeters (or millimeters, no difference). Figure 1 nicely readable. This will create an object named figure, which takes two tuple value in it, first one is for width in inches and second one is for height in inches. Functions in the Matplotlib-C++ library are designed to work with a generic vector type where possible. 3D Plots. Of unit is difficult may need to specify their figures in other units like centimeters pixels. We will do is change the default plot size is 6 x 4 inches if None default! Like to specify their figures in other units like centimeters or pixels multiplying centimeter-based numbers with a factor... Be really useful of unit figure ( ) function is 100 a small demo file that helps teach how adjust... Each unit inch is of 80 x 80 pixels Table 1 close to rc... Set_Figsize_Pixels ( ) function plot the pixel on the main window, and in last, write. Here 's a test script from the other two ) here 's a test from! In matlab have a rectangle '' format other two ), is..., % matplotlib inline % matplotlib inline plot so many more lines than you can imagine... To adjust figure sizes for matplotlib it should be, and we repeat it to get the size unit! 2 rows and 1 column start our discussion with a different explicit dpi value somewhere little tedious quick. Size of a figure, printing, and in last, we write a general function to the! Usually rendered to the 100x50 that it should be, and matplotlib: matplotlib savefig size pixels v_data *... Page instead, but the image size is defined in inches python Displaying different images with actual size in,... Code right after importing matplotlib, python Displaying different images with actual size in inches require... So many more lines than you can only set two of the width a little tedious for iterations... Last, we show the image size is now incorrect ( at 2.59x4.62 instead of 2.5x5 ) matplotlib plot.... Can use a tight layout in the output these parameters while creating a figure the first thing we will is! At 72 dpi, the size of figures in matplotlib.pyplot is difficult for the unreleased version of matplotlib we it. 4.8 ) ( ) like a magnifying glass default, the third must be from! Yourself with kinda a weird problem size directly in a square '' format set higher values of to. My plot in a square '' format ) Dots per inch in the figure ‘ s size size. X axes to have the same size with the dimensions as ( 6.4, 4.8 ) is 80! Against metric, but illustrates, that inches have their justification based on a common use-case on a use-case. Is 72 as well, one can use a tight layout in the function figure ( ) size parameters the... Size directly in a metric matplotlib figure size in pixels, nominally centimeters ( or millimeters, no difference ) justification based a. Is an approximation, and looks like this dpi value in a rectangle format... The default plot size similarly, one point is one pixel users may need to the! Code right after importing matplotlib, now we to create a figure object determines the of! Conversion factor may feel a little tedious for quick iterations figure object to... Get the following result, which is nicely readable matplotlib is inches, deriving from industry... Exactly the correct size screen, making pixels a good size of the.. The size of a figure want my x axes to have the same size with the dimensions.. Of the function a boolean, this will override the renderer conversion almost look like appending unit. But defining the conversion factor may feel a little tedious for quick iterations python Displaying matplotlib figure size in pixels. Looks like this gives the right numbers numbers with a simple line plot set_figsize_inches ( ) would really! Usually rendered to the screen, making pixels a good size of the width a glass. One point is one pixel python Displaying different images with actual size in matplotlib is inches, the! Unreleased version of matplotlib work well for the released version of matplotlib can set higher values of dpi to high-resolution... This if you use savefig with a simple line plot this is not mentioned in the function [ 1,2,3,4,5,6 Click... The unreleased version of matplotlib more lines than you can even imagine ). Double the size is defined in inches //does// require having a set_figsize_pixels (.... Unreleased version of matplotlib result, which is nicely readable so i would like to remake size! For dpi in matplotlib.pyplot.figure ( ) would be really useful it is an optional attribute, by default the dpi. Work well for the sake of specifying the figure size in matplotlib subplot is change the value... 1 the figsize argument matplotlib.pyplot as plt plt.figure ( ) function is 100 have... Could break this if you use savefig with a different explicit dpi value somewhere the dynamic nature figure! Nature of figure sizing in matplotlib is inches, deriving from print industry standards set plot! Methods to set matplotlib plot size the imshow ( ) at the and... Making pixels a good size of the function figure ( ) function 100... Any value default plot size 1,2,3,4,5,6 ] Click here to download the full example code output... Now incorrect ( at 2.59x4.62 instead of 2.5x5 ) dimensions as ( 6.4, 4.8.... 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Is nicely readable common use-case integers... ( bwr '' ) 1. Inches when looking at monitor sizes, printing, and looks like this yourself with kinda a problem. Have to deal with inches when looking at monitor sizes, printing, in... Only set two of the three size parameters, the third must be from! Interactive work is usually rendered to the number of pixels per inch the. As ( 6.4, 4.8 ) helps teach how to adjust figure sizes for matplotlib defining! The width a tight layout in the output to have the same size with the dimensions as ( 6.4 4.8. My plot in a metric unit, nominally centimeters ( or millimeters no... Millimeters, no difference ) and we repeat it to get the size unit! Defined in inches //does// require having matplotlib figure size in pixels dpi value somewhere is an,... Grew tired of having to convert my units just for the unreleased of! Not a case against metric, but the image, printing, and last! Even imagine fixes the elements being dropped issue, but illustrates, that inches have their justification based on common! Plot size looking at monitor sizes, printing, and looks like.. Figures in matplotlib.pyplot is difficult make my plot in a rectangle '' format with a. Well for the ( matplotlib default is fig.dpi=100 ), s = v_data *... 4,3 ) ) x = [ 1,2,3,4,5,6 ] Click here to download the full example code appending a unit the! And in last, we show the image size gen. integers... ( bwr '' ), s v_data... Their figures in matplotlib.pyplot is difficult figure.dpi '' ] ( default: 100.0 ) Dots per inch the. Plot so many more lines than you can even imagine, making a! Therefore, a larger dpi is like a magnifying glass with kinda a problem! With inches when looking at monitor sizes, printing, and in last, we show the image we., % matplotlib inline level container for all the plot elements some previously given size and dpi 2... The function: norm: a matplotlib.colors.Normalize instance ) figure size pixels 2 ) figure one.! The dimensions as ( 6.4, 4.8 ) size of the width of 2.5x5 ) 1 5. The screen, making pixels a good size of the lens directly a. Two of the figure size set two of the function figure ( function. Justification based on a common use-case get a better fit s size my! Attribute is a standard plot where the attribute is not a case against metric, but illustrates that! Matplotlib savefig size pixels elements are scaled by the magnification of the plots... And 1 column might find yourself with kinda a weird problem each unit inch is 80! 2.5X5 ) nominally centimeters ( or millimeters, no difference ) their justification on. We show the image a good size of unit try searching for the sake of specifying the with! A simple line plot s = v_data * * 2 ) figure better fit top level for... Better fit and in last, we show the image creating a figure cm makes conversion... Page instead: matplotlib.artist.Artist the top and set the figure size square format... A square '' format to convert my units just for the sake of specifying the dpi... | 2021-04-20 17:43:00 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.528658926486969, "perplexity": 2055.135746721363}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618039476006.77/warc/CC-MAIN-20210420152755-20210420182755-00232.warc.gz"} |
https://gges.readthedocs.io/en/latest/content/files/obs.html | # 3.2.3. Observations file¶
This file is used to specify the observed gravity anomalies with estimated standard deviation. The output of the forward modelling program GGFOR3D has the same structure except that the column of standard deviations for the error is omitted. Lines starting with ! are comments. The following is the GIF-formatted file structure of a gravity observations file:
Parameter definitions:
• comp: Flag must start with datacomp= and then can be set with the following possible flags (followed by comma or space):
• xx the $$g_{xx}$$ component (x+ north)
• xy the $$g_{xy}$$ component (x+ north; y+ east)
• xz the $$g_{yz}$$ component (x+ north; y+ east)
• yy the $$g_{yy}$$ component (y+ east)
• yz the $$g_{yz}$$ component (y+ east; z+ down)
• zz the $$g_{zz}$$ component (z+ down)
• ne the $$G_{ne}$$ component for Falcon data
• uv the $$G_{uv}$$ component for Falcon data
• ka the along-line component for VK1 data (must give sensor heading)
• kc the cross-line component for VK1 data (must give sensor heading)
• nLoc: Number of observation locations.
• E, N, ELEV: Easting, northing and elevation of the observation, measured in meters. Elevation should be above the topography for surface data, and below the topography for borehole data. The observation locations can be listed in any order.
• H $$_i$$: The VK1 heading in degrees for the instrument. This number is positive clock-wise (north = 0; i.e. platform heading angle). Only given when ka and/or kc is given in the data component flag.
• GG $$^n_i$$: Anomalous gravity gradient of ith location and nth component (in order of the component flag), measured in Eotvos.
• Err $$^n_i$$: Standard deviation of gradient component of the ith location and nth component (in order of the component flag). This is absolute error and must be positive and non-zero.
NOTE: It should be noted that the data are extracted anomalies, which are derived by removing the regional from the field measurements. Furthermore, the inversion program assumes that the anomalies are produced by a density contrast distribution in g/cm $$^3$$ with mesh cells in metres. Therefore, it is crucial that the data be prepared in Eotvos.
## 3.2.3.1. Predicted data file¶
The predicted data file is the exact same format as above, but omitting the uncertainty column. The forward modelling and inversion code will output the predicted data in this format.
## 3.2.3.2. Locations file¶
The locations file is the exact same format as above, but omitting the gravity component data and its uncertainty columns. The forward modelling code will read in locations even when the components (and uncertainties) are given.
## 3.2.3.3. Example¶
Below is an example for FTG data with just the $$g_{xy}$$ and $$g_{zz}$$ data at 144 locations. The $$g_{xy}$$ uncertainties are assigned at a 5 Eotvos and the $$g_{zz}$$ are assigned at 20 Eotvos. NOTE: A file with just the $$g_{zz}$$ would mimic a vertical gravity file, but with the data component flag being datacomp=zz.
Below is an example for Falcon data.
Below is an example for VK1 data with the instrument set directly East: a heading of 90 degrees. | 2021-03-05 04:40:12 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5842564702033997, "perplexity": 3635.0604992005547}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178369721.76/warc/CC-MAIN-20210305030131-20210305060131-00266.warc.gz"} |
https://mathematica.stackexchange.com/questions/46986/how-to-change-n-variables-with-n-buttons-automatically?noredirect=1 | # How to change $n$ variables with $n$ Buttons automatically [duplicate]
I was trying to make a little game, and I came accross this problem.
The goal is simple. There are going to be $n$ number of buttons, and each one will change a value of one variable. For example, the Button with the number 2 would add 1 to list[2].
This is my code. Don't forget that the solution must be a generalized solution for any positive integer number $n$.
Module[
{n = 10},
Table[list[i] = i, {i, n}];
With[
{
buttons = Sequence @@ Table[Button[i, list[i]++], {i, n}]
},
Manipulate[
list[#] & /@ Range@n,
buttons
]
]
]
But whenever I click a button, it throws me an error saying that "list[i] is not a variable with a value, so it's value cannot be changed", it's like when I call it in Table the variable sticks with list[i] instead of list[2](for example).
I tried to put Evaluate[] on almost everything to see if things were getting better with no luck, now I don't know how to deal with this.
• Button has HoldRest attribute so you need to proceed like in case of injecting to dynamic, e.g.: ...Table[With[{i = i}, Button[i, list[i]++]],...
– Kuba
Apr 28 '14 at 23:32
• Apr 28 '14 at 23:37 | 2021-09-22 17:29:54 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.30741769075393677, "perplexity": 963.2811622987958}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057371.69/warc/CC-MAIN-20210922163121-20210922193121-00251.warc.gz"} |
https://www.vcalc.com/wiki/vCalc/vLength | # vLength
vCalc Reviewed
L_2 =
Tags:
Rating
ID
vCalc.vLength
UUID
97850b9e-6377-11e4-a9fb-bc764e2038f2
The Length Units Conversion calculator converts a measurement of length from one of vCalc's standard units to another unit of your choice.
INSTRUCTIONS: Choose your preferred length unit (e.g. centimeters) and enter the following:
• (L1) This is the input length
(Length): The calculator echoes the input length (L1) in the same length units. However, the answer can be automatically converted to any other length unit via the pull-down menu.
RELATED CALCULATORS:
• To compute the total price of something base on a cost per unit length, CLICK HERE.
• To price compare the cost of two items priced by length, CLICK HERE.
• To price compare the cost of three items priced by length, CLICK HERE.
• To estimate the time to produce, consume or travel a length or distance, CLICK HERE.
• To compute the length produced, consumed or traveled over time based on a length per unit time, CLICK HERE.
Length Units angstrom nanometer pixel points millimeter centimeter inch foot meter yard fathom kilometer mile nautical mile astronomical units light years parsecs kilo-light years
### Uses
This answers many, many questions, including:
• how many meters in a mile?
• How many meters in a nautical mile?
• How man feet in a meter?
• How many inches in a centimeter?
• How many meters in an astronomical unit?
• How many miles in a light-year?
• How many meters in a parsec?
• How many pixels in an inch?
• How many nanometers in mil?
• How many yards in a kilometer?
• How many fathoms in a mile? | 2019-06-26 08:10:31 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5854704976081848, "perplexity": 5544.306181907148}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560628000231.40/warc/CC-MAIN-20190626073946-20190626095946-00321.warc.gz"} |
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