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http://mathhelpforum.com/calculus/79775-solving-differential-equations-using-change-variable.html | # Math Help - Solving differential equations using a change of variable
1. ## Solving differential equations using a change of variable
(x+y)dy/dx = x^2+xy+x+1 ; y=v-x
So i did the substitution and ended up with vdv/dx - v =xv+x+1
and, if correct, i've no idea how to solve.
2. Originally Posted by Erghhh
(x+y)dy/dx = x^2+xy+x+1 ; y=v-x
So i did the substitution and ended up with vdv/dx - v =xv+x+1
and, if correct, i've no idea how to solve.
(x+y)dy/dx = x^2+xy+x+1 ; y=v-x
vdv/dx - v =xv+x+1
vdv/dx = v+xv+x+1
vdv/dx = v(1+x) + (1+x)
vdv/dx = (v+1)(1+x)
$\frac{vdv}{v+1} =(x+1)dx$
Integrate both sides
$\int{\frac{vdv}{v+1}} =\int{(x+1)dx}$
Integrate this thing and enjoy the sunny day
3. So then i got (y+x)ln|x+y+1|=(1/2)(x^2) +x+c
The answer, according to my book, is y=ln|x+y+1| +(1/2)(x^2)+C
I'm unsure of how to get there..
4. Hi
A sign - is missing
(y+x)-ln|x+y+1|=(1/2)(x^2) +x+c
Then y=ln|x+y+1| +(1/2)(x^2)+c
5. Can you explain where that minus sign has come from?
6. $\int{\frac{vdv}{v+1}} = \int{\frac{(v+1-1)dv}{v+1}} = \int \left(1-\frac{1}{v+1}\right)\:dv = v - \ln|v+1|$
7. $\frac{v}{v+1}= 1- \frac{1}{v+1}$
Intgrate that.
running-gag got in ahead of me! | 2016-07-26 18:08:42 | {"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": 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": 0.8525439500808716, "perplexity": 5421.972645345058}, "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-2016-30/segments/1469257825048.60/warc/CC-MAIN-20160723071025-00139-ip-10-185-27-174.ec2.internal.warc.gz"} |
https://smart-answers.com/mathematics/question8196484 | , 12.11.2019 03:31, oopfloop2
# Can someone me with this. is it a b c. or d
### Other questions on the subject: Mathematics
Mathematics, 21.06.2019 18:00, cfigueroablan
(this is the problem)- write a polynomial equation with a leading coefficient of 1 and the given zeros (0,5,-5+√8). seriously need on this. | 2021-06-18 21:03:49 | {"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": 0.9773638844490051, "perplexity": 3203.451522695995}, "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-2021-25/segments/1623487641593.43/warc/CC-MAIN-20210618200114-20210618230114-00608.warc.gz"} |
https://hpmuseum.org/forum/thread-7845.html | How to plot an integral on Prime?
02-28-2017, 11:53 PM (This post was last modified: 02-28-2017 11:55 PM by TheKaneB.)
Post: #1
TheKaneB Member Posts: 175 Joined: Jul 2014
How to plot an integral on Prime?
Hi,
I'm trying to plot the integral of a function, just like this: http://www.wolframalpha.com/input/?i=plo...x+of+x%5E2
I can do it very easily with Wolfram / Mathematica, and the TI calcs also work but they are slow.
I tried this on my Prime:
CAS.int(x*x, x, 0, x)
but all I get is a Syntax Error.
If I try to enter the function using the Integral graphical template, it will enter, but the plot is empty and the Numerical Table is full of NaN.
PS: It would be nice to plot this also in my 50g. I'm struggling with it, which is a shame since it's my favourite calc!
Software Failure: Guru Meditation
--
Antonio
IU2KIY
03-01-2017, 01:10 AM
Post: #2
TheKaneB Member Posts: 175 Joined: Jul 2014
RE: How to plot an integral on Prime?
Update:
on the 50g I've found a way to plot the function I want:
y(x) = INTVX(f(x)) - INT(f(x), x, 0)
Example: on the TI-89 I plot: ( I will use $for the integral symbol) y(x) =$(ln(x), x, 0, x)
and on the 50g:
y(x) = INTVX(LN(x)) - INT(LN(x), x, 0)
On the 50g the function entry is quite tedious, BUT it's many times faster than the TI. While the TI has drawn the first 2 pixels, the 50g has already finished the whole graph 3 times in a row
But still no luck on the Prime
Honestly, I'm getting tired of this calculator... If I can't solve this issue I'll stick to my 50g for everything
Software Failure: Guru Meditation
--
Antonio
IU2KIY
03-01-2017, 01:56 AM
Post: #3
Han Senior Member Posts: 1,883 Joined: Dec 2013
RE: How to plot an integral on Prime?
1. Press the [Apps] key. Select the Function app.
2. Press [Symb] and enter in: $$\int$$(T^2, T, 0, X) (in algebraic entry mode) or $$\displaystyle \int_0^X T^2\ dT$$ (in textbook entry mode)
3. Press [Plot]
You cannot use the X for your variable of integration because the system uses X as the input variable of the function being plotted. It evaluates the formula at various values of X, but it cannot do so if your formula is $$\int$$(X^2,X,0,X).
Think of it this way:
If $$\displaystyle f(x) = \int_0^x x^2\ dx$$ then would
$f(2) = \int_0^2 2^2\ d2$
make much sense? (Pay attention to the differential "$$d2$$")
Graph 3D | QPI | SolveSys
03-01-2017, 02:20 AM (This post was last modified: 03-01-2017 02:31 AM by TheKaneB.)
Post: #4
TheKaneB Member Posts: 175 Joined: Jul 2014
RE: How to plot an integral on Prime?
It works, thank you!
Now I have another problem.
I tried to plot the integral from 0 to x of tan(t^2) and it's stuck forever. Keyboard and screen are unresponsive, [Esc] and [On] keys don't seem to stop the computation.
After 2 minutes I decided to reset, then I tried again in Table view ( [Num] key ) and at least it's calculating correctly. Maybe it's just too heavy of an integral for the plot view.
Anyway, this is another issue. Thanks again!
EDIT: Your explanation is spot on, I tought that the HP would substitute the 'x' only inside the expression, but that would require a special case to handle the integral correctly. I wonder if TI and Wolfram did a special code path just for the integral, it would make sense for an educational market.
Software Failure: Guru Meditation
--
Antonio
IU2KIY
03-01-2017, 03:13 AM (This post was last modified: 03-01-2017 03:14 AM by Han.)
Post: #5
Han Senior Member Posts: 1,883 Joined: Dec 2013
RE: How to plot an integral on Prime?
Try this alternate method:
In the CAS, create a function like so:
f(x):=int(tan(t^2),t,0,x);
Then in the [Symb] view, use f(X) as your formula. (Note upper vs lower case) I generally prefer this method since it means I can use the function f for other calculations as well as graphing.
Graph 3D | QPI | SolveSys
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https://www.gamedev.net/forums/topic/690861-win32-application-cout-output-both-on-console-and-on-file/ | • 9
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# Win32 application| cout output both on console and on file
## Recommended Posts
Hi everyone, the code below is my setup for opening a console in a Win32 project (using visual studio) and having the cout print stuff on it, it is mostly copy-pasted from stackoverflow with some trial and error changes I did without being sure of what I was doing, but it works. Though now I want to understand it, code below
void debugConsole(bool create = true);
int WINAPI WinMain(HINSTANCE instance, HINSTANCE prevInstance, LPSTR cmdLine, int show)
{
#if defined(DEBUG) || defined(_DEBUG)
debugConsole();
#endif
return 0;
}
void debugConsole(bool create)
{
if (create)
{
//Create Console
FILE* stream;
AllocConsole();
freopen_s(&stream, "conout$", "w", stdout); } } So from what I can tell, I am telling it that now the stdout stream (stuff I send using std::cout) get written (that's why the "w") to the console output, which is specified using "conout$".
So basically freopen_s job is to send a stream somewhere else?
But where is the "conout$" coming from? There is like a switch inside freopen_s that tells it the meaning of "conout$", which would be "send stuff to console"?
What is the FILE* stream sent to freopen_s doing though?
also let's say that under that line I write
freopen_s(&stream, "output.txt", "w", stdout);
I tried this out and it creates said file and put the cout output into it, which is great, but what if I want both? How do I set it up in a way than now cout content is cloned and sent both to the console and to my output file?
Thanks
Edited by MarcusAseth
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52 minutes ago, MarcusAseth said:
So basically freopen_s job is to send a stream somewhere else?
The documentation is here. It closes the file pointer and re-assigns the stream, you can read more at the link.
52 minutes ago, MarcusAseth said:
But where is the "conout$" coming from? There is like a switch inside freopen_s that tells it the meaning of "conout$", which would be "send stuff to console"?
Close. It is not handled inside that function, but it is handled by the system.
It is one of several special file names that Windows recognizes. There are a bunch of them for things like console input/output, serial port input/output, and various other special devices and special features. There are similar special device names on other operating systems like Linux or OSX or other systems.
Both CONIN$and CONOUT$ are managed by Windows so you don't have to. Assuming they exist and haven't already been redirected in your program, that can work as you describe, sending stuff to the console.
52 minutes ago, MarcusAseth said:
I tried this out and it creates said file and put the cout output into it, which is great, but what if I want both? How do I set it up in a way than now cout content is cloned and sent both to the console and to my output file?
The cout object is nothing particularly fancy, it is an output stream that happens to point to a specific location. You have an output file that is also an output stream pointing to a different specific location.
If you want to write to them both, then do it:
cout << stuffToWrite;
myfile << stuffToWrite;
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I see.
This gives me an idea, can I create my personal stream object that overload the operator<< so that when I call
MySuperCout << "important stuff" << endl;
it sends the content both to cout and to myfile as in your example above.
Seems reasonable, I go to try it out, thanks!
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I've encountered some obstacles
I was thinking something like the code below should do the trick
#include <iostream>
#include <string>
#include <fstream>
using namespace std;
class MyCout {
public:
MyCout(string filename) :mFilename{filename} {}
MyCout& operator<<(const string s)
{
mMyFile.open(mFilename, ofstream::out);
cout << s;
mMyFile << s;
mMyFile.close();
return *this;
}
private:
ofstream mMyFile;
string mFilename;
};
int main()
{
MyCout stream1("outputFile1.txt");
stream1 << "test_test_test" << endl;
}
But it only works with string since I've overloaded the operator<< only for that, therefore endl don't work with it (unleass I overload for that as well).
There is a more clever way to do this, like inheriting from something similar to cout to have my own stream class while getting all the operator<< overload behaviours of the cout?
What would really solve my problem is something like this
MyCout& operator<<(WatheverType& t)
{
cout << t;
}
the ability of having my operator<< accept every type because inside, cout and the fstream are going to handle wathever anyway.
There is any wizardry I can do with templates or something to achieve that?
Edited by MarcusAseth
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Yes you could write something like
template <typename T> void Log(const T &t)
{
std::cout << t;
}
that will work as expected for the reason of compile time resolve of T.
What I've did a long time ago was redirecting the standard output and error channels to achive something like you would like to using the rdbuf properties
std::ofstream out("log.txt");
std::streambuf *coutbuf = std::cout.rdbuf(); //save old buf
std::cout.rdbuf(out.rdbuf()); //redirect std::cout to file
//do all the logging between here
std::cout.rdbuf(coutbuf); //reset to standard output
using an own implementation of a buffer object that was intended to do tripple; output to file, output to game console, output to debug console whenever buffer was filled.
class logbuf : public std::streambuf
{
private:
char buffer[STREAMBUFFER_SIZE];
int overflow(int c)
{
if (!std::streambuf::traits_type::eq_int_type(c, std::streambuf::traits_type::eof()))
{
*this->pptr() = std::streambuf::traits_type::to_char_type(c);
this->pbump(1);
}
return this->sync()? std::streambuf::traits_type::not_eof(c): std::streambuf::traits_type::eof();
}
int sync()
{
if (this->pbase() != this->pptr())
{
if(callback)
this->callback(std::string(this->pbase(), this->pptr()));
this->setp(this->pbase(), this->epptr());
}
return 0;
}
public:
delegate<void (std::string)> callback;
logbuf()
{
memset(buffer,0,sizeof(buffer));
this->setp(this->buffer, this->buffer + sizeof(this->buffer) - 1);
}
};
Here a delegate was called whenever something was pushed into the buffer where the delegate could be bound to anything that accepts std::string as parameter and has no return type.
This code is higly obsolete so should not be used but you could get a view of how your goal could be achieved. Meanwhile I use a different approach away from the STL simply similar to C#'s string.Format function as a thread-safe templated argument to text conversion function.
#define __log(...) Log::Write(Log::Message, __VA_ARGS__)
#define __err(...) Log::Write(Log::Error, __VA_ARGS__)
...
__log("{0} Cores Found", GetSystemCores()); //results in '16 Cores Found'
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Thank you for the examples Shaarigan, though actually the template example doesn't quite fit my needs because I want the ability to concatenate a series of operator<< as when you normally do a cout.
I went with this (code below), I've overloaded operator<< on a sstream adding my class, so when I pass it it flushes the stringstream both into cout and into my file. I can both concatenate and write a single line, seems a reasonable way to do it, right?
#include <Windows.h>
#include <iostream>
#include <string>
#include <sstream>
#include <fstream>
using namespace std;
struct MyCout {
MyCout(string filename) { myFile.open(filename, ofstream::out); }
inline stringstream& print() {
string s; stream >> s;
cout << s; myFile << s;
return stream;
}
stringstream stream;
ofstream myFile;
};
ostream& operator<<(ostream& stream, MyCout& debug) { return debug.print(); }
int main()
{
MyCout debug("outputFile1.txt");
debug.stream << "test_test_test" << endl << debug;
return 0;
}
Edited by MarcusAseth
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In operator case, macro definitions could be your friend but your solution seems fair enougth when working for your needs
#define InputOperator(type) std::ostream& operator<<(type const& tp) \
{ \
std::cout << tp; \
myFile << tp; \
return *this; \
}
InputOperator(unsigned char)
InputOperator(signed char)
InputOperator(unsigned short)
InputOperator(signed short)
InputOperator(unsigned int)
InputOperator(signed int)
InputOperator(unsigned long)
InputOperator(signed long)
InputOperator(float)
InputOperator(double)
InputOperator(const char*)
InputOperator(std::string)
Edited by Shaarigan
##### Share on other sites
lol it won't compile
Edit: apologize, it works, it was missing some '\' because maybe I messed up while pasting, but learned a new thing, thanks a lot!
Edited by MarcusAseth | 2018-04-21 02:28:52 | {"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": 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": 0.23375512659549713, "perplexity": 5351.524100669892}, "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-2018-17/segments/1524125944851.23/warc/CC-MAIN-20180421012725-20180421032725-00282.warc.gz"} |
http://ajm.asj-oa.am/229/ | # Note on Matuzsewska-Orlich indices and Zygmund inequalities
Samko, N. (2010) Note on Matuzsewska-Orlich indices and Zygmund inequalities. Armenian Journal of Mathematics, 3 (1). pp. 22-31. ISSN 1829-1163
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## Abstract
In this note we call attention to the fact that there exist some relations between the Matuszewska-Orlicz indices $m(\varphi)$ and $M(\varphi)$ of the function $\varphi$, and possible values of the constants in Zygmund type inequalities.
Item Type: Article 46-xx Functional analysis26-xx Real functions 229 Professor Anry Nersesyan 08 Apr 2010 16:13 19 Apr 2011 02:24
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http://www.maxxidistribuidora.com.br/megiddo-the-xmzsm/f3a9a9-carbonate-ion-bond-order | # carbonate ion bond order
When the ammonium ion, NH 4 + , is formed, the fourth hydrogen is attached by a dative covalent bond, because only the hydrogen's nucleus is transferred from the chlorine to the nitrogen. Why do massive stars not undergo a helium flash, The proofs of limit laws and derivative rules appear to tacitly assume that the limit exists in the first place. Likewise the two minus charges are distributed equally over the three O atoms so that the charge on each is 2/3-. What is the C-O bond order in the carbonate ion, CO 3 2-?. Assertion : Carbon-oxygen bonds are of equal length in carbonate ion. The Lewis dot structures of NO2– highlight a difference in the bond order of the two N-O bonds. Answer: sodium carbonate ( Na2CO3 ) is ionic bond What is chemical bond, ionic bond, covalent bond? Solution for Consider the resonance structures for the carbonate ion. Use MathJax to format equations. Preparing for entrance exams? What is the point of reading classics over modern treatments? This affords a bond order for the carbon - oxygen bond of 1 1/3. For benzene one resonance form for each bond will be single and the other double $(2 + 1)/2$. Carbon dioxide is soluble in water; it reversibly converts to carbonic acid (H2CO3). NCI Thesaurus (NCIt) Hydrogencarbonate is the carbon oxoanion resulting from the removal of a proton from carbonic acid . The b… The Lewis structure of the carbonate ion has two (long) single bonds to negative oxygen atoms, and one short double bond to a neutral oxygen. The Lewis structure of the carbonate ion has two single bonds to negative oxygen atoms and one short double bond to a neutral oxygen. CO+ has one electron removed from a bonding MO, so its bond order decreases by 1 2 to become 2.5. Bond order is the number of chemical bonds between a pair of atoms and indicates the stability of a bond. Looking for a short story about a network problem being caused by an AI in the firmware, MacBook in bed: M1 Air vs. M1 Pro with fans disabled. Contact Us | (1 answer) Closed 3 years ago. The true order of this bond is the average of these three numbers: (2 + 1 + 1) ÷ 3 = 4 / 3 (the same as the other two bonds) Using the resonance theory, we predict that the three bonds in the carbonate ion should be identical, with a bond order of 4 / 3.In fact, this is correct: the three bonds in the carbonate ion really are the same length. The ion has an overall negative two charge so we add 2 e- to give a total of 24 e- to be placed in the Lewis structure. The salt of carbonic acids are called carbonates and are characterized by the carbonate ion, CO32-. win exciting gifts by answering the questions on Discussion Forum If you have questions about how to beautify your posts, have a look at the, Bond order for carbonate ion for resonance. This structure is, however, incompatible with the … The bond order in ion between C-O is 2:00 11.0k LIKES. What's the earliest treatment of a post-apocalypse, with historical social structures, and remnant AI tech? For example, in diatomic nitrogen, N≡N, the bond order is 3; in acetylene, H−C≡C−H, the carbon-carbon bond order is also 3, and the C−H bond order is 1. carbon (C) has four valence electrons x 1 carbon = 4 e-. There is a formula for this too... it is = 1×[(no. Pay Now | It is a quantum-mechanical theory for determining the energies of $\pi$ orbitals, and it defines a method to determine a measure of the $\pi$ bond order between two atoms. Can this equation be solved with whole numbers? Franchisee | Chemical bond A chemical bond is a lasting attraction between atoms, ions or molecules that enables the formation of chemical compounds. Complete JEE Main/Advanced Course and Test Series. Thanks for contributing an answer to Chemistry Stack Exchange! So in general, how should we calculate the bond order for resonance structures? Some of the bicarbonates can only be detected in aqueous medium. Bond order of each carbon‑oxygen bond in the carbonate ion = 1.33. In the nitrite ion, the bond lengths of both nitrogen-oxygen bonds are equal. MathJax reference. Carbon monoxide < carbon dioxide < carbonate ion. This affords a bond order for the carbon - oxygen bond of 1 1/3. In the first structure this bond is a double bond (bond order of 2), in the second it is a single bond (bond order of 1), and in the third it is a single bond (bond order of 1). Privacy Policy | Register yourself for the free demo class from Applying this same method to the carbonate ion, we have 3 resonance structures with bond orders of 2, 1, 1 when considering the bond between carbon and a single oxygen. 500+ SHARES. The "$2$" on the bottom of the equation is the number of resonance structure being considered. Let's try this approach to figure out the C-O bond order in the carbonate ion, CO32-. In the first structure this bond is a double bond (bond order of 2), in the second it is a single bond (bond order of 1), and in the third it is a single bond (bond order of 1). One of the easiest examples that comes to mind is benzene. Sitemap | chemical bonding; class-11; Share It On Facebook Twitter Email. Careers | Which, among the following, is not a main factor of production? In certain molecules, axial and equatorial positions are unique. Option b provides this alternative. You cannot, for example, calculate in any simple way a bond order for. Roots given by Solve are not satisfied by the equation. 2- Identify which carbon and oxygen electron orbitals overlap to create each single and double C-O bond in the structure Terms & Conditions | a. Since there are 3 structures the answer is $(2+1+1)/3 = 1.33333$ or $4/3$. What do you infer about the CO bonds in the carbonate ion. Tutor log in | Step 1. Answer Would Mike Pence become President if Trump was impeached and removed from office? (enter a decimal number) In which species (CO32 or CO2) are the C-O bond(s) longer?| In which species (CO32 or CO2) are the C-O bond(s) weaker? Their shapes are trigonal planar with 120 o of bond angles at carbon atom. How many resonance structures does the oxalate ion have? There definitely is an easy way to do this. We should notice that for the pi bond order, there will be 2 pi electrons delocalized onto three bonds, making each bond on average having 2/3 of a pi electron, thereby giving a pi bond order of 1/3. subject, carbon (C) has four valence electrons x 1 carbon = 4. Is there an English adjective which means "asks questions frequently"? Preparing for entrance exams? Three resonance structures so C=O double bond is equally spread over the three C-O single bonds to give a bond order of 1.33. Since Bond length is inversely proportional to bond order, and bond order depends on number of bonds, here as CO will have triple bonds, CO2 will have two double bonds (linear structure with carbon as central atom O=C=O) however in case of CO3^ … The bond order would be 1 and 1/3 since the double bond occurs one-third of the time between each oxygen atom and the carbon atom from a resonce point of view Email, Please Enter the valid mobile Points, Please choose a valid How to find the bond order in delocalized pi bonding of more than two atoms? The central carbon atom undergoes sp 2 hybridization. , This structure is incompatible with the observed symmetry of the ion, which implies that the three bonds are equally long and that the three oxygen atoms are equivalent. Asking for help, clarification, or responding to other answers. askiitians. before and after hybridization. 2. Since the charges of the atoms are already given, we can notice that two of O atoms have a charge of -1 where C and O are neutral. So lost!! CARBONATE ANION By considering its resonance delocalization, the bond order on this molecular ion can be determined. Carbonate ion < carbon dioxide < carbon monoxide. carbon (C) has four valence electrons x 1 carbon = 4 e- oxygen (O) has six valence electrons x 3 oxygens = 18 e- The ion has an overall negative two charge so we add 2 e- to give a total of 24 e- to be placed in the Lewis structure. I'll add that this only works for resonance structure that are equivalent by symmetry… since they have the same weight. combine 4 p orbitals and get 4 molecular orbitals, 2 bonding and 2 antibonding. Analyze the bonds in the carbonate ion. Using MO theory will only get you the total bond order for the molecule, since there are no localized bonds. We are all IITians and here to help you in your IIT JEE preparation. O = C(−O−)2 the which structure distributes 12 ⋅electrons.... All ∠O− C− O = 120∘ as we would anticipate. 1 Answer +1 vote . Find the correct order of increasing C − O bond length in C O, C O X 2, C O X 3 X 2 −. Carbonates are readily decomposed by acids. School Tie-up | Refund Policy, 879 To subscribe to this RSS feed, copy and paste this URL into your RSS reader. NCI Thesaurus (NCIt) Carbonate is a carbon oxoanion. one more likely shows the correct connectivity for NSF. site design / logo © 2021 Stack Exchange Inc; user contributions licensed under cc by-sa. COMPOUNDS CONTAINING CARBONATE OR BICARBONATE ANIONS. Given the double bond is shared between the three oxygen atoms, the bond order will be 1.33. If the bond order of carbonate ion (C O32−) is expressed by the simple ration x: y, the value of (x+ y) will be. Consider the "top" NO bond in the nitrate ion, $$NO_3^-$$, as shown in the resonance structure below. 1 b. Dear If we look at the structure: we see that each of the carbon bonds are either single bonds to the adjacent carbon or double bonds to the carbon in the other direction. Blog | 1.33 c. 1.5 d. 2 e. 1.25. Why is the LOX header tank on Spacex Starship at the front of the vehicle? name, Please Enter the valid One of our academic counsellors will contact you within 1 working day. Explanation: The carbonate ion (CO₃²⁻) is an organic compound, in which a carbon atom is covalently bonded to three oxygen atoms. A Land B Labour C Capital D Product, Water drops are spherical because of A. polarity B. viscosity C. surface tension D. density is one. The two bonds are shorter than a single bond but longer than double bond. Explain resonance with reference to carbonate ion. Their shapes are trigonal planar with 120 o of bond angles at carbon atom. oxygen (O) has six valence electrons x 3 oxygens = 18 e-. 500+ VIEWS. Carbonate Ion is a polyatomic ion with formula of CO3 (2-). This problem has been solved! consider the carbonate ion, co 3 2- assume the carbon and oxygens are sp 2. hybrids. Welcome to chemistry.se! Arrange the following in order of increasing bond strength of the carbon oxygen bond: Carbon monoxide < carbonate ion < carbon dioxide. If you like this answer please approve it.... win exciting gifts by answering the questions on Discussion Forum. SQL Server 2019 column store indexes - maintenance. (There are probably also ways to tackle the problem from an experimental side, although I'm not all sure about this; I'm thinking about perhaps determining electron distributions through NMR chemical shifts, or bond strengths through vibrational spectroscopy.). y p explains why bond lengths are equal. When a microwave oven stops, why are unpopped kernels very hot and popped kernels not hot? Usually metal ions with bigger atomic size form stable carbonates and bicarbonates. , Chemistry Stack Exchange is a question and answer site for scientists, academics, teachers, and students in the field of chemistry. We are all IITians and here to help you in your IIT JEE preparation. See the answer. Given the double bond is shared between the three oxygen atoms, the bond order will be 1.33. In the case of the carbonate ion, VSEPR is easier to use in determining the bond order which in this case is 1.33. Answer: The correct answers are: Each oxygen of carbonate ion has -2/3 or -0.67 charge. Register Now. Usually metal ions with bigger atomic size form stable carbonates and bicarbonates. Why burning of candle is a chemical change? RD Sharma Solutions | Salts or ions of the theoretical carbonic acid, containing the radical CO2 (3-). Bond order of HCO3- as compared to (CO3)2-, Forming the resonance structures for the nitrite anion. Step-by-step answer 01:55 0 0. Learn to Create the Famous Tic Tac Toe Game in Our Free Robotics Webinar. Comparison of experimental bond lengths for related molecules (for example, the cyclopentadienyl anion is symmetric) and for tetrahydrofuran and the the dihydrofuran isomers may get you an estimate. Videos. Become a member and unlock all Study Answers Try it risk-free for 30 days (4 bonds averaged over three structures.) What is the bond order of the C-O bonds in the carbonate ion ? The Lewis structure of the carbonate ion has two single bonds to negative oxygen atoms and one short double bond to a neutral oxygen. Bicarbonate Ion is a polyatomic ion whose formula is HCO3-. Analyze each structure and determine the charges in each atom.The sum of the charges will be the net charge of the molecule.. For the bond order, identify the bonds in the structure.. Acetate ion forms a resonance structure where the negative charge is delocalized over all three atoms and therefore, two carbon-oxygen bonds are of equal length. CO32- has three resonating structures. It only takes a minute to sign up. Media Coverage | It is a conjugate base of a hydrogencarbonate. The way to calculate the bond order for most conpounds having resonating structures is: (No.of bonds/No.of resonating structures) Since, CO32- has 4 bonds, Thus answer will be 4/3 or 1.3333.. Questions 1. "nec sit terris ultima Thule" - how should terris be interpreted? If you want to go beyond that, you will have to look further into quantum chemistry and different schemes for bond localization and population analysis. If you like this answer please approve it.... Dear The carbonates of the alkali metals are water-soluble; all others are insoluble. Specifically, compare the standard bond lengths for C- and C=O (in Tables A and 2) with the WebMO-computed bond length (Table 3. Structural Organisation in Plants and Animals, which compound will have a better stability constant [Ni(H20)6]^2+ or [Ni(NH3)6]^2+. Register yourself for the free demo class from Carbon dioxide < carbon monoxide < carbonate ion. Use Coupon: CART20 and get 20% off on all online Study Material, Complete Your Registration (Step 2 of 2 ).
Reason : Bond length decreases with the multiplicity of bond between two atoms. If we draw the other resonance structure these bonds shift by 1 atom to look like the following: Thus, the overall structure can be obtained by looking at those two structure and averaging the bond order between them. Can 1 kilogram of radioactive material with half life of 5 years just decay in the next minute? Answer Sagar Singh About Us | Learn to build the famous Tic Tac Toe Game. Ceramic resonator changes and maintains frequency when touched, Colleagues don't congratulate me or cheer me on when I do good work. FAQ's | :0: :0: :0: How much negative charge is on each oxygen of the What is the bond order of… If you want a somewhat quantitative yet simple approach to bond orders in delocalized systems, have a look at the Hückel method. COMPOUNDS CONTAINING CARBONATE OR BICARBONATE ANIONS. CO2+ DICATION CO2+ has an additional bonding electron removed relative to CO+, so it has a bond order of 2. Show transcribed image text. Did Trump himself order the National Guard to clear out protesters (who sided with him) on the Capitol on Jan 6? I saw in a textbook that for carbonate ion, there are 3 resonance forms and the bond order is 1 and 1/3. The negative charge is spread over the end of the molecule equally. And given that resonance is a figment invented to make valence bond theory handle delocalization, there is likely no theoretical approach to determine the relative weight of furan's resonance structures. The resonance hybrid of this polyatomic ion, obtained from its different resonance structures, can be used to explain the equal bond lengths, as illustrated below.The resonance hybrid of NO2– suggests that each oxygen atom holds a partial charge of magnitude -½. Thus, for benzene the bond order is $1.5$. I hope I was able to help you out. 2.0k LIKES. Thus, with 3 resonance structures, the $$\overline{\rm BO}$$ will be: Ammonium ions, NH 4 +, are formed by the transfer of a hydrogen ion from the hydrogen chloride to the lone pair of electrons on the ammonia molecule. B.Tech IIT Delhi. To learn more, see our tips on writing great answers. rev 2021.1.8.38287, The best answers are voted up and rise to the top, Chemistry Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us, Indeed. Some of the bicarbonates can only be detected in aqueous medium. What is the C-O bond order in the carbonate ion, CO 3 2-?. The net formal charge on a carbonate ion is −2. In many cases there is no one definite answer, but rather, your results will depend heavily on the quantum-chemical calculations and assumptions for the bond-order analysis itself. Analyze the resonance structures. y n explains why both oxygens are equally minus and the sulfur is positive . What Is The Bond Order Of Each Carbon-oxygen Bond In The Rbonate Ion? (4 bonds averaged over three structures.). This question already has an answer here : How to rationalise the increasing bond length order in the carbonate ion, carbon monoxide, and carbon dioxide? For the carbonate ion, CO3 2− 1- Draw the electron orbital diagram for the valence electrons of the central carbon. 500+ VIEWS. CO3^2- AX3 system; Trigonal planar: two C-O(-) bonds and one C=O bond (to give C an octet). Only in simple cases, it is possible to make reliable estimates of the relative weight of resonance structures from the Lewis structure alone. Click hereto get an answer to your question ️ If the bond order of carbonate ion (CO^2 - 3) is expressed by the simple ration x : y , the value of (x + y) will be. Making statements based on opinion; back them up with references or personal experience. This structure is, however, incompatible with the ion’s observed symmetry, which implies that the three bonds and oxygen atoms are equivalent. The carbonate ion is the simplest oxocarbon anion, consisting of one carbon atom surrounded by three oxygen atoms in a trigonal planar arrangement. We must first realize that... See full answer below. Applying this same method to the carbonate ion, we have 3 resonance structures with bond orders of 2, 1, 1 when considering the bond between carbon and a single oxygen. Free webinar on Robotics. grade, Please choose the valid Thus, with 3 resonance structures, the $$\overline{\rm BO}$$ will be: By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. This is consistent with the experimental fact that the C-O bond lengths in sodium carbonate are longer than a C-O single bond but shorter than a C-O double bond when compared to reference compounds. answered 1 day ago by Maisa (45.6k points) selected 4 hours ago by Panna01 . Use the example above to verify via the equation. Since there are 3 structures the answer is (2 + 1 + 1) / 3 = 1.33333 or 4 / 3. Carbon dioxide < carbonate ion < carbon monoxide Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. number, Please choose the valid All the best. Therefore we describe the carbon-oxygen bonds in the carbonate ion as being between a single and double bond in character. How Much Negative Charge Is On Each Oxygen Of The Carbonate Ion? The central carbon atom undergoes sp 2 hybridization. Help!! askiitians. bond order of C-O in CO, CO2 and [CO3]2- bond order of P-O in [PO4]3- bond order of N-O in [NO2]- bond order of S-O in [SO4]2- Why are unpopped kernels very hot and popped kernels not hot simple cases, is. A proton from carbonic acid reading classics over modern treatments chemistry Stack Exchange a pair atoms!, Forming the resonance structure that are equivalent by symmetry… since they have the weight. Of service, privacy policy and cookie policy him ) on the bottom of the equation is a ion. Each carbon‑oxygen bond in character about how to beautify your posts, have look. To subscribe to this RSS feed, copy and paste this URL into RSS. Chemical bond is shared between the three O atoms so that the charge on each oxygen of equation. Which structure distributes 12 ⋅electrons.... all ∠O− C− O = C ( −O− ) 2 the structure., Complete your Registration ( Step 2 of 2 chemical bonds carbonate ion bond order a single bond but longer than double is! Lewis structure of the carbonate ion is a polyatomic ion whose formula is HCO3-: two C-O -... Hours ago by Maisa ( 45.6k points ) selected 4 hours ago by Maisa ( 45.6k points selected! And one short double bond is a lasting attraction between atoms, the bond order in the ion! The resonance structures does the oxalate ion have ; user contributions licensed under cc by-sa and answer site scientists... Than a single and the bond order in the resonance structures does the ion. With him ) on the bottom of the two N-O bonds acids are called carbonates and bicarbonates all are. Stack Exchange Inc ; user contributions licensed under cc by-sa get 4 molecular orbitals, 2 bonding and 2.. Lewis dot structures of NO2– highlight a difference in the carbonate ion, CO 3?... Url into your RSS reader must first realize that... See full answer below as we anticipate... A lasting attraction between atoms, the bond order for and 2.! Mike Pence become President if Trump was impeached and removed from office distributed equally the... Rss reader to carbonate ion is a polyatomic ion with formula of CO3 ( 2-.. 1 ) /2 $nitrogen-oxygen bonds are equal on Jan 6 longer than double bond is shared between three... Length in carbonate ion we would anticipate trigonal planar with 120 O of bond angles at atom!, privacy policy and cookie policy beautify your posts, have a look at the front of bicarbonates. The example above to verify via the equation 1.5$ simple cases, it is to! Resonance structure that are equivalent by symmetry… since they have the same weight changes and maintains frequency touched... ; user contributions licensed under cc by-sa not satisfied by the carbonate ion, CO32- Spacex at. Let 's Try this approach to figure out the C-O bond order of each Carbon-oxygen bond carbonate ion bond order the order... Benzene one resonance form for each bond will be single and double bond to a neutral oxygen questions about to. Become President if Trump was impeached and removed from office the Capitol on 6! Molecule, since there are no localized bonds contact you within 1 working.. Order on this molecular ion can be determined structure below chemical bonding ; class-11 Share! % off on all online Study material, Complete your Registration ( Step carbonate ion bond order of 2 assertion: bonds... Bond strength of the relative weight of resonance structures for the carbon - oxygen bond of 1/3... More, See our tips on writing great answers 1 and 1/3 have a look at the Hückel method Colleagues! At carbon atom symmetry… since they have the same weight = 18 e- ; class-11 ; Share it on Twitter. Any simple way a bond order of HCO3- as compared to ( CO3 ) 2-, Forming the structures! Within 1 working day are trigonal planar: two C-O ( - bonds. A member and unlock all Study answers Try it risk-free for 30 days Explain resonance with to... < carbonate ion has two single bonds to negative carbonate ion bond order atoms and one short double bond to a oxygen... 5 years just decay in the carbonate ion, CO 3 2-? ) / 3 = 1.33333 or., CO 3 2-? sulfur is positive is $( 2+1+1 ) /3 = 1.33333 4... Ion has two single bonds to negative oxygen atoms in a textbook that for carbonate ion bond order ion, bond! Structures from the removal of a bond order in ion between C-O is 2:00 11.0k LIKES this into... Microwave oven stops, why are unpopped kernels very hot and popped kernels not hot you infer the. For NSF oxocarbon anion, consisting of one carbon atom surrounded by three atoms! It.... win exciting gifts by answering the questions on Discussion Forum logo © 2021 Stack Inc. Satisfied by the carbonate ion, CO 3 2-? averaged over three structures )... 45.6K points ) selected 4 hours ago by Maisa ( 45.6k points ) selected 4 hours ago by Maisa 45.6k. Bond to a neutral oxygen = 4 e- off on all online Study material, Complete your Registration Step. Our tips on writing great answers, VSEPR is easier to use in determining the order. Academic counsellors will contact you within 1 working day carbonate anion by considering its resonance delocalization the. Bond to a neutral oxygen symmetry… since they have the same weight resonance structures unlock all Study answers Try risk-free... Difference in the carbonate ion a post-apocalypse, with historical social structures, and remnant AI?. The net formal charge on each is 2/3- forms and the other double$ ( 2 + 1 /2... Whose formula is HCO3- remnant AI tech the easiest examples that comes to mind is benzene bonding of than. For contributing an answer to chemistry Stack Exchange Inc ; user contributions under... Contributions licensed under cc by-sa stability of a proton from carbonic acid ( H2CO3 ) 120 O bond... Inc ; user contributions licensed under cc by-sa are not satisfied by the carbonate ion < carbon dioxide popped. Personal experience on a carbonate ion as being between a single and the other double $carbonate ion bond order... Pair of atoms and indicates the stability of a post-apocalypse, with historical structures! X 1 carbon = 4 e- among the following in order of each carbon‑oxygen in... Bond will be 1.33, have a look at the Hückel method or molecules that enables the of. Each bond will be 1.33 of our academic counsellors will contact you within 1 working day the negative charge on... Pence become President if Trump was impeached and removed from office molecules, axial and equatorial positions are unique the. ( Step 2 of 2 of increasing bond strength of the carbon oxygen bond of 1/3... Realize that... See full answer below popped kernels not hot on 6... Of bond angles at carbon atom social structures, and remnant AI tech equally minus and the double... Formula is HCO3- from office bond length decreases with the multiplicity of bond angles at carbon atom to out... Co+, so it has a bond order in ion between C-O is 11.0k! It.... win exciting gifts by answering the questions on Discussion Forum they have the same weight or. The simplest oxocarbon anion, consisting of one carbon atom of radioactive material with life! Of more than two atoms a single bond but longer than double bond to a neutral.. Clear out protesters ( who sided with him ) on the bottom of carbonate! For benzene one resonance form for each bond will be single and the sulfur is positive our... Is possible to make reliable estimates of the molecule, since there are localized. Ion = 1.33 unlock all Study answers Try it risk-free for 30 days Explain resonance reference! And paste this URL into your RSS reader VSEPR is easier to use in determining bond. To use in determining the bond order of the carbonate ion is the bond order for the free class. 2-? delocalization, the bond order is$ 1.5 $Rbonate ion in your IIT JEE preparation /.! Answer below bicarbonates can only be detected in aqueous medium Jan 6, your. Localized bonds your answer ”, you agree to our terms of,! Too... it carbonate ion bond order possible to make reliable estimates of the central carbon '' - how should we the... The electron orbital diagram for the molecule, since there are 3 resonance forms and the bond order for free... On Facebook Twitter Email carbonic acids are called carbonates and are characterized by the carbonate ion two! 20 % off on carbonate ion bond order online Study material, Complete your Registration ( Step 2 of.... Carbon carbonate ion bond order academic counsellors will contact you within 1 working day the correct connectivity for NSF, there 3..., so it has a bond order of 2 ) counsellors will you... Are sp 2. hybrids agree to our terms of service, privacy policy and cookie policy this... The C-O bond order of increasing bond strength of the vehicle 1 kilogram of material! ; Share it on Facebook Twitter Email each oxygen of the carbon - oxygen bond of 1/3!: carbon monoxide < carbonate ion, CO32- ), as shown the! Add that this only works for resonance structure being considered bicarbonates can only be carbonate ion bond order. Chemical bonds between a single and the sulfur is positive ”, you agree to our terms service! As shown in the nitrate ion, the bond order of… questions.. The Rbonate ion carbon oxoanion resulting from the removal of a post-apocalypse, with historical social structures and! Diagram for the carbon oxoanion structures the answer is$ 1.5 \$ realize that... See full answer below molecule! Salt of carbonic acids are called carbonates and are characterized by the carbonate ion and short! See our tips on writing great answers one C=O bond ( to give C an octet ) one. Given the double bond is shared between the three O atoms so that the charge on a ion... | 2021-05-12 23:27:46 | {"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": 0.35022205114364624, "perplexity": 2732.3503913511154}, "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/1620243991413.30/warc/CC-MAIN-20210512224016-20210513014016-00403.warc.gz"} |
http://commons.apache.org/proper/commons-math/apidocs/org/apache/commons/math3/stat/inference/ChiSquareTest.html | org.apache.commons.math3.stat.inference
## Class ChiSquareTest
• public class ChiSquareTest
extends Object
Implements Chi-Square test statistics.
This implementation handles both known and unknown distributions.
Two samples tests can be used when the distribution is unknown a priori but provided by one sample, or when the hypothesis under test is that the two samples come from the same underlying distribution.
Version:
$Id: ChiSquareTest.java 1416643 2012-12-03 19:37:14Z tn$
• ### Constructor Summary
Constructors
Constructor and Description
ChiSquareTest()
Construct a ChiSquareTest
• ### Method Summary
Methods
Modifier and Type Method and Description
double chiSquare(double[] expected, long[] observed)
Computes the Chi-Square statistic comparing observed and expected frequency counts.
double chiSquare(long[][] counts)
Computes the Chi-Square statistic associated with a chi-square test of independence based on the input counts array, viewed as a two-way table.
double chiSquareDataSetsComparison(long[] observed1, long[] observed2)
Computes a Chi-Square two sample test statistic comparing bin frequency counts in observed1 and observed2.
double chiSquareTest(double[] expected, long[] observed)
Returns the observed significance level, or p-value, associated with a Chi-square goodness of fit test comparing the observed frequency counts to those in the expected array.
boolean chiSquareTest(double[] expected, long[] observed, double alpha)
Performs a Chi-square goodness of fit test evaluating the null hypothesis that the observed counts conform to the frequency distribution described by the expected counts, with significance level alpha.
double chiSquareTest(long[][] counts)
Returns the observed significance level, or p-value, associated with a chi-square test of independence based on the input counts array, viewed as a two-way table.
boolean chiSquareTest(long[][] counts, double alpha)
Performs a chi-square test of independence evaluating the null hypothesis that the classifications represented by the counts in the columns of the input 2-way table are independent of the rows, with significance level alpha.
double chiSquareTestDataSetsComparison(long[] observed1, long[] observed2)
Returns the observed significance level, or p-value, associated with a Chi-Square two sample test comparing bin frequency counts in observed1 and observed2.
boolean chiSquareTestDataSetsComparison(long[] observed1, long[] observed2, double alpha)
Performs a Chi-Square two sample test comparing two binned data sets.
• ### Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
• ### Constructor Detail
• #### ChiSquareTest
public ChiSquareTest()
Construct a ChiSquareTest
• ### Method Detail
• #### chiSquare
public double chiSquare(double[] expected,
long[] observed)
throws NotPositiveException,
NotStrictlyPositiveException,
DimensionMismatchException
Computes the Chi-Square statistic comparing observed and expected frequency counts.
This statistic can be used to perform a Chi-Square test evaluating the null hypothesis that the observed counts follow the expected distribution.
Preconditions:
• Expected counts must all be positive.
• Observed counts must all be ≥ 0.
• The observed and expected arrays must have the same length and their common length must be at least 2.
If any of the preconditions are not met, an IllegalArgumentException is thrown.
Note: This implementation rescales the expected array if necessary to ensure that the sum of the expected and observed counts are equal.
Parameters:
observed - array of observed frequency counts
expected - array of expected frequency counts
Returns:
chiSquare test statistic
Throws:
NotPositiveException - if observed has negative entries
NotStrictlyPositiveException - if expected has entries that are not strictly positive
DimensionMismatchException - if the arrays length is less than 2
• #### chiSquareTest
public double chiSquareTest(double[] expected,
long[] observed)
throws NotPositiveException,
NotStrictlyPositiveException,
DimensionMismatchException,
MaxCountExceededException
Returns the observed significance level, or p-value, associated with a Chi-square goodness of fit test comparing the observed frequency counts to those in the expected array.
The number returned is the smallest significance level at which one can reject the null hypothesis that the observed counts conform to the frequency distribution described by the expected counts.
Preconditions:
• Expected counts must all be positive.
• Observed counts must all be ≥ 0.
• The observed and expected arrays must have the same length and their common length must be at least 2.
If any of the preconditions are not met, an IllegalArgumentException is thrown.
Note: This implementation rescales the expected array if necessary to ensure that the sum of the expected and observed counts are equal.
Parameters:
observed - array of observed frequency counts
expected - array of expected frequency counts
Returns:
p-value
Throws:
NotPositiveException - if observed has negative entries
NotStrictlyPositiveException - if expected has entries that are not strictly positive
DimensionMismatchException - if the arrays length is less than 2
MaxCountExceededException - if an error occurs computing the p-value
• #### chiSquareTest
public boolean chiSquareTest(double[] expected,
long[] observed,
double alpha)
throws NotPositiveException,
NotStrictlyPositiveException,
DimensionMismatchException,
OutOfRangeException,
MaxCountExceededException
Performs a Chi-square goodness of fit test evaluating the null hypothesis that the observed counts conform to the frequency distribution described by the expected counts, with significance level alpha. Returns true iff the null hypothesis can be rejected with 100 * (1 - alpha) percent confidence.
Example:
To test the hypothesis that observed follows expected at the 99% level, use
chiSquareTest(expected, observed, 0.01)
Preconditions:
• Expected counts must all be positive.
• Observed counts must all be ≥ 0.
• The observed and expected arrays must have the same length and their common length must be at least 2.
• 0 < alpha < 0.5
If any of the preconditions are not met, an IllegalArgumentException is thrown.
Note: This implementation rescales the expected array if necessary to ensure that the sum of the expected and observed counts are equal.
Parameters:
observed - array of observed frequency counts
expected - array of expected frequency counts
alpha - significance level of the test
Returns:
true iff null hypothesis can be rejected with confidence 1 - alpha
Throws:
NotPositiveException - if observed has negative entries
NotStrictlyPositiveException - if expected has entries that are not strictly positive
DimensionMismatchException - if the arrays length is less than 2
OutOfRangeException - if alpha is not in the range (0, 0.5]
MaxCountExceededException - if an error occurs computing the p-value
• #### chiSquare
public double chiSquare(long[][] counts)
throws NullArgumentException,
NotPositiveException,
DimensionMismatchException
Computes the Chi-Square statistic associated with a chi-square test of independence based on the input counts array, viewed as a two-way table.
The rows of the 2-way table are count[0], ... , count[count.length - 1]
Preconditions:
• All counts must be ≥ 0.
• The count array must be rectangular (i.e. all count[i] subarrays must have the same length).
• The 2-way table represented by counts must have at least 2 columns and at least 2 rows.
If any of the preconditions are not met, an IllegalArgumentException is thrown.
Parameters:
counts - array representation of 2-way table
Returns:
chiSquare test statistic
Throws:
NullArgumentException - if the array is null
DimensionMismatchException - if the array is not rectangular
NotPositiveException - if counts has negative entries
• #### chiSquareTest
public double chiSquareTest(long[][] counts)
throws NullArgumentException,
DimensionMismatchException,
NotPositiveException,
MaxCountExceededException
Returns the observed significance level, or p-value, associated with a chi-square test of independence based on the input counts array, viewed as a two-way table.
The rows of the 2-way table are count[0], ... , count[count.length - 1]
Preconditions:
• All counts must be ≥ 0.
• The count array must be rectangular (i.e. all count[i] subarrays must have the same length).
• The 2-way table represented by counts must have at least 2 columns and at least 2 rows.
If any of the preconditions are not met, an IllegalArgumentException is thrown.
Parameters:
counts - array representation of 2-way table
Returns:
p-value
Throws:
NullArgumentException - if the array is null
DimensionMismatchException - if the array is not rectangular
NotPositiveException - if counts has negative entries
MaxCountExceededException - if an error occurs computing the p-value
• #### chiSquareTest
public boolean chiSquareTest(long[][] counts,
double alpha)
throws NullArgumentException,
DimensionMismatchException,
NotPositiveException,
OutOfRangeException,
MaxCountExceededException
Performs a chi-square test of independence evaluating the null hypothesis that the classifications represented by the counts in the columns of the input 2-way table are independent of the rows, with significance level alpha. Returns true iff the null hypothesis can be rejected with 100 * (1 - alpha) percent confidence.
The rows of the 2-way table are count[0], ... , count[count.length - 1]
Example:
To test the null hypothesis that the counts in count[0], ... , count[count.length - 1] all correspond to the same underlying probability distribution at the 99% level, use
chiSquareTest(counts, 0.01)
Preconditions:
• All counts must be ≥ 0.
• The count array must be rectangular (i.e. all count[i] subarrays must have the same length).
• The 2-way table represented by counts must have at least 2 columns and at least 2 rows.
If any of the preconditions are not met, an IllegalArgumentException is thrown.
Parameters:
counts - array representation of 2-way table
alpha - significance level of the test
Returns:
true iff null hypothesis can be rejected with confidence 1 - alpha
Throws:
NullArgumentException - if the array is null
DimensionMismatchException - if the array is not rectangular
NotPositiveException - if counts has any negative entries
OutOfRangeException - if alpha is not in the range (0, 0.5]
MaxCountExceededException - if an error occurs computing the p-value
• #### chiSquareDataSetsComparison
public double chiSquareDataSetsComparison(long[] observed1,
long[] observed2)
throws DimensionMismatchException,
NotPositiveException,
ZeroException
Computes a Chi-Square two sample test statistic comparing bin frequency counts in observed1 and observed2. The sums of frequency counts in the two samples are not required to be the same. The formula used to compute the test statistic is
∑[(K * observed1[i] - observed2[i]/K)2 / (observed1[i] + observed2[i])] where
K = &sqrt;[&sum(observed2 / ∑(observed1)]
This statistic can be used to perform a Chi-Square test evaluating the null hypothesis that both observed counts follow the same distribution.
Preconditions:
• Observed counts must be non-negative.
• Observed counts for a specific bin must not both be zero.
• Observed counts for a specific sample must not all be 0.
• The arrays observed1 and observed2 must have the same length and their common length must be at least 2.
If any of the preconditions are not met, an IllegalArgumentException is thrown.
Parameters:
observed1 - array of observed frequency counts of the first data set
observed2 - array of observed frequency counts of the second data set
Returns:
chiSquare test statistic
Throws:
DimensionMismatchException - the the length of the arrays does not match
NotPositiveException - if any entries in observed1 or observed2 are negative
ZeroException - if either all counts of observed1 or observed2 are zero, or if the count at some index is zero for both arrays
Since:
1.2
• #### chiSquareTestDataSetsComparison
public double chiSquareTestDataSetsComparison(long[] observed1,
long[] observed2)
throws DimensionMismatchException,
NotPositiveException,
ZeroException,
MaxCountExceededException
Returns the observed significance level, or p-value, associated with a Chi-Square two sample test comparing bin frequency counts in observed1 and observed2.
The number returned is the smallest significance level at which one can reject the null hypothesis that the observed counts conform to the same distribution.
See chiSquareDataSetsComparison(long[], long[]) for details on the formula used to compute the test statistic. The degrees of of freedom used to perform the test is one less than the common length of the input observed count arrays.
Preconditions:
• Observed counts must be non-negative.
• Observed counts for a specific bin must not both be zero.
• Observed counts for a specific sample must not all be 0.
• The arrays observed1 and observed2 must have the same length and their common length must be at least 2.
If any of the preconditions are not met, an IllegalArgumentException is thrown.
Parameters:
observed1 - array of observed frequency counts of the first data set
observed2 - array of observed frequency counts of the second data set
Returns:
p-value
Throws:
DimensionMismatchException - the the length of the arrays does not match
NotPositiveException - if any entries in observed1 or observed2 are negative
ZeroException - if either all counts of observed1 or observed2 are zero, or if the count at the same index is zero for both arrays
MaxCountExceededException - if an error occurs computing the p-value
Since:
1.2
• #### chiSquareTestDataSetsComparison
public boolean chiSquareTestDataSetsComparison(long[] observed1,
long[] observed2,
double alpha)
throws DimensionMismatchException,
NotPositiveException,
ZeroException,
OutOfRangeException,
MaxCountExceededException
Performs a Chi-Square two sample test comparing two binned data sets. The test evaluates the null hypothesis that the two lists of observed counts conform to the same frequency distribution, with significance level alpha. Returns true iff the null hypothesis can be rejected with 100 * (1 - alpha) percent confidence.
See chiSquareDataSetsComparison(long[], long[]) for details on the formula used to compute the Chisquare statistic used in the test. The degrees of of freedom used to perform the test is one less than the common length of the input observed count arrays.
Preconditions:
• Observed counts must be non-negative.
• Observed counts for a specific bin must not both be zero.
• Observed counts for a specific sample must not all be 0.
• The arrays observed1 and observed2 must have the same length and their common length must be at least 2.
• 0 < alpha < 0.5
If any of the preconditions are not met, an IllegalArgumentException is thrown.
Parameters:
observed1 - array of observed frequency counts of the first data set
observed2 - array of observed frequency counts of the second data set
alpha - significance level of the test
Returns:
true iff null hypothesis can be rejected with confidence 1 - alpha
Throws:
DimensionMismatchException - the the length of the arrays does not match
NotPositiveException - if any entries in observed1 or observed2 are negative
ZeroException - if either all counts of observed1 or observed2 are zero, or if the count at the same index is zero for both arrays
OutOfRangeException - if alpha is not in the range (0, 0.5]
MaxCountExceededException - if an error occurs performing the test
Since:
1.2 | 2014-10-02 12:34:56 | {"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": 0.5862388610839844, "perplexity": 1454.2287585671602}, "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-2014-41/segments/1412037663754.0/warc/CC-MAIN-20140930004103-00171-ip-10-234-18-248.ec2.internal.warc.gz"} |
https://dsp.stackexchange.com/questions/51219/simulating-two-signals-with-a-desired-coherence | # Simulating two signals with a desired coherence
I'm trying to simulate two frequency-domain signals with a desired coherence, and I'd like to check if my idea is right.
To simulate two time-domain signals with a desired correlation, we can use the following method:
Suppose $\Sigma$ is the desired correlation. Let $X \sim N(0,1)$.
Then if we take
$X_1 = \Sigma^{1/2} X$,
$X_1$ will have the desired correlation:
$\mathbb{E} [X_1 X_1^{\dagger}] = \mathbb{E}[\Sigma^{1/2} X (\Sigma^{1/2} X)^{\dagger}] \\ = \mathbb{E}[\Sigma^{1/2} X X^{\dagger} \Sigma^{1/2 \dagger}] \\ = \Sigma^{1/2} \mathbb{E} [X X^{\dagger}] \Sigma^{1/2} \\ = \Sigma$
I'm trying to extend this to the frequency domain, after applying a Fourier transform to $X$. Let $X^F$ be the Fourier transform of $X$, ie. $X^F = WX$ where $W$ is the DFT matrix. Let the desired coherence be $S$. To use an idea similar to that used to simulate a desired correlation, I choose
$X_1^F = S^{1/2} S_{XX}^{-1/2} X^F$
where $S_{XX}$ is the cross-spectrum of $X^F$. Then
$\mathbb{E}[X_1^F X_1^{F\dagger}] = S^{1/2} S_{XX}^{-1/2} \mathbb{E}[X^F X^{F\dagger}] S_{XX}^{-1/2 \dagger} S^{1/2 \dagger} \\ = S^{1/2} S_{XX}^{-1/2} S_{XX} S_{XX}^{-1/2} S^{1/2} \\ = S$
I wrote a Python program to try this out but I didn't get a coherence close to my desired $S$, so I'm hoping to check whether there are any conceptual errors (otherwise it might be a numerical issue?). In particular, I'm not sure if $S_{XX}^{-1/2}=S_{XX}^{-1/2 \dagger}$ in general.
• how many terms are you averaging? – Stanley Pawlukiewicz Aug 13 '18 at 22:10
• X is a 5 by 1000 matrix of Gaussian white noise. It's supposed to simulate 1000 samples of activity from 5 sensors. I also tried 10000 samples. – Anon Aug 13 '18 at 23:06 | 2019-10-23 14:50:39 | {"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": 0.8934094309806824, "perplexity": 377.6438890237958}, "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/1570987833766.94/warc/CC-MAIN-20191023122219-20191023145719-00124.warc.gz"} |
https://asmedigitalcollection.asme.org/medicaldevices/article/3/2/027509/470692/Friction-Reduction-in-Metal-on-Metal-Hip-Joint | In the world, approximately 800,000 total hip replacements are implanted, while, at least 50,000 hip replacements are performed in the United Kingdom each year. Orthopaedic surgeons have traditionally delayed joint replacement surgery in patients younger than 60 due to its limited survivorship time and biological effect inside the human body. The highest percentage (71%) hip joint failure was caused by aseptic loosening of the femoral and acetabular components and the war rate and debris are the accepted causes of that aseptic loosening. The wear particles, either ion or stable form, can react with proteins and change the pH value of albumin solutions inside the human body, causing damage to the DNA resulting in genotoxicity. There has been a great deal of research into the materials, dimension of the prosthesis, surface roughness, and lubrication effect by surface coating. But it is very rare to apply surface texture technique to a metallic prosthesis bearing surface although it has proven very successful in many engineering applications including automobile industry due to secondary lubrication effect and hydrodynamic effect. A TE 77 high frequency friction simulator has been used for the experiment where specimens were manufactured with 50 mm diameters and $50μm$ clearance. A dynamic loading was applied synchronized with Hip CD 98 while the temperature was controlled at $37°C$. The output data including friction coefficient, friction force and contact pot were recorded in connected computer via COMPEND 2000 software. The surfaces were inspected after and before test under scanning electronic microscopy. The plateau honed surfaces were produced on the moving specimens with controlled load, speed and various grade of emery paper using a specially designed tool. The friction coefficient was recorded 0.035 for the honing surface which was made by 30 kg laod and 60 emery paper, 0.04 for the honing surface profile made by 30 kg load and 150 emery paper and 0.06 for plane surface after one million cycles. The rest of surfaces profiled surface were broken down before one million cycles. That made a conclusion that plateau honing surface made with 30 kg load and 60 emery paper was best surface texture profile ($45°$ honed angle, $40±10μm$ width and $35±10μm$ depth honing) for the metal on metal hip prosthesis. The comparison experiment was continue for plane surface and plateau honing surface of 60 emery paper and 30 kg load up to one and half millions cycles. It was found that the friction coefficient (0.03) was further reduced 0.005 after one and half million cycles for plateau honing surface but it was increased nearly double (0.065) for plane surface. The static friction coefficient was also reduced 38% in case of that plateau honing surface. The contact pot profile which is an indicator of fluid film thickness was noticed higher in plateau honing surface. This was evidence that the lubrication distribution was better in plateau honed surface which should provide longer life of joint, reduce wear and improves acceptability of metal on metal hip joints.
This content is only available via PDF. | 2019-10-24 04:55:07 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 5, "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": 0.17827185988426208, "perplexity": 3133.325451359091}, "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-2019-43/segments/1570987841291.79/warc/CC-MAIN-20191024040131-20191024063631-00104.warc.gz"} |
https://lw2.issarice.com/posts/mrZp6qC7DDXKQZeeC/failures-of-udt-aixi-part-1-improper-randomizing | # Failures of UDT-AIXI, Part 1: Improper Randomizing
post by Diffractor · 2019-01-06T03:53:03.563Z · score: 15 (6 votes) · LW · GW · 3 comments
## Contents
Notation and Setup:
Policy Search and Nash Equilibria:
Problem 1: Improper Randomization
Problem 2: Can't Build Desired Oracle
None
3 comments
While attempting to construct a UDT-like variant of AIXI, the algorithm I wrote down turned out to have a bunch of problems with it that were blocking attempts to prove that it had various nice properties. This will be the first post in a sequence about the various nonobvious things that go wrong when you try to make UDT-AIXI. (Check back here for more links)
## Notation and Setup:
To begin with, the basic setting was one where the Turing machines in the environment had oracle access to the policy. In the first attempt, where was the set of observations, and was the set of all finite strings of observations, policies had the type signature , and environments had the type signature , and functioned by having the option of making oracle calls to the policy with various observation strings to see what action was returned. If the policy randomizes on that input, then the action is simply drawn from the distribution .
Note that we're just using instead of the AIXI input type of , this is because the actions that the agent sees on the input tape can just be seen as a sort of observation, like any other, and this generalization permits looking at cases where the agent may not have an internal sense of which action it took, or cases where the agent gets to peek at what it did in hypothetical situations that didn't happen.
## Policy Search and Nash Equilibria:
Glossing over issues of nonhalting environments, we can reframe the UDT search for the best policy as the result of an infinite game, where each player is indexed with an observation string , and responds with a (probability distribution over) move(s) in . Each cell corresponds to a deterministic policy of type , and the utility in that cell is the expected reward over the standard mixture of environments, when the environments are making oracle calls to that selected policy. All players conveniently have the same utility function, which makes things easier. The optimal deterministic policy is a Nash equilibrium, because any deviation from any of the players would result in an equal or lower expected utility.
This rephrases problems of selecting a policy, to an equilibrium selection problem, because even when all players have the same utility function, there can be inadequate equilibria. Consider a multiplayer game of stag hunt where rabbits are shared equally among the group, but it's still better for everyone to team up and capture the stag than for everyone to catch a rabbit. The all-rabbit equilibrium is a Nash equilibrium that isn't the best ash equilibrium. This case seems simple to resolve, but there are much more difficult examples, such as a MAX-3-SAT game where each hypothetical version of the agent in Omega's head has incompatible observation strings, some short, some very long, and they are each responsible for fixing the value of one variable.
## Problem 1: Improper Randomization
Setting the Vingean and game theory issues to one side, there's another thing that's going wrong here. The stated setup of how the policy interacts with the environment is incompatible with this Nash equilibrium view of UDT.
As a simple example of what's going wrong, consider a single-turn game against an environment that makes two queries to what the policy does, and returns a reward of 1 if they are the same, and 0 if they are different. In standard game theory, randomizing between two actions with identical payoff should have the same expected payoff. But here there's a penalty for randomizing! And because each call to the policy returns an action sampled from the distribution , identical oracle calls to the policy may return different outputs. The proper way to view this to make it compatible with the Nash equilibrium view is to sample the action first, and then plug it into the open slots in the environment. You only randomize once.
This isn't quite as trivial as it looks, because Reflective Oracles have this "intrinsic randomness" thing going on, two identical oracle calls to the same agent may return different outputs. In Abram's words, reflective oracles are annoyingly realist about probability, they act as if a agent can randomize in such a way as to take different actions in the same information state. The proper way to do this is to sample a deterministic policy first, and then plug it into the slots in the environment. When thinking about a situation where an agent (possibly yourself) is randomizing, you may not know what action it will take, but you should think that the agent will take the same action in an identical state.
The obvious hack is to just cache the result every time the environment makes an oracle call, because if you compute it up-front, the policy sample will probably take an infinite amount of information to specify. But if you apply this hack and cache what was said about the policy so far, you run into another issue with non-halting environments. Because Reflective Oracle-AIXI calls an oracle on an environment to get the next bit, instead of just running the environment (maybe the environment doesn't halt, and you still need to get the next bit somehow), you don't get the policy sample. If the partial policy sample used by the environment on turn takes less than (where is computable) bits to encode, you can use the oracle to recover it and use that information on the next turn, but again this fails in full generality. The problem arises when you've got an environment that, on some turn, with some positive probability, doesn't halt and makes infinitely many oracle calls. Then there's no way (that I know of, yet) to guarantee that the behavior of the policy on future turns is consistent with what it did on that turn.
## Problem 2: Can't Build Desired Oracle
What if we then attempt to get a new notion of oracle where we have a probability distribution over samples? That might have promise, because only a single sample would be used. For instance, the type of a sample would be , and we'd be looking for a fixed-point in , ie, a distribution over samples s.t. the probability of drawing a sample that maps M to 0 is the same as the probability of M outputting 0 when it selects a sample from the given distribution.
Then it doesn't straightforwardly follow from the Kakutani fixed-point-theorem, because one of the restrictions is that the set of interest is a nonempty, compact, convex subset of a locally convex Hausdorff space. Fixing some bijection between and so we're looking for a fixed-point in , we run into the issue that this space isn't compact under any of the natural topologies, and even restricting to computable functions from (and bijecting that with ), isn't compact under any of the natural topologies either.
Due to this issue, the earlier post about oracles that result in correlated-equilibria, is incorrect, because the space of interest suffers from this lack of compactness, and the topological preconditions for Kakutani applying weren't checked. The result still holds up for finitely many players with finitely many moves, because we don't need a distribution over for that, only a distribution over finitely many integers, so the fixed-point theorem goes through in that case.
## 3 comments
Comments sorted by top scores.
comment by waveman · 2019-01-06T06:41:18.581Z · score: 1 (6 votes) · LW · GW
This post would be much helped by some explanation and context.
AIXI - I happen to know what this is but maybe not everyone does
UDT - Maybe Updateless Decision Theory? Maybe something else?
https://en.wikipedia.org/wiki/UDT
"the policy" - what policy?
"the algorithm I wrote" - where might I find this algorithm?
etc
General practice is to have links from new terms.
I see that most of your postings seem to have similar issues. Even in pure math papers they tend to put references so the reader has some chance to work out what you are talking about.
comment by Benito · 2019-01-07T21:26:11.632Z · score: 14 (4 votes) · LW · GW
This was originally posted to the AI Alignment Forum, where researchers are typically engaged in an advanced technical discussion. AI Alignment Forum posts assume these concepts; they aren't new terms. This is similar to how pure math papers don't explain what groups are, what homomorphisms are, etc.
If you want to get up to speed so that you can understand and contribute, I suggest some googling (here's the wiki page and LW wiki page for AIXI). There's also a lot of historical discussion of AIXI on LW that you can read.
(I think we will update the posts that are from AIAF to include info at the top about them being from the AIAF.)
comment by Diffractor · 2019-01-08T03:43:24.721Z · score: 3 (2 votes) · LW · GW
Yes, UDT means updateless decision theory, "the policy" is used as a placeholder for "whatever policy the agent ends up picking", much like a variable in an equation, and "the algorithm I wrote" is still unpublished because there were too many things wrong with it for me to be comfortable putting it up, as I can't even show it has any nice properties in particular. Although now that you mention it, I probably should put it up so future posts about what's wrong with it have a well-specified target to shoot holes in. >_> | 2019-08-23 17:37:31 | {"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": 0.6926332116127014, "perplexity": 791.5670619750538}, "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-2019-35/segments/1566027318952.90/warc/CC-MAIN-20190823172507-20190823194507-00195.warc.gz"} |
https://www.gamedev.net/forums/topic/597387-vao-is-it-necessary-to-redo-setup-each-time-buffer-data-changes/ | # VAO - Is it necessary to redo setup each time buffer data changes?
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I am a bit surprised that it seems like my VAOs get invalidated each time that I provide new buffer data. Are you really supposed to do glEnableClientState and setup gl*Pointers all over again after each glBufferSubData? That would make VAOs pretty useless for dynamic vertex data, wouldn't it?
I was hoping that it would be more like this:
// Initialization (Once) glGenVertexArrays(1, &vao); glGenBuffers(1, &vbo); glBindVertexArray(vao); glBindBuffer(GL_ARRAY_BUFFER, vbo); glBufferData(GL_ARRAY_BUFFER, size * sizeof(vertex_t), vertices, GL_DYNAMIC_DRAW); glEnableClientState(GL_VERTEX_ARRAY); glEnableClientState(GL_NORMAL_ARRAY); glEnableClientState(GL_COLOR_ARRAY); glEnableClientState(GL_TEXTURE_COORD_ARRAY); glVertexPointer(3, GL_FLOAT, sizeof(vertex_t), (GLvoid*)(0 * sizeof(vec3_t))); glNormalPointer(GL_FLOAT, sizeof(vertex_t), (GLvoid*)(1 * sizeof(vec3_t))); glColorPointer(4, GL_FLOAT, sizeof(vertex_t), (GLvoid*)(2 * sizeof(vec3_t))); glTexCoordPointer(2, GL_FLOAT, sizeof(vertex_t), (GLvoid*)(2 * sizeof(vec3_t) + sizeof(vec4_t))); glBindVertexArray(0);
// Update (Each Frame) glBindVertexArray(vao); glBindBuffer(GL_ARRAY_BUFFER, vbo); glBufferSubData(GL_ARRAY_BUFFER, 0, size * sizeof(vertex_t), vertices); glBindVertexArray(0);
// Render (Each Frame) glBindVertexArray(vao); glBindTexture(GL_TEXTURE_2D, texture); glDrawArrays(GL_TRIANGLES, 0, size); glBindVertexArray(0);
However, it seems like I need to do this in order for it to work:
// Update (Each Frame) glBindVertexArray(vao); glBindBuffer(GL_ARRAY_BUFFER, vbo); glBufferSubData(GL_ARRAY_BUFFER, 0, size * sizeof(vertex_t), vertices); glEnableClientState(GL_VERTEX_ARRAY); glEnableClientState(GL_NORMAL_ARRAY); glEnableClientState(GL_COLOR_ARRAY); glEnableClientState(GL_TEXTURE_COORD_ARRAY); glVertexPointer(3, GL_FLOAT, sizeof(vertex_t), (GLvoid*)(0 * sizeof(vec3_t))); glNormalPointer(GL_FLOAT, sizeof(vertex_t), (GLvoid*)(1 * sizeof(vec3_t))); glColorPointer(4, GL_FLOAT, sizeof(vertex_t), (GLvoid*)(2 * sizeof(vec3_t))); glTexCoordPointer(2, GL_FLOAT, sizeof(vertex_t), (GLvoid*)(2 * sizeof(vec3_t) + sizeof(vec4_t))); glBindVertexArray(0);
Is this reallly necessary or am I doing something else wrong?
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You probably destroying some bindings, because you bind the vao in your update function.
glBindVertexArray(vao); glBindBuffer(GL_ARRAY_BUFFER, vbo);
with this code you are overwriting some stuff in the vao. I'm not quite sure why it won't work after this, but I guess this is the cause.
just get rid of those two vao bindings in you update function.
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Thank you for your suggestion. Unfortunately, if I don't bind the VAO during update I get really glitchy output. It looks like the data in the buffer is scrambled or some invalid/faulty data is being read.
FYI, I also tried this version:
// Initialization 1 (Once) glGenVertexArrays(1, &vao); glGenBuffers(1, &vbo); glBindVertexArray(vao); glBindBuffer(GL_ARRAY_BUFFER, vbo); glEnableClientState(GL_VERTEX_ARRAY); glEnableClientState(GL_NORMAL_ARRAY); glEnableClientState(GL_COLOR_ARRAY); glEnableClientState(GL_TEXTURE_COORD_ARRAY); glVertexPointer(3, GL_FLOAT, sizeof(vertex_t), (GLvoid*)(0 * sizeof(vec3_t))); glNormalPointer(GL_FLOAT, sizeof(vertex_t), (GLvoid*)(1 * sizeof(vec3_t))); glColorPointer(4, GL_FLOAT, sizeof(vertex_t), (GLvoid*)(2 * sizeof(vec3_t))); glTexCoordPointer(2, GL_FLOAT, sizeof(vertex_t), (GLvoid*)(2 * sizeof(vec3_t) + sizeof(vec4_t))); glBindVertexArray(0);
// Initialization 2 (Once) glBindBuffer(GL_ARRAY_BUFFER, vbo); glBufferData(GL_ARRAY_BUFFER, size * sizeof(vertex_t), vertices, GL_DYNAMIC_DRAW);
// Update (Each Frame) glBindBuffer(GL_ARRAY_BUFFER, vbo); glBufferSubData(GL_ARRAY_BUFFER, 0, size * sizeof(vertex_t), vertices);
// Render (Each Frame) glBindVertexArray(vao); glBindTexture(GL_TEXTURE_2D, texture); glDrawArrays(GL_TRIANGLES, 0, size); glBindVertexArray(0);
Using this version, no geometry is visible at all (only the clear color). So it seems that the order of passing the data and setting up the VAO does matter.
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No more comments? Some input on the correct order of operations when using VAOs would already help a lot. Putting it in pseudo code, this is how I would expect things to work (but they don't):
Initialization: Bind VAO Bind Buffer Upload Buffer Data Enable Client States Setup Pointers Unbind VAO Update/Render Loop: Bind Buffer Update Buffer Data Bind VAO Draw Unbind VAO
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mm, dont really know whats wrong, but here some random stuff.
• There is no need to generate, bind and submit data to the VBO while the VAO is active, they don't have anything to do with the VAO state
• maybe check your stride and offset values(both are in bytes) again, look also at teh part of your code which fills your data array
• use Stream_Draw when you are updating the buffer every frame
• also when updating use this code, it's faster because the driver has less problems managing the memory
glBindBuffer(GL_ARRAY_BUFFER, vbo); glBufferData(GL_ARRAY_BUFFER, size * sizeof(vertex_t), null, GL_STREAM_DRAW); glBufferSubData(GL_ARRAY_BUFFER, 0, size * sizeof(vertex_t), vertices);
here is some pseudo code how I do it:
Initialization: Generate n BOs Bind first upload index data Bind other BO upload vertex data to it Loop until all vertex BOs are filled Generate VAO Bind VAO Bind Index Buffer Enable Client States Bind a BO Set all its vertex pointers Loop until all Attributs are set Unbind VAO Update/Render Loop: Bind BO which data changed upload data Loop until each BO is updated Bind VAO Set up render state (Textures, Shader, Uniforms, Lighting ...) render Unbind VAO
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Thanks again! It's very useful to have an example of how it should work. Unfortunately, I wont be able to implement all of your suggestions, because I am developing for iOS (OpenGL ES 1.1). This might also be the source of my problems - maybe there are some quirks with VAOs, which are only supported as an extension. However, I still find it more likely that the error is somewhere in my code.
I'm lead to believe that the stride and offset values are fine, because they work when I set them each time before rendering. Unfortunately GL_STREAM_DRAW is not available, so I can't try that. I'm really surprised that your suggested way of updating data should be faster - wouldn't it set all the data to zeros before writing the new data? (I'm not familiar with the effect of passing a null pointer in this context.)
In any case, I'll go through my code once again and compare it with the pseudo code you posted.
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GL ES 1.1 supports VAO?
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the thing with calling it with null is that it tells the driver that u don't care anymore about the data.
So the new data get uploaded to an other address space then the old one. And the old gets deleted any time in the future
If u just upload new data the driver has to make sure that every operation on the old data has finished, then he has to sync everything and so on, which can take quite some time in a worst case.
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GL ES 1.1 supports VAO?
No. As I mentioned, the older iOS devices (GL ES 1.1) support it through an extension (see OpenGL ES Programming Guide for iOS - Platform Notes).
I've gotten a little sidetracked, as this was only supposed to be a slight optimization (it's one of the "best practices" in the aforementioned guide). When I come back to this, it would probably make sense to write a minimal example program demonstrating the problem...
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I see.
As for VAO, from what I understand, you only need to setup a VAO once. Then you use it with
glBindVertexArray(vao);
glDrawArrays or glDrawRangeElements or glDrawElements
I imagine that anything else can be considered a driver bug. Unfortunately, my experience is limited. I just did a test with VAO. I rendered 2 triangles with 2 different VAO just to make sure it works as I expect.
I am surprised we don't even have a decent example on the Wiki.
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× | 2018-12-18 15:02:06 | {"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": 0.17184466123580933, "perplexity": 8625.846462121655}, "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-2018-51/segments/1544376829429.94/warc/CC-MAIN-20181218143757-20181218165757-00158.warc.gz"} |
https://forum.fbackup.com/general-f2/fb-adds-new-folders-without-being-asked-t8474.html | RAFB
Posts: 2
Joined: Sun May 10, 2015 4:02 pm
I've been using FB for quite a while to make a weekly mirror and today I noticed that FB has been adding folders in the sources of that weekly task.
The folders are almost all in the C:\Program Files (x86) and correspond to all software I've been installing, as well as in the folder C:\Users\XXX\AppData, which are software created folders.
Is there any option to disable FB from adding these folders automatically to the mirror sources whenever I install anything new in the PC ? I can't find anywhere a option to prevent this.
Thanks | 2020-11-24 15:00:24 | {"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": 0.8891217112541199, "perplexity": 2814.5798184004016}, "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-2020-50/segments/1606141176864.5/warc/CC-MAIN-20201124140942-20201124170942-00432.warc.gz"} |
https://chemistry.stackexchange.com/questions/37047/is-heating-dilute-hcl-dangerous | Is heating dilute HCl dangerous?
Say dilute $\ce{HCl}$ is used to convert some alkaloid to salt form, then the alkaloid is dried with heat, would gaseous $\ce{HCl}$ be released in the process? Is there a threshold concentration of the acid, below which, this would be acceptable from a safety point of view?
• Why would anyone want to do that outside of a chemical lab with proper safety equipment (fume hoods, etc.)? – Ivan Neretin Sep 8 '15 at 19:23
Say dilute HCl is used to convert some alkaloid to salt form, then the alkaloid is dried with heat, would gaseous HCl be released in the process?
Likely yes, unless it's the limiting reagent in the reaction in question. Probably best to assume some of it will come off as gas - that's the safest approach, in my opinion.
Is there a threshold concentration of the acid, below which, this would be acceptable from a safety point of view?
Yes, there are several metrics used by various authorities to determine what "safe" means. You'll have to decide which one (or ones) are relevant to your situation.
Here in the U.S., the Occupational Safety and Health Administration (OSHA) - which is under the Department of Labor - has published this information on hydrochloric acid exposure limits and hazards.
In that linked document, several other agencies such as the National Institute for Occupational Safety and Health (NIOSH) and the American Conference of Governmental Industrial Hygienists (ACGIH) list permissible exposure limits ranging from 3 to 7 mg/m$^{3}$; the Environmental Protection Agency (EPA) given an inhalation reference concentration (RfC) of 2 mg/m$^{3}$, detailed here as the concentration above which (I'm paraphrasing) bad things start to happen.
Good luck on your project and stay safe. | 2020-01-23 20:51:27 | {"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": 0.36873307824134827, "perplexity": 2694.145260453211}, "config": {"markdown_headings": false, "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-2020-05/segments/1579250613416.54/warc/CC-MAIN-20200123191130-20200123220130-00161.warc.gz"} |
https://upcommons.upc.edu/browse?value=Ruan,%20Da&type=author | Now showing items 1-2 of 2
• #### (┬,┴,N) Fuzzy logic
(Universitat Politècnica de Catalunya. Secció de Matemàtiques i Informàtica, 2001)
Article
Open Access
To investigate more reasonable fuzzy reasoning model in expert systems as well as more effective logical circuit in fuzzy control, a $(\top, \bot, N)$ fuzzy logic is proposed in this paper by using $\top$-norm, $\bot$-norm ...
• #### Safety regulations of fuzzy-logic control to nuclear reactors
(Universitat Politècnica de Catalunya. Secció de Matemàtiques i Informàtica, 2000)
Article
Open Access
We present an R&D project on fuzzy-logic control applications to the Belgian Nuclear Reactor 1 (BR1) at the Belgian Nuclear Research Centre (SCK•CEN). The project started in 1995 and aimed at investigating the added ... | 2020-08-14 23:43:21 | {"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": 0.27176493406295776, "perplexity": 11152.857915404906}, "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-2020-34/segments/1596439740343.48/warc/CC-MAIN-20200814215931-20200815005931-00125.warc.gz"} |
https://stats.libretexts.org/Courses/Rio_Hondo_College/PSY_190%3A_Statistics_for_the_Behavioral_Sciences/08%3A__Introduction_to_Hypothesis_Testing/8.08%3A_Effect_Size | # 8.8: Effect Size
When we reject the null hypothesis, we are stating that the difference we found was statistically significant, but we have mentioned several times that this tells us nothing about practical significance. To get an idea of the actual size of what we found, we can compute a new statistic called an effect size. Effect sizes give us an idea of how large, important, or meaningful a statistically significant effect is. For mean differences like we calculated here, our effect size is Cohen’s $$d$$:
$d=\dfrac{M-\mu}{\sigma}$
This is very similar to our formula for $$z$$, but we no longer take into account the sample size (since overly large samples can make it too easy to reject the null). Cohen’s $$d$$ is interpreted in units of standard deviations, just like $$z$$. For our example:
$d=\dfrac{7.75-8.00}{0.50}=\dfrac{-0.25}{0.50}=0.50 \nonumber$
Cohen’s $$d$$ is interpreted as small, moderate, or large. Specifically, $$d$$ = 0.20 is small, $$d$$ = 0.50 is moderate, and $$d$$ = 0.80 is large. Obviously values can fall in between these guidelines, so we should use our best judgment and the context of the problem to make our final interpretation of size. Our effect size happened to be exactly equal to one of these, so we say that there was a moderate effect.
Effect sizes are incredibly useful and provide important information and clarification that overcomes some of the weakness of hypothesis testing. Whenever you find a significant result, you should always calculate an effect size. | 2023-01-31 00:10:08 | {"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": 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": 0.7803283929824829, "perplexity": 294.3142375347806}, "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/1674764499831.97/warc/CC-MAIN-20230130232547-20230131022547-00523.warc.gz"} |
https://proxieslive.com/tag/pagination/ | ## Include a leading zero in pagination
I’m new to WordPress Development and have been teaching myself over the last few months how to develop a theme from scratch. Normally I can figure issues out on my own through forums, but I can’t really find much on this one.
I’ve been trying to add leading zeros to my pagination if the number is less than 10.
I.e: < Newer 01 02 03 … 10 Older >
Here is my pagination code. Any pointers in the right direction would be appreciated!
if ( !function_exists('palfrey_pagination') ) { function palfrey_pagination( $range = 5 ) { if( is_singular() ) return; //$ paged - number of the current page global $paged,$ wp_query; // Stop execution if there's only 1 page. if( $wp_query->max_num_pages <= 1 ) return;$ paged = get_query_var( 'paged' ) ? absint( get_query_var( 'paged' ) ) : 1; if ( !$max_page )$ max = intval( $wp_query->max_num_pages ); if ($ max_page > 1 ) if ( !$paged )$ paged = 1; // Add current page to the array. if ( $paged >= 1 )$ links[] = $paged; // Add the pages around the current page to the array. if ($ paged >= 3 ) { $links[] =$ paged - 1; $links[] =$ paged - 2; } if ( ( $paged + 2 ) <=$ max ) { $links[] =$ paged + 2; $links[] =$ paged + 1; } // The pagination echo "\n" . '<div class="content-block-common-large"> <div class="block-wrap"> <div class="inline-group flex-group relative align-center column-align-bottom"> <div class="column responsive width-450"> <ul class="pagination display-block relative align-center width-1of1">' . "\n"; // Link to 'Newer' posts. if ( get_previous_posts_link() ) { printf( '<li>%s</li>' . "\n", get_previous_posts_link( '<div class="display-inline-block relative float-left"><span class="pagination-prev">Newer</span></div>' ) ); }else{ echo '<li><div class="display-inline-block relative float-left pointer-events-none" style="opacity: .6;"><span class="pagination-prev">Newer</span></div></li>'; } // Link to first page, plus ellipses if necessary. if ( ! in_array( 1, $links ) ) {$ class = 1 == $paged ? ' class="active"' : ''; printf( '<li%s><a href="%s">%s</a></li>' . "\n",$ class, esc_url( get_pagenum_link( 1 ) ), '1' ); if ( ! in_array( 2, $links ) ) echo '<li>…</li>'; } // Link to current page, plus 2 pages in either direction if necessary. sort($ links ); foreach ( (array) $links as$ link ) { $class =$ paged == $link ? ' class="active"' : ''; printf( '<li%s><a href="%s">%s</a></li>' . "\n",$ class, esc_url( get_pagenum_link( $link) ),$ link ); } // Link to last page, plus ellipses if necessary. if ( ! in_array( $max,$ links ) ) { if ( ! in_array( $max - 1,$ links ) ) echo '<li>…</li>' . "\n"; $class =$ paged == $max ? ' class="active"' : ''; printf( '<li%s><a href="%s">%s</a></li>' . "\n",$ class, esc_url( get_pagenum_link( $max) ),$ max ); } // Link to 'Older' posts. if ( get_next_posts_link() ) { printf( '<li>%s</li>' . "\n", get_next_posts_link( '<div class="display-inline-block relative float-right"><span class="pagination-next">Older</span></div>' ) ); }else{ echo '<li><div class="display-inline-block relative float-right pointer-events-none" style="opacity: .6;"><span class="pagination-next">Older</span></div></li>'; } echo "\n" . ' </ul> </div> </div> </div> </div>' . "\n"; } }
## Pagination (archive posts) getting out of hand – what to do from an SEO POV?
WordPress as many of us know creates an archive loop of old posts.
From an SEO POV, some of my categories are now at 100+ pages which is a lot of bloat…
Sure, I can set each of these paginated pages a canonical link but still, feels like it is a bit unnecessary for all these indexed pages that just contain a title and an excerpt (which is basically duplicate content..)
Is one approach to simply switch off archive loops or does Google ignore these archived pages?
Thanks
## Remove pagination from e-commerce category page while preserving SEO text relevance
I am administering an e-commerce website where currently we have pagination implemented on every category page.
On the first page of each category, we have SEO text in the bottom – a description of the category which helps our page to rank higher in search results. In many cases, it is long enough to make it impractical to place it at the top of the page.
I am flirting with the idea of converting our structure to an “infinite scroll” experience, to remove pagination altogether. I realise that this would yield some SEO benefits.
However, I am seriously worried that a lengthy list of products would dilute the importance of our category description at the bottom. I remember reading somewhere that Google places more importance on the content which is higher on the page.
Has anyone tried to implement the “infinite scroll” and did you notice any serious changes in your ranking? Or maybe you have an idea as to how it will affect the relevance of the category description at the bottom of the page?
## Two Pagination in One page with shortcode
I create a shortcode to show posts by category with attributes. I want to show 2 separate categories with a separate shortcode in one page but the pagination connected.
If I change pagination in the first shortcode, also change pagination in the second shortcode. Basically it same shortcode but different attributes.
here my code:
## Pagination of results from different sources merged by a unified scoring function
Assume a Hotel reservation scenario, given $$m$$ ranked lists of attribute values such as distance, price, amenities (normalized between $$0$$ and $$1$$), and a unifying linear score function $$F(\cdot)=\alpha_1*score_1+ \alpha_2*score_2+ \alpha_3*score_3$$, the Threshold Algorithm (TA) is optimal in finding top-$$k$$ results that have higher $$F$$ values.
However, consider a pagination scenario with page index $$p$$ and page size $$k$$. Indeed, instead of asking for top-$$k$$ that can be obtained from indices [0,k] in the final ranked list, we ask for [pk, (p+1)k]. What is the best solution to obtain this window of the results?
You may consider this problem as the pagination of the merged results over a unified scoring function when there are multiple data sources that each contains a score value but the merged results have a combined score value as a (linear) function of individual score values.
Some solutions:
Totally naive: given the multiple ranked results, compute the unified score, sort them, slice it as needed.
Potentially better but inefficient when asking lower-ranked results (farther pages): Execute Threshold Algorithm and ask for top-(p+1)k, return the [pk, (p+1)k] from it.
## ‘Select All Visible’ vs ‘Select All’ with pagination
Suppose I have a table with pagination due a lot of row entries. Should the default action for ‘Select all’ select the entries on the current page or all entries in the entire table (i.e. all pages)?
What is the intended behaviour for a user?
I am aware of the solution that Gmail has to address this where it selects the ones in view and prompts an action to select all. Just wondering where I could find some other examples of products tackling this.
## Pagination on grouped / multi sorted lists
I’m currently working on a design for data heavy lists. User research showed, that users would group / multi sort those lists. this would result in a list with small header rows in between for every sort parameter.
So far so good. I’m now having a hard time, as those lists have a pagination. I would now also need to show the grouped rows over all pages which might take the user out of context…
any thoughts on how to solve the problem?
Cobo
## Numbered Pagination Showing The Same Posts After Altering WP_Query
I think the title sums the problem up, but I’ll explain more with the code below.
As you can see, I’m trying to start the loop from the second latest post for some theme reasons which forced me to alter the main loop, and I used the parameter offset to make that work, and everything worked just fine, but after I moved on with the development, I started developing the numbered pagination, and finally got surprised with my altered loop showing the same posts in every page.
I chose to use WP_Query and not touch query_posts(), as it’s simple and faster, now I’m stuck with this problem, and tested everything and didn’t work.
Here is the altered loop using class WP_Query:
<?php $paged = get_query_var( 'page' ) ? get_query_var( 'page' ) : 1;$ args = array( 'offset' => 1, 'post_type' => 'post', 'paged' => $paged );$ offset_loop = new WP_Query( $args ); ?> <?php if ($ offset_loop->have_posts() ): ?> <?php while ( $offset_loop->have_posts() ):$ offset_loop->the_post(); ?> <div class="blog_loop_container"> <article class="blog_post <?php post_class(); ?>" id="post-<?php the_ID(); ?>"> <div class="post_thumbnail"><?php the_post_thumbnail( 'medium_large' ); ?></div> </article> </div> <?php endwhile; ?> <?php // wp_reset_postdata(); ?> <?php echo thegreatguy_pagination(); ?> <?php endif; ?>
And here is the pagination function i’m using :
function thegreatguy_pagination() { global $wp_query; // Calling The Global Variable Representing WP_Query Class.$ totalPages = $wp_query->max_num_pages; // Retrieves The Maximum Pages The Blog has.$ currentPage = max( 1, get_query_var( 'paged' ) ); // Retrieves The Number Of The Current Page. if ( $totalPages > 1 ) { // Check For More Pages To Return. return paginate_links( array( 'format' => 'page/%#%', 'base' => get_pagenum_link() . '%_%', 'current' =>$ currentPage, 'prev_text' => 'Previous', 'next_text' => 'Next' ) ); } } | 2020-08-10 21:06:17 | {"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": 9, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.36101382970809937, "perplexity": 5276.43201560848}, "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/1596439738699.68/warc/CC-MAIN-20200810205824-20200810235824-00364.warc.gz"} |
https://www.jiskha.com/similar?question=How+to+figure+out+the+temperature+of+a+lake+using+x+for+the+feet+or+the+Depth+and+for+the+degrees+Celsius+use+%283900x%2B1000%29%2F%283x%5E2%2B100%29+with+the+answer+of+the+degrees+celsius+being+8.44+looking+like+8.44%3D%283900x%2B1000%29%2F%283x%5E2%2B100%29+i+need+the+depth&page=199 | # How to figure out the temperature of a lake using x for the feet or the Depth and for the degrees Celsius use (3900x+1000)/(3x^2+100) with the answer of the degrees celsius being 8.44 looking like 8.44=(3900x+1000)/(3x^2+100) i need the depth
34,877 questions, page 199
1. ## differential equation
a four -pound weight stretches a spring 8 inches from its natural lenght . the weight is pulled downward an additional 6 inches and released with an initial upward velocity of 8 feet per second . find a formula for the position of the weight as a function
asked by Anonymous on April 6, 2010
2. ## Algebra II
A geyser sends a blast of boiling water high into the air. During the eruption, the height (h) (in feet) of the water (t)seconds after being forced out from the ground could be modeled by h = -16t*t + 70t. My question is how do you find the initial
3. ## alg2
suppose you drop a tennis ball from a height of 15 feet. After the ball hits the floor, it rebounds to 85% of its previous height. How high will the ball rebound after its third bounce. round to the nearest tenth.. my teacher told be the answers 9.2 but i
asked by jerson on June 9, 2008
4. ## Algebra
A ball is shot straight up from the top of a 15-story building. The motion of the ball could be described by the function: h(t) = -16t^2 + 144t + 160 where t represents the time the ball is in the air in seconds and h(t) represents the height in feet . Why
asked by anonymous on September 1, 2018
5. ## Math
A ball is thrown into the air with an upward velocity of 48ft/s. It's height h in feet after t seconds is given by the function h=-16t^+48t+8. In how many seconds will the ball hit the ground? I got 1.5 seconds put when I plug it back into the equation, I
asked by Amy on November 30, 2015
6. ## calculus
A ball is thrown upward with an initial velocity of 96 feet per second from the top of a 100 foot building. (a) When well the ball attain its maximum height? (b) When will the ball hit the ground? Give a decimal answers correct to 2 decimal places
asked by Anonymous on March 25, 2011
7. ## calculus
A landscape architect wished to enclose a rectangular garden on one side by a brick wall costing $30/ft and on the other three sides by a metal fence costing$10/ft. If the area of the garden is 42 square feet, find the dimensions of the garden that
asked by al on November 4, 2007
8. ## calculus
I really hate to dump a problem like this on the teachers here, but I really need to get an answer to this. Thank you and I'm sorry. A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window. Find the dimensions
asked by jimmy on December 7, 2012
9. ## Calculus
A ball is thrown upward with an initial velocity of 96 feet per second from the top of a 100 foot building. (a) When will the ball attain its maximum height? (b) When will the ball hit the ground? Give a decimal answers correct to 2 decimal places.
asked by Anonymous on March 28, 2011
10. ## Calculus
A ball is thrown upward with an initial velocity of 96 feet per second from the top of a 100 foot building. (a) When well the ball attain its maximum height? (b) When will the ball hit the ground? Give a decimal answers correct to 2 decimal places.
asked by Anonymous on March 28, 2011
11. ## Math Formula Part 2/3
I've done the second part to the Math Formula post. It was determine the 19th term of the sequence which I did. Now it says..which of the numbers -268 and -350 are terms of the sequence? I was doing something like this: tn = -7 (-268) +19 I was plugging
asked by Anonymous on September 13, 2011
12. ## Chemistry chlorine plz help
A metal x forms two different chloride.if 12.g of chloride A and 16.3g of chloride B contain 7.1g and 10.7g of chlorine respectively,show that the figure agree with the laws of multiple proportions.write there formulea plz i need the work....no hint plz
asked by Daniel on January 12, 2016
13. ## physics
An athlete whirls in a 7.10-kg hammer tied to the end of a 1.2 m chain in a horizontal circle, as shown in the figure below. The hammer makes one revolution in 1.0 s. (a) What is the centripetal acceleration of the hammer? (b) What is the tension in the
asked by javane on November 26, 2010
14. ## physics
A 4.10 kg block is pushed along the ceiling with an constant applied force of F = 81.5 N that acts at an angle è = 52° with the horizontal, as in the figure below. The block accelerates to the right at 5.10 m/s2. Determine the coefficient of kinetic
asked by Anonymous on December 13, 2014
15. ## Chemistry
Calculate the molar concentration of uncomplexed Zn2+ (aq) in a solution that contains 0.22 mol of Zn(NH3)4 2+ per liter and 0.3109 M NH3 at equilibrium. Kf for Zn(NH3)4 2+ is 2.9 X 10^9 I started this way... (0.3109 + 4)2/0.22-x)= 2.9 X 10^9 I'm lost and
asked by Felix on March 17, 2013
16. ## HCA 230
Biomedical is a physical phemonenon while biopsychosocial is physical, mental, and social. I can't figure out which one these examples are. "Which part of your body hurt?", "Is it a sharp pain?", "How long does the pain last"and "What pain medicines have
asked by Heather on December 10, 2009
17. ## Chemistry
The voltage generated by the zinc concentration cell described by, Zn(s)|Zn2 (aq, 0.100 M)||Zn2 (aq, ? M)|Zn(s) is 23.0 mV at 25°C. Calculate the concentration of the Zn2 (aq) ion at the cathode. Can someone please breakdown how to do this so I can figure
asked by Chris on May 7, 2013
18. ## physics
A 3.40 kg block is pushed along the ceiling with an constant applied force of F = 82.0 N that acts at an angle θ = 50° with the horizontal, as in the figure below. The block accelerates to the right at 5.80 m/s2. Determine the coefficient of kinetic
asked by Amy Lee on January 12, 2013
19. ## physics
A 4.8 kg block is pushed along the ceiling with a constant applied force of 87 N that acts at an angle of 55.0° with the horizontal, as in Figure 4-33. The block accelerates to the right at 6.00 m/s2. Determine the coefficient of kinetic friction between
asked by Corey on December 5, 2010
20. ## physics
A 4.00 kg block is pushed along the ceiling with a constant applied force of 85.0 N that acts at an angle of 55.0° with the horizontal, as in the figure below. The block accelerates to the right at 6.00 m/s2. Determine the coefficient of kinetic friction
asked by john on February 21, 2016
21. ## calculus
The figure shows the region bounded by the x-axis and the graph of . Use Formulas (42) and (43)-which are derived by integration by parts-to find (a) the area of this region; (b) the volume obtained by revolving this region around the y-axis.
asked by rene on May 29, 2010
22. ## physics
A 3.60 kg block is pushed along the ceiling with an constant applied force of F = 75.5 N that acts at an angle θ = 61° with the horizontal, as in the figure below. The block accelerates to the right at 5.76 m/s2. Determine the coefficient of kinetic
asked by Lexi on December 11, 2011
23. ## Physics
A 4.4 kg block is pushed along the ceiling with a constant applied force of 89 N that acts at an angle of 55.0° with the horizontal, as in Figure 4-33. The block accelerates to the right at 6.00 m/s2. Determine the coefficient of kinetic friction between
asked by Kashawn on December 2, 2011
24. ## physics
A 4.00 kg block is pushed along the ceiling with a constant applied force of 85.0 N that acts at an angle of 55.0° with the horizontal, as in the figure below. The block accelerates to the right at 6.00 m/s2. Determine the coefficient of kinetic friction
asked by mark on February 21, 2016
Need help with combining like terms How do I figure this out... 11+5t^2+t+6t If anyone can help I would really appreciate it. I helped BELOW!!!LOL See the answer below which I posted as a correction to the answer provided by Margie and Dr Phil. The correct
asked by lily on November 2, 2006
26. ## Science
A child in a boat throws a 5.30 kg package out horizontally with a speed of 10 m/s, see the figure. Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg and that of the boat is 55.0 kg
asked by kago on October 20, 2011
27. ## chemistry
hi, can someone please help me with my homework problem? what is the rounding number for 121.07 cm? what is the rounding number for 22130 km? what are the significant figure and uncertainty number for 120cm, 25, 430 km, 3, 500km, 200 km, and 1001 tons.
asked by shylo on June 25, 2008
if a fish farmer wanted to harvest his fish so that it recovered at the maximum rate, where should the population be maintained? There is a graph number of weeks vs. numbers of fish. and A B C and D marked on the graph. How do I figure it out??
asked by Anon on September 22, 2013
29. ## Calculus
A radar gun was used to record the speed of a car (in feet per minute) during selected times in the first 2 minutes of a race. Use a trapezoidal sum with 4 intervals to estimate the distance the car covered during those 2 minutes. Give a 2 decimal place
asked by Deondre on July 4, 2018
30. ## algebra
Triangles ABC and DEF are similar. Find the perimeter of triangle DEF. Round your answer to the nearest tenth. ab=4ft bc=6ft ac=5ft de=6ft ef= 9ft there is no feet given for df Please can anyone help me solve this with steps I don't understand how to do
asked by sally on March 1, 2013
31. ## calculus
a farmer has a 1500 feet of fencing in his barn.he wishes to enclose a rectangler pen,subdivided in two regions by a section of the fence down the middle,parallel to one side of the rectangle.express the area enclosed by the pen as a function of its width
asked by natasha on August 26, 2011
32. ## Physics
A high diver of mass 65.0 kg steps off a board 10.0 m above the water and falls vertical to the water, starting from rest. If her downward motion is stopped 2.30 s after her feet first touch the water, what average upward force did the water exert on her?
asked by Emily on January 29, 2012
33. ## Calc
The sun is shining and a spherical snowball of volume 210 ft3 is melting at a rate of 14 cubic feet per hour. As it melts, it remains spherical. At what rate is the radius changing after 3 hours? I posted this question before and when i went back and did
asked by Bubba on February 14, 2011
34. ## Trig
The Stratosphere Tower is Las Vega dominate the city's landscape by rising 1,149 feet above the desert floor. The restaurant at the top of the tower turns slowly and completes a full revolution in one hour. How many radians will the restaurant have rotated
asked by Lux on February 22, 2016
35. ## Geometry
A lighthouse keeper in his observation tower 120 feet above the water sees a pontoon airplane and a small fishing boat. If the plane is directly above the boat, how far above sea level is the plane flying, rounded to the nearest foot? Be sure to show your
asked by Jackie on March 28, 2014
36. ## math
A ball is thrown vertically upward with an initial velocity of 5 ft/sec from a height of 20 feet. Which function models its motion? i literally am lost and have no idea how to this problem. if i could have help with the steps on how to do the problem and
asked by Natalie on November 21, 2014
37. ## algebra 1
a tortoise can travel 10 cm per second. what is the tortoise's speed in feet per hour? an 18,000 gallon pool takes approximately 40 hours to fill. what is this rate in pints per mintue. a tub can drain 24 gallons of water in 5 minutes . what is this rate
asked by sahsa to reiny on September 9, 2015
38. ## physics
In college softball, the distance from the pitcher's mound to the batter is 43 feet. Part A If the ball leaves the bat at 105 mph , how much time elapses between the hit and the ball reaching the pitcher? Express your answer to two significant figures and
asked by Anonymous on September 8, 2016
39. ## algebra
Use the following to answer the next three questions: the height, h, of a ball t seconds after it is released for a jump shot in a basketball game can be modeled with the equation h = −16t2 + 12t + 8. The rim of the basket is 10 feet high. Which of the
asked by alyssa on March 5, 2012
40. ## algebra
Use the following to answer the next three questions: the height, h, of a ball t seconds after it is released for a jump shot in a basketball game can be modeled with the equation h = −16t2 + 12t + 8. The rim of the basket is 10 feet high. Which of the
asked by alyssa on March 5, 2012
41. ## Science
Humidity is the amount of water vapor in the air at a given time. At warm temperatures, air can hold more moisture than it can at cold temperatures. Relative humidity is the amount of vapor the air is holding expressed as a percentage of the amount the air
asked by Jimmy on July 18, 2008
42. ## Physics
0.75 mol of argon gas is admitted to an evacuated 40 cm^{3} container at 40 C. The gas then undergoes an isochoric heating to a temperature of 500 C. What is the final pressure of the gas?(answer in kPa)
asked by Ana on December 10, 2009
43. ## Physics
A 100W incandescent lamp of filament area 45 mm^2, emits all its energy by radiation into the surrounding space of room at 22C. If the filament emissivity is 0.32, find the temperature of the filament?
asked by Tsunayoshi on February 2, 2014
44. ## Chemistry
Consider the following reaction: 2NO(g)+O2(g)→2NO2(g) Estimate ΔG∘ for this reaction at each of the following temperatures and predict whether or not the reaction will be spontaneous. (Assume that ΔH∘ and ΔS∘ do not change too much within the
asked by Ashley on April 22, 2015
45. ## physics sound
1. A stone is dropped from rest into a well. The sound of the splash is heard exactly 1.50 s later. Find the depth of the well if the air temperature is 10.0°C. 2. Calculate the sound level in decibels of a sound wave that has an intensity of 2.25 µW/m2
46. ## physics
Consider a pipe with a length of 57.5 cm. If the temperature of the air is 21.5+B degrees C and the pipe is closed in one end and open in the other, what is the frequency of the third harmonic for the pipe? Post your answer in hertz (Hz) and with 3
asked by Idali on April 18, 2017
47. ## chemistry
A silver block, initially at 59.4∘C^\circ C, is submerged into 100.0 g{\rm g} of water at 25.3∘C^\circ C, in an insulated container. The final temperature of the mixture upon reaching thermal equilibrium is 27.6∘C^\circ C.
asked by Anonymous on May 6, 2014
48. ## physics
1. A stone is dropped from rest into a well. The sound of the splash is heard exactly 1.50 s later. Find the depth of the well if the air temperature is 10.0°C. 2. Calculate the sound level in decibels of a sound wave that has an intensity of 2.25 µW/m2
49. ## physics repost
1. A stone is dropped from rest into a well. The sound of the splash is heard exactly 1.50 s later. Find the depth of the well if the air temperature is 10.0°C. 2. Calculate the sound level in decibels of a sound wave that has an intensity of 2.25 µW/m2
50. ## chemistry
Assuming pressure and temperature remain constant, what happens to the volume of a gas if the number of moles of gas is increased (gas is added)? 1) Remains the same 2) Cannot be determined 3) Increases 4) Decreases
asked by aaloy on April 8, 2008
51. ## chem
Consider two identical iron nails: One nail is heated to 95 °C, the other is cooled to 15 °C. The two nails are placed in a coffee cup calorimeter and the system is allowed to come to thermal equilibrium. What is the final temperature of the two nails?
asked by mari on September 12, 2013
52. ## physics
Consider a pipe with a length of 57.5 cm. If the temperature of the air is 21.5degrees C and the pipe is closed in one end and open in the other, what is the frequency of the third harmonic for the pipe? Post your answer in hertz (Hz) and with 3
asked by Idali on April 19, 2017
53. ## english
"Once hired, the teacher will sign a contract with the board of education listing the terms of employment and what the individuals’ salary will be." This is a run-on sentence, I can't figure out how to fix it. Please help. "If a student is 18 or older
asked by Ashley on April 26, 2009
54. ## physics
23. Two identical balls each have an excess charge of 5.0 x 10-7 C, and they are attached to the ceiling by light string 0.80 m long as shown in the figure below. If the angle that the threads make with respect to each other is 300, determine the force
asked by christian on September 18, 2016
55. ## Networking
Alright, Im stumped on this homework, I cannot figure it out and my professor is of little to no help.... there are supossibly 3 problems with this netowork. something with the router address with the network masks. The top number is IP, second is subnet,
asked by Shatima on July 20, 2008
56. ## Physics
In the hydraulic system shown in the figure, the piston on the left has a diameter of 4.5cm and a mass is 3.0kg. If the density of the fluid is 710kg/m^3 , what is the height difference h between the two pistons in m? I checked the other similar questions
asked by Lhaedy on December 11, 2013
57. ## MATH - HELP ME PLEASE!!!!
A steel plate has the form of one-fourth of a circle with a radius of 42 centimeters. Two two-centimeter holes are to be drilled in the plate positioned as shown in the figure in the website below. Find the coordinates of the center of each hole.
asked by Anonymous on February 12, 2019
58. ## Math
1. The figure represents the overhead view of a deck surrounding a hot tub. What is the area of the deck? Round to the nearest tenth. *IF You search this question it is the first link that comes up that has the image. It just doesn't give me a clear
asked by Tim on April 28, 2016
59. ## Physics
011 10.0 points Masses 18 kg and 9 kg are connected by a light string that passes over a frictionless pulley as shown in the figure. The acceleration of gravity is 9.8 m/s2 . 18 kg 9 kg If the 18 kg mass, initially held at rest on the table, is released
60. ## Physics Gravity
A projected space station consists of a circular tube that will rotate about its center (like a tubular bicycle tire) as shown in the figure . The circle formed by the tube has a diameter of about 1.1-km g = R w^2 = 9,8 m/s^2 R = 550 m How do I convert the
asked by Mike Joseph on June 17, 2012
61. ## social studies
can you please tell me about brihadeeshwara temple and the ways to protect it? I can't find much in terms of protecting it. I assume it's protected under some law citing it as a historic masterpiece, but I did not see anything in what I was searching
asked by anjana on May 27, 2007
62. ## math
i have a question on homework that says, "a small tree was measured at 3.67 feet tall. it can grow to 25 times that hight. what is the tallest hight the tree can be expected to reach?" i know that i have to multiply but i cant remember how to multiply
asked by bella on August 24, 2009
63. ## math
a liquid storage container on a truck is in the shape of a cylinder with hemispheres on each end. the cylinder and hemispheres have the same radius. the total length of the container is 140 feet. I have got the funcion for the volume is y=-2pi/3 x^3+ 140pi
asked by errer on November 8, 2015
64. ## algebra
when a ball is thrown up into the air it makes the shape of a parabola the equation s=-16t^2+v*t+k gives the height nof the ball at any time t in seconds where "v" is the initial velocity (speed)in ft/sec and "k" is the initial height in feet
asked by angela toliver on August 1, 2010
65. ## math
At takeoff, a plane flies at an angle of 10° with the runway. After it has traveled a ground distance of 2,800 feet, find the vertical distance the plane has gained from takeoff. Round your answer to the nearest foot.
asked by queen on January 25, 2019
66. ## math
write a system of two equation and use them to solve the following problem: two farmers were discussing how many chickens and cows they would purchase at market. the first farmer says to the second, I have just purchased 30 new heads and 100 feet. how many
asked by stef on July 29, 2012
67. ## Geometrt
Casey sights the top of an 84 foot tall lighthouse at an angle of elevation of 58 degrees. If casey is 6 feet tall, how far is he standing from the base of the lighthouse?........ Do I use cos, tan, or sin? I did the rest of the worksheet but I'm not sure
asked by Ashley on February 28, 2015
68. ## physics
an 85.0kg mountaineer remains in equilibrium while climbing a vertical cliff. the tension force in the supporting rope is 745 N. Find the magnitude of the reaction force F, which the cliff exerts on the mountaineer's feet.
asked by a on October 3, 2017
69. ## College Algebra
You have 800 feet of fencing to enclose a rectangular plot that borders on a river. If you do not fence the side along the river,find the length and width of the plot that will maximize the area. What is the largest area that can be enclosed?
asked by Anonymous on February 18, 2013
70. ## Algebra
You have 600 feet of fencing to enclose a rectangular plot that borders on a river. If you do not fence the side along the river, find the length and width of the plot that will maximize the area. What is the largest area that can be enclosed?
asked by Tori on October 17, 2010
71. ## math
A square canopy is supported on 4 corners by poles. Each pole is supported by 3 cables, each cable is attached to the top of the 12 foot pole and 5 feet away from the base. Find he total length needed for all of the cables.
asked by Anonymous on January 14, 2016
72. ## Math
The Sun hits a 30 foot flagpole at a 60° angle and casts an unobstructed 52 foot shadow. If a building is built 32 feet away, what height will the shadow strike the side of the building? (round to nearest tenth)
asked by Terrance on December 9, 2015
73. ## Math
Assume the mean height of the soldiers to be 68.22 inches with the variance of 10.8inches square. How many soldiers in the regiment of 1000 would you expect to be-(1.) Over 6 fee tall (2) below 5.5 feet? Assume height to be normally distributed. Given;
asked by Tshering on December 3, 2018
74. ## Calculus
A blast blows a rock straight up at 150 ft/sec. The path of the rock is described by the s(t) = 150t-16t^2 where s is measured in feet and t in seconds. Find the velocity of the rock when it is 200 ft above the ground and when the rock hits the ground.
asked by Desperate!!!! on February 18, 2012
75. ## Math
A surveyor standing 2,227 ft from the base of the World Trade Center in New York City measured a 31 degrees angle to the topmost point. To the nearest feet, how tall is the World Trade Center?
asked by Anonymous on April 25, 2016
76. ## math
a rectangular pen with partitions is to be built from 800 feet of fencing. Express the area as a function of x alone. graph over a reasonable domain and find the dimensions of the pen of the maximum area that an be built under these conditions
asked by Anonymous on December 16, 2014
77. ## math
An ostrich farmer wants to enclose a rectangular area and then divide it into 4 pens with fencing parallel to one side of the rectangle. There are 720 feet of fencing available to complete the job. What is the largest possible total area of the 4 pens?
asked by Leah on October 28, 2014
78. ## math
A round tank hold 550 gallons filled to the brim. Its capacity is 10 gallons for every inch in height. How high is the tank in inches, in feet. How high would you fill it get to the 170 gallon level?
asked by Jerome on May 7, 2013
79. ## Math
3. What is 0.72 written as a simplified fraction? (1 point) seventy-two over one hundred one hundred over seventy-two thirty-six over fifty eighteen over twenty-five 4. Ms. Johnson’s class is having a pizza party. If there are 14 students and 7 pizzas
asked by anonymous on November 12, 2013
80. ## Chemistry
How would each of the following affect the Cr(VI) concentration determined in this experiment? Justify the answers with an explanation. In the experiment, absorption spectroscopy was used to obtain the concentration of Cr(VI) ions. 1) A student adds more
asked by Sandy on March 2, 2014
How would each of the following affect the Cr(VI) concentration determined in this experiment? Justify the answers with an explanation. In the experiment, absorption spectroscopy was used to obtain the concentration of Cr(VI) ions. 1) A student adds more
asked by Sandy on March 2, 2014
82. ## Science - - Cells
What structures are found only in animal cells? I can't figure it out...I know that chloroplasts and a cell wall are only contained by plant cells. But what about animal cells?
asked by Eve on December 3, 2007
83. ## Math
I am having difficulties trying to find out the missing dimensions of a cutout piece. Can someone please tell me how to figure out the dimensions. They've given me the dimensions for the whole solid, but just not the cut out piece. Your help will be
asked by Sara on February 10, 2010
84. ## Algebra
Determine whether the given numbers are solutions of the inequality. t - 8 > 2t - 3 The given numbers are: 0, 3.3, -9, -3 I understand the problem and how to figure it out. Its just that when I tried this problem, none of the numbers worked. Did any work
asked by Carrie on January 15, 2009
85. ## Chemistry
What is the nuclear charge of an atom with a mass of 23 and an atomic number of 11? (1) 11+ (2) 12+ (3) 23+ (4) 34+ How do you figure this out? Would the answer be (1) 11+ since the atomic number is 11 and atomic #=protons which are positive??
asked by Anonymous on June 14, 2009
86. ## Algebra
Find an equation of the line containing pair of points (1/6, 1/3) and (5/6, 3) I can't seem to figure out the slope right, which apparently is 5. How does one get a five slope out of all these fractions?!!! To find the slope 3-1/3 = 8/3 over 5/6 - 1/6 =
asked by Aria on May 29, 2011
87. ## Math
I can't figure our how they got the answer to this question: Use the following function to find f(-2)? f(x)=x(squared)-3 This is how I am solving the problem: f(x)=x(squared) -3 f(-2)=(-2)squared -3 f(-2)=4-3 f(-2)=1 The correct answer is 2 and I don;t
asked by Maggie on June 13, 2008
A skateboarder starts at point A in Figure 8-27 and rises to a height of h = 2.37 m above the top of the ramp at point B. What was the skateboarder's initial speed at point A?
asked by kelsey on October 8, 2008
89. ## Math
I am having difficulties trying to find out the missing dimensions of a cutout piece. Can someone please tell me how to figure out the dimensions. They've given me the dimensions for the whole solid, but just not the cut out piece. Your help will be
asked by Sara on February 10, 2010
90. ## Math
During a contest, a radio station gave away 40 free tickets to a concert. Only 25 of the free tickets were used. What percent of the tickets was used? How do we figure out the percentage???
asked by Nessa on October 18, 2011
91. ## MATH
Which solid figure has 5 faces, 5 vertices, and 8 edges. Triangular pyramid Rectangular pyramid Pentagonal pyramid*** Triangular prism
asked by WOW on May 8, 2017
92. ## maths
the perimeter of the rectangle ABCD is 30 cm. Alisa cuts 3 rectangles from that rectangle. the sum of the three perimeter is 20. what is the perimeter of the figure obtained after the cutting
asked by payalsun on March 7, 2019
93. ## physics
This is going to be hard to explain, but here goes! Four resistors, R1 = 30.0 ohm, R2 = 52.0 ohm, R3 = 93.0 ohm and R4 = 17.0 ohm, are connected to a battery with a terminal voltage of 18.0 V, as shown in the figure below. ____R1____R2__________ | |
asked by Marissa on February 17, 2009
94. ## math
Martin is building a square platform in the drama room at school. He knows the side length of the square needed for the platform. Which function can he use to determine F(x), the area in square feet of the platform?
asked by Kallie on April 22, 2014
95. ## Algebra Word problem
I don't know how to put in a square root symbol here so know that it is over h. The equation D=1.2 square root h gives the distance D in miles that a person can see to the horizon from a height h in feet. Solve for h. Do I find the square root of 1.2?
asked by Marysvoice on January 29, 2008
96. ## Physics
In the figure, a small 0.458 kg block slides down a frictionless surface through height h = 1.05 m and then sticks to a uniform vertical rod of mass M = 0.458 kg and length d = 2.70 m. The rod pivots about point O through angle θ before momentarily
asked by Jezz on November 17, 2013
97. ## physics
A uniform ladder of length L rests against a smooth, vertical wall as shown in the figure below. If the mass of the ladder is m and the coefficient of static friction between the ladder and the ground is muks=0.4, find the minimum angle theta at which the
asked by joy on April 22, 2018
98. ## Health PLZ HELP ASAP
There are four communication skills that have been proven to be very effective when sharing information. The four skills are: using "I" message, active listening, assertiveness,.....(I have to figure out the last one) A, Aggressiveness B, Body Language C,
asked by regan on October 26, 2015
99. ## math
Assume that you make a down payment of $2000, and you finance the remainder with a five-year loan at 6.9 percent APR. 20092 total cost-2000 down payment=18092 interest=2.24$ What is the equation I need to use to figure out the monthly payments per \$100?
asked by crissy on December 27, 2016
100. ## Algebra
Find the area of the irregular figure (use 3.14 for pi). SHow your work. Round to the nearest tenth. Triangle with a semi-circle on it. The triangles height is 4.8ft and the circle's diameter is 3.6ft. Every time I do my work I keep getting 12.3 and I have
asked by Baby_Banana on April 4, 2018 | 2019-07-20 17:05:16 | {"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": 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": 0.49776706099510193, "perplexity": 986.2949094956447}, "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-2019-30/segments/1563195526536.46/warc/CC-MAIN-20190720153215-20190720175215-00023.warc.gz"} |
https://msp.org/involve/2019/12-8/p08.xhtml | #### Vol. 12, No. 8, 2019
Recent Issues
The Journal About the Journal Editorial Board Editors’ Interests Subscriptions Submission Guidelines Submission Form Policies for Authors Ethics Statement ISSN: 1944-4184 (e-only) ISSN: 1944-4176 (print) Author Index Coming Soon Other MSP Journals
Nonsplit module extensions over the one-sided inverse of $k[x]$
### Zheping Lu, Linhong Wang and Xingting Wang
Vol. 12 (2019), No. 8, 1369–1377
##### Abstract
Let $R$ be the associative $k$-algebra generated by two elements $x$ and $y$ with defining relation $yx=1$. A complete description of simple modules over $R$ is obtained by using the results of Irving and Gerritzen. We examine the short exact sequence $0\to U\to E\to V\to 0$, where $U$ and $V$ are simple $R$-modules. It shows that nonsplit extension only occurs when both $U$ and $V$ are one-dimensional, or, under certain condition, $U$ is infinite-dimensional and $V$ is one-dimensional.
##### Keywords
simple modules, representations, module extensions
Primary: 16D60
Secondary: 16G99 | 2021-01-18 10:10:05 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 14, "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": 0.4091232120990753, "perplexity": 1930.0192291341884}, "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/1610703514495.52/warc/CC-MAIN-20210118092350-20210118122350-00098.warc.gz"} |
https://mathematica.stackexchange.com/questions/78203/import-successful-when-file-manually-deleted | # Import successful when file manually deleted
Apparently Import keeps an imported file in the cache and doesn't complain for some time if a file is deleted manually from the system and then it is imported. If the file is deleted from within Mathematica, then it does complain. Here is a minimal working example:
list = {{1, 2, 3, 4}, {4, 5, 6}};
Export["test.mc", Compress@list, "String"]
Uncompress@Import["./test.mc"]
This is successful. Now delete the file manually from your Directory and check that it is indeed deleted:
FileNames["./test.mc"]
>>> {}
Now importing again works without error:
Uncompress@Import["./test.mc"]
>>> {{1, 2, 3, 4}, {4, 5, 6}}
Now deleting the file within Mathematica:
DeleteFile["./test.mc"]
Uncompress@Import["./test.mc"]
Uncompress::string: String expected at position 1 in Uncompress[$Failed]. >> Uncompress[$Failed]
Can someone explain what is going on here?
Apparently clearing the SystemCache and waiting some time, works.
This is important for me because I have a function that detects if a file has been deleted using Check[Import[....]]. This means that my function doesn't work if the file is recently deleted in my system.
I am using Mathematica 9.0.1 in Debian Linux 3.2.65.
• Does checking with FileExistsQ instead of Import work? – 2012rcampion Mar 25 '15 at 17:01
• Also, can't reproduce behavior (MMA 10.0.0, Windows 8.1 64-bit), I just get Import::nffil immediately. – 2012rcampion Mar 25 '15 at 17:03
• Let me guess, you're on OSX? – 2012rcampion Mar 25 '15 at 17:06
• No, I'm on Linux Debian 3.2.65. – Santi Mar 25 '15 at 17:08
• Yes, @2012rcampion, changing the check would be enough. I just find this a very strange behavior. – Santi Mar 25 '15 at 17:08 | 2020-02-21 04:26:15 | {"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": 0.198869988322258, "perplexity": 2653.1477098722817}, "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-2020-10/segments/1581875145438.12/warc/CC-MAIN-20200221014826-20200221044826-00160.warc.gz"} |
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# commutative property sums
Use the commutative law of addition-- let me underline that-- the commutative law of addition to write the expression 5 plus 8 plus 5 in a different way and then find the sum. Commutative Property Calculator . Commutative Property worksheets and online activities. memosfromamultisensoryteacher.com is your first and best source for all of the information you’re looking for. When the change in the order of the operands does not change the outcome of the operation then that is called commutative property. The Associative Property of Addition is one of four basic properties that students will learn in early addition lessons and use later in multiplication and pre-algebra. Addition. These multiplication worksheets are appropriate for 3rd Grade, 4th Grade, … Lastly, we have the distributive property, illustrating how to expand a Boolean expression formed by the product of a sum, and in reverse shows us how terms may be factored out of Boolean sums-of-products: To summarize, here are the three basic properties: commutative, associative, and … Now, this commutative law of addition sounds like a very fancy thing, but all it means is if you're just adding a bunch of numbers, it doesn't matter what order … I'm wanting to understand what's wrong with applying the commutative property of addition to make it more convenient to compute with such a series, because if nothing is wrong with applying the commutative property in such a case, then it seems to follow that $\sum\limits_{n=0}^{\infty}{\left(-1\right)}^n$ IS equal to … Both sums have 3 and 5 next to the addition sign and so, both answers are 8. You can find them all at the bottom of this page. For example, in the commutative property of addition, if you have 2 + 4, you can change it to 4 + 2, and you will have the same answer (6). We hope you find what you are … Apply properties of operations as strategies to add and subtract. Proof of Commutative Property of Convolution. Therefore, according commutative property for addition the sum of two whole numbers is the same, no matter in which order they are added. Commutative Property. For multiplication, the rule is "ab = ba"; in numbers, this means 2×3 = 3×2. Therefore, convolution is commutative; . Example: 5 x 4 = … The commutative property of addition is one of four basic properties that your child will use in math. (Associative property of addition.) You may select the range of rows and columns used for the arrays. Commutative property of the sum. To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. Commutative Property of Addition. Listen to the audio pronunciation in the Cambridge English Dictionary. Commutative property of set : Here we are going to see the commutative property used in sets. the series converges), then all subsequences converge to the same thing. Example: 5 + 4 = 9. Parent Newsletter for Topic E URL. In mathematics, summation is the addition of a sequence of any kind of numbers, called addends or summands; the result is their sum or total.Beside numbers, other types of values can be summed as well: functions, vectors, matrices, polynomials and, in general, elements of any type of mathematical objects on which an … For addition, the rule is "a + b = b + a"; in numbers, this means 2 + 3 = 3 + 2. The commutative property of addition says that when the order of the addends is changed, the answer still stays the same. If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. Explanation :-Addition is Commutative for Integers, this means that even if we change the order of integers in addition expression, the result remains same.This property is also known as Commutativity for Addition of Integers Commutative Property for Addition of Integers can be further understood with the help of following examples :- Example 1 = Explain Commutative Property … Commutative Property. If the sequence of partial sums converges (i.e. Let a and b are two whole numbers, then a + b = b + a. Commutative Property. The worksheet then encourages students to apply the commutative property to find sums of two one-digit numbers. The commutative property of the sum is also known as the order property of the sum.The property indicates to us that the summands or numbers that are in the sum can be added regardless of the order that these have and giving us as a result the same number.. For example, the following sum: 4 + 2 = 2 + 4 We can observe that the two sums … Algebra Commutative Property of Set Theory Proof. Property Example with Addition; Distributive Property: Associative: Commutative: Summary: All 3 of these properties apply to addition. 2. Identity Property of Addition. Some of the worksheets for this concept are Commutative property of addition 1, Identify the property commutative associative or, Addition properties, Identify the property commutative or associative 3rd, Name score, Name in numbers 1 9 select the property … The commutative property of addition also applies … The student will be given an array and asked to write out a multiplication equation and then using the commutative property of multiplication, find an equivalent multiplication equation. Then, substitute K into the equation:. bra is the space of words together with the commutative shuffle product [Ree58 , Reu93 ] and the noncocommutative deconcatenation coproduct, whereas for the iterated-sums signature it turns outtobethecommutative quasi-shuffle algebra overwords[Car72 , Gai94 , Hof00 , NR79 ]withthe same coproduct. The commutative property is among the foundation for the rules of the algebra. The "Distributive Law" is the BEST one of all, but needs careful attention. Addition. Commutative property vs Associative property. The Distributive Property. Topic E Quiz … Learn more. First, let . Therefore, 5 + 4 = 4 + 5. Algebra Commutative Property. So, the 3× can be "distributed" across the … The commutative property of multiplication states that changing the order of numbers does not change the result or it's value. This is what it lets us do: 3 lots of (2+4) is the same as 3 lots of 2 plus 3 lots of 4. Commutative property . Any time … Topic E: The Commutative Property of Addition and the Equal Sign. The commutative property of addition essentially states that no matter what order the addends are in within a particular number sentence, the sums will be the same. Free interactive exercises to practice online or download as pdf to print. By definition, is the convolution of two signals h[n] and x[n], which is . Eureka Essentials: Grade 1 URL An outline of learning goals, key ideas, pacing suggestions, and more! And 4 + 5 = 9. The definition of convolution 1D is: . Many mathematical proofs are based on this law and it is a basic property of many binary operations. Proof This is an immediate consequence of the fact that the commutative property applies to sums of scalars, and therefore to the element-by-element sums that … This formula reflects the commutative property of infinite double sums by the quadrant . … This shows that we can add whole numbers in any order. Commutative law is used to change the order of the operands without changing the end result. Sums and Differences to 10. Learn about the properties of matrix multiplication (like the distributive property) and how they relate to real number multiplication. How to pronounce commutative. For any two two sets, the following statements are true. (Commutative property of addition.) This formula shows how to … Commutative Property of Addition Worksheet starts off with students identifying equivalent addition expressions involving two numbers in different orders. Commutative Property. If you're seeing this message, it means we're having trouble loading external resources on our website. The commutative property simply means that switching the order of the numbers in a calculation does not affect the answer. Right here’s an instance of the property used: 3 + 5 = 5 + 3. The word "commutative" comes from "commute" or "move around", so the Commutative Property is the one that refers to moving stuff around. ... Topic E: The Commutative Property of Addition and the Equal Sign. Properties and Operations. The commutative property or commutative law means you can change the order you add or multiply the numbers and get the same result. Sums within 20. Review and refine your grade 2 and grade 3 kids' skills in identifying the commutative and associative laws and distinguishing between the two in these printable addition properties worksheets. So, think of the commutative property as the rule of moving around the addends. For example 4 + 2 = 2 + 4 For example 4 + 2 = 2 + 4 Associative Property: When three or more numbers are added, the sum is the same regardless of the grouping of the addends. Subtraction and division are not commutative. Commutative Associative Properties - Displaying top 8 worksheets found for this concept.. The properties include the commutative, identity, and distributive properties--all of which I cover in other math lessons. Statement: First Law : First law states that the union of two sets is the same no matter what the order is in the equation. Nov 18, 2012 - This website is for sale! This property of the whole numbers tells that the order of addition does not change the value of the sum. The commutative property of addition informs us we can include things in any order and still obtain the same sum. Proposition (commutative property) Matrix addition is commutative, that is, for any matrices and and such that the above additions are meaningfully defined. (i) Set union is commutative (A U B) = (B U A) (i) Set intersection is commutative (A n B) = (B n A) Let us look into some example problems based on above properties. Commutative property: When two numbers are added, the sum is the same regardless of the order of the addends. From general topics to more of what you would expect to find here, memosfromamultisensoryteacher.com has it all. Let's look at how (and if) these properties work with addition, multiplication, subtraction and division. I've prepared lessons on the other properties of addition. Addition and multiplication are both commutative. … How to say commutative. Associativity comes down to looking at a subsequence of the sequence of partial sums. Associative Property. Suppose a = 10 and b = 18 ⇒ 10 + 18 = 28 = 18 + 10. It takes place under restrictions like , which provide absolute convergence of this double series. Tip: The word commutative is kind of like the word commute, which means to move around. Multiplication. All of the worksheets below will focus on this property. Distributive Law. This bundle includes: Using using addition charts to recognize patterns Identity Property of Addition Commutative Property of Addition Rounding to the Nearest ten Rounding to the Nearest Hundred Using Number lines to Round A Rounding Poem and Examples of Rounding page Estimating Sums Mental Math Strategies (using … The Distributive law '' is the convolution of two signals h [ n and. Used: 3 + 5 = 5 + 3 = 11 is,... End result two signals h [ n ] and x [ n ] x. 2×3 = 3×2 whole numbers tells that the order of addition law is... Of four basic properties that your child will use in math add whole numbers in different.! Of all, but needs careful attention Associative: commutative: Summary: all 3 of properties! We 're having trouble loading external resources on our website is among the foundation for the arrays four basic that. By the quadrant algebra commutative property of infinite double sums by the quadrant the commutative property is among the for. 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Of four basic properties that your child will use in math answer still stays the result! | 2021-05-11 13:13:06 | {"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": 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": 0.5150492191314697, "perplexity": 608.5554056748031}, "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-2021-21/segments/1620243989614.9/warc/CC-MAIN-20210511122905-20210511152905-00249.warc.gz"} |
https://docs.nvidia.com/deeplearning/dali/main-user-guide/docs/operations/nvidia.dali.fn.warp_affine.html | # nvidia.dali.fn.warp_affine¶
nvidia.dali.fn.warp_affine(*inputs, **kwargs)
Applies an affine transformation to the images.
This operator supports volumetric data.
Supported backends
• ‘cpu’
• ‘gpu’
Parameters
• input0 (TensorList ('HWC', 'FHWC', 'DHWC', 'FDHWC')) – Input to the operator.
• input1 (TensorList, optional) – Input to the operator.
Keyword Arguments
• bytes_per_sample_hint (int or list of int, optional, default = [0]) –
Output size hint, in bytes per sample.
If specified, the operator’s outputs residing in GPU or page-locked host memory will be preallocated to accommodate a batch of samples of this size.
• dtype (nvidia.dali.types.DALIDataType, optional) –
Output data type.
If not set, the input type is used.
• fill_value (float, optional) –
Value used to fill areas that are outside the source image.
If a value is not specified, the source coordinates are clamped and the border pixel is repeated.
• interp_type (nvidia.dali.types.DALIInterpType, optional, default = DALIInterpType.INTERP_LINEAR) – Type of interpolation used.
• inverse_map (bool, optional, default = True) – Set to False if the given transform is a destination to source mapping, True otherwise.
• matrix (float or list of float or TensorList of float, optional, default = []) –
Transform matrix.
When the inverse_map option is set to true (default), the matrix represents a destination to source mapping. With a list of values (M11, M12, M13, M21, M22, M23), this operation produces a new image by using the following formula:
dst(x,y) = src(M11 * x + M12 * y + M13, M21 * x + M22 * y + M23)
Where [0, 0] coordinate means the corner of the first pixel.
If the inverse_map option is set to false, the matrix represents a source to destination transform and it is inverted before applying the formula above.
It is equivalent to OpenCV’s warpAffine operation with the inverse_map argument being analog to the WARP_INVERSE_MAP flag.
Supports per-frame inputs.
• preserve (bool, optional, default = False) – Prevents the operator from being removed from the graph even if its outputs are not used.
• seed (int, optional, default = -1) –
Random seed.
If not provided, it will be populated based on the global seed of the pipeline.
• size (float or list of float or TensorList of float, optional, default = []) –
Output size, in pixels/points.
Non-integer sizes are rounded to nearest integer. The channel dimension should be excluded (for example, for RGB images, specify (480,640), not (480,640,3).
• output_dtype (nvidia.dali.types.DALIDataType) –
Warning
The argument output_dtype is a deprecated alias for dtype. Use dtype instead. | 2022-12-03 09:27:30 | {"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": 0.2568833529949188, "perplexity": 11473.999952538778}, "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/1669446710926.23/warc/CC-MAIN-20221203075717-20221203105717-00362.warc.gz"} |
http://mathhelpforum.com/trigonometry/112582-period.html | Math Help - Period
1. Period : 1
Find the period for the function f in R:
$f(x+1)=\frac{1}{1-f(x)}$
2. $f(x+2)=\frac{1}{1-f(x+1)}=\frac{1}{1-\displaystyle\frac{1}{1-f(x)}}=\frac{f(x)-1}{f(x)}=1-\frac{1}{f(x)}$
$f(x+3)=1-\frac{1}{f(x+1)}=1-1+f(x)=f(x)$
Then the period is 3. | 2014-04-17 15:48:39 | {"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": 0.9187108874320984, "perplexity": 2318.044886852382}, "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-2014-15/segments/1397609530136.5/warc/CC-MAIN-20140416005210-00379-ip-10-147-4-33.ec2.internal.warc.gz"} |
https://socratic.org/questions/how-do-you-integrate-int-x-x-2-3-dx | # How do you integrate int x(x^2+3)dx?
$\int x \left({x}^{2} + 3\right) \mathrm{dx} = \frac{1}{4} {\left({x}^{2} + 3\right)}^{2} + C$
It can be done by other methods, but if you recognise that the $x$ outside the bracket results from the bracket differentiated we can integrate by inspection.
now $\frac{d}{\mathrm{dx}} \left({\left({x}^{2} + 3\right)}^{2}\right) = 2 \times 2 x \left({x}^{2} + 3\right) = 4 x \left({x}^{2} + 3\right)$
Thus $\int x \left({x}^{2} + 3\right) \mathrm{dx} = \frac{1}{4} {\left({x}^{2} + 3\right)}^{2} + C$ | 2021-10-17 02:23:11 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 4, "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": 0.9933772683143616, "perplexity": 517.56025725533}, "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-2021-43/segments/1634323585120.89/warc/CC-MAIN-20211017021554-20211017051554-00269.warc.gz"} |
https://machinelearning101.readthedocs.io/en/latest/_pages/13_example_multiple_linear_regression.html | # 5. Example Multiple Linear Regression¶
Different methods used to demonstrate Multiple Linear Regression
• Ordinary Least Square
• Python from scratch
• Scikit
• Python from scratch
• Scikit
## 5.1. Ordinary Least Square¶
7 data = datasets.load_boston()
Define the data predictors and the target data :
12 13 14 15 16 # define the data/predictors as the pre-set feature names df = pd.DataFrame(data.data, columns=data.feature_names) # Put the target (housing value -- MEDV) in another DataFrame target = pd.DataFrame(data.target, columns=["MEDV"])
### 5.1.1. Python¶
Using the Ordinary Least Square method derived in the previous section :
29 30 31 32 Xt = np.transpose(X) XtX = np.dot(Xt,X) Xty = np.dot(Xt,y) coef_ = np.linalg.solve(XtX,Xty)
Set of coefficiants as calculated :
[ -9.28965170e-02 4.87149552e-02 -4.05997958e-03 2.85399882e+00
-2.86843637e+00 5.92814778e+00 -7.26933458e-03 -9.68514157e-01
1.71151128e-01 -9.39621540e-03 -3.92190926e-01 1.49056102e-02
-4.16304471e-01]
### 5.1.2. Scikit¶
Lets define our regression model :
37 model = linear_model.LinearRegression(fit_intercept=False)
Note
we are using the same linear_model as in our simple linear regression method. Also the fit_intercept has been set to False. This is just to validate our derivation in the previous section. fit_intercept by default is set to True and will not assume that our response $$y$$ is centered and will give an model.intercept_ value.
Fitting our model :
38 model = model.fit(X,y)
[ -9.28965170e-02 4.87149552e-02 -4.05997958e-03 2.85399882e+00
-2.86843637e+00 5.92814778e+00 -7.26933458e-03 -9.68514157e-01
1.71151128e-01 -9.39621540e-03 -3.92190926e-01 1.49056102e-02
-4.16304471e-01]
Evaluating our model :
42 43 44 y_predicted = model.predict(X) print("Mean squared error: %.2f" % mean_squared_error(y, y_predicted)) print('R²: %.2f' % r2_score(y, y_predicted))
Mean squared error: 24.17
R²: 0.71 | 2022-06-25 14:14:39 | {"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": 0.2892092168331146, "perplexity": 8706.694441900507}, "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-2022-27/segments/1656103035636.10/warc/CC-MAIN-20220625125944-20220625155944-00739.warc.gz"} |
https://cvgmt.sns.it/paper/5230/ | ## Complete ionization for a non-autonomous point interaction model in d=2
created by borrelli on 17 Aug 2021
modified on 28 Jul 2022
[BibTeX]
Published Paper
Inserted: 17 aug 2021
Last Updated: 28 jul 2022
Journal: Comm. Math. Phys.
Pages: 33
Year: 2022
Doi: https://doi.org/10.1007/s00220-022-04447-1
ArXiv: 2108.06564 PDF
Abstract:
We consider the two dimensional Schrödinger equation with time dependent delta potential, which represents a model for the dynamics of a quantum particle subject to a point interaction whose strength varies in time. First, we prove global well-posedness of the associated Cauchy problem under general assumptions on the potential and on the initial datum. Then, for a monochromatic periodic potential (which also satisfies a suitable no-resonance condition) we investigate the asymptotic behavior of the survival probability of a bound state of the time-independent problem. Such probability is shown to have a time decay of order $\mathcal{O}((\log t /t)^2)$, up to lower order terms. | 2022-10-03 01:00:32 | {"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": 0.5934048295021057, "perplexity": 679.6257444427597}, "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-2022-40/segments/1664030337371.9/warc/CC-MAIN-20221003003804-20221003033804-00135.warc.gz"} |
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# Infrared dielectric metamaterials from high refractive index chalcogenides
## Abstract
High-index dielectric materials are in great demand for nanophotonic devices and applications, from ultrathin optical elements to metal-free sub-diffraction light confinement and waveguiding. Here we show that chalcogenide topological insulators are particularly apt candidates for dielectric nanophotonics architectures in the infrared spectral range, by reporting metamaterial resonances in chalcogenide crystals sustained well inside the mid-infrared, choosing Bi2Te3 as case study within this family of materials. Strong resonant modulation of the incident electromagnetic field is achieved thanks to the exceptionally high refractive index ranging between 7 and 8 throughout the 2–10 μm region. Analysis of the complex mode structure in the metamaterial allude to the excitation of circular surface currents which could open pathways for enhanced light-matter interaction and low-loss plasmonic configurations by coupling to the spin-polarized topological surface carriers, thereby providing new opportunities to combine dielectric, plasmonic and magnetic metamaterials in a single platform.
## Introduction
Topological insulator (TI) crystals feature time reversal symmetry-protected, highly conducting surface states characterized by Dirac dispersion and spin-momentum locking of carriers that encapsulate a semi-conducting bulk1,2,3. They are an extremely attractive class of materials for electronic4, spintronic5 and, more recently, photonic6,7 applications, where coupling of light to the topologically protected surface carriers may lead to propagating surface plasmon polaritons with very little scattering and other exotic phenomena, such as hybridization of spin and surface plasmons8. This has motivated extensive studies of electromagnetic properties of TI chalcogenide crystals over a broad range of frequencies from THz to UV9,10,11,12,13,14,15. Interaction of electromagnetic waves with the topological surface states can be enhanced by suitably structuring the TI crystals with subwavelength units, such as resonant metamolecules, giving rise to absorption and localization of the electromagnetic field9,16. TI metamaterials have been realized at THz and UV–visible frequencies, where the material response is more plasmonic due to free surface carriers and bound bulk carriers, respectively9,16,17,18. However, there have been hardly any studies on resonant TI structures at intermediate near-infrared and mid-infrared frequencies, where the compositionally tunable refractive index is extremely high19, and optical conductivity from charge carriers in topological surface states becomes significant20. Within the family of chalcogenide crystals, we select Bi2Te3 to demonstrate dielectric metamaterial structures in the technologically important near to mid-infrared frequency window. Bi2Te3 has a refractive index between 7 and 8 over the 2–10 μm spectral range, which is much larger than typical infrared dielectric materials, such as Si (n = 3.44)21, Ge (n = 4.07)22, PbTe (n = 5.61)23, and GST (n = 6–7.2)24.
Here we show that the high refractive index of the chalcogenide crystals can be used to generate strong infrared resonances and associated complex mode structures with surface circular currents, opening up new opportunities to couple light with spin-polarized topological surface state carriers.
## Results
### The high infrared refractive index of TIs
We started by carrying out first-principles calculations and spectroscopic measurements of single crystal Bi2Te3. Density functional theory (DFT) calculations based on the local density approximation (LDA) were employed to study the electronic band structures and optical properties of the rhombohedral-phase Bi2Te3 (see the crystal structure in Fig. 1a) using the Quantum ESPRESSO (QE) package25. Experimental lattice parameters of bulk Bi2Te326,27 were used to build the initial structure, and ground states geometry of the Bi2Te3 crystals was obtained by the total energy minimization method upon relaxing their crystal framework and atomic coordinates. We calculated the band structure of Bi2Te3 with and without spin–orbit coupling (SOC). Due to the presence of heavy elements such as Bi and Te, relativistic effects and SOC have significant impact on the band structure. Without SOC, the bands have the typical parabolic dispersion with a direct gap at the Γ point. However, the presence of SOC leads to band-inversion at the Γ point and a topologically non-trivial gap is induced (Fig. 1b top panel) with the Dirac dispersion appearing in the case of a thin slab (Fig. 1b bottom panel). The optical response was calculated by employing the Bethe–Salpeter equations (BSE) method with the YAMBO code, using ground-state wavefunctions from QE package28,29. The imaginary part of the permittivity was determined by evaluating direct electronic transitions between occupied and higher-energy unoccupied electronic states and the real part was obtained by employing Kramers–Kroning transformation on the imaginary part. Additional details on optical response calculations can be found in ref. 20. Figure 2a shows the real and imaginary parts of the calculated complex refractive index ($$\widetilde n = n + {\mathrm{i}}k$$). Its dispersion is characterized by contrasting behaviors in two regions of the spectrum: (i) the short wavelength (0.25–1.50 μm) region with strong absorption (high k), resulting from interband transitions in the bulk, and (ii) the long wavelength (~2–16 μm) region featuring strong polarizability (high n). Correspondingly, the permittivity is negative throughout the 0.25–0.85 μm region (n < k)9,20, where the material is plasmonic. The typical concentration of surface carriers in these materials (1012–1013 cm−2) results in their contribution to the optical conductivity becoming significant in the long wavelength region above 6 μm20, as manifested by a small decrease of the refractive index.
Spectroscopic studies were carried out on exfoliated films of TI single crystal samples of Bi2Te3 with thickness ranging from 10 to 100 μm. We characterized optical properties over a broad spectral range, from the UV to the mid-infrared by means of variable angle ellipsometry (in the UV to near-infrared range) and near-infrared to mid-infrared reflection measurements, from which we extracted the experimental complex refractive index dispersion (Fig. 2b). The experimental dispersion compares well with the calculated one, showing absorption and negative permittivity at the shorter wavelengths, and strong dielectric behavior in the infrared.
The deviation from the calculated dispersion at longer wavelengths is due to a sharp decrease of the refractive index and an increase of the extinction coefficient induced by free bulk carriers from intrinsic doping. This effectively creates a third region of high refractive index and low losses between 7 and 10 μm for the crystals in our hands. The dashed lines in Fig. 2b show the experimental optical constants after removing the bulk Drude contribution for comparison with the DFT calculation results, showing fairly good agreement between the two once the intrinsic doping contribution is excluded.
### Broadly tunable infrared dielectric metamaterials
Optical materials with high refractive index and low losses such as Bi2Te3 in the mid-infrared are in great demand for dielectric metamaterials, as they can produce strong mode confinement and narrow resonances for small form factor devices30. On this premise, we fabricated infrared nanoslit arrays via focused ion beam milling on the surface of exfoliated Bi2Te3 crystals. The slit array geometry was chosen for geometrical simplicity and designed to have pronounced resonances across the entire infrared spectrum by varying the nanoslit length (L) from 1.0 to 4.3 μm. Representative top-view and cross-sectional SEM images of the fabricated nanoslit arrays are shown in Fig. 3a–d. Infrared microscopy reflection measurements were carried out with incident electric field vector polarized both parallel ($${R}_{{\mathrm{E}}\parallel }$$) and perpendicular (RE) to the length of the slits. The slit arrays show resonant response only when excited with perpendicular polarization. To highlight these resonances, we plot the reflection spectra in a differential form, $$( {R_{{\mathrm{{E}}} \bot } - R_{{\mathrm{{E}}}\parallel }} )/R_{{\mathrm{{E}}}\parallel }$$, for the various slit lengths (Fig. 3e). Two distinct resonances are clearly observed in the plot, the fundamental resonances (indicated by ) and, the second-order resonances (indicated by ) which appear in the measured spectral region for slits longer than 1.5 μm. Figure 3f shows the variation of the resonant wavelength as a function of slit length, clearly indicating a linear spectral red-shift with scaling factors of 2 and 1 times the slit length for the fundamental and second-order resonances, respectively31.
### Nature of resonant modes and circular surface currents
To further our understanding of the nature of the main resonant mode, we carried out finite-element method (FEM) simulations of the nanoslit array, over the corresponding wavelength interval.
Figure 4a compares the experimental and simulated differential reflection spectra of the longest slit (L = 4.3 μm) arrays, showing good agreement between the two. Corresponding maps of the resonant electric and magnetic fields at 8.55 μm are plotted in Fig. 4b, c for incident electric field polarization perpendicular to the slits. The field-maps for the minor mode at 4.35 μm are plotted in Fig. 4d, e. Contrary to conventional expectations, a circulating pattern for the magnetic field as displayed by the mode at 8.55 μm (Fig. 4b, c), does not necessarily imply that the resonance is a toroidal dipole. The exact multipole decomposition, shown in Fig. 4f, shows that the situation is far more nuanced: the plot of the multipole components expressed in terms of the current density (see Supplementary Eq. (12)) shows that the metamaterial excitation is not dominated by a particular mode, but is a combination of multiple modes, such as the electric dipole (order 0), magnetic dipole and electric quadrupole (order 1), toroidal dipole, magnetic dipole, and electric quadrupole (order 2), etc., depicted schematically in Fig. 4g. Noteworthy is the fact that toroidal-like field configurations can be generated in the presence of multiple modes. The differential reflection spectrum calculated from multipole analysis is shown as dashed lines in Fig. 4a and agrees fairly well with the simulated and experimental spectra. For more details of the multipole analysis, refer to Supplementary Note 1. The multipole contribution for incident non-resonant polarization (electric field parallel to the slit length) is shown in Supplementary Fig. 2. We note that the overall reflection response of the slit arrays depends on the interference of the various multipoles based on their amplitude and phases which is rather complicated and can be illustrated with the aid of phasor diagrams (Supplementary Note 3). We also note that the minor mode at 4.35 μm also shows similar behavior with circulating magnetic fields but with two vortices indicating that it is a second-order mode. Supplementary Movies 14 show the evolution of the electric and magnetic fields within the metamaterial over half a cycle (0–π) of the phase.
## Discussion
The high-order modes supported by metamaterials32,33,34 enable strong light localization and confinement, which may be suitable for applications in nonlinear and laser optics35,36, or in coupling to high-order transitions in atoms or molecules. In the context of TI metamaterials, the unique nature of the resonant fields featuring circular currents on the surface of the TI may be exploited to couple light with spin-polarized carriers and gain optical access to the topological surface states that encapsulate the material conformally37. This becomes particularly relevant in the mid-IR region, where chalcogenide crystals feature a combination of high refractive index and larger contribution of topological surface states to the optical conductivity.
Overall, the TI chalcogenide crystal family is an exceptionally versatile material platform for infrared applications based on high-index, low-loss dielectric metamaterial architectures38, including ultrathin flat optical elements39, sub-diffraction light confinement and waveguiding40, and nonlinear optics41. Low-loss mid-IR metamaterials are also highly sought for enhanced sensing of molecular fingerprints based on strong light confinement42,43. Chalcogenide crystal metamaterials add broadband tunability of the resonances by compositional44 and structural design to the high refractive index. Moreover, as shown here for Bi2Te3, the inverse geometry of nanoslits carved in high-index crystals induces higher-order complex modes outside the dielectric medium, which provide additional pathways to sense changes in the surrounding environment.
In conclusion, chalcogenide TI crystals are a compelling materials platform for photonic applications in the infrared part of the spectrum. We have shown that Bi2Te3 exhibits a strong polarizability with refractive index that exceeds 7 in the 2–10 μm range, larger than conventional dielectric materials that aids strong nanostructure resonances sustained deep into the mid-infrared. The exceptionally high index facilitates formation of circular currents at the surface of the material that may potentially be coupled to spin-polarized topological surface states. This opens the path to new infrared metamaterials combining dielectric, plasmonic, and magnetic properties for applications including molecular fingerprinting, environmental sensing, and integrated mid-IR photonics.
## Methods
### Optical characterization
Bi2Te3 crystals were purchased commercially from 2D Semiconductors Inc. The infrared reflection/transmission spectra of the unstructured TIs crystals and microscopy reflection spectra of structured Bi2Te3 were measured using a Bruker Hyperion microscope coupled to a Bruker Vertex 80v spectrometer. Spectroscopic ellipsometry data were collected using a J.A. Woollam VASE ellipsometer in the 250–1650 nm spectral range over three angles of incidence (30°, 50°, and 70°), and analyzed using the CompleteEASE ellipsometry data analysis program. The refractive index values in the infrared were determined using the experimentally measured near-to-mid-infrared reflection spectrum and the dielectric constants in the UV–near infrared range measured from ellipsometry. This analysis was carried out using the RefFIT program wherein a combination of Tauc–Lorentz, Lorentz, and Drude oscillators were used to model simultaneously, the ellipsometric dielectric constants as well as the infrared reflection spectrum, from which the refractive index of the material in the infrared spectral range was determined. In the Reffit program, the infrared reflection response was modeled using the model ‘Reflectivity of a Film (Epsilon + Mu) on a Substrate (code = −18)’. The parameters of the oscillators describing the material optical function are shown in Table 1.
### Simulations
The optical response of the nanoslit array was simulated using full-wave Maxwell equations solver COMSOL45. The simulations were carried out for a 3D structure using perfect electric/magnetic conductor boundary conditions on the mirror symmetry plane containing the long axis of the slit for electric field polarized perpendicular/parallel to the slit. In the multipole analysis, the number of higher-order modes obtained is dependent on the position of the air–metamaterial interface relative to the z = 0 plane. The optimal position of this interface is chosen such that the differential reflection as well as the field induced in the metamaterial can be quantified with the minimum possible number of modes (in this case 5), and corresponds to z = −1200 nm for the mode contributions shown in Fig. 4f.
## Data availability
Following a period of embargo, the data from this paper can be obtained from the University of Southampton ePrints research repository, https://doi.org/10.5258/SOTON/D1252.
## Code availability
Following a period of embargo, the codes used in this paper can be obtained from the University of Southampton ePrints research repository, https://doi.org/10.5258/SOTON/D1252.
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## Acknowledgements
This research was supported by the Singapore Ministry of Education (Grant no. MOE2016-T3-1-006), the Agency for Science, Technology and Research (Grant no. A*STAR-SERC A18A7b0058), and the Engineering and Physical Sciences Research Council, UK (Grant no. EP/M009122/1).
## Author information
Authors
### Contributions
C.S. and H.N.S.K conceived the idea. H.N.S.K. performed all optical measurements, extracted experimental optical constants, and drafted the manuscript. G.A. fabricated the metamaterial samples and performed COMSOL simulations. J.Y. performed DFT calculations of the bandstructure and optical constants. V.S. performed multipole analysis of the metamaterial response. C.S. and N.I.Z. supervised the work. All authors discussed the results and contributed to the revision of the paper.
### Corresponding authors
Correspondence to H. N. S. Krishnamoorthy or C. Soci.
## Ethics declarations
### Competing interests
The authors declare no competing interests.
Peer review information Nature Communications thanks the anonymous reviewer(s) for their contribution to the peer review of this work.
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Krishnamoorthy, H.N.S., Adamo, G., Yin, J. et al. Infrared dielectric metamaterials from high refractive index chalcogenides. Nat Commun 11, 1692 (2020). https://doi.org/10.1038/s41467-020-15444-0
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• Published: | 2021-10-27 23:47:19 | {"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": 0.6691856980323792, "perplexity": 4223.180090993967}, "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-2021-43/segments/1634323588244.55/warc/CC-MAIN-20211027212831-20211028002831-00640.warc.gz"} |
https://www.nature.com/articles/s41598-017-18171-7?error=cookies_not_supported&code=fbf8b52c-9651-46e3-9c89-c04f63906ea5 | ## Introduction
Ghost imaging was first demonstrated as a manifest of quantum entanglement1 as biphoton source was used. But soon after that it has been demonstrated that the quantum source is not necessary2. Despite of the debate on the physics, GI has been demonstrated further by using pseudothermal light generated by dynamically modulating the illumination laser beam with a spatial light modulator (SLM)3. Although the source changes, the final image are mostly reconstructed using the correlation of signals from the image arm and the reference arm. The ‘reference’ arm now can be physically unexisted as its function can be calculated with the knoledge of the random phase patterns displayed on the SLM. And thus this technique comes with the term of computational ghost imaging (CGI)3. CGI has been used in the study of lensless imaging4, X-ray imaging5,6 imaging in low light7 and and harsh environments8. However, the requirement of large number of measurements is one of the main issues that prevent it from practical applications9,10,11,12. Many efforts have been made to reduce the sampling rate. For example, non-computational13,14,15 and computational methods have been proposed to increase image quality under low sampling rate9,10,11,16,17,18,19,20. In particular, compressive sensing GI (CSGI)10,16,17,18,19 and iterative GI11,20 model the problem of image reconstruction in GI as an optimization problem.
In this letter, we propose a new framework of CGI for high quality image reconstruction under low sampling condition. The proposed method uses deep learning (DL) and thus we term it Ghost imaging using deep learning (GIDL). DL is a machine learning technique for data modelling, and decision making with a neural network trained by a large amount of data21,22. The application of machine learning techniques in optical imaging was first proposed by Horisaki et al.23 who used Support Vector Degression (SVG) architecture to learn the scatterer. In the last two years, we have witnessed the rapid development of the application of deep learning in solving various inverse problems in optical imaging. For example, people have used it in fluorescence lifetime imaging24 phase imaging25,26 and imaging through scattering media27,28 By combining GI and DL, we show in this manuscript that GIDL can also decrease the number of measurements significantly as CSGI, but with much better reconstruction. Also, detailed comparisons between the performances, including the image quality and the noise robustness, of CSGI and GIDL are discussed. Our analysis suggests that the GIDL promises great potentials in applications such as imaging and sensing through harsh environments.
### Numerical Simulation
In ghost imaging, the unknown object, T(x), is illuminated by a sequence of speckle patterns, I m (x), where the subscript integer (m = 1…M) denotes the mth illumination. Then, for the mth speckle, the signal collected by a bucket detector can be written as $${S}_{m}=\int {I}_{m}(x)T(x){\rm{d}}x$$. Traditionally, the image reconstructed using GI is obtained by the correlation of the signal fluctuation δS m with the speckle patterns δI m (x)
$$O(x)=\langle \delta {S}_{m}\delta {I}_{m}\rangle \mathrm{.}$$
(1)
In CGI, the speckle intensities I m (x) are calculated numerically from the phase patterns displayed on the SLM.
It has been demonstrated that the signal-to-noise ratio (SNR) of the image reconstructed in this way is proportional to the measurement ratio, i.e., the ratio between the number of illumination patterns M and the (average) number of speckle in each of these patterns N spec 9,11, namely, β = M/N spec . To show how it works, we take the images (digits ‘0’, ‘3’, ‘5’ and ‘6’) shown in Fig. 1(a) as examples in our simulation study. These ground truth images have 32 × 32 pixels. By using the algorithm defined by Eq. (1) one can reconstruct the images as shown in Fig. 1(b). The reconstructed image set in the columns are corresponding to the sampling ratio β = 1, 0.4 and 0.1, respectively. The results clearly suggest that, as the ratio β decreases from 1 to 0.1, the reconstructed images degrade significantly. The digits can be seen clearly when β = 1, although noise appears. But they are completely corrupted by noise when β = 0.1.
In order to increase the image quality, one usually sets $$\beta \gg 1$$ in the the conventional GI and CGI framework, so that the image acquisition procedure is very time-consuming. One popular solution to decrease the acquisition time is to combine GI and compressive sensing (CS) theory10,16,18. The CS theory allows the object to be recovered precisely from a smaller number measurements if it is sparse in a presentation domain29. So far several frameworks of CSGI have been demonstrated. But high-quality image reconstruction when β is small, i.e., $$M\ll {N}_{spec}$$, is still a challenging problem10,16,18. In CSGI, one actually aims at solving the following inverse problem instead of calculating Eq. (1):
$$\mathop{{\rm{\min }}}\limits_{T}\parallel \nabla T\parallel 1+\frac{u}{2}\parallel {\bf{A}}T-S{\parallel }_{2}^{2},$$
(2)
where T is the discrete gradient of T, u is a weighting factor between the first term and the second term in Eq. (2), which represents the linear model between the image measurement matrix A and the detected signal vector $$S={[{S}_{1},{S}_{2},\ldots ,{S}_{M}]}^{\perp }$$, where the symbol denotes transposition. In this study, we solve Eq. (2) using the open source CS solver TVAL330 and reconstruct the images. The images reconstructed in this way are shown in Fig. 1(c). Because of the sparse constraint, the measurement ratio β for a good reconstruction of the object image can be decreased to 0.1 in our simulation. With a measurement ratio β = 0.4, the object can be recovered nearly precisely. However, the image reconstructed using a measurement ratio 0.1 is not so smooth due to the sparse regulation. This problem always exists in CS when the number of measurements is small29.
In the proposed scheme, the reconstruction is a two-step process. First, the image is reconstructed from the acquired data directly by solving Eq. (1). As shown in Fig. 1(b), the reconstructed image, O, in this way is usually very noisy when β is small. But the deep learning is then involved in the second step. The neural network attempts to reconstruct the object image T from the noisy, or even, corrupted, O. As schematically shown in Figs 2 and 3, the image reconstruction procedures of GIDL is also consist of two steps: training and testing. In the training step, we used a set of 2000 handwritten digits of 32 × 32 pixels in size from the MNIST handwritten digit database31 to train the network in our experiments. Some of the digits are shown in Fig. 3. To train the network, we first reconstructed the images of the digits in the training set according to Eq. (1). Then we fed these images together with the corresponding ground-truth digits into the neural network, and optimize the weighting factors that connect every two nerons in two neighboring hidden layers. In this work, we used a deep neural network (DNN) model with two reshaping layers, three hidden layers and one output layer. For demonstration, we used a very simple model. The reshaping layer at the input end shapes the 32 × 32 input speckle pattern into a 1 × 1024 vector. All the hidden layers and the output layer have 1024 neurons. The activate function of these neurons is rectified linear units (ReLU) which allow for faster and effective training of deep neural architectures on large and complex datasets compared with the sigmoid function32. The reshaping layer at the output end reshapes the 1 × 1024 vector back to the 32 × 32 image. The loss function and optimization in the DNN model is mean square error (MSE) and stochastic gradient descent (SGD). Once the training is finished (after 500 epochs in our experiments), the DNN can be used to reconstruct the object image T from O. The program was implemented using Python version 3.5 and the DNN was implemented using Keras framework based on TensorFlow. The GPU-chip NVIDIA Tesla K20c was used to accelerate the computation.
The simulation results plotted in Fig. 1(d–f) show the reconstructed images using GIDL after 10, 100 and 500 training epochs, respectively, for different measurement ratios β. From these images we can conclude that: First, as the number of iteration (epoch) increases, the DNN model is better optimized. As a consequence, the reconstructed images becomes clearer and brighter. However, when the number of epoch becomes too large, we observed over-fitting of the data, which yield bit error in the reconstructed images as evidenced by the black spots. Second, the GIDL is not very sensitive to β. The MSE values between the images in Fig. 1(f) and the corresponding ground truth images in Fig. 1(a) are all around 0.03 even when β = 0.1. This means that by using GIDL for image reconstruction, one can significantly reduce the number of measurements in the GI acquisition procedure. As a consequence, the time efficiency can be improved without sacrifice of image quality. We note that one can achieve the reduction of measurement by using the CSGI framework as well10. However, when one takes a closed look at the zoomed-in images of any of the reconstructed digits, say, digit ‘6’, in the inset of Fig. 1, it is clearly seen that the image reconstructed using CSGI is not so smooth because of the regulation, while GIDL gives much better reconstruction. This is one major difference between the images reconstructed using GIDL and CSGI.
An additional advantage of GIDL over other GI frameworks is its robustness against noise. Now we provide a theoretical analysis. For a sufficiently large number of photons, the observed signal S m by the single pixel camera can be represented by an additive random Gaussian noise18
$${S}_{m}=\int {I}_{m}(x)T(x){\rm{d}}x+w{\sigma }_{m}{\varepsilon }_{m},$$
(3)
where the variance $${w}^{2}{\sigma }_{m}^{2}={w}^{2}\int {I}_{m}(x)T(x){\rm{d}}x$$, and ε m is the standard Gaussian white noise. In the variance, w represents the noise level. A larger value of w will result in a worse detection image. For speckle field illumination of the same statistics, $${\sigma }_{m}^{2}$$ can be regarded as invariant so that one can replace it by a constant value, $${\sigma }^{2}\simeq \Sigma {\sigma }_{m}^{2}/M$$.
The simulation results are shown in Fig. 4. Figure 4(a) shows the images reconstructed using CSGI under different levels of detection noises. For CSGI, when the noise level w is small (w = 1), the reconstructed images are close to the ground truths, meaning that CSGI can tolerate low level noises. But as the noise increases to a certain level, CSGI fails. The reconstructed image quality is also influenced by the measurement ratio β in CSGI. For the case of w = 50 and β = 0.1, the reconstructed images by CSGI are totally corrupted by noise according to our simulation.
In contrast, GIDL has a much better performance. Figure 4(b) shows the images reconstructed using GIDL under different levels of detection noises. In consist with Fig. 2(d–f), all the images in Fig. 4(b) are smooth as compared to the ones reconstructed using CGSI. The inset shows the zoomed-in images of the digit object ‘5’ reconstructed using CSGI and GIDL for a high noise level and a low measurement ratio (β = 0.1). It is seen that the feature details of the digit ‘5’ is clearly recognizable in the image reconstructed by GIDL while it is not by CSGI. This demonstrates the advantage of GIDL over CSGI for imaging and sensing in harsh environments. Although the sparse constraint can be used to decrease the influence of the random detection noise to a certain level, CSGI can not work for high noise levels in which case the linear model Eq. (2) is affected severely. In contrast, in GIDL, the deep learning architecture takes all the noise into account in building up the network model and fits sharply all the partially reconstructed O to the corresponding object image T. However, when the noise level keep increasing together with the reduction of β, the effect of the additive noise cannot be ignored completely. As shown by the digit images ‘4’ and ‘5’ in Fig. 4(b), the reconstructed image becomes blurred, distorting the feature of the object.
### Experiment
Now we demonstrate the proposed GIDL using some proof-of-principle experiments. We adopted a setup of ghost imaging as the one illustrated in Fig. 5. A laser beam with the wavelength λ = 532 ± 2 nm (Verdi G2 SLM, Coherent, Inc.) was expanded using a 4 f system consisting of lens 1 and lens 2. An SLM 1 (Pluto-Vis, Holoeye Photonics AG) was used to subsequentially display the phase distributions that generate speckle illumination I m , whereas the objects were displayed onto an SLM 2 (Pluto-Vis, Holoeye Photonics AG). The collimated laser beam shone onto SLM 1 and was modulated by the speckle displayed on it. The beam reflected from it was projected onto SLM 2 using the other 4 f system consisting of lens 3 and lens 4. In the setup, P1, P2 and P3 are linear polarizers. P1 and P3 are vertically polarized, and P2 is horizontally polarized, with respect to the laboratory corrdinate, so that to achieve amplitude-only modulation for the SLMs. We displayed different digits from the MNIST database31 on SLM 2, serving as the objects in our experiments. The beam reflected from SLM 2 was collected using a sCMOS camera (Zyla 4.2 PLUS sCMOS, Andor Technology Ltd.) because we do not have a bucket detector. We integrated each acquired intensit patterns to produce S m . This does not affect the experimental results except the frame rate and signal amplification because the integration of a recorded intensity pattern acquired by the camera is proportional to the optical power.
In the experiments, we used the same training set and testing set as in the simulation. 2000 different digit images in the training set were used to train the network. To demonstrate the proposed scheme, we acquired a very small amount of data to reconstruct the testing digits. In order to speed up the convergence of the DNN model, we used the optimization Adam, and an algorithm for first-order gradient-based optimization of stochastic objective functions33, instead of SGD, in the training. The experimental results for β = 0.1 and β = 0.05 are plotted in Fig. 6. In this figure, the images in the first row are the ground truth images of four digits in the testing set. Due to the small β and noise in the system, the reconstructed images using the conventional GI are corrupted by noise as shown in the second row in Fig. 6. One cannot recognize any the visible feature about the target digits from these reconstructed images. However, when we sent them into the trained DNN model, we obtained the corresponding images shown in the third row in Fig. 6. Although they do not resemble exactly the ground truths, the image reconstructed by GIDL contain enough features to recognize. In contrast, the images reconstructed using CSGI are still recognizable at the measurement ratio β = 0.1, but become totally corrupted when β = 0.05. This suggests that GIDL has a better performance than CSGI at low measurement ratio.
## Conclusion
In conclusion, we have demonstrated the novel technique of GIDL using both numerical and optical experiments. We have analyzed the performance of conventional GI, CSGI and GIDL under different noise and measurement ratio conditions, and observed that GIDL has much better performance than the others especially when the measurement ratio β is small. This allows the significant reduction of data acquisition time in ghost imaging, giving a promising solution to this challenges that prohibits GI from practical applications. What’s more, our study opens up new possibility for artificial intellectual techniques in the applications of ghost imaging, and in an even more sense, computational imaging. | 2023-02-07 23:08:50 | {"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": 2, "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": 0.7301807999610901, "perplexity": 777.1286931654693}, "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/1674764500641.25/warc/CC-MAIN-20230207201702-20230207231702-00334.warc.gz"} |
https://solvedlib.com/scenario-1-george-has-gonorrhea-he-does-not-want,282906 | # Scenario 1: George has gonorrhea. He does not want his wife to find out, but he...
###### Question:
Scenario 1:
George has gonorrhea. He does not want his wife to find out, but he wants to protect her from the disease. He asks their family doctor to test his wife without her knowledge. When the wife comes in for her annual Pap smear, the physician tests her for gonorrhea, saying, “I just want to run another test on you to rule out a possibility.” He finds that she has been infected and treats her without telling her the diagnosis. He merely tells her, “I want you to take these antibiotics as a precaution.”
Question 1: Would the physician have violated George’s confidentiality if the physician had told his wife she tested positive for gonorrhea? Why or why not?
Scenario 2:
Dr. Smith has been the Jones’s family doctor for more than 20 years. He is shocked when Mary, the 16-year-old daughter, tests positive for gonorrhea. He is appalled that she has had premarital sex and informs her parents of her condition.
Question 2: Based on the assigned reading, how might Dr. Smith’s actions affect the good of the profession and the good of society?
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https://www.gamedev.net/blogs/entry/1264792-untitled/ | • entries
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# Untitled
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omfg.
Hippo convinced me to sit down and read through the Python docs. I have to say, the Python Tutorial is fucking awesome. I loved it.
but... omfg. Python is scary. Its the embodiment of the phrase "NOTHING IS SACRED". Honestly. Like, if you want to make a class -
>>> class MyClass : def foo(self): print "lol hi" def __init__(self): self.rah = 3; self.foo = 2;
That creates an object. A mutable object. Which you can treat like a ragdoll and do shit with. Like...
>>> rah = MyClass() #create an instance of our class>>> del MyClass #...then delete the class definition
Now this one threw me for a loop. I assumed that our class would now be bork bork, but guess what -
>>> rah.__class__ #returns a valid reference to the class definition>>> rawr = rah.__class__() #creates another instance of it
It took me a while to figure out that, dur dur, objects are reference counted, and that there was still an outstanding reference to the definition so it was still in memory. Hur hur.
Anyway, there were some other things I screwed up, like declaring class members is wonky (you have to do it in the __init__ function, rather than in the class definition) but it makes sense why that is. Had to ask for help on that one, because it was really really confusing. lolz.
But yeah, I think I've got some grip over the basics. Extending/Embedding Python sounds fun as shit, can't wait until I've got my engine bound and running. Hur hur!
NOTHING IS SACRED
Quote:
Original post by Mushu Extending/Embedding Python sounds fun as shit
Right. I guess sticking the fork in the wall socket sounds fun, too. :-/
Now that you mention it.... *grabs fork*
Nothing is sacred, huh? Just you wait until you really get knee-deep in python meta-programming.
...freely mixing class members..runtime inheritance..dynamically building classes from schratch..so much forbidden fruit to taste [wink]
And if you're extending/embedding using C++, I can't recommend boost::python enough, it makes an otherwise painful endeavour quite simple.
Yeah, I decided against looking at the metaprogramming stuff for exactly that reason. I think it would cause my brain to a splode.
I took a look at boost.python, and honestly, its overkill for my purposes. It isn't going to be that hard to implement the stuff I need though, I've already got the prototype for the cross-calls coded and working. Just got to dress it up in a pretty interface and such, then I can work on the shared data representation stuff, and voila done.
<3
## Create an account
Register a new account | 2018-07-22 15:33:36 | {"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": 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": 0.1867523044347763, "perplexity": 4456.832650578381}, "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-2018-30/segments/1531676593302.74/warc/CC-MAIN-20180722135607-20180722155607-00303.warc.gz"} |
https://socratic.org/questions/a-triangle-has-sides-a-b-and-c-sides-a-and-b-are-of-lengths-8-and-1-respectively | # A triangle has sides A, B, and C. Sides A and B are of lengths 8 and 1, respectively, and the angle between A and B is pi/12. What is the length of side C?
Mar 2, 2016
≈ 7.039
#### Explanation:
Given 2 sides and the angle between them , as in this question use the $\textcolor{b l u e}{\text{ Cosine rule }}$
For this triangle this is ${C}^{2} = {A}^{2} + {B}^{2} - \left(2 A B \cos \left(\frac{\pi}{12}\right)\right)$
hence:${C}^{2} = {8}^{2} + {1}^{2} - \left(2 \times 8 \times 1 \cos \left(\frac{\pi}{12}\right)\right)$
= 64 + 1 -( 16 cos(pi/12)) ≈ 49.545
rArr C^2 = 49.545 rArr C = sqrt49.545 ≈ 7.039 | 2019-01-17 16:49:08 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 5, "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": 0.8454126119613647, "perplexity": 830.713369478394}, "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-2019-04/segments/1547583659056.44/warc/CC-MAIN-20190117163938-20190117185938-00004.warc.gz"} |
https://stats.stackexchange.com/questions/106289/stratified-random-sampling-and-its-distribution | # Stratified random sampling and its distribution
I'm learning stratified random sampling and I'm having hard time to solve this problem. consider the following population of six units:
x1=1, x2=2, x3=2, x4=4 x5=4 x6=5
Suppose units 2 3 4 and 5 are in one stratum and units 1 and 6 are in a second stratum. Take a simple random sample of 2 units from the first stratum and a simple random sample of 1 unit from the second stratum. What is the exact distribution of the stratified estimator for the population average?
So, possible mean of sample from first stratum is 2, 3 or 4 and from second stratum is 1 or 5. overall sample mean is
2/3 * 2 + 1/3 * 1 = 5/3
2/2 * 2 + 1/3 * 1 = 7/3
2/3 * 4 + 1/3 * 1 = 3
2/3 * 2 + 1/3 * 5 = 3
2/3 * 3 + 1/3 * 5 = 11/3
2/3 * 4 + 1/3 * 5 = 13/3
and each probability is 1/12, 4/12, 1/12, 1/12, 4/12, 1/12. Now what should I do for finding exact distribution?
• "possible mean of sample from first stratum is 2, 3 or 4 and from second stratum is 1 or 5" -- unless I misunderstood something, both those statements aren't correct. – Glen_b Jul 9 '14 at 8:58 | 2019-08-20 18:59:17 | {"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": 0.6191747188568115, "perplexity": 394.7490613119549}, "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-2019-35/segments/1566027315558.25/warc/CC-MAIN-20190820180442-20190820202442-00304.warc.gz"} |
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The more weights, the better the filter, but there is a greater loss of data. 1€ Filter: A Simple Speed-based Low-pass Filter for Noisy Input in Interactive Systems Géry Casiez, Nicolas Roussel, Daniel Vogel To cite this version: Géry Casiez, Nicolas Roussel, Daniel Vogel. 42 has transfer function 0. filter) audio frequency generator which produces low (bass) audio frequencies from the range of 20Hz to 150Hz. These filters are small in size and compact by design. Key introduced a set of circuits for implementing second-order low-pass, high-pass, and band-pass filter sections. The capacitor passes higher frequencies, causing the voltage across it to be reduced and keeping the output voltage closer to ground. The High pass filter option is an edge-enhancement filter. Build this Universal Band Pass Filter Available for 10, 12, 15, 17, 20, 30, 40, 80 and 160 meters. Free shipping. 2D-LPF - Two Dimensional Low Pass Filter. The major difference between high pass and low pass filter is the range of frequency which they pass. The input matrix data and its 2D FFT filter result, with High-Pass filter type and Gaussian window. Schumann H, Koppenhöfer E, Wiese H. In the infrared region of the spectrum, bandpass filters are frequently used for gas analysis applications. Chebyshev Pi Low Pass Filter Calculator Enter Fc, Zo, r and n (all four are required) to calculate filter component values. Assuming you have mastered the design of low pass LC filters we will now proceed to the design of a high pass filters. the same controls, inputs and outputs. As you should expect for a low-pass filter, the output is a smooth rise to the steady state level. Low Pass Filters Signal Conditioning are available at Mouser Electronics. Low-pass FIR Filter Specifications. Low Pass Filter Sets designed for amateur Radio segments in bands 160, 80, 60/40, 30/20, 17/15, 12/10, 6 Meters. Ask Question Asked 8 years, 3 months ago. Look at a new filter that can give you that extra boost. SKU: #200-120-2 Category: Low Pass Filters. There is no low pass filter in Spectrum mode, but the 200kHz bandwidth limit under analog options is there. Corner frequency -3 dB cutoff frequencies -3dB bandwidth calculate filter center frequency band pass quality factor Q factor band pass filter formula 3 dB bandwidth in octaves vibration frequency conversion - octave 3 dB bandwidth calculator corner frequency half-power frequency EQ equalizer bandpass filter - Eberhard Sengpiel sengpielaudio. Low pass filter with cutoff pi*Wc radians:. Some basic uses are the removal of DC offsets, removal of low-frequency noise, as a part of a pass-band filter, among many others. In other words, low-frequency signals go through much easier and with less resistance and high-frequency signals have a much harder getting through, which is why it's a low pass filter. Adams design is a 132 MHz - 142 MHz Butterworth bandpass filter which gives about 35 dB attenuation outside of the pass band. Low Pass Filters. Now as we increase the size of 1, blurring would be. A band-pass filter is one that will transmit a selected band of frequencies with substantially no loss, but that will attenuate all frequencies either higher or lower than the desired band. High-Pass Filter. 904A Low Pass Filter. There was a request for the 200 MHz Low-pass filter, so here it is, maybe somebody else may find it useful in his project. I’m sure this could be written in other software languages as well, just don’t ask me how. Another is low-frequency ground roll. The early oil filters used on cars were low performance and not really effective. 40m, 7 - 7. Define low-pass filter. An interval of several weeks should be expected for delivery. Each channel is capable of digitizing high-frequency signals at up to 100,000 samples per second. The graph is unable to plot below 1Hz at the moment. If we recall from section 3, the impedance of an inductor is: hence if the frequency is 0 (i. Once the input is given to the circuit of the LPF, then the resistance will give a stable obstacle, however, the capacitor position will have an effect on the output signal. 3 is more efficient and gives better results than the RC filter shown in Fig. Thus, Low pass FIR filter is implemented in MATLAB using its functions, using FDA tool and also implemented using Verilog. 40m 7MHz High power band-pass filter 4kW High power 40m 7-7. 2 KW Low Pass Filter for 160-6 Meters A color copy of this document is located at http://w6pql. A low-pass filter is one which does not affect low frequencies and rejects high frequencies. Low Pass Filter. What do these figures tell you about the nature of this filter circuit (whether it is a low-pass or a high-pass filter), and also about the definition of cutoff frequency (also referred to as f−3dB)? file 00646 Question 17 Filter circuits don’t just attenuate signals, they also shift the phase of signals. Assuming you have mastered the design of low pass LC filters we will now proceed to the design of a high pass filters. The filter is then applied by performing pointwise multiplication with the transform matrix and the rectangular filter that cancels out high frequencies if it is a high-pass filter or low frequencies if a low-pass filter. The input matrix data and its 2D FFT filter result, with High-Pass filter type and Gaussian window. This is important because otherwise it is a high pass filter. 저역통과 필터, RC Low pass filter OP AMP - 1's order & 2's order RC filter :: 네이버 블로그. This variant is also called RC bandpass. The low=pass filter lets us filter out the high=frequency components of a signal, letting us focus on the low frequencies we may be interested in. Kits are available for 16 bands 2200, 600, 160, 80, 60, 40, 30, 20, 17, 15, 12, 10, 6, 4, 2m and 222MHz. filter () method constructs a new jQuery object from a subset of the matching. Figure 19-2 shows an example of what is called a single pole low-pass filter. The assumption is made here that the frequency components of the signal fall predominantly at low frequencies and those of the noise fall predominantly at high frequencies. Antonyms for Low pass filter. This would be important if one band was low in output due to interference from reflected harmonic energy, while the others were OK (keep in. 9 to 28 MHz with little attenuation. Untuk sinyal berupa data-data digital dapat difilter dengan melakukan operasi matematika seperti konvolusi. Here k is Boltzman’s constant and T = 293. Active Band Stop Filter; Active Low Pass Filter. Low-Pass Filter: Opposite in nature to a high-pass filter, a low-pass filter is a filter that allows signals with a frequency lower than the cut-off frequency (the frequency at which the output voltage is 70. 2D-LPF - Two Dimensional Low Pass Filter. Then, the values of R2 and C2 required for the low pass stage to give a cut-off frequency of 30kHz are, R = 10kΩ and C = 530pF. Rectify and digital low pass filter. The lack of low-pass filter can be considered a feature, so it's something that some camera vendors hype. The cut-off frequency of second order low pass filter is given as. 00 The LPF2000-FM designed for FM radio transmitter. 0-2KW 144-148 MHZ Low pass filter coupler LPF LDMOS BLF - $49. They should identify one circuit arrangement as a high pass filter and the other as a low pass filter. The function giving the gain of a filter at every frequency is called the amplitude response (or magnitude frequency response). The Values Of The Components Are R = 110 Q And C 0. The default is "low" if wc is a scalar and "bandpass" if wc is a two-element vector. For example: The low pass filter transfer function can be calculated by using the following formula if we know the values of the resistor and capacitor in the circuit. Low-pass filters are less likely to be specified merely with a lower-bound period-of-interest cutoff; oftentimes low-pass filters are constructed deliberately to have the same shape as a canonical HRF, to help highlight signal with that shape (as per the matched-filter theorem). [5] [a] A second order low pass IIR filter with a 3-db cut off frequency at s = 0. HF Low Pass Filter LPF 2 kW with Excellent Suppressions of all harmonics LPF30-2000W. DCI low pass filters are constructed with seven elements, with coaxial inductors and Teflon capacitors. It too uses the cutoff point to determine the frequency at which filtering will occur but rather than letting low frequencies through to be heard, it lets high frequencies through instead. This low pass filter will convert the PWM signal into a voltage level. from 1KHz to 110GHz including Coaxial, Drop in, Surface Mount,etc. Notch filter A notch filter'' rejects a narrow frequency band and leaves the rest of the spectrum little changed. 5 ppm) RFPRO (500 MHz and 1 GHz) Low Noise RF / Clock Sources. 01 99152831101 Filler Swr Swa Porsche Boxster 981 2. Figure 1-16A. large #8 awg inductors. HF Low Pass Filter LPF30-2000W FM 88-108MHz and 2m 144-146MHz Attenuation. The cutoff frequency for a low-pass filter is that frequency at which the output (load) voltage equals 70. The response of the filter is displayed on graphs, showing Bode diagram, Nyquist diagram, Impulse response and Step response. Just like RC low-pass and high-pass circuits. Band-reject windowed-sinc FIR filter (more info in How to Create Simple Band-Pass and Band-Reject Filters). is the voltage at the output. Ultra Low Phase Noise. Connector Type: Type "N". Sometimes with handle but for mains only). A scalar used only when a band-pass filter is desired. Ideally, I would like to run an FFT, truncate the signal to only include low frequency content then run an inverse FFT. A Converse icon from the 1970's remastered for today with superior craftsmanship and premium materials. Operational amplifiers or op-amps provide a very effective means of creating active low pass filters providing high levels of performance. For switching filters applied powerful relays with a current capacity 16A. 8-30 Mhz Ham Amateur Radio BLF LDMOS. This means you should not use analog=True in the call to butter, and you should use scipy. After opening the Project file or entering the band data, hit the "Design" button, which will bring up a plot of the frequency response: Low-pass FIR Filter Frequency Response. The RFAP Harmonic Low Pass Filter is offered in a variety of frequency bands compatible with. They don't absolutely pass some frequencies and absolutely reject others. 2kW FM Low Pass Filter-Teflon 2000 watt low pass filter86-110MHz9th order Chebyshev typology. The coils are wire wound (home-brew) 65nH. A robust low-pass (fig ») filter can be made of 6 mm² thick tinned blank earth wire that is used for earthing metal objects in the house. ±14 KHz bandwidth. Sets the boost or attenuation for frequency bands, and the per-octave slope of the band-pass filters. Variable Low-Pass Filter Bass Boost; KAC-9106D. This article is complemented by a Filter Design tool that allows you to create your own custom versions of the example filter that is shown below, and download the resulting filter coefficients. • T avg > 90% 235 – 505. Fair warning - I'm not an analog electronics pundit, nor am I well versed in C. Richard Patrick is working on new music. The fact that our products are manufactured by Anatech Electronics, gives us the flexibility to modify electrically or mechanically any electrical parameters, or mechanical style to match and fit that specific requirement. TTE Filters is a pioneering leader in the design, development, and manufacture of high quality RF and microwave filters. AVX offers a full line of Low Pass and Broadband Filters for frequencies from 500 KHz to 26 GHz. Ideal Low Pass Filter Impulse Response. Back in October we released a broadcast FM bandstop filter for removing strong signals in the 88 - 108 MHz region. low pass A low-pass filter is a filter that passes low-frequency signals but attenuates (reduces the amplitude of) signals with frequencies higher than the cutoff frequency. Model the filter in MatLab, 3. The next most-common filter type is a high-pass filter (HPF), which does precisely the inverse of a low-pass filter. The response of the filter is displayed on graphs, showing Bode diagram, Nyquist diagram, Impulse response and Step response. The simplest low pass filters consist of a resistor and capacitor but more sophisticated low pass filters have a combination of series inductors and parallel capacitors. This voltage level is higher when the PWM duty cycle is closer to 0%, and lower when the duty cycle is closer to 100%. TV-42-LP 1605 Low Pass Filter, 100 watts continuous TV-52-20LP 52 OHM Low Pass Filter TV-52-40LP 1 KW Low Pass Filter TV-5500-LP 1609 Low Pass Filter, 1 Kw to 30 MHz, 100 watts continuous on 6 meters TV-72-HP 72 OHM 50 MHZ High Pass Filter TV-75-HP 1610 High Pass Filter, 75 ohms, TV coax TV-CB-LP Citizen Band Low Pass. These simple circuits can give you a foundational understanding of how filters work so you can build more-complex filters. 1 x 10-6s = 1. My attempt at filtering is shown in the next two columnns. Signal attenuations of the low-pass Chebyshev filters can be expressed as. In other words, low-frequency signals go through much easier and with less resistance and high-frequency signals have a much harder getting through, which is why it's a low pass filter. By setting the filter at the correct level, it will reduces some of the boominess that inexperienced car audio people actually like, but high end autoaudiophiles laugh at. Fairview Microwave's bandpass filters were developed for use in various applications including GPS, ISM, RFID and Wi-Fi systems and operate in several bands, some as low as 824 MHz and some as high as 5. Frequency range: 144-148 MHzPower: 0-2KW Impedence: 50 ohmsLoss: Typ 0. Figure 2 A Sallen-Key low pass filter showing all noise sources. • Laser Wavelength = 244 nm. The cut-off, or transition frequency (f t) is always between 0 and 0. On the contrary, low pass filter is an electronic circuit which allows the low frequency to pass through it and blocks the high-frequency signal. A low-pass filter is one which does not affect low frequencies and rejects high frequencies. Low-pass filters are commonly used to implement antialias filters in data-acquisition systems. The circuit is an AC voltage divider with an output which falls off at high frequencies at the rate of 6 dB per octave. High-Pass Filter. 1 x 10-6s = 1. The notch output is a little unique in that it has a “balance” control that lets you shift between all low pass and all high pass. Parameters. The kit uses a high-quality double-sided PCB with silk-screen, solder-mask and through-hole plating. To summarize, two functions are presented that return a vector of FIR filter coefficients: firceqrip and firgr. The Moog Moogerfooger Low Pass Filter contains 2 complete modular functions: a voltage-controlled lowpass filter and an envelope follower. • Go to Section 2, and design a low pass filter for the high end of the lower band. It can be used in applications where the cycletime will be constant and where it is dynamic. This article is complemented by a Filter Design tool that allows you to create your own custom versions of the example filter that is shown below, and download the resulting filter coefficients. The High pass filter option is an edge-enhancement filter. You might argue that a high pass filter also passes the medium band, but we are following the convention that is used in Eagleware's Genesys simulation tool. THIS FILTER DUMPS THE REFLECTED ENERGY INSTEAD OF REFLECTING IT BACK AT THE AMP. Nilai-nilai pengurangan untuk frekuensi berbeda-beda untuk tiap-tiap filter ini. de in English and German language. After entering your required passband cut-off frequency (Fco) and choosing your other requirements, you can generate a data sheet with a valid model number, price, mechanical drawings and a summary of all your specifications. Low pass filters are made using resistor and capacitor combination (RC) for filtering out up to 100Khz but for the rest 100khz-300khz Resistor, Capacitor and Inductor is used (RLC). The gain falls as the frequency increase. Finished Low Pass Filter installation. The * actual amount of attenuation for each frequency varies from filter to filter. A band-reject filter is a parallel combination of low-pass and high-pass filters. 12 dB insertion loss maximum; 0. Of itself, this is a recipe for high harmonic output and a well designed low pass filter is essential. When ordering, please specify the Band(s) you want in an EMAIL or in the COMMENTS section of the PAYPAL order Specs: Values taken from Year 2000 ARRL Handbook, page 30. AM-2: The AM-2 filter has a cutoff at 520 KHz. The notch output is a little unique in that it has a “balance” control that lets you shift between all low pass and all high pass. Input/Output Impedance: 50 ohm. A few comments: The Nyquist frequency is half the sampling rate. Each band can be configured for correct signal levels • On-board attenuators set the correct signal levels for the detector diodes. The circuit shown in Figure 1 is known as the unity gain low. However, low pass and high pass filters do not have centre frequency. THIS FILTER DUMPS THE REFLECTED ENERGY INSTEAD OF REFLECTING IT BACK AT THE AMP. We can also produce custom filters at wavelengths up to 14µm. Low Pass Filter Sets designed for amateur Radio segments in bands 160, 80, 60/40, 30/20, 17/15, 12/10, 6 Meters. The XM46SB is the same filter, but in a small metal utility cabinet. You can turn the low-pass filter for the subwoofer output on or off. A Converse icon from the 1970's remastered for today with superior craftsmanship and premium materials. The second-order low pass also consists of two components. • For the single supply case only: • Calculate Cin = Cout = 100 to 1000 times C1 in the low pass filter section (not critical): _____ DONE. Many years OEM experience for clients mainly from North America and Europe. A coltage controlled voltage source might be used to prevent any loading of the output under test. This page provides a 'Java' experiment which you can use to explore its properties when the applied signal is a sinewave. Low-pass FIR Filter Specifications. The first use of a full flow oil filter on mass production vehicles occurred in. Now as we increase the size of 1, blurring would be. Low Pass Filters from Analog Devices are specifically designed to reject higher frequency noise and unwanted signals while allowing desired signals to pass through. Series RC Filter Determine The Expression For The Transfer Function [email protected]) = Expression In The Form L. The output frequency is rounded to the second decimal place. Model: Low Pass Filter TVI-2K - Workman Electronic Products: Material: Metal case : Shape: Tablemodel, Mantel/Midget/Compact up to 14" width, but not a Portable (See power data. Of itself, this is a recipe for high harmonic output and a well designed low pass filter is essential. The 12db slope on a low-pass filter limits higher-end frequencies but lets more of them through than the 24db filter. The magnitude response varies in the pass-band in the range from to 1. We eliminate excessive In-Band ripples due to out-of-band reflected energies. T106-6 Toroid Cores. Attenuation is more than 90 dB between 90 and 300 MHz. Cutoff Freq - Sets the cutoff frequency for the lowpass/bandpass/highpass filters. While extreme details are lost in the process, the problem of moiré is completely resolved. The T network low pass filter has one capacitor between the RF line and. 8-30 Mhz Ham Amateur Radio BLF LDMOS. Low Pass Filters. Here k is Boltzman’s constant and T = 293. A series LR circuit is shown below: If we consider the frequency response of this circuit we will see that it is a low pass filter. Presently I open. In this tutorial we will look at the simplest type, a passive two component RC low pass filter. The input consists of the design specifications for the desired Butterworh analog filter. 160 meter High Power Band-Pass filter 4 kW Top Band - 160 meter 1. 1€ Filter: A Simple Speed-based Low-pass Filter for Noisy Input in Interactive Systems Géry Casiez, Nicolas Roussel, Daniel Vogel To cite this version: Géry Casiez, Nicolas Roussel, Daniel Vogel. In other words, low-frequency signals go through much easier and with less resistance and high-frequency signals have a much harder getting through, which is why it's a low pass filter. Lowpass Filter Design provides an overview on designing lowpass filters with DSP System Toolbox. If a low frequency is applied to the input, part of the voltage across the high pass filter will drop. 2 KW Low Pass Filter for 160-6 Meters (rev 6) A full color assembly guide for this kit is located at http://www. A few comments: The Nyquist frequency is half the sampling rate. This is really obvious if you play something with a lot of harmonics. 1 Low-pass and high-pass filters The preliminary step to obtain the coefficients for a second-order filter is the calculation of. Rectify and digital low pass filter. If the final input argument is "s" design an analog Laplace space filter. Our RF lowpass filters have very low insertion loss at 1 dB. 7% of the input, and vice versa. The box holds two channels. An image is sharpened when contrast is enhanced between adjoining areas with little variation in brightness or darkness (see Sharpening an Image for more detailed information). FIGURE 1: If a programmable low-pass filter is used in the application circuit, it can be placed after the analog multiplexer. From capacitor theory, the charge in the capacitor is , where. Quartz Crystals. The Low Pass Filter. There is no low pass filter in Spectrum mode, but the 200kHz bandwidth limit under analog options is there. Where n is the order or number of stages. 2KW TARA 20000 Watt Car Amplifier. For switching filters applied powerful relays with a current capacity 16A. Once you have designed your filter you can apply it using the function filter or filtfilt. fc -> Low Pass cut-off frequency, in MHz fs1, fs2-> Stop band refection frequency, in MHz Rej1 and Rej2 -> Stop band rejection at fs1 and fs2, in dB. The low insertion loss of this filters makes them well suited for use at power levels as low as 10 watts on up to 2000 watts! These units are constructed using PTFE laminate for capacitors and silver-plated coil wire!. AMSOIL Ea Bypass Oil Filters provide maximum filtration protection against wear and oil contamination. This variant is also called RC bandpass. It's convenient to think in terms of the signals in the figure as being volts and amperes per square root Hertz rather than of volts and amperes. Collecting suitable capacitors for high power is not easy. The frequency component above that certain value will be suppressed to almost zero. Add to favorites Remove from favorites. The Par BCST-LPF is a 5 pole elliptic low pass filter designed to eliminate AM broadcast problems in the 0 to 500 kHz range. The sinc function (normalized, hence the $$\pi$$'s, as is customary in signal processing), is defined as. We eliminate excessive In-Band ripples due to out-of-band reflected energies. For this example, the input signal is a step function. I have to make an Active Low Pass Filter of 1st Order like this : The problem is that I have many errors when I try to run the simulation with my actual model I don't know with block should I use to make a good model and measure the gain (dB) depending the frequency (Hz). Given a jQuery object that represents a set of DOM elements, the. The STANDS4 Network A low-pass filter is a filter that passes low-frequency signals and attenuates signals with frequencies higher than the cutoff frequency. I wanted to use the Raspberry Pi SDR TX capabilities using the IO pins to generate RF. Realization is simple ,very easy and repetitive. Fruity Filter. The gain falls as the frequency increase. What is BiFilter? BiFilter is a stereo multi-mode filter with a selection of 47 different sounding filter types. Richard Patrick is working on new music. Rectify and digital low pass filter. The filter is designed around a cut off frequency, and only allows the low frequencies to pass through. 00 Shipping. An audio pass filter attenuates an entire range of frequencies. The exact frequency response of the filter depends on the filter design. The default is "low" if wc is a scalar and "bandpass" if wc is a two-element vector. Where n is the order or number of stages. HIGH PASS FILTERS. The input matrix data and its 2D FFT filter result, with High-Pass filter type and Gaussian window. • The transfer function of an ideal low pass filter where D(u,v) : the distance from point (u,v) to. Pass-band attenuation determines the maximum allowable attenuation in the pass-band. BAND PASS: is a combination of a high pass capacitor and low pass coil that creates a mid band with both the lows and highs blocked out. Since capacitive reactance decreases with frequency, the RC circuit shown discriminates against high frequencies. TTE Filters is a pioneering leader in the design, development, and manufacture of high quality RF and microwave filters. 2 KW Low Pass Filter for 160-6 Meters A color copy of this document is located at http://w6pql. A max = 1 since unity gain. Its continuous-time transfer function (Fourier Transform) is$1/(1+j\omega RC)$and in in this Wikipedia article you can find a sample code of how to realize it for discrete-time samples, and references to the literature. The filters go between the linear and the antenna and reduce the broadband noise and harmonics generated in the linear. Notice the difference in the gain outside of the pass band. More than 10 years producing experience in low pass emi filters and obbligato gold premium audio capacitors. The LOW filter option is an averaging (smoothing) filter. The ideal low-pass filter response can be approximated by a rational function approximation scheme such as the Butterworth response. so select the one for you. In stereo mode, the right and left sides can be filtered independently or. Is there an easier/better way to filter this data using a low pass filter that I am missing? Thanks for your help!. Each band can be configured for correct signal levels • On-board attenuators set the correct signal levels for the detector diodes. The housing has an SO-239 jack for input and one for output (accepts standard PL259 plugs). 21 or Best Offer; Free Shipping. This is a high-pass filter - high-frequency signals pass through virtually unchanged, but low-frequency signals are attenuated. High-Pass Filter. A low-pass filter is an electronic filter that passes the frequency component of a signal below a certain value (cutoff frequency). What is BiFilter? BiFilter is a stereo multi-mode filter with a selection of 47 different sounding filter types. 8 V Is Fed Into The Filter. DCI low pass filters are constructed with seven elements, with coaxial inductors and Teflon capacitors. The cost is the same as the BCFM bandstop filter at$14. For the low pass case, we know its transfer function is, H(z) = 1 + z 1; which means that, there exists a zero at z=-1. These low-pass filters are designed to be driven by a low-impedance source and terminated directly into high-impedance equipment. Be the first to review "1MHz Low Pass Filter" Cancel reply. 7% of the input, and vice versa. frequencies with a low-pass filter and to cut off bass frequencies with a high-pass filter. Kuhn March 9, 2013, rev. Passive band pass filter 1st order. Band Pass Filter Board for Low-level stages are. The circuit diagram of an active low pass filter is shown in the following figure − We know that the electric network, which is connected to the non-inverting terminal of an op-amp is a passive low pass filter. 저역통과 필터, RC Low pass filter OP AMP - 1's order & 2's order RC filter :: 네이버 블로그. If the filter's clock is running at 1 MHz, t=40 means 40µs. It can also be decided if the filter is supposed to be a low pass filter (LPF) or a high pass filter (HPF). 3 nm in the UV/VIS to as wide as 4 µm band pass in the IR. Low Pass Filters: Low Pass filters allow low frequencies to pass below a selected crossover frequency, filtering out all frequencies above it. 1€ Filter: A Simple Speed-based Low-pass Filter for Noisy Input in Interactive Systems. If a filter passes high frequencies and rejects low frequencies, then it is a high-pass filter. The fact that our products are manufactured by Anatech Electronics, gives us the flexibility to modify electrically or mechanically any electrical parameters, or mechanical style to match and fit that specific requirement. Hand-crafted by User:Vadmium in a text editor. In addition, it graphs the bode plot for magnitude in decibels and the phase in radians. The size is 4. The simplest and classic low pass filter is the RC filter. Parameters. 2kW HF Low Pass Filter LPF30-2000W 6m 50MHz, 50. The input data type may be BYTE, INTEGER*2, INTEGER*4, or REAL*4. -23dB return loss; -25. An ideal filter, whether low pass, high pass, or band pass will have a minimal amount of loss within the pass band. The filter simply connects in-line between your transmitter and antenna. A low pass filter does just what the name implies, it passes low frequencies (HF) while blocking higher frequencies (VHF) and above. It is a 4 pole filter, so its slope is 24dB/octave. Tuning: The easiest way is to just tune for maximum forward power, minute changes may be made on 80 meters by expanded or compressing the turns on the cores for best power. Classification of filter systems by regeneration method The majority of regenerating (as opposed to disposable, Figure 1) diesel filter systems utilize thermal regeneration, during which the particulates are oxidized to produce gaseous products. Note : This is the specification chart for Low pass filter please fill in the appropriate boxes to state your requirments. For example: The low pass filter transfer function can be calculated by using the following formula if we know the values of the resistor and capacitor in the circuit. UIY offers a broad range of RF Circulator,RF Isolator,Amplifier,Attenuator,Termination,Filter,Combiner,etc. Nov10 by kirit89. 2 kw, 2 - 30 MHz. With cutoff frequencies ranging from 1 kHz to 50 MHz, these filters are ideal for blocking unwanted signals and noise at specific frequencies. Bessel low pass filters, therefore, provide an optimum square wave transmission behavior. High Pass, Low Pass Transmitting and Receiving Filters. For a first-order low-pass filter, v OUT always lags v IN by some phase angle betweeen 0 and 90°. The coils are wire wound (home-brew) 65nH. The phase shift on the sub is probably an all pass filter that shifts the phase of the incoming signal by set amounts (user selectable presets in your sub's case) at the crossover frequency between the sub and the other speakers in your setup. New technology isn't always cheap. The red signal is the raw signal and the green signal is the filtered signal. Thus, Low pass FIR filter is implemented in MATLAB using its functions, using FDA tool and also implemented using Verilog. 7% of the input, and vice versa. It has a cutoff frequency of 30 MHz, but passes RF from 1. In this section, we explore two methods of inverse filtering - a thresholding method and an iterative method. An interval of several weeks should be expected for delivery. Ultra low loss Teflon PCB; tightly controlled dielectric constant. Active 5 years, 1 month ago. These integrated low pass filters feature. BAND PASS: is a combination of a high pass capacitor and low pass coil that creates a mid band with both the lows and highs blocked out. Input NoData cells may receive a value in the output if the Ignore NoData in calculations option is checked, provided at least one cell within the filter neighborhood has a valid value. Information and translations of Low-pass filter in the most comprehensive dictionary definitions resource on the web. Measures 11 inches long x 3 inches wide. lowpass_rc_bode. There are several different kinds of RF filters at Future Electronics. The A-105 is very similar to the A-122 that is made with a CEM chip. The filter of is low passage with variable frequency of cutting off. 높은 주파수 대역은 통과하기 어렵고 감쇠한다라고 볼 수 있고 High Cut Filter 라고도 불립니다 - Low-pass Filter의 주파수 응답, 위상 응답 그래프. Ideally, I would like to run an FFT, truncate the signal to only include low frequency content then run an inverse FFT. Fig 17: Low-Pass, second order, RC circuit Better filtering results are obtained if we cascade 2 or more filters--commonly, up to 7. 21 or Best Offer; Free Shipping. Delivery Thu, Jun 4 - Thu, Jun 18. The frequency response plot shows that the filter is slightly better than required, because its response is between the lines. Here k is Boltzman's. Ideal Low pass Filters (ILPFs) • The simplest low pass filter is a filter that “cuts off” all high-frequency components of the Fourier transform that are at a distance greater than a specified distance D0 from the origin of the transform. lowpass_rc_bode. Alligator Technologies is a technology company dedicated to providing services that meet all your data acquisition filter needs. 9th order Chebyshev typology. It has a cutoff frequency of 30 MHz, but passes RF from 1. Low Pass - Spectrum Seeing previous impulse response, it is not intuitively straight forward to gure out whether it is low pass, band pass, or high pass. Attenuation is more than 90 dB between 90 and 300 MHz. You might argue that a high pass filter also passes the medium band, but we are following the convention that is used in Eagleware's Genesys simulation tool. This approach is very fast compared with solving Maxwell’s equations in 3D. The filter is then applied by performing pointwise multiplication with the transform matrix and the rectangular filter that cancels out high frequencies if it is a high-pass filter or low frequencies if a low-pass filter. The amount of DC power will depend on how large the signal will be amplified at the output. 3 nm in the UV/VIS to as wide as 4 µm band pass in the IR. The filters used in audio applications are much more complex than the example provided here. Kits are available for 16 bands 2200, 600, 160, 80, 60, 40, 30, 20, 17, 15, 12, 10, 6, 4, 2m and 222MHz. RL circuits consist of resistor and inductor. This recursive filter uses just two coefficients, a 0 = 0. ±14 KHz bandwidth. Sony's kept with the 'One-with, one-without' option for its new full-frame mirror-less camera, the A7 and A7R, but Nikon's D5300 is low-pass filter-free and so is the Ricoh Pentax K-3. Max Power 500W Low-Pass Filter. 35 Chapter 4 Image Enhancement in the Frequency Domain 4. Resonance - Boosts a frequency band near the cutoff level, to create a sound 'sharpening' special effect. A digital image is composed of a group of pixels. So the idea is to pass the accelerometer signals through a low-pass filter and the gyroscope signals through a high-pass filter and combine them to give the final rate. While it will only pass lower frequencies and filter the spikes what the ECU sees will be less than the O2 sensor sends, that may be a downside waiting for 5 RC Time Constants. For best results, use 2. The cutoff frequency of the filter is set to 2Hz. Two Dimensional Low Pass Filter listed as 2D-LPF. A high pass filter tends to retain the high frequency information within an image while reducing the low frequency information. Schematic below for FM Broadcast Lowpass Filter 88-108 MHz. With simple RC circuits, you can build first-order RC low-pass (LPF) and high-pass filters (HPF). If the input voltage is Vin, the output voltage Vout is expressed as Vout = Vin × R2 R1 + R2 This is a simple equation, but when the resistors are numbered differently, or if they are replaced by some. low-pass filter synonyms, low-pass filter pronunciation, low-pass filter translation, English dictionary definition of low-pass filter. Several low pass filter circuits for subwoofer application are presented all over the net however this one is an upgraded example. From capacitor theory, the charge in the capacitor is , where. A low-pass filter (LPF) is a filter that passes signals with a frequency lower than a selected cutoff frequency and attenuates signals with frequencies higher than the cutoff frequency. This low pass filter will convert the PWM signal into a voltage level. The specific arrangement of RC components in an active filter determine whether the net- work is a low pass, high pass, band pass or band reject filter. to ground one of 1-7 contacts. A low-pass filter allows for easy passage of low-frequency signals from source to load, and difficult passage of high-frequency signals. Band-reject windowed-sinc FIR filter (more info in How to Create Simple Band-Pass and Band-Reject Filters). Setting the filter higher will allow more sound to pass into the sub. large #8 awg inductors. Where n is the order or number of stages. The simple bandpass consists of an RC low-pass and a RC high-pass, each 1st order, so two resistors and two capacitors. Second-Harmonic-Optimized Low-Pass Filters QST February 1999, pp 44-46. # ##### form Low pass filter files comment Directory of source sound files text sound_directory c:\temp\ sentence Sound_file_extension. At low (relative to the-3dB point)4 frequencies, the transfer function is close to 1, while at high values of frequency, the output voltage is attenuated and will be quite small relative to the input voltage. They have the equivalent of a centre frequency known as the natural resonant frequency and if you think about a series L and C making a notch filter: - This becomes a 2nd order high pass filter if the output is taken from the. Many surplus reference oscillators are appearing on the market today at such places as E-Bay and your local surplus shops. LPF1500 allows you to filter the power to 1500W PEP. Avens Signal Equipment Offers Electronic Filters, Frequency Filters, Highpass and Lowpass Filters, Bandpass Filters, Miniature Filtures, Programmable Filters, Anti Aliasing Filters, Signal Conditioning Filters, Signal Conditioning Instruments. For ongoing replies, application and updated information for this Wiki, please see @Stumbo's TB High Pass Filter (HPF) and Low Pass Filter (LPF) Mega Thread TERMS The terms High Pass Filter and Low Pass Filter are somewhat unintuitive. low-pass filter A filter that removes high-frequency waves from a sample, allowing only those below a specified frequency to pass. The simplest and classic low pass filter is the RC filter. The T network low pass filter has one capacitor between the RF line and. Example: Solnik et al. 8-30 Mhz Ham Amateur Radio BLF LDMOS. T106-2 Toroid Cores. 2 High-Pass Filter. If we talk about high pass filter, so it is a circuit which allows the high frequency to pass through it while it will block low frequencies. Note : This is the specification chart for Low pass filter please fill in the appropriate boxes to state your requirments. It can be used in applications where the cycletime will be constant and where it is dynamic. Untuk rangkaian induktif sendiri hanya dibuat menggunakan sebuah induktor dan beban, sedangkan untuk rangkaian kapasitif hanya menggunakan dua buah komponen, yaitu resistor dan kapasitor. 18 7 Element Chebyshev Low-Pass filter Designs for 50 ohm Impedance. I'm mainly writing this post to save my recent learning for the future and hopefully help some others who are just as lost as I was. Each band can be configured for correct signal levels • On-board attenuators set the correct signal levels for the detector diodes. The filter is then applied by performing pointwise multiplication with the transform matrix and the rectangular filter that cancels out high frequencies if it is a high-pass filter or low frequencies if a low-pass filter. The Par BCST-LPF is a 5 pole elliptic low pass filter designed to eliminate AM broadcast problems in the 0 to 500 kHz range. 19" rack mount. 180831368 Si838x Product Revision For The Low Pass Debounce Filter Operation Impact on Form, Fit, Function, Quality, Reliability The debounce filter function has changed to match the published data sheet. The filter is sometimes called a high-cut filter, or treble-cut filter in audio. 높은 주파수 대역은 통과하기 어렵고 감쇠한다라고 볼 수 있고 High Cut Filter 라고도 불립니다 - Low-pass Filter의 주파수 응답, 위상 응답 그래프. Thus a filter symbol with the botton and middle sine waves "blocked" indicates a high-pass filter. Unit 1 The Green, Fountain Street Macclesfield, SK10 1JN, UK. by Hank Zumbahlen Download PDF A previous article 1 examined the relationship of the filter phase to the topology of its implementation. an LPF need not be an integrator, but an integrator is an example of a low-pass filter since the gain at lower frequencies is more than the gain at higher frequencies. EQing needs a critical ear, and knowing what pass filters do and how they work is vital for improving skills. Active 3 years ago. # ##### form Low pass filter files comment Directory of source sound files text sound_directory c:\temp\ sentence Sound_file_extension. Add to cart. • For the single supply case only: • Calculate Cin = Cout = 100 to 1000 times C1 in the low pass filter section (not critical): _____ DONE. We start with the group delay function T(W) of an all-pass filter, which is usually defined as d dw 7(w) = - - [arg A(e/")]. 40m, 7 - 7. Crystek manufactures a broad line of frequency control devices. T106-6 Toroid Cores. Maximum input power is 1000 watts PEP. FSensor implements an IIR single-pole low-pass filter. Freq - Cutoff/bandpass/bandcut frequency (depending on the filter type). The size is 4. i bought this on ebay from r3kbo. this is the current DOM element. 1 Standard induction motors 10 1. Notify me when this item is nearly out of stock. Theoretically, the ideal (i. 50 ohms and. However the low pass filter I am using produces a smoothed set of rotations but the forward vector sometimes flips around violently (takes the long-way round). Above: A QRP 20-meter CWAZ low-pass filter installed on a piece of perf board in a small (1×27/ 8×2-inch, HWD) plastic box available from Farnell (Ref 4), order #645-680, $1. Parameters. Assuming you have mastered the design of low pass LC filters we will now proceed to the design of a high pass filters. A band-pass filter is one that will transmit a selected band of frequencies with substantially no loss, but that will attenuate all frequencies either higher or lower than the desired band. The Moog Moogerfooger Low Pass Filter contains 2 complete modular functions: a voltage-controlled lowpass filter and an envelope follower. A band-pass filter can be formed by cascading a high-pass filter and a low-pass filter. The v2 board is a good improvement. 2kW Low Pass Filter for LDMOS power amplifiers covers 160m up to 6m band in 7 filter banks. , “6th order, high pass filter at 20 Hz”, for surface EMG from vastus lateralis. I have also included the plot of the original ECG signal. These low-pass filters are designed to be driven by a low-impedance source and terminated directly into high-impedance equipment. Here I want to describe how to build a low-pass filter for 145 MHz as required after power amplifiers to prevent harmonics to be emitted by the antenna. English: A low-pass filter. Inductive low-pass filters insert an inductor in series with the load; capacitive low-pass filters insert a resistor in series and a capacitor in parallel with the load. The estimated power handling capability is 2 KW and the passband loss is about 0. All filters and capacitors are delivered by air or express (DHL/FedEx) OEM is available. This is "LOW PASS FILTER RC" by Ali on Vimeo, the home for high quality videos and the people who love them. The inside diameter of the coils is 2 cm and the wire ends are 1 cm. It is built in a die-cast box, and has been tested up to 80W input power. IN Input image. These filters are provided in C, L and Pi configurations with metric threading available… LP13-LP24 S2(& S2,0 F,. The simplest band-pass filter can be made by combining the first order low pass and high pass filters that we just looked at. 1 x 10-6s = 1. Updated 02 Jun 2014. The cost is the same as the BCFM bandstop filter at$14. When an input is passed through a low-pass filter, the output is delayed by some fraction. Such filters can easily be made using a slight variation on the all-pass filter. R/C low-pass filter component selector. 5 - 4 MHz bandpass filters for B. The output frequency is rounded to the second decimal place. An audio pass filter attenuates an entire range of frequencies. Here is the circuit in this image: RC Low Pass Filter. f (-3dB) = fc √ (2 (1/n) - 1). -23dB return loss; -25dB typical. If an active filter allows (passes) only low frequency components and rejects (blocks) all other high frequency components, then it is called as an active low pass filter. Band Pass Filters, BPF, Power up to 8 kW, Low loss Receiving filters. The low=pass filter lets us filter out the high=frequency components of a signal, letting us focus on the low frequencies we may be interested in. Wavelets Decomposition low-pass filter (copy. Delivery Thu, Jun 4 - Thu, Jun 18. The second-order low pass also consists of two components. T106-6 Toroid Cores. The bandwidth of membrane current measurements in potential-clamped Ranvier nodes is limited by the low-pass filter properties of the internodes. The LOW filter option is an averaging (smoothing) filter. The inside diameter of the coils is 2 cm and the wire ends are 1 cm. 1 May 18, 2008) Type Poles 3 db cutoff frequency I/O Impedance in ohms This web based application allows the user to. finding the roots of D(s). Series RC Filter Determine The Expression For The Transfer Function [email protected]) = Expression In The Form L. The cutoff frequency for a low-pass filter is that frequency at which the output (load) voltage equals 70. Test the design in the Lab. Calculate the amount. 1 word related to low-pass filter: filter. 2kW Low Pass Filter for LDMOS power amplifiers covers 160m up to 6m band in 7 filter banks. 30 mhz, RF Limited. To apply the filters, the discrete Fourier transform of the image is taken and then changed through a series of steps. He's also posted a write up documenting the. Figure 1-16B. The signal and filtered data was generated using the example code below LowPassFilterExampleImage1. 75 mW drives to 1500 watts out. Each band can be configured for correct signal levels • On-board attenuators set the correct signal levels for the detector diodes. 2 IEC low voltage motor ranges 10 1. Example 2: 2000 ÷ 200 inches = 1000 square inches of 40" X 24" filter. In a first order (6dB per octave) filter, this consist of a coil in series with a loudspeaker. Low Pass and Bandpass SMA Coaxial Filters from Fairview Microwave Fairview Microwave’s bandpass filters were developed for use in various applications including GPS, ISM, RFID and Wi-Fi systems and operate in several bands, some as low as 824 MHz and some as high as 5. Mouser offers inventory, pricing, & datasheets for Low Pass Filters SMD/SMT Signal Conditioning. One application of this type of Butterworth low pass filter is anti-aliasing. Frequency Cutoff: 14. Low-pass filters with defected ground structure (DGS) [10-15] have been received increased attention in recent years for their unique features such as sharp cut-off frequency response, compact size and good performance in both the pass band and the stop band. The gain of a passive low pass filter is always less than or equal to 1. 3 Complete product offering 16 2. , perfect) low-pass filter is the sinc filter. Product Identification Si8380S-IU Si8380S-IUR Si8380PS-IU Si8380PS-IUR Si8380PM-IU Si8380PM-IUR. Optical bandpass filters covering 200 nm to 16 µm with bandwidths ranging from 0. 9 ms 1/(2π RC ) = 145 Hz. Band-Pass Filter: uses a combination of a High Pass Crossover and a Low Pass Crossover to allow a range of frequencies above and below two chosen crossover frequencies (one High Pass and one Low Pass) to pass through to. Ultra low loss Teflon PCB; tightly controlled dielectric constant. Use this utility to calculate the Transfer Function for filters at a given frequency or values of L and R. 50 ohms and. (Although, again, thinking of the high-pass filter as a frequency dependent voltage divider may be more strictly correct. But I would like to alter its frequency response so that it cuts off frequencies higher than 20khz. Low pass filter with cutoff pi*Wc radians:. • Go to Section 3, and design a high pass filter for the low end of the upper band. Find many great new & used options and get the best deals for LOW PASS FILTER PT-1000 LP at the best online prices at eBay! Free shipping for many products! Find many great new & used options and get the best deals for LOW PASS FILTER PT-1000 LP at the best online prices at eBay! 0-2KW 144 MHz Low pass filter coupler LPF LDMOS BLF MOSFET. This low pass filter directional coupler provides a DC voltage at the forward and reflect iWin LPF2000 2kW Low Pass Filter ₤ 82. Generally an input signal is applied to this series combination of resistor and non. The specific arrangement of RC components in an active filter determine whether the net- work is a low pass, high pass, band pass or band reject filter. Standard IR Long Pass Filters. 5MHz, 51MHz and 54MHz Attenuation. DF3000 Low pass filter, 4kw pep, 1 kw rms. The filter of is low passage with variable frequency of cutting off. 2 High-Pass Filter. Low-pass filter definition is - an electric-circuit filter that transmits only frequencies below a prescribed frequency limit. I've used the freeware tool "RFSim99" to design the following filter: It has a cutoff frequency of about 150 MHz. Passive low pass 2nd order. Viewed 7k times 4. Low-Pass Filter Design Example • Design a Low-Pass Filter with cut-off frequency of 900 MHz and a stop band attenuation of 18 dB @1. There are many pieces of equipment that can generate EMI, variable frequency drives included. The circuit shown in Figure 1 is known as the unity gain low. A low-pass filter is one which does not affect low frequencies and rejects high frequencies. , LTD Customized production,RF & Microwave cavity band-pass filter, band-stop filter/Notch Filter, high-pass filter, low-pass filter, power splitters, combiner, duplexer, coaxial attenuator, coaxial load, circulator and isolator. 95 USD including free international air shipping. The filters are 8-pole, 6-zero elliptic-type with 115 dB per octave rolloff, 0. We offer a wide range of filters and our products are found all over the world.
bya1r6mznba7, wl08babvplyj, dss12xlg98, 13mt53sgt8ac4x, lyxherod5jw6c, i489zmvexq6o, 7ht0xt2pzjn62u, sv3gi9nvsiq4r3, vrwvtgzl59, l9l35auvxhx8b, sf46pvefa76u, ga5abo2od4mr7l, uvnxe8p8mxhw5fj, q5gx455u7p, iu8b9wkkkyyrsdk, b38x5755u1ncpq, 4oo7wz5htoc3i8, 121rkq8m1uvk, ib5gztwz7z, 4ei73j2i27dkhx, is9duqz1bu4f, 5xq801a3kjbe, uds03fgkmd7a, e3wqq80oprysx, ojh7y535tnj, hclm7rfsff, 5ejo1pbi2191jl7, 7i71v1sdl3z | 2020-07-04 14:47:58 | {"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": 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": 0.33580201864242554, "perplexity": 2323.7392052913297}, "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-2020-29/segments/1593655886178.40/warc/CC-MAIN-20200704135515-20200704165515-00370.warc.gz"} |
https://www.gradesaver.com/textbooks/science/physics/college-physics-4th-edition/chapter-6-problems-page-228/25 | ## College Physics (4th Edition)
Published by McGraw-Hill Education
# Chapter 6 - Problems - Page 228: 25
#### Answer
We can rank the points in order of mechanical energy, from greatest to least: $A=B=C=D=E$
#### Work Step by Step
By conservation of energy, the mechanical energy is constant for all points in the motion. That is, the sum of the gravitational potential energy and the kinetic energy is constant for all points in the motion. If the skier moves to a higher vertical position, the gravitational potential energy increases, and the kinetic energy decreases by the same amount. If the skier moves to a lower vertical position, the gravitational potential energy decreases, and the kinetic energy increases by the same amount. The mechanical energy is constant throughout the motion. We can rank the points in order of mechanical energy, from greatest to least: $A=B=C=D=E$
After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback. | 2019-11-22 15:23:26 | {"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": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6879753470420837, "perplexity": 372.3463650990425}, "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-2019-47/segments/1573496671363.79/warc/CC-MAIN-20191122143547-20191122172547-00196.warc.gz"} |
https://www.physicsforums.com/threads/can-group-have-a-volume.643551/ | # Can group have a volume ?
1. Oct 13, 2012
### raopeng
Can group have a "volume"?
For example, SL(n, R) is a subgroup in a linear matrix space with det A = 1. So can this equation represent a certain "region" in the n-dimensional linear space and therefore that it has a "volume"?
2. Oct 13, 2012
### Erland
Re: Can group have a "volume"?
If so, it would be in n^2-space, not n-space, because this is the dimension of the matrix space. But it would be a subset of an n^2-1-dimensional manifold in this space, thus having volume 0.
3. Oct 13, 2012
### raopeng
Re: Can group have a "volume"?
Thank you. Didn't think it through carefully...
4. Oct 13, 2012
### Bacle2
Re: Can group have a "volume"?
But your region may have non-zero k-volume for k< n^2 . The topology on subgroups
I'm familiar with turns a matrix [ai] into a point in R^(n^2) by [ai]<-->[a11,a12
,...ann] . This is a region in R^(n^2), and, while, as Erland said, it has zero
n^2-volume, it may have non-zero k-volume for k<n^2 .
5. Oct 13, 2012
### Ben Niehoff
Re: Can group have a "volume"?
In fact, SL(n,R) is non-compact, so it has infinite volume.
The compact Lie groups all have finite volume, which you can compute without too much difficulty. Constructing a volume form is similar to the construction of a metric (i.e., the Cartan-Killing metric). Then you just integrate this over the group.
Note: As a subset of R^n^2, most groups have measure zero. What I mean is the intrinsic volume of the group manifold, which is k-dimensional (and k < n^2).
6. Oct 13, 2012
### A. Bahat
Re: Can group have a "volume"?
There is a related notion of what's called a 'Haar measure' on a topological group, which allows one to define an integral over the group.
7. Oct 13, 2012
### mathwonk
Re: Can group have a "volume"?
excellent point! presumably Haar measure is a translation invariant measure.
integration is about averaging. thus an integration on a group allows one to average
the action of a group on a set. so even if volume is not the main idea, integration is still important.
8. Oct 14, 2012
### A. Bahat
Re: Can group have a "volume"?
Yes, the key property of Haar measure is translation-invariance. So this generalizes averaging over the elements of a finite group by summing as well as integrating over some familiar topological group like the reals. Plus, the Haar integral allows us to do harmonic analysis on locally compact abelian groups (or even non-abelian groups, for that matter, but this is more complicated) which is really cool. But I barely know anything about this, so I should stop now...
9. Oct 15, 2012
### raopeng
Re: Can group have a "volume"?
And I am still a bit confused about how to construct a Killing metrics of, say, SU(2) for integration. And also how can we write the defining region of the group for the integration?
I really appreciate all the help, but some of them are quite beyond my current level. So I have to consider SO(n) in an easier way:
Define Killing form as $\langle A, A \rangle = tr(AA^{T})=tr(E)=n$. So for SO(n) the region is a sphere with radius √n? And employing the general formula for n^2-sphere volume I obtain: V = $\frac{\pi^{n^2/2}}{\gamma (n^2/2 + 1)}n^{n^2/2}$. but it looks a bit ridiculous...
10. Oct 15, 2012
### raopeng
Re: Can group have a "volume"?
I think for SU(n) it is similar, except the dimension is now 2n^2. | 2018-02-24 10:44:14 | {"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": 0.8496736288070679, "perplexity": 1147.2368967681527}, "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-2018-09/segments/1518891815544.79/warc/CC-MAIN-20180224092906-20180224112906-00597.warc.gz"} |
https://www.shaalaa.com/question-bank-solutions/i-define-couple-ii-state-si-unit-moment-couple-turning-effect-of-a-force_70156 | # (I) Define Couple. (Ii) State the S.I. Unit of Moment of Couple. - Physics
Short Note
(i) Define couple.
(ii) State the S.I. unit of moment of couple.
#### Solution
(i) Two equal and opposite forces acting prependicular and separated by some distance d is called couple
A couple causaes pure rotation.
(ii) SI unit : N m
Concept: Turning Effect of a Force
Is there an error in this question or solution?
Share | 2022-05-19 12:02:50 | {"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": 0.8963598012924194, "perplexity": 6233.907682995283}, "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/1652662527626.15/warc/CC-MAIN-20220519105247-20220519135247-00422.warc.gz"} |
http://mechanicaldesign.asmedigitalcollection.asme.org/article.aspx?articleid=1449251 | 0
GUEST EDITORIAL
# Continuous Improvement Processes: Why They do not Work and How to Fix ThemOPEN ACCESS
[+] Author and Article Information
George A. Hazelrigg
For example, see and , 2004, “ Are Pair Wise Comparisons Reliable?,” Res. Eng. Design, 15, pp. 62–71.
J. Mech. Des 129(2), 138-139 (Feb 01, 2007) (2 pages) doi:10.1115/1.2406094 History:
Continuous improvement processes are all around us during the engineering design process. Indeed, any meeting with a focus on review and improvement of a design may be viewed as part of a continuous improvement process. Yet many of us often look at the changes that result and wonder if they really are for the good. We can certainly see continuous degradation processes working in many areas of our lives—television and radio, the evolution of web sites, the tax laws—and we could all add to the list. The question is, are we part of the solution or part of the problem?
To get to the root of the issue, we need to understand the mathematics of a continuous improvement process. Let us say a group of three engineers are working on a product design, and decide that it might be good to make some changes. The three are quite happy with the design as it stands, but feel it could be better. So they go over the product, and a number of changes are suggested. Then they go through the proposed changes one by one, and agree that many should be made. With each proposed change, the group agrees by some mechanism, such as majority vote, that the change should either be made or not. Clearly, if the design starts off good, and a series of changes are made, each of which improves the product, it should be better at the end of the process. But, not so fast. How many of you have gone through just such a process only to wind up with a design that you think is quite a bit worse than it was at the start? I surely have. It might surprise you to find that it could well be the case that everyone thinks the design is worse for the changes, even while the group agreed that each individual change improved it. How can this happen?
Problems arise because there are competing issues that the designers are trying to cope with. For example, these could include issues of reliability, manufacturing, and customer appeal. For the sake of simplicity here, let us assume that there are no technical issues. The designers are in complete agreement on the technical performance of the product. Now let us take a series of three changes, $A$, $B$, and $C$, on the status quo, $S$, which may address the competing issues. So the possible end states can be designated $S$ (status quo with no changes), $SA$ ($S$ modified by change $A$), $SB$, $SAB$, $SC$, $SAC$, $SBC$, and $SABC$, depending upon which changes the group adopts. Let us say that the preference orderings on these changes by three designers are the following:
$Jan:SAB>SA>S>SB>SC>SAC>SBC>SABCPat:SA>S>SB>SC>SBC>SAC>SABC>SABMichael:SB>S>SC>SCB>SAC>SABC>SAB>SA$
Where, for example, $SA>S$ would be read $SA$ is preferred to $S$, which is to say that the designer feels that product $SA$ is better than product $S$. From these preferences, it is easy to see that all three designers have a rather strong preference for $S$ over $SABC$. Now let us see how they would choose by simple majority vote. By a vote of 2:1, the group would adopt change $A$ over the status quo. Then they would consider adding change $B$. Change $B$ (from state $SA$ to state $SAB$) is also adopted by a vote of 2:1. And finally, change $C$, leading to the final state $SABC$, is adopted over $SAB$ by a vote of 2:1. So the group moves from $S$ to $SABC$ even though everyone in the group would agree that the product is worse for these changes. What is more insidious is that everyone in the group will walk away from the process thinking that it was fair and honest and that, somehow, the product must actually be better. And, of course, the process will not stop with only three changes. It will go on through changes $D$, $E$, $F$, and so on, in what we could appropriately call a continuous degradation process.
Some people will be quick to argue that I have done something wrong here. If only I used a different selection process, a different form of voting, whatever. But I can assure you that I have not made a mistake, nor would a different selection process fix this mess. There is a proof (Arrow's Impossibility Theorem) that it is impossible to find a selection process that will prevent these problems from arising. Some might argue that I cooked the example by picking a rare pathological case. But, once you understand how selection processes work, you will see that it is harder to cook the preferences to get a good outcome than a bad one, such as this example. Further, as more and more “improvements” are offered, or as more people get involved in the process, the more likely it is that the product will get worse for the changes. And the likelihood that a continuous improvement process will morph into a continuous degradation process gets higher with every change. If you question this, I refer you to the extensive literature on the subject.
The implications of these mathematics are profound. Our continuous improvement processes are often making things worse rather than better. I give you the following challenge: step back and look at the continuous improvement processes in which you have been involved, not just for product design, and ask yourself if the current state is really better than the starting state. As you take this moment of introspection, be sure to recognize the possibility that the process is likely to have been a degradation process. Can we fix this?
The first step toward fixing any problem is recognizing that there is a problem. How could it be that a process that has received so much attention by so many people for so long could be so wrong? Maybe you just do not believe me. If not, solutions I would offer are superfluous. Take time to reflect on this. Nothing is as simple as it might seem. Processes developed in the absence of a sound theoretical base, and I can assure you that there is no sound base underpinning continuous improvement processes, just are not likely to be valid. Nature provides us with too many things that can go wrong.
What we know from game theory, which is the mathematics of group behavior, is that group selection processes are unstable in the sense that the outcome of a group process is as much dependent (perhaps even more so) upon the rules of the interaction between the members of the group as it is upon the preferences or desires of the individuals who comprise the group. Just how unstable can these processes be?
Suppose, in our example, just as Pat was about to suggest change $A$, she dropped her pencil and, while bending down to pick it up, Michael suggests change $B$. Of course, the proposal to make change $B$ will be defeated as $S$ is preferred 2:1. Now Pat, pencil in hand, suggests change $A$, which is adopted, leading to state $SA$. Next, change $C$ is proposed. But state $SA$ is preferred to state $SAC$, so change $C$ is defeated and the final state is $SA$. $SA$ results rather than $SABC$ simply because Pat dropped her pencil. This is indeed the sort of instability that occurs in every such meeting. The results are changed by a sneeze, a cough, a pencil drop. And the changes are big. It certainly scares me to think that “improvements” hinge on such trivial events as a pencil drop, or just by who speaks first.
So how do we fix it? We have to address the two fundamental problems with continuous improvement processes: (1) they are most often group processes, which have inherent issues, and (2) they are continuous, that is, they use sequential decision making, which also have inherent problems. The more we can move away from group processes and continuous processes, the better off we are.
Let us look at the continuous aspect of continuous improvement first. A quick glance back at our example shows that we got into a lot of trouble by considering the changes sequentially. If we had merely listed the eight possible end states and chosen from them, things would have been quite different. Different, yes, but right, no. Nonetheless, you should do your best to minimize sequential decision making. But there are problems, and we will come back to them shortly.
A big problem is that of choosing among the end states. No method of selection can be guaranteed to be free of trouble. But some methods are better than others. And the best method, that is, the method that allows the least offensive outcomes, is the Borda method. In the Borda method, each person in the group first rank orders all possible outcomes and then assigns a score to each, beginning with 0 for the least preferred outcome, 1 for the next least preferred, then 2, 3, and so on. These scores are added for all persons in the group to get the group score. If we had done that for our design example, $S$ would have a score of 17, $SA$ a score of 13, and $SABC$ a score of 3, and we would have concluded that we should leave the product alone. The Borda method does not guarantee selection of the “best” alternative, but it has the rather nice property that it will not select the worst alternative (as we see from the example, other methods can).
Of course, rank ordering the alternatives gets to be a problem as the number of alternatives grows. Note that, for three suggested changes to the product there were 8 (that is $23$) end states. For only 10 changes ($210=1,024$), it becomes pretty much impossible to rank order the end states. The only practical way around this is to find an index (a real scalar) such that all the end states can be mapped onto the real number line, preferably by computer, in such a way that they precisely reflect the preferences of each of the persons in the group. And still, we are left with the problem of aggregating the resulting scores, and the vagaries associated with such aggregations. In the end, it may help to appoint a “dictator,” namely, a person in the group who does all the decision making on which changes to adopt. It is only in this way that the decision making relative to such changes can be made rational, and only in this way that the accumulated changes can be guaranteed of actually making things better—albeit (necessarily) only in the eyes of the dictator. But at least they will be better in the view of that person.
Unfortunately, continuous improvement processes are both continuous and group processes, and there is no way to get around this or the problems that come with such processes. But I can suggest a procedure that can keep you from doing utterly foolish things. First, set a baseline, such as state $S$ in our example above. Second, make a change only if the group, by whatever selection method chosen, determines that the change results in an improvement over both the current state, $Si$, and the baseline state. This way, no change will be accepted that results in a degradation over the baseline state. Third, whenever, but only whenever every member of the group feels that a new state, $Sj$, is a better state than the baseline state, $S$, update the baseline state to state $Sj$, and use the updated baseline state in successive tests. This double test on every change does not assure continuous improvement. Indeed, the group may well make a series of changes such that they would agree that state $Si+2$ or $Si+3$ is worse than state $Si$, but at least it would not be worse than state $S$ (note that the change to state $Si+1$ is made because it is deemed an improvement over $Si$).
The scary thing is that we have only two choices—to leave a product alone or to change it. If we want it better, we have to change it. Yet, if we make more than one change, we risk actually making the product worse. And we see that mathematics is not so kind as to allow our simple product improvement processes to work. Nor should you try to fix such processes by adding complexity to the decision process, namely adding nuances like fancy or multilayered voting methods, colored hats, reflexive processes, toss-the-ball talking, and so on. Any attempt to fix this through complexity merely adds opportunity for things to go south faster. In the end, you want to keep your processes as simple as possible, with as few steps as possible, and with as few people involved as possible. If you want to have a continuous improvement process that has any degree of reliability, you should follow these rules:
• Set a baseline state against which you will compare changes.
• Group changes into bundles as much as possible.
• Use the Borda method to select changes.
• Use a double test—elect to make a change only if it results in a better state than both the current state and the baseline state.
• Update the baseline state upon unanimous consent of the group.
So I have not solved all your problems. But at least now you know about one that you probably did not think you had, and you have some tools to stay out of deep trouble.
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Topic Collections | 2017-12-17 13:55:12 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 64, "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": 0.5690987706184387, "perplexity": 457.9389375036138}, "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/1512948596051.82/warc/CC-MAIN-20171217132751-20171217154751-00746.warc.gz"} |
https://planetmath.org/characteristic | # characteristic
Let $(F,+,\cdot)$ be a field. The characteristic $\operatorname{Char}(F)$ of $F$ is commonly given by one of three equivalent definitions:
• if there is some positive integer $n$ for which the result of adding any element to itself $n$ times yields $0$, then the characteristic of the field is the least such $n$. Otherwise, $\operatorname{Char}(F)$ is defined to be $0$.
• if $f:\mathbb{Z}\to F$ is defined by $f(n)=n\cdot 1$ then $\operatorname{Char}(F)$ is the least strictly positive generator of $\operatorname{ker}(f)$ if $\operatorname{ker}(f)\neq\{0\}$; otherwise it is $0$.
• if $K$ is the prime subfield of $F$, then $\operatorname{Char}(F)$ is the size of $K$ if this is finite, and $0$ otherwise.
Note that the first definition also applies to arbitrary rings, and not just to fields.
The characteristic of a field (or more generally an integral domain) is always prime. For if the characteristic of $F$ were composite, say $mn$ for $m,n>1$, then in particular $mn$ would equal zero. Then either $m$ would be zero or $n$ would be zero, so the characteristic of $F$ would actually be smaller than $mn$, contradicting the minimality condition.
Title characteristic Characteristic 2013-03-22 12:05:01 2013-03-22 12:05:01 Mathprof (13753) Mathprof (13753) 16 Mathprof (13753) Definition msc 12E99 | 2020-07-15 01:46:22 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 28, "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": 0.9784884452819824, "perplexity": 193.35285528128986}, "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-2020-29/segments/1593657154789.95/warc/CC-MAIN-20200715003838-20200715033838-00100.warc.gz"} |
https://byjus.com/free-ias-prep/upsc-exam-comprehensive-news-analysis-jan13-2019/ | 13 Jan 2019: UPSC Exam Comprehensive News Analysis
A. GS1 Related
B. GS2 Related
POLITY AND GOVERNANCE
1.Farmers under KALIA scheme to get money by January 26
C. GS3 Related
ENVIRONEMENT
1.‘70% towns along Ganga let out garbage into the river’
HEALTH
1.Artificial Intelligence (AI)
D. GS4 Related
E. Editorials
1.Is there a renewed quota debate?” (10 per cent reservation in government jobs and educational institutions to “economically weaker” sections in the General category.)
2.The lowdown on HAL’s order book
F. Tidbits
1.‘Mental health apps have gaps in information’
2.Quota Bill gets President’s assent, becomes law
G. Prelims Facts
1. ‘Monkey fever’ cases hit 62 in Shivamogga
H. UPSC Prelims Practice Questions
I. UPSC Mains Practice Questions
A. GS1 Related
Nothing here for today!!!
B. GS2 Related
1. Farmers under KALIA scheme to get money by January 26
Context
• Beneficiaries who have enrolled under the Krushak Assistance for Livelihood and Income Augmentation (KALIA) scheme in the first phase will receive monetary assistance by January 26, Odisha’s Cooperation Minister S.N. Patro said on Saturday.
KALIA scheme
• KALIA is progressive, inclusive and will make a direct attack on poverty by way of massive investment in the agriculture sector and making benefits reach the most needy through direct benefit transfer (DBT) mode.
• KALIA scheme covers the cultivators, loanee, as well as non-loanee farmers, share croppers and landless agricultural labourers. It also specifically takes care of vulnerable agricultural families identified through gram panchayats and crop loans are made available at 0% interest.
• All the small and marginal farmers of the State (92% cultivators) will be covered under the scheme. An amount of ₹10,000 per family at the rate of ₹5,000 for Kharif and Rabi shall be provided as financial assistance for taking up cultivation.
• The farmers will have complete independence to take up interventions as per their needs. This component is not linked to extent of land owned and will greatly benefit share croppers and actual cultivators most of whom own very small extent of land.
• Under this initiative, 10 lakh landless households will be supported with a unit cost of ₹12,500 to take up activities like small goat rearing units, mini layer units, duck units, fishery kits for fishermen and women, mushroom cultivation and bee keeping.
• As regards financial assistance to vulnerable agriculture households and landless labourers, an annual financial assistance of ₹10,000 per household will be provided to take care of their sustenance. Deserving families will be identified and selected by gram panchayats. About 10 lakh households will be covered over two years.
• Further, life insurance cover of ₹2 lakh and additional personal accident cover of ₹2 lakh will be provided to both cultivators and agricultural labourers covering about 57 lakh households.
C. GS3 Related
1. ‘70% towns along Ganga let out garbage into the river’
Context
• Four-and-a-half years after the Centre launched its flagship Namami Gange programme to clean up the Ganga, a government- commissioned assessment has found that 66 towns and cities along the river still have nullahs or drains flowing directly into the Ganga. Almost 85% of these nullahs do not even have screens set up to stop garbage from entering the river.
• Of the 92 towns surveyed, 72 still have old or legacy dump sites on the ghats. Only 19 towns have a municipal solid waste plant, according to an assessment done by the Quality Council of India (QCI).
Namami Gange Programme
• Namami Gange programme was launched as a mission to achieve the target of cleaning river Ganga in an effective manner with the unceasing involvement of all stakeholders, especially five major Ganga basin States – Uttarakhand, Uttar Pradesh, Jharkhand, Bihar and West Bengal.
• The programme envisages: River Surface Cleaning, Sewerage Treatment Infrastructure, River Front Development, Bio-Diversity, Afforestation and Public Awareness.
• The program would be implemented by the National Mission for Clean Ganga (NMCG), and its state counterpart organizations i.e., State Program Management Groups (SPMGs).
• In order to improve implementation, a three-tier mechanism has been proposed for project monitoring comprising of a) High level task force chaired by Cabinet Secretary assisted by NMCG at national level, b) State level committee chaired by Chief Secretary assisted by SPMG at state level and c) District level committee chaired by the District Magistrate.
• The program emphasizes on improved coordination mechanisms between various Ministries/Agencies of Central and State governments.
1. Artificial Intelligence (AI)
Context
• A study in 2018 by the Centre for Internet & Society India claimed that artificial intelligence (AI) could help add \$957 billion to the Indian economy by 2035.
A note on artificial intelligence
• From the early days of human civilization efforts have been made to replace human hands with machines to make lives easier. Human beings then started looking beyond machines, developing robots and other advanced technologies that could just read the human mind and do the required work.
• Intelligence is the ability to take variables from our senses and to process certain decisions using the brain. Artificial intelligence helps a machine in doing the same. Such a system has a receptor, sensors (to pick data from environment), a memory (that tells what to do depending on what signal it gets), and then it takes a decision that will communicate to another device.
• The term Artificial Intelligence was first coined by American scientist John McCarthy in 1955. Over the years improvement in technology, algorithms, computing power and storage power has made the concept realistic.
• This can be termed as the fourth Industrial Revolution. Each cycle of the Industrial Revolution changes the lives of the common man in unpredictable ways. This has already helped in improvements like in healthcare making surgeries of eye easier, predicting floods and droughts, etc.
• The partnership between think tank in India NITI Aayog (National Institute for Transforming India) with Google to develop India’s artificial intelligence ecosystem will help to improve healthcare, education, agriculture, transportation, develop innovative governance systems and improve overall economic productivity. This will also help in promoting entrepreneurs associated with it, research in the field in premier institutions like IITs and providing crash course to students across India.
• Development in such advanced technologies affects employment opportunities also as machines can do the work of many labours. Whether they can compete with a human brain is also a question.
• India is already making progress in computing technologies with its Digital India campaign in the recent past. Now taking a step towards Artificial Intelligence brings with it various new applications. But the drawbacks of using them are also predicted and how it will design our future is to be seen.
D. GS4 Related
Nothing here for today!!!
E. Editorials
1. Is there a renewed quota debate?” (10 per cent reservation in government jobs and educational institutions to “economically weaker” sections in the General category.)
Note to Students:
• In the following sections, we cover the recent development where the Lok Sabha passed a landmark bill providing 10 per cent reservation in government jobs and educational institutions to “economically weaker” sections in the General category.
• We combine the perspectives from three articles, namely, “Quota questions” that was published by The Hindu on 9th January, 2019, “A solution in search of a problem” that was published by The Hindu on 11th January, 2019, and “is there a renewed quota debate?” that was published by The Hindu on 13th January, 2019.
Context:
• The Constitution (124th Amendment) Bill 2019 provides 10 per cent reservation in jobs and educational institutions to the economically weaker sections in the general category.
• President Ram Nath Kovind on 12th January, 2019 gave his assent to this bill.
Current Status:
• A nine-judge Constitutional Bench of the Supreme Court had in the Indira Sawhney case capped the reservation at 50%.
• It had struck down a provision that earmarked 10% for the economically backward on the ground that economic criteria cannot be the sole basis to determine backwardness.
• The Constitution provides only for reservation based on social and educational backwardness, such additional quota would need legislative action, including Constitutional amendments.
• Experts point out that Articles 15 and 16 of the Constitution would need to be amended for implementation of the decision.
124th Constitution Amendment Bill
• It will provide 10% reservation to economically backward sections in the general category.
• The Bill will also cover those from the Muslim, Sikh, Christian, Buddhist and other minority communities.
• The quota will be over and above the existing 50% reservation to Scheduled Castes, Scheduled Tribes and Other Backward Classes (OBC).
• Those who have an annual salary of less than Rs. 8 lakh per year and possess less than 5 acres of land will be able to avail reservation in educational institutions and jobs.
• The quota will be available to only those economically backward poor people not availing the benefit of reservation as of now, who have a residential house below 1,000 square feet, a residential plot below 100 square yards in a notified municipality, residential plot below 200 square yards in non-notified municipality area.
Concerns
• If the Supreme Court indeed agrees to lift the 50% cap, all States of India can extend the quantum of reservation and “upper castes” will stand to lose in State services and merit will be the casualty .
• If the Supreme Court rejects the idea of breaching the 50% cap, Economically Weaker Section (EWS) quotas can be provided only by eating into the SC, ST and OBC quota pie, which will have social and political implications.
It violates Equality Principle
• There have been issues where the quotas were increased by State governments exceeding the 50% limit thereby offending the equality norm.
• In Nagaraj (2006), a Constitution Bench ruled that equality is part of the basic structure of the Constitution.
• It said the 50% ceiling, among other things, was a constitutional requirement without which the structure of equality of opportunity would collapse. There has been a string of judgments against reservations that breach the 50% limit.
Lack of data on representation
• Another question is whether reservations can go to a section that is already adequately represented in public employment.
• It is not clear if the government has quantifiable data to show that people from lower income groups are under-represented in its service.
• Reservations have been traditionally provided to undo historical injustice and social exclusion suffered over a period of time, and the question is whether they should be extended to those with social and educational capital solely on the basis of what they earn.
A Closer Look:
• Finally, it is important to note that if the EWS is treated as a category just like the SC, ST and OBC, a large chunk of general category candidates will apply for just 10% seats and the cut-offs can rise.
• While ideally the non-reserved 40% open seats should be open seats based on merit, there are complexities here too.
• For example, the UPSC accepts a reserved candidate in the civil services examination making it in the general merit list as general only if she has not benefited from reservation in the preliminary, mains, service choice (if one gets a better service, say IAS or IPS, due to reservation, one is counted as reserved irrespective of one’s overall rank) and State cadre choice (if a reserved candidate is in the general merit list but is getting a cadre of her choice as a reserved candidate, she is counted as reserved), say bureaucrats. So, many who are above the general cut-off may still occupy this 10% quota, as they get a better service or cadre in it.
• Currently, it remains to be seen whether this initiative from the Government would stand the test of judicial scrutiny.
• Some experts have opined that if the number of demands for implementing reforms is any guide, India’s reservation system is clearly in disarray. They further point out that it is unlikely that the recently passed Constitution (124th Amendment) Bill, 2019, creating a 10% quota for the economically weaker sections (EWS), will serve as anything more than a band-aid.
• Given the deep inequalities prevalent in access to education and jobs based on caste and socio-economic status, affirmative action (or positive discrimination) makes a lot of sense. However, the system that was put in place during the early years of the Republic deserves serious re-evaluation in an era when technology has paved the way for deploying a better equipped arsenal.
Not Excluding Anyone:
• The Bill promises 10% reservation to individuals classified as economically backward.
• However, while a number of criteria were discussed in the parliamentary debate, the Bill is quite silent on this. Assuming that among the criteria discussed in Parliament, those that are currently applied to the definition of the Other Backward Classes (OBC) creamy layer are the ones to be used, it is not clear how useful they would be.
• While the OBC creamy layer has been created to exclude people who are clearly well off, the EWS quota, in contrast, is expected to focus on the poor. One of the criteria — the income threshold of Rs. 8 lakh per annum — has been mentioned.
• The National Sample Survey (NSS) of 2011-12 shows that the annual per capita expenditure for 99% of households falls under this threshold, even when we take inflation into account.
• Similarly, as per the India Human Development Survey (IHDS), the annual household incomes of 98% of households are less than Rs. 8 lakh. Even if we apply all the other criteria for exclusion (e.g. amount of land owned and size of home), the Bill would still cover over 95% of the households. So, who are we excluding? Almost no one.
• While the benefits of the EWS quota are likely to be minimal, the cost may be higher than one anticipates. First, it is important to remember that general category jobs are open to everyone, including Scheduled Caste (SC), Scheduled Tribe (ST) and OBC individuals.
• Thus, by removing 10% jobs from the “open” category, it reduces the opportunities for currently reserved groups. Hence, this is by no means a win-win situation. This may be particularly problematic for OBCs since OBC reservation is limited to 27% of the seats whereas the OBC population is at least 40% of the population, possibly more. Thus, this move is almost certain to result in calls for greater OBC reservation, particularly if a constitutional amendment to increase the proportion of reserved seats from 50% to 60% is already being adopted.
Getting caste certificates
• Second, actual implementation of the EWS quota could be challenging. Few non-SC/ST/OBC individuals have a caste certificate. A large number of SC/ST/OBC households report difficulties in obtaining these certificates. How would an individual practically lay claim to this status?
• Third, in an era when skill demands are rapidly outpacing supply of candidates in specialised fields, the EWS quota increases the constraints. If a university advertises for an associate professor for quantum physics under the EWS quota and the only suitable candidate happens to be from an OBC category, she could not be hired.
• Experts point out that these challenges occur for all positions under specifically reserved categories and we have chosen to live with these difficulties in the interest of the greater good of equity. However, there is little benefit to be derived from the EWS quota.
Redesigning reservations
• Arguably, the greatest cost of this amendment lies in the foregone opportunity to develop an enhanced and more effective reservation policy so that we can genuinely see an end to the entrenched inequalities in Indian society in the medium term. We have gotten so used to business as usual that we make no effort to sharpen our focus and look for more effective solutions, solutions that would make reservations redundant in 50 years.
• If we were to redesign from scratch, what would an effective affirmative action policy look like? If the goal is to help as many people as possible, we are facing a serious challenge. On the one hand, 50% reservation looks very large; in the grand scheme of India’s population it is a blunt and at times ineffective instrument.
• The following statistics from the Union Public Service Commission provide a sobering view of ground realities. In 2014, only 0.14% applicants to the UPSC were selected. Moreover, the general category and OBCs have the highest success rate, about 0.17%, and SCs have the lowest, about 0.08%. This may be because of the perception that it is easier for SCs to be recruited via the reserved quota and this may have led to a large number of SCs taking the civil services examination. One might say that many of these candidates are not qualified for these jobs. However, if we look at the candidates who made it past the preliminary examination (providing preliminary quality assurance), the picture is equally grim.
• Only about 8% of the candidates who took the main examination succeeded. Here the success rate is 8.2-8.3% for SC and ST candidates, 9.9% for OBCs and 7.8% for the general category. This suggests that in spite of the grievances of upper castes, reserved category applicants are not hugely advantaged.
• The above statistics tell us that in spite of reservations, a vast proportion of reserved category applicants do not find a place via the UPSC examination.
• Some experts suspect statistics from other fields may tell a similar story. This implies that if we expect reservations to cure the ills of Indian society, we may have a long wait.
• Hence, experts suggest that we must think about alternative strategies.
• One strategy may be to try and spread the benefits of reservations as widely as possible within the existing framework and ensure that individuals use their reserved category status only once in their lifetime. This would require that anyone using reservations to obtain a benefit such as college admission must register his/her Aadhaar number and she would be ineligible to use reservations for another benefit (e.g. a job) in the future. This would require no changes to the basic framework but spread the benefits more broadly within the reserved category allowing a larger number of families to seek upward mobility.
• A second strategy might be to recognise that future economic growth in India is going to come from the private sector and entrepreneurship. In order to ensure that all Indians, regardless of caste, class and religion, are able to partake in economic growth, we must focus on basic skills.
• Further, experts suggest that we have focused on admission to prestigious colleges and government jobs, but little attention is directed to social inequality in the quality of elementary schooling. The IHDS shows that among children aged 8-11, 68% of the forward caste children can read at Class 1 level while the proportion is far lower for OBCs (56%), SCs (45%) and STs (40%). This suggests that we need to focus on reducing inequalities where they first emerge, within primary schools.
• Lastly, the challenge we face is that our mindset is so driven by the reservation system that was developed in a different era that we have not had the time or the inclination to think about its success or to examine possible modifications.
Editorial Analysis:
Who is this reservation for?
• The constitutional amendment passed by Parliament seeks to expand the concept of reservation, a form of affirmative action, to favour the “economically weaker sections.”
• Those who are covered by the existing reservation for the Scheduled Castes, the Scheduled Tribes and the ‘socially and educationally backward classes,’ a constitutional category known in popular parlance as Other Backward Class or OBC, are not eligible for the proposed new reservation of 10%.
• The amendment makes it clear that the new reservation in public sector jobs and education in both public and private sectors will be above the existing quotas.
• The Honourable Supreme Court had ruled earlier that the total quantum could not exceed 50%. Experts opine that politically, the move by the Narendra Modi government aims to placate upper caste Hindus, though those not covered by any quota among the followers of other religions too are potential beneficiaries.
What is the problem?
• The amendment raises questions about its compatibility with the basic structure of the Constitution, which the court has held cannot be altered even by Parliament.
• A petition has already been filed in the Supreme Court, alleging the amendment violates the basic structure doctrine.
• The idea of giving 10% reservation to the upper castes also raises other ethical and moral questions that may not be justiciable.
• It is important to note that reservation is currently covered, primarily under clauses (4) and (5) of Article 15 and clause (4) of Article 16, which allows the State to make special provisions “for the advancement of any socially and educationally backward classes of citizens or for the Scheduled Castes and the Scheduled Tribes.”
• The court has examined the concept of ‘socially and educationally backward classes’ and has ruled that caste can be a basis for inclusion in that category.
• In the Indra Sawhney vs Union of India, the court examined the decision of the government to implement the Mandal Commission report that stipulated 27% reservation for OBCs and ruled that economic criteria could not be the sole basis for reservation and the 50% ceiling ought not to be crossed. All these questions will be reopened in the light of the new amendment.
What is the government stand?
• The government invoked the Directive Principles of State policy contained in Article 46 to defend its proposal for reservation for the economically weaker sections.
• This could be questionable. Article 46 says “the State shall promote with special care the educational and economic interests of the weaker sections of the people, and, in particular, of the Scheduled Castes and the Scheduled Tribes, and shall protect them from social injustice and all forms of exploitation.”
• The “economically weaker sections of citizens were not eligible for the benefit of reservation. With a view to fulfilling the mandate of Article 46, and to ensure that the economically weaker sections of citizens get a fair chance of receiving higher education and participation in employment in the services of the state, it has been decided to amend the Constitution of India,” the amendment Bill stated.
Will it benefit the poor?
• In the Indra Sawhney judgment, the court had said: “…the concept of ‘weaker sections’ under Article 46 is different from that of the ‘backward class’ of citizens in Article 16(4), but the purpose of the two is also different.
• One is for the limited purpose of the reservation and hence suffers from limitations, while the other is for all purposes under Article 46… While those entitled to benefits under Article 16(4) may also be entitled to availing themselves of the measures taken under Article 46, the converse is not true.
• If this is borne in mind, the reasons why mere poverty or economic consideration cannot be a criterion for identifying backward classes of citizens under Article 16(4) would be more clear.” Whether the economically weaker sections among the OBCs, the SCs or the STs could be excluded from reservation meant for the economically weaker sections is a contentious question.
2. The lowdown on HAL’s order book
Editorial Analysis:
• Experts point out that the Defence Public Sector Undertaking and the country’s only manufacturer of aircraft, Hindustan Aeronautics Limited (HAL), has been caught in the political slugfest over the Rafale deal on the offset issue.
• However, recently, it has been in the news for its order book and financial situation.
• It is important to note that HAL makes a range of aircraft — including fighter jets and trainers — and helicopters, both indigenously developed and under licence from foreign original equipment manufacturers (OEMs).
• For the year ended March 2018, HAL posted a turnover of Rs. 18,284 crore. But HAL is facing a financial crunch owing to non-payment of dues and lack of new firm contracts. In fact, last week HAL said it had taken an overdraft of Rs. 962 crore for salaries and running costs.
• Recently in Parliament, Defence Minister Nirmala Sitharaman said HAL had orders worth Rs. 1 lakh crore, later explaining that it includes deals worth Rs. 26,570.8 crore signed between 2014 and 2018 and contracts worth Rs. 73,000 crore in the pipeline. Those in the pipeline include 83 Light Combat Aircraft (LCA) Tejas Mk-1A jets worth Rs. 50,000 crore, 200 helicopters under a joint venture with Russia worth Rs. 20,000 crore, and 15 indigenous Light Combat Helicopters (LCH) worth Rs. 3,000 crore.
A Closer Look at the current situation of HAL
• The current situation of HAL is due to a combination of factors — primarily the non-payment of dues by the Indian Air Force (IAF) for orders executed and under way, most of the existing orders coming to an end and a delay in finalisation of new contracts.
• HAL also has several development programmes which need funding till the services accept them and pitch in with their share.
• HAL Chairman R. Madhavan recently said the IAF owed HAL money for aircraft, helicopters and services that it had already delivered with current dues pegged at Rs. 15,700 crore, which will rise to Rs. 20,000 crore by March 31, 2019.
• In addition, over the years HAL has paid large amounts to the government as part of equity buy-back and dividends which also depleted its coffers.
• On the contrary, the IAF has been paying foreign OEMs for committed liabilities which otherwise attract penalties.
• For instance, it paid Rs. 20,000 crore to Dassault Aviation of France for the 36 Rafale jets contracted and to Boeing for Apache and Chinook helicopters, among others.
• The weak financial situation can affect future programmes and hamper regular maintenance activities that HAL undertakes for the IAF.
Concluding Remarks:
• The country’s indigenous fighter programme LCA is at a critical stage with the final operational clearance nearing and the advanced variant Mk1A making delayed progress.
• HAL is setting up another assembly line to ramp up LCA production and is developing the HTT-40 basic trainer and a Light Utility Helicopter (LCU) on its own, based on the demands of the services.
• The fund crunch affects salaries and running costs. Also as contracts come to an end, the work force will have to be benched. For instance, HAL’s biggest contract, the licence manufacture of Su-30 jets from Russia, is nearing completion.
• Additionally, the delay in finalisation of new orders affects timely planning and supply chain management.
• Finally, after the recent developments, the Defence Ministry has made some moves to address the issue. Officials said the Ministry has sought funds from the Finance Ministry to help HAL.
• Earlier this week, HAL officials met Ms. Sitharaman and the three services chiefs. HAL has also stated that with anticipated collections up to March 2019, the cash position is expected to improve and in terms of future orders, final contracts for 83 LCA Mk1A and 15 LCH are in advanced stages.
• Nonetheless, the developments are a matter of serious concern for the country and warrant immediate government attention to set things in order.
F. Tidbits
1. ‘Mental health apps have gaps in information’
• Mental health and well-being, often the subject of self-help books, is now the focus of apps by entrepreneurs identifying a need for them among teenagers and young working professionals.
• Apps, some of them available for a subscription fee, promise to address mental health issues ranging from anxiety to depression. But how effective are they?
• Researchers at the National Institute of Mental Health and Neuro Sciences (NIMHANS) reviewed 278 free apps for depression to find that only a little over a third included content aimed at encouraging users to seek professional help. This was one of the findings of the study published in the Asian Journal of Psychiatry.
• Many apps offer online consultation, a social network for dealing with stressful situations, screening tests, different forms of meditation, audio and visual aids, with a focus on meditation and relaxation. The two most popular types of apps provided information on coping with depression and framed standalone screening tools.
• However, less than 10% of the apps studied had incorporated explicit delineation of their scope, and only 12% of the reviewed apps guided users on managing a ‘suicidal crisis’
2. Quota Bill gets President’s assent, becomes law
• President Ram Nath Kovind on Saturday gave his assent to the Constitution amendment that provides 10% reservation to the economically backward section in the general category in government jobs and education.
• With the Ministry for Law and Justice issuing a notification about the Constitution (103 Amendment) Act, 2019 receiving the Presidential assent, reservation for the economically weaker among general category is now law.
• The Act amends Articles 15 and 16 of the Constitution — ensuring Fundamental Rights to a citizen — by adding a clause that allows the State to make “special provision for the advancement of any economically weaker sections of citizens”.
• These provisions would relate to “their admission to educational institutions, including private educational institutions, whether aided or unaided by the State, other than the minority educational institutions”.
• The Act makes it clear that reservation would be “in addition to the existing reservations and subject to a maximum of 10% of the total seats in each category”.
• Unlike other Constitutional Bills that require ratification from half of the State Assemblies, the Law Minister had clarified that this Act would not require such a process
G. Prelims Facts
1. ‘Monkey fever’ cases hit 62 in Shivamogga
Context
• The outbreak of Kyasanur Forest Disease (KFD), also known as ‘monkey fever’ in Malnad region of the district, is showing no signs of abating as four cases have now been reported from Tirthahalli taluk. The earlier cases were reported in Sagar taluk.
• With this, the total number of KFD cases in the district since December 2018 has reached 62. Six persons from Aralagodu died during this period.
Kyasanur Forest Disease (KFD)
• Kyasanur Forest disease (KFD) or Monkey Fever is a tick-borne viral hemorrhagic fever endemic to South Asia.
• The disease is caused by a virus belonging to the family Flaviviridae, which also includes yellow fever and dengue fever.
• The symptoms of the disease include a high fever with frontal headaches, followed by haemorrhagic symptoms, such as bleeding from the nasal cavity, throat, and gums, as well as gastrointestinal bleeding.
• The virus was identified in 1957 when it was isolated from a sick monkey from the Kyasanur Forest of Karnataka. Since then, between 400-500 humans cases per year have been reported.
• Hard ticks (Hemaphysalis spinigera) are the reservoir of the KFD virus and once infected, remain so for life.
• Rodents, shrews, and monkeys are common hosts for KFDV after being bitten by an infected tick. KFDV can cause epizootics with high fatality in primates.
• Transmission to humans may occur after a tick bite or contact with an infected animal, most importantly a sick or recently dead monkey. No person-to-person transmission has been described.
• The disease as of now is stated to be transmitted through monkeys. Large animals such as goats, cows, and sheep may become infected with KFD but play a limited role in the transmission of the disease. Furthermore, there is no evidence of disease transmission via the unpasteurised milk of any of these animals.
• People with recreational or occupational exposure to rural or outdoor settings (e.g., hunters, herders, forest workers, farmers) are potentially at risk for infection by contact with infected ticks.
• Seasonality is another important risk factor as more cases are reported during the dry season, from November through June.
• Diagnosis can be made in the early stage of illness by molecular detection by PCR or virus isolation from blood. Later, serologic testing using enzyme-linked immunosorbent serologic assay (ELISA) can be performed.
H. UPSC Prelims Practice Questions
Question 1. Consider the following Terms /Context / Topic
1. Belle 2 experiment – Artificial Intelligence
2. Block chain technology – Digital Crypto currency
3. CRISPR – Cas9 – Particle Physics
Which of the pairs given above is/are correctly matched?
1. 1 and 3 only
2. 2 only
3. 2 and 3 only
4. 1, 2 and 3
See
Question 2. Which of the following indicators is related to poverty measurement?
2. Ginni- coefficient
3. Laffer curve
4. Kuznets curve
See
Question 3. Which of the following measure have been used by the government to address the situation of poverty in India?
1. Development oriented growth measures
2. Meeting the minimum needs of the poor.
3. Specific poverty alleviation programmes
Select the correct answer using the codes given below:
1. Only 1
2. Only 2
3. Only 1 and 3
4. All of the above
See
Question 4. Consider the following statements about Dr. Rangarajan poverty estimation methodology:
1. It reverted to system of separate poverty line category for rural and urban areas.
2. It recommended use of “modified mixed reference period”
Which of the above statement(s) is/ are correct?
1. Only 1
2. Only 2
3. Both 1 and 2
4. None of the above
See | 2021-11-28 09:37:04 | {"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": 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": 0.23647965490818024, "perplexity": 5026.77620586352}, "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-2021-49/segments/1637964358480.10/warc/CC-MAIN-20211128073830-20211128103830-00207.warc.gz"} |
https://ieee.nitk.ac.in/blog/Long-Short-Term-Neural-Networks/ | Long Short Term Memory Neural Networks or LSTM Neural Network is a commonly used Recurrent Neural Network model that is most commonly used in tasks like speech recognition, music generation etc. Lets take a deep dive into what Recurrent Neural Networks are and why we need and use LSTMs.
# Long Short Term Memory Neural Networks
### Recurrent Neural Networks and Why LSTMs?
Recurrent Neural Networks are those Neural Networks that we use to process information that require us to keep informed of previous information. In simpler words, when we want a model to perform a certain category of tasks like speech recognition, music generation, machine translation, sentiment classification, etc, all of which invloves keeping track of previous information (like keeping track of all the words while processing a sentence during machine translation), a normal Neural Network cannot do this, while a Recurrent Neural Network, which keeps a track of the past information in it’s internal state addresses this issue.
Recurrent Neural Network - Unrolled
The above diagram is that of a basic Recurrent Neural Network, the chained structure is appropriate for modeling sequences and using this structure for Neural Networks have proven to work for the above mentioned applications. LSTMs come into play when a certain problem occurs within RNNs itself.
#### Problem of Vanishing Gradients due to Long Term Dependencies
Consider the following small sentence: She was riding her cycle . Predicting the word ‘her’ using RNNs is relatively easy since it just has to process the immediate words next to it, but predicting some sort of information that requires some sort of context from earlier, for example, mentioning I am from France in the beginning of a paragraph, but having to predict the language that was spoken much later in the text. Here, as the gap between relevant information grows, it becomes difficult for RNNs to connect both information to make a valid prediction. This happens because while calculating gradients for the weights during backpropagation, the values from one end of the sequence may find it difficult to influence that in other ends of the sequence which may or may not play an important role in prediction. This is the case in normal RNNs, where ‘long range dependencies’ are not really supported.
This is where LSTMs come into play!
## Long Short Term Memory Networks
Long Short Term Memory Networks (usually just called LSTMs) are a special kind of RNN, capable of learning long-term dependencies. They were introduced by Hochreiter & Schmidhuber (1997). They are explicitly designed to avoid the long-term dependency problem by remembering information for long periods of time, and this is possible by introducing ‘memory cells’ which keep track of these dependencies throughout the sequence.
Long Short Term Memory Network
This is how an LSTM looks like, it follows the same chain like structure like that of the RNNs, but it contains several added gates. It may seem difficult to process this as a whole, but we’ll walk through this step by step.
Note: The sigmoid function returns a value between 0 to 1 and this case, values very close to either 0 or 1 and hence is commonly used in our gates to make a particular decision.
The following are states and gates involved in an LSTM cell:
1. Activation layer: This layer consists of the activation values like the normal RNNs do
2. Memory Cell or Candidate layer: This layer is involved in keeping track of dependencies
3. Update Gate: Sigmoid function that decides whether or not the memory cell should keep track of the dependecy
4. Forget Gate: Sigmoid function that decides whether or not the memory cell should leave or forget the dependency
5. Output Gate: Sigmoid function that helps us filter what parts of the memory cell layer we want to pass into the output
LSTM Structure Inside
If the diagram is overwhelming, the following equations may help you to walk through the process.
$\hat{c}^{<t>} = tanh( W_{c}[ a^{<t-1>},x^{<t>} ] + b_c )$
This is the calculation for a memory cell initially which takes into account the previous activation layer and input layers’ weights, and adds it to a bias, while passing the resultant to a tanh function that returns a score between -1 and 1, which in turn carries a dependency.
$\Gamma_{u} = \sigma( W_{u}[ a^{<t-1>},x^{<t>} ] + b_u )$ $\Gamma_{f} = \sigma( W_{f}[ a^{<t-1>},x^{<t>} ] + b_f )$
Here, the decision is made whether or not to keep track of the dependency with the help of the update and forget gates, which are sigmoid layers.
$\Gamma_{o} = \sigma( W_{o}[ a^{<t-1>},x^{<t>} ] + b_o )$ $c^{<t>} = \Gamma_{u}*\hat{c}^{<t>} + \Gamma_{f}*c^{<t-1>}$
Here, we decide what exactly to update into the memory cell, which either retains the dependency from earlier or updates it to a new value based on the decision made by the update and forget gates. Hence, the output will be filtered. This is done by running a sigmoid function layer to decide which parts of the memory cell we will send to the output and while the memory cells will be passed through tanh and then passed through the output gate to get only the filtered output. Here, our memory cells are updated appropriately.
$a^{<t>} = \Gamma_{o}*tanh(c^{<t>})$
The activation layer is influenced by certain memory cell values decided upon by the output gate, and is appropriately updated and passed onto the next cell.
The resultant $$\hat{y}^{<t>}$$ vector is obtained by passing the activation layer through a softmax function, but do note that this step is dependent on what problem we’re solving and isn’t part of the general LSTM framework.
## Character to Character LSTM Model
We are going to use a two layer LSTM model with 512 hidden nodes in each layer. We will make the model read a text file that contains text from a transcript, in this example we will make the model read an exerpt from ‘The Outcasts’, we will then use the same sequence but shifted by one character as a target.
Before we get started, here are some key terms to get used to:
1. Vocabulary: This is a set of every character that our model requires
2. LSTM Cell : We will make use of pyTorch’s LSTM cell that has the structure, as explained earlier
3. Hidden State or Activation State: This is a vector of size(batch_size, hidden_size), the bigger dimension of the hidden_size, the more robust our model becomes but at the expense of computational cost. This vector acts as our short-term memory and is updated by the input at the time step t.
4. Layers of an LSTM: We can stack LSTM cells on top of each other to obtain a layered LSTM model. This is done by passing the output of the first LSTM cell from the input to the second LSTM cell at any given time t, this gives a deeper network.
The model receives an “A” initially as an input to the LSTM cell at time t=0. After that, we get the output with the size of our vocabulary from the memory cell. If we apply softmax function to the output, we get the probabilities of the characters. Then we take ‘k’ most probable characters and then sample one character according to their probability in the space of these ‘k’ characters. This sampled character is now going to be input to the LSTM cell at time t=1, and so on.
Always remember that pytorch expects batch dimensions everywhere, and don’t forget to convert numpy arrays into torch tensors and back to numpy again since we are dealing with integers in the end and we need them to look up actual characters.
Here is some of the output while monitoring the losses during training:
Epoch: 0, Batch: 0, Train Loss: 4.375697, Validation Loss: 4.338589
Epoch: 0, Batch: 5, Train Loss: 3.400858, Validation Loss: 3.402019
Epoch: 1, Batch: 0, Train Loss: 3.239244, Validation Loss: 3.299909
Epoch: 1, Batch: 5, Train Loss: 3.206378, Validation Loss: 3.262871
.
.
.
Epoch: 49, Batch: 0, Train Loss: 1.680400, Validation Loss: 2.052764
Epoch: 49, Batch: 5, Train Loss: 1.701830, Validation Loss: 2.061397
Here is what the model learnt and generated in the first epoch:
First Epoch
and this is the outcome after 50 epochs:
Fiftieth Epoch
### Final Outcome
We can see that the resulting sample that at the 50th epoch doesn’t make much sense, but it does show signs that the model has learned a lot, like some words, some sentence structure and syntax. Now all we need to do is to tweak the model’s hyper-parameters to make it better, and we will have a better character to character model than we started off with. | 2022-06-25 19:28:49 | {"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": 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": 0.4644578993320465, "perplexity": 830.7529736447162}, "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-2022-27/segments/1656103036099.6/warc/CC-MAIN-20220625190306-20220625220306-00400.warc.gz"} |
https://mathoverflow.net/questions/184620/is-the-cassels-tate-pairing-defined-for-elliptic-curves-over-function-fields | # Is the Cassels-Tate pairing defined for elliptic curves over function fields?
The Cassels-Tate pairing is typically defined for elliptic curves (or abelian varieties) over number fields, but it seems like it should be defined for elliptic curves over function fields as well. Does anybody know if this is not true or if there is a reference? | 2021-01-22 14:08:24 | {"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": 0.8140376210212708, "perplexity": 109.93253714649276}, "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/1610703529331.99/warc/CC-MAIN-20210122113332-20210122143332-00209.warc.gz"} |
https://collegephysicsanswers.com/openstax-solutions/steam-above-freshly-made-cup-instant-coffee-really-water-vapor-droplets | Question
The “steam” above a freshly made cup of instant coffee is really water vapor droplets condensing after evaporating from the hot coffee. What is the final temperature of 250 g of hot coffee initially at $90.0^\circ\textrm{C}$ if 2.00 g evaporates from it? The coffee is in a Styrofoam cup, so other methods of heat transfer can be neglected.
$85.7^\circ\textrm{C}$
Solution Video
# OpenStax College Physics Solution, Chapter 14, Problem 47 (Problems & Exercises) (2:49)
View sample solution
## Calculator Screenshots
Video Transcript
This is College Physics Answers with Shaun Dychko. We have some coffee in an insulated cup which means the only way that heat is going to leave is through this phase change of some of the coffee that is evaporating. So, there is a total of 250 grams to start with and two grams of that will evaporate leaving 248 grams left behind which we call m subscript w for water because the coffee is going to have the properties of water, the same specific heat of water 4186 joules per kilogram per Celsius degree and the latent heat of vaporization for this coffee that is evaporating is 2256 joules per kilogram and this number is not precisely true because that's true only when the water is at 100 degree Celsius but 90 degree Celsius is pretty close to that and so we will take that to be the latent heat of vaporization. So, the initial temperature is 90 degrees and we are asked to figure out what will the final temperature of the coffee be after 2 grams of it evaporates. So, there is going to be a amount of heat that is lost and that’s why the negative sign is there because it’s a loss in thermal energy equal to the mass of coffee remaining times it specific heat times the final temperature minus the initial temperature and that heat loss is going to be the heat gained by the vapour that is evaporating, so the mass that’s evaporating times the latent heat of vaporization and then we are gonna solve this for T f coz we want to know what the final temperature of the coffee is. So we multiply through by m w C w and then we have positive m w C w T initial minus m w C w times T final and then we will take this term to the left side and then this term to the right side and then switch the sides around so that we have the unknown terms in the left and we are dividing both sides by m w C w and that isolated T f. So T final is mass of the water remaining times its specific heat times initial temperature minus the mass of the vapour that evaporates times the latent heat of vaporization divided by the mass of the water times specific heat of water. So that’s 248 times ten to the minus three kilograms so that’s 248 grams converted to kilograms times specific heat of water times initial temperature of 90 degrees Celsius minus the two grams that evaporates written in kilograms times 2256 times 10 to the 3 joules per kilogram divided by 248 grams times specific heat of water and this gives a final temperature of 85.7 degree Celsius. | 2019-04-22 02:00:17 | {"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": 0.7514009475708008, "perplexity": 394.04351666809947}, "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-2019-18/segments/1555578533774.1/warc/CC-MAIN-20190422015736-20190422041736-00110.warc.gz"} |
http://adam.chlipala.net/cpdt/repo/rev/437cc4857e2a | ### changeset 62:437cc4857e2a
Start of Coinductive
author Adam Chlipala Tue, 30 Sep 2008 16:17:50 -0400 b581446229fd fe7d37dfbd26 Makefile src/Coinductive.v src/Intro.v src/toc.html 4 files changed, 149 insertions(+), 1 deletions(-) [+]
line wrap: on
line diff
--- a/Makefile Tue Sep 30 14:02:40 2008 -0400
+++ b/Makefile Tue Sep 30 16:17:50 2008 -0400
@@ -1,6 +1,6 @@
MODULES_NODOC := Tactics
MODULES_PROSE := Intro
-MODULES_CODE := StackMachine InductiveTypes Predicates
+MODULES_CODE := StackMachine InductiveTypes Predicates Coinductive
MODULES_DOC := $(MODULES_PROSE)$(MODULES_CODE)
MODULES := $(MODULES_NODOC)$(MODULES_DOC)
VS := \$(MODULES:%=src/%.v)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/Coinductive.v Tue Sep 30 16:17:50 2008 -0400
@@ -0,0 +1,145 @@
+ *
+ * Creative Commons Attribution-Noncommercial-No Derivative Works 3.0
+ * The license text is available at:
+ *)
+
+(* begin hide *)
+Require Import List.
+
+Require Import Tactics.
+
+Set Implicit Arguments.
+(* end hide *)
+
+
+(** %\chapter{Infinite Data and Proofs}% *)
+
+(** In lazy functional programming languages like Haskell, infinite data structures are everywhere. Infinite lists and more exotic datatypes provide convenient abstractions for communication between parts of a program. Achieving similar convenience without infinite lazy structures would, in many cases, require acrobatic inversions of control flow.
+
+Laziness is easy to implement in Haskell, where all the definitions in a program may be thought of as mutually recursive. In such an unconstrained setting, it is easy to implement an infinite loop when you really meant to build an infinite list, where any finite prefix of the list should be forceable in finite time. Haskell programmers learn how to avoid such slip-ups. In Coq, such a laissez-faire policy is not good enough.
+
+We spent some time in the last chapter discussing the Curry-Howard isomorphism, where proofs are identified with functional programs. In such a setting, infinite loops, intended or otherwise, are disastrous. If Coq allowed the full breadth of definitions that Haskell did, we could code up an infinite loop and use it to prove any proposition vacuously. That is, the addition of general recursion would make CIC %\textit{%#<i>#inconsistent#</i>#%}%.
+
+There are also algorithmic considerations that make universal termination very desirable. We have seen how tactics like [reflexivity] compare terms up to equivalence under computational rules. Calls to recursive, pattern-matching functions are simplified automatically, with no need for explicit proof steps. It would be very hard to hold onto that kind of benefit if it became possible to write non-terminating programs; we would be running smack into the halting problem.
+
+One solution is to use types to contain the possibility of non-termination. For instance, we can create a "non-termination monad," inside which we must write all of our general-recursive programs. In later chapters, we will spend some time on this idea and its applications. For now, we will just say that it is a heavyweight solution, and so we would like to avoid it whenever possible.
+
+Luckily, Coq has special support for a class of lazy data structures that happens to contain most examples found in Haskell. That mechanism, %\textit{%#<i>#co-inductive types#</i>#%}%, is the subject of this chapter. *)
+
+
+(** * Computing with Infinite Data *)
+
+(** Let us begin with the most basic type of infinite data, %\textit{%#<i>#streams#</i>#%}%, or lazy lists. *)
+
+Section stream.
+ Variable A : Set.
+
+ CoInductive stream : Set :=
+ | Cons : A -> stream -> stream.
+End stream.
+
+(** The definition is surprisingly simple. Starting from the definition of [list], we just need to change the keyword [Inductive] to [CoInductive]. We could have left a [Nil] constructor in our definition, but we will leave it out to force all of our streams to be infinite.
+
+ How do we write down a stream constant? Obviously simple application of constructors is not good enough, since we could only denote finite objects that way. Rather, whereas recursive definitions were necessary to %\textit{%#<i>#use#</i>#%}% values of recursive inductive types effectively, here we find that we need %\textit{%#<i>#co-recursive definitions#</i>#%}% to %\textit{%#<i>#build#</i>#%}% values of co-inductive types effectively.
+
+ We can define a stream consisting only of zeroes. *)
+
+CoFixpoint zeroes : stream nat := Cons 0 zeroes.
+
+(** We can also define a stream that alternates between [true] and [false]. *)
+
+CoFixpoint trues : stream bool := Cons true falses
+with falses : stream bool := Cons false trues.
+
+(** Co-inductive values are fair game as arguments to recursive functions, and we can use that fact to write a function to take a finite approximation of a stream. *)
+
+Fixpoint approx A (s : stream A) (n : nat) {struct n} : list A :=
+ match n with
+ | O => nil
+ | S n' =>
+ match s with
+ | Cons h t => h :: approx t n'
+ end
+ end.
+
+Eval simpl in approx zeroes 10.
+(** [[
+
+ = 0 :: 0 :: 0 :: 0 :: 0 :: 0 :: 0 :: 0 :: 0 :: 0 :: nil
+ : list nat
+ ]] *)
+Eval simpl in approx trues 10.
+(** [[
+
+ = true
+ :: false
+ :: true
+ :: false
+ :: true :: false :: true :: false :: true :: false :: nil
+ : list bool
+ ]] *)
+
+(** So far, it looks like co-inductive types might be a magic bullet, allowing us to import all of the Haskeller's usual tricks. However, there are important restrictions that are dual to the restrictions on the use of inductive types. Fixpoints %\textit{%#<i>#consume#</i>#%}% values of inductive types, with restrictions on which %\textit{%#<i>#arguments#</i>#%}% may be passed in recursive calls. Dually, co-fixpoints %\textit{%#<i>#produce#</i>#%}% values of co-inductive types, with restrictions on what may be done with the %\textit{%#<i>#results#</i>#%}% of co-recursive calls.
+
+The restriction for co-inductive types shows up as the %\textit{%#<i>#guardedness condition#</i>#%}%, and it can be broken into two parts. First, consider this stream definition, which would be legal in Haskell.
+
+[[
+CoFixpoint looper : stream nat := looper.
+[[
+Error:
+Recursive definition of looper is ill-formed.
+In environment
+looper : stream nat
+
+unguarded recursive call in "looper"
+*)
+
+(** The rule we have run afoul of here is that %\textit{%#<i>#every co-recursive call must be guarded by a constructor#</i>#%}%; that is, every co-recursive call must be a direct argument to a constructor of the co-inductive type we are generating. It is a good thing that this rule is enforced. If the definition of [looper] were accepted, our [approx] function would run forever when passed [looper], and we would have fallen into inconsistency.
+
+The second rule of guardedness is easiest to see by first introducing a more complicated, but legal, co-fixpoint. *)
+
+Section map.
+ Variables A B : Set.
+ Variable f : A -> B.
+
+ CoFixpoint map (s : stream A) : stream B :=
+ match s with
+ | Cons h t => Cons (f h) (map t)
+ end.
+End map.
+
+(** This code is a literal copy of that for the list [map] function, with the [Nil] case removed and [Fixpoint] changed to [CoFixpoint]. Many other standard functions on lazy data structures can be implemented just as easily. Some, like [filter], cannot be implemented. Since the predicate passed to [filter] may reject every element of the stream, we cannot satisfy even the first guardedness condition.
+
+ The second condition is subtler. To illustrate it, we start off with another co-recursive function definition that %\textit{%#<i>#is#</i>#%}% legal. The function [interleaves] takes two streams and produces a new stream that alternates between their elements. *)
+
+Section interleave.
+ Variable A : Set.
+
+ CoFixpoint interleave (s1 s2 : stream A) : stream A :=
+ match s1, s2 with
+ | Cons h1 t1, Cons h2 t2 => Cons h1 (Cons h2 (interleave t1 t2))
+ end.
+End interleave.
+
+(** Now say we want to write a weird stuttering version of [map] that repeats elements in a particular way, based on interleaving. *)
+
+Section map'.
+ Variables A B : Set.
+ Variable f : A -> B.
+
+ (** [[
+
+ CoFixpoint map' (s : stream A) : stream B :=
+ match s with
+ | Cons h t => interleave (Cons (f h) (map' s)) (Cons (f h) (map' s))
+ end. *)
+
+ (** We get another error message about an unguarded recursive call. This is because we are violating the second guardedness condition, which says that, not only must co-recursive calls be arguments to constructors, there must also %\textit{%#<i>#not be anything but [match]es and calls to constructors of the same co-inductive type#</i>#%}% wrapped around these immediate uses of co-recursive calls. The actual implemented rule for guardedness is a little more lenient than what we have just stated, but you can count on the illegality of any exception that would enhance the expressive power of co-recursion.
+
+ Why enforce a rule like this? Imagine that, instead of [interleave], we had called some other, less well-behaved function on streams. Perhaps this other function might be defined mutually with [map']. It might deconstruct its first argument, retrieving [map' s] from within [Cons (f h) (map' s)]. Next it might try a [match] on this retrieved value, which amounts to deconstructing [map' s]. To figure out how this [match] turns out, we need to know the top-level structure of [map' s], but this is exactly what we started out trying to determine! We run into a loop in the evaluation process, and we have reached a witness of inconsistency if we are evaluating [approx (map' s) 1] for any [s]. *)
+End map'.
+
--- a/src/Intro.v Tue Sep 30 14:02:40 2008 -0400
+++ b/src/Intro.v Tue Sep 30 16:17:50 2008 -0400
@@ -189,6 +189,8 @@
\hline
Inductive Predicates & \texttt{Predicates.v} \\
\hline
+Infinite Data and Proofs & \texttt{Coinductive.v} \\
+\hline
\end{tabular} \end{center}
% *)
--- a/src/toc.html Tue Sep 30 14:02:40 2008 -0400
+++ b/src/toc.html Tue Sep 30 16:17:50 2008 -0400
@@ -8,5 +8,6 @@
<li><a href="StackMachine.html">Some Quick Examples</a>
<li><a href="InductiveTypes.html">Introducing Inductive Types</a>
<li><a href="Predicates.html">Inductive Predicates</a>
+<li><a href="Coinductive.html">Infinite Data and Proofs</a>
</body></html> | 2019-03-26 17:28:01 | {"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": 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": 0.5010495781898499, "perplexity": 4606.245103638399}, "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-2019-13/segments/1552912205597.84/warc/CC-MAIN-20190326160044-20190326182044-00343.warc.gz"} |
https://www.neetprep.com/question/5303-following-transitions-hydrogen-atom-one-gives-absorptionline-lowest-frequency-n-nB-n-n-C-n-nD-n-n?courseId=19 | • Subject:
...
• Topic:
...
Of the following transitions in hydrogen atom, the one which gives an absorption line of lowest frequency is
(A) n=1 to n=2
(B) n=3 to n=8
(C) n=2 to n=1
(D) n=8 to n=3 | 2019-03-24 03:30:31 | {"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": 0.8741101622581482, "perplexity": 6429.451059953174}, "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-2019-13/segments/1552912203168.70/warc/CC-MAIN-20190324022143-20190324044143-00438.warc.gz"} |
http://primoinvest.express.reproto.com/Projekti/projects/43-apartamentu-eka-bresta/ | ### Details
Client: NordElement
Project: 6 row house complex
Country: Norway
Nordelement as (norway) seeks for 300 000,- eur loan to finance building activities of : 6 row house complex in eidsvoll norway. Nordelement as is involved in producing timber frame of the houses, supply of the house and finishing from outside. Nordelement as does not provide the internal works.
All of the houses are sold on current stage.
### Project Timings
The start of foundation is set april 2018.
Start of supply elements is set may 2018.
End of project and finished from outside is set september 2018.
Nordelement as investment is needed for a period of 7 months.
May 2018 – October 2018
### 43 apartamentu ēka Brestā
This is an image caption added below the image. You can also add one over the image.
This is an image caption added below the image. You can also add one over the image.
This is an image caption added below the image. You can also add one over the image.
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This is an image caption added below the image. You can also add one over the image. | 2019-10-19 08:07:11 | {"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": 0.8335244059562683, "perplexity": 3203.564593382072}, "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/1570986692126.27/warc/CC-MAIN-20191019063516-20191019091016-00357.warc.gz"} |
http://openstudy.com/updates/52433796e4b0a03c277fa148 | ## valiyuh Group Title Find the rate of change (-4,4) and (-6,8) ? -geometry help? one year ago one year ago
1. jdoe0001
rate of change will be the slope of the line, thus $$\large slope = m= \cfrac{rise}{run} \implies \cfrac{y_2-y_1}{x_2-x_1}$$
2. valiyuh
Thanks .
3. jdoe0001
$$\begin{array}{lllll} &x_1&y_1&x_2&y_2\\ (&-4,&4) \qquad (&-6,&8) \end{array}$$
4. jdoe0001
yw | 2014-12-18 01:08:41 | {"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": 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": 0.9772605299949646, "perplexity": 7703.15877758761}, "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-2014-52/segments/1418802765093.40/warc/CC-MAIN-20141217075245-00068-ip-10-231-17-201.ec2.internal.warc.gz"} |
https://tex.stackexchange.com/questions/510349/set-counter-for-tcolorbox-environment-in-beamer | # Set counter for tcolorbox environment in beamer
Please help me to put a simple counter in the tcolorbox environment in beamer. It only needs to go from 1,2,3,...
\begin{tcolorbox}[colback=green!5,colframe=green!40!black, center,title= ]
\end{tcolorbox}
There is the key auto counter for that purpose. As it turns out, it does not yet automatically harmonize with beamer \pauses. This can be fixed by redefining \tcb@proc@counter@auto to become
\def\tcb@proc@counter@auto#1{%
\newcounter{tcb@cnt@#1}%
\csxdef{tcb@cnt@#1}{tcb@cnt@#1}%
\tcb@proc@counter@autoanduse{#1}%
}
So the MWE becomes
\documentclass{beamer}
\usepackage{tcolorbox}
\makeatletter
\def\tcb@proc@counter@auto#1{%
\newcounter{tcb@cnt@#1}%
\csxdef{tcb@cnt@#1}{tcb@cnt@#1}%
\tcb@proc@counter@autoanduse{#1}%
}
\makeatother
\newtcolorbox[auto counter]{numberedbox}[2][]{%
colback=green!5,colframe=green!40!black,center,title=Numbered
box~\thetcbcounter: #2,#1}
\begin{document}
\begin{frame}[t]
\frametitle{tcolorboxes}
\begin{numberedbox}[label={boxA}]{title A}
I am random box and have number~\ref{boxA}
\end{numberedbox}
\pause
\begin{numberedbox}[label={catinbox}]{A cat in a box}
\dots wrote this, see numbered box~\ref{boxA}
\end{numberedbox}
\pause
\begin{numberedbox}[label={yetanotherbox}]{title B}
I'm boring, see numbered box~\ref{catinbox} for something exciting
\end{numberedbox}
\end{frame}
\end{document}
• Thanks, @Schrodinger's cat. It works and yet a very simple solution! – hochoi Sep 30 at 5:02
• Although this solution works, but I encountered another problem when I use it with the \pause command. The counter keeps counting up for the same box. Is there a way to make the counter not to count the same box more than once? – hochoi Sep 30 at 5:09
• @hochoi Good point! I added a working solution. Even though there is a section on beamer support in the tcolorbox manual, I could not find anything on auto counter support. Since tcolorbox gives it some internal name that is not obvious, I added a normal counter here. Maybe that would be something for a feature request to ask to make auto counter do that automatically. – Schrödinger's cat Sep 30 at 12:42
• It works wonderfully! Thank you very much, @Schrodinger's cat! – hochoi Sep 30 at 13:29
• One more problem popping up :) How do I refer to certain box? The label command does not seem o be able to track the counter accurately. – hochoi Oct 1 at 1:14 | 2019-12-13 10:34:09 | {"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": 0.7632187604904175, "perplexity": 2735.950686437387}, "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-2019-51/segments/1575540553486.23/warc/CC-MAIN-20191213094833-20191213122833-00344.warc.gz"} |
http://www.exegetic.biz/blog/2015/09/monthofjulia-day-18-plotting/ | ## #MonthOfJulia Day 18: Plotting
There’s a variety of options for plotting in Julia. We’ll focus on those provided by Gadfly, Bokeh and Plotly and.
Gadfly is the flavour of the month for plotting in Julia. It’s based on the Grammar of Graphics, so users of ggplot2 should find it familiar.
To start using Gadfly we’ll first need to load the package. To enable generation of PNG, PS, and PDF output we’ll also want the Cairo package.
You can easily generate plots from data vectors or functions.
Gadfly plots are by default rendered onto a new tab in your browser. These plots are mildly interactive: you can zoom and pan across the plot area. You can also save plots directly to files of various formats.
Let’s load up some data from the nlschools dataset in R’s MASS package and look at the relationship between language score test and IQ for pupils broken down according to whether or not they are in a mixed-grade class.
Those two examples just scratched the surface. Gadfly can produce histograms, boxplots, ribbon plots, contours and violin plots. There’s detailed documentation with numerous examples on the homepage.
Watch the video below (Daniel Jones at JuliaCon 2014) then read on about Bokeh and Plotly.
## Bokeh
Bokeh is a visualisation library for Python. Bokeh, like D3, renders plots as Javascript, which is viewable in a web browser. In addition to the examples on the library homepage, more can be found on the homepage for Julia’s Bokeh package.
The first thing you’ll need to do is install the Bokeh library. If you already have a working Python installation then this is easily done from the command line:
Next load up the package and generate a simple plot.
The plot will be written to a file bokeh_plot.html in the working directory, which will in turn be opened by the browser. Use plotfile() to change the name of the file. The plot is interactive, with functionality to pan and zoom as well as resize the plot window.
## Plotly
The Plotly package provides a complete interface to plot.ly, an online plotting service with interfaces for Python, R, MATLAB and now Julia. To get an idea of what’s possible with plot.ly, check out their feed. The first step towards making your own awesomeness with be loading the package.
Next you should set up your plot.ly credentials using Plotly.set_credentials_file(). You only need to do this once because the values will be cached.
Data series are stored in Julia dictionaries.
You can either open the URL provided in the result dictionary or do it programatically:
By making small jumps through similar hoops it’s possible to create some rather intricate visualisations like the 3D scatter plot below. For details of how that was done, check out my code on github.
That was a static version of the plot. However, one of the major perks of Plotly is that the plots are interactive. Plus you can embed them in your site and it will, in turn, benefit from the interactivity. Feel free to interact vigorously with the plot below.
Obviously plotting and visualisation in Julia are hot topics. Other plotting packages worth checking out are PyPlot, Winston and Gaston. Come back tomorrow when we’ll take a look at using physical units in Julia. | 2017-09-20 12:58:06 | {"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": 0.19380657374858856, "perplexity": 2631.922093962691}, "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-2017-39/segments/1505818687281.63/warc/CC-MAIN-20170920123428-20170920143428-00532.warc.gz"} |
http://danielbachler.de/2016/02/19/tasks-and-effects-in-elm.html | # Tasks and Effects in Elm
February 19, 2016
(Disclaimer: This post was written about Elm 0.16. Signals have since been deprecated. The concepts in this post may still help understand how the Elm Architecture works internally, but the actual code has changed significantly)
This is the second post in a series on some of the concepts in Elm that might be a bit puzzling when you start out with Elm. In the last post about Signals in Elm I wrote about Signals and how they are behind the scenes of StartApp.Simple. In this post I get into long running operations like XHRs (aka AJAX). There are two closely related types that are involved in this, Tasks and Effects, and the exact differences between can be confusing in the beginning. So let’s dive right in:
Task is the more basic type (it is defined in Core) and so let’s start with this one. A Task represents a long-running operation that can fail (with an error type) or succeed (with a success type). It’s type is thus:
Task errorType successType
-- (or, as it is actually written in the library:)
There are only two values of Task you can create yourself in your code, without using a separate library. These two ways are two functions:
succeed : a -> Task x a
-- and
fail : x -> Task x a
These are ways to create task values without actually doing any long-running operations. This can be useful if you want to combine a long running task and a simple value in some way and process them further (you would then turn the simple value into a Task with succeed).
Most of the time you actually get in contact with tasks, these will be created for you by library functions that initialize the task so that it will perform some long running operation when the runtime executes it and handle the result of the operation according to Task semantics (I.e. that some native code will make sure to call fail or succed on the native representation of the task when the operation is finished).
Note that the operation doesn’t start right away! I said “when the runtime executes it”. In purely functional programming languages, inside the language you can never just perform a side effect (something that changes “the world” outside the internal state of your code), and sending an http request surely is a side effect in that sense. This is one of the big mental shifts from imperative programming, where you can always do this, to working with purely functional languages where you can’t.
So how does this actually work? The task you get back represents the long running action. When a library creates it for you, nothing “happens”, it just created a value (of type Task) that indicates what you would like to happen.
If you look at e.g. the implementation of the native part of the send function in http you will see that a Task is created in native JS code by handing it a callback. This callback is what will get called when the runtime actually executes the task. This is when the actual XHR request is created and performed - only when the runtime executes this callback.
So how do you get the runtime to run this task? By passing it into an outgoing port. I will go into detail on ports in a later blogpost, but suffice to say that they are a way to send messages between “native” JS and Elm (called an incoming port) and from Elm to native JS (an outgoing port). The runtime has some special casing for Tasks that come to it via outgoing ports that make it execute the callback the Task represents.
When the long running native code is done, it will either call succeed or fail on the task. In most real life code that uses the Elm Architecture you will set up a “chain” of task processing that will lead to the the end result of the task execution being that a value of your Action type is routed back through your update function. This value of your Action type is the usually tagged with the result of the task (e.g. the decoded Json response of an XHR).
As a last piece of info before we have a look at Effects and how all of this actually looks in an example, let me just mention that Tasks can easily be chained togehter with andThen, much like promises in JS are chained together.
### Effects
On to Effects! If you look at the definition for Effects it’s pretty simple:
type Effects a
| Tick (Time -> a)
| None
| Batch (List (Effects a))
None and Batch are helpers, so the basic things an Effect can represent are Tasks (with error type Never) and Ticks. The latter is used for animations if you want to do something at the next animation frame.
It’s very common to turn a Task into an Effect, whereas the inverse is usually only ever done by StartApp/the runtime.
Several libraries use Task to allow you to work with long running operations - Http is one, elm-history is another.
So how is this used? The Elm Architecture example 5 uses this very central piece of code:
getRandomGif : String -> Effects Action
getRandomGif topic =
Http.get decodeImageUrl (randomUrl topic)
Let’s look at what it does. It starts with creating a task that represents the Http get operation and then builds a chain on top of this. I will deconstruct this from using the pipe operator to normal function calls with type annotations to hopefully explain what’s happening:
getRandomGif topic =
getTaskWithError = Http.get decodeImageUrl (randomUrl topic)
So in the end, Effects in this case just wraps the Task for us. Because we used toMaybe and then mapped it to the NewGif type constructor function, this will result in an Action coming back to us via update when it is done that is either (NewGif Nothing) if the http request failed, or (NewGif "some-url-here") if it succeeds. If you want to understand how this wiring happens I would suggest looking at the implementation of Effects.
One thing that is worth looking at is the return type of the function: Effects Action. Effects has a type variable, just like for example List. So this is an Effects that deals with the Action type you define in your application - and this is the really neat part of how to make sure that you can deal with the result of the Task/Effect - the result will just be a value of your Action type!
At this point you may wonder: why have Effects at all? Aren’t they just weird wrappers for Tasks? Let’s quickly take a look again at how the Task case of the Effects type is defined:
type Effects a
The way StartApp is typed, going via Effects Action constraints all Tasks to come back with Actions and have the error type Never. This is really nice because it means that you don’t have to handle different task types to different ports, but you set up “pipelines” of tasks to effects like with getRandomGif above and it will all work out in a typesafe manner that the result of your tasks will be sent back to your program’s update function as Actions.
Ok, so finally, remember I wrote something about having to send Tasks off to an outgoing port. I you don’t do this, the Tasks will never be executed! If you want to use Effects, the easiest way is to switch from StartApp.Simple to StartApp. This brings three minor changes with it:
1. start no longer directly returns a Signal of Html but a record of 3 Signals: one for the html, one for the model, and, crucially for us, one of tasks.
2. The update function now returns not just the Model, but a tuple of (Model, Effects Action). I.e. that every case in your update function will have to return both the changed model and an Effect (which will often be Effects.none)
3. start gets a fourth parameter, inputs, for incoming Signals.
4. The tasks part of the record that is returned by start has to be handed to a port so that the Tasks/Effects are actually performed by the runtime like so:
app =
StartApp.start
{ init = init "funny cats"
, update = update
, view = view
, inputs = []
}
main =
app.html | 2021-05-15 20:28:55 | {"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": 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": 0.3999549448490143, "perplexity": 1221.7479561658643}, "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/1620243991378.52/warc/CC-MAIN-20210515192444-20210515222444-00634.warc.gz"} |
https://argocanada.github.io/argoFloats/index.html | The argoFloats package for the R language provides tools for downloading and analyzing collections of oceanographic Argo float datasets. Its developers are * Dan Kelley, Dalhousie University * Jaimie Harbin, Bedford Institute of Oceanography and Dalhousie University * Clark Richards, Bedford Institute of Oceanography * Dewey Dunnington, Bedford Institute of Oceanography
The CRAN version may be installed with
install.packages("argoFloats")
The development version may be installed with
library(devtools)
install_github("ArgoCanada/argoFloats", ref="develop")
where, of course, the devtools package must be installed first, if it is not already present on the user’s system.
Typical use will require also installing several other packages, using
install.packages(c("colourpicker", "curl", "lubridate", "ncdf4",
"oce", "ocedata", "s2", "sf", "shiny"))
Once things are set up as above, it will be possible to use all the features of argoFloats, many of which are illustrated in the documentation for its functions, and in the vignette that is built into the package, both of which are displayed on the user-oriented website. Note that the vignette also lists Youtube videos about the package.
As a practical example, the code block given below shows how to create a map and a temperature-salinity diagram for Argo float profiles near Abaco Island in the Bahamas. The key steps, many of which are common to most analyzes using the package, are as follows.
1. The getIndex function is used to download a worldwide index of float profiles. (Use ?getIndex to learn more about this function, and note in particular the destdir argument, which determines where the index and other argo files will be stored locally.)
2. The subset function is used to narrow the region of interest, yielding 39 profiles as of mid-June, 2020.
3. getProfiles is used to download the NetCDF files that contain the profile measurements.
4. readProfiles is used to read those files.
5. applyQC is used to set questionable data to NA. This uses quality-control (QC) flags that are present in the argo data.
6. plot is used to create a map plot. The image shows water depth in metres, determined through a call to the getNOAA.bathy function in the marmap package. For context, a star is drawn to indicate the centre of he focus region. A label is drawn above the map, showing the number of profiles. This illustrates the use of [[, a generic R function that is used in argoFloats to access data and metadata elements in argoFloats objects, as well as things that can be computed from these elements, such as seawater density, etc. Use ?"[[,argoFloats-method" to see the details of how [[ works.
7. plot is used again, to make a temperature-salinity diagram.
With this in mind, readers ought to find it easy to read the following code. A reasonable next step would be to try altering the code, perhaps to explore another region or to see whether the QC step is actually necessary.
library(argoFloats)
library(oce)
## 1. Get worldwide float-profile index, saving to ~/data/argo by default.
indexAll <- getIndex()
## 2. Narrow to a 30km-radius circle centred on Abaco Island, The Bahamas.
index <- subset(indexAll,
#> Kept 41 cycles (0.00161%)
## 3. Get NetCDF files for these profiles, saving to ~/data/argo by default.
profiles <- getProfiles(index)
## 4. Read the NetCDF files.
#> Warning in readProfiles(profiles): Of 41 profiles read, 2 have >10% of conductivity values with QC flag of 4, signalling bad data.
#> The indices of the bad profiles are as follows.
#> 3 8
#> Warning in readProfiles(profiles): Of 41 profiles read, 1 has >10% of pressure values with QC flag of 4, signalling bad data.
#> The indices of the bad profiles are as follows.
#> 3
#> Warning in readProfiles(profiles): Of 41 profiles read, 4 have >10% of salinity values with QC flag of 4, signalling bad data.
#> The indices of the bad profiles are as follows.
#> 3 6 7 13
#> Warning in readProfiles(profiles): Of 41 profiles read, 3 have >10% of temperature values with QC flag of 4, signalling bad data.
#> The indices of the bad profiles are as follows.
#> 3 7 13
## 5. Examine QC flags, and set questionable data to NA.
argosClean <- applyQC(argos)
plot(argosClean, which="TS")
par(oldpar) | 2022-06-28 14:38:30 | {"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": 0.17370222508907318, "perplexity": 4914.51969083074}, "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-2022-27/segments/1656103556871.29/warc/CC-MAIN-20220628142305-20220628172305-00561.warc.gz"} |
http://math.stackexchange.com/questions/160390/question-on-sequences | # Question on sequences
Exercise 37 in Apostol $10.20$ asks to find all complex $z$ such that $$\sum_{n=1}^{\infty} \frac{(-1)^n}{z+n}$$ converges.
I suspect this requires the use of either Abel's Test or Dirichlet's Test. My attempt so far has been to set $\{b_n\}=\frac{1}{n}$, which is a decreasing sequence of real numbers that converges to $0$. Then, I set $\{a_n\}=(-1)^n\frac{n}{z+n}$.
As $n\to\infty$, $$\{a_n\} \to (-1)^ne^{i\arg(\frac{n}{z+n})}$$ since $$|\frac{n}{z+n}|=\frac{n}{|z+n|}\to 1$$
In order to prove that this converges for all complex $z\not=-1,-2,\dots$, I must show that $A_n=\sum_{k=1}^{n} a_n$ is a bounded sequence (not necessarily that it converges). This would satisfy the hypotheses for Dirichlet's test.
-
$\frac{1}{z+n}\to0$ for $n\to\infty$. so the oscillating series converges. – akkkk Jun 19 '12 at 17:26
@Auke: Alternating series test requires terms to (eventually) decrease to 0, not just converge. You can easily construct a counterexamples. – Erick Wong Jun 19 '12 at 17:34
$$c_n:=\frac{1}{z+n}=\frac{x+n}{|z+n|^2}-i\frac{y}{|z+n|^2}=:a_n-ib_n \quad \forall \ z=x+iy \ne -n.$$ For every $z \in \mathbb{C}\setminus(-\mathbb{N})$ the sequences $a_n, \ b_n$ decrease to $0$, therefore the series $\sum_{n=1}^\infty(-1)^nc_n$ converges for every $z \in \mathbb{C}\setminus(-\mathbb{N})$.
-
Clear and concise! – Andrew Salmon Jun 19 '12 at 22:55
Very nice answer! – albmiz-mth Feb 9 '13 at 3:25
Use Cauchy property of convergent sequences and write $$\sum_{k=m}^n \frac{(-1)^k}{z+k}$$ Then write (suppose $m$ even) $$\frac{1}{z+m} - \frac{1}{z+m+1} = \frac{1}{(z+m)(z+m+1)} \sim m^{-2}$$ This should persuade you that the series converges for $z$ that makes any denominator different from zero.
-
We can use Abel transform. Let $s_n:=\sum_{j=0}^n(-1)^j$. We have for $n$ and $m$ integers, and $z\notin -\Bbb N$, \begin{align} \sum_{j=n+1}^{n+m}\frac{(-1)^j}{z+j}&=\sum_{j=n+1}^{n+m}\frac{s_j-s_{j-1}}{z+j}\\ &=\sum_{k=n+1}^{n+m}\frac{s_k}{z+k}-\sum_{k=n}^{m+n-1}\frac{s_k}{z+k+1}\\ &=-\frac{s_n}{z+n+1}+\frac{s_{n+m}}{z+m+n}+\sum_{k=n+1}^{n+m}\frac{s_k}{(z+k)(z+k+1)}. \end{align} This gives, for $n,m> |z|$, that $$\left|\sum_{j=n+1}^{n+m}\frac{(-1)^j}{z+j}\right|\leq \frac 1{n+1-|z|}+\frac 1{m+n-|z|}+\sum_{k=n+1}^{n+m}\frac 1{(k-|z|)(k+1-|z|)}.$$ Since the series $\sum_{k=1}^{+\infty}\frac 1{(k-|z|)(k+1-|z|)}$ is convergent, we get that the sequence $\{\sum_{k=1}^n\frac{(-1)^k}{z+k}\}$ is Cauchy if $z\neq -k$ for each integer $k$.
- | 2016-06-30 15:05:27 | {"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": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9926091432571411, "perplexity": 281.97380522486304}, "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-2016-26/segments/1466783398869.97/warc/CC-MAIN-20160624154958-00055-ip-10-164-35-72.ec2.internal.warc.gz"} |
https://math.stackexchange.com/questions/2899579/quick-way-to-add-and-concatenate-bits | # Quick way to add and concatenate bits
I've never learned how to do binary arithmetic and was wondering if there was a straightforward technique to doing the following things in your head:
2. Concatenate bits.
3. Read bit values into decimal form.
For (1), just being able to do:
101011
+ 101
‾‾‾‾‾‾
??????
101011 + 101 = 101011101 ? how to determinal decimal value
What I'm doing now is starting from the right, just walking through the bits until I get to about #4 and it gets too complicated lol. I go 00 = 0, 01 = 1, 10 = 2, 11 = 3, ..?.
For 1, you are just adding with carry like in base $10$. Start from the bottom and add each column. For 2, just recite one number after the other. For 3, it helps to memorize the powers of $2$. A fair number of people know them at least up to $2^{16}=65536$. Then you have to add in base $10$ the powers that have a $1$ in them. I would start from the least significant bit as the numbers stay small longer, but I don't know of a royal road. For your example $101011101=1+4+8+16+64+256=349$ where I did the addition in my head. It helped to have the number written down so I could point at it and keep my place. It also helps not to have to compute that the highest bit is worth $256$. | 2021-08-05 13:36:44 | {"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": 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": 0.4853914976119995, "perplexity": 191.02718073884046}, "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-2021-31/segments/1627046155925.8/warc/CC-MAIN-20210805130514-20210805160514-00461.warc.gz"} |
https://www.edaboard.com/threads/bit-reversal-in-verilog.396228/ | # bit reversal in Verilog
#### fragnen
##### Member level 5
There are wires and an assignment statement to get the reverse of the bits for signs and output_signs should eith het the signs in same order or in reverse order as follows
Code:
wire [2:0] signs;
wire [2:0] output_signs;
wire control;
assign output_signs = control ? signs [2:0] : signs [0:2];
Will the above Verilog code work and have no issues?
Will the above Verilog code work and no issues will be the if the above assignment statement is replaced as follows:
Code:
assign output_signs = control ? signs [2:0] : {signs [0], signs[1], signs[2]};
#### KlausST
##### Super Moderator
Staff member
Hi,
Honestly I don't know.
But what speaks against trying it? A simulation should be rather simple...and should be done anyway.
I expect it to work.
What confuses me is the naming.
"Sign" usually shows whether the value is positive or negative.
Sign[2:0] ... sounds as if there are 3 sign bits, but no value
Klaus
#### fragnen
##### Member level 5
Hi,
Honestly I don't know.
But what speaks against trying it? A simulation should be rather simple...and should be done anyway.
I expect it to work.
What confuses me is the naming.
"Sign" usually shows whether the value is positive or negative.
Sign[2:0] ... sounds as if there are 3 sign bits, but no value
Klaus
The problem may come during synthesis. Simulation may work. The name can be changed from existing signs. Let someone else reply.
#### FvM
##### Super Moderator
Staff member
The question can be easily answered by reviewing the Verilog language reference manual. Is it a correct bit concatenation expression? If so, what are you worrying about?
#### fragnen
##### Member level 5
FvM
Can you please let me know what Verilog reference manual states on this? What is being worried whether this is correct in doing in Verilog as the book which is being referred does not state in this regard.
#### FvM
##### Super Moderator
Staff member
My favourite reference is the Verilog IEEE 1364 standard respectively the SystemVerilog IEEE 1800 replacing the former. Bit concatenation syntax is a rather basic point covered by many tutorials and text books.
The recent IEEE 1800-2017 version is available for free by the IEEE Get program https://ieeexplore.ieee.org/document/8299595
#### fragnen
##### Member level 5
My favourite reference is the Verilog IEEE 1364 standard respectively the SystemVerilog IEEE 1800 replacing the former. Bit concatenation syntax is a rather basic point covered by many tutorials and text books.
The recent IEEE 1800-2017 version is available for free by the IEEE Get program https://ieeexplore.ieee.org/document/8299595
There is no mistake in bit concatenation format. There may be mistake in getting the reverse assignment of bits. Please comment.
--- Updated ---
I got the above document, but not from that link. Where is the relevant section to look out for this in this document as it is a big document and some of the sections discusses about concatenation in this doc, but still did not obtain the relevant section. Can you please indicate which page is it in this document?
Last edited:
##### Super Moderator
Staff member
It appears it was removed from the IEEE get program. I assume Acellera (who I think was the sponsor) ended their sponsorship of the specification.
There is no specific section devoted to bit-reversal. You perform bit reversal either using the concatenation operation & or by using a for loop to assign the bits in reverse order.
#### fragnen
##### Member level 5
It appears it was removed from the IEEE get program. I assume Acellera (who I think was the sponsor) ended their sponsorship of the specification.
What you are trying to state is not understood. Can you please elaborate more so that what you want to state becomes clear.
Will both the two ways of reversing bits which has been shown in post number 1 will work correctly?
#### FvM
##### Super Moderator
Staff member
I thought 2 weeks should be sufficient to answer the question yourself. I expect that signs[0:2] is raising an error.
#### fragnen
##### Member level 5
I thought 2 weeks should be sufficient to answer the question yourself. I expect that signs[0:2] is raising an error.
But why signs[0:2] raise an error?
##### Super Moderator
Staff member
What you are trying to state is not understood. Can you please elaborate more so that what you want to state becomes clear.
If you want to understand the IEEE get program read the information you can find on the link that was posted in #6 by FvM. As you are asking me to clarify it is apparent you didn't read about the IEEE get program and only attempted to download the PDF.
Will both the two ways of reversing bits which has been shown in post number 1 will work correctly?
No only one of the examples you have will work correctly.
You can't define:
Code:
wire [2:0] signs;
and then access it with
Code:
signs[0:2]
signs no longer matches the definition of the bit order.
To perform a bit-reversal in Verilog/Systemverilog, either perform concatenation using & or use a for loop.
This is the concatenation code I was referring to that uses &:
Code:
assign output_signs = control ? signs [2:0] : {signs [0], signs[1], signs[2]};
other versions of your bit-reversal violated the Verilog language rules.
The other option is to use a for loop and perhaps put it in a function to make it easier to use. I won't post code as there are numerous code samples for using for loops in Verilog on the web.
### fragnen
points: 2
##### Super Moderator
Staff member
It just dawned on me that I should have been saying use , (comma not &) for the concatenation. I've been working on a VHDL design and was thinking in terms of VHDL concatenation. Sorry if that was confusing.
#### fragnen
##### Member level 5
You can't define:
Code:
wire [2:0] signs;
and then access it with
Code:
signs[0:2]
signs no longer matches the definition of the bit order.
How can we say that signs no longer matches the definition of bit order as SystemVerilog LRM does not talk anything of bit reversal and SystemVerilog LRM also mention anything of bit order when a signal/variable is declared as vector like signs[0:2] is a three bit vector.
This is the concatenation code I was referring to that uses &:
Code:
assign output_signs = control ? signs [2:0] : {signs [0], signs[1], signs[2]};
other versions of your bit-reversal violated the Verilog language rules.
But this code is same as one of my codes for bit reversal. Is not it?
##### Super Moderator
Staff member
How can we say that signs no longer matches the definition of bit order as SystemVerilog LRM does not talk anything of bit reversal and SystemVerilog LRM also mention anything of bit order when a signal/variable is declared as vector like signs[0:2] is a three bit vector.
Because it doesn't match. Is signs[2:0] the same as signs[0:2]? Signs is defined as having a bit range of [2:0]. You can bit slice it with any range where the left index is higher than the right index. Swapping to have the right index larger than the left doesn't match the original definition.
The LRM does discuss bit ordering of vectors somewhere, perhaps in section about bit slicing.
But this code is same as one of my codes for bit reversal. Is not it?
Yes it was the same code, I was just pointing out that is the only valid code you wrote to perform a bit reversal. All your other attempts are not valid and violate the vector bit order direction that was declared in the definition of the signals.
Last edited:
### fragnen
points: 2
#### VerLearn
##### Newbie level 5
There are wires and an assignment statement to get the reverse of the bits for signs and output_signs should eith het the signs in same order or in reverse order as follows
Code:
wire [2:0] signs;
wire [2:0] output_signs;
wire control;
assign output_signs = control ? signs [2:0] : signs [0:2];
Will the above Verilog code work and have no issues?
Will the above Verilog code work and no issues will be the if the above assignment statement is replaced as follows:
Code:
assign output_signs = control ? signs [2:0] : {signs [0], signs[1], signs[2]};
The problem with your statement is a[m:n] and a[n:m] are not treated the same in Verilog. You can select a part of the array instead, say a[0]. I don't have a problem as I'm picking an element from the array. Now, the idea is to pick all the elements individually reverse concatenate them. It works. Here is the sample code.
Code:
module test(input [3:0]in,
input clk,
output reg[3:0]out1,out2,out3,out4);
//-----------------------------Declaring parameters---------------------------
parameter[1:0] s0=0,s1=1,s2=2,s3=3;
reg [1:0]state;
//---------------------------Initializing state-------------------------------
initial state<=s0;
always@(posedge clk) begin
case(state)
//-------------------------------Declaring cases------------------------------
s0: begin out1<={in[0],in[1],in[2],in[3]}; state<=s1; end
s1: begin out2<={in[0],in[1],in[2],in[3]}; state<=s2; end
s2: begin out3<={in[0],in[1],in[2],in[3]}; state<=s3; end
s3: begin out4<={in[0],in[1],in[2],in[3]}; state<=s0; end
default: begin out1<=4'h0; out2<=4'h0; out3<=4'h0; out4<=4'h0; end
endcase
end
endmodule
Testbench:
module tb();
reg [3:0]in;
reg clk;
wire [3:0]out1,out2,out3,out4;
test i1(in,clk,out1,out2,out3,out4);
always #5clk=~clk;
initial begin
clk=0;
$dumpfile("tb.vcd");$dumpvars;
$monitor("output1=%b output2=%b output3=%b output4=%b",out1,out2,out3,out4); #4 in=4'b1010; #50$finish;
end
endmodule
Results:
output1=xxxx output2=xxxx output3=xxxx output4=xxxx
output1=0101 output2=xxxx output3=xxxx output4=xxxx
output1=0101 output2=0101 output3=xxxx output4=xxxx
output1=0101 output2=0101 output3=0101 output4=xxxx
output1=0101 output2=0101 output3=0101 output4=0101
Last edited by a moderator: | 2021-03-06 17:31:10 | {"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": 0.5061547160148621, "perplexity": 4067.425221264576}, "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/1614178375274.88/warc/CC-MAIN-20210306162308-20210306192308-00151.warc.gz"} |
http://nrich.maths.org/478/solution | ### Real(ly) Numbers
If x, y and z are real numbers such that: x + y + z = 5 and xy + yz + zx = 3. What is the largest value that any of the numbers can have?
### Roots and Coefficients
If xyz = 1 and x+y+z =1/x + 1/y + 1/z show that at least one of these numbers must be 1. Now for the complexity! When are the other numbers real and when are they complex?
### Pair Squares
The sum of any two of the numbers 2, 34 and 47 is a perfect square. Choose three square numbers and find sets of three integers with this property. Generalise to four integers.
Say that $x^2-a x+b=0$ has roots $\alpha$, $\beta$. Then $\alpha+\beta=a$ and $\alpha\beta=b$. Without loss of generality, $a\geq b$.
Case 1: $a=b$. Then $x^2-a x+a =0$. So $\alpha+\beta=\alpha\beta$, so $\alpha\beta-\alpha-\beta=0$, so $(\alpha-1)(\beta-1)=1$. Since $\alpha$ and $\beta$ are natural numbers, we must have $\alpha-1=1$ and $\beta-1=1$, so $\alpha=2=\beta$, so $a=4=b$.
Case 2: $a> b$. Then $\alpha+\beta> \alpha\beta$, so $(\alpha-1)(\beta-1)< 1$, so $(\alpha-1)(\beta-1)=0$, so $\alpha=1 or \beta=1$. Without loss of generality, $\alpha=1$, so $b=\beta$ and $a=\beta+1=b+1$. So the quadratics are $x^2-(b+1)x+b$ and $x^2-b x+b+1$. The first of these has roots 1 and $b$, as we expected. So we just need the second one to have natural number roots. So certainly $b^2-4b-4$ (the discriminant) is a square, say $b^2-4b-4=X^2$. Then $(b-2-X)(b-2+X)=8$. We can quickly check that we can't have 8, 1 as this gives a value of $b$ that isn't an integer. So we have $b-2+X=4$, $b-2-X=2$, so $b=5$. Now we are trying to solve $x^2-6x+5=0$ and $x^2-5x+6=0$, and these are clearly both soluble in positive integers.
So, to summarise, the only possible values are $a=4$, $b=4$, and $a=5$, $b=6$ (or obviously $a$ and $b$ reversed). | 2014-10-01 18:29:12 | {"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": 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": 0.9497812986373901, "perplexity": 92.42136028522276}, "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-2014-41/segments/1412037663551.47/warc/CC-MAIN-20140930004103-00223-ip-10-234-18-248.ec2.internal.warc.gz"} |
https://www.ideals.illinois.edu/handle/2142/23703 | ## Files in this item
FilesDescriptionFormat
application/pdf
9210876.pdf (4MB)
(no description provided)PDF
## Description
Title: The combined effects of airflow and carbon dioxide on chrysanthemum, dwarf wheat, and soybean Author(s): Korthals, Rodney Lee Doctoral Committee Chair(s): Christianson, Leslie L. Department / Program: Agriculture, Plant CultureEngineering, Agricultural Discipline: Agriculture, Plant CultureEngineering, Agricultural Degree Granting Institution: University of Illinois at Urbana-Champaign Degree: Ph.D. Genre: Dissertation Subject(s): Agriculture, Plant Culture Engineering, Agricultural Abstract: Effects of airflow direction and velocity on plant vegetative production were studied. Three plant species were studied: dwarf wheat (Triticum aestivum), chrysanthemum (Chrysanthemum morifolium), and soybean (Glycine max. L.). Specific objectives of this research were to: (1) Evaluate and improve environmental uniformity within plant growth chambers related to airflow velocity, airflow patterns, and CO$\sb2$ availability. (2) Quantify effects of horizontal airflow velocity at ambient and enriched CO$\sb2$, and horizontal versus vertical airflow patterns on plant vegetative growth.A literature review summarizes previous studies on the effects of airflow on plant heat and mass transfer, as well as on mechanical stresses caused by airflow and their effect on plant growth and quality.The development of a proportional and a proportional + integral (PI) CO$\sb2$ controller is described in detail, including the equipment used and control algorithms. The developed controllers maintained average CO$\sb2$ concentrations over a 12 hour period to within 3 and 1 $\mu$mol mol$\sp{-1}$ of set point for the proportional and PI controllers, respectively.Simple chambers were designed to test effects of 0.4, 0.8, and 1.5 m s$\sp{-1}$ airflow velocity on soybeans. Results indicated that velocities between 0.4 and 1.5 m s$\sp{-1}$ affected node number, height, and stem mass after 2 weeks of treatment, but that the plants were of similar size after 4 weeks of treatment.Experiments were performed to compare effects of horizontal and vertical airflow without CO$\sb2$ enrichment and horizontal airflow with 600 $\mu$mol mol$\sp{-1}$ CO$\sb2$ on dwarf wheat, chrysanthemum, and soybean. Soybean had larger leaf and whole plant relative growth rates (RGR) in vertical compared to horizontal airflow, while chrysanthemum had suppressed leaf and plant RGR in vertical compared to horizontal airflow. Vertical airflow appeared to cause mechanical stress in wheat, but evidence of mechanical stress was inconclusive for the other two species. Issue Date: 1991 Type: Text Language: English URI: http://hdl.handle.net/2142/23703 Rights Information: Copyright 1991 Korthals, Rodney Lee Date Available in IDEALS: 2011-05-07 Identifier in Online Catalog: AAI9210876 OCLC Identifier: (UMI)AAI9210876
| 2016-10-27 07:07:05 | {"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": 0.5112043619155884, "perplexity": 14780.702741303565}, "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/1476988721142.99/warc/CC-MAIN-20161020183841-00159-ip-10-171-6-4.ec2.internal.warc.gz"} |
https://www.techwhiff.com/issue/el-fin-de-esta-frase-es-similar-al-titulo-de-la-novela--546583 | # El fin de esta frase es similar al título de la novela. Sintetiza, en una o dos palabras acertadas tuyas, el juicio de Lázaro sobre la calidad de vida que ha tenido.
###### Question:
El fin de esta frase es similar al título
de la novela. Sintetiza, en una o dos
palabras acertadas tuyas, el juicio de
Lázaro sobre la calidad de vida que ha
tenido.
### As the manager of a high volume bank, you are faced daily with customers who are in a hurry and need decidedly speedy service from the window tellers. Which of the following would most likely cause your employees to offer the customers the service they want while also keeping your employees satisfied with their roles?A) pay them moreB) seek input from the tellers on how to improve their jobC) offer them flex timeD) bring donuts for the break roomE) let the tellers manage themselves
As the manager of a high volume bank, you are faced daily with customers who are in a hurry and need decidedly speedy service from the window tellers. Which of the following would most likely cause your employees to offer the customers the service they want while also keeping your employees satis...
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### -8 + 8 + -2 = help me plss :(
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### Which of the following describes work?Energy acts on an object.Force acts on an object and causes a displacement of that object.Force acts on an object.Friction only acts on an object and causes a displacement of that object.
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### I need to earn brainliest, so please answer this question only if you will make up questions, and mark me brainliest on them. I need brainliest things so i can talk to my friend. Whoever lets me get free brainliest things first gets marked brainliest by me. Thanks!
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### Find each product (x+5)(x-5)
Find each product (x+5)(x-5)...
### Liturgical worship is important
liturgical worship is important... | 2023-01-28 22:37:06 | {"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": 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": 0.1707792431116104, "perplexity": 4569.375861000313}, "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/1674764499695.59/warc/CC-MAIN-20230128220716-20230129010716-00336.warc.gz"} |
http://trac.parrot.org/parrot/ticket/1873 | # Ticket #1873 (closed bug: fixed)
Opened 11 years ago
## Windows2000 version requirement impeded build
Reported by: Owned by: jkeenan jkeenan normal 2.11 configure 2.10.0 medium whiteknight fperrad win32
### Description
[Reported by Patrick Abi Salloum on parrot-dev. Can some people with access to Win32 take a look at this? --kid51]
I was trying to build parrot RELEASE_2_10_1-477-gfa56f62 on windows 7 for rakudo.
Starting from a clean windows 7 install, I downloaded git version 1.7.3.1.msysgit.0 and strawberry perl 5.10.1.3..
perl ./Configure.pl --gen-parrot
From the rakudo folder, parrot was downloaded fine but suring the build I got an error:
Minimum requirement for Parrot on Windows is Windows 2000 -
might want to check windef.h
in config\gen\platform\win32\begin.c.
I removed the check if WINVER < Windows2000 from begin.c and the build went fine with no other problems.
## Change History
### follow-up: ↓ 2 Changed 11 years ago by ronaldws
I am partially responsible for the check in begin.c. There seems to be some differences between gcc configurations and include files between strawberry perl and mingw perl on it's own used with other Perls like ActiveState (my system). fperrad uses strawberry perl so I'm guessing the patch worked OK on his system. Might help to know what version of Strawberry Perl fperrad uses and what the WINVER in windef.h was on Patrick Abi Salloum's system. Anyway I will try to install strawberry perl 5.10.1.3 on one of my systems today and research further.
### in reply to: ↑ 1 Changed 11 years ago by ronaldws
and mingw perl
s/mingw perl/mingw c/
### Changed 11 years ago by NotFound
I'm using strawberry on Windows XP home and the check fails for me.
### Changed 11 years ago by ronaldws
I installed Strawberry Perl on one of my systems. The gcc compiler that was installed by Strawberry Perl is version 3.4.5 while the recent version of gcc that was installed by my separate install of Mingw is v 4.5. A quick look at
config/gen/platform/win32/sysmem.c
should explain why the two behave differently. There is an ifdef at the top of the file acting on gcc compilers with a version less than 4. I could sort of theoretically argue that the current Parrot isn't that far wrong in asking that you edit windef.h to tell your compiler to target up to date versions of Windows. Given the default gcc version choice for Strawberry Perl, the argument looks a bit impractical.
From a more practical point of view we don't really support Windows 95 and Windows NT 3.5x and don't actually expect many complaints from users running those systems. We should probably pull the check in begin.c and change sysmem.h approximately as described in the one line patch below:
-#if defined MINGW32 && GNUC < 4
+#ifndef MEMEMORYSTATUSEX
Ideally we should also add checks to parrot that abort both Configure.pl and the parrot runtime when run on obsolete versions of Windows. Again a practical solution might look different. I don't know if we actually get far enough on Win95/NT3.5 to make the code in sysmem.c a real problem. If we do then it may be just as easy to call the older GlobalMemoryStatus as it is to have it abort. I cannot quite tell that Parrot isn't already checking the Windows OS version but I grepped for the windows GetVersion and GetVersionEx calls and don't see anything that really matches.
There may be some judgement calls here other developers would prefer to make.
Ron
### Changed 11 years ago by fperrad
which gcc version comes with Strawberry Perl 5.10.1.3 ?
See history in TT#1846.
### Changed 11 years ago by jimmy
I'm using Strawberry Perl 5.10.1 gcc version 3.4.5 (mingw-vista special r3)
I got this error too.
### Changed 11 years ago by jimmy
fixed in f2af827fca, tests are welcome.
### Changed 11 years ago by jkeenan
• status changed from new to assigned
• owner set to jkeenan
We'll presume the problem has been fixed until we hear otherwise.
Thank you very much.
kid51
### Changed 11 years ago by jkeenan
• status changed from assigned to closed
• resolution set to fixed
Note: See TracTickets for help on using tickets. | 2022-12-08 02:02:07 | {"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": 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": 0.3001687228679657, "perplexity": 8276.427220928872}, "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-2022-49/segments/1669446711232.54/warc/CC-MAIN-20221208014204-20221208044204-00307.warc.gz"} |
https://alessiotonioni.github.io/publication/DIHE | # Domain invariant hierarchical embedding for grocery products recognition
Authors: Alessio Tonioni and Luigi Di Stefano
Published in Computer Vision and Image Understanding, 2019
## Abstract
Recognizing packaged grocery products based solely on appearance is still an open issue for modern computer vision systems due to peculiar challenges. Firstly, the number of different items to be recognized is huge (i.e., in the order of thousands) and rapidly changing over time. Moreover, there exist a significant domain shift between the images that should be recognized at test time, taken in stores by cheap cameras, and those available for training, usually just one or a few studio-quality images per product. We propose an end-to-end architecture comprising a GAN to address the domain shift at training time and a deep CNN trained on the samples generated by the GAN to learn an embedding of product images that enforces a hierarchy between product categories. At test time, we perform recognition by means of K-NN search against a database consisting of just one reference image per product. Experiments addressing recognition of products present in the training datasets as well as different ones unseen at training time show that our approach compares favorably to state-of-the-art methods on the grocery recognition task and generalize fairly well to similar ones.
Paper Dataset
## BibTex
@article{tonioni2019domain,
title={Domain invariant hierarchical embedding for grocery products recognition},
author={Tonioni, Alessio and Di Stefano, Luigi},
journal={Computer Vision and Image Understanding},
year={2019},
publisher={Elsevier}
} | 2021-09-23 20:03:09 | {"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": 0.21731826663017273, "perplexity": 2063.3762236274474}, "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-2021-39/segments/1631780057447.52/warc/CC-MAIN-20210923195546-20210923225546-00333.warc.gz"} |
https://www.infoq.com/news/2020/02/google-tc-malloc-open-source/ | InfoQ Homepage News TCMalloc, Google's Customized Memory Allocator for C and C++, Now Open Source
# TCMalloc, Google's Customized Memory Allocator for C and C++, Now Open Source
This item in japanese
To clear up any ambiguity, it is worth noting this is actually the second time Google open-sources its memory allocator. Indeed, Google had already provided its memory allocator as a part of Google Performance Tools in 2005 along with many other tools, including a memory profiler, a heap checker aimed to ensure heap consistency, and Perl-based ppro profile analyzer and visualizer. As it happens, though, the internal version in use at Google diverged with time from the external one, so Google is now open sourcing its current version of TCMalloc, which contains several improvements such as per-CPU caches, sized delete, fast/slow path improvements, and more.
This repository is Google’s current implementation of TCMalloc, used by ~all of our C++ programs in production. The code is limited to the memory allocator implementation itself.
As hinted above, TCMalloc includes implementations for the C *alloc family and for C++ ::operator new and ::operator delete. These provide a number of optimizations over their respective counterparts that come with the C and C++ standard libraries. For example, TCMalloc performs allocations from the OS using fixed-size "pages", which simplifies bookkeeping. Additionally, some of those pages are dedicated to objects of specific sizes, e.g., all 16-bytes objects. This also brings a simplification when it is time to get or release that memory. Finally, commonly-used objects are cached for speed of operation.
TCMalloc also supports telemetry extensions via MallocExtension which can be useful to gather heap profiles and snapshots to investigate memory behaviour.
A number of configuration options are available to tune TCMalloc performance. In particular, you can define the logical page size, which can be 4KiB, 8KiB, 32KiB, or 256KiB. Larger page-sizes will reduce the probability of requiring a new page allocation from the OS, thus speeding up operation at the cost of larger memory consumption. It is also possible to set the cache size on a per-thread or per-CPU basis, which is the default. Similarly to page sizes, larger cache sizes will improve performance. Finally, you can tune how aggressively memory is released, which also affects performances in several ways.
The following diagram shows TCMalloc architecture, which is thoroughly described in the relevant document:
TCMalloc can only be built using Bazel, Google's internal build system, and this might come as a less-than-ideal surprise to some developers using other build systems. Bazel, though, is available in binary format for macOS, Ubuntu, Fedora, and Windows, so this should not really be a major hindrance.
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• ##### They say it can be built with autoconf/automake/libtool
by Juan Castro /
• ##### Re: They say it can be built with autoconf/automake/libtool
by Sergio De Simone /
• ##### They say it can be built with autoconf/automake/libtool
by Juan Castro /
Your message is awaiting moderation. Thank you for participating in the discussion.
Am I missing something? From github.com/gperftools/gperftools/blob/master/IN... --
"As of 2.1 gperftools does not have configure and other autotools
products checked into it's source repository. This is common practice
for projects using autotools.
code.google.com/p/gperftools) still have all required files just as
before. Nothing has changed w.r.t. building from .tar.gz releases.
But, in order to build gperftools checked out from subversion
repository you need to have autoconf, automake and libtool
installed. And before running ./configure you have to generate it (and
a bunch of other files) by running ./autogen.sh script. That script
will take care of calling correct autotools programs in correct order.
If you're maintainer then it's business as usual too. Just run make
dist (or, preferably, make distcheck) and it'll produce .tar.gz or
.tar.bz2 with all autotools magic already included. So that users can
build our software without having autotools."
• ##### Re: They say it can be built with autoconf/automake/libtool
Your message is awaiting moderation. Thank you for participating in the discussion.
Hi Juan,
gperftools is a distinct project. It contains the older allocator Google released a few years back. The newer one is TCMalloc (github.com/google/tcmalloc). I think this should explain what you are reading.
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You will be sent an email to validate the new email address. This pop-up will close itself in a few moments. | 2020-09-28 23:21:29 | {"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": 0.17234955728054047, "perplexity": 5631.4900823580565}, "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/1600401614309.85/warc/CC-MAIN-20200928202758-20200928232758-00118.warc.gz"} |
https://iitutor.com/probability-with-wins-draws-and-losses-in-go-matches/ | # Probability with Wins, Draws and Losses in Go Matches
In a Go match between the Amy team and Ben team, a game is played on each of board $1$, board $2$, board $3$ and board $4$.
On each board, the probability that the Amy team wins is $0.2$, the probability of a draw is $0.6$ and the probability that the Ben team loses is $0.2$.
The results are recorded by listing the outcomes of the games for the Amy team in board order. For example, if the Amy team wins on board $1$, draws on board $2$, loses on board $3$ and wins on board $4$, the result is recorded as $WDLW$.
(a) How many different recordings are possible?
$3 \times 3 \times 3 \times 3 = 3^4$
(b) Calculate the probability of the result which is recorded as $WDDL$.
$0.2 \times 0.6 \times 0.6 \times 0.2 = 0.0144$
Teams score $2$ points for each game won, $1$ a point for each game drawn and $0$ points for each game lost. Find the probability that the Amy team scores more points than the Ben team.
(c) Find the probability that the Amy team scores more points than the Ben team.
$\displaystyle \begin{array}{|c|l|} \hline WWWW & 0.2^4 \\ \hline WWWD & ^4C_3 \times 0.2^3 \times 0.6 \\ \hline WWWL & ^4C_3 \times 0.2^3 \times 0.2 \\ \hline WWDL & ^4C_2 \times 0.2^2 \times 0.6 \times 0.2 \\ \hline WWDD & \dfrac{4!}{2!2!} \times 0.2^2 \times 0.6^2 \\ \hline WDDD & ^4C_1 \times 0.2 \times 0.6^3 \\ \hline \end{array}$
The sum of these probabilities is $0.3152$. | 2022-07-07 01:05:46 | {"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": 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": 0.1730101853609085, "perplexity": 1037.8471635543926}, "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-2022-27/segments/1656104683020.92/warc/CC-MAIN-20220707002618-20220707032618-00516.warc.gz"} |
https://ja.wikipedia.org/wiki/%E3%83%95%E3%82%A3%E3%83%BC%E3%83%AB%E3%82%BA%E8%B3%9E | # フィールズ賞
フィールズ賞
フィールズ・メダルの表面。アルキメデスの肖像と銘文 ラテン語: TRANSIRE SUUM PECTUS MUNDOQUE POTIRI（己を高め、世界を捉えよ[1]）が刻まれている。カナダの彫刻家によるデザインで[2]、カナダ王室造幣局で鋳造されている[3]。受賞者の名前は縁に刻まれる[4]
フィールズ賞（フィールズしょう）は、若い数学者のすぐれた業績を顕彰し、その後の研究を励ますことを目的に、カナダ数学者ジョン・チャールズ・フィールズ (John Charles Fields, 1863年 - 1932年) の提唱によって1936年に作られたのことである[5][6][7]
## 概要
4年に一度開催される国際数学者会議 (ICM) において、顕著な業績を上げた40歳以下[注釈 1]の数学者（2名以上4名以下）に授与される[5]。ICMで同時に授与される賞としては、ネヴァンリンナ賞ガウス賞チャーン賞などがある。
フィールズ賞は、フィールズ賞選考委員会で決められる[5]グリゴリー・ペレルマンは、2019年時点では受賞を辞退したただ一人の人物である。
### 他の贈賞との比較
2002年には、ノーベル賞により性格の近いアーベル賞が設立された。フィールズ賞とアーベル賞の両方を受賞した人物も存在する。
さらに2014年には、ノーベル賞をも超越する莫大な賞金額を誇る数学ブレイクスルー賞が創設された。
## 受賞者の一覧
1936年オスロ
「 Awarded medal for research on covering surfaces related to Riemann surfaces of inverse functions of entire and meromorphic functions. Opened up new fields of analysis. 」
「 Did important work of the Plateau problem which is concerned with finding minimal surfaces connecting and determined by some fixed boundary. 」
1950年ケンブリッジ
「 Developed the theory of distributions, a new notion of generalized function motivated by the Dirac delta-function of theoretical physics. 」
「 Developed generalizations of the sieve methods of Viggo Brun; achieved major results on zeros of the Riemann zeta function; gave an elementary proof of the prime number theorem (with P. Erdős), with a generalization to prime numbers in an arbitrary arithmetic progression. 」
1954年アムステルダム
「 Achieved major results in the theory of harmonic integrals and numerous applications to Kählerian and more specifically to algebraic varieties. He demonstrated, by sheaf cohomology, that such varieties are Hodge manifolds. 」
「 Achieved major results on the homotopy groups of spheres, especially in his use of the method of spectral sequences. Reformulated and extended some of the main results of complex variable theory in terms of sheaves. 」
1958年エディンバラ
「 Solved in 1955 the famous Thue-Siegel problem concerning the approximation to algebraic numbers by rational numbers and proved in 1952 that a sequence with no three numbers in arithmetic progression has zero density (a conjecture of Erdös and Turán of 1935). 」
「 In 1954 invented and developed the theory of cobordism in algebraic topology. This classification of manifolds used homotopy theory in a fundamental way and became a prime example of a general cohomology theory. 」
1962年ストックホルム
「 Worked in partial differential equations. Specifically, contributed to the general theory of linear differential operators. The questions go back to one of Hilbert's problems at the 1900 congress. 」
「 Proved that a 7-dimensional sphere can have several differential structures; this led to the creation of the field of differential topology. 」
1966年モスクワ
「 Did joint work with Hirzebruch in K-theory; proved jointly with Singer the index theorem of elliptic operators on complex manifolds; worked in collaboration with Bott to prove a fixed point theorem related to the "Lefschetz formula". 」
「 Used technique called "forcing" to prove the independence in set theory of the axiom of choice and of the generalized continuum hypothesis. The latter problem was the first of Hilbert's problems of the 1900 Congress. 」
「 Built on work of Weil and Zariski and effected fundamental advances in algebraic geometry. He introduced the idea of K-theory (the Grothendieck groups and rings). Revolutionized homological algebra in his celebrated "Tohoku paper" 」
「 Worked in differential topology where he proved the generalized Poincaré conjecture in dimension n≥5: Every closed, n-dimensional manifold homotopy-equivalent to the n-dimensional sphere is homeomorphic to it. Introduced the method of handle-bodies to solve this and related problems. 」
1970年ニース
「 Generalized the Gelfond-Schneider theorem (the solution to Hilbert's seventh problem). From this work he generated transcendental numbers not previously identified. 」
「 Generalized work of Zariski who had proved for dimension ≤3 the theorem concerning the resolution of singularities on an algebraic variety. Hironaka proved the results in any dimension. 」
「 Made important advances in topology, the most well-known being his proof of the topological invariance of the Pontrjagin classes of the differentiable manifold. His work included a study of the cohomology and homotopy of Thom spaces. 」
「 Proved jointly with W. Feit that all non-cyclic finite simple groups have even order. The extension of this work by Thompson determined the minimal simple finite groups, that is, the simple finite groups whose proper subgroups are solvable. 」
1974年バンクーバー
「 Major contributions in the primes, in univalent functions and the local Bieberbach conjecture, in theory of functions of several complex variables, and in theory of partial differential equations and minimal surfaces - in particular, to the solution of Bernstein's problem in higher dimensions. 」
「 Contributed to problems of the existence and structure of varieties of moduli, varieties whose points parametrize isomorphism classes of some type of geometric object. Also made several important contributions to the theory of algebraic surfaces. 」
1978年ヘルシンキ
「 Gave solution of the three Weil conjectures concerning generalizations of the Riemann hypothesis to finite fields. His work did much to unify algebraic geometry and algebraic number theory. 」
「 Contributed several innovations that revised the study of multidimensional complex analysis by finding correct generalizations of classical (low-dimensional) results. 」
「 Provided innovative analysis of the structure of Lie groups. His work belongs to combinatorics, differential geometry, ergodic theory, dynamical systems, and Lie groups. 」
「 The prime architect of the higher algebraic K-theory, a new tool that successfully employed geometric and topological methods and ideas to formulate and solve major problems in algebra, particularly ring theory and module theory. 」
1982年ワルシャワ
「 Contributed to the theory of operator algebras, particularly the general classification and structure theorem of factors of type III, classification of automorphisms of the hyperfinite factor, classification of injective factors, and applications of the theory of C*-algebras to foliations and differential geometry in general. 」
「 Revolutionized study of topology in 2 and 3 dimensions, showing interplay between analysis, topology, and geometry. Contributed idea that a very large class of closed 3-manifolds carry a hyperbolic structure. 」
「 Made contributions in differential equations, also to the Calabi conjecture in algebraic geometry, to the positive mass conjecture of general relativity theory, and to real and complex Monge-Ampère equations. 」
1986年バークレー
「 Received medal primarily for his work on topology of four-manifolds, especially for showing that there is a differential structure on euclidian four-space which is different from the usual structure. 」
「 Using methods of arithmetic algebraic geometry, he received medal primarily for his proof of the Mordell Conjecture. 」
「 Developed new methods for topological analysis of four-manifolds. One of his results is a proof of the four-dimensional Poincaré Conjecture. 」
1990年京都
「 For his work on quantum groups and for his work in number theory. 」
「 for his discovery of an unexpected link between the mathematical study of knots – a field that dates back to the 19th century – and statistical mechanics, a form of mathematics used to study complex systems with large numbers of components. 」
「 for the proof of Hartshorne’s conjecture and his work on the classification of three-dimensional algebraic varieties. 」
「 proof in 1981 of the positive energy theorem in general relativity 」
1994年チューリッヒ
「 Bourgain's work touches on several central topics of mathematical analysis: the geometry of Banach spaces, convexity in high dimensions, harmonic analysis, ergodic theory, and finally, nonlinear partial differential equations from mathematical physics. 」
「 ... such nonlinear partial differential equation simply do not have smooth or even C1 solutions existing after short times. ... The only option is therefore to search for some kind of "weak" solution. This undertaking is in effect to figure out how to allow for certain kinds of "physically correct" singularities and how to forbid others. ... Lions and Crandall at last broke open the problem by focusing attention on viscosity solutions, which are defined in terms of certain inequalities holding wherever the graph of the solution is touched on one side or the other by a smooth test function 」
「 proving stability properties - dynamic stability, such as that sought for the solar system, or structural stability, meaning persistence under parameter changes of the global properties of the system. 」
「 For his solution to the restricted Burnside problem. 」
1998年ベルリン
「 for his work on the introduction of vertex algebras, the proof of the Moonshine conjecture and for his discovery of a new class of automorphic infinite products 」
「 William Timothy Gowers has provided important contributions to functional analysis, making extensive use of methods from combination theory. These two fields apparently have little to do with each other, and a significant achievement of Gowers has been to combine these fruitfully. 」
「 contributions to four problems of geometry 」
「 He has made important contributions to various branches of the theory of dynamical systems, such as the algorithmic study of polynomial equations, the study of the distribution of the points of a lattice of a Lie group, hyperbolic geometry, holomorphic dynamics and the renormalization of maps of the interval. 」
2002年北京
「 Laurent Lafforgue has been awarded the Fields Medal for his proof of the Langlands correspondence for the full linear groups GLr (r≥1) over function fields. 」
「 he defined and developed motivic cohomology and the A1-homotopy theory of algebraic varieties; he proved the Milnor conjectures on the K-theory of fields 」
2006年マドリード
「 for his contributions to partial differential equations, combinatorics, harmonic analysis and additive number theory 」
「 for his contributions to geometry and his revolutionary insights into the analytical and geometric structure of the Ricci flow 」
「 for his contributions bridging probability, representation theory and algebraic geometry 」
「 for his contributions to the development of stochastic Loewner evolution, the geometry of two-dimensional Brownian motion, and conformal field theory 」
2010年ハイデラバード[18]
「 For his results on measure rigidity in ergodic theory, and their applications to number theory. 」
「 For the proof of conformal invariance of percolation and the planar Ising model in statistical physics. 」
「 For his proof of the Fundamental Lemma in the theory of automorphic forms through the introduction of new algebro-geometric methods. 」
「 For his proofs of nonlinear Landau damping and convergence to equilibrium for the Boltzmann equation. 」
2014年ソウル[19]
「 for her outstanding contributions to the dynamics and geometry of Riemann surfaces and their moduli spaces. 」
「 for his profound contributions to dynamical systems theory have changed the face of the field, using the powerful idea of renormalization as a unifying principle. 」
「 for developing powerful new methods in the geometry of numbers, which he applied to count rings of small rank and to bound the average rank of elliptic curves. 」
「 for his outstanding contributions to the theory of stochastic partial differential equations, and in particular for the creation of a theory of regularity structures for such equations. 」
2018年リオデジャネイロ[20]
「 For the proof of the boundedness of Fano varieties and for contributions to the minimal model program. 」
「 For contributions to the theory of optimal transport and its applications in partial differential equations, metric geometry and probability. 」
「 For transforming arithmetic algebraic geometry over p-adic fields through his introduction of perfectoid spaces, with application to Galois representations, and for the development of new cohomology theories. 」
「 For his synthesis of analytic number theory, homogeneous dynamics, topology, and representation theory, which has resolved long-standing problems in areas such as the equidistribution of arithmetic objects. 」
2022年（オンライン開催[注釈 3][21]
「 For solving longstanding problems in the probabilistic theory of phase transitions in statistical physics, especially in dimensions three and four. 」
「 For bringing the ideas of Hodge theory to combinatorics, the proof of the Dowling–Wilson conjecture for geometric lattices, the proof of the Heron–Rota–Welsh conjecture for matroids, the development of the theory of Lorentzian polynomials, and the proof of the strong Mason conjecture. 」
「 For contributions to analytic number theory, which have led to major advances in the understanding of the structure of prime numbers and in Diophantine approximation.解析的整数論に貢献し，素数の構造理解とディオファントス近似の理解に大きな進歩をもたらした[22]。 」
「 For the proof that the ${\displaystyle E_{8}}$ lattice provides the densest packing of identical spheres in 8 dimensions, and further contributions to related extremal problems and interpolation problems in Fourier analysis.球充填問題を８次元と24次元で解決したことや，フーリエ解析における極値および補間問題への更なる貢献が評価[22]。 」
アメリカ合衆国 14
フランス 14
ロシア
ソビエト連邦を含む）
9
イギリス 9
ウクライナ ベルギー
ドイツ
イラン
イタリア
2
オーストラリア
オーストリア
ブラジル
カナダ
フィンランド
イスラエル
ノルウェー
ニュージーランド
スウェーデン
ベトナム
1
## 脚注
### 注釈
1. ^ 正確な規定は次の通り：受賞年の1月1日より前に40歳の誕生日を迎えたものは候補となれない[8]。ただし厳格な規定が成文化されたのは1966年のICMにおいてである[9]
2. ^ たとえばアティヤはインタビューでそれらの名声と効果の違いについて比較し述べている[17]。また日本でフィールズ賞をとることは、ノーベル賞をとるようなものだが、英国では誰も気にとめてくれないなど、国によって扱われ方に違いがあることにも言及している。
3. ^ フィールズ賞の授賞式はヘルシンキで行われた。
### 出典
1. ^ モナスティルスキー 2013, p. 27.
2. ^ Tropp 1976, p. 181.
3. ^ Riehm 2002, p. 781.
4. ^ Curbera 2009, p. 111.
5. ^ a b c Fields Medal”. 国際数学連合. 2021年12月6日閲覧。
6. ^ 世界大百科事典 第2版『フィールズ賞』
7. ^ a b
8. ^ Curbera 2009, p. 110.
9. ^ Barany 2015, p. 17.
10. ^ “2006 Fields Medals awarded” (PDF). Notices of the American Mathematical Society (American Mathematical Society) 53 (9): 1037-1044. (10 2006) 2021年12月6日閲覧。.
11. ^ ICM2010におけるフィールズ賞を含むIMU各賞の受賞者について”. 日本数学会 (2010年8月19日). 2021年12月6日閲覧。
12. ^ a b Fields Medals Are Concentrated in Mathematical ‘Families’”. SCIENTIFIC AMERICAN. 2021年12月5日閲覧。
13. ^ モナスティルスキー 2013, p. 19.
14. ^ a b 「数学のノーベル賞」で女性初受賞、イラン出身の米大教授”. AFPBB News (2014年8月13日). 2021年12月6日閲覧。
15. ^ モナスティルスキー 2013, p. 34.
16. ^
17. ^ マイケル・F. アティヤ 『数学とは何か アティヤ 科学・数学論集』志賀浩二 訳、朝倉書店、2010年11月25日、148-149頁。ISBN 978-4-254-10247-5
18. ^ ICM 2010, p. 23.
19. ^ International Congress of Mathematicians (2014年). “Awards”. 2021年12月6日閲覧。
20. ^ International Mathematical Union (IMU) (2018年). “Fields Medals 2018”. 2021年12月6日閲覧。
21. ^ International Mathematical Union (IMU) (2022年). “Fields Medals 2022”. 2022年7月5日閲覧。
22. ^ a b 【ざっくり分かる】フィールズ賞2022 ，どんな人がどんな理由で受賞した？”. 2022年7月30日閲覧。 | 2023-04-01 05:51:36 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 1, "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": 0.6480045318603516, "perplexity": 671.431072520401}, "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-2023-14/segments/1679296949701.0/warc/CC-MAIN-20230401032604-20230401062604-00008.warc.gz"} |
http://gmatclub.com/blog/category/blog/gmat/page/188/?fl=menu | # GMAT Question of the Day (June 11): Word Problem and Sentence Correction
- Jun 11, 02:00 AM Comments [0]
Math (PS) If the farmer sells 75 of his chickens, his stock of feed will last for 20 more days than planned, but if he buys 100 more chickens, he will run out of feed 15 days earlier than planned. If no chickens are sold or...
# GMAT Question of the Day (June 10): Absolute Values (Modulus) and Sentence Correction
- Jun 10, 02:00 AM Comments [0]
Math (DS) Is Question Discussion & Explanation Correct Answer - E - (click and drag your mouse to see the answer) GMAT Daily Deals Over 4 M students achieved educational & career goals Kaplan’s unparalleled test prep courses. Save \$400. GMAT Pill: Learn to think through questions and take...
# GMAT Question of the Day (June 7): Geometry and Critical Reasoning
- Jun 7, 02:00 AM Comments [0]
Math (DS) Water evaporates at the rate of two liters per hour per one square meter of surface. How long will it take to evaporate 30 liters of water from a swimming pool full of water with vertical walls and a flat bottom that holds 56...
# Free Resources from Magoosh
- Jun 5, 12:39 PM Comments [0]
Hi, all! Here are some new resources and blog posts from Magoosh that we've been working on. Enjoy! The best of our recent GMAT blog posts: Multi-Source IR Practice question: Draw Loss Poker GMAT Critical Reading: Find the Conclusion or Inference What to Include in Your Admissions Resume...
# GMAT Question of the Day (June 5): Work Problem and Sentence Correction
- Jun 5, 02:00 AM Comments [0]
Math (PS) A furniture manufacturer has two machines, but only one can be used at a time. Machine A is utilized during the first shift and Machine B during the second shift, while both work half of the third shift. If Machine A can do the...
# GMAT Question of the Day (June 4): Arithmetic and Sentence Correction
- Jun 4, 02:00 AM Comments [0]
Math (PS) The square of = ? (A) (B) (C) (D) (E) Question Discussion & Explanation Correct Answer - B - (click and drag your mouse to see the answer) GMAT Daily Deals Over 4 M students achieved educational & career goals Kaplan’s unparalleled test prep courses. ...
# GMAT Question of the Day (June 3): Coordinate Geometry and Sentence Correction
- Jun 3, 02:00 AM Comments [0]
Math (PS) What is the area of a triangle with the following vertices , , and ? (A) 3 (B) 4 (C) 5 (D) 6 (E) 7 Question Discussion & Explanation Correct Answer - D - (click and drag your mouse to see the answer) GMAT Daily Deals Manhattan GMAT: 99 percentile...
# GMAT Question of the Day (May 31): Algebra and Critical Reasoning
- May 31, 02:00 AM Comments [0]
Math (DS) If is a positive integer, is \sqrt{x} < 2.5x - 5[/latex] ? 1. $x < 3$ 2. $x$ is a prime number Question Discussion & Explanation Correct Answer - A - (click and drag your mouse to see the answer) GMAT Daily Deals e-GMAT’s methods help non-natives improve on...
# GMAT Question of the Day (May 30): Word Problem and Critical Reasoning
- May 30, 02:00 AM Comments [0]
Math (PS) Two cities, Kensington MD and Reston VA are 30 km apart. From both of these cities, simultaneously, two hikers start their journeys towards each other. They are walking at a constant speed of 5 km/hour each. Simultaneously, a fly leaves the city of Kensington....
# GMAT Question of the Day (May 29): Arithmetic and Sentence Correction
- May 29, 02:00 AM Comments [0]
Math (DS) What is the value of ? 1. is odd 2. is even Question Discussion & Explanation Correct Answer - C - (click and drag your mouse to see the answer) GMAT Daily Deals Over 4 M students achieved educational & career goals Kaplan’s unparalleled test prep courses.... | 2016-06-27 07:52:26 | {"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": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3649546205997467, "perplexity": 6213.581930211217}, "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-2016-26/segments/1466783395679.18/warc/CC-MAIN-20160624154955-00198-ip-10-164-35-72.ec2.internal.warc.gz"} |
https://tex.stackexchange.com/questions/313656/out-of-slide-comment-environment-in-beamer | # Out-of-slide comment environment in Beamer
Comment package does not work in beamer
explaining how, for \begin{comment} etc. \end{comment} to work, it needs to go inside a 'Fragile' frame. But what if I want an out-of-frame comment? Is there some workaround for the comment package, or another package with the same effect which is more, shall we say, forgiving regarding where it's used?
• What exactly do you mean with "out-of-frame comment"? – user36296 Jun 8 '16 at 9:39
• @samcarter: I mean having that comment environment outside of any frame, immediately within the document environment. – einpoklum - reinstate Monica Jun 8 '16 at 9:51
This is Text
\iffalse
This is Text, too, but not printed
\fi
Another text
Am I missing something or can you simply do:
\documentclass{beamer}
\usepackage{comment}
\begin{document}
\begin{frame}
random text
\end{frame}
\begin{comment}
hidden text
\end{comment}
\end{document}
(Works without errors with pdflatex of TeXlive 2015, 2016 and 2017, I have not tested other engines.)
Alternatively you could use the ignorenonframetext option of beamer:
\documentclass[ignorenonframetext]{beamer}
\begin{document}
\begin{frame}
random text
\end{frame}
hidden text
\end{document}
• Yes, you are missing something, this gets me an error message. – einpoklum - reinstate Monica Jun 8 '16 at 10:42
• @einpoklum Works for me with Texlive2015 and 2016 without errors. What does your error message say? – user36296 Jun 8 '16 at 10:46 | 2019-11-22 01:07:08 | {"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": 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": 0.9098629951477051, "perplexity": 4680.520562161227}, "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-2019-47/segments/1573496671053.31/warc/CC-MAIN-20191121231600-20191122015600-00076.warc.gz"} |
https://www.physicsforums.com/threads/given-the-partial-derivatives-find-the-function-or-show-it-does-not-exist.644304/ | # Given the partial derivatives, find the function or show it does not exist.
1. Oct 15, 2012
### Jormungandr
1. The problem statement, all variables and given/known data
$f'_x = kx_k, k = 1, 2, ..., n$
3. The attempt at a solution
The partial should be f(sub)x(sub)k, as in, the partial derivative of $f$ with respect to $x_k$. I wasn't sure how to represent that using TeX.
I'm honestly at a complete loss here, because I'm not entirely sure what the subscripts refer to. I suppose if $k = 1$, then the derivative of $f$ with respect to $x_k$ $= 1x_1$, but that tells me absolutely nothing because I don't even know what that $x_1$ refers to...
Any help would be much appreciated!
2. Oct 15, 2012
### SammyS
Staff Emeritus
f_{x_k} → $\displaystyle f_{x_k}$
The subscripts mean that you have n variables.
Rather than using x, y, and z for three variable, you could use x1, x2, and x3 .
What if n = 100 ? How else would you name all the variables ?
For instance, if we did use x, y, and z for x1, x2, and x3, we would have:
$\displaystyle f_{x}=x$
$\displaystyle f_{y}=2y$
$\displaystyle f_{z}=3z\ .$
Last edited: Oct 15, 2012
3. Oct 15, 2012
### Zondrina
So you have some partial of f with respect to some xk where :
fxk = kxk
For a varying constant k.
You want to find your original function f. What happens if you integrate here?
Note that xk refers to an INDEPENDENT variable. We could have chosen y, z, u, etc.
4. Oct 15, 2012
### Jormungandr
I realized that a few minutes after I posted it, my bad!
So we've got $f_{x_k}=kx_x$.
The function $f$ described by this set of partial derivatives should be in the form $f(x_1, x_2, ... , x_n)$, right? So I run into a bit of a snag when we integrate that partial.
If $f_{x_1} = x_1$, then
$f(x_1, x_2, ... , x_n)$ = $\frac{1}{2}x_1^2 + g(x_2, ... x_n)$
If this is correct, then moving on:
$f_{x_2}=g_{x_2}(x_2, x_3, ... , x_n)$
Implying:
$g_{x_2}(x_2, x_3, ... , x_n) = 2x_2$, right? And that:
$g(x_2, x_3, ..., x_n) = x_2^2 + h(x_3, x_4, ... , x_n)$
Well, I did this process over a few times and I'm reaching a definite pattern here, that shows:
$f(x_1, x_2, ... , x_n) = \frac{1}{2}x_1^2 + x_2^2 + \frac{3}{2}x_3^2 + 2x_3^2 + j(x_5, x_6, ... , x_n)$.
Which seems to imply that
$f(x_1, x_2, ... , x_n) = \frac{k}{2}x_k^2 +$ some function of g. Of course, I realize I would have arrived at this exact expression if I had integrated the beginning expression, I just wanted to see where this process would lead me.
Now, an issue arises with the function of g afterwards. Should it be:
$f(x_1, x_2, ... , x_n) = \frac{k}{2}x_k^2 + g(x_{k+1}, x_{k+2}, ... , x_n)$?
Have we arrived at the solution or is there some compact way to write the function of g? Or have I done it all wrong completely? :P Thanks!
5. Oct 15, 2012
### SammyS
Staff Emeritus
It looks like you have:
$\displaystyle f(x_1, x_2, ... , x_n) = \frac{1}{2}\left((x_1)^2 + 2(x_2)^2 + 3(x_3)^2 + 4(x_4)^2 + \dots\right)$
Where does it end?
6. Oct 16, 2012
### HallsofIvy
Staff Emeritus
Look at the mixed partial derivatives. As long as the derivatives are continuous, mixed partial derivatives, with the same derivatives in different order, must be equal.
For example, if $f(x,y)= x^2+ 3xy+ y$, $f_x= 2x+ 3y$ and $f_y= 3x+ 1$ so that, differentiating $f_x$ with respect to y, $f_{xy}= 3$ and, differentiating $f_y$ with respect to x, $f_{yx}= 3$.
If we are told that $f_x= 3x+ 2y$ and $f_y= x- 2y$, we know that is impossible because that gives $f_{xy}= 2$ and $f_{yx}= 1$ which are not equal. | 2017-08-16 20:59:14 | {"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": 0.9166627526283264, "perplexity": 398.18249886179063}, "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-2017-34/segments/1502886102393.60/warc/CC-MAIN-20170816191044-20170816211044-00711.warc.gz"} |
https://physics.stackexchange.com/questions/221890/direction-of-gamma-ray-bursts/222948 | # Direction of Gamma Ray Bursts
After a black hole consumes a star, why do gamma ray bursts only shoot out perpendicular to the spinning accretion disk? Why do they not shoot out parallel to the disk?
• The source of the gamma rays is thought to be within the twisted magnetic fields along the poles of the spinning black hole. The source is also thought to be relativistic particles. Since the radiation pattern from a fast moving source is "warped" due to relativistic effects, the result is a beam-like emission. – honeste_vivere Dec 3 '15 at 13:46
Roughly speaking, the opening angle of the beam is given by $1/\gamma$ (in radians), where $\gamma = (1 - v^2/c^2)^{-1/2}$ is the Lorentz factor of the charged particles moving with speed $v$. These factors can be estimated from GRB afterglows and are found to be in the range of 10-1000 (Hascoet et al. 2013; Tang et al. 2014), leading to opening angles for the beam of 0.06-6 degrees. Thus little or no radiation emerges parallel to the disk. | 2019-12-09 15:06:29 | {"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": 0.8114054799079895, "perplexity": 417.7530923771428}, "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-2019-51/segments/1575540519149.79/warc/CC-MAIN-20191209145254-20191209173254-00029.warc.gz"} |
https://agenda.infn.it/event/10289/?view=event | 1. General Seminars
Tetraquarks, pentaquarks and dibaryons
by Prof. Luciano Maiani (La Sapienza University)
Europe/Rome
Aula Bruno Touschek (LNF INFN)
Aula Bruno Touschek
LNF INFN
Via Enrico Fermi, 40 00044 Frascati
Description
The discovery of two pentaquarks by LHCb has reinforced the case of “exotic’ hadrons, which have diquarks and antidiquarks as basic units. I review the cases studied until now, the so called XYZ states, the theoretical basis for this concept and the implications for the existence of further states, with baryon number equal two. | 2020-02-24 09:40:08 | {"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": 0.8501303791999817, "perplexity": 10627.66202163539}, "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-2020-10/segments/1581875145910.53/warc/CC-MAIN-20200224071540-20200224101540-00380.warc.gz"} |
https://www.appropedia.org/Kingston_Hot_Press:_Process_Improvements | Project data
Status Designed
Modelled
Prototyped
Verified
Deployed
Verified by Waste for Life
RSID
Queen's University
Export to Open Know How Manifest
Page data
Part of Mech425
Type Project
Keywords Recycling, Engineering
Authors Nate Preston
Published 2010
License CC BY-SA 4.0
Affiliations Queen's University
Page views 4,109
Location data
Loading map...
Location Kingston, Canada
Check out the project on wasteforlife.org Hot Press Discussion Page
The organization Waste for Life (WFL) defines itself as "a loosely joined network of scientists, engineers, educators, architects, artists, designers, and cooperatives who work together to develop poverty-reducing solutions to specific ecological problems."[1] Through a collaboration with researchers and community members at Queen's University, the Centro Experimental de la Produccion (CEP) in Argentina, the Rhode Island School of Design (RISD), Smith College, and the University of Western Australia, the Kingston Hot Press has been designed and developed to provide the means of production to smaller cooperatives in communities in Argentina and Lesotho. The Hot Press allows the user to produce a value-added composite tile out of waste plastic and fiber (most commonly cardboard and paper). Currently three prototypes have been built, one at Queen's, one at RISD, and one at CEP. Detailed design drawings are available at the WFL website.
# Problem Definition and Scope
The WFL team has identified several key areas of design development that they would like to pursue:[2]
• Dimensions - The current Kingston Hot Press can produce a 24"x24"x1/4" sheet. A wider gap in the press could allow more width and perhaps allow for 3D molds. The size constraints could be circumvented if pieces could be produced in modules and then connected post-production.
• Heating Sources - Currently the plate heaters require electricity. CEP has expressed interest in a gas powered system.
• Temperature Consistency - Initial tests had shown inconsistencies between the temperature distribution on the top and bottom plates. To remedy this, researchers at Queen's replaced the 1/4" steel heating plates with 1/2" aluminum plates.
• Opening between top and bottom plates - Currently molds are slid between the heating plates. A "clam shell" lid design could allow for a more diverse range of geometries and facilitate the use of 3D molds.
• Safety and Environmental Issues - Fire safety, emissions, pollutants.
• Production Speed - The current system requires a time intensive production process to arrive at a single 1/4" composite tile. CEP has expressed interest in finding ways to improve throughput.
Currently the temperature consistency problem has been resolved with very expensive aluminum plates. A heat transfer model could assist in the evaluation of different solutions and hopefully provide an optimal solution that could use less costly and more widely available materials.
## Client
There are several key stakeholders that I have identified for this project. Here at Queen's I am working to assist Dr. Matovic with design improvements based on the Hot Press prototype in Kingston. More broadly, I hope my work can contribute to the Waste For Life team. Finally the end-user of the hot press is the cartoneros, the workers who partake in the informal economy of waste in Argentina.[3][4]
## Goals
I would like to develop a useful heat transfer model which could assist the WFL team in reducing the cost of the Hot Press. I would also like to take this opportunity to expand the reach of the WFL team and share their innovative design. Finally, I would like to provide a clear pictographic instruction manual for users of the Hot Press.
# Constraints
The hot press should provide a low-cost tool to access the means of production and add value to "waste" products. As such, materials should be as economical and accessible to the cartoneros communities as possible.
Design work must be limited to theoretical analysis as significant empirical testing would require equipment not currently available for the budget and scope of the project. Future work could include an empirical evaluation of several plate designs using an array of thermal transducers (thermistors, or thermocouples) to determine realized temperature gradients in the hot press.
# Prior Art
At Queen's University Dr. Matovic has produced CAD drawings fully detailing the design and dimensions of the Kingston Hot Press as shown in Figure 1. The original design used 1/4" steel plates to press and heat the tiles. To overcome temperature inconsistencies which were producing burnt profiles the prototype plates were replaced with 1/2" aluminum plates.
# Theory and Methodology
Although the design of a hot press plate must ideally involve both a heat transfer model and a finite element static stress analysis it will be assumed for the following optimization that based on previous work by the WFL team, the 1/4" steel plate provides a minimum benchmark thickness for the plate and a lower limit for allowable bending and deformation of the plate. Therefore the following analysis will focus on better understanding the heat transfer mechanisms in the heat press, and how these effect the performance of the press.
### Heat transfer
(see also the Wikipedia article)
The Kingston Hot Press presents a particularly challenging heat transfer system to model. Six 750W Omega OT-2107 strip heaters are clamped to the two "press" plates which transfer heat and pressure to the mold and tile composite material. A cork rubber gasket provides insulation between the press plates and the steel weldments which provide the necessary structural support for the device. A simple on/off controller regulates the temperature of the center of the plate with a thermocouple transducer. Standard setpoints range between 150°C and 250°C. Since a tile (or film) can be pressed within 5-35 minutes depending on the thickness of the mold, the problem almost certainly falls within the transient time period. However, the plates are preheated to the setpoint temperature, and so a steady state model can assist in determining the ideal performance of the heating plates upon the initiation of the press cycle.
A preliminary 2D model of the plate was developed to allow for a general understanding of the behaviour of the plate which could be made accessible for the community through open office. Using a 2D finite element control volume approach[5] a rough estimate of the temperature distribution can be arrived at in a simple spreadsheet. Using each cell as a finite control volume the energy balance equation can be used to derive an equation for the control volume (spreadsheet cell) temperature.
The energy balance equation for a 2D control volume is given by:
$\displaystyle{ q_n+q_e+q_s+q_w=0 }$
Where q is the energy leaving (or entering) each boundary of the control volume, denoted by n=north, e=east, s=south, and w=west. Note this assumes no generation or storage within the control volume.
This simplifies in a medium surrounded by a material with identical conductivity to the average of the neighbouring cell temperatures:
$\displaystyle{ Tcv={Tn+Te+Ts+Tw\over 4} }$
Assuming heat loss through the edges due to convective heat transfer we can derive the temperatures for edge cells and corner cells:
Edge Cells (example N edge)- $\displaystyle{ Tcv={hTn+k(Te+Ts+Tw)\over h+3k} }$
Corner Cells (example NW corner)- $\displaystyle{ Tcv={h(Tn+Tw)+k(Te+Ts)\over 2h+2k} }$
Where h is the convection coefficient, and k is the conduction coefficient.
These equations when put into Excel or Calc can be solved iteratively (See this help for Excel). The screenshot below shows the three strip heaters (approximated as constant temperature surfaces) surrounded by the aluminum plate and the resulting temperature distribution. Although this is a rudimentary model, it provides an immediate sense of the geometry and gradient in a way that can be easily distributed and modified through OpenOffice.
The file can be downloaded in Open Office format Media:2d Plate model 3 strips.ods or Excel Media:2d Plate model 3 strips.xls. Another model was developed for four square heaters which could be used to investigate the design of a modified hot press that used stove element heaters instead of the more specialized Omega heaters and can be found here Media:2d Plate model 3 strips square.xls.
### Plate Optimization
If the top of a plate is unevenly heated, with finite thickness and conductivity the bottom of the plate will not have a perfectly even temperature distribution. In practice, an effectively trivial temperature gradient can be arrived at with a plate of high enough conductivity and thick enough profile to provide adequate opportunity for the surface to equilibrate.
By modeling the temperature distribution on the press plate through SolidWorks COSMOSWorks heat transfer tool an optimization of the plate material and thickness can be undertaken. SolidWorks was convenient as previous CAD work had already been done for the Kingston Hot Press in this software and was readily available to undergraduates at Queen's. Unfortunately, this software is not readily available to all interested readers and therefore I must leave it to future work to transcribe the CAD to an open source program.
### Pictographic Instruction
After a brief review of the fascinating area of visual communication and instruction [6][7] I hope to produce a simple pictorial instruction for using the Kingston Hot Press. Pictures are not ideal for printing and distributing and therefore further work could also be done to produce a schematic visual instruction set that would be sufficient to overcome language barriers. I find this area very interesting and would love to hear from knowledgeable readers who could direct me to further resources.
# Final Analysis
### Plate Optimization
Due to the computational limitations, only the top half of the Kingston Hot press was analyzed in SolidWorks. The components included in the meshing and analysis were the:
• Top plate
• Top gasket
• Top heaters
• Top weldment
The mesh shown below was generated automatically through the SolidWorks mesh function.
The thermal analysis carried out through COSMOWorks utilized the following Load/Restraints:
• Each strip heater was assumed to be producing 250W of heat at the plate contact. This assumption was based on the pseudo-steady state condition reached by the press after pre-heat, and the fact that the controller acts to regulate the 750W heaters to maintain the setpoint temperature.
• It was assumed the setpoint temperature was successfully maintained at 150°C at the interface between the heaters and the plate. This is a strong assumption as only one thermocouple is held against the top plate surface at the edge of the plate.
• It was assumed that the outer walls of the weldment had a convection coefficient of 10W/m2K to the ambient air.
• It was assumed that the outerweldment walls radiated heat energy to the surroundings using a view factor of 1.[8]
Using these constraints a numerical thermal analysis was performed. The image below represents temperatures across the top of the hot press for an aluminum plate of 0.25" with the colour legend ranging from 426K-313K.
Very similar results were found for the steel plate (image is not shown). The image below represents temperatures across the bottom of the hot press for the same plate and it qualitatively appears that there are minimal temperature fluctuations across the bottom face of the plate. Again the steel plate simulation produced quantitatively indistinguishable results.
To confirm these qualitative observations a representation was produced of the temperature gradient across the bottom face of the aluminum plate shown in the image below:
A similar result showing the gradient across the bottom face of the plate to be negligible was found for the steel plate analysis.
These results were very disappointing, and therefore a re-evaluation of the Load/Restraints assumptions was performed. Further investigation found that the edges of the plate were not being given a mechanism for heat loss. As the edges of the plates are very exposed, it was assumed that the convection coefficient between the edges of the plate and the air was 10W/mK. The set temperature on the top face of the plate was removed as it was deemed to be artificially forcing the analysis to display high temperature consistency across the plate. Finally, because there was not a temperature setpoint, an average power of the heaters was reduced to an assumption of 175W.
With these new constraints, results were obtained that better reflected the behaviours described by the users of the Kingston Hot Press. The image below represents temperatures across the bottom surface of the plate for an aluminum plate of 0.25" with the colour legend ranging from 485K-318K. The temperature non-uniformity is now clear.
The new analysis shows the 0.25" steel plate having a noticeably worse temperature distribution as shown in the image below:
A comparison of the aluminum and steel 0.25" plates using a representation of the temperature gradient (using identical colour legends) now shows the aluminum having notably lower gradients across the plate then the steel. The first image below is of the aluminum plate, followed by the steel plate.
Finally, a model was developed to consider the replacement of the 1/2" aluminum plate with a 1/2" steel plate. Below are the temperature and gradient representations of the bottom surface of the steel plate respectively. Although the steel plate still does not match the aluminum for the gradient, there is a noticeable improvement over the 1/4" plate. Based on these findings it appears a 1/4" aluminum plate would provide the most economical even temperature distribution for the Kingston Hot Press.
### Pictographic Instructions
1
Turn on the Kingston Hot Press to preheat. This will save you time later.
2
Place down the thin steel sheet.
3
Place the release surface onto the thin steel sheet.
4
Place several plastic bags on the release surface.
5
Place sheets of paper on the plastic bags.
6
Place several more plastic bags on top of the paper layer.
7
Place another release surface onto the plastic bags.
8
Place another thin steel sheet over the release surface.
9
Take the thin film mold and slide it between the two press plates of the Kingston Hot Press.
10
Using a lever pump the hydraulic press to bring the press plates together. Stop once the pressure gauge indicates an acceptable pressure (Approximately 3000psi).
11
Wait approximately 15-30 minutes.
12
Very carefully remove the mold, but remember the plates are hot! Peeling off the release you will see the final product (first image is a thin film, second a tile).
13
If you are making a film, it is now time to shred the material to make feedstock for the final tile. You can use scissors, or if available a shredder.
14
Repeat the previous steps but filling a metal mold as shown on the right instead of making layers with raw bags and paper.
15
Finally you have a tile!
I would like to sincerely thank Shanil Vaja at Queen's for his patient assitance taking me through the steps of the Hot Press process and helping me to produce the photo instructions.
# Conclusions and Recommendations
The preliminary heat transfer analysis shows that there is little to no difference between a 1/4" aluminum plate, and a steel plate. Refinement of the model showed that although a 1/2" steel plate improved upon the 1/4" steel plate, the 1/4" aluminum plate provides substantially better temperature consistency then either thickness of steel plate and is the recommended plate design for the Kingston Hot Press.
To compliment this model it is recommended that given an available budget, an empirical study is done in parallel which tests the performance of a steel 1/2" plate and aluminum 1/4" plate which could provide major cost reductions for the overall system. An array of high temperature/pressure thermistors could also provide an empirical measure of the temperature distribution and gradients across the plate.
During the development of the model and visual production guide, several other potential areas of development were identified for future design work. Currently, the user must use a short and un-ergonomic lever to actuate the hydraulic piston which provides the clamping pressure for the system. The Hot Press frame currently makes the use of a longer lever impractical. The design of a lever system which can circumvent the frame while allowing the user to ergonomically actuate the piston would provide a much needed solution to a problem which currently has been ignored at significant cost to the user. If this device is to be used regularly, the current system would be very difficult to operate for prolonged periods of time.
Mineral wool has been used to cover the strip heaters to improve the efficiency and effectiveness of the heat delivery system. Although this material is very effective, it is unclear what the availability of this material is throughout the communities the WFL team is collaborating with. Furthermore, the models developed in this analysis showed that significant radiative heat loss occurred due to the dark steel weldments. A deeper investigation into the potential opportunities for improved insulation throughout the system design, with considerations for locally available materials, could prove very fruitful considering the WFL's interest in investigating other energy sources such as gas (where a fuel tank would limit supply more profoundly then a grid-tied system).
The release material currently used to prevent bonding between the tile and film products and the thin steel sheets is a high quality composite (teflon and a metallic substance) that has a seemingly short shelf-life (based on the quality of some of the older release sheets seen in the lab). The procurement of such materials on a regular basis presents a serious hurdle to potential users of this technology. An investigation of potential natural oils or waxes that could provide the same function of releasing the product post-pressing would be a worthwhile and fascinating application of green chemistry.
# References
1. About. Retrieved 04/15, 2010, from http://wasteforlife.org/?page_id=2
2. Technology. Retrieved 04/10, 2010, from http://web.archive.org/web/20140327052957/http://wasteforlife.org/?page_id=425
3. Robinson, K. (2006, December 22, 2006). Cartoneros: Recycling the city. The Argentimes
4. Needs and feasibility: A guide for engineers in community projects - the case of waste for life. Retrieved 04/11, 2010, from http://web.archive.org/web/20171208105541/http://secure.aidcvt.com:80/mcp/ProdDetails.asp?ID=9781608451630&PG=1&Type=RLMa&PCS=MCP
5. Incropera, F.P. et al., 2007. Fundamentals of Heat and Mass Transfer 6th ed., Hoboken, NJ: John Wiley & Sons.
6. Design, development and evaluation of pictographic instructions for medications used during humanitarian missions. (2007). Retrieved 04/10, 2010, from Nelm NH UK
7. Logan, R.S. (1982) Instructional Systems Development:An International View of Theory and Practice. Academic Press, New York.
8. Incropera, F.P. et al., 2007. Fundamentals of Heat and Mass Transfer 6th ed., Hoboken, NJ: John Wiley & Sons. | 2021-10-21 07:39:27 | {"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": 0.2970021665096283, "perplexity": 1799.7865778368848}, "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-2021-43/segments/1634323585382.32/warc/CC-MAIN-20211021071407-20211021101407-00532.warc.gz"} |
https://rosettacommons.org/category/post-situation/unsolved?page=269 | # Unsolved
The problem hasn't been solved
## I'm a total beginner to Rosetta 3.2 and there are no tutorials for me to follow. Can someone help.? =)
Hi, I'm currently an undergraduate research student in Singapore. My prof has just tasked me to try out Rosetta for docking. However, he is also new to the program, and so we are sort of stuck on how to start even a basic docking. We are using SUSE Linux. We hope that someone would be kind enough to get us started on a very basic tutorial on docking like the commands used, before we proceed on to explore the features further.
Thanks. =)
Post Situation:
The software I build and install gets pushed to standalone installations on about 100 different machines, and the installation usually lives on higher-cost storage (i.e. RAID or a SAN, etc), and then all those installations are backed up somewhere or other, so I usually take the time to weed out as many unnecessary files as possible. It makes everyone's life a little better.
Looking at the Rosetta packaging, there are a number of opportunities for improvements. The first one is very easy. Here's an expanded rosetta3.2_bundles.tgz:
Post Situation:
## Rosetta parallel installation
Hi all,
have been using Rosetta for a while, but could not figure out exactly how to install parallel. I am very happy to see Rosetta3.2 latest version. I will be grateful to you if anyone suggest me how to install (best way)parallel and how to run applications in parallel.
Best regards,
vamsi
Post Situation:
## Rosetta 3.2
I used pc with Fedora 14. I used gcc 4.5 and mpich2 to compile Rosetta 3.2. However I encounter this erros when I try to compile Rosetta 3,2 with scons.
src/core/conformation/symmetry/util.cc: In function 'void core::conformation::symmetry::make_symmetric_pose(core::pose::Pose&, core::conformation::symmetry::SymmetryInfo)':
src/core/conformation/symmetry/util.cc:360:37: error: expected type-specifier
src/core/conformation/symmetry/util.cc:360:37: error: conversion from 'int*' to non-scalar type 'core::pose::PDBInfoOP' requested
Post Situation:
## unable to propagate location of libraries to scons for Rosetta 3.1 [FIXED...SORT OF...]
I am unable to propagate our cluster environment to the Rosetta scons scripts (most likely the library environment)
Here is my situation: | 2022-01-19 11:45:02 | {"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": 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": 0.37097635865211487, "perplexity": 3063.6528275118876}, "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-20220119094810-20220119124810-00392.warc.gz"} |
https://threesixty360.wordpress.com/2009/08/18/humor-from-alum/ | ## Humor from alum
by
(There’s got to be a chemistry joke in there somewhere about humours and aluminium.)
So I’m cleaning my office, and I’m cleaning out my Inbox too (I was briefly down to under 200 messages — woo hoo! Then the summer ended.), and I ran across a couple of pieces that a couple of our alumni had sent me over the past year.
Here’s the first:
Proof that Dating is Evil:
First we state that dating requires time and money.
$Dating = Time \times Money$
And we all know “time is money”.
$Time = Money$
Therefore:
$Dating = Money \times Money = (Money)^2$
And because “money is the root of all evil”:
$Money = \sqrt{Evil}$
Therefore:
$Dating = (\sqrt{Evil})^2$
And we are forced to conclude that:
$Dating = Evil$.
The second piece is a link to a page with a lot of comics and quotes, which seems to be updated at least periodically (since there is one piece from the Monthly in 2009). For lots of distractions and ways to avoid ever getting that Inbox cleaned out, check out this site.
Thanks Lacey and Sarah! And while I’m at it, the original piece was a proof that Girls are Evil, sent by a female alumna to me, a female professor of hers, but after going back and forth a bit I decided to change it to be gender-neutral.
### 3 Responses to “Humor from alum”
1. Chris Says:
I’ve seen this exact equation joke except it is Women = Time x Money. This way is a little less sexist I suppose.
2. Avi Steiner Says:
But (sqrt(evil))^2 = |evil| ! So, in truth, dating is absolute evil.
3. TwoPi Says:
Avi: I believe you have that backwards. sqrt(x^2) = |x| is an identity on the entire real line, while (sqrt(x))^2 = x is an identity on [0, infty), whose left hand side is only defined if x is nonnegative.
Perhaps the root of all evil is complex? | 2018-06-24 20:13:47 | {"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": 0, "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": 0.37180185317993164, "perplexity": 2621.0697946269784}, "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-2018-26/segments/1529267867055.95/warc/CC-MAIN-20180624195735-20180624215735-00063.warc.gz"} |
https://socratic.org/questions/57ef7f3711ef6b2a9fd5eeaa | # Question #5eeaa
Oct 1, 2016
The equation is $x = 2$
#### Explanation:
The line you are asked to find (also called axis of symetry) must divide both bases in half, so to calculate its equation you have to find the $x$ coordinate of the midpoint of any base.
If you take the upper base you get:
${x}_{M} = \frac{- 2 + 6}{2}$
${x}_{M} = \frac{4}{2}$
${x}_{M} = 2$
So the line's equation is: $x = 2$ | 2021-12-03 13:36:04 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 6, "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": 0.8779441714286804, "perplexity": 714.1043407355767}, "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-2021-49/segments/1637964362879.45/warc/CC-MAIN-20211203121459-20211203151459-00195.warc.gz"} |
http://www.mzan.com/article/47700532-how-can-i-access-a-single-cell-from-a-range-of-cells-stored-in-a-series-xvalues.shtml | Home How can I access a single cell from a range of cells stored in a series.xvalues?
The backstory of why I'm trying to do this is because I need to place callout labels at the peaks of local maximas, but the values need to be the x-values and not the y-values. I have tried doing this multiple way, most recently like this: Dim c As Chart Set c = sht.Shapes.AddChart.Chart With c .ChartType = xlXYScatterLinesNoMarkers .SeriesCollection(8).Name = "Data Labels" .SeriesCollection(8).XValues = Range(sht.Cells(start, 2), sht.Cells(ender, 2)) .SeriesCollection(8).Values = Range(sht.Cells(start, 9), sht.Cells(ender, 9)) .SeriesCollection(8).Format.Line.Visible = msoFalse End With For i = 1 To c.SeriesCollection(8).Points.count c.SeriesCollection(8).Points(i).HasDataLabel = True c.SeriesCollection(8).Points(i).DataLabel.Position = xlLabelPositionAbove c.SeriesCollection(8).Points(i).DataLabel.Format.AutoShapeType = msoShapeRectangularCallout c.SeriesCollection(8).Points(i).DataLabel.Format.Line.Visible = msoTrue error--->c.SeriesCollection(8).Points(i).DataLabel.Text = c.SeriesCollection(8).XValues.Cells(i, 1) Next i This returns an error "Object Required" I have also tried c.SeriesCollection(8).Points(i).DataLabel.Text = c.SeriesCollection(8).XValues(i) c.SeriesCollection(8).Points(i).DataLabel.Text = c.SeriesCollection(8).XValues(i).value And A few more that I am most likely forgetting off of the top of my head. What I really want and need is to retrieve the value located in the "i" position of c.SeriesCollection(8).XValues Thanks for any help. | 2018-07-18 04:47:29 | {"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": 0.34296441078186035, "perplexity": 3050.481608664519}, "config": {"markdown_headings": false, "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-2018-30/segments/1531676590051.20/warc/CC-MAIN-20180718041450-20180718061450-00500.warc.gz"} |
https://www.science20.com/standup_physicist/blog/cant_buy_gauge_symmetry-84390 | Gauge symmetry is a clear, direct idea in EM, as I will detail. This property is essential, [correction: due to redundancy found in the 4-potential description of light and not any issue of the speed of travel for the wave]. Any proposal for gravity must also have [gauge symmetry]. I will show how the Lagrangians I have discussed over the last few months do not have this property, therefore they are wrong. I have altered three titles to say "RETRACTION", including a brief explanation at the start. [Note: the corresponding YouTube video titles have also been marked.] A different Lagrangian I am toying with might have a chance, but that will be discussed at another time.
Click or skip this reading of the blog.
Gauge symmetry is like all other symmetries: find changes that are both real and don't matter. Rotate a circle and the circle looks the same (the group S1 for those in the know). In EM, one works with derivatives of potentials, here written using quaternion products instead of tensor notation:
$\nabla \times A = (\frac{\partial \phi}{\partial t} - \nabla \cdot A, \frac{\partial \vec{A}}{\partial t} + \vec{\nabla} \phi + \vec{\nabla} \times \vec{A})$
The vector part is the difference of the magnetic and electric fields. What about the first term? Note: I avoided calling it the scalar term as I am prone to do because people might think it was invariant under a Lorentz transformation which is not the case. The first term does not play a part in the EM Lagrangian, so subtract it away:
$(\nabla \times A - (\nabla \times A)^*)/2 = (0, \frac{\partial \vec{A}}{\partial t} + \vec{\nabla} \phi + \vec{\nabla} \times \vec{A})$
The same subtraction happens in the tensor notation. In a path integral approach to quantum mechanics, the field strength tensor goes upstairs into the exponent of an exponential as part of the process to form the action. Take the product of these fields with the field strength formed by reversing the order of the derivative and the potential to generate the Lorentz invariant magnetic field squared minus the electric field squared. The exponential of the field strength tensor would have a norm of one, since this is a property of quaternions whose first term is zero in the exponent of an exponential. Unit quaternions have SU(2) symmetry, and U(1) is a subgroup of that symmetry. I don't feel on solid ground, reaching up to an exponential cloud as it were, so just file this one under a tentative observation related to U(1) symmetry.
Devise something that can be added to the 4-potential, but will not change these fields. The addition makes the operation a transformation, while the lack of change makes it a symmetry. A primary target is the curl. A gradient is like radial change, while curl is perpendicular change. The curl of a gradient of a scalar function is always zero. Try the transformation:
$(\phi, \vec{A}) \rightarrow (\phi', \vec{A'}) = (\phi, \vec{A}) + (0, \vec{\nabla} f)$
where f is an arbitrary scalar field. Plug this into the definition of the magnetic field:
$\inline \vec{B} \rightarrow \vec{B'} = \vec{\nabla} \times \vec{A'} = \vec{\nabla} \times \vec{A} + \vec{\nabla} \times \vec{\nabla} f = \vec{B}$
The job is half complete. See how this effects the other two terms that constitute the electric field:
$\inline -\vec{E} \rightarrow -\vec{E'} = \frac{\partial \vec{A'}}{\partial t} + \vec{\nabla} \phi = \frac{\partial \vec{A}}{\partial t} + \frac{\partial \vec{\nabla}f }{\partial t} + \vec{\nabla} \phi \ne -\vec{E}$
That is a no go. Nothing has been done with the phi. Pick the signs wisely:
$\inline (\phi, \vec{A}) \rightarrow (\phi', \vec{A'}) = (\phi, \vec{A}) + (-\frac{\partial f}{\partial t}, \vec{\nabla} f)$
The new phi transformation will not effect the magnetic field. See the effect on the electric field:
$\inline -\vec{E} \rightarrow -\vec{E'} = \frac{\partial \vec{A'}}{\partial t} + \vec{\nabla} \phi' = \frac{\partial \vec{A}}{\partial t} + \frac{\partial \vec{\nabla}f }{\partial t} + \vec{\nabla} \phi - \vec{\nabla} \frac{\partial f}{\partial t}= -\vec{E}$
That works.
Here is the Lagrangian for EM:
$\mathcal{L}_{EM}&=\mathcal{L}_{matter} + \mathcal{L}_{interaction} + \mathcal{L}_{fields} \\ &=\sum_{particles}(-\frac{m c^2}{\gamma} - (J \times A + (J \times A)^*)/2) \\ &\quad-\frac{1}{8}\int(\nabla \times A - (\nabla \times A)^*)\times(A \times \nabla - (A \times \nabla)^*) \\ &\quad \quad+ (\nabla \times A - (\nabla \times A)^*)\times(A \times \nabla - (A \times \nabla)^*)^*)~dx~dy~dz \\ &\approx\sum_{particles}(\frac{1}{2} m v^2 - q \phi + q V \cdot A) -\frac{1}{2}\int(B^2-E^2)~dx~dy~dz$
The only places derivatives of the potential appear are in the field terms. One uses the Lagrangian to get force equations, field equations, and the stress-energy tensor.
What does one do with this newly proved gauge symmetry? One can pick a gauge. Here are three popular examples:
Coulomb gauge: $\inline \nabla \cdot A = 0$
Static gauge: $\inline \frac{\partial \phi}{\partial t} = 0$
Lorenz gauge: $\inline \frac{\partial \phi}{\partial t} + \nabla \cdot A= 0$
Pick any of these gauges, and that will not change the EM Lagrangian at all. Picking a gauge does change how equations that result from varying the action are written.
To say a Lagrangian is invariant under a gauge transformation has three attributes: the tentative observation regarding the subtraction, examples of gauge choices that do not alter the Lagrangian, and most importantly, a proof of symmetry under a gauge transformation. Some will argue that only the third issue is of consequence. I mention the first two because the Lagrangians I have worked with did have those properties. It indicates I was not totally negligent to the issue of gauge symmetry. Two out of three is bad when the third one is the most important.
Start down the hypercomplex gravity dead end as before with the fields defined for the hypercomplex product:
$\nabla^* \boxtimes A = (\frac{\partial \phi}{\partial t} - \nabla \cdot A, \frac{\partial \vec{A}}{\partial t} - \vec{\nabla} \phi - \vec{\nabla} \otimes \vec{A})$
Toss out the first term:
$\nabla^* \boxtimes A - (\nabla^* \boxtimes A)^* = (0, \frac{\partial \vec{A}}{\partial t} - \vec{\nabla} \phi - \vec{\nabla} \otimes \vec{A})$
Propose a similar gauge transformation, taking note of the change in signs in the first two terms:
$(\phi, \vec{A}) \rightarrow (\phi', \vec{A'}) = (\phi, \vec{A}) + (\frac{\partial f}{\partial t}, \vec{\nabla} f)$
See how the first two terms do:
$\frac{\partial \vec{A}}{\partial t} - \vec{\nabla} \phi \rightarrow \frac{\partial \vec{A'}}{\partial t} - \vec{\nabla} \phi' = \frac{\partial \vec{A}}{\partial t} + \frac{\partial \vec{\nabla}f }{\partial t} + \vec{\nabla} \phi - \vec{\nabla} \frac{\partial f}{\partial t}= \vec{e}$
That works. On to the final term:
$\vec{\nabla} \otimes \vec{A} \rightarrow \vec{\nabla} \otimes \vec{A'} = \vec{\nabla} \otimes \vec{A} + \vec{\nabla} \otimes \vec{\nabla} f \ne \vec{b}$
That doesn't.
Big picture people spotted this long ago (the start of October). I am the lab tech sort. I spent four or five hours this weekend trying a wide variety of gauge transformations. I now have a few pages of futility, a good Zen practice. There are so many masters to satisfy: field equations, force equations, solutions to both field and force equations, and of course gauge symmetries. I pondered the lessons swallowed trying to staple a force equation to my previous field theory efforts. I have no problem admitting I became a desperate man in the comments section, willing to give up a rule of calculus to make things work.
And I have one other mandate. The Maxwell equations are drop dead gorgeous. Should equations for gravity stand beside them, they must also have that quality. While the hypercomplex gravity equations got close, a flaw is a flaw is a flaw by any other name.
One of the lessons learned flopping around like a fish on the ground was the rules for vector calculus are so wired into my mind's eye, I was not able to see the Z2xZ2 symmetry powering the hypercomplex products, with the Klein 4-group behind the curtain. Playing with conjugates that were Z2-like appeared to be productive. There might be some there there. That will be left for another week.
Doug
Snarky puzzle: The oh-so-familiar conjugate operator is a tool of the quaternion Wall Street elite hiding in a velvet vector dress. The rectangular box world of Z2xZ2 prefers to divide the world in two. Doodle with these:
Let the Z2 conjugate *i, *j, and *k do flip two signs:
$\\ (\phi, Ax, Ay, Az)^{*i} \equiv (\phi, Ax, -Ay, -Az) \\ (\phi, Ax, Ay, Az)^{*j} \equiv (\phi, -Ax, Ay, -Az) \\ (\phi, Ax, Ay, Az)^{*k} \equiv (\phi, -Ax, -Ay, Az)$
Form the following products:
$\\ (\rho/\sqrt{3}, Jx, Jy, Jz) \boxtimes (\phi/\sqrt{3}, Ax, Ay, Az)^{*i}\\ (\rho/\sqrt{3}, Jx, Jy, Jz) \boxtimes (\phi/\sqrt{3}, Ax, Ay, Az)^{*j}\\ (\rho/\sqrt{3}, Jx, Jy, Jz) \boxtimes (\phi/\sqrt{3}, Ax, Ay, Az)^{*k}$
Just for fun, take the sum.
Google+ hangout: 11:00-11:45pm Eastern time, Tuesday-Friday. http://gplus.to/sweetser
This could be an efficient way to exchange a few ideas. If you have a question or two, hangout.
Next Monday/Tuesday: A Lagrangian between Newton and Maxwell | 2021-11-27 09:19:09 | {"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": 18, "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": 0.7024270296096802, "perplexity": 744.3539747650917}, "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-2021-49/segments/1637964358153.33/warc/CC-MAIN-20211127073536-20211127103536-00234.warc.gz"} |
https://ask.sagemath.org/question/44389/finding-solutions-with-exponential-series-expansion/?answer=44396 | # finding solutions with exponential series expansion
Hi, I couldnt recall how to solve the following for t
0.111t = 1- e^(-0.3t) . (The ans is t=8).
Thank you in advance !! Mich
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The steps (and graphs !) of this solution are available in Sagecell
Let's see. We suppose for now that this equation is to solve in reals :
var("t", domain="real")
Ex=0.111*t-(1- e^(-0.3*t))
We note an "obvious" root :
Ex.subs(t=0)
0
Is there an explicit solution ?
Ex.log_expand().log().solve(t)
[t == 1000/111*(2*e^(3/10*t) - 1)*e^(-3/10*t)]
No such luck : this is an implicit solution, no more informative than the original equation. Let's try a numerical solution. What is the shape of the representative curve of this expression ? A curve with a minimum around about 3, null at 0 and about 8, decreasing below 3 and increasing above 3 (see Sagecell). What can we prove ?
The first derivative is
Ex.diff(t)
-0.300000000000000*e^(-0.300000000000000*t) + 0.111000000000000
An increasing curve, null about 3. Can we prove that ? The second derivative is
Ex.diff(t,2)
0.0900000000000000*e^(-0.300000000000000*t)
Yay ! This is strictly positive for all reals. Therefore, the zero we "see" on the first derivative at about 3 is the only one, and is
Ex.diff(t).solve(t)
[t == 10*log(1/37*100^(1/3)*37^(2/3))]
Ex.diff(t).solve(t)[0].rhs().n()
3.31417424447956
Now we have proven that Ex is decreasing before this zero and increasing after that. At the minimum, it is :
Ex.subs(t==Ex.diff(t).solve(t)[0].rhs()).n()
-0.262126658862769
Since it is negative at this point and not upward bound (exercise for the reader : prove it !), it has two roots, one (0) being already known. The graphs suggest that Ex is positive for t=10. Let's try to find a numerical solution :
Ex.find_root(0.1,10,t)
8.25101463236195
Left to the reader : what are the complex roots (if any...) ? Fair warning : this one is much harder than the real case (bound to problems open since the XIXth century, and still not solved...).
EDIT : It turns out that Sympy can give us the non-trivial real root in symbolic form :
sage: import sympy
sage: sympy.solve(Ex, t)
[10*LambertW(-100*exp(-100/37)/37)/3 + 1000/111,
10*LambertW(-100*exp(-100/37)/37, -1)/3 + 1000/111]
The numerical values are as expected :
sage: [s.n() for s in sympy.solve(Ex, t)]
[8.25101463236202, 0.e-123]
This function is known to Sage, but the conversion is incorrect (loses the second argument)
sage: [s._sage_() for s in sympy.solve(Ex, t)]
[10/3*lambert_w(-100/37*e^(-100/37)) + 1000/111,
10/3*lambert_w(-100/37*e^(-100/37)) + 1000/111]
This is now Trac#26752
more
Thank you for your help!! ( I m still surprised that the eqn. looks simple, but yet it can be tricky to solve. But appreciate your help !)
( 2018-11-24 17:46:10 -0600 )edit
The value 8 is not a solution, but there is a solution whose approximate solution is 8.2510146...
Here are some ways to work on solving this equation.
Define t as a symbolic variable in the symbolic ring, and call eq the equation.
sage: t = SR.var('t')
sage: eq = 0.111*t == 1-exp(-0.3*t)
Try to solve with solve: unfortunately, Sage returns an equation which is equivalent to the equation we started with.
sage: solve(eq, t)
[t == 1000/111*(e^(3/10*t) - 1)*e^(-3/10*t)]
Use find_root to find an approximate solution between 5 and 10.
sage: eq.find_root(5, 10)
8.251014632362164
or
sage: find_root(eq, 5, 10)
8.251014632362164
The computation above is done using floating-point computations and it is not clear which digits are exact.
For a computation using arbitrary precision, use the mpmath library: define a function equal to the difference of the left-hand side and the right-hand side of eq and use mpmath.findroot to look for a root near 8:
sage: import mpmath
sage: mpmath.findroot(lambda t: 1 - exp(-0.3*t) - 0.111*t, 8)
mpf('8.2510146323620207')
See the answer by @Emmanuel Charpentier for how to use SymPy to get an exact solution in symbolic form. It is likely Giac or FriCAS could do it too.
more
Neither Fricas nor Giac can solve this symbolically :
sage: giac("solve(111*t/1000-(1-exp(-3*t/10)),t)")
list[-6.76523232004e-14,8.25101463236]
sage: fricas("solve(111*t/1000-(1-exp(-3*t/10)),t)")
[]
Mathematica gives an answer subsuming Sympy's and asserting the existence of an infinity of (complex) solutions :
sage: mathematica("Reduce[111*t/1000==1-Exp[-3*t/10],t]")
(Element[C[1], Integers] &&
t == 1000/111 + (10*ProductLog[C[1], -100/(37*E^(100/37))])/3) || t == 0
(Reformatted from Mathematica's help) :
ProductLog][z]
gives the principal solution for w in z == w e^w.
ProductLog[k,z]
gives the k^th solution.
From Sage's lambert_w? :
This function satisfies the equation
z = W_n(z) e^{W_n(z)}
Same difference...
( 2018-11-24 13:26:11 -0600 )edit
Thank you for your help!! ( I m still surprised that the eqn. looks simple, but yet it can be tricky to solve. But appreciate your help !)
( 2018-11-24 17:45:51 -0600 )edit | 2021-01-20 01:46:18 | {"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": 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": 0.5999091267585754, "perplexity": 2545.75704441106}, "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/1610703519843.24/warc/CC-MAIN-20210119232006-20210120022006-00158.warc.gz"} |
https://rohanchandra306.wordpress.com/2016/12/09/generalizing-the-find-the-missing-digit-trick/ | Generalizing the “Find the missing digit trick” !
In this entry, I shall generalize a very interesting math trick.
Background
A fun and intriguing math performing trick is the “find the missing digit” trick. The mathemagician asks you to think of a number N preferably long, 5 or 6 digits. He will not know this number. He asks you to subtract from it, the sum of the digits of N. He then asks you to call out ALL EXCEPT ONE of the digits of the answer that you got in the previous step and IN ANY ORDER. He will tell you the digit that you didn’t call out.
Example
Lets say audience chooses N= 264983. They subtract 2+6+4+9+8+3 = 32 from 264983. So they will end up with 264983- 32 = 264951. They call out… 2..9..4..6..5 and leave out 1. The mathemagician will have 2+9+4+6+5 = 26 in his hand and the next multiple of 9 is 27. So he will know that the audience left out 1.
The logic behind this trick is that subtracting the sum of digits from a number leaves the number as a multiple of 9.
Why we try to make this a multiple of 9 is because the sum of digits of a multiple of 9 is also a multiple of 9. Which means that if the mathemagician has 5 of the 6 digits, he can simply check which digit would make the sum of the digits a multiple of 9.
Generalization
The problem with the above method is that you need the number to be a multiple of 9 which makes this trick very specialized and the problem with most magic tricks is that once you’ve seen them enough times, they lose their charm. By attempting to generalize this particular trick, one can open the doors to whole new set of tricks. My goal is to find the missing digit when it is a multiple of not just 9, but any number like 4 or 7 or 3. For this we need to know the basics of number theory.
Let us take a start with a $n$ digit number $N$ that needs to be divisible by a number $p$. I shall define a set of base values S = {$a_1, a_2 ..., a_n$} where
$a_1=1, a_2 = 10^{2-1}(modp), a_3 = 10^{3-1}(modp)... a_n = 10^{n-1}(modp)$
The following table shows the base numbers for 4 digit numbers for various $p$
p Base Numbers
7 6,2,3,1
17 -3,-2,10,1
31 8,7,10,1
The principle will remain the same as before. In order to find the missing digit, the number of the audience $N$ should be a multiple of $p$ of our choosing. We shall use the base numbers $S$ corresponding to $p$.
Once we have $N$ and $p$, we’re almost good to go. Here is the caveat. You cannot allow the audience to scramble the digits and they have to tell you which position’s digit they omit.
Perform the following algorithm:
Step 1: Multiply the digits of the number $N$ with its corresponding base numbers. For instance, multiply the first digit by $a_1$, the second digit by $a_2$ .. and the $nth$ digit by $a_n$
Step 2: Add them all up. The sum will be a multiple of $p$.
Step 3: We check which is the nearest next or previous multiple of $p$ and figure out the missing digit either by quick observation or by using the euclidean algorithm
Much Needed Example:
Number: 6258 (multiple of 7). This you would make the audience end up with using some simple ‘mathemagic’ manipulations.
So you ask them to omit the 3rd digit from the right and say the rest. So they will say 6..5..8.
Step 1: Look up the table. The base digits for p=7 are 6, 2, 3 and 1. You will do $6 \times 6 + x \times 2 + 5 \times 3 + 8 \times 1$ inside your head, where $x$ is the missing digit.
Step 2: This equals $59+ (2 \times x)$
Step 3: we know that $59+ (2 \times x)$ is a multiple of 7. What is the next (since we’re adding to 59)nearest multiple of 7? 63! so $59+ (2 \times x) = 63$ and that gives us the missing number 2 !
Another Example!
Number: 1632 (multiple of 17).
So you ask them to omit the 3rd digit from the right and say the rest. So they will say 1..3..2
Step 1: Look up the table. The base digits for p=7 are -3, -2, 10 and 1. You will do $-3 \times 1 + x \times -2 + 10 \times 3 + 2 \times 1$ inside your head.
Step 2: This equals $29- (2 \times x)$
Step 3: we know that $29- (2 \times x)$ is a multiple of 7. What is the previous (since we’re subtracting from 29) nearest multiple of 7? 17! so $29- (2 \times x) = 17$ and that gives us the missing number 6
You will notice that the answers are pretty obvious here. That is because the base number of the corresponding missing digit is 2 which is a low number and is easy to calculate in your head. In cases where the base number of the missing digit is a large number, then the Euclidean algorithm would need to be used which I shall cover in another post. | 2018-10-15 13:41:50 | {"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": 28, "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": 0.5482078194618225, "perplexity": 328.0707901527481}, "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-2018-43/segments/1539583509196.33/warc/CC-MAIN-20181015121848-20181015143348-00278.warc.gz"} |
https://lavelle.chem.ucla.edu/forum/viewtopic.php?f=130&t=59552 | ΔU Equal 0
$\Delta U=q+w$
Abigail Menchaca_1H
Posts: 104
Joined: Sat Sep 07, 2019 12:19 am
ΔU Equal 0
If ΔU is zero why does the gas expand
Posts: 50
Joined: Mon Jun 17, 2019 7:24 am
Re: ΔU Equal 0
There is another similar question about change in internal energy for isothermal processes. Hopefully this gives some insight: Internal energy, or U, is a state function dependent on temperature. This means that for a process that is isothermal (delta T is 0), even if it is an expansion of a gas, the delta U will equal 0 because the internal energy does not change. Because delta U = q + w, even if work is done, q will be the exact opposite to ensure that delta U is 0. To clarify: delta U does not refer to the same quantity as work.
Posts: 53
Joined: Fri Aug 02, 2019 12:16 am
Re: ΔU Equal 0
If you are referring to an isothermal process, a gas can expand (-w) if it is heated (+q) for the same amount of energy. The energy lost by expanding is supplied by heat, and the change in internal energy is 0.
Sofia Barker 2C
Posts: 101
Joined: Wed Sep 18, 2019 12:21 am
Re: ΔU Equal 0
Delta U can be zero despite expansion because delta U represents a change in energy, so for there to be no change in energy, the energy gained / lost due to work would be made up for in a gain or loss of heat.
Tauhid Islam- 1H
Posts: 64
Joined: Fri Aug 02, 2019 12:15 am
Re: ΔU Equal 0
Delta U is the change in the internal energy if the system and that is equal to Q (heat added to the system) - W (work done by the system). If delta U is zero, the heat added to the system is the same as the work done by the system. The amount of heat that is added to the system has the same amount of energy as the amount of expansionary work done by the system to the surrounding. The work energy lost to the surrounding by the expansion of a gas is basically replaced by heat energy into the system, resulting in a delta U value of 0. | 2020-04-03 05:32:09 | {"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": 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": 0.5989295244216919, "perplexity": 597.3381131094994}, "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-2020-16/segments/1585370510287.30/warc/CC-MAIN-20200403030659-20200403060659-00413.warc.gz"} |
https://encyclopediaofmath.org/wiki/Morse_lemma | # Morse lemma
2010 Mathematics Subject Classification: Primary: 57R45 Secondary: 37-XX [MSN][ZBL]
A lemma which describes the structure of the germ of a twice continuously-differentiable function.
### Main statement
Theorem 1 Let $f:\mathbb R^n\to \mathbb R$ be a function of class $C^\infty$ for which $0$ is a non-degenerate critical point, namely $\nabla f (0) =0$ and the Hessian at $0$ has trivial kernel. Then in some neighbourhood $U$ of $0$ there is a local $C^\infty$ coordinate system, namely a $C^\infty$ diffeomorphism $\varphi = (x_1, \ldots , x_n): U \to V \subset \mathbb R^n\, ,$ with $\varphi (0)=0$ and such that the map $\tilde{f} = f\circ \varphi^{-1}$ (namely $\varphi$ in the "$x$-coordinates") takes the form $\tilde{f} (x) = f(0)- x_1^2 - \ldots - x_\lambda^2 + x_{\lambda+1}^2 + \ldots + x_n^2$.
Here the number $\lambda$ is the Morse index of the critical point $0$ of $f$, that is the number of negative eigenvalues of the Hessian of $f$ at $0$, counted with multiplicities. The assumption $C^\infty$ may be relaxed to $C^p$ for $p\geq 2$, but in this case the change of variables $\varphi$ is in general only of class $C^{p-2}$. If instead $f$ is real analytic, then $\varphi$ is real analytic. An analogue of the Morse Lemma holds for holomorphic functions of complex variables.
Theorem 2 If $f: \mathbb C^n \to \mathbb C$ is holomorphic in a neighborhood of $0$ and $0$ is a nondegenerate critical point (namely $\frac{\partial f}{\partial z_j} (0) =0$ for every $j$ and the matrix $M_{ij} = \frac{\partial^2 f}{\partial z_i \partial z_j} (0)$ is invertible), then there is a neighborhood $U$ of $0$ with an holomorphic local chart, namely a holomorphic invertible map $\varphi = (w_1, \ldots , w_n) : \mathbb C^n \supset U\quad \to\quad V\subset \mathbb C^n\, ,$ such that $\varphi (0) = 0$ and $\tilde{f} = f \circ \varphi^{-1}$ takes the form $f (w) = f(0) + w_1^2 + \ldots + w_n^2$.
### Generalizations
#### Infinite-dimensional case
The Morse lemma can be generalized to the infinite-dimensional setting: it holds, for instance, on Banach spaces, see [Pa2]. On separable Hilbert spaces it takes the following form.
Theorem 3 Let $H$ be a separable Hilbert space and $f:H \to \mathbb R$ a $C^k$ function $f$ with $k\geq 3$ (in the sense of Frechet differentiability) for which $0$ is a non-degenerate critical point. Then there are convex neighborhoods $U$ and $V$ of $0$, a diffeomorphism (of class $C^{k-2}$) $\varphi: U \to V$ with $\varphi (0)=0$ and a bounded orthogonal projection $P: H \to H$ such that $f (x) = f (0) - \|P (\varphi (x))\|_H^2 + \|\varphi (x) - P (\varphi (x))\|_H^2$.
Here the dimension of the space ${\rm Im}\, (P)$ coincides with Morse index of the critical point $0$.
#### Equivariant Morse lemma
Consider $f$ as in Theorem 2 and assume that it is invariant with respect to the action of a compact subgroup $G$ of transformations on $\mathbb C^n$. Then the change of variables $\varphi$ can be taken $G$-invariant. An analogous "equivariant Morse lemma" is true in the real-analytic and the differentiable context. Cf. [A] and [AGV].
#### Morse lemma depending on parameters
Let $f: \mathbb R^n \times \R^k \ni (x,\lambda) \mapsto f (x, \lambda)\in \mathbb R$ be a real-valued $C^p$ function with $p\geq 3$. Assume that $D_x f (0,0)=0$ and that $D^2_x f (0,0)$ is nonsingular. Then there exist $C^{k-1}$ coordinates $(z, \lambda)$ in a neighbourhood of $(0,0)$ which brings $f$ to the form $f (z, \lambda) = f (x(\lambda), \lambda) + \frac{1}{2} \langle A z\, z\rangle\,$ where $A$ is a diagonal matrix with entries $\pm 1$ and $\lambda \mapsto x (\lambda)$ is the local (unique) solution of the equations $D_x f (x, \lambda) = 0$ (the nondegeneracy assumption on $D^2_x f (0,0)$ allows to apply the implicit function theorem and infer that $x$ depends smoothly on $\lambda$). For a proof see [H], p. 502.
### References
[A] V.I. Arnol'd, "Wave front evolution and the equivariant Morse lemma" Comm. Pure Appl. Math. , 29 (1976) pp. 557–582 [AGV] V.I. Arnol'd, S.M. [S.M. Khusein-Zade] Gusein-Zade, A.N. Varchenko, "Singularities of differentiable maps" , 1 , Birkhäuser (1985) MR777682 Zbl 0554.58001 [H] L.V. Hörmander, "The analysis of linear partial differential operators" , 3. Pseudo-differential operators , Springer (1985) MR1540773 MR0781537 MR0781536 Zbl 0612.35001 Zbl 0601.35001 [M] M. Morse, "The calculus of variations in the large" , Amer. Math. Soc. (1934) MR1451874 MR1501555 MR1561686 MR1501489 MR1501428 Zbl 0011.02802 Zbl 60.0450.01 [Pa] R.S. Palais, "Morse theory on Hilbert manifolds", Topology , 2 (1963) pp. 299–340 MR0158410 Zbl 0122.10702 [Pa2] R.S. Palais, "The Morse lemma for Banach spaces", Bull. Amer. Math. Soc., 75 (1969), pp. 968-971.
How to Cite This Entry:
Morse lemma. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Morse_lemma&oldid=32324
This article was adapted from an original article by M.M. PostnikovYu.B. Rudyak (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article | 2022-07-06 17:33:17 | {"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": 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": 0.9545336961746216, "perplexity": 295.1588715860905}, "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-2022-27/segments/1656104675818.94/warc/CC-MAIN-20220706151618-20220706181618-00022.warc.gz"} |
http://www.risportsratings.com/5g13ws/limitations-of-741-op-amp-ed28ca | M�춓�Js�j�]�&!��n��&�����SU6Ø$_�O�:u��gx�v����Իwp}{�G the internal workings of an op amp, so in this work a more macro view will be taken. The differential amplifier has inverting and non-inverting input terminals, and has a high-impedance (constant-current) tail to give a high input impedance and good common-mo… 5 0 obj The op-amp can be considered to be a voltage amplifying device that is designed to be used with external feedback components such as resistors and capacitors between its … x��Vێ�F}G�걽 <> An ideal op-amp integrator uses a capacitor C1, connected between the output and the op-amp inverting input terminal, as shown in the figure below. For FET input devices it is typically 10^12 ohms. The high common-mode input voltage range and the absence of latch-up make the amplifier ideal for voltage-follower applications. ! The µA741 device is a general-purpose operational amplifier featuring offset-voltage null capability. <> stream In general, the output of the op amp swings positive and negative to a maximum voltage that is close to supply potentials. <> 9 0 obj We will use three approaches here. •An ideal op-amp has infinite gain and input impedance and zero output impedance. This offset current is typically on the order of a tenth of the input bias current, with 10nA being a representative offset current for a 741. For vI = 10 mV, 1 V, and … <> 7 0 obj In section 2 the basic specifications will be discussed. For high speed one may choose an op-amp with higher bias current at the cost of seeing some voltage drop across the resistors of the feedback network, bias network or source impedance. Limitations • The circuit has some serious limitations. All of these elements are integrated on a single chip and housed in an IC package. stream op-amp. For the 741 the input resistance measured to one input with the other grounded is about 2 Megohms. endstream In other words, the op-amp voltage comparator compares the magnitudes of two voltage inputs and determines which is the largest of the two. 741 op amp IC comes in 8 pin dual inline package. In its simplest form, a conventional op-amp consists of a differential amplifier (bipolar or FET) followed by offset compensation and output stages, as shown in Figure 1. An operational amplifier or op-amp is simply a linear Integrated Circuit (IC) having multiple-terminals. Its limitations are actually useful for as since we can measure them easily using relatively cheap lab equipment and simple simulation software. 14 0 obj 13 0 obj Low impedance Output. 2 0 obj 11 0 obj Input bias current is the average value of the inverting and non-inverting current. It ... the op amp's slew rate, and even a very fast op amp will be limited to low frequencies. (In other words, it’s like there’s this huge resistor at the input.) x��V[O�0~���p]$�oI !qb��N�{�R���&Y���� �nI7��Ǝ����\8���Ã���3GGprv This implies that the input impedance is infinite. Op-amp Input Impedance. Operation Amplifier Pin Configuration | Pin Layout. endobj There are a couple of times, however, that we will talk about the insides of the op amp. [ 10 0 R] �$��Ĉ �&Vd�WEE^��s�,�wk��������Tq��d02}f{�� /1?=�S)����a{[�5��Pp��^���ʒ����H�W�9�Ew����ւ@ � ��c��e�+��:}�;_d,�ЋoP�$��Z���W1d�3�bWow5��s��#�I��cё�2����wV�̡%�w/W9��@j�����GR�>��XϺ���v�U��< ������XOa�Φ�d�=���,��ޔ������ر;�X0N�s�H���������紮�2�y�謚�4lB/����l,#txi�����Qo�X'��F~�M�f�+�+���H����b They have basic general features as follows. <> Demonstrate this: If we connect a typical 741 op amp to a +/-18V, then the maximum output voltage is +/-15V. Input Bis Current. <>/Font<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 720 540] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>> endobj For FET input devices it is typically 10^12 ohms. The uA741 is a high performance operational amplifier with high open loop gain, internal compensation, high common mode range and exceptional temperature stability. The input current isn't exactly zero. There is a tiny input bias current for an op-amp which is about 80 nA for 741 type op-amps. The PIN number 7 is connected to positive supply and pin number 4 is connected to negative supply or ground. 12 0 obj Operational Amplifier General Description The LM741 series are general purpose operational amplifi-ers which feature improved performance over industry stan-dards like the LM709. High Impedance Input. They are direct, plug-in replacements for the 709C, LM201, MC1439 and 748 in most applications. For FET- input op-amps it may be a few picoamps. ��$*����O?���d���za�b�˾H.����N&q'q"��"�����@{Ѳ��|����IF��ѯ��fd Dc����*5�����Fa�lo��C��hC)�s���VCܰ��I4�eJc慴J�q�DE0�D���t��N����(����Y�9��|7{�ɼ�� O(6����������6�6�Ȋo8�p�gVs�Kq5V. ��=�2Ƹ,�D0����{_� ��.n#������a�b�Tpz���}������?��������Z�'#$��A 10 0 obj In this configuration, an op amp produces an output potential (relative to circuit ground) that is typically 100,000 times larger than the potential difference between its input terminals. 741 Op Amp UA741CP +-1V Out +-Out + DVM ground Now, lets explore the limitations of the simple rule: Rule 2: - The inputs draw no current. endobj It is an 8 pin IC. The IC 741 operational amplifier is used in two methods such as an inverting (-) and a non-inverting (+) The IC 741 Op Amp applications mainly includes an adder, comparator, subtractor, voltage follower, Integrator and differentiator.The circuit diagram of IC 741 op amp is given below. In the following circuit, IC 741 operational amplifier is used as a comparator. One of the practical op-amp limitations is that the input bias currents for the two inputs may be slightly different. This IC needs a dual polarity supply. Enjoy! Though common and inexpensive op-ampslike the 741come remarkably close to the ideal op-amp, there are practical limitations which come into play in circuit design. endobj <> endobj endobj endobj <> Maximum means that the op-amp can safely tolerate the maximum ratings as given in the data section of such op-amp without the possibility of destroying it. endobj endobj These are areas where you need to be explicit about ranges and limits. It is unavoidable. It is also essential that designers understand the significance and limitations of the op-amp performance specs defined in data-sheet EC tables. Even with identical source impedances, this offset current will produce a slight voltage between the input terminals, contrary to the ideal voltage rule. Apparatus Required: CRO, Function Generator, Bread Board, 741 IC, ±12V supply, Resistors 1KΩ, 10KΩ, and connecting leads. \$\begingroup\$ Just mentioning that Practical Wireless magazine ran an article on building a hi-fi amplifier, the "Texan", using 741s (and 748s which IIRC are just two 741s in one case) back in the May 1972 issue, pg 48.There was an update in the July 1975 issue for better shielding and a toroidal power transformer, but still using the same 741 op-amp. Exercise 13.24: Consider the operational amplifier in Figure 13.33(a), with R = 1 kΩ. A key part of using op amps in PSPICE is in choosing a model for the op amp. • Even though the inputs are designed to be symmetrical, slight differences which occur in the manufacturing process may give slightly different bias currents. <> The superbeta Darlington LM11 may have an input current of 25 picoamps and the MOSFET ICH8500 is one of the very lowest at 0.01 picoamp. The circuit has speed limitations at high frequency because of the slow negative feedback and due to the low slew rate of many non-ideal op-amps. In practice this finite impedance is usually not as big a problem as the input bias currents since the use of negative feedback raises the effective input impedance even higher. One of the practical op-amp limitations is that the input impedance finite, though very high compared to discrete transistor amplifiers. The amplifiers offer many features which make their applica- AIM: Design and realize Inverting and Non-inverting amplifier using 741 Op-amp. 7Э�U�˨��l0�C�n~⨈ȸ�uN�ԫh���?�\�t��\.3�%����^_���eB�� ݏ�=1��g��7"�����!M��\[+��jj���bl]e M[��tx'�v�WzI������u-��Pe�nd�/^89� 8 0 obj Using a 741 op-amp you can create a circuit which has negative resistance over a range, but once you go outside that range the linearity disappears and the relationship between voltage and current is otherwise. The first op amp to slew in this circuit is the 411, even though it is about 30 times faster than the 741 used in stage 1. The input impedance isn't infinite. 6 0 obj Any difference between the voltages ever if it is small drives the op-amp into saturation. Ideal Op-amp Integrator Circuit. Logarithmic output * The relationship between the input voltage v in {\displaystyle v_{\text{in}}} and the output voltage v … An op-amp integrating circuit produces an output voltage which is proportional to the area (amplitude multiplied by time) contained under the waveform. Op Amp Comparator Circuit. Note that if the final stage had a larger gain, say 5, the 318 would become the limiting factor. Introduction: Before proceeding with the laboratory, students are advised to read Sedra and Smith, "Micro-Electronic Circuits", the section in Chapter 10 on the 741 op-amp. … To increase the signal to a higher level to the output. <> An operational amplifier (often op amp or opamp) is a DC-coupled high-gain electronic voltage amplifier with a differential input and, usually, a single-ended output. "+�v��$u�� I6wy�M���}Ή�q ���J��j�RT�gO��_Fx3�24}q���5o�{�3��Cm&s/�h=�nt�/�!�i�d3]�1���-�bRLZ���D�&̪���w�R��8��ܺR��B�����TWc@�$)��IC-6�ݱ�s1���:���.���x��T����&��M"���D��F��P���f�U��(�&��w���pZ��Hr���9��6�y���vQͻ(yD鶪�vP�������J�����L�(�X;����*xH�Uk��V�a���\$�f��_Jl�o Then we will use a nearly-ideal model provided with PSPICE. It was first manufactured by Fairchild semiconductors in the year 1963. 4 0 obj T���xUa&Ӑf����E��'���_ 7. If the two inputs of a differential amplifier were to be shorted together (thus ensuring zero potential difference between them), there should be no change in output voltage for any amount of voltage applied between those two shorted inputs and ground: Voltage that is common between either of the inputs and ground, as “Vcommon-mode” is in this case, is called common-mode voltage. This is because of extreme high open loop gain of the op amp (10,000 to 1 million). endobj Operational Amplifiers picture Figure : What an Op-Amp looks like in today's world Figure: The Philbrick Operational Amplifier. The main one is speed. Operational Amplifier (op-amp) •An op-amp is a high-gain amplifier that has high input impedance and low output impedance. endobj •An integrated circuit (IC) contains a number of components on a single piece of semiconductor. 1 0 obj Theory: An inverting amplifier using opamp is a type of amplifier using opamp where the output waveform will be Some of the things which cause problems are. endobj Finally, we use a model for the 741 op-amp, also provided with PSPICE. endobj �#.�4V�v-ħEB����J One of the practical op-amp limitations is that the input impedance finite, though very high compared to discrete transistor amplifiers. %PDF-1.5 • One of the practical op amp limitations is that the input bias currents for the two inputs may be slightly different. Figure 1 is an illustration of the pin configuration … Even though the inputs are designed to be symmetrical, slight differences which occur in the manufacturing process may give slightly different bias currents. •Most op-amps are IC chips. �b���Gn����+�-�Mo��#7���fz��0���#�#{A��S����ȕH�p�F��-��5�� b�c|_���;����D�īNl�ݺE�u+I�����?dl�����M���f���_��\�v��G)�j��+R �����`�a��N@JŚ��oI�ɨ�! First, we will make our own model, using the standard two-port description of an amplifier. Even if we used as a comparator the IC still observes the weak signals so t… The Op-amp comparator compares one analogue voltage level with another analogue voltage level, or some preset reference voltage, V REF and produces an output signal based on this voltage comparison. %���� IC 741 Op Amp (Operational Amplifier) The 741 Op Amp IC is a monolithic integrated circuit, comprising of a general purpose Operational Amplifier. �TJic�o�NA��G��|i�zF�7�����}�8r�[׳�h��k�����p���H��|��ن�������+�7�۬\d�?�WE^����1 w�b+�#�/N,���{�ub���B'��]6&�X�Y�' 741 IC Operational Amplifier Several 1/4-Watt Resistors Decade Capacitor Box (0-10 μF) 9V Battery 9.5 INVERTING AND NON-INVERTING AMPLIFIERS 9.5.1 Non-Inverting Amplifier - Circuit 9.5.1 Using the 741 op amp with power supplies connected as described Section 2, … The reason for this is that it must handle signals 32 times as large. When the voltages supplied to both the inputs are of the same magnitude and the same polarity, then the op-amp output is 0Volts. Following the guidelines presented here, designers can select both the correct op amp and the right passive components with the correct configurations for their applications. endobj <> <> For the 741 the input resistance measured to one input with the other grounded is about 2 Megohms. 3 0 obj Some techniques to compensate for some of the op amps limitations will also be given. <>>> The main advantages of Differential Amplifier, it can eliminate noise present in the input signal, and linear in nature.The main disadvantage of the Differential Amplifier is, it rejects the common mode signal when operating. One of the practical op-amp limitations is that the input current is not exactly zero as we assume in the current rule. Pin number 2 and pin number 3 are the two input terminals of 741 op-amp. 741 op-amp pinout. Op-amp pin diagram There are 8 pins in a common Op-Amp, like the 741 which is used in many instructional courses. Though in some applications the 741 is a good approximation to an ideal op-amp, there are some practical limitations to the device in exacting applications. 16 0 obj Judgements have to be made because those with the lowest input bias currents cannot operate at high speed. The number 741 indicates that this operational amplifier IC has 7 functional pins, 4 pins capable of taking input and 1 output pin. I think you want to use 741 op-amps. We can enter either an AC or DC signal to the input. The input offset current isn't exactly zero either. <>/XObject<>/Pattern<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 720 540] /Contents 16 0 R/Group<>/Tabs/S/StructParents 1>> endobj Operational amplifier compares the voltage applied at one input to the voltage applied at the other input. The 741 op-amp is one type of solid state. High Gain rating. This may restrict you to smaller resistors and place practical limits on gain, or may produce some variations in output voltage. Circuit Diagram of Electric Thermometer Using OP-AMP 741. As stated before, an ideal differential amplifier only amplifies the voltage differencebetween its two inputs. As we vary … <> 15 0 obj main application of Differential Amplifier is, it creates a difference between two input signals and then amplifies the differential signal. The entire circuit of electric thermometer is built around two op-amp 741 IC, silicon diode and few passive components, where silicon diode D 1 is used as temperature sensor. +/-18V, then the op-amp voltage comparator compares the voltage applied at the other grounded is about Megohms... Stan-Dards like the LM709 in this work a more macro view will be limited to low.! Need to be made because those with the other input. is the of. Make their applica- op-amp: it is typically 10^12 ohms this huge resistor at the grounded... Input resistance measured to one input with the other grounded is about 80 nA for 741 op-amps... Input offset current is not exactly zero either about ranges and limits that we will talk the! Used in many instructional courses currents for the two inputs pins, pins... Very fast op amp, so in this work a more macro view will be to. Of components on a single piece of semiconductor slightly different EC tables their applica- op-amp and. Op-Amp output is 0Volts used as a comparator designers understand the significance and limitations of the two inputs may a. Circuit produces an output voltage, or may produce some variations in voltage! An operational amplifier IC has 7 functional pins, 4 pins capable of taking and... As stated before, an ideal differential amplifier limitations of 741 op amp used as a comparator when the supplied! And limitations of the practical op-amp limitations is that it must handle signals 32 as., then the maximum output voltage is +/-15V for FET- input op-amps it may be slightly.. Infinite gain and input impedance finite, though very high compared to discrete transistor amplifiers for this is because extreme... We connect a typical 741 op amp IC comes in 8 pin dual inline package because those with other. Following circuit, IC 741 operational amplifier compares the magnitudes of two voltage inputs and determines which is in. 13.24: Consider the operational amplifier general Description the LM741 series are general operational. Op-Amp performance specs defined in data-sheet EC tables in the current rule, may. 10,000 to 1 million ) words, the 318 would become the limiting factor and. Standard two-port Description of an amplifier voltage applied at one input with the other input. the magnitudes of voltage. Number 7 is connected to negative supply or ground is close to supply potentials or signal... Assume in the year 1963 is, it ’ s like there ’ s this huge at. Difference between two input signals and then amplifies the differential signal the input impedance and zero output impedance we. Then we will use a model for the 709C, LM201, MC1439 748... Drives the op-amp output is 0Volts the voltage applied at the input impedance finite, very. At high speed to discrete transistor amplifiers the standard two-port Description of an op amp ( to. Proportional to the voltage applied at the input resistance measured to one input with the other grounded is about nA! Which occur in the current rule high compared to discrete transistor amplifiers, with R = 1.! Million ) 741 operational amplifier in figure 13.33 ( a ), with R = kΩ... Compared to discrete transistor amplifiers the year 1963 where you need to be symmetrical, differences. Offset-Voltage null capability resistor at the input impedance finite, though very high compared to discrete transistor amplifiers input!, MC1439 and 748 in most applications the standard two-port Description of an op amp ( to. Different bias currents circuit, IC 741 operational amplifier in figure 13.33 ( a ), with R = kΩ! Inverting and non-inverting amplifier using 741 op-amp are a couple of times, however that! Range and the absence of latch-up limitations of 741 op amp the amplifier ideal for voltage-follower applications like the 741 the input is... Their applica- op-amp common-mode limitations of 741 op amp voltage range and the absence of latch-up make amplifier! Other grounded is about 80 nA for 741 type op-amps, an ideal differential amplifier only amplifies voltage... Variations in output voltage which is proportional to the area ( amplitude multiplied by time ) contained the... Zero output impedance of differential amplifier only amplifies the differential signal the average value of two. Like the LM709 for as since we can enter either an AC or DC signal to the input offset is... Input with the other input. the inputs are of the limitations of 741 op amp amps limitations will also given. Input voltage range and the same polarity, then the maximum output voltage 10,000. Proportional to limitations of 741 op amp area ( amplitude multiplied by time ) contained under the waveform 80 nA 741! Ic 741 operational amplifier in figure 13.33 ( a ), with R 1. Also essential that designers understand the significance and limitations of the op amp swings positive and negative a. The voltages supplied to both the inputs are of the op-amp into saturation latch-up. Two input signals and then amplifies the voltage applied at one input to the area ( amplitude by... Is typically 10^12 ohms are designed to be symmetrical, slight differences which occur in limitations of 741 op amp year 1963 which... Model, using the standard two-port Description of an amplifier the LM709 null capability input voltage range and same. Amplifiers offer many features which make their applica- op-amp amplifier IC has functional... A few picoamps illustration of the op amp IC comes in 8 pin dual inline package a couple of,. Ic ) having multiple-terminals is one type of solid state loop gain of the pin number 4 connected., the output a few picoamps level to the area ( amplitude multiplied time. Drives the op-amp into saturation produce some variations in output voltage is +/-15V limitations... This operational amplifier compares the voltage applied at one input with the lowest input bias currents supply.! Housed in an IC package practical op amp, so in this a... Zero as we assume in the current rule process may give slightly different bias currents the! And then amplifies the voltage applied at the input impedance finite, though very high compared to discrete transistor.! Aim: Design and realize inverting and non-inverting current the current rule bias current is largest... Op-Amp integrating circuit produces an output voltage of these elements are integrated on a chip! The high common-mode input voltage range and the same magnitude and the of! Amp, so in this work a more macro view will be.. Type op-amps lowest input bias currents can not operate at high speed or ground amplifier IC has 7 functional,... Or ground compared to discrete transistor amplifiers IC ) having multiple-terminals limitations of 741 op amp of. Had a larger gain, say 5, the op-amp voltage comparator compares the differencebetween. Simulation software judgements have to be explicit about ranges and limits the significance and limitations of the same,! Applica- op-amp limitations of 741 op amp connect a typical 741 op amp ( 10,000 to 1 million ) which feature improved performance industry... ) contains a number of components on a single limitations of 741 op amp and housed in IC. Year 1963 feature improved performance over industry stan-dards like the LM709 that understand! … input Bis current main application of differential amplifier is, it creates a between... In other words, the 318 would become the limiting factor its two inputs may be a picoamps... Internal workings of an amplifier practical op amp limitations will also be given that designers understand the significance and of... Can enter either an AC or DC signal to the area ( amplitude multiplied by time ) under... The 709C, LM201, MC1439 and 748 in most applications transistor amplifiers of differential amplifier,. ) contains a number of components on a single piece of semiconductor will talk the. Then amplifies the voltage applied at one input with the lowest input currents., slight differences which occur in the manufacturing process may give slightly different ideal for voltage-follower applications where you to...
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https://erj.ersjournals.com/highwire/markup/105448/expansion?width=1000&height=500&iframe=true&postprocessors=highwire_tables%2Chighwire_reclass%2Chighwire_figures%2Chighwire_math%2Chighwire_inline_linked_media%2Chighwire_embed | Table 1– The current smear microscopy market and the potential market for a replacement test for initial diagnosis of tuberculosis (TB) in the public sector of the 22 high-burden countries
Country Notified TB cases in 2012 n# Microscopy centres n Total microscopy centres % Total sputum smear volume (millions) Total sputum smear volume % Sputum smear market for initial diagnosis¶ Replacement test market+ Smears n (millions) Estimated (range) expenditure(US$millions) Tests n (millions) Potential market value (US$ millions) Non-BRICS Afghanistan§ 29 578 710 1.7 0.022 0.0 0.017 0.03 (0.02–0.05) 0.009 0.04 Zimbabwe 38 720 220 0.5 0.064 0.1 0.051 0.09 (0.07–0.14) 0.025 0.13 Cambodia 40 258 214 0.5 0.550 0.7 0.437 0.77 (0.56–1.18) 0.218 1.09 Uganda 47 211 1165 2.7 0.260 0.3 0.206 0.37 (0.26–0.56) 0.103 0.52 Mozambique 50 827 300 0.7 0.248 0.3 0.197 0.35 (0.25–0.53) 0.098 0.49 Thailand 61 208 1081 2.5 1.61 2.1 1.28 2.27 (1.64–3.45) 0.640 3.20 Tanzania 63 892 830 1.9 0.852 1.1 0.677 1.20 (0.87–1.82) 0.338 1.69 Nigeria 97 853 1341 3.1 1.33 1.7 1.06 1.88 (1.36–2.85) 0.530 2.65 Kenya 99 149 1818 4.2 4.86 6.3 3.86 6.83 (4.95–10.40) 1.93 9.64 Vietnam 103 906 818 1.9 2.46 3.2 1.95 3.46 (2.51–5.27) 0.977 4.89 Democratic Republic of Congo 112 499 1522 3.6 0.972 1.3 0.772 1.37 (0.99–2.08) 0.386 1.93 Ethiopia 147 592 2497 5.8 6.04 7.8 4.80 8.51 (6.16–12.94) 2.40 12.0 Burma 148 149 358 0.8 1.17 1.5 0.930 1.65 (1.19–2.51) 0.465 2.33 Bangladesh 173 619 1070 2.5 4.13 5.3 3.28 5.81 (4.21–8.83) 1.64 8.20 Philippines 235 608 2565 6.0 1.81 2.3 1.44 2.54 (1.84–3.87) 0.718 3.59 Pakistan 273 097 1171 2.7 1.79 2.3 1.42 2.52 (1.82–3.83) 0.711 3.55 Indonesia 331 424 5566 13.0 2.04 2.6 1.62 2.88 (2.08–4.38) 0.812 4.06 BRICS countries Brazil 82 755 2510 5.9 1.14 1.5 0.905 1.60 (1.16–2.44) 0.453 2.26 Russian Federation 149 921 1031 2.4 8.86 11.4 7.04 12.5 (9.04–19.0) 3.52 17.6 South Africa 349 582 240 0.6 4.57 5.9 3.63 6.43 (4.66–9.77) 1.81 9.07 China 900 678 2800 6.5 12.0 15.5 9.53 16.9 (12.2–25.7) 4.77 23.8 India 1 467 585 13 000 30.4 20.8 26.8 16.6 29.3 (21.3–44.6) 8.28 41.4 Total 5 005 111 42 827 100 77.6 100 61.7 109 (79.1–166) 30.8 154
• Countries listed in order of the number of notified TB cases in 2012. BRICS: Brazil, Russian Federation, India, China and South Africa. #: data obtained from [12]. : we assumed for all countries that, on average, 79% of the sputum smears were performed for initial diagnosis (the average proportion reported by 11 countries able to stratify smears for initial diagnosis and those performed for treatment monitoring). The number of initial smears was multiplied by US$1.77 (range US$1.28–2.69); the median unit costs for a smear according to Lu et al. [11]. Smear costs included various components (e.g. material, labour, equipment and overheads) although the exact components included differed across studies or were not always reported. +: we assumed that a replacement test would only need a single test on one sample (as opposed to an average of two samples for sputum smear microscopy) and multiplied these by US\$5, the anticipated costs for a hypothetical replacement test. §: smear volumes were recognised to be under-reported by laboratories. | 2022-01-20 18:05:31 | {"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": 0.3647754192352295, "perplexity": 4676.790138969163}, "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/1642320302355.97/warc/CC-MAIN-20220120160411-20220120190411-00179.warc.gz"} |
https://docs.habana.ai/en/latest/TensorFlow/Tensorflow_User_Guide/TensorFlow_Mixed_Precision.html | # TensorFlow Mixed Precision Training on Gaudi¶
This section describes how to run mixed precision training of TensorFlow models on Gaudi.
Note
For Keras models, the recommended mixed precision mechanism is tf.keras.mixed_precision.
Warning
The result of enabling both mixed precision mechanisms is undefined, so BF16 Conversion Pass and tf.keras.mixed_precision should not be used together.
## Op Lists for BF16 Conversion Pass¶
Gaudi supports mixed precision of float32 and bfloat16. Mixed precision in general can reduce memory size as well as memory bandwidth requirements and accelerate math operations.
To enable BF16 computations instead of FP32, you can:
• Explicitly modify the python script containing the model as in the example below:
# change op's dtype based on input param to script
if params['dtype'] == 'bf16':
op = tf.cast(op, dtype=tf.bfloat16)
• Or, automatically convert selected ops to be computed in lower precision using Habana’s automatic BF16 conversion pass.
The conversion pass uses a notion of Allowlists, Conditional Lists and Blocklists. We also make it possible to provide certain exceptions. Below, you can find an empty template for defining your own BF16 configuration:
{
"allow_list": [],
"conditional_list": [],
"strict_conditional_list": [],
"non_convertible_exceptions": [],
"convertible_exceptions": []
}
• Allowlists contain ops that are 100% numerically safe, which means they can always be converted to and computed in BF16.
• Blocklists contain ops that are not numerically safe for reduced precision computations. Such lists do not actually appear anywhere explicitly. Any operation that is not present in allow-, conditional or strict conditional lists is blocked by default.
• Conditional lists contain ops that may behave in an unstable manner if paired with blocked ones. Ops found in these lists are marked for conversion if at least one input or output is to be converted.
• Strict conditional lists differ from conditional lists in that their ops are converted only if either all of their inputs are to be converted or the inputs are Variables or Consts.
All nodes that are found suitable for reduced precision computations are divided into groups (based on adjacency) and converted to BF16 in such a manner that Cast nodes are inserted before the first and after the last to-be-converted node in the group.
## Exception Lists¶
In addition, there are two other lists, Non convertible exceptions and Convertible exceptions, that allow for more fine-grained control over the precision of specific instances of ops. This feature allows you to mark specified instances as suitable or unsuitable for BF16 conversion, regardless of the ops placed in allowlist, conditional or blocklists. For example, it is possible to run some isolated Mul operations in BF16 even if Mul does not appear in either allowlists or conditional lists. On the other hand, you can disable specific, for example, Conv2D instances from BF16 conversion even if Conv2D appears in the allowlist.
Specific op instances can be selected by means of providing a name/op-type pair in the convertible or non_convertible exception lists of ops. For example:
"allowlist": [
"BatchMatMul",
"BatchMatMulV2",
"MatMul”
],
"conditional_list": [],
"strict_conditional_list": [],
"non_convertible_exceptions": [
],
"convertible_exceptions": [
]
}
In the above example, BatchMatMul(V2) and MatMul are allowed and there are no ops in the conditional or strict conditional lists. There are also single pairs in both lists containing the convertible and non_convertible ops. In this scenario, all MatMul operations except for gradients/bert/encoder/layer_0/attention/self/key/MatMul_grad/MatMul_1 will be converted. Also, all AddV2 ops matching the name bert/encoder/layer_[0-9]+/attention/self/add will be run in BF16, even though AddV2 is not mentioned in either allow or conditional lists.
Note that the two additional lists require pairs. The first element is a regex for the name. The second element is a string defining the operation type, and is optional. If the second element is left empty, the mechanism will take all the operations matching the name regex, regardless of the type.
## JSON Recipe Files for BF16 Configuration¶
There are two ways to provide BF16 conversion list:
1. Using predefined lists:
• Full – Aims at achieving the best performance while still reaching the state of the art accuracy for most models.
• Basic – Only general matrix multiplications and convolutions are converted.
These lists can be dumped to a JSON file, modified and reused by setting TF_BF16_DUMP_PATH flag:
TF_BF16_DUMP_PATH=/path/to/output/file.json
2. Using existing topology specific configs provided in the Model-Reference GitHub page. For example, you can find bert.json here.
These conversion configs also define two strings - KEEP_FP32_PRECISION in the non_convertible_exceptions and FORCE_BF16_PRECISION in convertible_exceptions. Adding KEEP_FP32_PRECISION to the name scope prevents nodes containing this infix from being converted from FP32 to BF16. Similarly, adding FORCE_BF16_PRECISION forces the affected nodes to be converted to BF16. These strings can be injected using tf.name_scope.
Set the following environment variable to point to the path to the JSON recipe file for running mixed precision training on Habana:
TF_BF16_CONVERSION=/path/to/model/mixed_precision_config.json | 2022-08-07 22:17:07 | {"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": 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": 0.3408322036266327, "perplexity": 4217.98845612397}, "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-2022-33/segments/1659882570730.59/warc/CC-MAIN-20220807211157-20220808001157-00361.warc.gz"} |
https://runestone.academy/ns/books/published/welcomecs/CSPTeasers/computeNumbers.html | # 1.2. Compute with Numbers¶
Computers were first used for numeric calculations. You may be used to doing calculations with a calculator, but calculations are often easier if you can name the numbers you are working with. When you name a number, or the result of a calculation, you are creating a variable. A variable is a name associated with computer memory that can hold a value and that value can change or vary. One example of a variable is the score in a game. The score starts off at 0 and increases as you play the game.
One thing that you might want to calculate is the monthly payment on a loan for a car. To do so, you can use this mathematical formula:
$$A = P \frac{r(1 + r)^n}{(1 + r)^n - 1}$$
That formula uses the following variables:
• P : The principle - the amount of the original loan
• rThe monthly interest rate expressed as a decimal value. Loans are often described in
terms of an APR or Annual Percentage Rate that must be divided by 1200 to produce the right value for r.
• n : The number of monthly payments
It calculates the value A which is the payment amount.
The Python program below sets some values for these variables and then does the calculations needed to produce the payment.
Press the button below to make the computer execute these steps. The output from this program will be displayed to the right of the program.
You can only use the Save and Load buttons if you are logged in. The Save button will save the current program and the Load button will load a saved program.
Currently the code is calculating the payment for a $10,000 loan at an APR of 4.9% over 60 months. Try changing the numeric values for P, APR, and n in the program above, and press the Run button to calculate the payment for a different loan. Note that some of the symbols used in Python are different than those we normally use for math: * means “multiply” and ** means “to the power of”. Also visible in the code are some comments. Comments are pieces of text that come after a # symbol, like #$10,000 - notice we don't use ,'s in numbers. Python will ignore these comments and they are colored differently than the code to indicate that they are not actual code. Comments are used by programmers to leave notes to themselves and others about the code. Try deleting a # in the program above and then running it. You will get an error message because now Python is trying to run the note as if it was code.
Note
Notice how naming the values (using variables) for things like n makes it easier to see which values to change to make the program calculate a different loan. | 2023-02-09 06:52:45 | {"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": 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": 0.3432632088661194, "perplexity": 496.4317294593241}, "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-2023-06/segments/1674764501407.6/warc/CC-MAIN-20230209045525-20230209075525-00433.warc.gz"} |
https://www.physicsforums.com/threads/can-you-assume-that-jupiter-has-a-circular-orbit.11761/ | # Can you assume that Jupiter has a circular orbit?
1. Dec 30, 2003
### yxgao
When it is about the same distance from Jupiter, spacecraft on a mission to the outer planets has a speed that is 1.5 times the speed of Jupiter in its orbit. Why does the orbit of the spacecraft about the sun follow a hyperbolic orbit?
Can you assume that Jupiter has a circular orbit? So far I've tried caltulating the total energies of the spacecraft and of Jupiter but I don't think that's correct.
2. Dec 30, 2003
### enigma
Staff Emeritus
Use the Vis-Viva equation
$$V=\sqrt{\frac{2}{r}-\frac{1}{a}}$$
It's a safe assumption (unless they give it to you explicitly) that the eccentricity of planetary orbits are very small. That means that r~=a.
What is the semimajor axis of a parabolic (or hyperbolic) orbit? You can solve for escape velocity with that.
3. Dec 30, 2003
### enigma
Staff Emeritus
I made a mistake.
Vis Viva is:
$$V=\sqrt{\mu*(\frac{2}{r}-\frac{1}{a})}$$
Where mu is the gravitational parameter, G*M or 398600.4 km^3/sec^2 | 2017-08-21 18:50:00 | {"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": 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": 0.757391095161438, "perplexity": 1579.4113171765985}, "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-2017-34/segments/1502886109470.15/warc/CC-MAIN-20170821172333-20170821192333-00416.warc.gz"} |
http://blog.ryanwalker.us/2015/ | ## Tuesday, November 24, 2015
### Building a Streaming Search Platform
On average, Twitter users worldwide generate about 6,000 tweets per second. Obviously, there is much interest in extracting real-time signal from this rich but noisy stream of data. More generally, there many open and interesting problems in using high-velocity streaming text sources to track real-time events. In this post, I describe the key components of a platform that will allow for near real-time search of a streaming text data source such as the Twitter firehose.
Such a platform can have many applications far beyond monitoring Twitter. For example, a network of speech to text monitors could transcribe radio and television feeds and pass the transcriptions to the platform. When key phrases or features are found in the feeds, the platform could be configured to trigger real-time event management. This application is potentially relevant to financial, marketing, and other domains that depend on real-time information processing.
All code for the platform I describe here can be found in my github project Straw. The code base includes:
• Complete Java-based Storm implementation, including both Lucene-Luwak and Elasticsearch-Percolators implementations of streaming search.
• Scripts to automate AWS deployment using boto3
• A local run mode enabling testing on a single machine using dockerized components
• Benchmark utilities
• A demo multiuser web interface where users register queries and receive streaming matches from a simulated twitter firehose
I completed this project as a Fellow in the Insight Data Engineering Program. The original inspiration for for this project came from two excellent blog posts on streaming search:
# Streaming Search
The key data structure for solving a traditional text search problem is an inverted index built from the collection of documents you want to be able to query. In its simplest form, an inverted index is just a map whose keys are the set of all unique terms in the documents. The value associated to a particular term in the map is a list of all the documents which use that term.
After the index has been built, users can submit queries to run against the index. For example, we can have a query that should return all the documents that contain both words in the phrase "llama pajamas". The query engine will split the input phrase into the tokens "llama" and "pajamas", then it will check the inverted index to get the list of all documents that contain the word "llamas" and the list of all documents that contain the word "pajamas". The engine will then return the intersection of these two lists, i.e. the list of the documents that are present in both lists.
In the streaming case, documents arrive at a very fast rate (e.g. average of 6000 per second in the case of Twitter) and with this kind of velocity and volume it is impractical to build the inverted document index in real-time. Moreover, the goal is not to create a static index of tweets--rather it is to scan the tweets as they arrive in real-time and determine if they match a registered query. Here's where we can play a clever trick. Instead of building our inverted index from the documents, we can instead build the index from the queries themselves.
As a simple example, suppose a user wants to see all the tweets that contain the word "llama" and "pajamas". To add this query to the inverted index we would:
1. Create an identifier for the query, say "q1".
2. If "llama" is in the inverted index add "q1" to the list of keys at "llama". Otherwise, initialize "llama" in the index with a list containing "q1".
3. If "pajamas" is in the inverted index add "q1" to the list of keys at "pajamas". Otherwise, initialize "pajamas" in the index with a list containing "q1".
As tweets arrive in the stream, the query engine will break the text into tokens and then query engine would return the intersection of all the list values whose key is a token in the inverted index.
Fortunately, there are already several existing tools which can be used to build an inverted query index:
• Elasticsearch percolators is a standard feature of Elasticsearch that allows us to index queries and "percolate" documents.
• Luwak for Lucene is a Lucene module that uses significant pre-filtering to optimize matching against an inverted query index. Speed performance compared to percolators can be very significant.
# Architecture
Now that we've got the basic tools for streaming search (Elasticsearch-Percolators or Lucene-Luwak), lets describe the architecture for the platform. The Straw platform is made up of the following components:
• A streaming text source, such as the Twitter firehose, which emits a continuous stream of JSON documents
• An Apache Kafka cluster, which handles ingestion from the text stream
• An Apache Storm cluster, which distributes computation across multiple search engine workers
• A Redis server, which provides a PUBSUB framework to collect and distribute matches to subscribed users
• One or more clients, who submit queries and listen for matches on behalf of users
## Streaming Sources
The Twitter streaming API does not offer access to the firehose without special permission. To see how Straw would perform under firehose level load, we can instead use the sample endpoint to collect a large corpus of tweets. We can either store these tweets in a file or alternatively send them directly to the Kafka cluster's documents topic:
Alternatively, we can load tweets from a file into Kafka with a simple producer script:
To maintain a high load we can run multiple instances of this script and restart the script as soon as it finishes reading the file, using for example a supervisor.
Though the Straw project was designed for handling discrete JSON documents, by change the internal parsers it could be very easy to use other formats like XML. A more interesting challenge is handling continuous stream data, such as audio transcriptions. In this case, several strategies could be tried. For example, we could detect sentence breaks and treat each detected break as a separate document in the stream.
## Kafka
The Kafka cluster has two topics: documents and queries. The producer script above can be used to populate the documents topic. The frontend client populates the query topic with user subscriptions. In production, I found a 5 node Kafka cluster could easily accommodate Twitter level volume. For the documents topic, I used a partition factor of 5 and a replication factor of 2. While high availability is very important to accommodate the volume of the stream, document loss may not be a big concern. For queries, I used only 2 partitions with a replication factor of 3. Queries are infrequent so availability may not be important but query loss is not acceptable. Note that the partition factor should be less than or equal to the number of KafkaSpouts in our Storm topology, since each spout will consume from exactly one partition.
One other important Kafka configuration is in kafka.server.properties:
# The minimum age of a log file to be eligible for deletion
log.retention.hours=1
The Kafka default is 168 hours--far too big since you can easily fill a modestly sized disk under load. As messages should ideally be consumed in real-time, I recommend using the minimum value which is 1 hour. Note, however, that you may still need to ensure that you have a sufficiently large volume for the Kafka log. In production, I gave each Kafka node a 64GB volume with a 1 hour retention.
## Storm
The Storm topology implements KafkaSpouts for the documents and queries topics. In production, I used 5 document spouts and 3 query spouts (consistent with the Kafka partitioning). The bolts in the topology search the document stream and publish any matches to Redis. In production, I allocated a total of 6 workers. Sizing the cluster correctly proved to be somewhat challenging. I highly recommend this post which explains the key concepts of Storm parallelism. Also the Storm built-in UI can be helpful for monitoring and understanding how the cluster is performing.
In the most basic scenario, we assume that the number of queries is small and can fit easily into memory on a single machine. Then scaling to the volume of the stream is quite easy. The idea is to give each bolt a complete copy of the in memory Lucene-Luwak index (remember that the queries are what's being indexed here). So each time a user registers a new query, we must broadcast it to all of the bolts in the topology to maintain the local query index. When a document arrives from the stream, we can then randomly assign it to any bolt since each bolt has a full copy of the query index. To handle failover, we can also keep a global copy of the all the queries, so that if a bolt dies we can replace it with a new one and populate its index from the global store. This Java snippet defines such a topology:
TopologyBuilder builder = new TopologyBuilder();
builder.setSpout("query-spout", new KafkaSpout(query_spout_config), 3);
builder.setSpout("document-spout", new KafkaSpout(document_spout_config), 5);
builder.setBolt("search-bolt", new LuwakSearchBolt(), 5)
.allGrouping("query-spout")
.shuffleGrouping("document-spout");
Since this platform is intended to be multiuser and multitenant, we can easily imagine a situation where the number of queries can't practically fit in memory on a single bolt. In this case, we can add another layer of bolts to the Storm topology:
Here the complete query index is partitioned across a small cluster of bolts. Incoming queries are broadcast to the fan bolts. Each fan bolt will then randomly choose one Lucene worker to index that query. Documents from the stream can be shuffled among the fan bolts. Each fan bolt must then broadcast the document so that each Lucene bolt can check the document against its partition of the index.
If we use Percolators instead of Luwak then each bolt contains an Elasticsearch client. In this case, it is a good idea to collocate the Elasticsearch cluster with the search bolts and to use high replication so as to minimize network overhead. Note that Percolator queries are also stored in-memory, so we still face difficulties as the number of queries becomes large.
## Redis
Redis is most commonly used as an in-memory application cache, but it also has a simple and elegant publish-subscribe framework. Here's an example of pubsub using the Redis-cli:
In a terminal A, listeners subscribe to a topic:
127.0.0.1:6379> SUBSCRIBE "llama-topic"
In a separate terminal B, the publisher publishes to the topic:
127.0.0.1:6379> PUBLISH "llama-topic" "llamas love to wear pajamas"
Back in terminal A, the subscriber receives the message:
1) "message"
2) "llama-topic"
3) "llamas love to wear pajamas"
That's all there is to it. All standard Redis clients expose an API to interact with the PUBSUB framework.
When a user registers a query in the Straw platform, here's what happens:
1. The client passes the query to the Kafka queries topic.
2. The client computes the MD5 hash of the query which will be the ID for the query.
3. The client subscribes the user to the computed ID in Redis PUBSUB.
4. The Storm cluster receives the query from the Kafka spout and broadcasts it to the Lucene bolts
5. Each bolt computes the MD5 hash of the query and registers the query with Luwak using the hash as the query ID
6. When a bolt receives a document, it uses Luwak to check if the document matches any query in the index. If Luwak finds a match, it will return one or matching IDs. For each ID returned by Luwak, the bolt will use Redis PUBSUB to publish the original document using the ID as the topic.
7. Subscribed clients will receive documents as they are published to Redis.
Using the hash as the query ID allows two or more users to subscribe to the same query while only needing to actually index a single query.
## Clients
A client for Straw has the following duties:
1. Manage users. In particular, it must keep track of which users have subscribed to which queries
2. Push user queries to Kafka and subscribe to queries in Redis
3. Listen for responses from queries
The Straw platform comes packaged with a default client which is a simple Python Flask webserver. The webserver is sessionized so that users can follow particular queries. The server implements a basic Kafka producer to publish queries to Kafka and Redis keeps track of the list of subscribed query IDs for each user. The listening is handled by a single background thread that holds a Redis client subscribed to all unique queries across the entire set of active users. When a query ID and document pair are found, the background thread queries Redis to find which users are subscribed to that query ID. It will then copy the document text to a result pool for each subscribed user. The user interface will checks the user's pool for updates every half-second so that results stream into the console. Here is a video of UI in action:
# Benchmarks and Conclusions
One goal of the Straw project was to compare and measure performance of Elasticsearch-Percolators vs. Lucene-Luwak. Measuring this performance is not completely straightforward. I used the following very basic approach to measuring throughput:
• Fill Kafka's documents topic with a very large number of documents
• Add a fixed number of reasonably complex queries to the Kafka query topic
• Start the Kafka cluster
• Each worker Bolt has a counter and a stopwatch running in a background thread
• Each time a document is passed to Lucene and response (empty or non-empty) is recieved, increment the counter
• When the stopwatch reaches 10 seconds, publish the value of the counter to a special Redis topic e.g. "benchmark". Set the counter to 0 and restart the stopwatch
By monitoring the benchmark channel in Redis, we can then track the search throughput of the system. Pictured below are density plots for estimated total throughput per second obtained by running this procedure for several hours:
• In both cases, Lucene-Luwak strongly outperforms Elasticsearch-Percolators. However, the Elasticsearch cluster I used was not especially optimized for this experiment. I suspect that a portion of the differential would disappear if more effort was made to localize the Elasticsearch index to the search bolts
• As the number of queries increases we see significant reduction in the throughput. It would be very interesting to see if the fan bolt solution described above would improve this performance
• The variance of throughput is very high, particularly for Luwak
• In the small query case, we are easily accommodating average twitter level volume; for large queries we are close and could likely scale horizontally to obtain a solution
• The queries used here are available in the straw repository. I generated these by computing bigram frequency across a sample of 40M English language tweets and keeping the most frequent bigrams. It would be interesting to evaluate performance with more complex queries
• The documents here are tweets which are limited to 140 characters. It would be interesting to evaluate performance with longer text sources
## Sunday, March 8, 2015
### Sparse Quadratic Programming with Ipoptr
This post is a follow up to my last post on quadratic programming facilities in R. A commenter pointed me to the ipoptr project which exposes an R interface to the COIN-OR optimization routine Ipopt. COIN-OR is a suite of optimization utilities implemented in C++ and supported by a back-end of configurable FORTRAN linear system solvers. ipoptr may be a good solution for users wishing to solve sparse nonlinear constrained optimization problems through an R frontend. Some highlights of this solver are:
1. It is a general interior point solver that can handle nonlinear objectives with nonlinear constraints. In particular, no convexity assumptions are required to obtain local solutions.
2. It offers a flexible and lightweight specification of the objective function and a sparse matrix representation for the constraints and other problem data.
In this post, I'll explain how ipoptr can be applied to solve quadratic programs and I'll compare the performance of this solver to other quadratic program solvers (quadprog, ipop) available in R. We'll see that ipoptr is very fast and efficient on large sparse quadratic programs, seemingly an order of magnitude faster than quadprog on the demonstration problem considered in my previous post. Because the Ipopt backend is a bit tricky to install, the last section provides a detailed overview of how I successfully built this solver under Ubuntu Linux.
# The ipoptr interface
Before applying ipoptr to quadratic programming, it may be helpful to present a high-level picture of the ipoptr interface. The following is a summary of the ipoptr interface drawn from the documentation. ipoptr stages and invokes an interior point algorithm from within R to find a local solution of the following constrained optimization problem: \begin{aligned} \underset{\alpha \in \mathbb{R}^n}{\text{Minimize}}: \qquad & f(x) \\ \text{Subject to:} \qquad & g_L \leq g(x) \leq g_U \\ & x_L \leq x \leq x_U \end{aligned} where:
• $f:\mathbb{R}^n \to \mathbb{R}$ the objective function is twice continuously differentiable
• $g:\mathbb{R}^n \to \mathbb{R}^m$ defines the constraint set and is twice continuously differentiable
• $x_U$, and $x_L$ are fixed vectors in $\mathbb{R}^n$
• $g_U$, and $g_L$ are fixed vectors in $\mathbb{R}^m$
Note that the solver does not need to make any assumptions about the convexity of either $f$ or $g$. The solver makes use of the following ingredients to find a solution:
1. An initial guess $x_0$ for the solution
2. The objective function gradient $\nabla f$
3. the Jacobian of the constraint map $J_g$
4. Optionally, the Hessian of the problem Lagrangian in the form: $$H(x, \sigma_f, \vec{\lambda}) = \sigma_f \nabla^2 f(x) + \sum_{i=1}^m \lambda_i \nabla^2 g_i(x).$$
When $n$ is large, the dense matrix representations of $g$, $\nabla f$, and $J_g$ will have a substantial footprint. In application problems, however, the Jacobian and/or the Hessian object will often be sparse. For efficiency, ipoptr utilizes a sparse matrix representation for $H$ and $J_g$. This format is defined as follows. Let $A_{\mathrm{values}}$ be the list of all non-zero values in $A$ (read into the list from left to right along the rows of $A$). Then let $A_{\mathrm{mask}}$ be a list of lists, where the list at position $i$ in $A_{\mathrm{mask}}$ provides the column indexes of the nonzero elements in the $i$-th row of $A$. Then $(A_{\mathrm{values}}$, $A_{\mathrm{mask}})$ is a sparse representation of $A$.
Generally, it could be quite difficult to come up with the explicit representations of the Jacobian and Hessian that ipoptr consumes. Although the Hessian is an optional argument, including it can significantly improve convergence behaviour (try taking the Hessian arguments out in the examples below). For a quadratic program, however, it is simple to compute the Jacobian and Hessian directly. We'll do this in the next section and then provide an R wrapper function that can transform any symmetric positive definite quadratic program in standard matrix form into a quadratic program that can be solved by ipoptr.
# Solving Quadratic Programs with ipoptr
Consider the quadratic program: \begin{aligned} \underset{\alpha \in \mathbb{R}^n}{\text{Minimize}}: \qquad & f(x) = -d^Tx + \frac{1}{2}x^T D x \\ \text{Subject to:} \qquad & g(x) = Ax \leq b \end{aligned} where
• $D$ is an $n \times n$ matrix (which we'll assume is symmetric)
• $A$ is an $m \times n$ matrix.
• $d$ is a fixed vector in $\mathbb{R}^n$ and $b$ is a fixed vector in $\mathbb{R}^m$.
Then using some basic identities of vector calculus and the symmetry of $D$: \begin{aligned} \nabla f(x) &= -d + \frac{1}{2}(D^T + D) x = -d + Dx \\ \nabla^2 f(x) &= D \\ J_g(x) &= A^T \\ \nabla^2 g_i(x) &= 0 \mbox{ for all } i \\ H(x, \sigma_f, \vec{\lambda}) &= \sigma_f D. \end{aligned} Because $D$ is positive definite, the global minimizer $\tilde{x}$ of $f$ can be computed as: $$\nabla f(\tilde{x}) = 0 \rightarrow \tilde{x} = D^{-1} d.$$ Goldfarb and Idnani, whose QP algorithm is implemented in the quadprog package, use the global minimizer $\tilde{x}$ as the initial point for their interior point primal/dual method. This choice is based on empirical evidence cited by the authors that this selection can substantially reduce the number of iterations required to find a solution. We'll follow suit with ipoptr by setting $x_0 =\tilde{x}$ for our initial guess.
The following R function uses these facts to solve a quadratic program in standard form with ipoptr:
# Performance Comparison
In my previous post, I compared the performance of quadprog and kernlab's ipop solvers on the circus tent demonstration problem. For this post, I repeated the same experiment with the ipoptr solver and the results were very impressive. Ipoptr was substantially faster at solving this sparse demonstration problem than quadprog. Here are the solve times I obtained:
problem.size quadprog.time ipop.time ipoptr.time
1 64 0.002 0.024 0.010
2 256 0.048 0.710 0.034
3 576 0.518 4.759 0.126
4 1024 2.903 23.430 0.414
5 1600 10.815 77.708 0.855
6 2304 31.899 232.355 1.819
7 3136 79.749 544.193 3.318
8 4096 176.743 1521.225 8.297
9 5184 354.839 2543.754 9.039
10 6400 664.804 5053.922 19.551
Here is the experiment code:
It's not so surprising that the ipoptr package is substantially faster in this example because the matrix Dmat that defines the objective function for the tent problem is very sparse. Quadprog requires dense matrix representations to describe the QP that we wish to solve, while in ipoptr we need only specify the functional form the quadratic objective function. Here is the plot of Dmat's sparsity structure:
To investigate the performance of ipoptr on dense QPs, I generated some random positive definite QPs of differing sizes and compared solve times against the solver from quadprog and the ipop solver from the kernlab package. In this dense problem case, quadprog appears to have a significant advantage over ipoptr. Still, ipoptr shows solid performance and is considerably faster than the pure R implementation of the interior point solver found in kernlab's ipop.
problem.size quadprog.time ipop.time ipoptr.time
1 500 0.068 1.942 0.294
2 1500 0.909 35.352 5.374
3 2500 4.598 155.138 23.160
4 3500 13.186 414.762 60.888
5 4500 28.419 868.141 126.278
6 5500 49.608 1570.674 226.914
7 6500 81.756 2574.962 369.469
8 7500 128.451 3937.629 563.236
Here is the code for the randomly generated QP experiment:
In this post, we looked at how the ipoptr interface can be used to solve quadratic programming problems and compared the Ipopt solver to other quadratic program solvers available in R. We found:
• ipoptr is very efficient and well-suited for solving large, sparse quadratic programs, even outperforming the quadprog package solver in this case.
• However, for dense symmetric positive definite QPs, quadprog is much faster than ipoptr.
• Both solvers are substantially faster than the pure R interior point solver ipop from the kernlab package.
• For the experiments in this post, Ipopt was configured to use the MUMPS linear solver. It is possible to configure Ipopt to use other linear solvers and this could have an impact on performance.
• Initializing Ipopt with $x_0$ as the global minimum of the objective function (as done internally in the quadprog package) seems to be somewhat beneficial for reducing runtimes. This effect should be investigated more carefully, however.
• The timings presented above do not include the time required to translate from a QP specified in matrix format (e.g. Dmat, Amat, etc.) to the input format required by ipoptr. In practice, however, this step is rather expensive and users will probably want to generate the ipoptr input data directly instead of forming dense matrix inputs and then converting to the ipoptr format. The specifics of how this should be done will depend on the particular problem which the user is trying to solve.
# Installing ipoptr for Ubuntu Linux
Because of complex licensing issues in COIN-OR suite and its many dependencies, it's not possible to bundle the backend ipopt solver and its R interface into a simple package installable directly from R. Thus, installing ipoptr won't be as easy as installing most other R pacakges. Fortunately, the CoinOpt documentation and the R interface documentation are fairly complete.
After a bit of work, I was able to install everything on a Ubuntu-Linux box using the following steps.
# Change into directory where you want to put the ipoptr source and build path
cd ~/projects/
# install dependencies, including latest blas and lapack.
sudo apt-get update
sudo apt-get install gcc g++ gfortran subversion patch wget
sudo apt-get install libblas3 liblapack3
# get the project -- note, will need to accept SSL cert
svn co https://projects.coin-or.org/svn/Ipopt/stable/3.12 CoinIpopt
# get and build Mumps linear solver
cd CoinIpopt/ThirdParty/Mumps
./get.Mumps
cd ../..
# build and install Ipopt; it's a good idea to inspect the output of make test
# With this setup, AMPL test will fail (ok) but all the other tests should pass.
mkdir build
cd build
../configure
make
make test
make install
# Move RInterface Makevars from build to src directory
cp Ipopt/contrib/RInterface/src/Makevars ../Ipopt/contrib/RInterface/src
Now, we can fire up R and install the package from source using:
install.packages("~/projects/CoinIpopt/Ipopt/contrib/RInterface",
repos=NULL, type="source")
## Tuesday, February 10, 2015
### More on Quadratic Programming in R
This post is another tour of quadratic programming algorithms and applications in R. First, we look at the quadratic program that lies at the heart of support vector machine (SVM) classification. Then we'll look at a very different quadratic programming demo problem that models the energy of a circus tent. The key difference between these two problems is that the energy minimization problem has a positive definite system matrix whereas the SVM problem has only a semi-definite one. This distinction has important implications when it comes to choosing a quadratic program solver and we'll do some solver benchmarking to further illustrate this issue.
# QP and SVM
Let's consider the following very simple version of the SVM problem. Suppose we have observed $y_i \in \{-1,1\}$, $X_i \in \mathbb{R}^{m}$ for $n$ (perfectly linearly separable) training cases. We let $y$ denote the $n \times 1$ vector of training labels and $X$ the $n \times m$ matrix of predictor variables. Our task is to find the hyperplane in $\mathbb{R}^m$ which "best separates" our two classes of labels $-1$ and $1$. Visually:
library("e1071")
library("rgl")
train <- iris
train$y <-ifelse(train[,5]=="setosa", 1, -1) sv <- svm(y~Petal.Length+Petal.Width+Sepal.Length, data=train, kernel="linear", scale=FALSE, type="C-classification") W <- rowSums(sapply(1:length(sv$coefs), function(i) sv$coefs[i]*sv$SV[i,]))
plot3d(train$Petal.Length, train$Petal.Width,
train$Sepal.Length, col= ifelse(train$y==-1,"red","blue"),
size = 2, type='s', alpha = .6) | 2017-06-24 18:53:36 | {"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": 2, "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": 0.583712100982666, "perplexity": 1577.0328331228989}, "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-2017-26/segments/1498128320323.17/warc/CC-MAIN-20170624184733-20170624204733-00597.warc.gz"} |
https://physics.stackexchange.com/questions/436365/using-e-mc%C2%B2-to-simplify-particle-ke-calculations | # Using $E=mc²$ to simplify particle KE calculations?
In an old examination paper I found a question asking for the ratio between the KE of a nucleus and the KE of an alpha particle emitted from the nucleus.
For reference here is the question and answer (it's Question 1 (b) (iii)).
The answer can be found by using the exact values of the masses and velocities and $$KE = (1/2)mv²$$.
However, in the answer key, this (more simple) solution is also given: $$\frac{E_k\text{ of Ce}}{E_k\text{ of }\alpha}=\frac{m_dv_d^2}{m_\alpha v_\alpha^2}=\frac{m_d}{m_\alpha}\times\bigg(\frac{m_\alpha}{m_d}\bigg)^2=\frac{m_\alpha}{m_d}=\frac{1}{35}$$
I can't figure out what they are doing here.
In particular, I don't see where the substitution for $$v²$$ with the inverted masses comes from.
Is this some use of $$E=mc²$$?
I'm sure the answer is just some basic mathematics, but it escapes me.
Any help would be much appreciated.
• Please don't post formulas as pictures or plain text, but use MathJax instead. MathJax is easy for people on all devices to read, and can show up clearer on different screen sizes and resolutions. I've edited it here as an example. Look at this Math SE meta post for a quick tutorial. – user191954 Oct 23 '18 at 13:29
This is just conservation of momentum, no need for $$E=mc^2$$. In the problem you have a stationary nucleus that decays, so initially the system has no momentum. After the decay you need the particles to have equal and opposite momentum, so considering magnitudes: $$p_{\alpha}=p_{d} \implies m_{\alpha}v_{\alpha}=m_{d}v_{d} \implies \frac {v_d^2}{v_{\alpha}^2}=\frac{m_{\alpha}^2}{m_d^2}$$
Conservation of Momentum $$p=mv$$ is the key for understanding this equation.
The Ce nucleus starts initially at rest, i.e. without any Momentum. After Decay of the particle, one has nonvanishing momenta for the nucleus; one of the Ce nucleus AFTER the Decay $$p_{Ce}$$ and one of the Alpha particle $$p_\alpha$$. Add These momenta up and set the total Momentum $$p_{tot} = p_{Ce}+p_{\alpha}$$ to Zero (total Momentum in the final decay is the same as the total Momentum initially). Then you will have the answer. | 2020-05-30 02:56:24 | {"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": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 10, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8613421320915222, "perplexity": 228.43288526293878}, "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-2020-24/segments/1590347407001.36/warc/CC-MAIN-20200530005804-20200530035804-00035.warc.gz"} |
http://lhfp.allecottarze.it/latex-appendix-section-overleaf.html | qawqkxe2ycfh9 zyvt1t5skz8z ygka5ro6f6pd2fv qnv4tubszi09m otxa7cgw1sqk hanq7hbwl3rfl hxvc7wcxlo xzh4m3gliqsh 4zp37yemxq7 97vfxpdyhg vehkhtsqfc2 bsmyf2tgo3kyj ihnngtxca7e2 j8d986663cgqr50 3d1qxlut3amy f2uhfgrerps4i2 ebyhr9f04a y7g9v1tx7f8l au8myh5ch2 12tylcd4s6y s4l2d9wx4e 8d1b4tzg1oh 1fzl2a9bmav4k a0oswjv2f6zwx6u e1yyf0f85dllp0i pz1wpquddvym 30tfgjafcx 681gv9gqqxz5205 2l8rq644zz3ncvt | 2020-07-05 09:25:59 | {"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": 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": 0.8380768299102783, "perplexity": 3593.3864851722083}, "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-2020-29/segments/1593655887319.41/warc/CC-MAIN-20200705090648-20200705120648-00583.warc.gz"} |
https://stats.stackexchange.com/questions/117607/how-to-use-k-fold-cross-validation-in-naive-bayes-classifier | How to use k-fold cross validation in naive bayes classifier?
I'm trying to classify text using naive bayes classifier, and also want to use k-fold cross validation to validate the result of classification. But I'm still confused how to use the k-fold cross validation. As i know that k-fold divide data to k subsets, then one of the k subsets is used as the test set and the other k-1 subsets are put together to form a training set. And i think as training set the data must have label to be trained. So to use k-fold cross validation the required data is the labeled data?, is it right?, and how about non labeled data?.
• Do you have your answer? – cdeterman Oct 2 '14 at 19:12
You are very close to understanding k-fold cross-validation. To answer your questions in turn.
1. So to use k-fold cross validation the required data is the labeled data?
Yes, you must have some 'known' result in order for your model to be trained on the data. You are building a model, I assume, to predict some sort of outcome either regression or classification. In order to do so, a model must be built on data to explain some known result.
2. How about non labeled data?
For k-fold cross-validation, you will have split your data into k groups (e.g. 10). You then select one of those groups and use the model (built from your training data) to predict the 'labels' of this testing group. Once you have your model built and cross-validated, then it can be used to predict data that don't currently have labels. The cross-validation is a means to prevent overfitting.
As a last clarification, you aren't only using 1 of the 10 groups. Let's say you had 100 samples. You split it into groups 1-10, 11-20, ... 91-100. You would first train on all the groups from 11-100 and predict the test group 1-10. Then you would repeat the same analysis on 1-10 and 21-100 as the training and 11-20 as the testing group and so forth. The results typically averaged at the end.
As a simple example say I have the following abbreviated data (binary classification):
Label Variable
A 0.354
A 0.487
A 0.384
A 0.395
A 0.436
B 0.365
B 0.318
B 0.327
B 0.381
B 0.355
Let's say I want to do 10-fold cross-validation on this (nearly Leave-One-Out cross-validation in this case)
My first testing group will be:
A 0.354
A 0.487
My training set is the remaining data. See how the labels are present in both groups?
A 0.384
A 0.395
A 0.436
B 0.365
B 0.318
B 0.327
B 0.381
B 0.355
Please note that it is also best practice to randomize the grouping, this is purely for demonstration
Then you fit your model to the training set, which is using the variable(s) to best explain the labels (class A or B). The model that has been fit to this training set is then used to predict the testing dataset. You remove the labels from the testing set and predict them using the trained model. You then compare the predicted labels to the actual labels. This is repeated for all 10-folds and the results averaged.
Once everything is completed and you have your wonderfully cross-validated model, you can use it to predict unlabeled data and have some sort measure of confidence in your results.
Extended for Parameter Tuning
Let's say you are tuning a partial least squares (PLS) model (it doesn't matter if you don't know what this is for demonstration purposes). I would like determine how many components (the tuning parameter) I should have in the model. I would like to test 2,3,4, and 5 components and see how many I should use to maximize my predictive accuracy without overfitting the model. I would conduct the entire cross-validation series for each component number. Each iteration of the CV would be averaged (the average predictive accuracy of the entire analysis).
Assuming classification accuracy is your metric let's say these are my results (completely made up here):
2 components: 70%
3 components: 82%
4 components: 78%
5 components: 74%
Clearly, I would then choose 3 components for my model which has now been cross-validated to avoid overfitting and maximizing predictive accuracy. I can then use this optimized model to predict a new dataset where I don't know the labels.
• example if i had 100 samples, then i split it into 10 groups, first i choose to predict label of 1-10 groups, so the 11-100 have to be trained, but to trained the 11-100 i need label, right?, so i stil need label?, so i cant use non labeled data?. i'm still confused. – Muhammad Haryadi Futra Oct 2 '14 at 12:38
• @MuhammadHaryadiFutra, during this stage of building a model all of your data needs labels. The labels are initially removed from the testing subset but compared to after predication and therefore still required. Since you are trying to predict something, you must have some 'known' values to compare (i.e. labels). Once you have a properly built and validated model, then you can use the model to predict non-labeled data. – cdeterman Oct 2 '14 at 12:50 | 2019-07-17 15:02:13 | {"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": 0.5361943244934082, "perplexity": 1008.9376527111015}, "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-2019-30/segments/1563195525312.3/warc/CC-MAIN-20190717141631-20190717163631-00229.warc.gz"} |
https://www.gradesaver.com/textbooks/math/geometry/CLONE-df935a18-ac27-40be-bc9b-9bee017916c2/chapter-6-review-exercises-page-315/11 | ## Elementary Geometry for College Students (7th Edition) Clone
Published by Cengage
# Chapter 6 - Review Exercises - Page 315: 11
#### Answer
Angle 2: 44 degrees Angle 3: 90 degrees Angle 4: 46 degrees Angle 5: 44 degrees
#### Work Step by Step
Angle 3 is 90 degrees, for an inscribed angle is half of the value of the angle of the corresponding arc (the corresponding arc has an angle of 180 degrees). Angle 5, therefore, equals $180-90-46=44$. Since angle 1 corresponds to arc CB, arc CB is twice the measure of angle 1, making it 92 degrees. Angle 4 is half the measure of arc CB, so it is 46 degrees. Thus, angle 2 is: $180-90-46=44$ degrees.
After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback. | 2019-10-19 04:17:31 | {"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": 0.8476063013076782, "perplexity": 1089.1587737912118}, "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-2019-43/segments/1570986688826.38/warc/CC-MAIN-20191019040458-20191019063958-00489.warc.gz"} |
https://michalplachta.com/2018/02/19/building-functional-testable-http-apis/ | Majority of us intuitively know what separation of concerns is. However, knowing something and using it in practice are two different things. Developers in many projects are drowning in entangled spaghetti-like codebases. We need better tools that force us to think about the responsibilities more often. In this post I will introduce two simple functional techniques that will help us step up the game: functions as parameters and type parameters.
To show you how these tools can help us create separated concerns, let’s use a practical example. We are going to create a Pac-Man web server.
Example: Pac-Man server
For the sake of this post, let’s assume that our Pac-Man web server will use HTTP and will provide the following functionalities:
• starting a game based on provided name of the grid,
• moving Pac-Man,
• returning current position and direction of Pac-Man,
• changing Pac-Man’s direction.
In order to implement these features we will need a GameState object to hold the current state of the game.
case class GameState(pacMan: PacMan,
nextPacManDirection: Option[Direction],
grid: Grid,
dotCells: Set[Position])
case class PacMan(position: Position, direction: Direction)
It contains the current state of a PacMan, next chosen direction, the grid setup and remaining dot cells, which are cells that still contain a dot (the thing Pac-Man eats).
The GameState instances will be created and manipulated by GameEngine.
object GameEngine {
def start(gridName: String): Either[String, GameState]
def movePacMan(gameState: GameState): GameState
def changePacMansDirection(gameState: GameState,
newDirection: Direction): GameState
}
GameEngine has several functions that expect GameState as a parameter and return a new one. Nothing too fancy - very standard immutable approach.
Our objective is to create an HTTP layer that holds current GameState and publishes GameEngine functions for outside consumers. We will have 3 iterations, each of them will be better in terms of separation of concerns.
Standard approach: direct function calls
Let’s start with a standard approach which entangles the concerns of HTTP and logic (i.e. GameEngine). Please have a look at the following snippet:
class HttpRoutes extends Directives {
private var state = Map.empty[Int, GameState]
val routes: Route =
path("games") {
post {
entity(as[StartGameRequest]) { request =>
val startedGame = GameEngine.start(request.gridName, Grid.fromName)
startedGame match {
case Right(game) =>
val gameId = state.size
state = state + (gameId -> game)
complete(StartGameResponse(gameId))
case Left(errorMessage) =>
complete((StatusCodes.NotFound, errorMessage))
}
}
}
} ~
path("games" / IntNumber) { gameId =>
get {
val maybeGame = state.get(gameId)
maybeGame match {
case Some(game) => complete(PacManStateResponse(game.pacMan))
case _ => complete((StatusCodes.NotFound, s"Pac-Man ($gameId) not found")) } } } ~ ... } final case class StartGameRequest(gridName: String) final case class PacManStateResponse(pacMan: PacMan) We have defined several routes using Akka HTTP Route DSL and that looks completely fine. What’s not fine is how much the HTTP module knows about other concerns in the application, namely var state, GameEngine and GameState. Let’s analyse these problems carefully. Problems with standard approach Firstly, HttpRoutes knows everything about how state is implemented. Should HTTP know anything about state? I don’t think so, this concern should be separated. Secondly, HttpRoutes knows almost everything about GameEngine. It knows that it exists, it knows about start function. It may seem natural, because its job is to provide additional interface for GameEngine. However, I’d argue that this coupling is too tight. HttpRoutes doesn’t need to know anything about GameEngine. It needs to be able to start a game, which is not the same thing. Finally, the whole thing is totally untestable. HTTP & JSON should have their own unit tests that check whether the API is properly implemented. These particular tests shouldn’t test any game logic, which should be tested separately in GameEngine unit tests. All these issues tend to get worse and worse as projects get bigger.1 That’s why we need to take serious measures to make it right in the early days, when it’s still possible. In this post I will show you how to disentangle the concerns in our simple application using the following tools: functions as parameters and type parameters. Abstracting over state using type parameters First change I always try to do when I feel one of my modules deals with too many concerns is to abstract over as many concrete types as I can. This simple exercise gives me a lot of insight about the design and makes the rest of the refactoring steps more natural. To show you a concrete example, let’s get rid of GameState and use type parameter G instead. class HttpRoutes[G] extends Directives { private var state = Map.empty[Int, G] ... } Now the compiler will tell us which parts of the code were using GameState and we need to investigate each of those problems separately by asking the question: “Does it really need to know?”. In our case: “Does HttpRoutes really need to know about GameState?”. Let’s find out by trying to deal with compile errors. After making this change, the only compiler error in our case is this piece of code: val maybeGame = state.get(gameId) maybeGame match { case Some(game) => complete(PacManStateResponse(game.pacMan)) case _ => complete((StatusCodes.NotFound, s"Pac-Man ($gameId) not found"))
}
We can see that our HTTP layer needs to complete the request with the PacManStateResponse, which contains only a PacMan instance. This piece of code doesn’t need GameState at all! It only needs PacMan provided it has G. We can encode this sentence as a function G => PacMan and make sure HttpRoutes gets this function from the outside world.
class HttpRoutes[G](getPacMan: G => PacMan) extends Directives
val maybeGame = state.get(gameId)
maybeGame match {
case Some(game) => complete(PacManStateResponse(getPacMan(game)))
case _ => complete((StatusCodes.NotFound, s"Pac-Man ($gameId) not found")) } But… why? Why do we want to do that knowing that G will always be a GameState? Because it helps us get our design right and helps future developers understand our intentions. It is a straightforward way of telling that this piece of code is independent of GameState. It only depends on PacMan and needs a way to get it from a G. It cannot create an instance of G or modify G, because it doesn’t know what G is. The module is constrained which makes it far easier to comprehend2. Additionally, it gives much more liberty to the modules that use it, because they can choose whatever G they want as long as they also define how to get a PacMan from G.3 Using more functions as parameters We got rid of the dependency to GameState in one place, but we can do even better. Let’s think about the responsibility of our POST /games (game creation) endpoint. This is how the code that handles game creation looks like: val startedGame: Either[String, GameState] = GameEngine.start(request.gridName, Grid.fromName) startedGame match { case Right(game) => val gameId = state.size state = state + (gameId -> game) complete(StartGameResponse(gameId)) case Left(errorMessage) => complete((StatusCodes.NotFound, errorMessage)) } It gets a gridName string as an input and completes the request returning either gameId integer or a failure message. It uses GameEngine.start directly so it “knows” everything about it. However, when you think about it, this endpoint doesn’t really need to know about GameEngine! We can use the same technique to figure it out: replace direct call with a more generic function, which is passed as a parameter. Let’s see how it works in this case. What the code that handles game creation needs is: • a way to get a new instance of G (no matter what it is), • a way to add a G to the state and get gameId back. The first statement can be encoded as a function createGame: String => Either[String, G]. The second statement can be encoded addNewGame: G => Int. Note that there is no GameState, no GameEngine in this piece of code. Just as much information as this layer really needs, but no more. Truly separated concerns. Let’s pass these functions as parameters (dependencies) in HttpRoutes: class HttpRoutes[G](getPacMan: G => PacMan, createGame: String => Either[String, G], addNewGame: G => Int) extends Directives { private var state = Map.empty[Int, G] val routes: Route = path("games") { post { entity(as[StartGameRequest]) { request => val startedGame = createGame(request.gridName) startedGame match { case Right(game) => val gameId = addNewGame(game) complete(StartGameResponse(gameId)) case Left(errorMessage) => complete((StatusCodes.NotFound, errorMessage)) } } } } ~ ... } Removing state These two simple refactorings gave us another insight. We don’t need var state: Map.empty[Int, G] anymore! We just need a way to get a G based on Int. Speaking in Scala, the previous sentence can be translated as a function getGame: Int => G. Again, we are separating a concern of HTTP handling and state management by giving the HTTP layer as little power as it needs. We are constraining it as much as we can so that we can reason about it easier. Final touch: splitting routes to route factories The parameter list for HttpRoutes class got very big. It means that it does too much. The same can be said about val routes. Let’s solve both issues by breaking routes into smaller functions which get their dependencies as parameters and return partial Routes. object HttpRoutes extends Directives { def createGameRoute[G](createGame: String => Either[String, G], addNewGame: G => Int): Route = path("games") { post { entity(as[StartGameRequest]) { request => val startedGame = createGame(request.gridName) startedGame match { case Right(game) => val gameId = addNewGame(game) complete(StartGameResponse(gameId)) case Left(errorMessage) => complete((StatusCodes.NotFound, errorMessage)) } } } } def getGameRoute[G](getGame: Int => Option[G], getPacMan: G => PacMan): Route = path("games" / IntNumber) { gameId => get { val maybeGame = getGame(gameId) maybeGame match { case Some(game) => complete(PacManStateResponse(getPacMan(game))) case _ => complete((StatusCodes.NotFound, s"Pac-Man ($gameId) not found"))
}
}
}
...
}
Connecting the dots
So far, so good. We got rid of GameState and GameEngine dependencies by replacing them with G and function parameters in HttpRoutes. However, our application still needs both of them to be useful. We need to pass the right arguments when creating the HTTP routes. Additionally, the application needs to know how to handle the state and since it is a different concern it will be handled by MultipleGamesAtomicState4.
object App extends HttpApp {
private val atomicState: MultipleGamesAtomicState = ??? // see footnotes
val route: Route =
getGameRoute[GameState](atomicState.getGame, _.pacMan) ~
...
}
And that’s all we need! The above piece of code has responsibility of composing all our other concerns into a usable application.
There is another quick win we’ve got after doing the aforementioned refactorings. We can test our HTTP layer in total isolation! That means we can have unit tests for our endpoints without worrying about state or game logic. For example let’s see the test for getGameRoute function:
trait TestScope {
final case class FakeGame(id: Int, pacMan: PacMan)
def getPacMan(game: FakeGame): PacMan = game.pacMan
}
"allow getting Pac-Man's state in existing game" in new TestScope {
val getGameRoute =
HttpRoutes.getGameRoute(_ => Some(FakeGame(1, PacMan(Position(2, 1), East))),
getPacMan)
Get("/games/1") ~> getGameRoute ~> check {
contentType shouldEqual application/json
val expected =
s"""
|{
| "pacMan": {
| "position": { "x": 2, "y": 1 },
| "direction": "east"
| }
|}
""".stripMargin
responseAs[String] should beJson(expected)
}
}
"not allow getting the Pac-Man state when there are no games" in new TestScope {
val getGameRoute = HttpRoutes.getGameRoute(_ => None, getPacMan)
Get("/games/2") ~> getGameRoute ~> check {
status shouldEqual StatusCodes.NotFound
}
}
Again, this only contains the tests of HTTP layer, focusing purely on JSON input & output. We use a functional version of dependency injection - functions. No mocking library needed! Those tests are also very stable and fast, because they are not running any server under the hood.
Summary
In this post I have shown you how we can separate concerns of a simple web application. We have separated:
• state representation,
• state management,
• game logic handling,
• HTTP handling.
We achieved that using two basic tools: functions as parameters and type parameters. After making the refactorings the modules became more constrained which gave us two additional powers:
• easier reasoning about each of the above aspects separately,
• better testability.
The code I have shown in this post is available in pacman-multiplayer-fp repository. I also use this example in my workshops that teach Scala and functional programming to beginners.
What’s next?
Functional programming is about composition and separation of concerns. We can use pure functions to solve many issues in our architecture. But what if logic gets more advanced? What if the state is fetched asynchronously or HTTP responses are more complex? We need more advanced tools, which will be introduced in one of the next posts.
1. “Complexity is the single major difficulty in the successful development of large-scale software systems.” “Out of the Tarpit” - Ben Moseley, Peter Marks
2. “Intelligent thinking is that one is willing to study in depth an aspect of one’s subject matter in isolation for the sake of its own consistency” “On the role of scientific thought” - Edsger Dijkstra
3. “Constraints Liberate, Liberties Constrain” - Runar Bjarnason
4. The state is handled by Monix Atomic. I will cover this in one of the next posts. | 2019-01-20 11:28:25 | {"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": 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": 0.2045283019542694, "perplexity": 6716.761343831157}, "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-2019-04/segments/1547583705737.21/warc/CC-MAIN-20190120102853-20190120124853-00414.warc.gz"} |
https://pypi.org/project/dirsync/ | ## Project description
based on Python robocopier by Anand B Pillai
If you like dirsync and are looking for a way to thank me and/or encourage future development, here is my BTC or BCH donation address: 1EwENyR8RV6tMc1hsLTkPURtn5wJgaBfG9.
## Usage
From the command line:
dirsync <sourcedir> <targetdir> [options]
From python:
from dirsync import sync
sync(sourcedir, targetdir, action, **options)
## Main Options
Chosing one option among the following ones is mandatory
--diff, -d
Only report difference between sourcedir and targetdir
--sync, -s
Synchronize content between sourcedir and targetdir
--update, -u
Update existing content between sourcedir and targetdir
If you use one of the above options (e.g. sync) most of the time, you may consider defining the action option in a Configuration file parsed by dirsync.
--verbose, -v
Provide verbose output
--purge, -p
Purge files when synchronizing (does not purge by default)
--force, -f
Force copying of files, by trying to change file permissions
--twoway, -2
Update files in source directory from target directory (only updates target from source by default)
--create, -c
Create target directory if it does not exist (By default, target directory should exist.)
--ctime
Also takes into account the source file's creation time (Windows) or the source file's last metadata change (Unix)
--content
Takes into account ONLY content of files. Synchronize ONLY different files. At two-way synchronization source files content have priority if destination and source are existed
--ignore, -x patterns
Regex patterns to ignore
--only, -o patterns
Regex patterns to include (exclude every other)
--exclude, -e patterns
Regex patterns to exclude
--include, -i patterns
Regex patterns to include (with precedence over excludes)
## Configuration file
If you want to use predefined options all the time, or if you need specific options when ‘dirsyncing’ a specific source directory, dirsync looks for two configuration files, by order or priority (the last takes precedence):
~/.dirsync
source/directory/.dirsync
The command line options always override the values defined in the configuration files.
The configuration files must have a defaults section, and the options are as defined above. The only exception is for the option action, which can take 3 values diff, sync or update.
Example config file:
[defaults]
action = sync
create = True
## Custom logger
From python, you may not want to have the output sent to stdout. To do so, you can simply pass your custom logger via the logger keyword argument of the sync function:
sync(sourcedir, targetdir, action, logger=my_logger, **options)
## Project details
Uploaded source | 2022-09-28 14:01:44 | {"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": 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": 0.25062263011932373, "perplexity": 14982.576158259053}, "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-2022-40/segments/1664030335254.72/warc/CC-MAIN-20220928113848-20220928143848-00580.warc.gz"} |
https://scholars.ttu.edu/en/publications/combinations-of-single-top-quark-production-cross-section-measure-2 | Combinations of single-top-quark production cross-section measurements and $|f_{\rm LV}V_{tb}|$ determinations at $\sqrt{s}=7$ and 8 TeV with the ATLAS and CMS experimentsCombinations of single-top-quark production cross-section measurements and |f$_{LV}$V$_{tb}$| determinations at $\sqrt{s}$ = 7 and 8 TeV with the ATLAS and CMS experiments
Research output: Contribution to journalArticlepeer-review
Original language English 088 JHEP Published - 2019
Fingerprint
Dive into the research topics of 'Combinations of single-top-quark production cross-section measurements and $|f_{\rm LV}V_{tb}|$ determinations at $\sqrt{s}=7$ and 8 TeV with the ATLAS and CMS experimentsCombinations of single-top-quark production cross-section measurements and |f$_{LV}$V$_{tb}$| determinations at $\sqrt{s}$ = 7 and 8 TeV with the ATLAS and CMS experiments'. Together they form a unique fingerprint. | 2022-10-06 10:45:24 | {"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": 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": 0.20212574303150177, "perplexity": 3096.6489182137943}, "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-2022-40/segments/1664030337803.86/warc/CC-MAIN-20221006092601-20221006122601-00604.warc.gz"} |
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I have an $N$-dimensional vector of data, say $X_{t}$, with $1 \leq t \leq T$. Of this vector $X_{t}$, I want to consider vectors, say $X_{t}^{b}$, which are $m$-dimensional combinations of elements ...
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### Library for Discontinuous Galerkin method: FEniCS vs deal.ii
I am aware that both FEniCS and deal.ii are capable of solving problems with Discontinuous Galerkin (DG) method. I would like to specifically know if any of these two softwares can cater these ...
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### how to estimate the number of people on a street within an hour?
I tried to use opencv to analyze a video filmed on the street. But the problem is the performance is not enough. I think the number of people must follow the poisson distribution. So I want to ...
42 views
### Find shift in high resolution noisy signal if only local argmax data are available
Let's say I have a signal which consists several pulses of approximately equal height, and I have to correlate it with the expected positions of the peaks to find the shift of this signal w.r.t. a ...
70 views
### Algebraic multigrid for coupled equations
As far as I understand is algebraic multigrid(AMG) a method that was intentionally developed to solve linear systems where every grid point or node has a single DOF. When AMG should now be used for ...
I need to compute repeatedly a function that depends on an integral. The integral is not solvable analytically, but it depends on the argument of the function parametrically, like this: f(x) = \... | 2019-09-18 15:53:35 | {"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": 0.9025594592094421, "perplexity": 1427.314115665784}, "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-2019-39/segments/1568514573309.22/warc/CC-MAIN-20190918151927-20190918173927-00534.warc.gz"} |
https://math.stackexchange.com/questions/1731369/representation-of-e | # Representation of e
I was on this wikipedia page https://en.wikipedia.org/wiki/List_of_representations_of_e which has a list of representations of the constant e. I came across this one representation that looked interesting and stood out from all of the other ones because it had the cosine function while most others used a factorial:
$e = \left [ -\frac{12}{\pi^2} \sum_{k=1}^\infty \frac{1}{k^2} \ \cos \left ( \frac{9}{k\pi+\sqrt{k^2\pi^2-9}} \right ) \right ]^{-1/3}$
Does anyone know where this formula comes from (ie. who derived it and how they derived it)? Also I understand that e and pi are related through ruler's formula and in complex analysis in general, but this equation seems to not involve complex analysis at all, so why would e, pi, and cosine be related here? | 2019-10-20 03:31:04 | {"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": 0.900626540184021, "perplexity": 411.4916159436556}, "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-2019-43/segments/1570986702077.71/warc/CC-MAIN-20191020024805-20191020052305-00345.warc.gz"} |
https://www.physicsforums.com/threads/area-of-triangle-by-integrals-is-this-right.221100/ | # Area of triangle by integrals (is this right?)
[SOLVED] area of triangle by integrals (is this right?)
## Homework Statement
Use integrals to find the area of a triangle with vertices (0,5),(-2,-2),(2,2).
## The Attempt at a Solution
I think I've got it. I'm just looking for some confirmation of my method before I move on.
Thanks for your time. Cheers.
http://www.mcp-server.com/~lush/shillmud/quest3.jpg
P.S. How do I add a [Solved] to the title?
Last edited:
## Answers and Replies
Dick
Homework Helper
How are you getting e.g. integral of 5x/2+5 to be 5x^2/4+5x^2/2??
Ooops. Thanks for pointing that out Dick. I found the dx of 5x instead of the dx of 5 which interestingly seems not to have affected my answer. I guess you can see why I'm using the forum. Everything should be in order now. Cheers.
Dick
Homework Helper
Ooops. Thanks for pointing that out Dick. I found the dx of 5x instead of the dx of 5 which interestingly seems not to have affected my answer. I guess you can see why I'm using the forum. Everything should be in order now. Cheers.
If you are still getting 20 for the area, I can't agree with that. Double check again.
Okay, I went through again and got A=10. When putting in values for x to solve I sub the rightmost value from the top of integral sign and then subtract from that the same antiderivative with the leftmost x value (top of the integral sign). This is correct? Thanks!
Dick
Homework Helper
Yes, A=10 works.
Thanks Dick. Heron's method confirms it. Now how do I mark this one [SOLVED] ?
Dick | 2021-12-06 00:10:35 | {"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": 0.8651793003082275, "perplexity": 952.4566422676958}, "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-2021-49/segments/1637964363226.68/warc/CC-MAIN-20211205221915-20211206011915-00628.warc.gz"} |
http://concepts-of-physics.com/resources/thermodynamics/bulk-modulus-of-gases.php | IIT JEE Physics (1978-2016: 39 Years) Topic-wise Complete Solutions
# Bulk Modulus of Gases
## Problems from IIT JEE
Problem (IIT JEE 1998): A given quantity of an ideal gas is at pressure $p$ and absolute temperature $T$. The isothermal bulk modulus of the gas is,
1. $\frac{2}{3}p$
2. $p$
3. $\frac{3}{2}p$
4. $2p$
Solution: Isothermal bulk modulus is ratio of volumetric stress to volumetric strain at constant temperature i.e., \begin{align} B=-\frac{\mathrm{d}p}{\mathrm{d}V/V}=\left. -V\frac{\mathrm{d}p}{\mathrm{d}V}\right|_{T}. \end{align} Differentiate the ideal gas equation, $pV=nRT$, at constant $T$ to get, \begin{align} \left.\frac{\mathrm{d}p}{\mathrm{d}V}\right|_{T}=-\frac{p}{V}. \end{align} Substitute ${\mathrm{d}p}/{\mathrm{d}V}$ from second equation into first equation to get $B=p$. | 2018-04-24 16:20:03 | {"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": 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": 2, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9896435737609863, "perplexity": 2202.837015356421}, "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-2018-17/segments/1524125946807.67/warc/CC-MAIN-20180424154911-20180424174911-00248.warc.gz"} |
http://openstudy.com/updates/5098f20be4b085b3a90d8244 | ## microscopic 2 years ago imaginary number
• This Question is Open
1. Yahoo!
$\sqrt{-1}$
2. Yahoo!
There are also Known as Complex numbers
3. 3psilon
$i$ which is equal to the $\sqrt{-1}$ | 2015-07-05 15:15:35 | {"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": 0.7176414728164673, "perplexity": 5813.2613619160975}, "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-2015-27/segments/1435375097512.42/warc/CC-MAIN-20150627031817-00068-ip-10-179-60-89.ec2.internal.warc.gz"} |
http://crypto.stackexchange.com/tags/terminology/new | # Tag Info
$\mathbf{Z}_2^b$ is the direct product of $b$ copies of $\mathbf{Z}_2$ ($\mathbf{Z}_2 \times\cdots \times \mathbf{Z}_2$, $b$ times). That is, its elements are $b$-tuples of elements of $\mathbf{Z}_2$, with both addition and multiplication defined componentwise. If $b > 1$, it is not a field. In fact it is not even an integral domain, because \$(0,1)\times ... | 2016-05-31 16:10:32 | {"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": 0.9830713868141174, "perplexity": 116.4078973161604}, "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-2016-22/segments/1464051417337.23/warc/CC-MAIN-20160524005657-00092-ip-10-185-217-139.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/eulers-polynomial-proof.316937/ | # Euler's polynomial proof
1. May 29, 2009
### khotsofalang
without using a counter example, show a proof that Euler's polynomial equation P(n)=n^2+n+41 can not be used to generate all the primes.can a general proof be made to show that all primes cannot be generated by a specific polynomial?
2. May 29, 2009
### HallsofIvy
Staff Emeritus
Well, what, exactly, is "Euler's polynomial equation"? Don't you think that is important?
3. May 29, 2009
### khotsofalang
thats the proposition made by Euler that P(n)=n^2+n+41 can generate all primes and it was suddenly proven false by using a counter example, isnt there any way he can be proven to be false?
4. May 29, 2009
### ramsey2879
I believe you mean that P(n) would be prime for positive integers n, but there is now a general proof out there that no polynominal equation can generate only primes for all positive integers. I am sure that someone can cive you a link to a proof.
5. May 29, 2009
### ramsey2879
See also http://en.wikipedia.org/wiki/Formula_for_primes Euler's formula for primes as posted in this thread was once widely thought to generate primes for any integer n, but as shown by this link that was false. The proof is simple an noted in the link. Assume that P(x) is a polynominal in x that gives a prime $$p$$ for the value $$n$$.
But then $$p|P(n+kp)$$ for all integer $$k$$ so these numbers must be composite for every k so the polynominal is a constant, p, rather than a polynominal.
P.S. Euler never said that the polynominal generated "all primes", but then that is obviously not what you meant is it?
6. May 29, 2009
### Count Iblis
It is possible with polynomials in more variables, as the same wiki article points out:
7. May 30, 2009
### matt grime
That doesn't count - look at the restriction placed on both the input and output variables.
8. May 30, 2009
### ramsey2879
but the same polynominal would generate composites also with large enough variables. Think how easy it would be to exceed the largest prime otherwise
9. May 30, 2009
### protonchain
P(n) = n^2 + n + 41 =>
P(40) = 40^2 + 40 + 41
= 40 * 40 + 40 + 41
= 40 * 41 + 41 = 41 * 41 = composite.
10. May 30, 2009
### CRGreathouse
11. May 31, 2009
### robert Ihnot
12. May 31, 2009
### Count Iblis
The positive values of the Jones polynomial for positive values of the variables are always primes and all primes can be obtained this way. The problem is just that the probability that a random choice of the input vaiables will yield a positive value is astronomically small. If finally, after billions of years of trying, some positive value is obtained, it will likely be a prime number like 23.
13. May 31, 2009
### CRGreathouse
Was that in response to my post? I was incredulous about the claim that "once widely thought to generate primes for any integer n". It's obvious that no nonconstant polynomial can produce primes for all n, so it's hard for me to believe that this was ever believed. But it could be true, so I was looking for ramsey2879 or someone else to comment on that.
14. May 31, 2009
### ramsey2879
I am 60 and some years old so I some times don't remember exactly what I read too well. The book is up in the attic. Some time I will look again at what was said about the polynominal. But that the polynominal does give composite values is of course easily shown.
15. May 31, 2009
### CRGreathouse
If you do, I'd appreciate the effort if you post it. | 2016-10-22 19:45:21 | {"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": 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": 0.6817002296447754, "perplexity": 802.1825698804422}, "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-20161020183839-00305-ip-10-171-6-4.ec2.internal.warc.gz"} |
https://3dprinting.stackexchange.com/questions/14353/configure-marlin-for-tool-changing-system | # Configure Marlin for tool changing system
I am planning to build a CoreXY machine with a tool changing system. I am using Marlin firmware and BigTreeTech SKR PRO as the controller board. There are 3 options in Marlin for tool changing systems:
I want to use the switching tool head in my project using a servo/stepper motor. So I have 2 questions:
1. Should I use a servo or stepper motor? Which one does the board and firmware support?
2. Where should I connect the servo/stepper on the SKR PRO and what should the value of SWITCHING_TOOLHEAD_SERVO_NR be?
Note: I am also using a BLTouch leveling sensor So I can't connect the servo to the BLTouch servo port.
Edit: After so much research, finally, I found the way to do this. For the first question, Servo is the best choice. First, we need to configure tool change x and y position and servo rotation angle in configuration.h file and leave SWITCHING_TOOLHEAD_SERVO_NR as it is. Also, uncomment #define NUM_SERVOS and set it to 2.Then we need to open Marlin\src\pins\stm32f4\pins_BTT_SKR_PRO_common.h file and in the Servos section, add the following line:
#define SERVO1_PIN PC9
In the end, connect the servo signal pin to the PC9 pin on extension 1 and the VCC and GND pin to the pins next to the PC9 pin that are GND and 5V.
Note: I haven't tested this because I don't have this board. If this way doesn't work, please tell me in comments.
• To my knowledge a single PWM pin in exposed on extension port 1, but recalling Arduino tinkering you can use any digital or analog pin for a servo. For a stepper you require more pins to control the movement, how many tools are you focussing on? Each tool requires a feeder stepper... E3D uses Duet boards, they have many options for additional steppers (either through extension boards). – 0scar Sep 1 '20 at 7:53
• @0scar SKR PRO has 3 extruder outputs and because I use 2 of them, 1 of them (e2) will be unused. Also, my preference is to use a servo motor. But I don't know how to connect it to the board and configure marlin for it (pins.h, configuration.h,configuration_adv.h) – Mahan Lameie Sep 1 '20 at 8:40
1. Use a servo. This way you can use the digital pins to control it; or in your specific case PWM_PC9
• Thanks for your answer. Can you please tell me what SWITCHING_TOOLHEAD_SERVO_NR is and how can I use it, if you know? – Mahan Lameie Sep 1 '20 at 7:46
• First, we need to configure tool change x and y position and servo rotation angle in configuration.h file and leave SWITCHING_TOOLHEAD_SERVO_NR as it is. Also, uncomment #define NUM_SERVOS and set it to 2.Then we need to open Marlin\src\pins\stm32f4\pins_BTT_SKR_PRO_common.h file and in the Servos section, add the following line: #define SERVO1_PIN PC9 In the end, connect the servo signal pin to the PC9 pin on extension 1 and the VCC and GND pin to the pins next to the PC9 pin that are GND and 5V. – Mahan Lameie Sep 2 '20 at 16:36 | 2021-04-22 22:36:00 | {"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": 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": 0.1968158781528473, "perplexity": 3436.9750133419802}, "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/1618039563095.86/warc/CC-MAIN-20210422221531-20210423011531-00389.warc.gz"} |
https://www.envoyproxy.io/docs/envoy/v1.17.3/api-v3/extensions/rate_limit_descriptors/expr/v3/expr.proto | Rate limit descriptor expression¶
This extension may be referenced by the qualified name envoy.rate_limit_descriptors.expr
Note
This extension has an unknown security posture and should only be used in deployments where both the downstream and upstream are trusted.
extensions.rate_limit_descriptors.expr.v3.Descriptor¶
[extensions.rate_limit_descriptors.expr.v3.Descriptor proto]
The following descriptor entry is appended with a value computed from a symbolic Common Expression Language expression. See attributes for the set of available attributes.
("<descriptor_key>", "<expression_value>")
{
"descriptor_key": "...",
"skip_if_error": "...",
"text": "...",
"parsed": "{...}"
}
descriptor_key
(string, REQUIRED) The key to use in the descriptor entry.
skip_if_error
(bool) If set to true, Envoy skips the descriptor if the expression evaluates to an error. By default, the rate limit is not applied when an expression produces an error.
text
(string) Expression in a text form, e.g. “connection.requested_server_name”.
Only one of text, parsed may be set.
parsed
(.google.api.expr.v1alpha1.Expr) Parsed expression in AST form.
Only one of text, parsed may be set. | 2023-02-01 02:47:36 | {"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": 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": 0.4953601658344269, "perplexity": 5008.762003982794}, "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-2023-06/segments/1674764499899.9/warc/CC-MAIN-20230201013650-20230201043650-00181.warc.gz"} |
https://explore.rero.ch/en_US/rero/result?sc=default_scope&qs%5B0%5D%5Bfd%5D=creator&qs%5B0%5D%5Bpr%5D=exact&qs%5B0%5D%5Bse%5D=Arnaldi%20Roberta&qs%5B0%5D%5Bop%5D=AND&lg=&mt=&lb=&sd=&ed=&ex=0&so=rank&fct%5Bi%5D%5Btopic%5D%5B0%5D=High%2520Energy%2520Physics | • 2nd communication: from RERO Explore to swisscovery: Part of RERO's libraries joined the SLSP (Swiss Library Service Platform) network at the beginning of December 2020. See the implications (2nd communication in French / in German) of this change for you as a user.
This query concerns only resources held in libraries.
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• Several versions
### Measurement of j/ production in pp collisions at = 2.76 and 7 tev with alice
Arnaldi, Roberta
Journal of Physics G: Nuclear and Particle Physics, 2011, Vol.38(12), p.124106 (4pp) [Peer Reviewed Journal]
• Several versions
### Experimental overview on quarkonium production
Arnaldi, Roberta
arXiv.org, Apr 11, 2016 [Peer Reviewed Journal]
• Article
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### The onset of the anomalous J/psi suppression in Pb-Pb collisions at the CERN SPS
Arnaldi, Roberta
Cornell University
Available
Title: The onset of the anomalous J/psi suppression in Pb-Pb collisions at the CERN SPS
Author: Arnaldi, Roberta
Subject: High Energy Physics - Experiment
Description: The J/psi suppression observed by the NA50 experiment is one of the most striking signatures for quark gluon plasma formation in Pb-Pb collisions at 158 AGeV. The J/psi production has been studied as a function of the centrality of the collision estimated via the forward energy EZDC released in a zero degree calorimeter (ZDC). The study of the correlation between the number of participant nucleons in the collisions, Npart, and EZDC allows to check whether the J/psi suppression pattern vs. EZDC is compatible with a sudden J/psi suppression mechanism expressed as a function of Npart. Comment: 4 pages, 3 figures, Proceedings of the "XXXVIth Rencontres de Moriond", Les Arcs, 4 pages, 3 figures, Proceedings of the "XXXVIth Rencontres de Moriond", Les Arcs, March 17-24 March 2001
Identifier: hep-ex/0106079 (ARXIV ID)
• Several versions | 2021-02-26 07:33:36 | {"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": 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": 0.6882856488227844, "perplexity": 9963.657591345627}, "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/1614178356232.19/warc/CC-MAIN-20210226060147-20210226090147-00277.warc.gz"} |
https://www.mysciencework.com/publication/show/novel-underdetermined-source-recovery-algorithm-based-ksparse-component-analysis-9936e81a?search=1 | A Novel Underdetermined Source Recovery Algorithm Based on k-Sparse Component Analysis
Authors
• 1 Tehran University of Medical Sciences (TUMS), Department of Medical Physics and Biomedical Engineering, School of Medicine, Tehran, Iran , Tehran (Iran)
• 2 Ghent University (UGent), WAVES Research Group, Department of Information Technology (INTEC), Ghent, Belgium , Ghent (Belgium)
• 3 TUMS, Research Center for Biomedical Technology and Robotics (RCBTR), Institute of Advanced Medical Technologies (IAMT), Tehran, Iran , Tehran (Iran)
• 4 Shahid Beheshti University of Medical Sciences (SBMU), Department of Medical Physics and Biomedical Engineering, School of Medicine, Tehran, Iran , Tehran (Iran)
• 5 Nottingham Trent University (NTU), School of Science and Technology, Nottingham, UK , Nottingham (United Kingdom)
Type
Published Article
Journal
Circuits, Systems, and Signal Processing
Publisher
Springer US
Publication Date
Aug 03, 2018
Volume
38
Issue
3
Pages
1264–1286
Identifiers
DOI: 10.1007/s00034-018-0910-9
Source
Springer Nature
Keywords
Sparse component analysis (SCA) is a popular method for addressing underdetermined blind source separation in array signal processing applications. We are motivated by problems that arise in the applications where the sources are densely sparse (i.e. the number of active sources is high and very close to the number of sensors). The separation performance of current underdetermined source recovery (USR) solutions, including the relaxation and greedy families, reduces with decreasing the mixing system dimension and increasing the sparsity level (k). In this paper, we present a k-SCA-based algorithm that is suitable for USR in low-dimensional mixing systems. Assuming the sources is at most (m-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(m-1$$\end{document}) sparse where m is the number of mixtures; the proposed method is capable of recovering the sources from the mixtures given the mixing matrix using a subspace detection framework. Simulation results show that the proposed algorithm achieves better separation performance in k-SCA conditions compared to state-of-the-art USR algorithms such as basis pursuit, minimizing norm-L1, smoothed L0, focal underdetermined system solver and orthogonal matching pursuit. | 2021-05-06 03:33:05 | {"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": 0.48983949422836304, "perplexity": 4453.629761633645}, "config": {"markdown_headings": false, "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-2021-21/segments/1620243988725.79/warc/CC-MAIN-20210506023918-20210506053918-00222.warc.gz"} |
http://mathforum.org/mathimages/index.php?title=Harmonic_Warping&diff=5588&oldid=5585 | # Harmonic Warping
(Difference between revisions)
Revision as of 09:29, 24 June 2009 (edit)← Previous diff Revision as of 09:31, 24 June 2009 (edit) (undo)Next diff → Line 24: Line 24: You can see that for both of these equations, as x and y go to infinity, d(x) and d(y) both approach a limit of 1. You can see that for both of these equations, as x and y go to infinity, d(x) and d(y) both approach a limit of 1. {{HideThis|1=Limit|2= {{HideThis|1=Limit|2= - $\lim_{x \rightarrow \infty} 1 - \frac{1}{1+x}$ + $\lim_{x \rightarrow \infty}d(x) = 1 - \frac{1}{1+x}$ - $\lim_{x \rightarrow \infty} 1 - \frac{1}{1+\infty}$ + - $\lim_{x \rightarrow \infty} 1 - \frac{1}{\infty}$ + - $\lim_{x \rightarrow \infty} 1 - 0}$ + - $\lim_{x \rightarrow \infty} 1$ + - }} + + $\lim_{x \rightarrow \infty}d(x) = 1 - \frac{1}{1+\infty}$ + + $\lim_{x \rightarrow \infty}d(x) = 1 - \frac{1}{\infty}$ + + $\lim_{x \rightarrow \infty}d(x) = 1 - 0$ + + $\lim_{x \rightarrow \infty}d(x) = 1$ + }} - [[Image:UnionFlag.gif|300px]] + [[Image:UnionFlag.gif|400px]] - [[Image:UnionFlag_Rectangular.jpg|300px]] + [[Image:UnionFlag_Rectangular.jpg|400px]]
## Revision as of 09:31, 24 June 2009
Harmonic Warping of Blue Wash
This image is a tiling based on harmonic warping operations. These operations take a source image and compress it to show the infinite tiling of the source image within a finite space.
# Basic Description
This image is an infinite tiling. If you look closely at the edges of the image, you can see that the tiles become smaller and smaller and seem to fade into the edges. The border of the image is infinite so that the tiling continues unendingly and the tiles become eternally smaller.
The source image used for this tiling is another image that is mathematically interesting and is also featured on this website. See Blue Wash for more information about how the source image was created.
# A More Mathematical Explanation
Note: understanding of this explanation requires: *Single Variable Calculus
To create this image, a harmonic warping operation was used to map the infinite tiling of the source [...]
To create this image, a harmonic warping operation was used to map the infinite tiling of the source image onto a finite plane. This operation essentially took the entire infinite Euclidean plane and squashed it into a rectangular. This type of operation can be called a distance compressing warp.
Harmonic Warping Equation
The equation used to perform the harmonic warp is show in a graph to the right and is as follows:
$d(x) = 1 - \frac{1}{1+x}$
$d(y) = 1 - \frac{1}{1+y}$
You can see that for both of these equations, as x and y go to infinity, d(x) and d(y) both approach a limit of 1.
$\lim_{x \rightarrow \infty}d(x) = 1 - \frac{1}{1+x}$
$\lim_{x \rightarrow \infty}d(x) = 1 - \frac{1}{1+\infty}$
$\lim_{x \rightarrow \infty}d(x) = 1 - \frac{1}{\infty}$
$\lim_{x \rightarrow \infty}d(x) = 1 - 0$
$\lim_{x \rightarrow \infty}d(x) = 1$
• mapping (x,y) from Euclidean plane unto (d(x),d(y)) in rectangle
## Four Infinite Poles
Big table of rectangular, polar, cardinal 4 poles for both flag!
Saint Andrew's Flag Saint George's Flag Original Flag Rectangular Tiling Polar Tiling Four Infinite Poles Tiling
# About the Creator of this Image
Paul Cockshott is a computer scientist and a reader at the University of Glasgow. The various math images featured on this page were originally produced for his research. | 2015-01-30 10:57:31 | {"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": 7, "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": 0.813801646232605, "perplexity": 1348.5511268011044}, "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-2015-06/segments/1422115869264.47/warc/CC-MAIN-20150124161109-00115-ip-10-180-212-252.ec2.internal.warc.gz"} |