Finding $y=\sqrt{5+\sqrt{5+\sqrt{5+\sqrt{5 + \ldots}}}}$

I can't find the answer to this problem  Find $y$ when $y=\sqrt{5+\sqrt{5+\sqrt{5+\sqrt{5 + \ldots}}}}$  Any help is appreciated. Thank You


What components would produce this polarization/waveplate demo?

An optics demonstration that I saw many years ago involved two identical-looking transparent plastic "slides", about the size of microscope slides. Call them slides A and B. Individually, they were transparent to ordinary ambient light passing through them in either direction. However, when stacked together, the stack was transparent only when viewed from one side, and was opaque when viewed from the opposite side:          |   |   |           | A | B |           |   |   |        -------------> 1           |   |   |            |   |   |     0 <-------------          |   |   |     I recall that this had to do with polarization, and at least one of the slides was a waveplate (quarter?, half?), but I can't figure out exactly what must have been used to produce this effect. Help, please?


Why does this print false. Is it because month is string and true is boolean?  $month = "string"; if ($month === true) {     echo "true"; } else {    echo "false"; }


Find all occurrences and add them together

I have a file like this:  user1, 10 user2, 5 user2, 6 user1, 15 user3, 23 user1, 15   I'd like to have totals by column 1 (user1, user2, user3), and make it look like this:  user1, 40 user2, 11 user3, 23   What would be the best way forward? A while loop on the first column and sum up the 2nd column as long as it's the same?


How to exit from magnified screen that moves with the mouse on Kubuntu?

I have accidentally pressed some key combination that enabled a feature that I cannot turn off and cannot name. The visible desktop area I see on monitor is enlarged and as I move the cursor, the visible area moves with it. I do not see the whole desktop, only a part of it. How can I turn this off, whatever it is? Inside accessibility, the screen reader is turned off, it is something else.


Doubt about backshift (reported speech) for events that are still on going

I have a doubt about using backshift in this following situation:  Peter: "I have a good job now."  Peter said that he had a good job now.............or................Peter said that he has a good job now.  I appreciate that a similar phrase without the addition of 'now' would be changed to had:  "Peter said that he had a good job", but surely the inclusion of 'now' demands that has should remain in the present and not get backshifted.  It just seems to make more sense like this Thanks for any advice or comments


How to make a nice legend for a histogram with pgfplots

I am trying to make a histogram with the fitted curve plotted on it. Here's the mwe:   \documentclass[a4paper]{scrartcl}     \usepackage{tikz}     \usepackage{pgfplots,pgfplotstable}     \usepackage{filecontents}     \pgfplotsset{compat=1.10}     \usepackage[active,tightpage]{preview}     \setlength\PreviewBorder{2pt}     \newcommand{\plots}{0.611201}     \newcommand{\plotm}{2.19882}     \begin{filecontents}{data.dat}     2 0.0629921259843     3 0.0236220472441     4 0.0314960629921     5 0.125984251969     6 0.0629921259843     7 0.102362204724     8 0.110236220472     9 0.0551181102362     10 0.0629921259843     11 0.0314960629921     12 0.0236220472441     13 0.0314960629921     14 0.0629921259843     15 0.0551181102362     16 0.0393700787402     17 0.0472440944882     18 0.00787401574803     19 0.0393700787402     24 0.00787401574803     27 0.00787401574803     33 0.00787401574803     \end{filecontents}     \begin{document}     \begin{preview}      \begin{tikzpicture}     \begin{axis}[     yticklabel style={/pgf/number format/fixed},     scaled y ticks = false,     minor y tick num={1},     xtick pos=left,     legend cell align = left,     legend style={draw=none},     xlabel = {group size},     ylabel = {ratio}     ]     \addplot[blue,ybar,fill, fill opacity=0.3, bar width = 0.8,] table {data.dat};     \addplot[red, line width = 1,domain=1:40,samples=100] {1/(x*sqrt(2*pi)*\plots)*exp(-(ln(x)-\plotm)^2/(2*\plots^2))};     \legend{empirical,lognormal fit}     \end{axis}     \end{tikzpicture}     \end{preview}     \end{document}     As you can see, the legend is not really good. How can I change the legend so it looks more like this?


Hey I am completely lost. Despite me going to several websites and copying their commands directly, my LaTeX document refuses to generate either the citation or bibliography entry. Here is the LaTeX.  \documentclass[12pt]{amsart}  \usepackage{geometry}  \usepackage{qtree}  \usepackage{natbib}  \usepackage{cite}  \geometry{a4paper}  \title{Nominals of Modern Greek (Abstract)}  \author{Dingler, Ian}  \begin{document}  \maketitle  Important to note, is that if their are no other items in the lexical phrase, the D must appear to the left side of N i.e. *\textit{podia ta}, \citet{MG21}.  \bibliographystyle{te}  \bibliography{Syn3 Ref}  \end{document}   Here is my bib entry saved as "Syn3 Ref"  @book{MG21,         auTHor = {Brian D. Joseph and Irene Philippaki-Warburton},         YEAR = {1987},         Title = {Modern Greek},         publisher = {Biddles Ltd, Guilford and Kin'gs Lynn},         address = {Great Britain}      }   Both my .tex and .bib files are saved in the same folder yet all I get when I typeset is a ? where my citation should be and no bibliography entry what so ever.


New to BibTeX and APA syle: What do I do?

I'm completely lost. I use LaTeX, but not competently. I want to do a bibliography and in-text citations in APA style.  I downloaded JabRef and did a test entry. Then I wrote the following code:   \documentclass{article} \usepackage{apacite} \bibliographystyle{apacite}  \begin{document}  \bibliography{testname}  \end{document}   ...where testname is the name of my BibTeX file. My reference does not appear when I do this, though it does say "reference." I'm using TeXstudio, in case anyone is interested.  So, what do I do? Can someone explain to me in super simple terms how to get my entries from JabRef into an APA-style bibliography/in-text citations in TeXstudio?


Is "(the association bonus does not count)" considered official Stack Exchange policy?

ORIGINAL QUESTION (before the "possible duplicate" tag was added): Could someone please look at the last few comments under the main question at  I can find no valid (posted) policy why I am not allowed to answer the question. If there is such an official policy as "the association bonus does not count" please post a link to it in response to this question. REVISED QUESTION (after the "possible duplicate" tag was added): Apparently this question has morphed quite a bit. As I detail in my own answer to this question below (I used an answer to include screengrab images) there is a discrepancy between the two different Stack Exchange sites. There is also a discrepancy between the official policy on reputation and this "does not count" tangent policy that is not mentioned in the official policy. Can someone please tell me why: (1) If "doesn't count" is official policy why is it not in the official policy page on reputation? (2) If this is official Stack Exchange-wide policy then why are there different messages on different sites, some mentioning "doesn't count" and other not? (3) If "doesn't count" is official policy why did it change? Our co-founder Jeff Atwood wrote an official description of the purpose of cross-site association bonus points:  Nowhere in that description do I see an exception for protected questions.


Current consumption calculation and also battery life calculation

I'm a newbie, I need to know how to calculate the current consumption of circuit and also how do  calculation of  the battery life according to the circuit's current consumption? I'm using Li-Po battery ( 400mAH , 3.7 V, 1.48 WH). Thank you for your help in advance.


Why is Wolverine drawn on Avengers side in AvX Program Guide?

In Avengers vs. X-Men Program Guide (free at ), why is the Wolverine depicted fighting in the Avengers side of the brawl instead of X-Men?


I'd like to run a command at startup which pings a certain address every 10 minutes and writes the result to a file. I've figured out now how to do the pinging and file writing and the 10 min intervals:  while true; do my-command-here; sleep 600; done   My question is, can I put this in /etc/init.d/rc.local or should I be putting it in /etc/rc.local or somewhere else entirely? I'm specifically concerned because it's an infinite loop so I'm not sure if I could put it in one of these startup scripts.  Some help would be appreciated. I'm using Ubuntu 12.04.5


Does .Net contain a built in Line Endings conversion which checking input format

I'm getting a string from an external native library function which uses "\n" for line separation. I simply want to write this to disk using the appropiate line ending format on the system I'm running my .Net application, which will be usually windows. So "Environment.NewLine" results correctly in "\r\n".   I'm simply write the string to a textfile via   MyString = NativeLib.GetStringEitherLForCRLF(); File.WriteAllText(MyFile, MyString); // will not change LF format   This doesn't changes lineendings, which seems to be intented that way. However, I'm wondering while the same string in C using fwrite in asciimode would probably change the lineendings as I remember.   Since conversion would be an easy task I'm just curios, how the "correct" or best-practice way in .Net should be. Is there a standard function, which would automatically convert the lineendings according to the current environment settings ?   EDIT: So 5 mins and already downvoted...  Folks, I KNOW how to replace characters in strings, that is not the basic question. The exact question is:   Does there exist a .Net standard library function that will to line ending conversions already depending on OS and Environment settings or which maybe has to be used with a certain parameter to ensure this?   Like e.g.:  File.WriteAllText(MyFile, MyString, Lineencoding.CRLF); // which does not exist   or  File.WriteAllText(MyFile, MyString.ConvertLineendings(Line.CRLF)); // which also does not   But there maybe an option I've missed but it doesn't look like that. I do not want to write unnecessary boilerplate code to such a trivial task.   The problem is also described in  just to show that I can be more complex than most people think. I'm not completely sure whether the proposed regex solution will work in 100% of all cases.   Edit 2: I changed the title to make my intention more clear because it seems that the previous title motivated more to downvote for what reason ever...


I want to order my steam games by "unearned achievments" aka achievements I haven't gotten yet because I am trying to 100% every game I have.  Does anyone know how to do that? If that's not possible can you somehow sort every game in the Categories by hand?


I want to run a bash command at startup (~/.config/autostart/myCommand.desktop) that requires sudo, but rather than it prompting me every time, I would like to include the password in the command, something like:  sudo --some-flag [PASSWORD] [command]  I have seen answers suggesting to change sudoers, etc. but I am wondering if something more like what I said is possible.


In SFMC, I need to show a specific block at the 1st order and after that it needs to be displayed at every 4th order. Meaning 4+1 (5,9,13 and so on). My current ampscript looks like this, but I am very much in doubt on how to make the counts match. %%[  VAR @customerid, @orderrows, @rowCount, @modulo  SET @customerid = _subscriberkey /* value from attribute or DE column in send context */ SET @orderrows = LookupRows("Orders","subscriberkey", @customerid) SET @rowCount = rowcount(@orderrows)  SET @modulo  = mod(@rowCount, 4) IF rowcount(@orderrows) == 1 OR (@rowCount > 0 AND @modulo == 0) THEN     SET @purchase = ContentBlockByID("1")     ]%%      %%=v(@purchase)=%%      %%[ ENDIF ]%%  Thank you :)


Every time I try to animate my rig, the amount I can move the arrow transformation is fixed so I can't make any small adjustments.     How can I fix this?


"GPT detected. Please create a BIOS-Boot partition" while using boot-repair

Since I updated Windows to 8.1 my Grub menu disappeared. I ran Ubuntu using Live USB, I used Boot-Repair but something went wrong. If I click on Reccomended repair I get this error:     GPT detected. Please create a BIOS-Boot partition (>1MB, unformatted filesystem, bios_grub flag). This can be performed via tools such as Gparted. Then try again. Alternatively, you can retry after activating the [Separate /boot/efi partition:] option.   So I tried to set my sda9 (I think that it's the Ubuntu system partition, since it's ext4) with the bios_grub flag and then to run Boot-Repair again. It didn't work.  I don't know what to do. My Grub was working fine (using UEFI) before I updated Windows.  I removed the bios_grub flag. Then I used fsck and it didn't find any error. So I tried again with Boot-Repair but it always gives me the "GPT detected" error. My boot is on UEFI mode, Secure Boot is "off".  When I boot my PC with SecureBoot OFF, I can reach the GRUB menu. But it's empty (the only voice is "System Setup").  I mounted my Ubuntu system disk:  sudo mount /dev/sda9 /mnt   and the other things:  sudo mount --bind /dev /mnt/dev sudo mount --bind /proc /mnt/proc sudo mount --bind /sys /mnt/sys   I logged on the system with chroot:  sudo chroot /mnt   I re-installed grub:  grub-install /dev/sda update-grub2   But it still doesn't work.


How much time does it take to go from Frankfurt airport to the the city centre?

I have a transfer in Frankfurt. I will have five hours between flights. Will that be enough to visit the city center? And what should I use to get to the city center?


How to Get An Android Emulator On Ubuntu 16.04

Can someone please help me i want to get an emulator so I can play clash of clans but I don't know how, please help?


Questions with no close votes appearing in the close vote queue?

I've just been offered the wonderful opportunity to review .        ... but on closer inspection ?        Is this  (e.g I'm assuming this post did previous have a close vote, but has now aged away in ways I don't understand), or should questions with no active close votes be removed from the queue.  p.s. If it's , please expect my  asking for this not to be the case ;).


Deleted MySQL “root” user in phpMyAdmin through XAMPP local host…how to restore?

I was working in phpMyAdmin (XAMPP localhost) to add a user for a new database I created for a local WordPress website, and came upon the list of users named "root". Since I did not remember ever creating these root users, I tried to delete them. I don't know what I clicked. I don't remember hitting any delete button, but this resulted in deletion of root. After that, all my databases were gone along with all users. Now only "Database operations information_schema" is there in phpMyAdmin panel.  Now when I click on the "Databases" tab in phpMyAdmin, it simply returns a red warning "No privileges to create databases". There's no user tab. I can still see my databases in MySQL folder in XAMPP folder, and all WordPress websites work fine. But I am unable to create a new database/user nor am I seeing my existing databases. I searched google, and found a similar query here with a solution.  However, I tried most of the steps in the solution, but nothing came up. Could anyone please help me with a solution to add root user as well as databases back in phpMyAdmin using XAMPP localhost? I'm a novice, so need step-by-step instructions please. Your help will be greatly appreciated. Thank you!


Why doesn't my StackExchange flair show any of my associated accounts?

My StackExchange flair shows only my Area 51 rep  Even though I have multiple associated accounts with more than 200 rep:


Proof Check: Every Cauchy Sequence is Bounded

Sorry if I keep asking for proof checks. I'll try to keep it to a minimum after this. I know this has a well-known proof. I understand that proof as well but I thought I'd do a proof that made sense to me and seemed, in some ways, simpler. Trouble is I'm not sure if it's totally correct. It's quite short though. I was just hoping someone could look it over and see if it is a valid proof. Thank you!  Lemma: Every Cauchy sequence is bounded.  Proof: Let $(a_{n})$ be Cauchy. We choose $ 0<\epsilon_{0}$. So $ \forall \; n>m\geq N_{0}$ we have that $\vert a_{n}-a_{m} \vert < \epsilon_{0}$. Therefore $(a_{n})$ is bounded for all $ m \geq N_{0} $ by $ \epsilon_{0} $. Since $ \mathbb{N}_{N_{0}}$ is finite, it is bounded. So, for all $ m<N_{0} $, $ (a_{n})$ is bounded. Therefore $(a_{n})$ is bounded.  I realize I haven't said what the bounds are but I think that's sort of irrelevant. So long as we know it's bounded. Any help is much appreciated!


Why are the number of upvotes and downvotes not shown separately?

In all Stack Exchange sites we have an option for upvoting and downvoting. Now, I see that for a question one upvote is worth +5 reputation while a downvote is worth -2.  Now, there is a difference in value but, when a question with 1 upvote is downvoted it becomes 0. So,this value for upvote and downvote is same but the reputation value is not same.  Is it ok? Why don't we have a separate tabs beside the question that shows this number of upvotes and this number of downvotes?


As you can see at the bottom of the anvil are a little bit more shape down there, I am sorry I forget what you call them, but if some one could help me and get rid of them, that would be nice.


Is a system Liouville integrable if and only if its Hamilton-Jacobi equation is separable?

I am asked to show that, a system is completely integrable Liouville if and only if its  is completely separable. I get the idea and understand that is very related to the Action-Angle coordinates and one of Liouville's theorems. Two texts have been of help: Jose & Saletan and Arnol'd.   I see how separability leads to AA coordinates and thus to an integrable solution of the system, but why is it an "if and only if" relationship? Why can't there exist systems with non-separable HJ, but reducible to integrals?


Is there any way to open an OST file for extraction of info?

So I've got a weird one...   Whole network kind of went down. Server crashed and the backups don't seem to have worked. A workstation crashed. We have the OST file from the workstation thankfully, but have no idea how to extract data. We honestly just need to get to the contacts. Emails, calendars, etc. are not even desired. Just the contacts.  I hope someone can point us in the right direction of a free solution.


Legend symbol not being displayed correctly in pgfplots

I'm trying to create a horizontal bar plot with log axis. Adapting several examples I could get what I needed. However, the legend symbols are not being displayed the way I want.  Here's what I got so far:    But I want the legend to look like this:    I tried adding the \addlegendimage but it didn't work at all. In the code below, if I uncomment the commented lines, only the 'FEA' entry will get the correct symbol. Any ideas on what I'm doing wrong?  MWE:  \documentclass{article} \usepackage{pgfplots}  \begin{document}  \begin{tikzpicture} \begin{axis}[        xlabel=Time (sec),     legend style={     at={(0.95,-0.2)},     /tikz/every even column/.append style={column sep=0.2cm}},     legend columns=3,         xbar,     xmin=1,     xmode = log,     enlarge y limits=0.2,     height=8cm,     ytick=data, yticklabel style={text width=3cm,align=right},     bar width=10pt,     symbolic y coords={alg 1, alg 2, alg 3, alg 4}, ]  \addplot [fill=black!15!white] coordinates { (2.24e+000,alg 4) (1.91e+000,alg 3) (1.98e+000,alg 2)  (2.23e+000,alg 1)  }; %\addlegendimage{fill=black!15!white,area legend} \addlegendentry{Initialization}  \addplot [fill=black!45!white]  coordinates { (2.69e+003,alg 4) (1.08e+003,alg 3) (1.92e+003,alg 2)  (1.02e+003,alg 1) }; %\addlegendimage{fill=black!45!white,area legend} \addlegendentry{FEA}  \addplot [fill=black!70!white]  coordinates { (5.16e+000,alg 4) (5.18e+000,alg 3) (5.17e+000,alg 2) (5.81e+000,alg 1)  }; %\addlegendimage{fill=black!70!white,area legend} \addlegendentry{Optimization}  \end{axis} \end{tikzpicture}  \end{document}   Thanks!


Why it is so difficult to install Linux with English system language AND set non-English standard locales?

Every-time I have to install a new Debian Linux system I encounter the same troubles with locales -- I do precisely want English system language with standards set to the country where I live, i.e. Germany.  The debian installer, and probably others, is asking at installation time for your "preferred" language. And every time I choose English. But then, I cannot add the standard locales of my country, because only English speaking countries are shown for the previously chosen language.  It's clear. After installation with enough manual fiddling it's achievable. And there is also a workaround (at least for European-ish users)  by using en_IE.UTF-8 or en_DK.UTF-8 . However, this doesn't answer the question: Why it is so difficult to combine the preferred English system language with specific locales? I want to understand the reason/s and if there are any risks.  (Why do I want this? Because I can't see any advantage in (partially) traduced messages and software. Even more, it is much harder to find help when researching with English-foreign errors and messages got for the encountered issues.)  My actual configuration, AFAIK it works fine:  $ locale LANG=en_US.UTF-8 LANGUAGE= LC_CTYPE="en_US.UTF-8" LC_NUMERIC="en_US.UTF-8" LC_TIME="en_US.UTF-8" LC_COLLATE="en_US.UTF-8" LC_MONETARY=de_DE.UTF-8 LC_MESSAGES="en_US.UTF-8" LC_PAPER=de_DE.UTF-8 LC_NAME=de_DE.UTF-8 LC_ADDRESS=de_DE.UTF-8 LC_TELEPHONE=de_DE.UTF-8 LC_MEASUREMENT=de_DE.UTF-8 LC_IDENTIFICATION=de_DE.UTF-8 LC_ALL=


What if I offer a bounty and don't get any good answers?

I have started a bounty:   It expires in 3 days. I don't have an appropriate answer to accept, and the only answer which it has gotten has no votes.  So am I going to simply lose 100 reputation without getting a satisfactory answer?  Or should I accept the lone inappropriate answer so that I will not lose my right to accept answers to any questions which I might ask in the future, which is what the bounty rules claim?


Votes with 3 numbers or more are on different lines on Android app

In the Android app, votes with 3 numbers (or more, maybe) are showed on different lines.     We need to make the font smaller, or the sidebar containing the votes bigger, or some clever developer thing.  Might be worth mentioning this is on a tablet.


A package to help with layout generation? Graph paper in the background?

Once in a while I have to create a layout given by several parameters, such as "left margin 3cm, logo 4 cm from the right margin, 2cm high" etc. Now I use geometry package an other helpers to create a layout, but I need to print out the result in order to check if everything is correct (well, I use Acrobat for that, but not everyone has access to it).  What I am thinking: is there a package to put graph paper with a 1cm grid (and millimeter ticks) in the background, so I could easily check if my layout is correct?


In java i used TimeUtil package.  package org.core.java;  import java.util.concurrent.TimeUnit;  public class TimeUtil {      public static void main(String[] args) {         long millis = 20000000L;          String tt = String.format("%d days,%d hrs,%d min, %d sec",                 TimeUnit.MILLISECONDS.toDays(millis),                 TimeUnit.MILLISECONDS.toHours(millis),                 TimeUnit.MILLISECONDS.toMinutes(millis),                 TimeUnit.MILLISECONDS.toSeconds(millis) -                  TimeUnit.MINUTES.toSeconds(TimeUnit.MILLISECONDS.toMinutes(millis))             );         System.out.println(tt);         String metrics[] = tt.split(",");         String finalString = "";         for(String  metric : metrics) {             metric = metric.trim();             Integer indexChar = Integer.valueOf(metric.substring(0,1));             if(indexChar > 0) {                 finalString += metric+" ";             }         }         System.out.println(String.valueOf(finalString));     }  }   This returns 5 hrs 333 min 20 sec.  In this 333 should not come up.If min exceeded 60 then it will add +1 hrs.But in this its showing 5 hrs 333 min 20 sec.  Expected result approx 10 hrs : ... Please correct me .Am i wrong with the above code.  Thanks


Every matrix $A\in M_2(\mathbb{C})$ is similar to one of two forms

I'm in trouble at the following exercise:     (Ex. 6, page 143 - Um Curso de Álgebra Linear; Coelho, Flávio Ulhoa)   Show that if $A\in M_2(\mathbb{C})$, then $A$ is similar (or conjugated) to a matrix of one of the following forms   $$\left(\begin{array}{cc}a&0\\0&b\end{array}\right) \text{ or } \left(\begin{array}{cc}a&0\\1&a\end{array}\right), \text{ with } a,b\in\mathbb{C}.$$   What I've tried: Be $A\in M_2(\mathbb{C})$. Consider $T:\mathbb{C}^2\to\mathbb{C}^2$ the linear operator whose matrix at the standard basis $\mathscr{C}=\{(1,0),(0,1)\}$ of $\mathbb{C}^2$ is $A$, i.e., $[T]_\mathscr{C}=A$. Since $\mathbb{C}$ is algebraically closed and we know that the characteristic polynomial of $T$ is monic and has degree 2, we have that it is of the form $p_T(x)=(x-a)(x-b)$, for some $a,b\in \mathbb{C}$. Of course $a$ and $b$ are eigenvalues of $T$.    Case 1: $a\neq b$; Considering the dimensions of the eigenspaces of $T$, we conclude that $T$ is diagonalizable and, therefore, exists a basis $\mathscr{B}$ of $\mathbb{C}^2$ such that $$[T]_{\mathscr{B}}=\left(\begin{array}{cc}a&0\\0&b\end{array}\right),$$ and, through basis exchange, $A$ is similar to a matrix of the first kind.  Case 2: $a=b$ and $p_T(x)=(x-a)^2$ In this case, if the geometric multiplicity $m_g(a)=2$ then, again, there is a basis $\mathscr{B}$ of $\mathbb{C}^2$ of eigenvectors of $T$ and  $$[T]_{\mathscr{B}}=\left(\begin{array}{cc}a&0\\0&a\end{array}\right).$$ Now, if $m_g(a)=1$, then the eigenspace $Eig_T(a)$ spanned by the eigenvectors associated to the eigenvalue $a$ has dimension one, say, $Eig_T(a)=[v]$. And then, completing a basis $\mathscr{B}=\{u,v\}$ of $\mathbb{C}^2$, I only know that $$[T]_{\mathscr{B}}=\left(\begin{array}{cc}a_1&0\\a_2&a\end{array}\right).$$ From here, I've tried to find some suitable $u$ such that $T(u)=au+v$ in a way that $a_1=a$ and $a_2=1$, but solving this system seems impossible (in general) to me! Is this right?  Suggestions? Ideias? Thank you once more, guys...


So I messed up really bad and cheated on a homework assignment. I got a negative one for that assignment. I'm in my first year of undergraduate school in the US, second semester. I am so upset with myself for stooping so low to commit academic dishonesty by looking into the solution manual. I'm terrified of what will happen to me. Since this is a relatively minor offense, what do you think will happen? Where do I go from here?


existence of a function that is continuous at every rational and discontinuous at every irrational

Thomae's function  gives the existance of a function continuous at every irrational number and discontinuous at every rational number. Is there existance of a function that is  continuous at every rational and discontinuous at every irrational


Alternate (?) definition of sample variance

The variance of a sample can be defined as $$s^2 = \frac{1}{2}\frac{1}{n(n-1)}\sum_{i}\sum_{j\ne i}\left(x_i - x_j\right)^2$$  Apart from the factor of $1/2$, this can be paraphrased verbally as     The variance is the average of the squared distances between pairs of distinct data points   Mathematically, this is equivalent to the "usual" definition of variance, $s^2 = \frac{1}{n-1}\sum \left(x_i -\bar{x} \right)^2$.  Conceptually, however, it seems (to me) quite different, in two respects:   This definition makes no reference to the mean value $\bar{x}$; we are not measuring how far apart points are from the mean, but rather how far away points are from one another. The factor of $n-1$ in the denominator -- which is well-known to be a source of confusion for students (see, e.g., ) -- appears naturally because there are $n(n-1)$ ordered pairs of distinct data points $(x_i, x_j), i\ne j$.  No need for either hand-waving justifications about "cushioning" the sample variance, or for complicated calculations of estimator bias.   Again, just to be clear, I understand why the standard definition of $s^2$ includes a denominator of $n-1$, and I understand that the double-sum definition above is mathematically equivalent to the standard definition.  What I would like to know:  Are there contexts (pedagogical or otherwise) in which the alternate definition of variance (as a double-sum over pairs of data points) is more commonly referred to?  Are there any textbooks, for example, that take this as the primary definition?


Why is the list of "Hot Network Questions" not consistent?

As I browse around pretty much anywhere in Stack Exchange, I can't help but notice that the list of "Hot Network Questions" doesn't seem to be consistent.  Not only is the order not consistent between different SE pages, the content of the list itself is not always the same. Is it meant to be randomized like this, and if so, why?


Is it possible for moderators to "reset" a question?

This is a follow-up from , where there is a discussion about how to handle highly voted, but closed questions.  There are a number of closed questions on Programmers (and I'm sure on other sites, too) that are really close to being good. However, in their present state, they aren't good - they are too subjective, too localized, or just not useful in their current state. However, they can be cleaned up and made into really good questions.  In the post I linked to, I not only picked out one of these questions from Programmers, but also outlined how I would make it better. It's definitely in the same spirit as the original question, but also far more useful. If I were to simply rewrite the original question, most (if not all) of the already provided answers would be invalid or just not make sense.  Currently, the only option for such a massive "reboot" of a question are for it to be reasked, either by someone else or the original asker. If the original asker fixes it, then it would invalidate answers and be up to the answerers to fix their answers or delete them. If the original asker reasks the question as a new question, they get double reputation, unless the original is deleted. If someone else asks the question in the improved manner, they get reputation for a question that isn't theirs, and the original asker gets rep for their "bad" question.  I think that diamond moderators should have the ability to reboot a question. That is, they edit the question and get edit credit, but all existing answers are removed and reputation gained for answers and the question is reset. The question is returned to the front page, like it was just asked. This could also be expanded to allow 10k+ users to vote for a reboot, proposing new wordings as well as a reopen.  Thoughts, problems?


Why can we multiply different units but not add them?

Like units can be added together or, subtracted from one another. However, multiplication and division of units does not have such boundations. multiplication is just repeated addition, similarly division is repeated subtraction. How in the world we don't have same conditions as that on addition of like units?


Help for installing Ubuntu on Acer Chromebook 13

As it's stated in the title, I need some help on running Ubuntu on my Chromebook 13.  I know that there are multiple tutorials, even for the Chromebook 13, however none of them seem to work properly for me. Either Ubuntu kills my ChromeOS, or it simply won't work at all.


Expected Value of the sum of random variables

If i have two random variables X and Y, then $E[X+Y]=E[X]+E[Y]$ . However, do X and Y have to be independent ?  Do you know where i can find a proof of this principle ?


Serial comma in academic papers in mathematics and computer science

Is there a predominant style in academic papers in computer science concerning the usage or the omission of the serial comma? What do ACM and IEEE do in general? I failed to find it out on my own. Is there any style guide of an academic publisher that suggests (or prescribes) that US-English papers in the two disciplines (mathematics, computer science) omit the serial comma in general?


Why can't we say that moon attracts the earth?

We know that the Gravitational force at which earth attracts moon is also equal to the force in which moon attracts earth as the distance and the G and the masses are same then why can't we say that moon attracts the earth ?


Closed form for $1+\frac{1}{2} + \frac{1}{3} + \dots + \frac{1}{n}$?

Background  When I attempt questions in real analysis, frequently I encounter the following expression like harmonic series:   $$H_n=1+\frac{1}{2} + \frac{1}{3} + \dots + \frac{1}{n}$$  To my surprise when I arrive at something like this ,the solution book does not give me a closed-form of this expression.   Question   So my question is a simple one. What can you think of for this series? And besides the fact that it does not converge is it related to any mathematics that you know? And most importantly, does it have a closed-form?


"What power supply do i need to power 60 1.5v dc motors that draw about 200ma?"

We're trying to rig 6 bundles of 10 motors at a time, so 60 motors in total on the same power supply.  Each one normally is directly powered with 1.5v aa battery. We read the current as 200ma per motor.  PS. I am dyslexic, and have severe learning disabilities. Forgive any grammar and punctuation issues.


How do I print double in Python with exact precision?

I need to print double with precision equal exactly to 6, I found function round:  print(str(round(result, 6))   But in case result itself has less precision, the print function skips zeros at the end.  Gor example, the output of such code,  print(str(round(4.0, 6)))   is  4.0   But what I need is  4.000000   How can I reach this?


Is there a good resource or tool to help build a palette/color scheme around colors I select?

No matter how nice the composition, flow, and lines of my design are, if I am not copying directly from nature, I have a very difficult time picking a decent color scheme.  It either looks too drab, or too garish.  Is there a good resource that will help me to choose a color scheme that has 2 or 3 colors, and the colors do not clash?  I'm not looking for specific colors or color schemes.  What I need is a resource that will help me choose a color (or colors) that go nicely with, or provide a good accent to, whatever main color I am working with on the design.


Prove that for any two sets $|X|$ and $|Y|$, either $|X|\leq|Y|$ or $|Y|\leq|X|$.   I know that there is a proof using Zorn's Lemma but I can't figure out how to do it.


Are these scratches at carbon fiber something to worry?

the seller showed me all the scratches at the bike and told that they happened when he was carrying bike and & changing rear wheel all the time. I did not notice any other scratches at the frame. All of these are around rear wheel hub. Are they something to worry? Paint or just structural scratches?


So, as is clearly visible, I don't have ay splitting lines or such. I tried CTRL+UP and SHIFT+SPACE but that didn't work. Please help, because this project is nearly impossible without multiple views.


Evaluate $\int_{-\infty }^{\infty } \frac{\sin^2x}{x^2} \, dx$

How to evaluate:     $$\int_{-\infty }^{\infty } \frac{\sin^2x}{x^2} \, dx$$   This is a problem in my complex variables course. This integral is intended to be solved by contour, but I’m struggling with it. Thanks for anyone can give me some hints!


If all files on a computer memory disk, in their most basic form, are sequences of binary digits, that including text files, why do some FTP clients have text and binary modes for uploading files onto a server?


Expected value of a random variable with non-negative values

Let $X$ be a random variable with values in $[0,+\infty)$  Show that $E(X)=\int_{0}^\infty P(X \geq t) dt$   Hint: first show that the expected value of a random variable with values in $\mathbb{N}_{0}$  is given by $E(X)=\sum_{k=1}^\infty P(X \geq k)$.  I already proved the Hint, but I don't understand how to use it to prove the first statement. My approach would be the following:    from the definition we know that $E(X)=\int_{0}^\infty X dP$ now write $\int_{0}^\infty X dP=\int_{\mathbb{N}_{0}} X dP + \int_{\mathbb{R}_{\geq0}\setminus\mathbb{N}_{0}} X dP$    but here I get stuck because, even if we somehow success to use the hint to solve the first integral, i have no idea how to approach the second, but maybe my approach is totally wrong. I would be very grateful for any help you can give for solving this problem.


Could an electron be considered antimatter? Since annihilation occurs between the same types of particles and nucleons are baryons consisting of matter quarks, while electrons are leptons, they shouldn't annihilate, right?   Is there other physics that prevents electrons being considered as antimatter, like chirality for example? If yes, what?


Extra alignment tab has been changed to \cr?

I get the error mentioned in the title of the question. Can you help me please ?  \begin{table}[htb!]       \centering         \caption{\textit{others criterias : first scenario}} \label{Table2}         \resizebox{0.5\columnwidth}{!}{%      \begin{tabular}{c|ccc|cccc|c}     &\multicolumn{3}{c}{\underline{Instances}}     &\multicolumn{4}{c}{\underline{DPA}}     &&     &Staff &Activities &periods  &EA     &EB    &TG-AV   &RV-TD   \\ \hline        &3     &72        &10     &477    &47     &178    &1421    \\         \hline          &3     &72        &10     &1087   &34     &207    &1170    \\         \hline          &3     &72        &10     &1415   &22     &215    &932     \\         \hline          &5     &120       &10     &1925   &1977   &485    &1897    \\         \hline          &5     &120       &10     &457    &552    &216    &1123    \\         \hline          &6     &140       &10     &1605   &1981   &347    &3039    \\     \hline     \end{tabular}%     }     \end{table}


rewind_posts() - what actually the use of it, and where using is required or preferred?

The incomplete , says very simply:  rewind_posts(): Rewind the loop posts.  As per , with 's answer, I got: <?php // fetch first post from the loop the_post();  // get post type $post_type = get_post_type();   // rewind the loop posts rewind_posts(); ?>  With Ian Stewart's theme development tutorial, I found rewind_posts()'s use in archive.php, category.php, tag.php, author.php: <?php the_post(); ?> <!-- echo page title --> <?php rewind_posts(); ?> <?php while ( have_posts() ) : the_post(); ?>    <!-- echo content --> <?php endwhile; ?>  But in TwentyThirteen theme we can't see something like this, but a simple WordPress loop with conditional: <?php if ( have_posts() ) : ?> <!-- echo page title --> <?php while ( have_posts() ) : the_post(); ?>    <!-- echo content --> <?php endwhile; ?> <?php endif; ?>  So, I just want to know, while I have the WordPress loop to use, and that works with pagination also, then where do I need to REWIND THE LOOP, and why? EDIT Ok, after the first answer, I got a very good article describing the 3 Query-reset functions in WordPress:  »  by Jeff Starr - DigWP.com  I hope with this the answer can be a lot more educative than currently what we got.


I just received an "Enthusiast" badge on Code Review.   As much as I'd like to keep the badge, I'm certain that I did not visit Code Review every day, for 30 days straight.   Is this a bug?   I don't have the "consecutive days" stat:        But I still got the badge:        And it happened again. Reported .     Update: I just received a third badge in error; this time a fanatic badge for Software Engineering. This is even stranger, since I use that site less than I do CR, and I don't recall getting the 30 days badge.


How can a return flight from A to B cost 1000 euros, while the same flights from B to A cost 500 euros?

Why is a return flight from JFK to Brussels a 1000 euros and a return flight from Brussels to JFK 500 euros?   My girlfriend is American and I'm Belgian so we fly over a lot. Every time she wants to come see me she ends up paying roughly double of what I'm paying. And this is for every single time of the year, why is this?


This a question in context to rolling friction

Why is the velocity at the point of contact (between wheel and surface when the condition is rolling without slipping) with respect to the surface remains zero all the times although the center of wheel moves forward?


Is double/nested variadic template expansion allowed in modern C++?

I've been trying to use C++ metaprogramming to build constructs such as  f(g<0>(args...), g<1>(args...), ... g<n-1>(args...))   given callables f and g, integer n and variadic arguments args...  However I turn the problem, at some point, I need a nested variadic expansion : one for args... and one for 0 ... n-1, and given the compilation errors I'm getting, I'm wondering if/when it's possible in C++11/14/17, and if not, if there is a clever work-around ?  Below, and example of what I'd like to achieve:  struct add {     template<int n, class A, class B> static inline auto     f(const A & a, const B & b) -> decltype(std::get<n>(a)+b)         { return std::get<n>(a) + b; } };  template<class... Args> void do_stuff(const Args & ... args)     { /* do stuff with args */ }  std::tuple<char,short,int,float,double> data = {1,3,5};  map_call<3, add>(do_stuff, data, 1); //< what I'm trying to do // calls do_stuff(add::f<0>(data,2), add::f<1>(data,1),  add::f<2>(data,1) ) // i.e.  do_stuff(2,4,5)   Where one of the (failed try) implementations of map_call is given below:  // what I tried: template<class Mapped, class Indicies> struct map_call_help; template<class Mapped, int... indices> struct map_call_help<Mapped, std::integer_sequence<int, indices...>> {     template<class Callable, class... Args>     static inline void f(Callable && call, Args && ... args)     {         call( Mapped::f<indices>(std::forward<Args>(args)...) ...);         //                       ^^^^^^^^^^^^^^^^^^^^^^^^^^^      1         //    ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ 2         // nested expansion fails with parse error / expected ')'         // inner expansion is: std::forward<Args>(args)...         // outer expansion is: Mapped::f<indices>(_forwarded_args_)...     } }; template<int n, class Mapped, class Callable, class... Args> inline void map_call(Callable && call, Args && ... args) {     map_call_help<Mapped, std::make_integer_sequence<int, n>>::f(           std::forward<Callable>(call), std::forward<Args>(args)... ); }   integer_sequence related stuff needs #include <utility> and C++14, or it can be implemented in C++11 -- see e.g. answers to  if interested.


Harmonic function which is zero on the boundary is zero in the domain

Let $u$ be harmonic ($\Delta u=0$) on the unit circle, if $u\equiv 0$ on $\partial G$ then $u\equiv0$ on $G$   We set $P=-u\frac{\partial u}{\partial y}, Q=u\frac{\partial u}{\partial x}$  Using Green we get $$Q_x-P_y=(\frac{\partial u}{\partial x})^2+u \frac{\partial^2 u}{\partial x^2}+u\frac{\partial^2 u}{\partial y^2}+(\frac{\partial u}{\partial y})^2=(\frac{\partial u}{\partial x})^2+(\frac{\partial u}{\partial y})^2$$  By green  $$\iint_{G}(\frac{\partial u}{\partial x})^2+(\frac{\partial u}{\partial y})^2=\oint_{\partial G}u(-\frac{\partial u}{\partial y}dx+\frac{\partial u}{\partial x}dy)=0$$  how can I an conclude that $u\equiv 0$? must it be on the unit circle?


Lightning component : displaying some text

In a lightning component I display some text dynamically, from the field "Description" of a customized object "Article__c". So when in salesforce I fill the Description field, it appears in my component.  The problem is when, in Salesforce, I put a line break in the Description fiels, in my component I see "
"  Is there any way to fix that ?  In the developper console I saw that
 is not approved, it has to be
 but salsforce automatically create the
 tag...  here is a bit of my code:  <aura:component controller="ActuliteImageController" implements="forceCommunity:availableForAllPageTypes">  <aura:attribute name="art" type="Article__c[]"/>
 <aura:iteration var="a" items="{!v.art}">

{!a.Name} : <aura:unescapedHtml value="{!a.Description__c}"/>

 </aura:iteration>
  </aura:component>


how to remove all files exclude specific files

Under /var/log/hive we have a lot of log files  we want to remove all files exclude the following that should be not removed   hivemetastore.log hiveserver2-report.json.tmp hivemetastore-report.json.tmp


Why do I get "F - -" on my Nikon camera?

When I press the shutter release to focus, a message on the viewfinder displays F--.  Any photos snapped turn out black.   I switched the camera off, took out the battery and memory card and rested it a while, and then it was ok.  But again, after a few days, the error occurs again, and it seems it will keep happening.  What should I do?


What's the AppData/Local/Microsoft/WindowsApps folder for?

Tried to run a python command today and it opened up the page to install Python from the Windows Store for some reason. Somehow a zero-byte "program" called python.exe got installed here and it has precedence over the actual Python installation in the $PATH?  PS C:\> where.exe python C:\Users\me\AppData\Local\Microsoft\WindowsApps\python.exe C:\Users\me\AppData\Local\Programs\Python\Python36\python.exe   Contents of the folder:  Mode                LastWriteTime         Length Name ----                -------------         ------ ---- d-----        11/3/2019   3:02 AM                Microsoft.DesktopAppInstaller_8wekyb3d8bbwe d-----       10/10/2019   8:06 PM                Microsoft.MicrosoftEdge_8wekyb3d8bbwe d-----       10/24/2019   3:59 AM                Microsoft.WindowsTerminal_8wekyb3d8bbwe d-----       10/25/2019   2:36 PM                Microsoft.XboxGamingOverlay_8wekyb3d8bbwe -a---l       10/25/2019   2:36 PM              0 GameBarElevatedFT_Alias.exe -a---l       10/10/2019   8:06 PM              0 MicrosoftEdge.exe -a---l        11/3/2019   3:02 AM              0 python.exe -a---l        11/3/2019   3:02 AM              0 python3.exe -a---l       10/24/2019   3:59 AM              0 wt.exe   I removed it using command prompt, but I'm very curious how it appeared there overnight.


I was browsing around the new  and when I browsed to the  I was greeted with an "edit tag wiki" link. So I edited it and created some text. Very cool.  So I have a few questions.   What is the requirement to be able to edit this tag wiki? I clearly can't do it on all tags, so I'm guessing there is some activity requirement within the tag space before you get the ability to edit the wiki. What should the content be? I browsed around a little, but I couldn't find any other examples with any content. I just included some basic text for the  one. "Questions relating to the Microsoft .NET framework" with a link to http://www.microsoft.com/net/.


What procedure should be followed post spilling fluids onto a MacBook keyboard?

I know the first thing to do is dry with a towel the majority of the fluid. Next is to turn off the computer. Then flip over the laptop itself and whilst upside down cool dry the keyboard with a hairdryer for a few minutes. Also leave the computer upside down for a day or so. Is there anything I’m missing?


How to draw simple arrow between words in Beamer?

Under Beamer, how to draw a sipmle arrow between words in itemize?  I do not need to configure the size, location or any other detail settings. What I need is simply a default arrow.  I tried \rightarrow and \implies but without luck.


Difference between SQL batch, statement and RPC?

What is the difference between SQL batch, T-SQL statement and Remote Procedure Call? How can I tell if part of the T-SQL code is a batch or statement?


put a footnote just in down margin no near of body text

i want put footnote just margin down no near body text  i find this where i can handle the space between body text and down margin  but is hard calculate space for all my footnotes  \footins\setlength{\skip\footins}{2cm}\footnote{cf. F. P. Ramsey. \textit{The foundations of Mathematics}, London Mathematical Society.}   someone known method for do it automatically?


How to stop a script from running if it's not root (and echo "Not running as root! Exiting...")

Here's my source:  #!/bin/bash  echo "Running script to free general cached memory!" echo ""; echo "Script must be run as root!"; echo ""; echo "Clearing swap!"; swapoff -a && swapon -a; echo ""; echo "Clear inodes and page file!"; echo 1 > /proc/sys/vm/drop_caches; echo "";   It clears caches and stuff, and it echoes that it needs to be run as root in the terminal. I basically just want the script to cease running if it detects it's not being executed as root.   Example:  "Running script to free general cached memory!" "Warning: script must be run as root or with elevated privileges!" "Error: script not running as root or with sudo! Exiting..."   If run with elevated privileges, it just runs as normal. Any ideas? Thanks!


If we were able to make a perfect vacuum with no forms of energy in, including all forms of light would time still go on in that vacuum and if it doesn't how would we tell that it doesn't? Then if we could see that there is no time flowing does that mean that the energy flowing at the speed of light creates the flow of time?


I'm planning on building an online presence of a game I'm working on once it reaches a stage that would allow for creating marketing material (screenshots, trailers, etc).  Should I trademark/copyright my game before I start building online presence? How long does the trademarking/copyrighting process take? How much money can it cost?


Get the Selected radio button value via button click

I think this is a very dumb question sorry for this I am just doing some POC.  here is the code:    <lightning-radio-group          name="radioGroup"         label="Radio Group"         options={options}         value={value}         required         type="radio">     </lightning-radio-group>   <lightning-button          variant="base"          label="Base"          title="Looks like a link"          onclick={handleClick}          class="slds-m-left_x-small">     </lightning-button>   JS.  @track value;  get options() {     return [         { label: 'op1', value: 'op1' },         { label: 'op2', value: 'op2' },     ]; }  handleClick(event) {     console.log(this.value); }   The Console log is displaying me undefined...


I was in a hurry, put a pork butt and beef brisket in the sink with water and ice to thaw. (overnight) they were still cold this morning. Is it completely unsafe to try and smoke/cook on the grill? Or, can I still cook them just make sure they cook to a higher temp to ensure all bacteria is killed?


Problem:    How many triangles do $m$ lines form if   a) Every two lines intersect and no three lines intersect at one point.  b) There are $n$ lines among $m$ lines that are parallel to each other. No other line is parallel to these $n$ lines, and no other two lines are parallel to each other. Again no three lines intersect at one point.  Thank you.


Here are two examples of lists  list = [["mo", "thu"], ["we", "fri"], ["mo", "mo"]] list2 = [["mo", "fri", "fri"], ["we", "we"]]   So these lists come in random order. I've given two examples here. What I want to do is compute all possible ways these lists can be permutated. On the level where it's list[1] * list[2] * list[3]. All possible combinations. A smaller example what I would like to reach is this:  list3 = [["we", "thu"],["fri", "thu"]]   -->   [["we", "fri"], ["we", "thu"], ["thu", "fri"], ["thu", "thu"]]   Also, the lists are random so the amount of elements in the list or the nested lists can vary. I can python this out by alot of code but I was hoping there is an easier way to this.   Cheers


Is it bad design to use table tags when displaying forms in html?

I keep hearing that div tags should be used for layout purposes and not table tags. So does that also apply to form layout? I know a form layout is still a layout, but it seems like creating form layouts with divs requires more html and css. So with that in mind, should forms layouts use div tags instead?


To create the material for my model, I've constructed a node tree. This node tree is interactive (based on the dimension of the model it changes its values). When I export the final model as an obj file, the corresponding MTL file is generated. The problem is that when I import again the model in Blender the node tree is not present and the color of the model is white. I can' t create a group and simply load it, as the node tree is interactive and not unique, I've tried to check the box "copy" when I export the model and I've also checked that the files have the same name and are in the same directory. I don't understand if the problem is during the export or import operation. Do you have any suggestion?


Does the sequence $\sum_{n=3}^\infty (-\frac{1}{\sqrt{\ln(n)}})^{n+1}$ converge or diverge

Not sure how to about this. Spent a while racking my brain, tried comparison didn't work. I'm thinking I need to show how its similar to a p-series test since its to the power of $n+1$ where $n+1>1$ thus it converges, but not sure how to do that.


Name separators, if condition for same command

I am new to LaTeX, just a Beginner, Basically a perl developer,  I have created a .tex file  \begin{document}  \cont{\iname{\isurname{Name1}\ifname{K. C. G.}}\iname{\isurname{Name11}\ifname{Y. Q.}}\iname{\isurname{Name111}\ifname{C.-Z.}}\ititles{Some title Text}\ipage{995}}  \end{document}   Now my need is to define the commands, and the display should come as the below >   \iname - Person Name will repeat several times \isurname - Surname of a person \ifname - First Name of a person \iname will repeat any number of times, say 1 to ...   If only one \iname found inside \cont, display should be like the below     Name1 K. C. G. Some title Text - 995.   If only two \iname found inside \cont, display should be like the below     Name1 K. C. G. and Name11 Y. Q. Some title Text - 995.   If more than two \iname found inside \cont, display should be like the below (and should come after last \iname)     Name1 K. C. G., Name11 Y. Q. and Name111 C.-Z. Some title Text - 995.   I am able to define \iname seperated by comma, but I don't know how to write a macro to define \iname with different outputs based on the if condition,  Is it possible to define that, I am totally a beginner with LaTeX, please guide me  Thanks & Regards


How does electricity produce magnetisim?

I am in class 10 and I have just read the electromagnetism chapter. They always keep on saying that electricity produces magnetism! but how!? We know electrons move, but how do they produce something that can exert a force on something metallic far away from those electrons? I have tried to read about it on wikipedia but I am not able to understand the complicated terms! Please answer in such a way  that it will remove all my confusions!


Does driving an microcontroller's GPIO when it is powered off weaken the chip?

We are using the  in a project. The way our design is now, the IC's GPIO pins will sometimes be driven high (to 3.3V) or low when it is powered-off. Will this weaken the chip? The absolute maximum ratings state the voltage on any digital I/O pin is -0.3V to VSupply+0.3V. If the answer is no, could the IC be weakened during power up?  The LTC5800-IPM does not have the most detailed datasheet. If it is not clear for that device in particular, I'd be interested to know for CMOS microcontroller GPIOs in general.


For java List concurrent modification exception not thrown if remove method invoked before iteration

The following code does not throw ConcurrentModificationException      public static void main(String[] args)     {         List<String> l1 = new ArrayList<>();         l1.add("v1");         Iterator<String> it =  l1.iterator();         l1.remove(0);         while(it.hasNext()) {             System.out.println(it.next());         }     }   Whereas this code throws ConcurrentModificationException      public static void main(String[] args)     {         List<String> l1 = new ArrayList<>();         l1.add("v1");         Iterator<String> it =  l1.iterator();         l1.add("v2");         while(it.hasNext()) {             System.out.println(it.next());         }     }   Both operations are structural modifications of list, but why exception is thrown only in case of addition?


Proof of $\lim_{n\to \infty} \sqrt[n]{n}=1$

Thomson et al. provide a proof that $\lim_{n\rightarrow \infty} \sqrt[n]{n}=1$ in . It has to do with using an inequality that relies on the binomial theorem:  I have an alternative proof that I know (from elsewhere) as follows.  Proof. \begin{align} \lim_{n\rightarrow \infty} \frac{ \log n}{n} = 0 \end{align} Then using this, I can instead prove: \begin{align} \lim_{n\rightarrow \infty} \sqrt[n]{n} &= \lim_{n\rightarrow \infty} \exp{\frac{ \log n}{n}} \newline & = \exp{0} \newline & = 1 \end{align}  On the one hand, it seems like a valid proof to me. On the other hand, I know I should be careful with infinite sequences. The step I'm most unsure of is: \begin{align} \lim_{n\rightarrow \infty} \sqrt[n]{n} = \lim_{n\rightarrow \infty} \exp{\frac{ \log n}{n}} \end{align} I know such an identity would hold for bounded $n$ but I'm not sure I can use this identity when $n\rightarrow \infty$. Question: If I am correct, then would there be any cases where I would be wrong? Specifically, given any sequence $x_n$, can I always assume: \begin{align} \lim_{n\rightarrow \infty} x_n = \lim_{n\rightarrow \infty} \exp(\log x_n) \end{align} Or are there sequences that invalidate that identity?  (Edited to expand the last question) given any sequence $x_n$, can I always assume: \begin{align} \lim_{n\rightarrow \infty} x_n &=  \exp(\log \lim_{n\rightarrow \infty} x_n) \newline &=  \exp(\lim_{n\rightarrow \infty} \log x_n) \newline &=  \lim_{n\rightarrow \infty} \exp( \log x_n) \end{align} Or are there sequences that invalidate any of the above identities? (Edited to repurpose this question). Please also feel free to add different proofs of $\lim_{n\rightarrow \infty} \sqrt[n]{n}=1$.


Neural network model having high validation loss shows higher accuracy in test data during cross validation process

I am training 3 different models, with varying parameters like learning_rate, regularization_strength. But number of epochs is same for all. For a fixed no. of epoch, model 2 has the highest validation loss value. But the accuracy of it is highest in test set. How can it be possible ? Or I have some bug ?


No symbol table. Press any key to continue

Whenever I boot Ubuntu 16.10, just before the Plymouth screen, I'm seeing this message:  No symbol table found.  Press any key to continue...   and it remains there for a minute or so before showing me the log in screen. If I press any key it will be stuck for ever and I'll have to restart the computer.  Any help is appreciated..


Is on needed a second time in this sentence?        There is a bad effect either on human health or environment.    There is a bad effect either on human health or on environment.


Is cross product defined for vectors of more than three variables?


What is the role of $\hbar$ in quantum mechanics?

Planck's constant $\hbar$ appears in the Schrodinger equation:  $$i\hbar \frac{d|\psi\rangle}{dt}\ = \hat{H}|\psi\rangle$$  which implies for stationary states,  $$|\psi(x,t)\rangle=e^{-iE_n/\hbar}|\psi(x,t=0)\rangle \, .$$  What would you say is the role of $\hbar$ or is it worth considering the other formulations of quantum mechanics, like the Heisenberg equation of motion (where the operators carry the time evolution:  $$i\hbar \frac{d\hat{A}(t)}{dt} = [\hat{A}(t),H] + i\hbar\frac{\partial\hat{A}(t)}{\partial t} \, ?$$  Or is it worth considering this from the standpoint of the Path Integral Formulation where $\hbar$ is used to work out the probability amplitude of a specific path:  $$e^{iS/\hbar}.$$  I understand that $\hbar$ is often used to make equations dimensionally consistent and that it is often set to 1 when dealing with complicated equations. It is also sometimes stated that $\hbar \to 0$ is the "classical limit". I do not understand this.


I conducted a verification survey for my thesis with 7 point likert scale. Only one question was used in the survey and 18 participants responded to my survey.   The responses received from 18 participants are:                              1- Extremely disagree                             1- Mostly disagree                             2- Some what disagree                             1- Neither agree nor disagree                             8- Some what agree                             5- Mostly agree                             0- Extremely agree   I calculated weighted average as: ( (1*1)+(1*2)+(2*3)+(1*4)+(8*5)+(5*6)+(0*7) )/18= (83/18) = 4.611   Can someone please help me with the inference (Like what can be concluded from the result)


Using Named Credentials in OAuth 2 authentication (grant_type=password)

I want to get an access token from an external endpoint (HTTP callout to REST API) without hardcoding passwords. The external system expects a request with Oauth 2.0 authentication details provided in the body, like the following:  String body = 'client_id='+EncodingUtil.urlEncode('myClientId','UTF-8');  body += '&client_secret='+EncodingUtil.urlEncode('myClientSecret','UTF-8');  body += '&grant_type='+EncodingUtil.urlEncode('password','UTF-8');  body += '&username='+EncodingUtil.urlEncode('myUsername','UTF-8');  body += '&password='+EncodingUtil.urlEncode('myPassword','UTF-8');   Hardcoded request is successful, but I'd like to use Named Credentials. I can set up an Auth. Provider of type Open ID Connect and provide client_id and client_secret. But there I cannot set parameters like 'username' and 'password' which are needed in order to make a proper request. This makes me wonder if that kind of authentication is possible in SF.  An alternative would be using Custom Settings, but then the credentials would be too easily accessible (and concrete setting cannot be deployed) which is not a good practice.  So my question is: Can I securely authenticate with above credentials using Apex without hardcoding them?


Solving $\lim_{c \to +\infty}\int^{1/c}_{1} \frac{\sin u}{u} \, du$ using elementary methods

Is it possible to solve the following integral:  $$\lim\limits_{c \to +\infty} \displaystyle\int_{1}^{1/c} \dfrac{\sin u}{u}  \, du$$  using "elementary" methods? By "elementary", I mean those methods that do not involve Complex analysis, Lebesgue Integration, etc (basically, anything beyond an elementary first course in Real Analysis, say, from the first six chapters of Baby Rudin). I've seen many solutions to this integral (seemingly with different bounds, including the Dirichlet integral), but all of them seem to use methods that would generally not be accessible to someone with just a basic real analysis course.


Show that $X_n\to0$ in probability does not imply $\frac{S_n}{n}\to 0$ in probability, even if the $X_n$ are independent.

Show that $X_n\to0$ in probability does not imply $\dfrac{S_n}{n}\to 0$ in probability, even if the $X_n$ are independent.  How to approach this problem. Any hints will be appreciated. I  am not able to even start the problem.


What is Stack Overflow planning to do about indefinite questions with recurring updates?

The title of the question is hard to comprehend, please read on. I'm rather new to Stack Overflow, I joined just about a month ago, and since then I have been fairly active (top 0.41% of the current week's ranking). Since joining Stack Overflow I've come across a lot to see, I've starting noticing some trends in the questions being asked, the obvious ones are the broad questions, duplicate questions, and others, albeit a peculiar one which I've come across would be the recurring questions, this is how it works:  A given user will ask a question about a problem they are having while coding (this is a good thing, Stack Overflow is exactly the place for such problems) There is an answer given by another user which solves the problem. The user who asked the question marks the given answer as accepted and continues coding (amazing till here! but hold on to your seats because this is when it gets messy) With the code/solution provided by the answerer, the user who asked the question implements it and it works. It works well but soon after writing some lines of code something else goes wrong. The user hops back on to Stack Overflow and starts to comment on the post of the answer which was accepted earlier, posts about the new issue which has come up. The answerer gets back to the problem, reanalyzes it and solves it once again. Read from step 4.  Problems Primary Problem In the process of revisiting step 4, the user is highly likely going to edit the question content with additional updates. What happens? The entire question changes, initially the question was: a single well defined issue encountered while programming <- the question and its answer can be highly useful to other users in the future. however with all the subsequent tries and updates it turns into: a large blob of issues one after the other all in a single question <- equivalent to multiple separate good questions asked, as a sum of parts its not what other users facing one of the problems can relate to, as everything explained in the answer is tangled up like earphone wires. Secondary Problem About the the user who answers to all the updates. Personally, its something through which I've been through, I do not want to point my finger (I meant hyperlink) as I do not think that would be right here, however If you dive into the questions I've answer on my SO profile you won't have a hard time finding it (think sorting by activity?) I would loose respect for myself If I ignore the updates made by the user and not answer them all. However at the end of the day I would rather have the user opening up a separate question, because its almost a whole different question now. Tackling It The main similarity between broad questions, duplicate questions, questions of these types and the mentioned recurring question is the quality deteriorating affect they have on the base of Stack Overflow. The main difference is that broad/duplicate questions have flags to deal with them, whereas recurring questions seep through underneath unnoticed almost every single time. Valuable Q&A is lost in entanglement with the updated answer, all that was needed was, the user asking the question to post a separate question with the new issue. Which is better for Stack Overflow?  "MySQL syntax error, help?" -> answer given -> question updated (wants to know why the column names are different now) -> answer updated -> question updated (on testing with an initially empty table the given query's aggregating fails) -> answer updated    "MySQL syntax error, help" -> answer given "Column names different from expected query in MySQL query" -> answer given "This mysql query with empty tables results in aggregation that works in an unexpected way" -> answer given    Something for you to ponder upon: what should be the title of the former question? Note: there is another question which revolves around the exact same concept. This other question discusses about "exit strategies", which this question is not about.


What was the significance of Varys' appearance in Dorne?

In  S06E10 ("") we see Olenna Tyrell in Dorne, conversing with Ellaria Sand about a possible alliance between Dorne and Tyrell. Then suddenly Varys appears saying     Fire and blood.   What does this mean? It could point to an alliance between Dorne, Tyrell and Daenerys, which seems a reasonable choice, seeing that they both want to go against the Lannisters. But his appearance still seemed rather odd to me, since Varys should still be in Meereen, as we see him sailing on the ships that leave for Westeros with Daenerys later. So how was he suddenly in Dorne? Does this mean that scene was out of chronological order (in which case, was it earlier or later?)? Or does he have some other means for fast travel? Or was this maybe not even Varys?     I would not like this question to degrade too much into completely random speculation and hope I just missed something obvious or it isn't as odd for him to be there as I might think. If this is really supposed to be a huge mystery to ponder the viewers for the next year, then be it so. Or do the books offer some insights on the matter (even thought I know that the series might diverge further and further from them in many regards).


Is it possible to maintain the electric current permanently?

I thought this question when I learn about the superconductor which has no resistance.  If I made the round wire with the superconductor, I think it is possible for the current to flow through the wire that power consumption is zero. But I don't know that it is possible to flow permanently.   It is right that the round wire made with superconductor has no resistance. But I think the electron that flows through the wire does an acceleration exercise(circle motion), so it releases the electromagnetic waves.   But I don't know the exact answer. Is it possible to maintain the electric current permanently using the superconductor?   (I find it, but I think it is not clear answer)


How do I know if my system is vulnerable to the ShockShell vulnerability?

The recently discovered ShockShell vulnerability affects many Linux and Mac systems, because they are using the vulnerable BASH shell.  How do I know if I am vulnerable to this attack and how do I protect myself from it?


Convert a JavaScript number to a currency format, but without "$" or any currency symbol

I want to convert my JavaScript number into a currency number, but with any currency symbol Suppose this is my number: var number = 43434;  The result should be like this: 43,434  And not this: $43,434


The question may be trivial but with this simple for loop  for i in {1..10000000}; do echo "$i" line >> file done   my shell crashed after some elaboration time (the tab in the terminal emulator was automatically closed) and file was not created.  It is GNU bash, version 4.1.11(2)-release.  Is this due to a memory limit or what else? And if yes which should be this limit?  With {1..1000000} it worked correctly.


I have two lists like these:  a = [12, 23, 45, 56] b = [0, 0, 0, 0]   And I want to create a dict using a and b like this:  c = {12:0, 23:0, 45:0, 56:0}   Is there a easy method to do this?


Complex function’s injection(solve it please......)

Let $D=\{z| |z-z_0|<1\}$ If $f$ is analytic function on $D$ and $|f’(z)-f’(z_0)|<|f’(z_0)|$, Then $f$ is injective  First, I’m sorry This is my first time to use this page So, I want to solve this question. I heard this question is very hard But I believe you can solve it. I have been studying Complex analsis I spent time to solve this question I couldn’t prove this question.. Please answer me, How to solve it?


If any alternative numbering systems exist that simplify thinking about arbitrary numbers

In modern Western culture we think of numbers typically in base 10. By "we" I mean the vast majority of the public. For some reason this is easy, and I'm not sure why or how to pinpoint it down to some concrete reason for its success. The only thing I can think of is we have 10 fingers so we can count on them, and 10 divides pretty "easily" whatever that vague term means.  But we can think of extremely large numbers down to a very low level of precision using this system. For instance, you can think of the number $171,129,412$, which goes down to describing "two" at the scale of 100 million+. But it's as if in your head you can visualize every element in that set, even though you really aren't, but you get the sense that you can understand its size.  You start to lose track a little if the number is too big though: $12,918,274,182,183,182,874,371,173$. It's pretty much impossible now to know how big this is down to the $173$ scale at the end. I have no idea why but it just seems this way.  But you can get into the millions an billions down to the scale of 1, using our numbers represented in base 10 system.  We can use the base 10 system differently and do scientific notation to create orders of magnitude with it as well, leading to thinking of huge numbers at a broader scale / level of detail. Like $10^{30}$ is pretty large, but you can get a sense of it's relative size to $10^2$.  We can also use the base 10 system for decimals to a good degree, where we can go 9 or 10 decimal places in and still feel we are understanding the value's accuracy.  Given all this, I'm wondering if there are any other systems that work equally as well, or close to as well, or even better, when compared to the base 10 system.  Some common base x systems are base 2 for binary, base 16 for hex, base 60 in the past seems like it was popular. However, I personally can't easily look at one of these numbers and get its value down to an accuracy of 1 right away. TBH, I don't get any sense of value of it all all. I'm not sure if I could with practice, or there is something inherent about 10 that makes it simple and intuitive.  My question is, if there is anything other than base 10 that lends itself to easily understanding large and small numbers at any scales, in the same or similar way that the base 10 system does (as described above). In particular, wondering about base 2, base 3, base 4, base 5, ... base 16-ish, and then any arbitrary number after that that lends itself to understanding would be interesting. But mainly wondering if any of these smaller numbers have good properties for understanding like base 10.  One system that is interesting to consider is Roman numerals. Instead of going $1, 2, 3, 4, \cdots$, where it's 1-digit numbers, followed by 2-digit, followed by 3 digit, ..., you instead have $I, II, III, IV, V, \cdots$, so that was $1, 2, 3, 2, 1, \cdots$. So it's an interesting way to represent it while still keeping it base 10 or whatever base. This fits into the category of things I'm asking about in some way.


im new in here go easy on me,  I plan to securely erase an HDD with a microcontroller.   The ATA secure erase commands can be used to securely wipe HDD, is there a way that it can be reproduced by a microcontroller  to wipe a HDD  or  are there any microcontrollers which have SATA interface?  if so will there be bandwidth issue?


The captcha appears in an inconvenient location on Android

The captcha appears in an inconvenient location on  and . E.g. I saw the following after trying to post a question:  I had to zoom out or horizontally scroll to see where the captcha was:  I believe I was using the responsive design.


Solve the recurrence $$f_{n+2}=af_{n+1}+bf_n\qquad n\in\Bbb N_0\tag{1}$$   Where $a,b>0$ and $f_0,f_1$ are given.   I know that if $$F_{n+1}=c_nF_n+d_n$$ then $$F_n=F_0\prod_{k=0}^{n-1}c_k+\sum_{m=0}^{n-1}d_m\prod_{k=m+1}^{n-1}c_k\ .$$ But I am unsure of how to find a solution to the recurrence in question. I am fairly certain that a closed form exists, because the Fibonacci sequence $F_n$ (which is given by the case $a=b=f_1=1$ and $f_0=0$) has an explicit solution, namely  $$F_n=\frac{\varphi^n-\psi^n}{\sqrt5}$$ where $$\varphi=\frac{1+\sqrt5}2,\qquad \psi=\frac{1-\sqrt5}2\,.$$ Admittedly, I do not know how to prove said result, but I'm sure there is some sort of generalization of the proof to solve my recurrence.   I've defined the generating function $$f(x)=\sum_{n\geq0}f_nx^n$$ and shown that  $$f(x)=\frac{f_0+(f_1-af_0)x}{1-ax-bx^2}\ .$$ So of course $$f_n=\frac1{n!}\left(\frac{\partial}{\partial x}\right)^n\frac{f_0+(f_1-af_0)x}{1-ax-bx^2}\,\Bigg|_{x=0}$$ but that is way too inefficient. Is there a nice closed form solution for $(1)$? Thanks.


Difference between align and alignat environments

What is the difference between align and alignat environments?


Synchronisation of parameters between \begin and \end

If I create a new object that requires   \begin{}   and   \end{}   I want the contents within the braces to auto-synchronise with each other.   For example  \begin{itemize}     \item Example text \end{itemize}   And later I decide that I want an enumerated list, and I change one of the contents inside the { } to enumerate the other one should too automatically.  \begin{enumerate}     \item Example text  % Contents of {} should update here automatically if changed above % Or vice versa   \end{enumerate}   This 'auto-synchronization' sometimes occurs accidentally so I think it is an inbuilt feature, but I do not know how to trigger it.    Edit    by @Troy also explains this issue and he has used better terminology (mirroring vs auto-synchronisation). However, in that answer, the information by @Troy was additional and not what the OP was asking for.


So I am running this Drupal 7 website, I just checked users list and got surprised with this:   As you can see the usernames are spam and their emails are also spam. But I do not get it how they did that and even get themselves an admin role. Also log shows they even enabled the php filter module. Also the registrations are disabled so how? Even if the users where registered via site register form it would show its 1 week old or so, not the 44 years.  I don't get it. What should I do? Also I have User Protect module installed.


What is the appropriate statistical test when calculating the busiest day of the week?

We have 10 years of data and Monday is the busiest (most visits to the hospital) on average. If we wanted to assess whether that is true and report a p-value, what is the appropriate statistic?   We believe the answer is chi-square as we found a peer-reviewed medical article from the Annals of Emergency Medicine (highest circulating journal for that specialty) that used chi-square for this very calculation.   If chi-square is appropriate, what values do we use for observed and expected values for chi-square? One approach would be to list all the values for Monday as observed values, or all the means for Mondays averaged across a month, or all the means for Mondays averaged across a year.  If there were no busiest or least busy days, we would assume that the visits would be the same every day of the week. That means our "expected values" for Chi-Square would be the mean of the visits for any given week.


Use masks as part of materials in cycles

Intro:  Ok, so I'm new to blender and have looked all over the internet, and blender is not working as expected (and all the usual that seems to be the required greeting on this site...)  Question.  I can use masks created in the movie clip editor (or the UV/Image editor) in the compositor to combine elements.     How can I use masks to combine shaders and textures?  I could render the mask as an image sequence ,and plug the images as a texture in the material editor. But then every new adjustment  that has to be made in the mask means that the sequence has to be re-rendered. Not the best workflow. Masks being vectors have so many advantages over pixel based files, on top of that it is easy to rotoscope using tracking tools, also they are quite easy to animate and allow fine control when it comes to feathering.  Is there some python amazing script, animation node, add-on, or secret menu for the initiated that allows the mask information to be used interactively on the material editor?


How can I make functions in a script "unavailable" when the script is imported?

Suppose I have the following python "module" named bloop.py:  def f(x):     return x+1  def a(x):     return f(x)   How can I make function f(x) unavailable, or unusable, when the script is imported? This means that when the user attempts to do something like the below, it will fail.  import bloop print bloop.f(10)


How I can access a private static member variable via the class constructor?

How can I use and modify the s_member private static variable from the constructor or in general from an other member function?  This is what I tried.  a.h:  #ifndef A_H #define A_H  #include <set>  class A {     public:         A();         virtual ~A();      private:         static std::set<int> s_member; };  #endif   a.cpp:  #include "a.h"  A::A() {     A::s_member.insert(5); // It causes error. }   I get this error:  /tmp/ccBmNUGs.o: In function `A::A()': a.cpp:(.text+0x15): undefined  reference to `A::s_member' collect2: error: ld returned 1 exit status


Why this sort command gives me an empty file?

prova1 is a file with some text. When I run this code prova1 become empty:  sort prova1 > prova1   I know that to achieve the effect I can do:   sort prova1 -o prova1   I would just know the reason :)


How to implement GetHashCode() in a C# struct

I have a struct that overrides the Equals() method and the compiler complains about GetHashCode() not being overridden.  My struct:    private struct Key   {     ...      public override int GetHashCode()     {       return ?;     }      public int FolderID;     public MyEnum SubItemKind;     public int SubItemID;   }   What is the right way to implement the GetHashCode() method?  a)      return FolderID ^ SubItemKind.GetHashCode() ^ SubItemID;   or b)      return FolderID.GetHashCode() ^ SubItemKind.GetHashCode() ^ SubItemID.GetHashCode();


Posts and comments minimum length validation being bypassed by the U+2800 Unicode character "⠀"

Posts’ and comments’ minimum length validations are being bypassed by the U+2800 BRAILLE PATTERN BLANK Unicode character "⠀". It counts as an "Other Symbol", not as whitespace or a control character.  For example, see the comment beneath this post.   This needs to be fixed.


What to do if photoshop drawes pixels way off?

I love pixel art, and recently I got Photoshop cs6, but when I try to draw pixels then it draws them way off. Is there a way to fix this?


When and how did the word hashtag come about?

What caused the change from calling "#" a pound sign to calling it a hashtag? Why? I know that Twitter had much to do with the coinage, but how and why did it come about?


How to find out which package a particular file under /usr/share came from?

How do I find out which (apt-get-installed) package a particular file came from?


How to install .bundle packages in Ubuntu?

I've recently downloaded a package with .bundle extension. it's VMware-Player-6.0.3-1895310.x86_64.bundle. I want to install vmware-player, but when I open that, it opens with text editor.


python automatically adding numbers after decimal

Python program is automatically adding additional number in float longitude. I am creating new columns "src", "des" using others in csv. Can see the line number 4 in result csv, "des" contains longitude value different from that in Dropoff_longitude. But I want the same value with as it is. No modification while making tuple.   Code:  import pandas as pd import numpy as np  def loc(x):      return (round(x[0],14),round(x[1],14))   columns=["Pickup_latitude","Pickup_longitude","Dropoff_latitude","Dropoff_longitude"] df=pd.read_csv("demo.csv") df["src"]=df[ ["Pickup_latitude","Pickup_longitude"] ].apply(loc,axis=1) df["des"]=df[ ["Dropoff_latitude","Dropoff_longitude"] ].apply(loc,axis=1) df.to_csv("result.csv",index=False)   I have added a pic of my


Cannot use Ubuntu 17.10 ISO image for installation

While trying to write the ISO on an USB stick I get the following error "It looks like this is not a bootable image"    (Note: I can write Ubuntu 16.xx without any problem with the same software)


If you view the Earth from far enough away can you observe its past?

From my understanding of light, you are always looking into the past based on how much time it takes the light to reach you from what you are observing.  For example when you see a star burn out, if the star was 5 light years away then the star actually burnt out 5 years ago.  So I am 27 years old, if I was 27 light years away from Earth and had a telescope strong enough to view Earth, could I theoretically view myself being born?


$$\sum_{k=0}^n \cos(\alpha+k\theta)= \cos\left(\alpha+\left({n\theta\over2}\right)\right)*{\sin\left({(n+1)*\theta\over2}\right) \over \sin({\theta\over2})}$$  I have worked the left summation out to a couple of terms but I am not seeing how they are going to come together to get the right side. I wish I was better at writing on this site so I could show exactly what I have written. I also have to prove the summation of the sine but if I can figure out the cosine one above the sine should fall from that.  Sorry for the notation. I copied and pasted exactly like it said to do.


Consider $X = \{(x_1,x_2 \dots x_n) | x_i \geq 0\}$, a subset of $R^n$. Is $A(X)$ a closed set when $A$ is a linear map from X to $R^m$?

While I was trying to prove Farkas' Lemma in Linear Programming (Pg. 19 of ), I came across the question posted in the title. If $A$ is invertible, then the result is straightforward. But what happens if $A$ is not? I'm also aware that there are linear transformations that are not closed (a ). However, the set that I have here - $X$, is much "nicer" than the non-examples that I have seen.


Prove that a self-contracting sequence in R ^ n is Cauchy sequence

I need proof that: Let ${x}_n$ be a sequence of points in $\mathbb{R^d}$. Suppose that there exists an $\alpha \in (0,1)$ such that $$\Vert x_{m+1} - x_{m} \Vert \leq \alpha \Vert x_m - x_{m-1} \Vert$$ Prove that it is a Cauchy sequence. I tried to do the following: $$\Vert x_{m+1} -x_m \Vert \leq \alpha \Vert x_{m} -x_{m-1} \Vert \leq \alpha^2 \Vert x_{m-1}- x_{m-2} \Vert\leq ...\leq \alpha^m \Vert x_1 - x_0\Vert $$ Sea, $n>m$, then, $$\Vert x_n - x_m \Vert = \Vert x_n - x_{n-1} + x_{n-1}-x_{n-2}+x_{n-2}-...+x_m\Vert \leq \Vert x_n - x_{n-1}\Vert +\Vert x_{n-1}-x_{n-2}\Vert+...+\Vert x_{m+1}-x_m \Vert$$ But, $$\Vert x_{m+1} - x_m \Vert \leq \alpha^m \Vert x_1 - x_0 \Vert \hspace{20pt} \forall m \in \mathbb{N} $$ So, $$\Vert x_n-x_m \Vert \leq \alpha ^m \cdot (n-m-1)\Vert x_1-x_0\Vert$$ But i didn't know how continue, Any comments would be very helpful :)


What is crop factor and how does it relate to focal length?

I'm reading that a 50mm lens is recommended as a first prime lens for DSLR owners as it's supposed to give a 'natural' perspective, but when used on (most) DSLRs, the view is cropped, as if you were zoomed in by 1.5-1.6x, so it's more of a telephoto lens when used on a DSLR. I've also read however that the 50mm lens gives the same perspective on a DSLR and a 35mm, and shouldn't really be considered to be 'equivalent' to an 80mm lens as the crop factor isn't really a magic focal length changer.  Can someone explain how the image is different from (for example) a 50mm lens on a DSLR and an 80mm lens (assuming 1.6x crop factor) on a 35mm camera?


How to redirect complete outgoing phone's traffic to a proxy server?

How to redirect entire phone traffic (including all apps) to a proxy (with out rooting the phone)  We are developing a parental control app for Android, in that we have requirement to capture all out going traffic from Android phone for categorization. Is there a way to achieve this in Android with out rooting the phone.  Thanks, Gopi.


Can Monty Python Fluxx be used with the regular Fluxx deck, or is it a separate game?

As far as I understand,  is a separate game, not an expansion pack, that doesn't require the original Fluxx deck to play. But can it be used with the original deck  - can it be used to supplement the original cards, or does it not work like that?   (This related question  didn't quite answer my question.)


As electricity is transferred in earth by earthing and lightning, why it does not become negatively charged?


How do I use a dash at the end of speech?

How do I use a dash at the end of speech to signify an abrupt change of subject? I understand that when using an em dash, there is no space before or after the dash:  George sighed. “There is nothing to look forward to in life these days. I—” “Aren’t the flowers beautiful?” said Wendy.  But what happens when the style guide uses en dashes with spaces around them rather than em dashes? For example, the Guardian Style Guide:  I feel the en dash should be preceded but not followed by a space, as in the following example, but I haven't been able to find anything to confirm that feeling.  George sighed. “There is nothing to look forward to in life these days. I -” “Aren’t the flowers beautiful?” said Wendy.  Should the dash be preceded and followed by a space, as in the next example?  George sighed. “There is nothing to look forward to in life these days. I - ” “Aren’t the flowers beautiful?” said Wendy.


How do I show that if $f : [0,1] \to [0,1]$ is continuous, then there is some $c$ such that $f(c) = c$?

Theorem: Let $f:[0,1] \to [0,1]$. Assume $f$ is continuous. Then there exists   $c \in [0, 1]$ such that $f(c) = c$.         For any function $f$, let $g(x) = f(x) − x$. If the theorem is true, what does that say about $g(c)$?   Write a proof of the theorem. Do it by applying the Intermediate Value Theorem   in the appropriate way to the function $g(x) = f(x) − x$ with $a = 0$ and $b = 1$. Clearly state why the hypotheses of the IVT are satisfied here.        Well if the theorem is true, then there exists $c$ such that $f(c) = c$. Then $f(c) - c = 0$. Then $g(c) = 0$. Intermediate Value Theorem: Let $I$ be an interval and $f$ a function whose domain contains $I$. If $f$ is continuous, then for all $a, b \in I$ with $a < b$ and all real numbers $k$, if $k$ is strictly between $f (a)$ and $f (b)$, then there exists $c$ such that $a < c < b$ and $f (c) = k$.   Proof Attempt: Take $a = 0$ and $b = 1$. Then $a,b \in[0,1]$ and $a < b$. Since $f:[0,1] \to [0,1]$, it follows that for all real numbers $k$ such that $f(a) < k < f(b)$, then there exists $c$ such that $a < c < b$ so $0 < c < 1$ and $f(c) = k$. Then $f(c) - k = 0$. Thus, since $g(x)=f(x)-x$, it follows that $g(c) = 0$.   Looking to see if I did this correctly and/or if there is a more elegant way to prove problem 2. I am a little confused why the first theorem is true, but I went with it.


Have \cleardoublepage working in oneside scrreprt

That seems quite elementary, but I didn't find the answer. How can I have the \cleardoublepage command work in a oneside environment? That seems kind of odd to ask for that, but I have to send an application file with a bunch of documents added to a .tex file via pdfpages. And I don't know whether it will be seen only on screen, printed on a one-sided printer or printed on a two-sided printer.   So I want the layout to be one-sided for the file not to look too odd on a computer screen or if printed onesidedly. But I also want new parts of the document to start on an odd page, so that my id card is not printed on the back of my research statement in case of two-sided printing.  Here is an example :  \documentclass[oneside,openright]{scrreprt} \begin{document} Foo1. \newpage Foo2. \cleardoublepage Foo3. \cleardoublepage Foo4 \end{document}   I would like "Foo4" to be on page 5, as it is in twoside mode.


How to separate "mouse" and "trackpad" settings?

In System Preferences > Mouse there's a setting "Scroll direction: natural", which I don't like, so I unset.  The problem is that this also unsets the setting for Trackpad, which I do like.    How can you have different settings for mouse and trackpad?  (In case you can't understand the rationale for wanting them different, and think this is a ridiculous question, here is the reasoning.  Mice have had scroll wheels for decades, and the direction of the wheel turning has always been in sync with the motion of the scrollbar.  This is, in my opinion, the most natural way to do things, even though it is the opposite of what Apple calls "natural".  On the other hand, I'm perfectly willing to use Apple's "natural" scrolling for trackpads, because the metaphor here is that you're moving your fingers across a page, just as if you were using an iOS device's touchscreen.  The idea that Apple treats these as the same thing, when they are conceptually completely different is very odd to me.  I don't want to change a decades-old habit with the mouse, just because Apple changed their idea of how a trackpad should work.  I embrace the trackpad change because it makes sense to anyone who uses an iPhone or iPad (and I use both) but I'm not willing to rewire my brain's way of using the mouse.)


In my grammar book, in a chapter on subject-verb agreement, the author said that when two nouns, joined by and, are suggesting the same idea or person, we consider the nouns as one unit and use a singular verb, e.g. in  The novelist and poet is dead.   Among many examples he gave, I caught attention of this one:      Time and tide waits for none.    This didn't appear correct to me. I think it should have been:      Time and tide wait for none.    I went on to look on the internet and found conflicting resolutions to this. Different references said differently. What do you think is correct? And what's the reason behind your answer?   EDIT  A possible duplicate has been raised for my question: . However, in the mentioned duplicate, the OP is not interested in knowing which construct is correct. He's rather interested in knowing the nuance between tide and time. Hence, the answers provided there also talk about that nuance, rather than answering which construct is correct.


Elegant way to create a List just by (int)from and (int)to

I want an elegant way to create a new List<int> just by to integers.  Example:  var from = 2; var to = 5;   What I want is this:  List<int> { 2, 3, 4, 5 };   Of course I could do it in a simple loop like this:  var results = new List<int>(); for (var i = from; i <= to; i++) {      results.Add(i); }   But I want some kind of more efficient or elegant way.


Is there a way I can password protect a dropbox directory on my work pc?

I use dropbox a lot, and I'd like to start using my Dropbox account on my work PC, however I want to prevent anyone else from being able to access the files in my dropbox folder other than me on my work PC.  E.g. double clicking my dropbox asks for a password or something on my work PC.  Is this possible? If so, any suggestions?


Does anyone know where the factorial "!" symbol came from?  I can't decide if it is my favorite or least favorite notation in mathematics...


pressing arrow keys in vi inserts alphabets?

I am new to vi editor.I am using to edit one of my file. But when i opened it through vi i can't edit it properly. when pressing arrowkeys it inserts alphabets(toparrow-A,bottomarrow-B,leftarrow-D,rightarrow-C).I dont know what is happening?  How to solve this problem?


finding the summation of $\sum_{\ell=k}^n \binom{\ell}{k}$

$$\sum_{\ell=k}^n \binom{\ell}{k} =  \binom{n+1}{k+1}$$  Can someone explain how we got that equation? Expanding it we get   $$\binom{k}{k} + \binom{k+1}{k} + \binom{k+2}{k} + .....+ \binom{n}{k}$$  but how does that add up to  $$\binom{n+1}{k+1}$$


I'm trying to pass an argument to a bash script and have it iterate through letters      #!/bin/bash     for l in {$1..$2}; do          echo $l     done   When I try to run ./myscript.sh A D Instead of getting:  A B C D   I get:  {A..D}


when I'm trying to update through terminal I'm getting the following error:  E: Could not get lock /var/lib/dpkg/lock - open (11: Resource temporarily unavailable) E: Unable to lock the administration directory (/var/lib/dpkg/), is another process using it?   I am not sure if it is due to virus or any other reason.


Select the best point pair in the 2D grid

Suppose in the 2D space we have an array of points, and each point has a weighting factor, which is a float value ranging from 0 to 1. Each point also has a coordinate in the 2D grid. The following pseduo-codes show the property of the point:  class Point {  public:     float weightingFactor_; // [0,1].     float x_;     float y_;  }   Now my question is: given an array of points, how can we select the best point pair? The criterion for best point pair is: (1) both points should have large weighting factors; (2) the two points should be as far as possible spatially based on the Euclidean distance. For the time being, my solution is for each point pair calculate the following criterion:  Point1.weightingFactor_*Point2.weightingFactor*Distance(Point1, Point2)   Among all the point pair, then select the pair whose criterion value is the largest. I am not sure whether this is the best solution. Any ideas? Thanks.


Problem with makeindex, italics and whitespace

this code produces two entries for the sub-item in the Index: \documentclass{scrbook}  \usepackage{imakeidx}  \makeindex \begin{document} A word\index{A word!Subitem@\emph{Subitem}} and another word\index{A word!Subitem@\emph{Subitem}} and an \emph{italic word\index{A word!Subitem@\emph{Subitem}}}. \printindex \end{document}  The source of the problem seems to me the \emph{} envelopping the \index containing an \emph. (Same thing happens when I use \italics, b.t.w.) The .idx-file has a strange whitespace after the \emph:  \indexentry{A word!Subitem@\emph{Subitem}}{1} \indexentry{A word!Subitem@\emph{Subitem}}{1} \indexentry{A word!Subitem@\emph  {Subitem}}{1}  Is this a bug or is there a solution apart from changing to xindy? == Solution == With the solution provided below I understand now, that all is correct, when I wrap the \index-command in an empty newcommand. So this produces the correct output: \documentclass{book}  \usepackage{imakeidx}  \newcommand\findex[1]{\index{#1}}  \makeindex \begin{document} A word\findex{A word!Subitem@\emph{Subitem}} and another word\findex{A word!Subitem@\emph{Subitem}} and an \emph{italic word\findex{A word!Subitem@\emph{Subitem}}}.  \printindex \end{document}


x = 10 f1: for i in range(x):     for j in range(x):         print(j)         if j == 6:             break f1   1.How to break from outer loop in python?


For 2 vectors a and b, the dot product is defined as either:  a · b = ax × bx + ay × by  Or:  a · b = |a| × |b| × cos(θ) where θ is the angle between two vectors.   How can I prove these two formulas are the same?


Suppress output of Python operators (bpy.ops.*)

Every time the bpy.ops.remove_doubles() operator is used, it outputs to my terminal (where I called Blender from).  How can I suppress this output?  The code is:  bpy.ops.object.mode_set(mode='EDIT') bpy.ops.mesh.select_all(action='TOGGLE') bpy.ops.mesh.remove_doubles()   and the undesired output is:     Info: Removed 48 vertices


How many solutions are there in $\mathbb{N} \times \mathbb{N}$ to the equation $\dfrac{1}{x} + \dfrac{1}{y} = \dfrac{1}{1995}?$  How would you solve this? I have tried but am not sure how I should proceed with this.