Cauchy's Principal Value of $\int_{-\infty}^{\infty} \sin(x)/(a-x)dx$
Cauchy principle value of $\int_{-\infty}^{\infty}\sin(x)/(x-a)dx$
"Undefined reference to" template class constructor \bar vs. \overline - when to use what, semantically? Following the question "" which is simply about the lengths of both, I'd like to know when to use \bar and when to use \overline from a semantically viewpoint.  I always used \bar, because up until now I only had single letter mean values to type. But now I came to a problem where I needed a wider "bar".  Then I just tried  \documentclass{article}  \begin{document}   \[ \bar{a} \overline{a} \]   \[ \bar{abc} \overline{abc} \] \end{document}   where one can see that they also differ in position (\overline is lower), and also in thickness (\overline is thicker).  So, the question here is:  What does \bar represent semantically? And when to choose it over \overline and vice versa? Selecting features by attributes using ogr2ogr? Specifying latest revision of a particular branch with bower Excel: I need a formula that will count months between two dates. If it's 1-15 it should be a half month. Any ideas? So I am trying to find a formula for excel. Bascically I have two dates and I need to know the number of months between them. But to add complexity, I need a rule in there that if the earlier date is the 1st to 15th it will be a whole month but if it is 16th to end of the month it will be a half month.  For example: Date 1: April 4, 2012 Date 2: December 31, 2012 Answer: Number of months would be 9 months  If Date 1 was April 16, 2012, with the same Date 2 of December 31, 2012, then the number of months would equal 8.5.  Can anyone help me with this one? You help would be greatly appreciated. many thanks Can't do comparison on PageReference In my page constructor I call a method isFirstPageLoaded, to  check if the loaded page is the first page of the wizard.   private final PageReference FIRSTPAGE = Page.Maintenance_Lock_1;   private void isFirstPageLoaded() {          if(ApexPages.currentPage()!=this.FIRSTPAGE) {              throw new MaintenanceLockException(this.FIRSTPAGE + ' --- ' + ApexPages.currentPage());          }      }   The problem is: Even if I open the first page of the wizard, the exception is thrown. How can I compare two PageReferences? I would like to avoid to parse the URLs and remove parameters etc... Show that if $a$ and $b$ are positive integers with $(a,b)=1$ then $(a^n, b^n) = 1$ for all positive integers n  Hi everyone, for the proof to the above question,  Can I assume that since $(a, b) = 1$, then in the prime-power factorization of a and b, they have no prime factor in common, when they are taken to the $nth$ power, they will still have no prime factors in common, and so $(a^n, b^n) = 1$ for all positive integers n.  I think I'm jumping to conclusions here again, if so, leave some tips on how to do the proof properly, thanks :)  And also, I do not know how to approach the reverse problem where if $(a^n, b^n) = 1 then (a, b) = 1$, any guidance will be much appreciated! I'm trying to process some data in Excel. The data includes numeric account numbers and other long numeric strings (like cell phone MEIDs). I am not doing math operations on these strings, so I want Excel to treat them as plain text.  Here is what is making me nuts (this is Excel 2010):   Take a long number like 1240800388917 and paste it in a cell in a new worksheet. Excel's default cell format is general, so the string is presented in scientific notation as 1.2408E+12 Right click on the cell, select Format Cells, set the format to Text   The cell is still displayed in scientific notation, even though the format has been set to text.  Now, if I do the steps in a different order:   Format an empty cell as text. Right click on the cell, select Format Cells, set the format to Text Take a long number like 1240800388917 and paste it in to the text formatted cell   Now, the cell is displayed as a string and not in scientific notation.  The results remaining in scientific notation even though the cell is formatted as text just seems broken to me. I've seen suggested work-arounds like: use CSV import and set the format to text, add a space character to the beginning of each numeric string, and others.  Is there a simple good work around to easily keep these strings formatted as text?  Why on earth does Excel do this?  Related SU questions I found:  and Is logical implication always determinable from just the given statements? I am reading introductory texts on logic and am having a hard time understanding intuitively logical implication.  Specifically, I am wondering if logical implication can always be determined by two statements, P and Q alone? I'll try to give an example to clarify my question.  For example if the statement P is $x = 2$, and the statement Q is $x^2 &lt; 6$, then determining the truth of P $\Rightarrow$ Q is fairly straightforward:   If $x$ does equal 2, then $4&lt;6$ and Q is true, so $P \Rightarrow Q$ is true. And if $x$ does not equal 2, $P \Rightarrow Q$ is vacuously true.  In this example, with two statements P and Q, I can evaluate the truth/falsity of the statement P implies Q. However, what if the statement Q is changed such that it is now the statement $y = 5$?  So now I am trying to prove from that $$x = 2 \Rightarrow y = 5$$  Here is where things get murky for me. Say $x$ is not equal to 2, then $P \Rightarrow Q$ is vacuously true. But what about when $x$ does equal 2, now the statement Q could be true, but it could also be false, depending on some 'context'.   For example, if I said at the start: "Here are two statements, P and Q. Know that x = 2 and y = 4." Given this 'context', $P \Rightarrow Q$ is false. But if I say "Here are two statements, P and Q. Know that x = 2 and y = 5", then now $P \Rightarrow Q$ is true.  My discomfort here is that I assumed with two statements P and Q, I can determine the truth/falsity of $P \Rightarrow Q$ with just this information. Is this the wrong assumption?  As a secondary question, how can the truthfulness of the statement $P \Rightarrow Q$ be variable, depending on context? I have read on some other questions that implication can be interpreted as a promise. So how could it be that depending on some context the promise is sometimes true but sometimes false? Wouldn't this actually mean the promise is not always consistent and is therefore always false?  Some further information in case it is relevant, I recognise that in the first example, the statement Q is 'dependent' in some way on the statement P, since the object under examination in both statements is $x$, whereas in the second example there are two different objects which I am trying to make a logical connection between, which I am thinking may not be valid for some reason. I also recognise that there is still 'context' in the first example, in that we need information on whether $x$ is equal to 2 or not, however in that case it doesn't matter, since $P \Rightarrow Q$ is always true anyway.  Thanks very much in advance. "Neither Michael nor Albert is correct" or "Neither Michael nor Albert are correct"? What is the correct sentence?  Neither Michael nor Albert is correct.   Neither Michael nor Albert are correct. Yesterday I started the upgrade from 12.10 to 13.04, but I interrupted it because it was taking too long. Now if I restart it, it doesn't proceed.  Is there any possibility to clean the mess it left when I interrupted it and make a clean restart of this update? Here's an image from another question:    I get what the pull down resistor is there to do, but I don't really understand exactly how it works.  When there is no voltage applied through the base wire, why does any induced current then go through R2, but when a voltage is applied, it goes to the transistor? My understanding is that voltage always follows the path of least resistance, so if applying say, 5v turns the transistor on, that means that the transistor has a lower resistance than R2, so I would also assume any induced current would also flow through the resistor - so why does it then go through R2? What are the various units (ex, em, in, pt, bp, dd, pc) expressed in mm? How can one determine the length of the different units (measured 1ex, 1em, 1in, 1pt, 1bp, 1dd, 1pc) in mm? My only problem is making them line up three-across and have equal spacing. Apparently, spans can not have width and divs (and spans with display:block) don't appear horizontally next to each other. Suggestions?  &lt;div style='width:30%; text-align:center; float:left; clear:both;'&gt; Is what I have now. why is the output of the following code coming to be zero? How do I start Nautilus as root? I've got a problem with Nautilus in Ubuntu 12.04 LTS.  When I run the command gksu nautilus /, the password ask box appears and I type my super-user password, then the password box disappears and Nautilus is not opened.  When I try to open Nautilus as a normal user in with the command nautilus, the folder is opened.  When I try in terminal   $ sudo nautilus   I got the following error  $ sudo nautilus /  ** (nautilus:8523): WARNING **: Command line `dbus-launch --autolaunch=2c8ce9b7da2257c2609b749700000007 --binary-syntax --close-stderr' exited with non-zero exit status 1: Autolaunch error: X11 initialization failed.\n Could not parse arguments: Cannot open display:   How can I fix this error? Is it possible to do a multiline pattern match using sed, awk or grep? Take for example, I would like to get all the lines between { and }  So it should be able to match    1. {}  2. {.....}  3. {.....      .....}  Initially the question used &lt;p&gt; as an example. Edited the question to use { and}. Can I ask questions about software application recommendations anywhere in the stackexchange system?  For example, I have a requirement, which will involve software and hardware.  I want to type this requirement up somewhere where possible readers will be able to recommend hardware and software solutions to my requirements? Show that $E(XE[X|G])=E[(E[X|G)^2]$ Realtek RTL8723BE Wi-Fi incredibly weak