Period of small oscillations
Harmonic Motion
Unicode Regex; Invalid XML characters The list of valid XML characters is well known, as defined by the spec it's:  #x9 | #xA | #xD | [#x20-#xD7FF] | [#xE000-#xFFFD] | [#x10000-#x10FFFF]   My question is whether or not it's possible to make a PCRE regular expression for this (or its inverse) without actually hard-coding the codepoints, by using Unicode general categories. An inverse might be something like [\p{Cc}\p{Cs}\p{Cn}], except that improperly covers linefeeds and tabs and misses some other invalid characters. I understand there has been so much on this topic but I am still confused. I get that if the person is the subject it is who and anything else is whom. However, I'm really struggling to work out this rule for the following sentence:     The scope of which his account of morality applies to is therefore restricted to those whom/who the ‘notion of justification to a being of that kind makes sense.’   Should it be who or whom? I can't work out the subject and object. How to integrate $\int_0^{\infty} \frac{e^{ax} - e^{bx}}{(1 + e^{ax})(1+ e^{bx})}dx$ where $a,b > 0$. Add an "I don't understand" option for review audits "Yesterday" time specification shown when it was actually the day before yesterday When can we use 'much' in affirmative clauses? I found the below in  web-site:     We use much in questions and negative clauses to talk about degrees of something.      We don’t use much in affirmative clauses.   Also, it the same web-site, I found the following:     She runs much faster than he does.    also I noticed that some web-sites use much with affirmative clauses:     May we all be having this much fun and getting this much exercise when we're his age!    Is it Okey to use much in affirmative clauses? If yes, when can we use it? and what is the rules?  Update:  Here is another example on how often the word "much" is used  in informal style:     After much consideration I will NOT be performing at the Inauguration with my improv group Capitol Hill-arious I'm trying, but something is wrong with my code in LaTeX: \begin{asy} pair dynkinMark(real x, real y, string s = &quot;&quot;, pen p = defaultpen, pair B = dir(45)) { if (s != &quot;&quot;) { dot(&quot;$&quot;+s+&quot;$&quot;, (x,y), B, p); }     else { dot((x,y), p); }     return (x,y); }  dynkinMark(0,1, &quot;1&quot;, dir(135)); dynkinMark(0,2, &quot;2&quot;, dir(135)); dynkinMark(0,3, &quot;3&quot;, dir(135)); dynkinMark(0,4, &quot;4&quot;, dir(135)); dynkinMark(7,1, &quot;1'&quot;); dynkinMark(7,2, &quot;2'&quot;); dynkinMark(7,3, &quot;3'&quot;); dynkinMark(7,4, &quot;4'&quot;); path p1 = (0,1)..(2,2.0)..(5,3.5)..(7,4); path p2 = (0,2)..(2,1.2)..(5,2.5)..(7,3); path p3 = (0,3)..(2,2.8)..(5,1.5)..(7,1); path p4 = (0,4)..(2,3.8)..(5,3.5)..(7,2); draw(p1, blue); draw(p2, heavycyan); draw(p3, mediumcyan); draw(p4, lightblue); dot(&quot;$12$&quot;, IP(p1, p2), dir(90), heavygreen); dot(&quot;$13$&quot;, IP(p1, p3), dir(90), heavygreen); dot(&quot;$23$&quot;, IP(p2, p3), dir(90), heavygreen); dot(&quot;$14$&quot;, IP(p1, p4), dir(90), heavygreen); dot(&quot;$24$&quot;, IP(p2, p4), dir(90), heavygreen); real y = 0.8; label(&quot;$s_1$&quot;, (IP(p1,p2).x, y), heavygreen); label(&quot;$s_2$&quot;, (IP(p1,p3).x, y), heavygreen); label(&quot;$s_1$&quot;, (IP(p2,p3).x, y), heavygreen); label(&quot;$s_3$&quot;, (IP(p1,p4).x, y), heavygreen); label(&quot;$s_2$&quot;, (IP(p2,p4).x, y), heavygreen); \end{asy} How to do the same crop on a batch of photos? I've got a batch of photos (an owl coughing up a pellet in case you're curious).  I want to make an animated GIF out of them, but the result would be improved if they were all given an identical crop first.  I'm currently using Picasa for my basic photo editing on a Windows 7 PC.  While Picasa does have batch editing, crop is not one of the items on the batch menu.  Does Lightroom have a batch crop?  If there's a way to get Picasa to show me the coordinates of the crop selection rectangle, I could also use that information to do the same crop repeatedly.  Are there any tools that let you crop an animated GIF?  I know I can create the animated GIF by uploading the component images to Google+ and then looking in the Auto Awesome area. I don't know about tools for working with animated GIFs. Suppose the mean noon-time temperature for September days in San Diego is 24∘ and the standard deviation is 4.9. (Temperature in this problem is measured in degrees celsius)  On September 26, 1963, the all-time record of noon-time temperature in San Diego of 44∘ was hit. Assume the temperature distribution is symmetric around the mean, what is the Chebyshev bound for the probability of breaking (or tieing) this record?  I am having a hard time understanding this. Could someone explain to me how to do this? Directory-tree listing in Python Subdomain versus subdirectory I recently moved from having a main site like www.example.com with a subdomain associated site yyy.example.com, to moving everything off the subdomain to a subdirectory like www.example.com/yyy/, with the same hierarchy underneath the subdirectory, and now yyy.example.com is just a redirect page to the subdirectory, so yyy.example.com/abc/page-x is redirected to www.example.com/yyy/abc/page-x and so on.  The effect has been that the traffic increased by several times (the total page views are more than ten times at the present rate) what it was to the yyy subdomain. Previously almost all of the traffic to the yyy subdomain was from the www site. This is from monitoring the old yyy site for a year or more.  I'm curious to know if there's any research or results which would indicate whether this is universal (subdirectories beat subdomains) or "just me". Why were there 3-7-9 Rings of Power? How should "do my homework" questions be closed? (Missing "demonstrate minimal understanding") Just recently,  question was posted. Here's the body of the question:     Write a function called highlight() that prompts the user for a string. Your code should ensure that the string is all lower case. Next, prompt the user for a smaller 'substring' of one or more characters. Then replace every occurrence of the substring in the first string with an upper case. Finally, report to the user how many changes were made (i.e., how many occurrences of the substring there were).      What would a script for this be?   This is basically a "do my homework for me" style question. In the past, I would have voted to close this question for lacking minimal understanding and moved on. However, it looks like this close reason was removed, and I'm having difficulty figuring out which alternative to use (if at all).  Here were some of the close reasons I was considering, and ultimately decided against since they didn't seem to precisely match:   Duplicate of    I sort of doubt there exists a precise duplicate of this question -- the question is a fairly specific request for some code. I could maybe link to a duplicate question that answers a part of the original (for example, checking if the string is lowercase), but it wouldn't answer every aspect of the problem. Problem that can't be reproduced/typographical error    This sort of matches, since it asks the user to produce a SSCCEE, but doesn't really match since there isn't even a problem to begin with (and closing a question because I couldn't "reproduce" a non-existent problem feels a bit silly to me) Unclear what you're asking    It's pretty obvious what the user is asking -- I could produce a 5 line script in about 20 seconds that precisely matches his spec. Too broad    The text for "Too broad" states that "There are either too many possible answers, or good answers would be too long for this format". This doesn't apply to this question -- once again, the answer I could give would be fairly short and would closely resemble solutions other people would give.   So, what should I do here? Am I misunderstanding how the close reasons should now be used? Should I use the "other" close reason and explain that the OP should have put in more effort? Should I simply downvote, perhaps leave a comment, and move on? Or is the new policy to embrace these kinds of questions and just post an answer? I have a valid B1/B2 US visa expiring about a year from now. The passport it's in expired a few years ago, and I recently got a new one.   The passport number does not match, but the national ID number, mentioned in both, does (it used to be the same as your national ID, but not anymore)  Can I travel to the US carrying both passports? Or is it asking for trouble? (I read a few years ago that it was possible, but that might have changed)  Should I just get a new visa to avoid potential complications? How to generate a 2D array data structure in tikz? I need to illustrate a 2D array data structure in my document. This is a picture I found on the internet. I want something similar.    I also want to show the memory layout in the illustration. Something like this:   Can someone help me with drawing them in Tikz? Thanks in advance.  MWE  \documentclass{article} \usepackage[utf8]{inputenc} \usepackage{tikz} \usetikzlibrary{matrix,backgrounds}  \begin{document} \begin{tikzpicture}[font=\ttfamily, array/.style={matrix of nodes,nodes={draw, minimum size=7mm, fill=green!30},column sep=-\pgflinewidth, row sep=0.5mm, nodes in empty cells, row 1/.style={nodes={draw=none, fill=none, minimum size=5mm}}, row 1 column 1/.style={nodes={draw}}}]  \matrix[array] (array) { 0 &amp; 1 &amp; 2 &amp; 3 &amp; 4 &amp; 5 &amp; 6 &amp; 7 &amp; 8 &amp; 9\\   &amp;   &amp;   &amp;   &amp;   &amp;   &amp;   &amp;   &amp;   &amp;  \\}; \node[draw, fill=gray, minimum size=4mm] at (array-2-9) (box) {};  \begin{scope}[on background layer] \fill[green!10] (array-1-1.north west) rectangle (array-1-10.south east); \end{scope}  \draw (array-1-1.north)--++(90:3mm) node [above] (first) {First index}; \draw (array-1-10.east)--++(0:3mm) node [right]{Indices}; \node [align=center, anchor=south] at (array-2-9.north west|-first.south) (8) {Element\\ (at index 8)}; \draw (8)--(box); % \end{tikzpicture} \\ \begin{tikzpicture}[font=\ttfamily, array/.style={matrix of nodes,nodes={draw, minimum size=7mm, fill=red!30},column sep=-\pgflinewidth, row sep=0.5mm, nodes in empty cells, row 1/.style={nodes={draw=none, fill=none, minimum size=5mm}}, row 1 column 1/.style={nodes={draw}}}]  \matrix[array] (array) {  &amp;  &amp;  &amp;  &amp;  &amp;  &amp;  &amp;  &amp;  &amp; \\  &amp;   &amp;   &amp;   &amp;   &amp;   &amp;   &amp;   &amp;   &amp;  \\}; % \end{tikzpicture} \\ \begin{tikzpicture}[font=\ttfamily, array/.style={matrix of nodes,nodes={draw, minimum size=7mm, fill=blue!30},column sep=-\pgflinewidth, row sep=0.5mm, nodes in empty cells, row 1/.style={nodes={draw=none, fill=none, minimum size=5mm}}, row 1 column 1/.style={nodes={draw}}}]  \matrix[array] (array) {  &amp;  &amp;  &amp;  &amp;  &amp;  &amp;  &amp;  &amp;  &amp; \\  &amp;   &amp;   &amp;   &amp;   &amp;   &amp;   &amp;   &amp;   &amp;  \\}; % \end{tikzpicture} \end{document} Repeatedly taking differences on a polynomial yields the factorial of its degree? Prove: If $a\mid m$ and $b\mid m$ and $\gcd(a,b)=1$ then $ab\mid m$ Prove: If $a\mid m$ and $b\mid m$ and $\gcd(a,b)=1$ then $ab\mid m$  I thought that $m=ab$ but I was given a counterexample in a comment below.  So all I really know is $m=ax$ and $m=by$ for some $x,y \in \mathbb Z$. Also, $a$ and $b$ are relatively prime since $\gcd(a,b)=1$.   One of the comments suggests to use , i.e., $aq+br=1$ for some $q,r\in\mathbb{Z}$. Any more hints?  New to this divisibility/gcd stuff. Thanks in advance! Are there difference between those sentences?        Alex is getting married next month.     Alex will get married next month.      Seems that the first one is expressed in present continues, and the second on in future tense. Am I correct? Correct ssh config file settings to tunnel to a 3rd machine I'm trying to tunnel to a server via a bridge server. So far, I've been able to get it working from the command shell properly using the following command:  ssh -A -t bridge_userid@bridgemachine.com ssh -A remote_userid@remoteserver.com   But I've been trying to wrap this into my ~/.ssh/config file and I have troubles. I've tried:  Host axp   User          remote_userid   HostName      remoteserver.com   IdentityFile  ~/.ssh/id_rsa.eric   ProxyCommand ssh -A -t bridge_userid@bridge_userid.com ssh -A remote_userid@%h   But when I do, I get the following error message from remoteserver.com and I'm not sure what is causing it:     ksh: SSH-2.0-OpenSSH_6.8^M:  not found   I know that when I log into remoteserver.com , my shell is /usr/bin/ksh.  I've tried to add path arguments to the ssh commands in the config file, but it made no difference.  Any ideas what it can be? Proving there is a sequence convergent to a limit point of a set without axiom of countable choice? Often, we use a construction like this: Given a subset $ A $ of a metric space and its limit point $ a $, we know that for every $ \epsilon &gt; 0 $ there is another point $ x $  different from $ a $ such that $ d(x,a) &lt; \epsilon $. So for every natural $ n $ we let $ a_n $ be such a point within $ 1/n $ of $ a $, which gives us a sequence convergent to $ a $.  My question is, is the axiom of countable choice needed for this construction, or is it formally correct just in ZF?