How to show this equation below is true?  $$\int_{0}^{\infty}e^{-x}\ln^{2}x\:\mathrm{d}x=\gamma ^{2}+\frac{\pi ^{2}}{6}$$  Where $\gamma$ is the Euler-Mascheroni constant....
Is the proof of these identities possible, only using elementary differential and integral calculus? If it is, can anyone direct me to the proofs? ( or give a hint for the solution )  1)$$\int_0^\infty { e^{-x^2} \ln x }\,dx = -\tfrac14(\gamma+2 \ln 2) \sqrt{\pi} $$  2)$$\int_0^\infty { e^{-x} \ln^2 x }\,dx = \gamma^2 + \frac{\pi^2}{6} $$  3) $$\gamma = \int_0^1 \frac{1}{1+x} \sum_{n=1}^\infty x^{2^n-1} \, dx$$  and lastly,  4) $$\zeta(s) = \frac{e^{(\log(2\pi)-1-\gamma/2)s}}{2(s-1)\Gamma(1+s/2)} \prod_\rho \left(1 - \frac{s}{\rho} \right) e^{s/\rho}\!$$  I personally think the last is obtained from a simple use of the Weierstrass factorization theorem. I'm unsure as to what substitution is used.  $\gamma$ is the Euler-Mascheroni constant and $\zeta(s)$ is the Riemannian Zeta function.  Thanks in advance.
I am using ArcMap 10.1. The background: I have an .mxd that I intend to roll out across the company as our default template for all future maps/figure production. This .mxd contains two Data Frames; the first (&quot;Main&quot;) is larger (occupying almost the entire page) and is designed to be used to hold the majority of mapped data whilst the second (&quot;Inset&quot;) is much smaller and is to be used as an overview map. The problem: When choosing to import this new .mxd to an existing .mxd (using the Change Layout button on the Layout toolbar) the wizard automatically selects the smaller (&quot;Inset&quot;) Data Frame to occupy the larger part of the page. The screenshot below shows this interface with a red box indicating the two possible locations of each Data Frame:  Whilst it is possible to manually alter the order of the Data Frames using the Move Up or Move Down buttons, how do I change the default option for this setting (i.e. so that the &quot;Main&quot; Data Frame always appears in the larger space - &quot;2&quot;)? The reasoning is that I would like the process of using this new .mxd template to be as simple as possible, this is especially important as we have a wide range of users with varying abilities. Does anyone know how to choose/change this default setting? It does not appear to be in the Data Frame Properties &gt; Data Frame menu where I would expect it to be. Local TLD vs. .com and .com/nl vs .nl I basically have 2 questions about local TLD vs .com.  First question: There already exists a website "keyword.nl" with a crappy website, no SEO optimisation. Is it possible for a website "keyword.com" to rank higher than the "keyword.nl" website on "google.nl" when searching for "keyword"? Or will it always display the .nl website higher because it's a local TLD and the URL consists entirely and only from the searched keyword and it's searched on the .nl version of google?  Second question: I know it's good for SEO to have many websites link to your website. But I also read that local TLD's will score higher on that specific google TLD (.fr website will rank higher in google.fr, etc.) With both those facts in mind, is it better to create a "keyword.com/fr/" and "keyword.com/nl/" website or a "keyword.fr" and a "keyword.nl" website? (In other words, .com/langauge for more links to the website, or a "keyword.local-TLD" website for every different language version of the website) Or maybe even a subdomain? ("fr.keyword.com?")  Kinda new to this, so thanks in advance!  --Edit: additional info--  The reason that I phrased the original question like this is because I wanted to keep the question strictly "webmaster-side". However I feel like maybe I should clarify the background of this question more thoroughly, so the question becomes more clear, and thus the answer. But I don't know if this would make the question a more legal one instead of a "webmaster" one, so please correct me if this is the wrong place to post this question.  I'm a student working on websites in my sparetime, I have basic knowledge about SEO, but that was all local, for companies operating only in one country. However this time a friend contacted me who wants to found a company called "X" (e.g). He wants to ship/operate to multiple countries, but he will first found it (and he himself) lives in The Netherlands (.nl). However there already exists a company in The Netherlands called "x" with the website "x.nl". As far as I understood, the fact that both the companies are called "x" doesn't matter, in trademark/company registery terms, since they are both operating in different work sectors.    But the main issue here is, could my friends website "x.com/nl" outrank the "x.nl" on "google.nl" if you only search on the brand name; "x"?  @Closetnoc:  Hi, thanks a lot for your answer, it gave me some clarification however I feel you misunderstood my first question because of my use of "keyword.com" as an example URL. So I don't really know what conclussion I should draw from your first answer. I updated my question with additional info to clarify it more broadly. From your second answer this is what I understand: A .nl URL will not do that great on google.com, however a .com URL can do just as well as a .nl search on google.nl? So considering the info above, it's best to go with a x.com/fr and a x.com/nl URL, right? Please correct me if I misunderstood. However, if so, that still leaves the first question, if a "x.nl" is already taken, could a "x.com/nl" still outrank it at "google.nl"? Transfer game license So the problem is that account 1 and account 2 bought a game together, but account 1 isn't used anymore. Can we transfer the game license from account 1 to account 3?   The game was bought on account 1 and account 2 activated account 1 as primary. Alternatives to one-way ANOVA for heteroskedastic data I have data from 3 groups of algae biomass ($A$, $B$, $C$) which contain unequal sample sizes ($n_A=15$, $n_B=13$, $n_C=12$) and I would like compare if these groups are from the same population.  One-way ANOVA would definitely be the way to go, however upon conducting normality tests on my data, heteroskedascity seems to the main issue. My raw data, without any transformation, produced a  ratio of variances ($F_{\max} = 19.1$) which is very much higher than the critical value ($F_{\rm crit} = 4.16$) and therefore I cannot perform one-way ANOVA.   I also tried transformation to normalise my data. Even after trials of various transformations (log, square root, square), the lowest $F_{\max}$ produced after transformation with a $\log_{10}$ transformation was $7.16$, which was still higher compared to $F_{\rm crit}$.  Can anyone here advise me on where to go from here? I can't think of other methods of transformation to normalise by data. Are there any alternatives to a one-way ANOVA?  P.S.: my raw data are below:   A: 0.178 0.195 0.225 0.294 0.315 0.341 0.36  0.363 0.371 0.398 0.407 0.409 0.432     0.494 0.719 B: 0.11  0.111 0.204 0.416 0.417 0.441 0.492 0.965 1.113 1.19  1.233 1.505 1.897 C: 0.106 0.114 0.143 0.435 0.448 0.51  0.576 0.588 0.608 0.64  0.658 0.788 0.958 I am trying to pass a variable into jq like this '.Linux.date.$var' so far I have tried quoting them by name which is working fine. But I want to use variable to call them.  I have this, which is working fine  exectime=$(date -d now);     cp $check_exec_history $check_exec_history.tmp     jq --arg key1 true --arg key2 "$exectime" --arg name "$name" '.Linux.script_executed.first = $key1 | .Linux.date_executed.first = $key2' $check_exec_history.tmp &gt; $check_exec_history;      rm $check_exec_history.tmp;   I want to get to this, but not working:  name=first; exectime=$(date -d now); cp $check_exec_history $check_exec_history.tmp jq --arg key1 true --arg key2 "$exectime" --arg name "$name" ".Linux.script_executed.$name = $key1 | .Linux.date_executed.$name = $key2" $check_exec_history.tmp &gt; $check_exec_history;  rm $check_exec_history.tmp;   I came this far: using this answer  But I am not sure where I am doing mistake.  name=first; exectime=$(date -d now);     cp $check_exec_history $check_exec_history.tmp     jq --arg key1 true --arg key2 "$exectime" --arg name "$name" '.Linux.script_executed.name==$name = $key1 | .Linux.date_executed.name==$name = $key2' $check_exec_history.tmp &gt; $check_exec_history; rm $check_exec_history.tmp; Sending Text Cross Domain By Bookmarklet Why is it that they decided to make String immutable in Java and .NET (and some other languages)? Why didn't they make it mutable? I'm trying to use arcpy to save an .mxd and am having an issue.  It doesn't matter if I use mxd.save or mxd.saveACopy I get the same error.  I know it doesn't look like I am doing anything w/ it here, but it's just a portion of my code:  import arcpy import arcpy.mapping as map arcpy.env.overwriteOutput = True  env.workspace = r"C:\MGIS\FinalProject2.gdb     mxd = map.MapDocument(r"C:\MGIS\Finalproject2.mxd") df = map.ListDataFrames(mxd)[0]  for df in map.ListDataFrames(mxd): df.scale = 2000000  #Add layers into map document addLayer = map.Layer(OKXcounties) addLayer1 = map.Layer(contourLabelText) addLayer2 = map.Layer(contoursClipLyr) addLayer3 = map.Layer(clipOKXLyr) map.AddLayer(df, addLayer, "AUTO_ARRANGE") map.AddLayer(df, addLayer1, "AUTO_ARRANGE") map.AddLayer(df, addLayer2, "AUTO_ARRANGE") map.AddLayer(df, addLayer3, "AUTO_ARRANGE")  # Add contour Labels for lyr in map.ListLayers(mxd):     if lyr.name == "contourLabelText":         lyr.showLabels = True     if lyr.name == "Contour Features":         lyr.transparency = 100  mxd.saveACopy(mxd)   I get the following error:   Traceback (most recent call last):   File "C:\Python26\ArcGIS10.0\Lib\site-packages\pythonwin\pywin\framework\scriptutils.py", line 312, in RunScript     exec codeObject in __main__.__dict__   File "C:\MGIS\geog485\FinalProject2\mxdtest.py", line 7, in &lt;module&gt;     mxd.saveACopy(mxd)   File "C:\Program Files\ArcGIS\Desktop10.0\arcpy\arcpy\utils.py", line 181, in fn_     return fn(*args, **kw)   File "C:\Program Files\ArcGIS\Desktop10.0\arcpy\arcpy\_mapping.py", line 668, in saveACopy     self._arc_object.saveACopy(file_name) AttributeError: MapDocObject: Unable to save.  Check to make sure you have write access to the specified file and that there is enough space on the storage device to hold your document.   Space is not the issue, I have 60 GB of free space and I've checked the windows properties of the .mxd file.  Read-only box is unchecked and I've "allowed" all permissions for all groups:    Does anyone have any idea how if this is a bug or how I can fix this?  I'm using ArcInfo 10.0 SP4. When the ball is being bounced by the goalkeeper from his hands and a player steals it without touching the goalkeeper (while the goalkeeper is not touching the ball) and scores, is it legal or not?   shows what I'm talking about. What should main() return in C and C++? How do I calculate the date six months from the current date using the datetime Python module? I am using the datetime Python module.  I am looking to calculate the date 6 months from the current date. Could someone give me a little help doing this?  The reason I want to generate a date 6 months from the current date is to produce a review date.  If the user enters data into the system it will have a review date of 6 months from the date they entered the data. Basically, here's my MWE, and I need to include "Chapter" before every section title in the ToC (without changing anything else).      \documentclass[12pt]{article} \usepackage[utf8]{inputenc}  \usepackage[english]{babel} \usepackage[titles]{tocloft} \usepackage{titlesec} \usepackage{titletoc}  \addto\captionsenglish{ \renewcommand*\contentsname{\centerline{TABLE OF CONTENTS}}}  %\renewcommand{\thesection}{CHAPTER} %\renewcommand{\cftsecpresnum}{Chapter \thesection} \titleformat{\section}[display]% {\null\vskip1em\sffamily\bfseries\filcenter}{Chapter \thesection}{0em}{}[] \titlespacing*{\section}{0em}{1em}{1em}  \titlecontents{section} [1.5em] % ie, 1.5em (chapter) + 2.3em {} {\contentslabel{1em}} {\hspace*{-1.5em}} {\titlerule*[0.5pc]{.}\contentspage}  \begin{document} \newpage \tableofcontents \newpage  \section{Section One} \section{Section Two} Content \end{document}   The commented out code is what I've already tried. The first one just changes the number to "CHAPTER" and doesn't move the text in the ToC (so it just overlays on top of the name of the section), and if I include "\thesection" after "CHAPTER" it creates an infinite loop definition error. The second one causes no differences, and the code still compiles.  Thanks! I'm getting errors in a matrix equation. When I compile it looks fine, but I'd like to fix them so I don't have to press return for every error at compile time. The code for the equation is:  \begin{equation*}  \begin{bmatrix} U(1,t)  &amp; \cdots &amp; U(n,t) \\  \vdots &amp; \ddots &amp; \vdots \\ O_{n1} &amp; \cdots &amp; O_{nn}  \end{bmatrix} \times \begin{bmatrix} W(1,1)  &amp; \cdots &amp; W(1,n) \\  \vdots &amp; \ddots &amp; \vdots \\  W(n,1) &amp; \cdots &amp; W(n,n)  \end{bmatrix} = \begin{bmatrix}  D(1,t)  &amp; \cdots &amp; D(n,t) \\ \vdots &amp; \ddots &amp; \vdots \\ I_{n1} &amp; \cdots &amp; I_{nn} \end{bmatrix}  \end{equation*}   The errors I'm getting are related to missing $'s inserted. How can I know the default PGF line width? Is there some macro that will tell me what the default PGF line width is? I have tried creating my own macro by cloning \pgflinewidth before it has been modified, i.e.  \let\defaultlinewidth\pgflinewidth   but \defaultlinewidth seems to be affected by \pgfsetlinewidth anyway, and change to whatever \pgflinewidth is. So, the problem is that after I have called \pgfsetlinewidth, I don't know what the default pgf line width is anymore. Is there some way to get around this? How do I calculate the run rate in cricket? Admin password of MariaDb doesn't seem to work Execute a program at login How to include audio file in PDF How to prove the function is a constant Let $f\in C[0,1]$ be such  that $\forall \phi\in C[0,1]$ with $\int_0^1\phi \, dx=0$,we have $\int_0^1f\phi \, dx=0$.  Then $f$ is constant.  May be someone can help me proof this problem. Thanks! There several types of graphics files. In no particular order .jpeg .eps .pdf .png .tif .jif (and no doubt others). Some work with latex, dvips and some work with pdflatex. How am I supposed to know which?  Just to confuse matters, metapost produces .eps but I can use these with pdflatex as long as I put in a four line incantation.  Can anyone explain this?