Exception in thread "main" java.lang.ArrayIndexOutOfBoundsException
Exception in thread "main" java.lang.ArrayIndexOutOfBoundsException
Does everything with mass or energy have a gravitational pull? Show $$\frac{(2n)!}{n!\cdot 2^n}$$ is an integer for $n$ greater than or equal to $0$.   Could anyone please help me with this proving? Thanks! Windows 7 time issues If we map every integer to a string that represents a rational number, and produce a number different from all the ones listed, we are essentially following Cantor's algorithm. But why does it not apply? Is it because we can't be certain that the number produced is a rational number? Where should collision detection logic be placed? I am developing a small 2D game engine. The characters have a paint method which currently does the following:   Calculate the new position of the character as per its speed, etc. Update the collision grid cell ** Draw the character at the new position   ** I have created a collision grid to reduce the number of intersection checks  Now the basic algorithm which I have thought for detecting collision is:   For Each Character     Check intersection with characters in surrounding 8 cells   I can simply place this code in the paint method. But here is the problem I anticipate.  Suppose two characters A and B lie in adjacent cells in the collision grid. Now as per the above algorithm in the iteration of character A it will detect that it has collided with B. In the iteration for character B it will detect that it has collided with A.  But I have an idea that when A detects that it has collided with B, it should inform B that it has collided with A. This would save lot of comparisons when there are more than 2 actors colliding. But I am not sure how to handle this. I think instead of every character checking for its collision, I should check for the collision inside the game loop.   Would this approach be correct? How have you handled this kind of problem? I thought of the collision grid thing myself. Are there any alternatives to collision grid logic? How to run adb and fastboot commands from Termux? Brackets in if condition: why am I getting syntax errors without whitespace? I have not idea how to approach this differential equation.   $$y'-\int_0^xy(t)dt=2$$.  Basically, I did,  $$F''(t)-F(x)+F(0)=2 \;\;\;\;\;\;\; F'=y$$  I am stuck.  Thank You. Can you determine a formula for this problem? Given $\frac{a}{c} + \frac{b}{d} = 1$ Prove that $$\lim_{(x,y)\rightarrow(0,0)} \frac{|x|^{a}|y|^{b}}{|x|^{c} + |y|^{d}}$$ does not exist.  So I have done the proof for strict inequalities. And the limit only exists when the fractions add up to an integer greater than $1$. I'm not sure how to approach this other than counter examples. Why didn't Thanos come to Earth to retrieve Tesseract by himself? In the Avengers movie, why didn't Thanos personally come to Earth instead of Loki? Or, if Loki's skills were required, why didn't he come with Chitauri? He knew that humans were primitive; there wouldn't be any threat and he could personally secure Tesseract.  AFAIK, the movie didn't display much. Is there any other source answering this? I have this table definition as part of a invoice  \begin{tabularx}{\textwidth}[ht]{lXrr}%   It worked fine for years until I have a very short word in the X column for the first time. Now my table is very small in width and centered horizontally on the page.  In my expectation the X column should fill up all space until the width of the table reaches the width of the page except the margins.  I have read about workarounds specifying something like 1.2\textwidth, but I don't like that, because the table is a template included via \include, so it would affect all my invoices.  I also tried \linewidth, \hsize and \columnwidth, but everything results in the same layout.  Is there a way to make the only X column expand so that it uses all available space?    Complete included table definition (Rechnungstabelle.tex):  \newcommand{\Rechnungstabelle}[4]{% vielen Dank für Ihren Auftrag. \noindent \begin{tabularx}{\textwidth}[ht]{lXrr}% \toprule% \bf{Anzahl} &amp; \bf{Bezeichnung} &amp; \bf{Einzelpreis} &amp; \bf{Gesamtpreis} \\% \midrule% #1% \bottomrule% &amp; \bf{Rechnungsbetrag}  &amp; &amp; \bf{\EUR{#2}} \\% \ifthenelse{\equal{#3}{}}{}{&amp; Enthaltene MwSt. 19\% &amp; &amp; \EUR{#3} \\}% \ifthenelse{\equal{#4}{}}{}{&amp; * Enthaltene MwSt. 7\% &amp; &amp; \EUR{#4} \\}% \end{tabularx}% }   Changing the table header row to  \bf{Anzahl} &amp; \bf{Bezeichnung} \hspace{\textwidth} &amp; \bf{Einzelpreis} &amp; \bf{Gesamtpreis} \\%   is a workaround, but I don't think that would be good TeX style.  Minimum example for reproducing:  \documentclass[ fontsize=12pt,                  paper=a4,                 foldmarks=TBMPL,                 fromalign=center,                 ngerman                 ]{scrlttr2} \usepackage{babel} \usepackage[utf8]{inputenx} \usepackage[right]{eurosym} \usepackage{tabularx} \usepackage{ltablex} \usepackage{booktabs} \usepackage{ifthen}  \input{Rechnungstabelle} \begin{document} \begin{letter}  \Rechnungstabelle{     1,0 h &amp; Do something &amp; \EUR{99,00} &amp; \EUR{99,00} \\      }     {99,00}     {}{} \end{letter} \end{document} Example of a relation that is symmetric and transitive, but not reflexive Can you give an example of a relation that is symmetric and transitive, but not reflexive?   By definition,   $R$, a relation in a set $X$, is reflexive if and only if $\forall x\in X$, $x\,R\,x$.  $R$ is symmetric if and only if $\forall x, y\in X$,  $x\,R\,y\implies y\,R\,x$. $R$ is transitive if and only if $\forall x, y, z\in X$, $x\,R\,y\land y\,R\,z\implies x\,R\,z$.    I can give a relation $\leqslant$, in a set of real numbers, as an example of reflexive and transitive, but not symmetric. But I can't think of a relation that is symmetric and transitive, but not reflexive. "Cannot find this file" error when deploying from Visual Studio 2010 I'm getting an error in Visual Studio 2010 after pressing F5 to Debug:     Error occurred in deployment step 'Add   Solution': Error: Cannot find this   file specified in the manifest file:   G2_SiteDefinition_List_Instances_Feature\ListInstance1\Elements.xml   But elements.xml file is there with the ListIntance1 folder. What am I missing here? Why do diamonds shine? Calculate mean of ordinal variable I've read in a number of places that calculating the mean of an ordinal variable is inappropriate. I'm trying to get an intuition for why it might be inappropriate. I think it is because, in general, an ordinal variable is not normally distributed and so calculating the mean will give an inaccurate representation. Could somebody give more detailed reasoning for why calculating the mean of an ordinal variable might be inappropriate? Switch statement fallthrough in C#? Synonym for "Fellow Sufferers"? Why is my attempt at downloading Big Sur failing? I am currently using a MacBook Pro 13&quot; Mid 2018 with Touch Bar. Today macOS Big Sur was released and I tried to download it but it's getting stuck at 484.4 MB. Initially, it shows 16-17 minutes left, but as soon as it reaches 484.4 MB it's stuck and the timer goes till 10 hours! My Wi-Fi is totally stable with a speed of 100 Mbps. I tried to restart my Mac but it still gets stuck. Earlier there were similar issues in the App Store (even now they are). The issue was I was not able to download an app unless I connect to the US VPN. I even contacted support but they were not able to help out. It wasn't a big deal as a VPN could be used. But now even with VPN, it gets stuck. What's a good SSH tunneling client for OS X? I've been using SSH Tunnel manager to easily set up and stop port tunneling over SSH to various servers at my company. That saved me the pain of opening up a new terminal window which will hang out there just for the sake of having a tunnel open.  This worked great (well , sort of) but SSH Tunnel Manager is a PowerPC application. With Lion, it is not supported any more.  What is a good replacement?