Getting NullPointerException Error in Java
What is a NullPointerException, and how do I fix it?
Algorithms for computing multiplicative order modulo $n$ A group such that $a^m b^m = b^m a^m$ and $a^n b^n = b^n a^n$ ($m$, $n$ coprime) is abelian? Let $(G,.)$ be a group and $m,n \in\mathbb Z$ such that $\gcd(m,n)=1$. Assume that $$ \forall a,b \in G, \,a^mb^m=b^ma^m,$$ $$\forall a,b \in G, \, a^nb^n=b^na^n.$$  Then how prove $G$ is an abelian group?  Some context: Some of these commutation relations often imply that $G$ is abelian, for example , or . This looks like another example of this phenomenon, but the same techniques do not apply. After updating MiKTeX graphics package on 10/5/19 to version 1.3b (packaged on 10/4/2019 8:11:27 PM), I am unable to compile LaTex files that contain \includegraphics{}.  My system: Windows 10  with MiKTeX 2.9.7200  A minimum working example:  \documentclass{article} \usepackage{graphics}  \begin{document}  \begin{figure}    \includegraphics{MC_Antenna_Gain} \end{figure}  \end{document}   The error report   This is pdfTeX, Version 3.14159265-2.6-1.40.20 (MiKTeX 2.9.7200) entering extended mode (C:/Users/nicrog/Dropbox/T_P_2/Scholar/Grants/Written/EWU_20/Test.tex LaTeX2e &lt;2018-12-01&gt; ("C:\Program Files (x86)\MiKTeX 2.9\tex/latex/base\article.cls" Document Class: article 2019/08/27 v1.4j Standard LaTeX document class ("C:\Program Files (x86)\MiKTeX 2.9\tex/latex/base\size10.clo")) ("C:\Program Files (x86)\MiKTeX 2.9\tex/latex/graphics\graphics.sty" ("C:\Program Files (x86)\MiKTeX 2.9\tex/latex/graphics\trig.sty") ("C:\Program Files (x86)\MiKTeX 2.9\tex/latex/graphics-cfg\graphics.cfg") ("C:\Program Files (x86)\MiKTeX 2.9\tex/latex/graphics-def\pdftex.def")) No file Test.aux. ("C:\Program Files (x86)\MiKTeX 2.9\tex/context/base/mkii\supp-pdf.mkii" [Loading MPS to PDF converter (version 2006.09.02).] ) ("C:\Program Files (x86)\MiKTeX 2.9\tex/latex/oberdiek\epstopdf-base.sty" ("C:\Program Files (x86)\MiKTeX 2.9\tex/generic/oberdiek\infwarerr.sty") ("C:\Program Files (x86)\MiKTeX 2.9\tex/latex/oberdiek\grfext.sty" ("C:\Program Files (x86)\MiKTeX 2.9\tex/generic/oberdiek\kvdefinekeys.sty" ("C:\Program Files (x86)\MiKTeX 2.9\tex/generic/oberdiek\ltxcmds.sty"))) ("C:\Program Files (x86)\MiKTeX 2.9\tex/latex/oberdiek\kvoptions.sty" ("C:\Program Files (x86)\MiKTeX 2.9\tex/latex/graphics\keyval.sty") ("C:\Program Files (x86)\MiKTeX 2.9\tex/generic/oberdiek\kvsetkeys.sty" ("C:\Program Files (x86)\MiKTeX 2.9\tex/generic/oberdiek\etexcmds.sty" ("C:\Program Files (x86)\MiKTeX 2.9\tex/generic/oberdiek\ifluatex.sty")))) ("C:\Program Files (x86)\MiKTeX 2.9\tex/generic/oberdiek\pdftexcmds.sty" ("C:\Program Files (x86)\MiKTeX 2.9\tex/generic/oberdiek\ifpdf.sty"))) ! Undefined control sequence. \Ginclude@graphics ...\Ginput@path \set@curr@file                                                    {#1}\edef \uq@curr@file {\... l.8    \includegraphics{MC_Antenna_Gain}  ?    I will report this potential bug to  as well. divisibility of binomial coefficients by primes If $p$ is a prime number and $r = 1,2,3 \dots ,p -1$, how can I prove that the binomial coefficients $_nC_r(p,r)$ are divisible by $p$? By divisible I mean $_nC_r(p,r)/p$ leaves remainder $0$.  oivind Roots of unity filter, identity involving $\sum_{k \ge 0} \binom{n}{3k}$ How do I see that$$\sum_{k \ge 0} \binom{n}{3k} = (1 + 1)^n + (\omega + 1)^n + (\omega^2 + 1)^n,$$where $\omega = \text{exp}\left({2\over3}\pi i\right)$? What is the underlying intuition behind this equality? How can I protect my save data from casual hacking? What options are there for saving game data in a secure manner? I'm interested in solutions specifically tailored for C++.   I'm looking for something that is fast and easy to use. I'm only concerned about storing simple information such as   Which levels are and are not unlocked The user's score for each level   I'm curious again to know what's out there to use, any good libraries to use that give me nice, secure game data files that the average player can't mess with.   I just found  here which looks very nice, but it would be great to get some opinions on potential other libraries/options out there. A question occurred to me when browsing SE this evening, just curious.  What specifies the inside of a 3D construct? If I have a hollow sphere, what's to say that the world isn't the inside, and the center of the sphere isn't the outside. Picture the Asylum in the Hitchhiker's Guide to the Galaxy series, if you have read that.  Additionally, if the inside of a 3D object is defined as what is smaller than the outside, what happens when there is a a sphere with a volume equivalent to 51% of the universe? Can an integrated HDMI port work both ways? Say I had a laptop [Correction: notebook, don't want my thighs medium rare], any OS, and it has an HDMI port built into the side. Would it be remotely possible to hack it into an input, provided it wasn't already designed for that? I would figure all video ports operate straight off the graphics chip, however, are there ways to override that functionality on the driver level? Driver hacks already exist for plenty of things such as the classic example: Bluetooth adapters (so we can play with our PS3 controllers and save a buck) However, is HDMI one of these tamperable interfaces? As far as the interface standard is concerned, are HDMI ports designed to be either way or are they Input/Output specific? What does the dot product of two vectors represent? I know how to calculate the dot product of two vectors alright. However, it is not clear to me what, exactly, does the dot product represent.  The product of two numbers, $2$ and $3$, we say that it is $2$ added to itself $3$ times or something like that.  But when it comes to vectors $\vec{a} \cdot \vec{b}$, I'm not sure what to say. "It is $\vec{a}$ added to itself $\vec{b}$ times" which doesn't make much sense to me. E.g.  I know that I can browse the chat when I'm not logged on. But what if I am logged on and want to spare the inconvenience of logging off/multiple browsers? How to run a command that involves redirecting or piping with sudo? understanding "mount" as a concept in the OS I want to understand what mounting is. It is used in different contexts and situations and I can't find resources which:   Describe the mount concept Explain the actions taken by the computer/OS/utility when a mount is performed How and in which situations mount is used Which features in the Linux mount command are of frequent use and some examples   ( I hear mount applied to diverse entities directories, flash drives, network card, etc ) Highlight a word with jQuery Expectation values of the position operator is equal to zero in case of even potentials? Mint 18 will boot only to a black screen How do I specify unique constraint for multiple columns in MySQL? I'm having trouble editing this file on Windows 7:  C:\Program Files (x86)\CMake 2.8.7\share\cmake-2.8\Modules\FindJNI.cmake   If I edit it in Cygwin (vi) or TextPad, those two programs see the changes, so it's getting written to disk somewhere.  But if I "type" the file in a DOS cmd shell, it looks like the file hasn't been changed at all.  One thing I noticed is that in the cmd shell, the owner is Administrators, but in Cygwin's bash shell, the owner is Dan:  C:\Program Files (x86)\CMake 2.8.7\share\cmake-2.8\Modules&gt;dir /Q FindJ*  Volume in drive C is Windows7_OS  Volume Serial Number is 92CA-8707   Directory of C:\Program Files (x86)\CMake 2.8.7\share\cmake-2.8\Modules  12/30/2011  09:45 AM             1,480 BUILTIN\Administrators FindJasper.cmake 12/30/2011  09:45 AM             7,951 BUILTIN\Administrators FindJava.cmake 12/30/2011  09:45 AM            10,632 BUILTIN\Administrators FindJNI.cmake 12/30/2011  09:45 AM             1,669 BUILTIN\Administrators FindJPEG.cmake                4 File(s)         21,732 bytes                0 Dir(s)  132,524,654,592 bytes free   Dan@home /c/Program Files (x86)/CMake 2.8.7/share/cmake-2.8/Modules $ ls -al FindJ* -rwx------+ 1 Dan            None 10636 Jan 30 13:57 FindJNI.cmake -rwx------+ 1 Administrators None  1669 Dec 30 09:45 FindJPEG.cmake -rwx------+ 1 Administrators None  1480 Dec 30 09:45 FindJasper.cmake -rwx------+ 1 Administrators None  7951 Dec 30 09:45 FindJava.cmake   How can this be?  It's like there are two different files with the same name in the same directory. In the following method definitions, what does the * and ** do for param2?  def foo(param1, *param2): def bar(param1, **param2): I try to create a 2D game for Android. It looks like Cut the rope (it isn't a clone but it have same level representation) if it has a value. My problem that I can't understand that optimal sprite sizes I should use. I.e. what target screen resolution should I use to sprites didn't have anomalies on HD-devices (like Samsung Galaxy S7 and etc., phones and tablets)?    To make my question is clearer I ask about this 1 unit = X pixels for xxhdpi-screens. What is X?    P.S. Sorry if it's a duplicate I will be grateful for link on this post cuz I couldn't find it. Dropping one of the columns when using one-hot encoding