Why is energy calculated with respect to distance and not time?
Why does work depend on distance?
Proving that $(3n)!$ is divisible by $n! \times (n + 1)! \times (n + 2)!$ if $n$ is greater than 2 Prove that:  If $n$ is greater than 2, then $(3n)!$ is divisible by $n! \times  (n + 1)! \times  (n + 2)!$  From Barnard &amp; Child's "Higher Algebra".  I know that the highest power of a prime $p$ contained in $N$! is  $$ \left\lfloor{\frac{N}{p}}\right\rfloor + \left\lfloor{\frac{N}{p^2}}\right\rfloor + \left\lfloor{\frac{N}{p^3}}\right\rfloor ... $$  I'm unable to show that the formula above gives a higher value for $N = 3n$ than for the sum of its values when $N$ = $n$ , $n + 1$ and $n + 2$, considering the condition that $n &gt; 2$. What is the www-data user? Supersymmetry in Quantum Field Theory I have an idea of supersymmetry in quantum mechanics, can you suggest a book on "supersymmetry in quantum field theory", which has sufficient mathematical rigour like "Peskin and Schroeder" Windows 10 lets you 'schedule' a reboot for later. I want to disable it.  Evidently Windows scheduled itself for a reboot last night when I wasn't looking and just closed everything I had been working on the night before.  I reboot on the regular; I don't need Windows to do that for me.  Can I disable it completely? I don't mind if it downloads everything, and then says "hey, you should reboot," but it should never reboot itself, ever.  I'm using the "Pro" edition of Windows 10. Can Minecraft Pocket Edition play with a desktop Minecraft? My kids are playing Minecraft on 2 PCs, creative mode.  They are connected by the way of one of them starts a single player game on the other one than joins that game over the LAN.  Can I, using Minecraft PE on my iPad, join their game as well? What if I run a virus/trojan Windows EXE on Ubuntu with Wine? How to assign same Data to multiple object copies Is exponential map locally a diffeomorphism w.r.t. base point? Let $M$ be a riemannian manifold and $\exp_p: T_pM \rightarrow M$ the exponential map at $p \in M$.  At each point $p\in M$, $\exp_p$ can be restricted to a neighborhood $V$ of $0\in T_pM$ so that $\exp_p|_V$ is a diffeomorphism. Let $U\subset M$ denote image of $V$ under this map.  Choosing an orthonormal basis $\{E_i\}$ for $T_p M$ and using the isomorphism $E: \mathbb R^n \rightarrow T_pM$, where $E(x^1, \dots, x^n)= x^iE_i$, gives normal coordinates $(U, \phi)$, where  $$ \phi := E^{-1} \circ \exp^{-1}_p: U \rightarrow \mathbb R^n $$  My question is: can we fix some $z\in \mathbb R^n$ (small enough) and take some small neighborhood $\widetilde{U}$ of $p$ so that the function $\widetilde \phi$, defined as $$ \widetilde{\phi}_z (p) := \exp_p ( E(z)) $$ is a diffeomorphism when restricted to  $\widetilde{U}$?  (In the definition of $\widetilde \phi$, the isomorphism $E$ will also vary with $p$.) Proof of for-all / there-exists "negation"? I have installed a vlc in centos 6.5. I want to run it as root. But I get the following error,      "VLC is not supposed to be run as root. Sorry. If you need to use   real-time priorities and/or privileged TCP ports you can use   vlc-wrapper (make sure it is Set-UID root and cannot be run by   non-trusted users first)." vector space dimension of linear varieties Suppose $Y=Z(f_1,\cdots ,f_r)\subseteq \mathbb{A}^n_k$ where each $f_i$'s are linear homogeneous polynomials which are $k$-linear independent. Then $Y$ is also a vector space over $k$. My question: Is the vector space dimension of $Y$ is same as the dimension of $Y$ as an affine variety? If yes how?    Thank you. How can I take shallow depth of field photos with a point-and-shoot camera? iPhone 7 Plus takes days to turn on showing Apple logo or black screen I’ve had this issue for months but in the last couple of days it’s got very very bad.  When my phone runs out of battery it needs like 2–3 days to turn back on. At the beginning of this problem the phone would need about 1h. Every time when my phone goes off again the time to switching on goes up.  What does this all look like? Well, when my phone died I put it on the charger, then the logo appears and goes off. When it goes off, a black screen pops out with a little white line on in it, then it turns on back to Apple logo. It keeps doing this until it turns on which is 1 or 2 even now 3 days.  I tried to restore it and also update it but nothing happens, literally nothing happened. Is it normal for focal length to change while focusing? When I change the focus distance on my Pentax 55-300mm lens, the focal length appears to change.  More specifically, the lens appears to zoom in as I focus towards the minimum focusing distance.  This is most noticeable at the 55mm end of the lens.  Is this normal? 32-bit vs. 64-bit systems What are the differences between 32-bit and 64-bit systems?  If you have used both of them, what kind of sharp differences have you experienced?   Would it be a problem to use 32-bit programs on 64-bit systems in some cases? We know that continuous version of $\sum$ is $\int$, but, can there be a continuous version of $\Pi$? Auxhook warning cannot patch document using AtBeginDocument instead I'm using subfiles within my report (written on sharelatex), when I compile a subfile it produces a warning. Am I doing something wrong or is this normal?  Example  \documentclass[report.tex]{subfiles} % \usepackage{acronym} \begin{document}  some text  \end{document}   Error     /usr/local/texlive/2015/texmf-dist/tex/latex/oberdiek/auxhook.sty   Package auxhook Warning: Cannot patch \document, using \AtBeginDocument instead.   When I compile the main document it does not produce this warning.  The raw log file produces this warning     ......   Package: auxhook 2011/03/04 v1.3 Hooks for auxiliary files (HO)   Package auxhook Warning: Cannot patch \document,   (auxhook)                using \AtBeginDocument instead.   ) (/usr/local/texlive/2015/texmf-dist/tex/latex/oberdiek/kvoptions.sty   Package: kvoptions 2011/06/30 v3.11 Key value format for package options (HO)   ....    Packages  I'm using the following packages:    \documentclass[whitelogo]{tudelft-report}   % Used for referencing   \usepackage{natbib}   % For writing remarks in the text (is this going to be used?)   \usepackage{changes}   % used to write and render different subfiles   \usepackage{subfiles}   % used to draw boxed problems   \usepackage{mdframed}   % for subcaptions in combined figures   \usepackage{subcaption}    % used for Epigraphs of course   \usepackage{epigraph}   % Makes weblinks clickable   \usepackage{hyperref}   % used to display pictures   \usepackage{graphicx}   % used to add urls with strange symbols   \usepackage{grffile}   % used for H command in figures   \usepackage{float}   % used for tickz pictures (Causes a warning)   %\usepackage{pgfplots}   %used for the acronym page [printonlyused,withpage] are options   \usepackage{acronym}    % ######################### open section for code appendix #######################   \usepackage[utf8]{inputenc}   \usepackage{listings}   \usepackage{color}   \definecolor{codegreen}{rgb}{0,0.6,0}   \definecolor{codegray}{rgb}{0.5,0.5,0.5}   \definecolor{codepurple}{rgb}{0.58,0,0.82}   \definecolor{backcolour}{rgb}{0.95,0.95,0.92} Now that the , I've been seeing tag-only suggested edits from 1500-rep users.  For example, one had the summary of 'burninating [tagThatWasRemoved]'.  It's very tempting to reject these as Too Minor, but I know that these users used to have a Retag privilege (and are obviously trying to participate in a burnination.)  What should we do for tag-only edits from high(er) rep users? Are intermediate rings of finitely generated ring extensions also finitely generated? How do I print a double value with full precision using cout?