Must or should you use a hyphen in *Turing-complete* and *Turing-completeness?*
To hyphenate or not?
$ echo $(( 255 )) 255 $ echo $(( 33 )) 33 $ echo $(( ~33 )) -34 $ echo $(( ~255 )) -256 $    and my kernel is:  $ uname -a Linux HOSTNAME 3.2.0-40-generic-pae #64-Ubuntu SMP Mon Mar 25 21:44:41 UTC 2013 i686 i686 i386 GNU/Linux     QUESTION: ~ is for negating the number AFAIK. But why does ~33 produce -34 and why does ~255 produce -256? $G$ is a finite group such that $|G|=n$. Let $p$ be the smallest prime such that $p|n$. If $H\triangleleft G$ such that $|H|=p$, then prove that $H\subset Z(G)$.  My Work:  Since $|H|$ is a prime $H\cong \mathbb{Z}/(p)$. Hence $H$ is cyclic and abelian. I was stuck afterwards. Can anyone please give me a hint? Why does a light beam in a moving light clock follows a V shaped path? If I am standing on a platform moving along the X-axis and I throw a basketball vertically upward along the z-axis, the ball also travels along the x-axis. Does the same apply to a photon? According to a special relativity postulate  speed of light is not affected by the velocity of the inertial frame or the velocity of the emitter. If this postulate is true, shouldn't a photon fired vertically as above should travel only along the z-axis but not along the x-axis? How to make UV loft like 3ds Max in Blender using curves? I am try to make a car Body using the technique like UV loft in 3ds Max.  How to apply this technique in  Blender using curves or closer to this technique? I have seen this technique in a Blender tutorial, but I forgot about it. Is it implied that Porpetina and Queenie Goldstein are Jewish? Why does the order of the loops affect performance when iterating over a 2D array? How can I include value of sharepoint's version column in a word document? I'm trying to work out a way to display the contents of the version column from SharePoint (i.e. the value that changes every time a file is checked in) as a field (or something similar) inside of a Word document.  Ideally, I'd like to know how to configure SharePoint so I could click something like "Insert > Quick Parts > Document Property > Version", and it would include the version in the document.  The goal is to make it easier for someone to correlate a printed version of a document with the version history of SharePoint.  I have been able to add editable text columns to the Document content-type and have them show up as document property quick parts.  I've also been able to add a calculated column which gets the version as a text string... however this calculated column isn't showing up in Word as a document property.  (Perhaps I'm missing a setting on the calculated column) Samba+Windows: Allow multiple connections by different users? I have a machine running Ubuntu with Samba that I use to share stuff with my family's Windows machines in our local network.  Currently they access a share for movies/music/etc with one user.  I want to connect them to another share as a different user (for example, user "goytacaz").  When I try connecting to this new share, Windows gives me "Error 1219" and complains about multiple connections by the same user.  How do I get my machine to accept multiple connections by the same user? Is there a word to describe a person who likes chaos? I am wondering if there is a word to describe a person who likes chaos. By this I mean a few specific things:   The person is pleased to hear when chaos is created, or confusion emerges The person will take opportunities to create chaos or confusion The person enjoys taking part in chaotic or disorganized situations.   I can't seem to think of a word to describe the type of person who would act in this way.  I hope this question is clear.  EDIT: Below gbutters sums up nicely:     What I wonder is if there is a word for a generally good-natured person who just likes some good old-fashioned chaos. It seems like any person that thrives on chaos would have to have some extra baggage. How can I find out which apps I have already downloaded on my iPhone? When you attempt to download an app that costs money, you will not be charged if you already bought the app. After you press buy and enter your iTunes password, it will say "You have already purchased this item. To download it again for free, select OK."  The problem is that I deleted hundreds of apps from my phone, some of which were paid for. Later on I might find an app I like but notice that it costs money. It might be an app I had already paid for, or an app which I got when it was free.  How can I know if I tap the buy button if I will be charged for the app or not?  In other words, how can I know if I owned a previous version of an app before? How do I remove a malformed line from my sources.list? How to delete files listed in a text file Number theory in Physics As a Graduate Mathematics student, my interest lies in Number theory. I am curious to know if Number theory has any connections or applications to physics. I have never even heard of any applications of Number theory to physics. I have heard Applications of linear algebra and analysis to many branches of physics, but not number theory.  Waiting forward in receiving interesting answers! How to prove that if A, B, C are submodules of M module then $$ A \cap (B+C) = (A\cap B)+C \iff C \subseteq A $$  Any help would be appreciated! I have End Date column and I want to add 14 Days on it auto when created, can I do it by workflow? Can I do it via jQuery. If yes how? if no how I can do it? I have seen several times on TV documentaries where the presenter is taken to something like a library archive, and shown a book which they proceed to read an excerpt from.  On a couple of occasions the camera has shown the text they were reading and generally I have thought that I would struggle to read the words because of how the letters were formed (e.g. , or ).  This got me to wondering about how pronunciation and sentence formation may have changed over time as well, and how far back in time could I travel and still be understood while speaking my "modern" English in England (while obviously not talking about modern concepts like mobile phones or space travel)? Bash 'unbound variable' error when variables are referenced in multiline comment (set -u) I have an unexpected behaviour- following snippet fail with 'unbound variable' error:  #!/bin/bash set -u &lt;&lt;EOF a=a b=$a EOF   Tested on:  GNU bash, version 4.4.12(1)-release  GNU bash, version 4.2.46(2)-release How do you collect valuable information from regular "User Group" meetings? The scenario:   You work on a SaAS application.  Some of your users use your application heavily each day. Every 2 weeks (or month or whatever), a "User Group" of your most avid users gets together to talk shop and see how their progress is going in the context of a larger project they are working on. You can participate and potentially direct some group activities aimed at improving the application.   How do you gather valuable user information in this group setting? The  lists various combinatorial objects that are described by them. I posit that there might be bijections between these various combinatorial objects. For some of them (like Dyck paths, correctly matched parentheses and paths from the bottom left to top right of a $2n \times 2n$ grid) they are quite obvious.   I was then trying to find a bijection between the number of Dyck words and the number of ways of associating $n$ applications of a binary operator to $n+1$ items (third one on the list). I attempted to do this for a simple case ($n=3$ which is the example provided in the Wikipedia article). However, couldn't find one after multiple hours. Is it reasonable to expect such a bijection will exist? If so, how do we go about finding it?    EDIT: In addition to the very nice answer by @Marc, the following page also helped me see the bijection:   "Let $P$ be the Dyck path and $f(P)$ be the binary tree. If you go up in the Dyck path, create a left child. Otherwise, go up one vertex until creating a new right child is possible and create one."    Here is one of my attempts:   Number of Dyck words with length $2 \times 3$ is $\frac{6 \choose 3}{4} = 5$. They are:  hhhttt; hhthtt; hhttht; hthhtt; hththt  And the number of applications of a binary operator among $3+1=4$ factors is:  ((ab)c)d;     (a(bc))d;     (ab)(cd);     a((bc)d);     a(b(cd))  Both combinatorial objects have been arranged in a way that there is some kind of ordering between them. For the Dyck words for example, if h equals +1 and t equals -1, then the order is lexicographical from the left to the right of the cumulative score along the sequence.   Now, the first and last characters of the Dyck words are always h and t respectively. So, we can ignore them. We are left with:  hhtt; htht; htth; thht; thth  I tried to start from the left of the sequence abcd and if I see 'h', merge the character with the one to its right. This approach didn't produce a valid mapping from the third Dyck word to the third binary operator precedence order. Mysql strip time component from datetime I need to do a date comparison in Mysql without taking into account the time component i.e. i need to convert '2008-11-05 14:30:00' to '2008-11-05'  Currently i am doing this:  SELECT from_days(to_days(my_date))   Is there a proper way of doing this?