Adding Arabic sources to my bibliography Should I dedicate a separate part in my bibliography for my Arabic sources and thus write them in Arabic letters, or should I transliterate them and include them within the whole bibliography like any other source. I've searched the latest version of MLA (8th. ed.) and found nothing relevant. Could anybody help me, please?
How should references in non-Latin script language be treated in English paper? Let's say I want to cite a Russian text in my own paper which is written in English. Should I:   reference it as is, in the original Cyrillic alphabet, although the readers won't be able even to pronounce it? transliterate the authors' names, while keeping the rest as is? transliterate the names and translate the title of the work, journal name, etc. into English?
How to use an item in my off-hand? I am encountering two definitions of the special orthogonal lie algebra, and I would like to know if they are equivalent, and if there are advantages to working with one over the other.  If we begin with an $n$-dimensional vector space $V$ over a field $k$ and a chosen basis, we can define a bilinear form on $V$ by a matrix $S\in M_n(k)$, ie, let $\langle v,w\rangle=v^tSw$ for all $v,w\in V$.  Now $g\in GL_n(k)$ preserves the form ($\langle g(v),g(w)\rangle=\langle v,w\rangle$) if and only if $g^tSg=S$, so all such $g$ form a linear algebraic group $G$.  The tangent space at the identity of $G$ will be contained in that of $GL_n(k)$, so $T_eG\subset T_eGL_n(k)=M_n(k)$, and in fact, $T_eG=\{B\in M_n(k)\mid B^tS+SB=0\}$.  $T_eG$ becomes a lie algebra, $Lie(G)$, if we define the bracket to be the commutator of two matrices.  Now, if $S=I_n$, it follows that $G=O_n(k)$ is the orthogonal group of matrices satisfying $g^tg=I_n$, and $Lie(G)=\mathfrak{so}_n$ is the lie algebra of antisymmetric matrices.  In Humphrey's Introduction to Lie Algebras and Representation Theory, he defines $\mathfrak{so}_n$ to be all matrices $B$ satisyfing $B^tS+SB=0$, where $$ S=\begin{pmatrix} 1&amp;0&amp;0\\ 0&amp;O&amp;I_l\\ 0&amp;I_l&amp;O \end{pmatrix} \hspace{.5in}\text{or}\hspace{.5in} S=\begin{pmatrix} O&amp;I_l\\ I_l&amp;O \end{pmatrix} $$ depending on the parity of $n$.  The matrices obtained in this way are not antisymmetric, nor is the group $G$ preserving the form defined by $S$ the orthogonal group $O_n(k)$.  Are the two groups obtained from considering different $S$ isomorphic?  Are the two lie algebras isomorphic?  If so, why would one prefer one form to the other? Following the guidelines suggested in , I am going to post a proposed proof as an answer to the theorem below. I believe the proof works, but would appreciate any needed corrections.  Theorem If a series $\sum_{n=1}^{\infty}a_n$ of real numbers converges then $\lim_{n \to \infty}a_n = 0$ Are orbiting planets an  example of perpetual motion? Number theory proof mod p For a given prime $p$ and integer $k$,  $k∈&lt;1, p-1&gt;$ $S(k)$ is defined as a sum of remainders of $k, k^2, k^3, ..., k^{p-1}$ when divided by $p$. Prove that $S(k)=\frac{1}{2}p(p-1)$ is true for an odd number of different k. I managed to prove that $S(p-1)=\frac{1}{2}p(p-1)$ but can't see how to do it further. How can I remove whitespace when declaring an XSL variable? I have just discovered that my local bank, Nordea, has decided to remove the only good thing about their entire operation: the so-called "simplified login" feature on their website, which allows (soon allowed) the customer to log in to a kind of very limited "read-only" mode which basically just allowed you to see your current balance, the last few transactions (limited descriptions) and see whether or not there are any new "customer support messages", but not read those messages, not make any kind of payments, edit accounts, etc.  Now, they will only allow "full" logins, which 100% prevents any kind of automation and requires you to sit with a hardware device and enter numbers into it and then into the webpage before it allows you to see as much as your account balance. Other than being very obnoxious for every customer, it also blocks me and other "advanced" users out from our custom-programmed bots which have always regularly logged in with that "simplified" login method just to regexp out the current balance/new messages and then notify us via whatever mechanism we use privately.  I have previously asked them if they have any kind of JSON/RSS API of any kind, but no. They don't even have as much as e-mail notifications! Nothing except their spyware "smartphone app" which I would never install, nor would I ever allow such a surveillance device to track me 24/7 in the first place. Only by being a registered corporation with special, way more costly account types do you get any kind of "API" access from them, even to do this most basic imaginable task.  Before you tell me to switch banks, the others are at least just as bad (even worse from what I can tell, and for a longer time), and the act of switching banks is practically impossible for me personally.  What I'm asking is if maybe somebody knows of some sort of "hidden standard" or something which all banks in the world support, but don't have documented, for people like me to automate basic things such as knowing my account balance. Needless to say, I have looked for this countless times on their website, asked them about it, and asked other people about it. Nobody seems to know anything, or, if they do, won't tell me.  I know that there are a bunch of "Nordea-supporting" PHP libraries and whatnot on Github, but they are all ancient and even if they were up to date, they were most likely using the same method as I have been using: automating the login process through their "simplified login" mechanism, which is "soon" to be gone. (Probably at new year; they didn't even mention any dates or time frames.)  And yes, I have a Bitcoin wallet and have that fully automated. The problem is that virtually nobody else in the world cares about my Bitcoin, so "switching to Bitcoin" remains a pipe dream which I would be ready to do, but the world clearly isn't. Undefined control sequence error on \fancy@reset, \f@ncyolh and \f@ncyorh when using newlfm class I updated to TeXLive 2017 and couldn't get newlfm.cls to work without errors.  Here is a minimal example:  \documentclass{newlfm} \begin{document} \begin{newlfm} \end{newlfm} \end{document}   LaTex is throwing undefined control sequence errors on \fancy@reset, \f@ncyolh, and \f@ncyorh.  What causes the errors?  What am I missing? I often find  syntax very helpful, e.g. process substitution like in diff &lt;(sort file1) &lt;(sort file2).  Is it possible to use such Bash commands in a Makefile? I'm thinking of something like this:  file-differences:     diff &lt;(sort file1) &lt;(sort file2) &gt; $@   In my GNU Make 3.80 this will give an error since it uses the shell instead of bash to execute the commands. Prove $f(S \cup T) = f(S) \cup f(T)$ My Android phone is completely reset, whats the best way to recover the deleted data? My interest in combinatorics was recently sparked when I read about the many things that the Catalan numbers count, as found by Richard Stanley. I picked up a copy of Brualdi's Combinatorics, and while browsing the section on counting sequences I found a nice little puzzle that has definitely puzzled me.     Let $m$ and $n$ be nonnegative integers with $n\geq m$. There are $m+n$ people in line to get into a theater for which admission if $50$ cents. Of the $m+n$ people, $n$ have a $50$-cent piece and $m$ have a $\$ 1$ dollar bill. The box offices opens with an empty cash register. Show that the number of ways the people can line up so that change is available when needed is   $$ \frac{n-m+1}{n+1}\binom{m+n}{m}. $$     I first noted that the first person to enter must be one of the $n$ with a half-dollar. Now the register has a half-dollar change. The second person can be either a person with a half-dollar or a dollar. In the first case, the register will now have two half-dollars, in the second case, the register will now have one dollar bill. So it seems to me that when one of the $n$ people with a half-dollar enters, the number of half-dollars in the register increases by $1$, and when one of the $m$ people with a bill enters, the number of half-dollars decreases by $1$ but the number of bills increases by $1$.   I tried to model this by looking at paths in $\mathbb{Z}^2$. The $x$-axis is like the number of half-dollars, and the $y$-axis is the number of bills. You start at $(0,0)$, and you can take steps forward $(1,0)$ or backwards diagonally $(-1,1)$ corresponding to who enters, but you must always stay in the first quadrant of the plane without crossing over the axes. The goal is to make $m+n$ moves, and I figured maybe the number of such paths is counted by $\frac{n-m+1}{n+1}\binom{m+n}{m}$, but I'm not sure how to show this. I don't know if this observation simplifies the problem at all, as I don't know how to finish up. I'd be happy to see how this problem is done, thank you. I would like to prove that : If $H$ is a subgroup of $G$ and $K$ is a subgroup of $H$, then  $$|G:K|=|G:H||H:K|$$  I appreciate any clear explanation of this. Thanks ! A customer running Windows 7 Home must have reserved or okayed the Windows 10 upgrade because I am seeing daily messages that the upgrade is failing to install.   This customer is not ready for Windows 10 so it's good that the install is failing. But how to make it stop trying?  Once permission is granted for the upgrade, how do I revoke that permission so it stops attempting to upgrade?  I ran the Windows Update troubleshooter to clear out updates, and I uninstalled and hid KB3035583, but it is still trying to upgrade. In Task Manager, there is no GWX.EXE process.  Event log failure message:  Log Name:      System Source:        Microsoft-Windows-WindowsUpdateClient Date:          8/5/2015 1:28:58 AM Event ID:      20 Task Category: Windows Update Agent Level:         Error Keywords:      Failure,Installation User:          SYSTEM Description:   Installation Failure: Windows failed to install the following update with                 error 0x80240020: Upgrade to Windows 10 Home.   Relevant lines from WindowsUpdate.log:  2015-08-05  01:28:57:885    1068    6698    Agent   ************* 2015-08-05  01:28:57:885    1068    6698    Agent   ** START **  Agent: Installing updates [CallerId = AutomaticUpdates] 2015-08-05  01:28:57:885    1068    6698    Agent   ********* 2015-08-05  01:28:57:885    1068    6698    Agent     * Updates to install = 1 2015-08-05  01:28:57:885    1068    6698    Agent     *   Title = Upgrade to Windows 10 Home 2015-08-05  01:28:57:885    1068    6698    Agent     *   UpdateId = {27E79986-1150-4342-BDD2-76DF82C768D5}.201 2015-08-05  01:28:57:885    1068    6698    Agent     *     Bundles 1 updates: 2015-08-05  01:28:57:885    1068    6698    Agent     *       {FCD6621E-F5D4-4A95-AD43-28F0C58DD2F3}.201 2015-08-05  01:28:58:181    1068    6698    DnldMgr Preparing update for install, updateId = {FCD6621E-F5D4-4A95-AD43-28F0C58DD2F3}.201. 2015-08-05  01:28:58:181    27280   6f84    Misc    ===========  Logging initialized (build: 7.6.7601.18917, tz: -0700)  =========== 2015-08-05  01:28:58:181    27280   6f84    Misc      = Process: C:\Windows\system32\wuauclt.exe 2015-08-05  01:28:58:181    27280   6f84    Misc      = Module: C:\Windows\system32\wuaueng.dll 2015-08-05  01:28:58:181    27280   6f84    Handler ::::::::::::: 2015-08-05  01:28:58:181    27280   6f84    Handler :: START ::  Handler: Windows Setup Install 2015-08-05  01:28:58:181    27280   6f84    Handler ::::::::: 2015-08-05  01:28:58:181    27280   6f84    Handler   : Updates to install = 1 2015-08-05  01:28:58:181    1068    5ecc    AU  &gt;&gt;##  RESUMED  ## AU: Installing update [UpdateId = {27E79986-1150-4342-BDD2-76DF82C768D5}] 2015-08-05  01:28:58:181    1068    5ecc    AU    # WARNING: Install failed, error = 0x80240020 / 0x00000000 2015-08-05  01:28:58:181    27280   6f84    Handler   : WARNING: Exit code = 0x80240020 2015-08-05  01:28:58:181    1068    5ecc    AU  Write OSUpgradeState =14 with OSUpgradephase =2 2015-08-05  01:28:58:181    27280   6f84    Handler ::::::::: 2015-08-05  01:28:58:181    27280   6f84    Handler ::  END  ::  Handler: Windows Setup Install 2015-08-05  01:28:58:181    27280   6f84    Handler ::::::::::::: How to horizontally center an element Formatting Ticks and FrameTicks labels with a function Which Stack Exchange site is best for AutoCAD questions? How to add a description to the user name input field in the registration form? I want a description under the user name input field in the Wordpress registration form like in the next example. How can I do this?  //create an extra field in login page for invitation code add_action( 'register_form', 'add_invitation_code_field' );  function add_invitation_code_field() {    ?&gt;       &lt;p&gt;          &lt;label for="invitation_code"&gt;             Invitation code             &lt;input id="invitation_code" class="input" type="text" size="20" value="" name="invitation_code"/&gt;             &lt;span class="description"&gt;&lt;?php _e("Description text"); ?&gt;&lt;/span&gt;          &lt;/label&gt;       &lt;/p&gt;    &lt;?php } I thought of this a while ago, but can't make up a proof or a counterexample. Does anyone know more about this?  $$\sqrt{a+b}  \le \sqrt a + \sqrt b , \forall a,b \in \mathbb R_+$$  Moreover, what happens with more variables? Say:  $$\sqrt{x_1+x_2+...+x_n} \le \sqrt x_1 +\sqrt x_2 + ... + \sqrt x_n $$  with $ x_i \in\mathbb R_+ \forall i \in \{1,2,...,n\} $  Or when $i = \mathbb N$  PS: I tried looking on the internet for this but I don't know how I would call this. Can I travel to Schengen countries that were not on my itinerary when I applied?