How can I type/show the marking A(not just etalic) in math equation?  My working example is following and the mentioned A is appeared in the last of the code(last frame)-   \documentclass{beamer} \usepackage{tikz} \usepackage{amsmath} \usetheme{Madrid} \logo{%   %\includegraphics[width=1cm,height=1.5cm,keepaspectratio]{DUlogo}%   \includegraphics[width=1cm,height=1.5cm,keepaspectratio]{example-image-a}%   \hspace{\dimexpr\paperwidth-2cm-5pt}%   %\includegraphics[width=1cm,height=1cm,keepaspectratio]{GNR.png}%   \includegraphics[width=1cm,height=1cm,keepaspectratio]{example-image-b}% } \begin{document}   \title{Cross-Layer  Resource  Allocation with  elastic service scaling in Cloud Radio access network}   \author{   \parbox{2.5cm}{ \centering Md.Al-Helal\\Roll:SH-51}\hspace{1cm} \parbox{2.5cm}{ {\centering Jobayed Ullah\\Roll:EK-107}} } \institute{Computer Science \&amp; Engineering\\CSEDU} \begin{frame}   \maketitle \end{frame}   \title{Cross-Layer  Resource  Allocation with  elastic service scaling in Cloud Radio access network}   \author{Jianhua Tang\\ Wee Pen Tay\\ Tony Q. S. Quek} \institute{IEEE Transactions on Wireless Communications, vol 14, no. 9} \date{September 2015} \begin{frame}   \maketitle \end{frame}   \author{alhelal} \institute{CSEDU} \begin{frame}   \frametitle{Delay equation}   \begin{exampleblock}{}     \[       d_{i} = \frac{1}{\mu_{i}- \lambda_{i}} + \frac{1}{c_{i} - \lambda_{i}}   %    4545   \]   \end{exampleblock}   \centering   $d = \text{total delay}$\\ $\mu_{i} = \text{service rate}$\\ $\lambda_{i} = \text{arival rate}$\\   $c_{i} = \text{transmission rate}$\\ \end{frame} \begin{frame}   \frametitle{Equation}   \begin{exampleblock}{}    \[      \hat{x_{i}} = \sum_{j\in{A}}^{}h_{ij}^{H}w_{ij}x_{i} + \sum_{k\neq i}^{N}\sum_{j\in{A}}^{}h_{ij}^{H}w_{kj}x_{k} + \delta_{i}    \]   \end{exampleblock} \end{frame} %\begin{frame} %  \frametitle{Equation} %  \begin{exampleblock}{} %    \[ %    %SINR(A) = \frac{\lvert\sum_{j\in{A}}^{}h_{ij}^{H}w_{ij}\rvert^2}{\sigma_{i}^2 + \sum_{k\neq i}^{N}\lvet\sum_{j\in{A}}^{}h_{ij}^{H}w_{kj}\rvert} %%    SINR(A) = \sum_{j\in{A}}^{}h_{ij}^{H}w_{ij} %      34 %    %{\sigma_{i}^2 + \sum_{k\neq i}^{N}\lvet\sum_{j\in{A}}^{}h_{ij}^{H}w_{kj}\rvert} %     %  \] %  \end{exampleblock} %\end{frame} \begin{frame}   \frametitle{Equation}   \begin{exampleblock}{}    \[ %     \text{SINR}_{i}(A) = \frac{\lvert\sum_{j\in{A}}^{}h_{ij}^{H}w_{ij}\rvert^2}{\sigma_{i}^2 + \sum{k\neq i}^{N}     \text{SINR}_{i}(A) = \frac{\lvert\sum_{j\in{A}}^{}h_{ij}^{H}w_{ij}\rvert^2}{\sigma_{i}^2 + \sum_{k\neq i}^{N}\lvert\sum_{j\in{A}}^{}h_{ij}^{H}w_{kj}\rvert}    \]   \end{exampleblock} \end{frame} \end{document}
I know what my symbol or character looks like, but I don't know what the command is or which math alphabet it came from. How do I go about finding this out?
How can I find out which process is locking a file or folder in Windows?  For instance, when trying to delete a folder, Windows reports this:     The action can't be completed because the folder is open in another program   Happens the same with a file, but how do I find out what program or application is currently using it and preventing me from deleting the file or folder? Dark age of universe when all fusion process ceases? Some say we live in the golden age of the universe because there exits countless number of stars that shines in the dark universe. As the supply of gas for star formation is steadily being exhausted, it is estimated that star formation will cease in 100 trillion years.  Question: Will there be a day that the universe becomes completly dark when all the stars burn out? Does all the cooled bodies eventually collide due to gravitational forces? Will black holes eventually dominate the universe? Overriding the java equals() method - not working? I ran into an interesting (and very frustrating) issue with the equals() method today which caused what I thought to be a well tested class to crash and cause a bug that took me a very long time to track down.   Just for completeness, I wasn't using an IDE or debugger - just good old fashioned text editor and System.out's. Time was very limited and it was a school project.  Anyhow -   I was developing a basic shopping cart which could contain an ArrayList of Book objects. In order to implement the addBook(), removeBook(), and hasBook() methods of the Cart, I wanted to check if the Book already existed in the Cart. So off I go -  public boolean equals(Book b) {     ... // More code here - null checks     if (b.getID() == this.getID()) return true;     else return false; }   All works fine in testing. I create 6 objects and fill them with data. Do many adds, removes, has() operations on the Cart and everything works fine. I read that you can either have equals(TYPE var) or equals(Object o) { (CAST) var } but assumed that since it was working, it didn't matter too much.  Then I ran into a problem - I needed to create a Book object with only the ID in it from within the Book class. No other data would be entered into it. Basically the following:  public boolean hasBook(int i) {     Book b = new Book(i);     return hasBook(b); }  public boolean hasBook(Book b) {     // .. more code here     return this.books.contains(b); }   All of a sudden, the equals(Book b) method no longer works. This took a VERY long time to track down without a good debugger and assuming the Cart class was properly tested and correct. After swaapping the equals() method to the following:  public boolean equals(Object o) {     Book b = (Book) o;     ... // The rest goes here    }   Everything began to work again. Is there a reason the method decided not to take the Book parameter even though it clearly  was  a Book object? The only difference seemed to be it was instantiated from within the same class, and only filled with one data member. I'm very very confused. Please, shed some light? What happens when you plug two sides of a cable to a single networking device? What is likely to happen when you plug two ends of a network cable to a single switch/router? Will this create problems on the network, or just be ignored? Xml validation using XSD schema The following code helps me validate an XML file with an XSD schema.  XmlReaderSettings settings = new XmlReaderSettings(); settings.Schemas.Add(null, xsdFilePath); settings.ValidationType = ValidationType.Schema; settings.ValidationEventHandler += new System.Xml.Schema.ValidationEventHandler(settings_ValidationEventHandler); XmlDocument document = new XmlDocument(); document.Load(xmlFilePath); XmlReader rdr = XmlReader.Create(new StringReader(document.InnerXml), settings);  while (rdr.Read()) {  } isValid = true;   The ValidationEventHandler also tells me what the errors are, but doesn't tell me on 'where' or 'on which line' they are located. Is there any way to get the line number where the XML fails to be validated? How can you profile a Python script? How to find collisions in a hash function knowing its coefficent? Say I have a simple hash function where $x$ is a sequence of integers:  $$h(x)=(a_1\cdot x_1+...+ a_n\cdot x_n) \bmod N=\sum_i a_i\cdot x_i \bmod N$$  where $a_1,a_2,a_3,...,a_n$ is the coefficient known to the attacker, size of $x$ can be anything smaller than $N$.   How to find 2 different inputs that hashes to the same value, i.e $0$?  I feel like this has something to do with linear combination / euclid algorithm but I'm not sure how to proceed. Confidence Interval for variance given one observation This is a problem from the "7th Kolmogorov Student Olympiad in Probability Theory":     Given one observation $X$ from a $\operatorname{Normal}(\mu,\sigma^2)$ distribution with both parameters unknown, give a confidence interval for $\sigma^2$ with a confidence level of at least 99%.   It seems to me that this should be impossible. I have the solution, but haven't read it yet. Any thoughts?  I'll post the solution in a couple days.  [Follow-up edit: Official solution posted below. Cardinal's solution is longer, but gives a better confidence interval. Thanks also to Max and Glen_b for their input.] Desktop icons rearrange after using remote desktop connection I sometimes remote into my desktop PC (1900x1280) from my laptop (1280x900).  When I do, Windows (Vista) on the desktop PC rearranges all my desktop icons.  I could understand this if the RDP session's desktop size was too small to fit them in, but it's not.  I have about 12 icons, which do fit on the laptop's resolution (I've tried).  Why would Windows rearrange them all like this each time? If $H \leq G$ and $[G:H]! \leq |G|$ then $G$ is not simple Evaluate $\lim\limits_{x \to a} \frac{x^m-a^m} {x-a}$ What is the easiest way to encode a PHP string for output to a JavaScript variable?  I have a PHP string which includes quotes and newlines.  I need the contents of this string to be put into a JavaScript variable.  Normally, I would just construct my JavaScript in a PHP file, à la:  &lt;script&gt;   var myvar = "&lt;?php echo $myVarValue;?&gt;"; &lt;/script&gt;   However, this doesn't work when $myVarValue contains quotes or newlines. It is written everywhere that gravity is curvature of spacetime caused by the mass of the objects or something to the same effect. This raises a question with me: why isn't spacetime curved due to other forces or aspects of bodies?  Why isn't it that there are curvatures related to the charge of a body or the spin of particles or any other characteristics? Can I skip over releases when upgrading? I am currently using Ubuntu 10.04. I know there is a 10.10 release, but can I upgrade directly to 11.04? Could you walk me through the steps please? Let     $$ \mathbb{Z}^{'}_{\mathbb{C}}=\{ z \in \mathbb{C} | \exists f \in \mathbb{Z}[X] \text{ monic such that } f(z)=0\} $$   be the integral closure of $ \mathbb{Z} $ in $ \mathbb{C} $. Prove that $ \mathbb{Z}^{'}_{\mathbb{C}} $ is not finitely generated as a $ \mathbb{Z} $-module.  My attempt: Suppose $ \mathbb{Z}^{'}_{\mathbb{C}}=\mathbb{Z}\alpha_{1}+...+\mathbb{Z}\alpha_{n} $ for some $ \{ \alpha_{i}\}_{i=\overline{1,n}} \subset \mathbb{Z}^{'}_{\mathbb{C}} $. I know that given $ \alpha , \beta \in \mathbb{Z}^{'}_{\mathbb{C}} $ with minimal polynomials of degrees $ m $ and $ n $ respectively, then we can construct a monic polynomial with integral coefficients $ P(z)=\prod(z-(\alpha_{i}+\beta_{j})) $ where $ \alpha_{i},\beta_{j} $ are the conjugates of $\alpha $ , $\beta $ and therefore the minimal polynomial of $ \alpha + \beta $ has degree $ \leq mn $.   I was thinking that then the degrees of the minimal polynomials of the elements of $ \mathbb{Z}\alpha_{1}+...\mathbb{Z}\alpha_{n} $ could be somehow bounded by a certain constant, whereas $ \mathbb{Z}^{'}_{\mathbb{C}}$ contains elements whose degrees of the minimal polynomials are arbitrarily large, take $ 2^{\frac{1}{n}} $ for example,$ n\geq 2$. I think this works when we are asked to prove that the set of all algebraic numbers $ \overline{\mathbb{Q}} $ is not a finitely dimensional $\mathbb{Q}$-vector space, but I don't know how to proceed in my case.  I would really appreciate any ideas, hints or solutions. Thank you very much! Soundness vs completeness, am I understanding? And proving soundness? Allow setuid on shell scripts The setuid permission bit tells Linux to run a program with the effective user id of the owner instead of the executor:  &gt; cat setuid-test.c  #include &lt;stdio.h&gt; #include &lt;unistd.h&gt;  int main(int argc, char** argv) {     printf("%d", geteuid());     return 0; }  &gt; gcc -o setuid-test setuid-test.c &gt; ./setuid-test  1000  &gt; sudo chown nobody ./setuid-test; sudo chmod +s ./setuid-test &gt; ./setuid-test  65534   However, this only applies to executables; shell scripts ignore the setuid bit:  &gt; cat setuid-test2  #!/bin/bash id -u  &gt; ./setuid-test2  1000  &gt; sudo chown nobody ./setuid-test2; sudo chmod +s ./setuid-test2 &gt; ./setuid-test2  1000     Wikipedia :     Due to the increased likelihood of security flaws, many operating systems ignore the setuid attribute when applied to executable shell scripts.   Assuming I'm willing to accept those risks, is there any way to tell Linux to treat the setuid bit the same on shell scripts as it does on executables?  If not, is there a common workaround for this problem? My current solution is to add a sudoers entry to allow ALL to run a given script as the user I want it run as, with NOPASSWD to avoid the password prompt. The main downsides to that is the need for a sudoers entry every time I want to do this, and the need for the caller to sudo some-script instead of just some-script deploying and retrieving Address settings (State & Country picklists) I am trying to solve the exercises from the book Stochastic differential equations -An Introduction with applications by Bernt Oksendal and I am stuck on 1 question.  Prove directly from the definition of Ito's integral that   $$\int_0^t B_s^2 dB_s=\frac{1}{3}B_t^3-\int_0^t B_s ds$$  I have tried for a couple of hours but I simply cannot prove it . I would be grateful if somebody could help me out , even a hint would be very helpful What is the term for taking it out on someone even though you will be harmed by this too? When you are so mad at someone that you make a bad decision, even though you will be harmed by it as well, in order to harm that person; is there a good term for this?   For example burning $100 because he owns $20 of it.