Combining two means and SDs of one group
Combining two covariance matrices
Hello,   I create an app using the Promoted Links in Sharepoint 2013. I chose to do this because the feature has the awesome hover effect and is easy to customize the image.  The issue is that I have been trying to figure out how to change the tile sizes. They are awesome the way they are, however I just need them smaller. I still want the hover effect as well and for the text to match the same ratio as the tile. I have tried web zones, I have done each ID but with no luck. I have attached a sample image of the tiles I'm referring to. Please help. WinForms: How to programmatically fire an event handler? Size commands do not work in mathmode MWE:  \documentclass{article} \begin{document} $\wedge{\small\wedge}{\tiny\wedge}$ \end{document}   All the \wedges have the same size... I get how a normal fork bomb works, but I don't really understand why the &amp; at the end of the common bash fork bomb is required and why these scripts behave differently:  :(){ (:) | (:) }; :   and   :(){ : | :&amp; }; :   The former causes a cpu usage spike before throwing me back to the login screen. The latter instead just causes my system to freeze up, forcing me to hard reboot. Why is that? Both continually create new processes, so why does the system behave differently?   Both of the scripts also behave differently from  :(){ : | : }; :   which doesn't cause any problems at all, even though I would have expected them to be alike. The bash manual page states that the commands in a pipeline are already executed in a subshell, so I'm led to believe that : | : should already suffice. I belive &amp; should just run the pipeline in a new subshell, but why does that change so much?  Edit: Using htop and limiting the amount of processes, I was able to see that the first variant creates an actual tree of processes, the second variant creates all the processes on the same level and the last variant doesn't seem to create any processes at all. This confuses me even more, but maybe it helps somehow? How do I format a number in Java? How do I format a number in Java? What are the &quot;Best Practices&quot;? Will I need to round a number before I format it?  32.302342342342343 =&gt; 32.30 .7323 =&gt; 0.73  etc. Quick directory navigation in the bash shell Why can't a Federation Starship's transporter history be used to bring someone back to life? How to secure Elliptic Curve ElGamal encryption against known plaintext attacks? If I have an encoding function  $f(x)$ that maps a message $m$ to a point $P$ on a suitable Elliptic Curve $E$ . If I have the public key $Q$ of my recepient then I can encrypt the message as follows:  Choosing a random number $k &lt; n -1 $ where $n$ is the order of the curve E .  Calculating $C = [k] G $ where $G$ is the generator point of the curve E   Calculating $R = [k]Q $ where $Q$ is the recipient's public key   Now the message is encrypted by adding $P$ to $R$ to get          $C_e$ $( = R + P)$ which is sent along with $C$ to the recepient.  DECRYPTION:  Now for the recepient to decrypt my message they compute $R = [privatekey] C $ (where $C = [k]G $) and simply subtract $R$ from $C_e$ to get the encoded point $P$ back which is then decoded by an inverse function $f^{-1}(x)$ to recover $m$.  Now , two problems arise : If the attacker knows the plaintext (suppose if I follow a particular format of data while sending messages ) he could encode his guessed plaintext and subtract it from $C_e$ to recover $ R $ back ! . If I used that same $ R  $ to encrypt further "blocks" of my message then the security of the later parts of my message has been breached!   I realize that doing  something like a scalar multiplication over and over again for every block of data, would be a huge drawback in efficiency and speed.   Is there any way to compute a different $ R $ for every block of data, without using much resources and that too quickly ?   Does reusing the same $R$ for another message break security ?  NOTE: This question is for educational purposes only. It's for the sake of expanding my knowledge on Crypto. If $\sum_na_n=\infty$ and $a_n\downarrow 0$ then $\sum\limits_n\min(a_{n},\frac{1}{n})=\infty$ If $\sum_na_n=\infty$ and $a_n\downarrow 0$ then $\sum\limits_n\min(a_{n},\frac{1}{n})=\infty$     My  idea:  $$b_{n}=\min(a_{n},\tfrac{1}{n})\Longrightarrow b_{n}\le a_{n},b_{n}\le\tfrac{1}{n}$$ then I don't know how to go on. Three linked question on non-negative definite matrices. 1.a symmetric matrix in $\mathbb{M}_n(\mathbb{R})$ is said to be non-negative definite if $x^Tax≥0$ for all (column) vectors $x\in \mathbb{R}^n$. Which of the following statements are true? (a) If a real symmetric $n\times n$ matrix is non-negative definite, then all of its eigenvalues are non-negative. (b) If a real symmetric $n\times n$ matrix has  all of its eigenvalues are non-negative , then it is non-negative definite. (c) If $ A\in \mathbb{M}_n(\mathbb{R})$, then $AA^T$ is non-negetive definite. 2. only one of the following matrices is non-negetive definite. Find it. (a) $\begin{pmatrix} 5 &amp; -3 \\ -3 &amp; 5 \end{pmatrix}$. (b) $\begin{pmatrix} 1 &amp; -3 \\ -3 &amp; 5 \end{pmatrix}$. (c) $\begin{pmatrix} 1 &amp; 3 \\ 3 &amp; 5 \end{pmatrix}$.      3.let $B$ be the real symmetric non-negative definite $2×2$ matrix such that $B^2=A$ where $A$ where is the non-negetive definite matrix in question $2$.write down the characteristic polynomial of $B$.      My thoughts..  For1.  (a) &amp; (b) are true but not sure about (c). For 2. (a) is the correct option since it has all positive eigen values.they are $2,8$. For 3. Eigen values of $B$ will be $\sqrt{2}$ and $\sqrt{8}$. So the answer is $x^2-3√2x+4=0$.      Can anybody help me to verify the solutions of the above problems. How do you increase MAXSYMLINKS In a python script, I am creating a bunch of symbolic links chained together.  example: link1->link2->link3->.......->somefile.txt  I was wondering how you can change the max number of symlinks to be greater than 20? Is there any advantage to using pedal straps over clipless pedals? Change Error Message on FBA Login page On the default FBA Login Page, when a user enters wrong username/password an error message gets displayed:      "The server could not sign you in. Make sure your Username and Password are correct, and then try again.".    I want to change this error message to simple text      "Invalid Username and Password".    How can I achieve this? How can I vertically center a "div" element for all browsers using CSS? I can't use the terminal while gedit command is running calculate slope for a road network I am working on a road network for routing operations using postgis and QGIS.    I am new to both of these tools and need to calculate the slope for each edge (by retrieving the Z value for the start and end node for the edge from a raster). Any ideas of the best approach to this?   I know postgis can dump points and get the value from a raster, but can I get the slope attribute to the edge without breaking the network topology (with edges that have corresponding start/end nodes) using this method?   thanks How is the derivative of $\mbox{Trace}\left\{ X^T A X B\right\}$ with respect to matrix $X$ equal to $AXB + A^TXB^T$?  \begin{align}   \nabla_X \ \textrm{Trace}\left\{ X^T A X B\right\} = AXB + A^TXB^T \end{align}  where $A$ and $B$ matrices are given. I am a novice user and I am trying to install Oracle Java. The process calls for me to access /usr/local/java, but here is the problem. I get as far as /usr/local, then this is the message I get:  leonard@leonard-MT6452:/usr/local$ dir bin  etc  games  include  java  lib  man  sbin  share  src  leonard@leonard-MT6452:/usr/local$ cd /java/ bash: cd: /java/: No such file or directory  leonard@leonard-MT6452:/usr/local$ rm -r ~/java rm: cannot remove ‘/home/leonard/java’: No such file or directory   Help? Cannot translate vertice/edge will duplicate Most of the time when I try to move a vertex or an edge, instead of translating that, it extrudes it, it creates another face or, vertiex or whatever. I do not really get why it behaves like that. I hope I explained it in depth. I am sorry if this is a duplicate post but I could not find anything! Determinant of a square matrix in a field \begin{array}{rrrrr|r}     b &amp; a &amp; a &amp; \cdot \cdot \cdot &amp; a \\     a &amp; b &amp; a &amp; \cdot \cdot \cdot &amp; a \\     a &amp; a &amp; b &amp; \cdot \cdot \cdot &amp; a \\     \cdot &amp; \cdot &amp; \cdot &amp; \space &amp; \cdot\\ \cdot &amp; \cdot &amp; \cdot &amp; \space &amp; \cdot\\ a &amp; a &amp; a &amp; \cdot \cdot  \cdot &amp; b   \end{array}  I have the above matrix $A\in M_{n\times n}(F)$ where $F$ is a field and $n\geq1$, $a,b\in F$.  I'm trying to find out how to use row operations to make it into an upper triangular matrix in order to figure out the determinant. But I'm not sure how I would approach it.