3 Input XNOR gate made with XOR and not gates
3 input XNOR gate operation
Unexpected results when mounting two drives on a single mount point I was running out of /tmp space on one of my servers today so I attached a new 100GB disk to the system and did the following without unmounting /usr/tmpDSK from /tmp:  mkfs.ext4 /dev/xvde mount /dev/xvde /tmp   and now df -h outputs as:  Filesystem      Size  Used Avail Use% Mounted on /usr/tmpDSK      98G  4.5G   89G   5% /tmp /dev/xvde        98G  4.5G   89G   5% /tmp    The size of /usr/tmpDSK shows :  [root@server2 usr]# ll -h /usr/tmpDSK -rw------- 1 root root 2.3G Jan 27 17:32 /usr/tmpDSK    Different forums suggested using mhddfs to mount multiple drives on a single mount point, but I just did it directly and it seems to have worked -- or am I missing something?  I am hoping to better understand what actually happened. What to do before root and flash my phone? Meaning of completeness of a statistic? How can I install Windows after I've installed Ubuntu? Definite integral, quotient of logarithm and polynomial: $I(\lambda)=\int_0^{\infty}\frac{\ln ^2x}{x^2+\lambda x+\lambda ^2}\text{d}x$ I was thinking this integral : $$I(\lambda)=\int_0^{\infty}\frac{\ln ^2x}{x^2+\lambda x+\lambda ^2}\text{d}x$$ What I do is use a Reciprocal subsitution, easy to show that: $$I(\lambda)=\int_0^{\infty}\frac{\ln ^2x}{\lambda ^2x^2+\lambda x+1}\text{d}x =\frac{1}{\lambda}\int_0^{\infty}\frac{(\ln x-\ln \lambda)^2}{x^2+x+1}\text{d}x \\ =\frac{\ln ^2\lambda}{\lambda}\int_0^{\infty}\frac{1}{x^2+x+1}\text{d}x+\frac{1}{\lambda}\int_0^{\infty}\frac{\ln ^2x}{x^2+x+1}\text{d}x \\ =\frac{\ln ^2\lambda}{\lambda}\frac{2\pi}{3\sqrt{3}}+\frac{2}{\lambda}\int_0^1\frac{\ln ^2x}{x^2+x+1}\text{d}x$$ But I hav no idea on process the remaining integral:( Anyone knows how to solve it?  THX guys! I came with another method might work for this: Recall the handy GF $$\frac{1}{x^2+x+1}=\frac{2}{\sqrt{3}}\sum_{k=0}^{\infty}\sin \left(\frac{2\pi}{3}\left(k+1\right)\right)x^k$$ Then we have :  $$\int_0^1\frac{\ln ^2x}{x^2+x+1}\text{d}x=\frac{2}{\sqrt{3}}\sum_{k=0}^{\infty}\frac{2}{\left(k+1\right)^3}\sin \left(\frac{2\pi}{3}\left(k+1\right)\right)x^k$$ With $$\sum_{k=1}^{\infty}\frac{\sin (kx)}{k^3}=\frac{\pi ^2}{6}x-\frac{\pi}{4}x^2+\frac{x^3}{12}$$ What can we arrived? Question: If $(1+x)^n=\binom{n}{0}+\binom{n}{1}x+\binom{n}{2}x^2+\dotsm+\binom{n}{n}x^n$, prove that $\binom{n}{1}-2\binom{n}{2}+3\binom{n}{3}-\dotsm+(-1)^{n-1}n\binom{n}{n}=0$  My attempt:  I wrote the expression for $\binom{n}{k}$ for each term in the L.H.S and then tried to simplify but could not reach the R.H.S.  Please help. I have no idea on how to begin. I am not allowed to use calculus. I have CSV data loaded into a multidimensional array. In this way each "row" is a record and each "column" contains the same type of data.  I am using the function below to load my CSV file.  function f_parse_csv($file, $longest, $delimiter) {   $mdarray = array();   $file    = fopen($file, "r");   while ($line = fgetcsv($file, $longest, $delimiter))   {     array_push($mdarray, $line);   }   fclose($file);   return $mdarray; }   I need to be able to specify a column to sort so that it rearranges the rows.  One of the columns contains date information in the format of Y-m-d H:i:s and I would like to be able to sort with the most recent date being the first row. How can I make an application automatically start when I have logged in? Variance of Wilcoxon Rank-Sum Test (no ties) $\newcommand{\E}[1]{\mathbb{E}\left[#1\right]} \newcommand{\r}[1]{r\left(#1\right)} \newcommand{\P}[1]{\mathbb{P}\left(#1\right)} \newcommand{\Var}[1]{\text{Var}\left[#1\right]}$  Given two sets of data $X$ with $m$ points and $Y$ with $n$ points, unioned (keeping duplicates) to create a data set $Z = \{Z_i\}$ with $m + n = N$ data points, the Wilcoxon Rank-Sum Test Statistic is given by \begin{equation*} T = \sum\limits_{i=1}^{N}r(Z_i)\cdot \mathbb{I}(Z_i \in X)\text{,} \end{equation*} where $\mathbb{I}(Z_i \in X)$ is $1$ if $Z_i \in X$, $0$ otherwise. ($r(\cdot)$ denotes the rank of the data point.)  Suppose there are no ties. Then  \begin{align*} \E{T} = \sum\limits_{i=1}^{N}\r{Z_i}\cdot \E{\mathbb{I}(Z_i \in X)} &amp;= \sum\limits_{i=1}^{N}\r{Z_i}\cdot\P{Z_i \in X} \\ &amp;= \dfrac{m}{N}\sum\limits_{i=1}^{N}\r{Z_i} \\ &amp;= \dfrac{mN(N+1)}{2N} \\ &amp;= \dfrac{m(N+1)}{2}\text{.} \end{align*} This comes out to what it says in the book Nonparametric Statistical Inference, 5th ed., by Gibbons and Chakraborti.  Now for $\Var{T}$: \begin{align*} \Var{T} &amp;= \Var{\sum\limits_{i=1}^{N}\r{Z_i}\mathbb{I}(Z_i \in X)}\\ &amp;= \sum\limits_{i=1}^{N}\left[\r{Z_i}\right]^2\Var{\mathbb{I}(Z_i \in X)} \\ &amp;= \sum\limits_{i=1}^{N}\left[\r{Z_i}\right]^2\P{Z_i \in X}\left[1-\P{Z_i \in X}\right]\\ &amp;= \left(\dfrac{m}{N}\right)\left(1-\dfrac{m}{N}\right)\sum\limits_{i=1}^{N}\left[\r{Z_i}\right]^2 \\ &amp;= \left(\dfrac{m}{N}\right)\left(1-\dfrac{m}{N}\right)\left[\dfrac{N(N+1)(2N+1)}{6}\right] \\ &amp;= \left(\dfrac{m}{N}\right)\left(\dfrac{N-m}{N}\right)\left[\dfrac{N(N+1)(2N+1)}{6}\right] \\ &amp;= \left(\dfrac{m}{N}\right)\left(\dfrac{n}{N}\right)\left[\dfrac{N(N+1)(2N+1)}{6}\right] \\ &amp;= \dfrac{2N+1}{N}\left[\dfrac{mn(N+1)}{6}\right] \end{align*} The answer should be $\dfrac{mn(N+1)}{12}$. What did I do wrong? "To be subject to" vs. "to be subjected to" I read an article from  today which stated:     TTC workers are subject to alcohol and drug testing.   A later paragraph of the same article repeated it, except it used subjected to instead of subject to.  I have rarely seen the use of subjected to before. Is it legitimate in English as well? Why didn’t the author just keep it consistent by using subject to throughout the article? Does using varieties of forms enrich the expressions within an article? How do I build a native (command line) executable to run on Android? Prove that inequality is true for $x>0$: $(e^x-1)\ln(1+x) > x^2$ I was given a task to prove that inequality is true for x>0: $(e^x-1)\ln(1+x) &gt; x^2$. I've tried to use derivatives to show that the $f(x) = (e^x-1)\ln(1+x)-x^2$ is greater than zero, but has never succeeded.  Any help will be appreciated. How can I install a different version of Python using apt-get?  Obviously I realise I can install using the source tar ball, however I would prefer not to install from source and instead use the package manager, as that's what it's there for. Surely somewhere reputable builds .deb files for the latest Python releases (why python.org don't is beyond me) that I can reference.   What do I need to do to reference them and what issues might it create when upgrading to the next version?  If there is no way except for building from source, is there a (pseudo) package that I can can install that will provide all of the dependencies needed without having to find and install each individually? So that I don't get:  The necessary bits to build these optional modules were not found: _bz2                  _curses               _curses_panel       _dbm                  _gdbm                 _lzma               _sqlite3              _ssl                  _tkinter            readline              zlib a) Give a combinatorial proof that for every $n \geq r \geq 1$ that:  $$\sum_{i = 0}^{n} \binom{i}{r - 1} = \binom{n + 1}{r}$$  And use (a) to concoct a formula for $1^2 + 2^2 + ... + n^2$ How to pass an ArrayList to a varargs method parameter? How do you add a timer to a C# console application Just this - How do you add a timer to a C# console application? It would be great if you could supply some example coding. How to place a .png texture with transparency over a material I am trying to create a low poly face with a face from a .png file. The issue is I already have material placed for hair and skin, as shown in the picture below.   I have created a .png file with a face which I would like to overlay over the skin material on the front of the head.    All examples I searched so far assume I also want the color of the material from the .png texture.  Update:  I added UVMapping, changed view to texture, made sure one face is on the eye but nothing is displayed..... see image... I don't know what is going on. Highlight whole TreeViewItem line in WPF How to use exclamation marks in Minecraft commands? I know that you can use exclamation marks in Minecraft commands to check for an entity that does not have a specific tag. For example, you can use /kill @e[type=!Player] to kill all entities except for the player. I have, however, encountered two problems with using exclamation marks that I can't find a solution for.  For my first problem, I've set up a series of command blocks to summon shootable fireballs above the player’s head when a certain item is being held;  /scoreboard players add @a Fireball 1 {SelectedItem:{tag:{display:{Name:"Summon Fireball"}}}} /execute @a[score_Fireball_min=1,score_Fireball=1] ~ ~ ~ /summon Fireball ~ ~2.5 ~ {direction:[0.0,0.0,0.0]} /scoreboard players set @a Fireball 0   I used a comparator and a redstone torch so that the last command would activate when the first command would deactivate, that is, when the player is not holding the item.  The problem is, that when I move far away from the setup, the redstone stops working, leaving me unable to summon any new fireballs. Instead, I'm trying to use a command block to check when anything except for item is being held;  /scoreboard players set @a Fireball 0 {SelectedItem:{tag:{display:{Name:!"Summon Fireball"}}}}   I’ve either put it at the wrong place, or you simply can’t use exclamation marks in NBT tags. Could someone tell me where I should put the exclamation mark, or in the latter case, how I can check for anything except for a specific item?  Further, I’ve tried using exclamation marks to set the score of all entities, including the ones with a blank score, but except for the ones with a score of 2 or higher, to 0;  /scoreboard players set @e[score_arrows_min!=2] Arrows 0 /scoreboard players set @a Arrows 1 {SelectedItem:{tag:{display:{Name:"Rain of Arrows"}}}} /scoreboard players set @e[type=Arrow] Arrows 2 {inGround:1b}   The code does change the scores of entities without scores to 0, but it doesn’t exclude the arrows with a score of 2. Could anyone tell me what I’m doing wrong here? What are the existing datasets of world maritime routes?