Suppose we have $\bar{x}$ $\sim$ $N(\mu, 1/n)$, its pdf then is $f(\bar{x}) = \sqrt{\frac{n}{2\pi}}e^{-n(\bar{x}-\mu)^2/2}$  Let $T = (\bar{x})^2$, we want to calculate its pdf.  My first thought is:  $P(T \le t) = P(\bar{x}^2 \le t) = P(-\sqrt{t} \le \bar{x} \le \sqrt{t}) = \Phi(\sqrt{t}) - \Phi(-\sqrt{t}) = 2\Phi(\sqrt{t}) -1 $  where $t \ge 0$  Therefore, its pdf is:  $f(t) = \frac{1}{\sqrt{t}}\sqrt{\frac{n}{2\pi}}e^{-n(\sqrt{t}-\mu)^2/2}$  However, if I use calculator, the integral is not equal to 1.  The correct pdf should be:  $f(t) = \frac{1}{2\sqrt{t}}\sqrt{\frac{n}{2\pi}}(e^{-n(\sqrt{t}-\mu)^2/2} + e^{-n(-\sqrt{t}-\mu)^2/2})$  This integral is 1.  Any thoughts how to get the correct pdf?

I need to find the distribution of the random variable  $$Y=\sum_{i=1}^{n}(X_i)^2$$ where $X_i\sim{\cal{N}}(\mu_i,\sigma^2_i)$ and all $X_i$s are independent. I know that it is possible to first find the product of all moment generating functions for $X_i$s, and then transform back to obtain $Y$'s distribution. However, I wonder whether there is a general form for $Y$ like the Gaussian case: we know the sum of independent Gaussian is still a Gaussian, and thus we only need to know the summed mean and summed variance.   How about all $\sigma^2_i=\sigma^2$? Will this condition make a general solution?


I created a simple function and I noticed something unexpected about javascript. When I pass a variable in to a function, then change it, its not changing outside that function. Heres some code:  function check(val, isEven) {     if (val % 2 === 0){     isEven++;     console.log('incremented isEven is ', isEven);   } }  var arr = [1, 2, 3, 4, 5, 6, 7, 8];  var isEven = 0;  for (var x = 0; x < arr.length; x++) {    check(arr[x], isEven);    console.log('isEven is now ', isEven); }   Fiddle is .  Maybe I've been misinterpreting Javascript all these years, but I would have expected the isEven within check() to be the same as the original isEven.....But you can see in the logs, outside isEven stays as 0....

The primitive types (number, string, etc.) are passed by value, but objects are unknown, because they can be both passed-by-value (in case we consider that a variable holding an object is in fact a reference to the object) and passed-by-reference (when we consider that the variable to the object holds the object itself).  Although it doesn't really matter at the end, I want to know what is the correct way to present the arguments passing conventions. Is there an excerpt from JavaScript specification, which defines what should be the semantics regarding this?


I have Minecraft v1.11 and am trying this command to summon fallingsand but it is not working. Why?  Command:  /summon FallingSand ~ ~1 ~ {Block:command_block,Time:1,TileEntityData:{Command:/fill ~ ~-1 ~-1 ~ ~50 ~-1 redstone_block},Passengers:[{id:FallingSand,Block:redstone_block,Time:1}]}

I'm making an adventure map, and at some points I need there to be items on the ground. But when I use the /summon command, it always ends up as a stone block.  Here's what I've used:   /summon Item ~ ~ ~ {Item:{id:276,Count:1,tag:{display:{Name:"Mirage"},Unbreakable:1},Damage:0}}   This did not work, so I tried a simpler command:  /summon Item ~ ~ ~ {Item:{id:276,Count:1,tag:{},Damage:0}}   Which also summoned a stone block. Please note that I am in the Minecraft 1.9 snapshot 16w05b


I am learning some Lie group and I met the following problem:  Let $G$ be a Lie group and $Z$ its center. Then $Z$ is also a Lie group. Let $\mathfrak{g}$ be the Lie algebra of $G$ and $\mathfrak{z}$ be the center of $\mathfrak{g}$. Is the Lie algebra of $Z$ equal to $\mathfrak{z}$?  It seems that this correspondence is natural, yet I cannot find any source containing this. Could anyone suggest a (sketch of) proof, or give a counter example?  Thank you very much!

Let $G$ be a Lie group and $\mathfrak{g} = T_eG$ its Lie algebra (where $e \in G$ is the neutral element). Denote $Z(\mathfrak{g})$ the center of $\mathfrak{g}$ and $Z(g)$ the center of $G$. I've read the following statement but don't see how to prove it: $$Z(\mathfrak{g}) = 0 \Longleftrightarrow Z(G) \text{ is zero dimensional.}$$ I'm mainly interested in the "$\Leftarrow$" direction, as this is used in a corollary of the Bonnet-Myers theorem in the text I'm reading.  Now, my knowledge of Lie groups is very basic. For instance, I guess that the dimension of $Z(G)$ means its dimension as a manifold. So I would think that $Z(G)$ is a submanifold of $G$. But how do I even see this in general?  According to this question , it seems to be difficult to find conditions when $Z(\mathfrak{g}) = Z(G)$ holds in general, however the statement above looks more simple.  Would someone be able to prove the above equivalence?


I'm using Kubuntu 14.04 and I'm asked for password when:   Using sudo in terminal. Login. Installing/removing/updating programs with Muon. KWallet initiates or adds a password.   I don't want to write any password. Never tell me the risks.  It still ask me for password when installing programs with Muon.

I've been using Ubuntu 12.04 LTS since release and am trying to figure out a couple things about all of these passwords and key-ring prompts that I've just been living with for a while.  Ever since install it seems that every time I boot up my computer and want to do anything (ie. use the internet, use a internet browser, install something, delete something, pick my nose) I'm always prompted for either a normal password entry or a key-ring password entry.  Is there anyway to turn off all of this "security" and tell my Ubuntu that it can trust what I'm doing and go take a shower?


Will somebody please help me to understand what is role of millet plateau region in switching of MOSFETs?

I don't understand why the gate charge curve (exactly: the Miller plateau part) of MOSFETs is dependent on the drain-source voltage Vds.  As an example, the  shows on page 4 (Fig. 6) the gate charge curves for different Vds values.  Why is the Miller plateau longer for bigger Vds? Isn't the plateau dependent upon Cgd? But Cgd (= Crss) gets smaller for bigger Vds (see FIg.5 in datasheet). Shouldn't the Miller plateau get shorter?


Sometimes a paper is rejected but you obtain some useful suggestions or remarks on improving your paper, directly or indirectly.  When you improve your paper per the suggestions to a certain degree with the intention to submit the paper to another journal, how do you acknowledge the good opinions from the anonymous reviewers?  In addition, is this academically necessary?

My paper was rejected from a journal. However, remarks of one of the reviewers were useful, and I incorporated them into the next version of the paper.  Is there a general pattern of acknowledging such contribution (in the Acknowledgement section)?  Or should I leave it, not to advertise information that the paper was rejected from a particular journal?  (As a side note, this paper was rejected two times, each time with one positive review, and one of type "OK, but I think it is not of general interest".)  EDIT:  In my case (as in general in my field) reviewers were anonymous. (Otherwise I would just use their names.)   And in my case the helpful comments were in positive reviews (but I doubt whether it changes anything).


I am completely new to role-playing games, yet have an experience with board games. How should I start d&d without it overwhelming me?

I'm no gamer at all, so this could be like a very silly, basic question for you guys. The thing is that I always read about "Dungeons and Dragons" game (not the video game, but the normal game to play with friends that are actually gathered together). And I would like to know how to play it.  I've read that it is a book (or several ones, which is more confusing for me to understand), but I've read somewhere that it can be played as a normal "table" game, with a board, and pieces, and somewhat weird dice (or sets of dice).  Is it like a normal game, where you pull the stuff out of a box and start to play?  I don't know if any of you watch the show "The Big Bang Theory", but I think they have played the game in a recent episode, and it looks just like a regular game.  I've Googled it for more information, but I haven't found anything as basic as I need, because I've never played a role game (except in a video game).  I just want to learn how to play, so I can get my friends into it to play it each time we get together.


If I have arranged Finder to the left of the desktop and Slack to the right, and have Sketch further to the right, there's a reason for that. It's an organization strategy to make my work easier and keep track of the many windows I have open. BUT, macOS rearranges them if I click on the application icon from the Dock and rather than swiping over to the screen in the specified order, it moves it next the Desktop.  Is there a way to stop that from happening? A way to pin screens to the desired position?

You may have encountered a situation in which Mac changes the order of desktops based on some events like alerts on a program or a web page in browser. How could I disable this logical change? Note: I'm using El Capitan, but I had this problem since Mavericks.


I noticed recently that I can declare an array in java by putting the square brackets either after the type OR after the array variable name.   float[] x float x[]   Are there any differences between these two, aside from the syntax?  As an aside, I stumbled upon a discovery that float[] x[] is actually initializing a two-dimensional array - at least according to Eclipse. Is that true?

I have recently been thinking about the difference between the two ways of defining an array:   int[] array int array[]   Is there a difference?


Question: The value of: $$(1+\tan 1^o)(1+\tan 2^o)(1+\tan 3^o)...(1+\tan 44^o)$$ is:      A) 2       B) A multiple of 22      C) A multiple of 4      D) Not an integer   I'm not sure how I would solve this question. However, by intuition, I would say that the number wouldn't be an integer. As all the terms in the bracket are between 1 and 2, their product shouldn't give an integral value. Am I right?

Which  is the fastest paper-pencil approach to compute the product $$ \prod  \limits_{i=1}^{45}(1+\tan i^\circ) $$


If $A$ is a complex square matrix, I need to prove that the trace of $A$ is the sum of its eigenvalues. I've already proved that, if $p(x)$ is the characteristic polynomial, then  $$p(x)=det(xI-A)=(x-\lambda_1)...(x-\lambda_n)=x^n-(\lambda_1+...+\lambda_n)+...+(-1)^ndet(A)$$  But I´m stuck with the proof... Thank you!  PS: I know that is a direct consequence of the identity $p(x)=x^n-Tr(A)+...+(-1)^ndet(A)$, but in that case, I need a proof of this identity...

I have a question to ask down below, that I have been having some trouble with and would like some help and clarification on.  Suppose A  is an $n \times n$ matrix with (not necessarily distinct) eigenvalues $\lambda_{1}, \lambda_{2}, \ldots, \lambda_{n}$. Can it be shown that:     (a) The sum of the main diagonal entries of A, called the trace of A, equals the sum of the eigenvalues of A.   (b) A $- ~ k$ I has the eigenvalues $\lambda_{1}-k, \lambda_{2}-k, \ldots, \lambda_{n}-k$ and the same eigenvectors as A.  Thank You very much.


I am trying to calculate the factorial of some integer number (from 0 to 21) by using recursive method. I created a separete method outside the main class. But while printing the factorial in main method it shows an error. How to fix that?  package looping;  import java.io.PrintStream;  public class Looping {     public long fact(long num)     {         if(num<=1)         return 1;         else             return num*fact(num-1);     }     public static void main(String[] args) {          for(int i=0;i<=21;i++){          System.out.printf("%d!=d\n",i,fact(i));         }      } }

The very common beginner mistake is when you try to use a class property "statically" without making an instance of that class. It leaves you with the mentioned error message:     You can either make the non static method static or make an instance of that class to use its properties.   Why? I am not asking for solutions. I would be grateful to know what is the reason behind it. The very core reason!  private java.util.List<String> someMethod(){     /* Some Code */     return someList;             }  public static void main(String[] strArgs){                // The following statement causes the error. You know why..     java.util.List<String> someList = someMethod();          }


I created a .desktop file for an AppImage application that I downloaded. The icon I used for the application displays on the application screen and on the side-bar but not on the running application on the side-bar. So when I click on the application it starts running and creates a new icon in the side-bar but the new icon has no image and does not display the one specified in the .desktop file. The main application icon still displays correctly but not the icon for the running application. Hopefully this explanation makes sense...if not I can provide a screenshot to display what I am talking about. Is there a way I can make the running application icon use the same icon as the docked application icon specified in the .desktop file? Thanks

I've created an application launcher in /usr/share/applications that launches rdesktop. The file specifies an icon name and I've added the icons to:   /usr/share/icons/HighContrast/48x48/apps /usr/share/icons/HighContrast/22x22/apps /usr/share/icons/HighContrast/256x256/apps /usr/share/icons/HighContrast/32x32/apps /usr/share/icons/HighContrast/scalable/apps-extra /usr/share/icons/HighContrast/24x24/apps /usr/share/icons/HighContrast/16x16/apps /usr/share/icons/hicolor/scalable/apps /usr/share/icons/hicolor/128x128/apps /usr/share/icons/hicolor/16x16/apps   I then drug the launcher to the taskbar and the launcher with the correct logo is visible in the taskbar. However, when I start the task, a new icon is created in the taskbar, a square with a question mark in the center.  What icons do I need and where, so that the taskbar displays the correct icon for the application when it is launched?  The .desktop file contents:   [Desktop Entry] Version=1.0 Terminal=false Icon=mswindows Type=Application Categories=Network; Exec=rdesktop win7shared1 -g 1680x1000  Name=win7shared1 GenericName=rdesktop Comment=Open windows desktop  Keywords=Windows StartupNotify=false


Let $f$ be an entire function. And assume $f(z)$ is real on $Im(z)=0$ and $Im(z)=\pi$ lines. Show $f$ is $2\pi i$ periodic. No clue how to start this problem. I was thinking of maybe equating it to some iteration of $e^z$ but that got me nowhere.

Show that if $f(z)$ is an entire function such that it takes real values on the lines $Im(z)=0$ and $Im(z)=a$ (for some $a \in \mathbb{R}_{\neq 0})$, then $f$ is periodic with period $2 i a$.    So here is my thought process: First of all by reflection principle $f(\bar{z})=\overline{f(z)}$ so if our function $f$ is given in the strip $0 \leq Im(z) \leq a$, then its values on $-a \leq Im(z) \leq a$ follow by reflection principle. Then by imposing $f(z)=f(z+2 ia)$ we can intuitively see that this will define an entire function by looking at how the strips $na \leq Im(z) \leq 2na$ seamlessly stack on top of each other. Is this logical? And how would one prove this analytically?


What is the reasoning behind the fringe logo design? Why two F's back to back? I'm watching the series on Netflix and wanted to know can across this page through Google search.

Something seems very familiar about this logo, but for some reason I can't quite pin it down.  Is there a particular organization, real-life historical or fictional, from which this insignia might have been derived?  The particularly familiar-looking bits are large, red-on-black "F"s, back-to-back.  I'm not sure if they're familiar because they're opposing red letters, or because they resemble a pair of red wings outstretched, or perhaps they look like some other shape I've seen somewhere on some government or military organization's banner or insignia.  References from primary canon or official commentary or documentation are preferred, but I also welcome reasonable speculation.  Aside from simple demonstration or explanation of semblance, it would be good if any such speculation also included a logical reason for the similarity.


I can do the following to see if some word is available in the output of "cat":  cat filename | grep word   This filters the output and shows only those lines which contain "word". Now, is it possible to only highlight the "word" in the output, without dropping other lines?

Say I have the following file:  $ cat test  test line 1 test line 2 line without the search word another line without it test line 3 with two test words test line 4   By default, grep returns each line that contains the search term:  $ grep test test  test line 1 test line 2 test line 3 with two test words test line 4   Passing the --color parameter to grep will make it highlight the portion of the line that matches the search expression, but it still only returns lines that contain the expression. Is there a way to get grep to output every line in the source file, but highlight the matches?  My current terrible hack to accomplish this (at least on files that don't have 10000+ consecutive lines with no matches) is:  $ grep -B 9999 -A 9999 test test     If grep can't accomplish this, is there another command-line tool that offers the same functionality? I've fiddled with , but it doesn't seem to have an option for it either.


I've all ready tried to install this file pt_BR.dic in the TeXmaker, but when I went to pull the file through the TeXmaker configuration, it simply doesn't worked. I use Ubuntu 12.04 LTS. Is there any alternative form of installation for a Portuguese dictionary?

I began my physics studies last summer. All our written assignment is in LaTeX and that's ok - and I use Texmaker. I think Texmanker is a good program and I have just one problem with it. I can't install a danish spellcheck and use it in LaTeX. That is not nice, so I really need your help!  Help me please. Tell me where and how to install a danish spellcheck and how to use it in Texmaker, pls. I am desperate! :/


Let's say, I am having 4 users : User1, User2, User3 and User4. All Users assigned with Same Profile. The Profile which is assigned to them having all access - Create, Read, Edit and Delete. But User1 should have all access, User2 should have Read, Edit and Create, User3 should have Read, Edit and User4 should have only Read access. How to achieve this? Where am I lagging?

I have a set of users, who need access to one single tab or object on the existing profile. How can i do it with out of box functionality.


I have an iPad 2 wifi, and it is currently on 7.0.4. I would like to update to 7.1.2 not 8.0.2 which is the default update when I go into iTunes. I tried shift clicking and choosing 7.1.2 I have saved but I keep getting an error that says its not eligible for the requested build. I have checked my hosts file, and there seems to be nothing wrong there. What could be causing this error?

I'm trying to downgrade my iPhone from the current iOS to an older one, as per .  But every time I try, I always receive this error:     The iPhone could not be restored. This device isn't eligible for the requested build.     I have tried many times with and without DFU mode. Any ideas regarding this?


I'm aiming to have a theoremstyle which has hanging indentation, where all lines after the first line are indented by some amount of space. I've searched for previous answers to similar questions, but most of these do not use the amsthm package, or are difficult for me to understand. My current theoremstyle is as follows:  \newtheoremstyle{mystyle}% {3pt} {3pt} {} {} {\bfseries} { --}% Punctuation after theorem head {.5em}% Space after theorem head {}% Theorem head spec (can be left empty, meaning ‘normal’)   This looks like   which does not contain any sort of indentation currently.  I would like something which looks like this   which I have poorly approximated with an additional quotation environment inside. However, in doing so, the spacing is not correct. Hopefully, the idea is clear--the text should actually be formatted with a proper hanging indent.  Is there some sort of proper "hanging indent" setting I can put into the indentation parameter of the theorem style? Or do I have to do some more manual work? I would prefer not to replace amsthm (I'm trying to rewrite documents already made with amsthm), but having an additional package is not problematic.

I would like to create a theorem style which indents the theorem exactly like a \hangindent would do, expect that the indention should continue for all paragraphs of the theorem.   For example:  Theorem 1.2.3: Lipsum Lorem ipsum dolor sit amet,     consectetuer adipiscing elit.  Ut purus elit,      vestibulum ut, placerat ac, adipiscing vitae, felis.      Curabitur dictum gravida mauris. Nam arcu libero,      nonummy eget, consectetuer id, vulputate ...   I tried this, but it does not work correctly:  \documentclass[parskip=half]{scrartcl} \usepackage{amsthm,thmtools} \usepackage{lipsum} \usepackage{showframe}  \let\thm\relax \declaretheoremstyle[     headfont=\bfseries,     bodyfont=\normalfont\leftskip2.5em,     headindent={-2.5em} ]{INDENTthm} \declaretheorem[     within=section,     style=INDENTthm,     name=Theorem ]{thm}  \begin{document} \begin{thm}     \lipsum[1]      \lipsum[2] \end{thm} \end{document}   What happens is that the theorem header suddenly has a negative indention relative to the page, i.e. starts just a little to the left of the actual page, although I would expect "2.5em-2.5em=0em"... :-)


I'm somewhat new to the game so sorry if this question is a stupid one and my english isn't the best either so pls excuse that as well ^^.   That being said, I'm unsure how initiating combat with an assassination (rogue assassin) really works.   If i successfully sneak up on someone/something and declare an assassination (or attack), my target and me roll for initiative and combat proceeds. Right?  But that seems kinda weird to me. There could be the possibility of my target rolling a better initiative, going first (but not doing anything bc it is surprised), losing its surprised status on the end of its turn and giving me the turn to attack. This means I wouldn't get advantage (Assassinate ability) bc my target had its turn before me meaning I also wouldn't get my sneak attack bonus (Sneak attack ability) and since the target isn't surprised anymore I also wouldn't do crit damage (Assassinate ability). That just doesn't make any sense to me since I would have attacked from a totally advantageous position an enemy that wouldn't even be aware of me. Did I miss something?  Is my thinking of how this works correct or am I right in suspecting that I missed something?   Thanks alot!

I am trying to figure out if the surprised state ends on a creature after the first attack of a surprise round, or if the surprised state (which I would then see almost as an unofficial condition) ends only after the first round of combat.  In the second case, I would believe that a character (having the rogue's Assassinate ability) attacking a surprised creature AND having multiple attacks would score a critical hit on all hits.  Example: Does a Monk 5/Rogue 3 surprising a creature get automatic critical hits on all hits if he does 2 attacks (with extra attack) and additional unarmed strike(s)?  Or does the critical hit only affect the first hit? However, that would surprise me as the rules mention any hit is a critical hit.


I am trying to solve this problem:  Let $V$ be an $n\,$-$\,$dimensional vector space over some field $\mathbb{F}$ and $T:V\to V$ a diagonalizable linear operator that has $n$ distinct eigenvalues. Show that any other diagonalizable linear operator in $V$ is a polynomial in $T$, that is, if $S:V\to V$ is a diagonalizable linear operator than exists $g\in \mathbb{F}[x]$ such that $S=g(T)$.  Any tips?  Edit: Sorry for took so long to view this post again... I have read the answers and realize that this statment is false... But I was thinking, if I add the fact that $S$ commutes with $T$, then it would be true?

I'm trying to solve some problems in Hoffman and Kunze and I'm kind of stuck on this one. This is 6.5.3 on Hoffman and Kunze.  Here is the question:  Let $T$ be a a linear operator on an $n$-dimensional space, and suppose that $T$ has $n$ distinct characteristic values. Prove that any linear operator $U$ which commutes with $T$ is a polynomial in $T$.  My work so far: Since $T$ has $n$ distinct characteristic values and since the space it acts on is also $n$ dimensional, $T$ must be diagonalisable. Now using the fact $UT=TU$ I can show that $U$ must also be diagonalizable. So these two operators must be simultaneously diagonalizable. Now I'm stuck with where this is going. I'm thinking of simultaneous diagonalizability because this is section 6.5 of Hoffman and Kunze and it deals with simultaneous diagonalizability. Am I on the right track with this?. Can anybody help?  Thanks so much for your time and your answers.


Let $R$ be a ring A $(left) \ R-module$ consists of an additive group $R$ equipped with a mapping $R\times M\to M$, which is an action, meaning $ (rr')m=r(r'm)$ for $r,r'\in R$ and $m\in M$, it is distributive over addition, and it is unital: $1m=m$ for all $m$.  Dually there is the notion of a $right \ R-module$ with an action $M\times R \to R$. Apart from notation, it is the same thing as a left $R^{op}-module$. If R is commutative, the notion coincide. If $R$ is commutative, a left $R-module$ $M$ has a natural $R-R$ bimodule structure, by simply defining the right scalar action as $mr:=rm$ for $r\in R, m \in M$. What i don't get is why we need to distinguish left and right module since they are just a notation transposition? Why does the notation coincide when the ring is commutative. What is the meaning of opposite ring in simple words? And why do we need the ring to be commutative for the bimodule to make sense? Thanks for your help. I am a bit lost on this definition.

OK, this question may be induced by my highly commutative mind and the wee midnight hours.  Why do we bother with right R-modules vs left R-modules in view of the fact that given, say, a left R-module (M,+,$*$) (with scalar multiplication $*$) it is instantly a right R-module (M,+,$\circ$) with same addition and right multiplication $m\circ r =: r*m$ -- I believe the axioms for a right module check. In other words, in this way we have an isomorphism of the categories of right and left R-modules: RMod $\cong$ ModR  ???  Thus, whatever we say about one of these categories (or their objects and morphisms) is instantly true for the other? No? I may be wrong, but do people use a phrase "let us assume that M is an R-R bimodule" or something like that? Could they mean M is a left R-module and a right R-module with some secret scalar multiplication on the right, other than the one I defined above?   Now that @Qiaochu et al found an error in my thinking, pointing out that the categories of right and left R-modules may be quite different, let alone isomorphic, then why is it, that one waives one's hands often saying "This argument works exactly the same way for right R-modules as the one we just exhibited for the left R-modules." ? This in spite of the fact that the two categories may be totally different. Do we have any fair mechanisms enabling us to know when the proofs are left-right independent, or is it that we can say that only after we actually check the proofs one line at a time...?


Why is $\nabla_A \mbox{tr} (ABA^TC) = CAB + C^TAB^T$?   Here $A, B, C, D$ are all $n \times n$ matrices.  $$\nabla_A f(A) = \left[\begin{matrix} \frac{\partial f}{\partial A_{11}}... \frac{\partial f}{\partial A_{1n}}\\ ...\\ \frac{\partial f}{\partial A_{n1}}... \frac{\partial f}{\partial A_{nn}}\\ \end{matrix}\right]$$      I tried to prove it in this way:  $$\begin{align} \nabla_A \mbox{tr} (ABA^TC) &= \nabla_Atr (BA^TC)A\\ &= \nabla_A \mbox{tr} DA ......let  \ D=BA^TC\\ &= \nabla_A \mbox{tr} AD\\ &=D^T\\ &=B^TAC^T\end{align}$$  Since $B^TAC^T \neq CAB + C^TAB^T$, there must be something wrong in my derivation. How to prove this property?

Given three matrices $A$, $B$ and $C$ such that $ABA^T C$ is a square matrix, the derivative of the trace with respect to $A$ is:  $$ \nabla_A \operatorname{trace}( ABA^{T}C )  = CAB + C^T AB^T $$  There is a proof . However, I was not able to understand the second line of the proof. it says something like this:  $$ \nabla_A \operatorname{trace}( ABA^T C )= \nabla_\bullet \operatorname{trace}(f(\bullet)A^{T}C) + \nabla_\bullet \operatorname{trace}(f(A) \bullet^T C) $$  Where  $f(A) = AB$  I tried searching the proof or any hint using google, but I couldn't fine anything. Could anyone please help me with this second line. I cannot sleep. I am obsessed with this proof.


Example text : "jhon's email address is jhon@gmail.com"  I got an error when identifying jhon's email address from regex.I'm new for this regex so like to have your valuable answers .Thanks in advance Expected result : jhon@gmail.com

Over the years I have slowly developed a  that validates MOST email addresses correctly, assuming they don't use an IP address as the server part.  I use it in several PHP programs, and it works most of the time.  However, from time to time I get contacted by someone that is having trouble with a site that uses it, and I end up having to make some adjustment (most recently I realized that I wasn't allowing 4-character TLDs).  What is the best regular expression you have or have seen for validating emails?  I've seen several solutions that use functions that use several shorter expressions, but I'd rather have one long complex expression in a simple function instead of several short expression in a more complex function.


My Windows disk partitions are appearing under “Other Locations”, When I access the partitions, I can open files, read them, but I cannot create a new folder. I'm using dual boot with Windows 10 and Ubuntu 20.04.

Whenever I boot Ubuntu, I get a message that it cannot mount my windows partition, and I can choose to either wait, skip or manually mount.  When I try to enter my Windows partition through Nautilus I get a message saying that this partition is hibernated and that I need to enter the file system and properly close it, something I have done with no problem so I don't know why this happens.    Here's my partition table, if any more data is needed please let me know.     Device Boot      Start         End      Blocks   Id  System /dev/sda1            2048    20000767     9999360   83  Linux /dev/sda2        20002814   478001151   228999169    5  Extended /dev/sda3   *   478001152   622532607    72265728    7  HPFS/NTFS/exFAT /dev/sda4       622532608   625141759     1304576   82  Linux swap / Solaris /dev/sda5        20002816   478001151   228999168   83  Linux


Do not allow people to post the minute they created an account.  Let them ask the question but not allow them to post.  Let them stew for 30 minutes and force them through a nice animated tutorial on what they should do before they post and enforcing the fact that bad questions will not get an answer.  If they had a Need to know! basic rules introduction forced on them asking them at the end to check a box I understand! some might ask better questions and help the community instead of flooding the site with bad questions.  The presentation should be on a timer without the ability to skip and highlight the similar questions asked before that might give them the answer.  Also for the first next 9 posts they should have to check a box next to the first 5 of each similar questions before posting.  I do not mean to be harsh, but the truth is I see more negative votes on questions then positive. It's like 90% of the time people give -1 to first questions.

I'll start with  which sparked my thinking cap. It's becoming extremely overwhelming with the great number of new users who seem to think that Stack Overflow is a forum, that they can ask whatever they want, ignoring the FAQ and the strict guidelines we have here. It seems that anyone who has a simple question can come create a new account here, throw their entry-level question up, and expect a bunch of people to tell them exactly what they need. Unfortunately, that's of course not how these sites work.  Imagine a new user who's never used any Stack Exchange sites, and doesn't know how it works, coming to Stack Overflow for the first time. They are new to programming, and have a lot of learning to do. They create a new account, and ask their question such as "How to write a web hook with a third-party API?". Now imagine how critical people will be to them. That user will cringe and start fighting back in the comments with "Why do you have to be so mean?"  Now, imagine a new user, same as before, coming to Stack Overflow for the first time. When they go to register, first of all a page will show with a message explaining that Stack Overflow is not a forum, and doesn't work like the rest of the sites they might be used to. Make this mandatory for them to read and approve before even creating an account. Then, once they've registered, require that they go through a short but thorough step-by-step tutorial to understand how they should contribute to the site. Make sure they understand how everything works before they dive into it.  I personally work for a software company which has troubles getting our clients to understand how to use our software, and they always mis-use it. Kind of like selling someone a 747, but instead of flying it, they strap a bunch of mules to the front and sit on top with a whip. It's very huge and complex (inventory/point-of-sale) and there's a lot to know before using it. Well, Stack Overflow works in the same precise manner, and it's expected that people follow by the rules of how it was designed. So now I'm making training videos for them.  Currently, when you sign up, there is nothing that really forces you to read and accept before using the site. I signed up for an account a short while ago, and I did not face anything which really made sure I knew how the site worked before letting me in. Sure, there's a first question guide, but it's just one single step, kinda like a terms & conditions checkbox, which everyone tends to ignore anyway. This needs to be a step-by-step (not all in one page) tutorial. And a clear warning before they even create an account. It really sucks when you sign up for something all excited, then when you finally get to ask your first question, you're faced with terror. It's a lot better to tell someone the truth up front before they begin than to lure them in and once they're here we practically say "Oh, by the way, your questions probably will not be answered."  It's simple. We educate the newbies.


When I wanted to execute   hadoopmaster@dhruvhadoop3-HP-Compaq-dc5800-Small-Form-Factor:~$ sudo gedit ~/.bashrc   It gave me the following error  sudo: unable to resolve host dhruvhadoop3-HP-Compaq-dc5800-Small-Form-Factor [sudo] password for hadoopmaster: hadoopmaster is not in the sudoers file.  This incident will be reported.

Every time I try to use sudo I get this:  sudo: unable to resolve host ubuntu-server   My /etc/hosts file:  127.0.0.1       localhost 127.0.1.1       ubuntu-server  # The following lines are desirable for IPv6 capable hosts  ::1     ip6-localhost ip6-loopback fe00::0 ip6-localnet ff00::0 ip6-mcastprefix ff02::1 ip6-allnodes FF02::2 ip6-allrouters   /etc/hostname has:  ubuntu-server   I think there is some other setting that causes the unable to resole host error, but I cannot find these.


I have an object array from a Hibernate query that I want to show in a logger message.  I have   //row output for (Object[] objs : results)  {     logger.info(objs.toString()); }    but I get [Ljava.lang.Object;@60cf75a9 for each.  How do I convert the array to a string output?

In Java, arrays don't override toString(), so if you try to print one directly, you get the className + '@' + the hex of the  of the array, as defined by Object.toString():  int[] intArray = new int[] {1, 2, 3, 4, 5}; System.out.println(intArray);     // prints something like '[I@3343c8b3'   But usually, we'd actually want something more like [1, 2, 3, 4, 5]. What's the simplest way of doing that? Here are some example inputs and outputs:  // Array of primitives: int[] intArray = new int[] {1, 2, 3, 4, 5}; //output: [1, 2, 3, 4, 5]  // Array of object references: String[] strArray = new String[] {"John", "Mary", "Bob"}; //output: [John, Mary, Bob]


I'm new to ubuntu and Linux and just installed Ubuntu 18.04 LTS.  I know there are tons of tutorials out there how someone could create a shortcut. Unfortunately none of them really worked for me.  I have a ~/shellscript.sh which I'd need to call periodically.  How can I create a shellscript launcher as simply as   e.g. ln -s ~/shellscript.sh ~/Desktop/run-shellscript  where I simply can click on it to run it? (Remark: ln command above doesn't work)  Thanks for your contributions!

So I tried making a desktop shortcut which executes a very simple shell script. But when i double click/right click->execute it, it does nothing. (or at least I think it does nothing)  heres how my shortcut and shell script looks: Note the shortcut has "Terminal" set to 1, and i hope that means that it opens the shell script in a new terminal window.. (i have a couple terminals already open, which arent ready for usage (have scripts running))  Shortcut:  [Desktop Entry] Version=1.0 Type=Application Name=Test Comment=Test Exec=/home/(myusername)/test/test.sh Icon=utilities-terminal Terminal=true StartupNotify=false GenericName=Test   Shell Script:  #!/bin/sh # (I tried both, /bin/bash and /bin/sh) echo "hi"


I'm looking for a Linux application to catalog the files on my many external HDs and search them. I'm using Ubuntu, so i prefer a normal deb in the repositories but i can't find one. After some research by Google, I find no proper application - does any GUI exist ? See this old forum entry : "printable file catalog or index for (external) USB and flash drives" (  ) -- here are some key texts of this page :  Question: I'm very surprised that there is no [relatively] mature application to address these issues ?! Like diskettes of years past, we now accumulate external drives that are USB, Firewire, e-SATA, or flash. Unlike diskettes, these new drives hold hundreds or thousands of files. It is so easy (and inexpensive) to grab a drive a copy files that it is trivial to accumulate duplicates or more instances of the same files. All of this makes a catalog very valuable AND makes duplicate identification all the more so. Answer: It is possible that this (making a catalogue with find /media/Disk1 * > ~/Indices/Disk1_index ) and then searching for a filename in those catalogues with grep filename ~/Indices/* is so trivial from the command line, that no one has bothered to develop anything more complicated than gwhere (which seems to work, though I only used it the once). Duplicates are another matter altogether: Same filenames does not necessarily mean that the contents of those files are the same. Conversely, different filenames does not necessarily mean that the contents of the files are different. Remark: There are several *nix utilities for dealing with this sort of problem, fdupes comes to mind, but there are others. No application could compete with the method "find for indexing, grep for search"  I tried "gwhere" but it's limited and slow and its last version is of 2007. Most file catalog utilities i find are for Windows .. Must Linux users really learn to use command line functions like "find" and "grep" to do all kinds of queries ? Eg. in a search, we often want to exclude some file types or include only images, search by date / period, etc. Someone must have created some nifty GUI which sets all proper find & grep parameters as our options ? Does anyne know of a good modern Linux GUI application to catalog and search files ? maybe using a DB, not some big CSV / XML file ?

One of the things I like best when using OS X is the  tool. You can click a magnifying glass in the corner, and search for apps, files, anything. Windows 7's Start Menu search tool is similar. Does Ubuntu have anything like this?  Gnome Do has some similarities, but it's really more about doing things than searching for things. Something with a panel applet like Spotlight would be ideal.


My highly configured Dell Latitude E6410 laptop has become extremely slow, even for browsing or multitasking for the past 14 months. I thought it was because of Windows, so I tried fresh installations of win7, 8.1 and 10 - Still didn't solve the issue. But it was amazingly fast when it was new. The laptop originally came with a 95w power adapter, which I lost, and using a 65w adapter. Could this be causing the trouble? Machine also seems to overheat quickly.  Full specs  Core i5 2.5 ghz  8gb 1600 mhz  Nvidia M3100 graphics chipset  SSD 256GB

I have two laptops (same manufacture), with the same type of power connector.  However, the power supplies/transformers are slightly different.    The output on the first laptop's power supply is 15.6 V at 8.0 A. The output on the second laptop's power supply is 15.6 V at 5 A.  Clearly the voltages are the same, but the currents are different. I assume the second laptop's power supply can not be used on the first, because it can't supply enough power to the laptop.   However, can the first laptop's power supply be safely used on the second laptop?


After upgrading from Desktop 12.04 LTS to Desktop 14.04 LTS. The File Manager seems to be severely degraded. The sidebar no longer allows a tree-structured view of directories. The menu bar is very limited with no File, Edit, View, etc. There does not seem to be any alternate means of doing what these things did in 12.04. Any insights appreciated. -chaz

Using dconf-editor I tried enabling   org -> gnome -> nautilus -> list-view -> use-tree-view     but even after the check box is selected, plus a reboot, it still doesn't switch to the tree view on the side bar.  In previous versions of Nautilus / Ubuntu the side-pane-view setting used to be in the window-state section (which is now missing)    I'm I missing something, or is there no way to enable Tree View on the side bar in 14.04?  Is there a way to manually create the missing entry back in window-state ?


//asp <asp:DropDownList ID="ddlGroups" runat="server"></asp:DropDownList>  //code behind  protected void SelectAccessLevel()         {             List<string> ADGroups = new List<string>();             ADGroups.Add("Group1");             ADGroups.Add("Group2");             ADGroups.Add("Group3");              ddlGroups.DataSource = ADGroups;             ddlGroups.DataBind();         }   Create a drop down list in ascx page, bind to list in code behind and display on screen. Nothing displays in DD on screen..as to why? is it correct to bind the drop down or do I need to create another dd in code behind it to that?

List<String> nameList = new List<String>(); DropDownList ddl = new DropDownList();   List is populated here, then sorted:  nameList.Sort();   Now I need to drop it into the dropdownlist, which is where I'm having issues (using foreach):  foreach (string name in nameList){     ddl.Items.Add(new ListItem(nameList[name].ToString())); }   No workie - any suggestions? It's giving me compile errors:  Error - The best overloaded method match for 'System.Collections.Generic.List<string>.this[int]' has some invalid arguments   Error - Argument '1': cannot convert from 'string' to 'int'


I want a user to supply 2 or more parameters that i can use for the where clause of my query. What would the best and also safest way (to avoid sql injection) be?   the query might look like this:  "select * from table where id in (x1,x2);"   or it might be:  "select * from table where id in (x1,x2,x3,4,x5);"

What are the best workarounds for using a SQL IN clause with instances of java.sql.PreparedStatement, which is not supported for multiple values due to SQL injection attack security issues: One ? placeholder represents one value, rather than a list of values.  Consider the following SQL statement:  SELECT my_column FROM my_table where search_column IN (?)   Using preparedStatement.setString( 1, "'A', 'B', 'C'" ); is essentially a non-working attempt at a workaround of the reasons for using ? in the first place.    What workarounds are available?


Can anybody help me to produce this? I couldn't find anything similar on the forum.  No need for a grid.     Thank you,  Mironas

I'm using TikZ to plotting some functions for a document. For example, I want to plot 1/(x+1). So I did something like this:  \begin{tikzpicture}[>=stealth,x=3mm,y=3mm] \draw (0,5) node[above]{\fimg $y=f(x+1)=\dfrac{1}{x+1}$}; \clip (-5,-5) rectangle (5,5); \ejes[1]{-4}{4}{-4}{4} \draw[samples=100] plot(\x,{1/(\x+1)}); \end{tikzpicture}   where \ejes[style]{xmin}{xmax}{ymin}{ymax} is command, that I have defined before to draw the axes (join with \fimg). My expected output for the code below was just the function, but I get this:    So, TikZ automagically put the vertical asymptote at x=-1. That isn't a bad thing, but now I want to have some control over it. For example I want dotted lines for vertical asymptotes. How can I do that?


My wifi adapter RTL8821CE doesn't work. I managed to solve this issue in Ubuntu 18.04, but now after installing 19.04 it's not working anymore. Does anyone know how to solve this issue?  The output for lshw -c network is   $ sudo lshw -c network    *-network UNCLAIMED               description: Network controller        product: RTL8821CE 802.11ac PCIe Wireless Network Adapter        vendor: Realtek Semiconductor Co., Ltd.        physical id: 0        bus info: pci@0000:01:00.0        version: 00        width: 64 bits        clock: 33MHz        capabilities: pm msi pciexpress cap_list        configuration: latency=0        resources: ioport:3000(size=256) memory:a1100000-a110ffff   *-network        description: Ethernet interface        physical id: 3        logical name: enp0s20f0u1        serial: 96:c8:e8:52:94:a7        capabilities: ethernet physical        configuration: broadcast=yes driver=rndis_host driverversion=22-Aug-2005 firmware=RNDIS device ip=192.168.42.79 link=yes multicast=yes   The output of rfkill list all is:  $ rfkill list all 0: hci0: Bluetooth     Soft blocked: yes     Hard blocked: no

We just bought a Lenovo  (which is supposed to have the Intel 8265 for wireless). This laptop was bought in part because it is certified to run Ubuntu and as such to me at least it would make sense for things to work out of the box... but no such luck.  First, I installed Ubuntu 17.10 and after installation realised Wi-Fi was not working. I also tried Ubuntu 16.04 from a USB drive since that is the version of Ubuntu it is certified for, but no luck there either.  The wireless chip is not detected by lshw (or even lspci by the looks of it), ip link does not show a wireless interface, and the iwlwifi kernel module is not loaded at boot (I can load this myself using modprobe iwlwifi but this does not make Wi-Fi work). I think it is a combined Wi-Fi/Bluetooth chip, and Bluetooth does appear to work (or at least Bluetooth shows up in Gnome and rfkill list).  modinfo iwlwifi | grep 8265 shows me a file ending in -34 is supposedly loaded but only a file ending in -33 (and some other lower numbers) is present in /lib/firmware, if that helps).  I have also installed the Linux 4.14.9 kernel in an attempt to get things to work, but this did not resolve the issue either.  Further information  root@ThinkPad-E570:~# modinfo iwlwifi | grep 8265 firmware:       iwlwifi-8265-34.ucode root@ThinkPad-E570:~# rfkill list all 0: tpacpi_bluetooth_sw: Bluetooth     Soft blocked: no     Hard blocked: no 1: hci0: Bluetooth     Soft blocked: no     Hard blocked: no root@ThinkPad-E570:~# dmesg | grep iwl root@ThinkPad-E570:~# lspci -nnk | grep 0280 -A3 05:00.0 Network controller [0280]: Realtek Semiconductor Co., Ltd. Device [10ec:c821]     Subsystem: Lenovo Device [17aa:c024]   Update  I just noticed that the laptop does not have an Intel wireless chip at all, but in fact has a Realtek one... which means that the  of the shop I bought this laptop at were not accurate... Sigh. Same problem stands, however, just with a crappier wireless chip.


I have this sentence: The best engineers optimize every aspect of their lives.   Should it be "lives" or "life"?  I'm thinking lives because engineers is plural.  Thanks

What is the rule for singular noun objects of plural subjects? For example I and  agree that     They gave their word.   is better than     They gave their words.   To my mind, this is because each has but a single word to give and cannot give more. However, google seems to  on     They gave their life.   vs     They gave their lives.   As you can see in the linked N-gram, the second is far more common than the first. What's going on here? People (cats excluded) only have one life and it seems passing strange that they would be able, let alone willing, to give more.   If pressed, I would claim that the object should only be plural if each of the subjects has many. For example     They called their friends   If each of the "they" in question has only one of whatever object we are talking about I would call it ungrammatical to have that object in the plural form. Am I wrong?    EDIT:  This question was prompted by a comment on  on S&F.SE defending the use of consciousnesses as the plural form of consciousness by referring to . The word was used in this sentence:     Looking for a story where people download their consciousnesses into bodies   It occurred to me that whether or not consciousnesses is correct, it should not be used in that (admittedly bizarre) context since each person only has one consciousness to download. I would have therefore said     Looking for a story where people download their consciousness into bodies   This to me seems like an equivalent sentence to they gave their word or they gave their life. In all three cases I would use the singular form of the noun since each of the subjects can only give (or download as the case may be) one.


The sentence:      Two of the three crew members are killed, one of whom dies later in   hospital.   There are initially three people, and two of them are dead. Let's call them A and B. Let's say B dies later. Then the sequence of event goes like this.   Plane crashes -> A dies -> B dies in the hospital.   To describe this sequence of events, I would say:      Two of the three crew members were killed; one of whom have died later   in hospital.   because there's a need to differentiate the time of each death, but I'm not too sure if I have achieved it correctly. I would argue that the first sentence is wrong because the later clause indicates the present, which clearly does not make sense.

I am preparing a book for publication which contains the following passage:     Stromberg in Religious Liberalism in Eighteenth-Century England   (1954) noted that 'the critical moment in the emergence of a positive   spirit of reform...consisted in the awareness of evil as being social   and remediable. It begins about 1750.'   My proof reader (my wife) has picked this out suggesting it should be the past tense. However if I say It began about 1750 it seems to convey too much certainty about the exact date. I just want to convey an impression of it being something which emerges in the mid-eighteenth century. I believe use of the present tense is the way to go.   But what is this artifice called, this use of the present to convey mild uncertainty?


In the following problem, you are given three pieces of information. Use them to answer the question.   $GCF(a,b)= 13\cdot 7$ $LCM(a,b) = 13^2 \cdot 7^3 \cdot 41$ $b=13^2 \cdot 7 \cdot 41$ $a \in \mathbb{N}$      What is $a$ ?

Given: $\operatorname{gcf}(x,36)=9$ and $\operatorname{lcm}(x,36)=108$. Find $x$.   p.s I tried $54$ but although the $\operatorname{lcm}$ of $54$ and $36$ is $108$ the GCF is $18$ and it has to be $9$. Help me please.


I'm writing a command for a customised enchantment that teleports a player holding a certain item to the direction that it's facing. However, according to my knowledge, there's no statistic in /scoreboard that could simply detect a player's left-click. The scores that I've though about include damage_dealt that detects whether a player causes damage. However, I don't actually need the player to cause damage to activate the teleporting, so this may not work because the player can click without causing damage also thought about the ITEM_USE score, but this does not include left-click either, only right click. Anyone could tell me how to detect the player's left-click please? Thank you!

Is there a way so that I make make it when I left click/right click with a certain item it applies an effect? I know that you can apply attributes to wearing armor and things but I want it so when you use the item it applies an effect on your player.  For example, let's say I want something so that when I right click with a certain item (let's say an iron ingot that was given to me) I'll then have a jump boost for 10 seconds. So kinda like a potion in a way.  Is this possible with command blocks/commands/any mods?


I just noticed that the little green-encased number in the Activity tab's Reputation pane is bumped up too far:    For reference, that red line is perfectly straight and used to be level across the top of the green box and the black number. The problem seems to have appeared at the same time the reputation number in usercards got darker.  I see this issue on Meta Stack Exchange and Super User, suggesting that it affects all/most/many sites.

Here is a screenshot of my reputation information box.  The green +5 next to the 1,892 seems a bit too high. The numbers on the graph also look not quite right, and in fact, looking at the tooltip when moving over it, it is in the wrong place numerically.   It happens on both Firefox and Google Chrome.


I updated my Android phone with Android N using Android Beta Program, Now if I factory reset my phone, will it revert the OS version back to the old one?

I have upgraded my phone to Android 2.1. I need to reset my phone but I don't want to lose the upgrade. Is it possible to do this? How?


I have to create a counter with 4 flip flops jk synchronous. The counter shall count in this order: 3 to 13 and then to 3 to 13 and so on..  I have to use logisim simulator.   Until now what i´ve achieved is this:  it counts from 0 to 13 but i dont know how to to add the count 3 at the beggining... Could someone show me the simulation done on the logisim?

I have to create a counter with 4 flip flops jk synchronous. The counter shall count in this order: 3 to 13 and then to 3 to 13 and so on..  I have to use logisim simulator.   Ok. So i think its solved. I realized that the circuit needs to start at 0 ou 1 and stabilize after the 13 and then it goes to 3. Thanks for your help.  Hope this will help for somebody else too.  Thank you all for your help!


On some long-standing unanswered questions there is often an answer that is probably the right answer, with more upvotes, comments including positive words & chatter.  So could the system itself offer a 'soft' decision on long-standing unanswered questions by using an algorithm to determine which answer should be accepted based on various indicators.  This would be especially useful on answers to questions where the OP has left, is dormant or if nothing is accepted after a year.  Perhaps a 'soft' accept would be worth half the reputation improvement of a 'hard' accept.  So should an algorithm determine the probably right answer in certain situations where the OP hasn't, can't or won't make the call?

I think it would be cool if a question would eventually open up to moderators to accept answers on the user's behalf, once a time period has passed. The asking user would get the rep score for the accept.  I know I've seen questions successfully answered with lots of upvotes and no accepted answer that sit there for months unaccepted. This would give superusers a little more functionality and would tie up a lot of loose ends.  What do you think?


I'm confused by the exercise solutions of the book Applied Predictive Modeling.  In   at the beginning of page 4  Resampling results   RMSE   Rsquared  RMSE SD  Rsquared SD   1.382  0.8716    1.014    0.08729 The RMSE is slightly more than 1.4%   To my knowledge RMSE isn't a % (of what?) It's  mse <- mean(residuals(fit)^2) rmse <- sqrt(mse)   Can someone help me on this?

I am running the classify in Weka for a certain dataset and I've noticed that if I'm trying to predict a nominal value the output specifically shows the correctly and incorrectly predicted values. However, now I'm running it for a numerical attribute and the output is:  Correlation coefficient                 0.3305 Mean absolute error                     11.6268 Root mean squared error                 46.8547 Relative absolute error                 89.2645 % Root relative squared error             94.3886 % Total Number of Instances               36441    How do I interpret this? I've tried googling each notion but I don't understand much since statistics is not at all in my field of expertise. I would greatly appreciate an ELI5 type of answer in terms of statistics.


What would you call the thing on this image:      I am looking for the general term, I know that it has more types:   wheat barley oat rye   Suggestions:    grain cereal cereals

In most languages, the word used for a single caryopsis seed is a good equivalent of grain — it is not only the translation for this kind of seeds, but also the translation for other meanings of the word, such as a grain of sand. In English, this is used for grain of rice and other cereals, and even for botanical non-grains like amaranth. But then suddenly, other similar seeds are called by other words whose primary meaning is much less suited than that of grain. The examples I have in my head are kernel of maize and wheat berry.   Why this strange mixing of words? A grain is well aligned with maize and wheat not only in its meaning as a caryopsis seed, but also the other meanings like grain of salt exhibit some similarity, as this is a single very small discrete dry piece of something encountered as a large mass, which has fluid-like dynamics as a whole (you can pour salt, and you can even have phase separation with two different sizes of grains). Many other languages follow this logic.   A kernel as I understand it is something which is at the middle of a thing, somehow giving it definition. If you want a look at it, you have to extract it from its outer layers. Also, there is definitely only one of it, just like a human has many bones, but only one skeleton. This is true to some extent for both “normal” plant kernels (like peach kernels) and the new meaning of an OS kernel. I think that the mathematical meanings of kernel follow this metaphor, like the kernel of a matrix. But maize — which should logically have grains — has kernels, which are unlike all the other objects I have heard being called kernels.   A berry is a word I like, too. While I am aware that botanically, the fruits we call berries belong to different categories of fruit, they have very similar culinary properties. They are always juicy, taste best when raw, combine a sweet and a sour taste, are small, not starchy at all, and make good jams. The color is also mostly somewhere between red and blue. But they don't have a shape in common — compare the classically heart-shaped strawberry, the round blueberry, and the agglomeration called a raspberry. And then we have wheat, which differs from true berries in all points I listed — and somebody calls its grains wheat berries.    Edit: I was probably too mired in descriptions to state the question clearly. While there probably isn’t an all-encompassing reason for all existing cases (but if there is one, I’ll be glad to hear it), I’d like to hear the reasons for the two specific cases I listed, as in kernel of maize and wheat berry. Why was an exception made for exactly these two, and why was the specific word chosen for them?


When I copy large files to an external drive, although nautilus's progress popup indicates it's finished, the transfer is not actually completed, I need to open terminal and use sync to make sure it is finished, and for large files, sync will take a long time. Is it possible to let the GUI, e.g. nautilus tell me the actual progress.

I don't know why it's happening only to me. Whenever copying bigger or sometimes smaller < 1GB files from PC to pendrive literally gets stuck at the end.


I have Macbook pro 15" early 2011 and my GPU died a couple of weeks ago. I contacted Apple service center about the costing and they said a whooping 1000 USD to replace the board. From one of my friend I got contact of former apple technician and he said he will change the logic board for half the price.   After a week he returned my macbook saying he had replaced the logic board. Now I am little confused if he really had changed the logic board or get it repaired? Because the serial number on logic board is same as previous.   I know this question is asked before here but I am not able to get a straight answer from there.   Can any apple technician confirm if Apple replace the logic board do they provide the same serial number on new logic board?

I recently had the Logic Board in my Retina MBP 15″ 2012 replaced under a warranty extension program and Apple paid for it. I've reinstalled OS X several times and feel things aren't running properly. Also, I also couldn't find a way to merge my Time Machine old backups with new one.  The problem I have is confirming that I actually got a new board installed. I have not found a way to confirm this. My Mac help isn't helpful and Google is even less helpful. Why is it so hard to confirm that new hardware is really installed after this repair?


How do I transfer songs purchased from my iphone to itunes on my computer?  I only want to transfer purchased music, not apps or other purchases.

So, I wiped my drive clean on my MacBook and reinstalled the OS. Happily the best of my music was safe on my iPhone and I figured it would easily flow back to my iTunes library.  Not so happily, I can't seem to figure out how to get this music, which is mine, to the laptop, which is mine, from the iphone, which is mine.    I don't want to jailbreak my phone just for this one task, I'm running iOS 4.2.1 on an iPhone 3G and my MacBook 5,1 runs OS X version 10.6.5.  I would like my music back.  How to do this?


I would like to change equation numbering like: (1a) (1b) (1c). How should I do this? My code is like this:  \begin{equation} first equation with number(1a) \end{equation} \begin{equation} first equation with number(1b) \end{equation} \begin{equation} first equation with number(1c) \end{equation}

Sometimes it is convenient to refer to a group of equations by a letter and a number.  For example:   2+1   (A1) 2+4   (A2) x^4   (B3) x^e   (B4)   Placing  \tag{A\theequation}\label{eqn:thisone}\stepcounter{equation}} instead of just \label{eqn:thisone} works, but seems hacky (especially manually stepping the counter).   Is there a better way?


When I export my project to fbx some materials disappear and Its white But some materials are normal rendering. For example glass disapear but some easy materials are normal rendering.

I used node textures in a mesh I exported to .FBX.  I then imported it into Unreal Engine 4 and it didn't import any textures; I clicked the Upload Textures option in Unreal Engine.  Is there something I'm doing wrong or is it Blender?


I have a .txt file in here "C:\failass.txt". It contains the following info:  AA051245445454552117989 LT647044001231465456 LT517044077788877777 LT227044077788877777 CC051245445454552117989   I have found a code which scans if the user input matches the info contained in the file:  package ibanas;  import java.util.Scanner; import java.io.File; import java.io.FileNotFoundException; import java.io.IOException; import java.util.Scanner;  public class ReadFromFile {  public static void main(String[] args) throws IOException {     Scanner myScanner = new Scanner(System.in);     System.out.println("What number would you like to check for?");     String number = myScanner.nextLine();     if(isFound(number)){         System.out.println("The number "+number+ " is there");     }else{         System.out.println("The number "+number+ " doesn't exist");     } }  public static boolean isFound(String number) {      Scanner sc = new   Scanner(ReadFromFile.class.getResourceAsStream("C:\failass.txt"));     String word="";     while (sc.hasNextLine()) {         word = sc.next();          if (word.equals(number.trim())) {              return true;         }     }     return false; } }   But when i enter (for example) this line AA051245445454552117989 it gives me the following error:  What number would you like to check for? AA051245445454552117989 Exception in thread "main" java.lang.NullPointerException at java.io.Reader.<init>(Unknown Source) at java.io.InputStreamReader.<init>(Unknown Source) at java.util.Scanner.<init>(Unknown Source) at ibanas.ReadFromFile.isFound(ReadFromFile.java:24) at ibanas.ReadFromFile.main(ReadFromFile.java:15)   Thanks for any advice :)

What are Null Pointer Exceptions (java.lang.NullPointerException) and what causes them?  What methods/tools can be used to determine the cause so that you stop the exception from causing the program to terminate prematurely?


I have four shapes that make up a circle. I've grouped them and I'm trying to rotate them together. But instead of rotating all object together as a circle, all four objects rotate individually around the individual object centres.   How can I rotate all four objects around the group's centre?

Is there a way to specify the center of rotation in Sketch? Normally it simply rotates the object around its center. If there is no native way maybe it's possible to write a plugin!?


I need to define a command to create a notation like     because I don't want to write     However, the spacing in the first image is not cool. I'd like it to be like the space between tan and theta here:    How can I do that? Thanks.

Mathematical operators, such as function names, should be set in roman type, not italics. Latex already has commands for some operators, including \max, \min, and \log.  How can I define additional such commands?


There's a certain class of problematic questions which appears regularly in Stack Overflow: live website help questions. They generally go like this:   The asker has a problem with their website. The CSS isn't working, their JavaScript isn't broken, or their HTML isn't cooperating. They link their website directly, and provide no code samples in the question - often because the code concerned would be most of the webpage and its enormous quantity of HTML, CSS and JS, and there's no way to provide some simple code extracts.   This is the latest example:   The problem is these questions are useless to all future visitors  Code questions generally need code examples. That way, future visitors can look at the problem, understand it, and recognise whether it's their issue or not.  In the case of questions where the only example is a live website, the problematic code will probably be fixed within days, and the webpage may be entirely replaced or cease to exist within months.  Essentially: within a few days, nobody will be able to understand and recognise the problem, or learn from the questions. I would go as far as to say these questions only help the asker.  How do we respond to these questions?  Do we downvote them? Do we close them with the close reason of "Questions concerning problems with code you've written must describe the specific problem — and include valid code to reproduce it — in the question itself"? Do we need a specific close reason, or do we need to specifically mention somewhere that a live website is not a sufficient code example?

I notice a steady stream questions in the HTML and CSS tags that point to a site or CSS style sheet, and describe a problem without incorporating any code into the question. A few random examples:      (at least has a screenshot, but still)  Although it is totally understandable and natural for an OP to ask this way - they probably even think they are doing the site a service by not cluttering it! -  I can't shake the feeling that these questions are a problem: They will lose all value to future generations when the problem has been fixed. The OP is likely to fix the problem in the site source, and it becomes impossible to ever again see the source code of the problem that the answers solve. Asking the OP to incorporate code into the answer will work sometimes, but usually it won't. Is this a real problem? If it is, what to do?


Prove the following a tautology : (P ∧ ¬Q) ↔ ¬(P → Q)  I started with trying to seek a contradiction for (P ∧ ¬Q), but honestly I'm lost and don't know how to proceed. Any help would be appreciated.

For example:     Is (A ∨ B ∨ C) ∧ (D ∨ E ∨ F) the same as   (A ∧ D) ∨ (A ∧ E) ∨ (A ∧ F) ∨ (B ∧ D) ∨ (B ∧ E) ∨ ( B ∧ F) ∨ (C ∧ D) ∨ (C ∧ E) ∨ (C ∧ F)?   How would I check equivalence in general?


Should you use it or they when referencing a group of people?  Here is the example sentence:     A group of students was walking on the road when a truck hit them/it and it/they was/were immediately admitted to hospital.   Could native speakers and grammarians please answer this question? For me, it should be used because I am taking about the group as whole, and the group is one thing not many things.

Possible Duplicate:          When I'm referring to a group of multiple things, should it be considered singular or plural for the purposes of applying a verb to it?  For example, which is correct in the examples below?     A sentence is a group of words that is followed by a period.   A sentence is a group of words that are followed by a period.      The group of people constitutes a jury.   The group of people constitute a jury.      A group of crows is called a 'murder'.   A group of crows are called a 'murder'.   My instinct is that it depends on whether the verb is referncing the group itself or the members of the group directly, but is that right?


I owe a HP 15bs-146tu i5 8th gen Laptop and have installed ubuntu on it.!  the network adapter is "Realtek RT8723DE 802.11B/G/N PCLe Adapter".There is no option for wifi connectivity in ubuntu.PLease help ASAP.

How do I install Wi-Fi drivers for Realtek RTL8723DE device in Ubuntu 16.04?  lspci -v | grep -i network 02:00.0 Network controller: Realtek Semiconductor Co., Ltd. Device d723


I know this question has been asked , and  before ,  But I have problem with  answers, so here is mine :  I have changed my urls structure ( not my domain ), and I want  google to remove the old urls and replace the new ones, and  I can't make redirection because I dont know what is it exactly ( its very dynamic ), How can I do this ?

I have used so many things like url removal request and deleted the pages etc., but still the errors are shown in my webmaster tools.  How can I remove the urls completely from Google?


Will a downvote from a user below 125 give you reputation penalty (-2)?  I just want to know how it works. I tried to register a new account and downvoted on one of my answers. I didn't get the -2 penalty.  But I wonder if a user with higher reputation (higher than 1, but below 125) would make me lose 2 reputation when downvoting one of my answers.

Users below 15 reputation can't effectively vote. It says:     Votes cast by those with less than 15 reputation are recorded, but do not change the publicly displayed post score   Does it mean that they will take effect after I reach 15 reputation or because they were cast before, they're recorded but ignored?


I have a class called "summoners" with properties :  public string Name; public string Id; public int summonerLevel; public string division;  public string tier; public int leaguePoints;   To debug, i wanted to create a List<PorpertyInfo> and store every property name in it, i have :          public void listProperties()     {         List<PropertyInfo> t = new List<PropertyInfo>();          foreach (var attr in this.GetType().GetProperties())         {             t.Add(attr);         }     } //-> breakpoint   I placed a brakepoint and it tells me that there is no value in "t"

In C#, what makes a field different from a property, and when should a field be used instead of a property?


Only now you can even get them on top of wrinkles.   Only infrequently does it happen.      As one of our members has said, inversion happens when a sentence starts with "only" and never otherwise. So why does no inversion happen in the first sentence?

I have seen this construction quite often:      Online ads have been around since the dawn of the Web, but only in   recent years have they become the rapturous life dream of Silicon   Valley.   What is the rule there?. When your sentence doesn't start with pronoun + verb, invert them as verb + pronoun?. I know it sounds awkward but is it possible (grammatically correct) to use something similar to:      Online ads have been around since the dawn of the Web, but only in   recent years they have become...   And in any case, does this only work with have (or has)? Maybe it works fine with 'had' but I can't think of an example right now.


Trying to prove that $1 + 2 +\dots + n = (n + 1)n/2$.  I have let $n = 1$ in the basis step, which lead to $1=1$, so it is true for $n = 1$.  For the induction step, I have assumed that $k\geq 1$ and let $n = k$ leading to:  $$1 + 2 + . . . + k = (k + 1)k/2$$  For which we then have to use to prove that the statement is valid for $n = k + 1$, which is where I get confused because this the statement is supposed to become:  $$1 + 2 + . . . + k + (k + 1) = (k + 2)(k + 1)/2$$  While I thought it would have just been  $$1 + 2 + . . . + (k + 1) = (k + 2)(k + 1)/2  $$  Via the substitution of $k = k + 1$. Why is there still a singular $k$ in the $k + 1$ statement?

This is from  :     Use mathematical induction to prove that    $$1 + 2 + 3 +\cdots+ n = \frac{n (n + 1)}{2}$$   for all positive integers $n$.      Solution to Problem 1: Let the statement $P(n)$ be    $$1 + 2 + 3 + \cdots + n = \frac{n (n + 1)}{2}.$$      STEP 1: We first show that $P(1)$ is true.       Left Side $= 1$      Right Side $= \frac{1 (1 + 1)}{2} = 1$      Both sides of the statement are equal hence $P(1)$ is true.       STEP 2: We now assume that $P(k)$ is true   $$1 + 2 + 3 + \cdots + k = \frac{k (k + 1)}{2}$$   and show that $P(k + 1)$ is true by adding $k + 1$ to both sides of the above statement    $$ \begin{align} 1 + 2 + 3 + \cdots + k + (k + 1) &= \frac{k (k + 1)}{2} + (k + 1) \\ &= (k + 1)\left(\frac{k}{2} + 1\right) \\ &= \frac{(k + 1)(k + 2)}{2} \end{align} $$   The last statement may be written as    $$1 + 2 + 3 + \cdots + k + (k + 1) = \frac{(k + 1)(k + 2)}{2}$$   Which is the statement $P(k + 1)$.   My question is how in the very last line is the statement $P(k + 1)$ equal to $\frac{(k + 1)(k + 2)}{2}$. I don't get the last step.


By definition, for any $a\in\mathbb R$, there exists $k\in\mathbb N^*$ such that, if $n\in\mathbb N+k$, then $n!^{\large\frac1n}>a$. Therefore, by induction, I must:   find some $k$ that satisfies $k!>a^k$; show that, for each $n\ge k$, if $n!>a^n$, then $(n+1)!>a^{n+1}$.   For the 2nd part, it's enough that $k\ge a-1$. I noticed the smallest adequate $k$ is $4$ for $a=2$ and $7$ for $a=3$, and I'm convinced that one can always find a $k$, but I would like a function of $a$ to make an actual argument.  Definition aside, methods other than this one are welcome. I tried picking a sequence dominated by $\big(n!^{\large\frac1n}\big)$ that went to infinity as well, but couldn't find any.

How do I prove that $ \displaystyle\lim_{n \to{+}\infty}{\sqrt[n]{n!}}$ is infinite?


I have a dozen of included \usepackages and I'd like to collapse them using curly brackets { } in TeXstudio, but I'm getting error when I do that.                          ↓    Do you know either how to avoid errors, or another method to collaps a chunk of \usepackages in my preambule?

Using TeXstudio's GUI, I would like to collapse the calls of \usepackage{} similar to what can be done for a \paragraph{}, a \section{} etc. The fact that some code can be collapsed in the GUI is identified with a little arrow pointing downward (if expanded) or to the right (if collapsed) next to the first line of code that can be collapsed (see below).    I've tried using  \documentclass[a4paper,12pt]{article} { % this allows collapsing in the GUI (1/2)     \usepackage{color} } % this allows collapsing in the GUI (2/2) \begin{document}     text \end{document}   which allows me to collapse the \usepackage{} calls but doesn't compile.   In short: I want code that compiles and allows me to collapse the code like show in the picture below (as identified by the gray arrow in line 4). So far, I can either get the code to compile (not using the { } around the \usepackage) or I am able to collapse the calls in the GUI.    Does anyone have a solution or idea?


Is there an alternative to gpedit.msc for "Home" versions of Windows (ie: Vista Home Premium)?

I want to make some changes to Windows that require using the Group Policy Editor (gpedit.msc).  Unfortunately the Group Policy Editor is not included with the Starter Edition, Home and Home Premium editions of Windows.  How can I install it?


When I git pull, I pull from the default branch on my default remote. If I would like to pull from the remote "upstream", I have to specify the upstream branch that I would like to pull from:   git pull upstream name_of_branch.  I would like to specify a default branch for a given remote, so that I can achieve the above just by  git pull upstream  The reason is one of laziness - name_of_branch is in this case a bit of an long awkward name, and I have to do this relatively often.  I have not found a way to do this. Do you have any suggestions?

I'm not a git master, but I have been working with it for some time now, with several different projects.  In each project, I always git clone [repository] and from that point, can always git pull, so long as I don't have outstanding changes, of course.  Recently, I had to revert to a previous branch, and did so with git checkout 4f82a29.  When I was again ready to pull, I found that I had to set my branch back to master.  Now, I can not pull using a straight git pull but instead, have to specify git pull origin master, which is annoying, and indicates to me that I don't fully understand what is going on.  What has changed which does not allow me to do a straight git pull without specifying origin master, and how to I change it back?  UPDATE:  -bash-3.1$ cat config [core]     repositoryformatversion = 0     filemode = true     bare = false     logallrefupdates = true [branch "master"] [remote "origin"]     url = git@github.com:user/project.git     fetch = refs/heads/*:refs/remotes/origin/*   UPDATE 2: To be clear, I understand that my original method may have been incorrect, but I need to fix this repo so that I can simply use git pull again.  Currently, git pull results in:  -bash-3.1$ git pull You asked me to pull without telling me which branch you want to merge with, and 'branch.master.merge' in your configuration file does not tell me either.  Please name which branch you want to merge on the command line and try again (e.g. 'git pull  '). See git-pull(1) for details on the refspec.  If you often merge with the same branch, you may want to configure the following variables in your configuration file:      branch.master.remote =      branch.master.merge =      remote..url =      remote..fetch =   See git-config(1) for details.   I can tell git pull which branch to merge, and it works correctly, but git pull does not work as it did originally before my git checkout.


I'm studying boxing and unboxing topic from C# 5.0 in a Nutshell by Joseph Albahari and Ben Albahari. Copyright 2012 Joseph Albahari and Ben Albahari, 978-1-449-32010-2, but I need to extend the deep of knowledge and I found the MSDN article: , on it I found this example code (evidently not intrinsically related to the main topic):  Console.WriteLine (String.Concat("Answer", 42, true));   Once executed it returns:  Answer42True   Why this is happening with the literal 'true' (the same occurs with 'false')?  .  Thanks in advance.

true.ToString()  false.toString();  Output: True False   Is there a valid reason for it being "True" and not "true"? It breaks when writing XML as XML's boolean type is lower case, and also isn't compatible with C#'s true/false (not sure about CLS though).  Update  Here is my very hacky way of getting around it in C# (for use with XML)  internal static string ToXmlString(this bool b) {     return b.ToString().ToLower(); }   Of course that adds 1 more method to the stack, but removes ToLowers() everywhere.


I am attempting to follow the below solution for part (a) of Chapter 12, Problem M.7 in Artin's Algebra textbook. I am having trouble understanding why $\exists f_1,f_2\in M[f_1, f_2$ have no common factor].   By "common factor," I presume that this really means $\exists f_1,f_2\in M \forall d\in M$[$d|f_1$ & $d|f_2$ $\implies$ $d$ is a unit]. (Correct me if I am wrong.) But how would I go about proving that this is true?

Let $R$ be a principal ideal domain and let $P$ be a nonprincipal prime ideal of $R[x]$. I'm having trouble seeing why $P$ must contain two elements with no common divisor.    Can anyone help me? Thanks.


I am using a Samsung Note 2 (N7100) running on root. I want to know where Chrome for Android saves its cache files. Like on Windows, the cache is located on ..\AppData\Local\Google\Chrome\User Data\Profile 1\Cache. Where is the location for Chrome for Android's cache?

I'm wondering if it's possible to recover files from the Google Chrome cache from an Android phone, specifically, an HTC One S running Android 4.0.2.  I'm trying to recover the stylesheet from a site whose data has been partially lost, and of course this phone is the only device to have accessed it today before the crash.


Here in my class I have provided the serialVersionUID explicitly, but while using 'serialver' command in command prompt for this same class the UID is generated by the system as well.  Could anyone please throw some light over the understanding of use for explicit  and implicit SerialVersion UID?     class Emp implements Serializable {  private static final long serialversionUID =                              1293488886969693L;          int age;    public Emp(int age)  {      this.age = age;  }   }

Eclipse issues warnings when a serialVersionUID is missing.       The serializable class Foo does not declare a static final   serialVersionUID field of type long   What is serialVersionUID and why is it important?  Please show an example where missing serialVersionUID will cause a problem.


I have no idea how to read Dirac notation.   $$\left|↑↑ \right\rangle \tag{1}$$ $$\left|↑↓\right\rangle+\left|↓↑\right\rangle \tag{2}$$ $$\left|↑↓\right\rangle-\left|↓↑\right\rangle \tag{3}$$ $$\left|↓↓\right\rangle \tag{4}$$  What do the above expressions mean? Can you explain this in terms of the superposition?  Note: I am a sophomore in high school and have no linear algebra background. I am taking a science research course on quantum computing. Obviously, Dirac notation pops up a lot, but I don't know how to read it or tell what it is saying.

Quantum algorithms frequently use bra-ket notation in their description. What do all of these brackets and vertical lines mean? For example: $|ψ⟩=α|0⟩+β|1⟩$  While this is arguably a question about mathematics, this type of notation appears to be used frequently when dealing with quantum computation specifically. I'm not sure I have ever seen it used in any other contexts.     Edit  By the last part, I mean that it is possible to denote vectors and inner products using standard notation for linear algebra, and some other fields that use these objects and operators do so without the use of bra-ket notation.   This leads me to conclude that there is some difference/reason why bra-ket is especially handy for denoting quantum algorithms. It is not an assertion of fact, I meant it as an observation. "I'm not sure I have seen it used elsewhere" is not the same statement as "It is not used in any other contexts".


In my understanding, all things in python are object and some of them per-allocate memory to them (for int the range is from -5 to 256).  My question is if the address not per-allocate, does it create in fly?  for example:  print id(256) a = 256 print id(a)  36609008 36609008   this example indicates variable a is referring the object 256's memory, thus they have same address.   print id(300) a = 300 print id(a)  106711544 106708304   for the example above:   does python create two objects? (it seems yes) why -5 to 256? would those per-allocated object be reused to create new objects?

Why does the following behave unexpectedly in Python?  >>> a = 256 >>> b = 256 >>> a is b True           # This is an expected result >>> a = 257 >>> b = 257 >>> a is b False          # What happened here? Why is this False? >>> 257 is 257 True           # Yet the literal numbers compare properly   I am using Python 2.5.2. Trying some different versions of Python, it appears that Python 2.3.3 shows the above behaviour between 99 and 100.  Based on the above, I can hypothesize that Python is internally implemented such that "small" integers are stored in a different way than larger integers and the is operator can tell the difference. Why the leaky abstraction? What is a better way of comparing two arbitrary objects to see whether they are the same when I don't know in advance whether they are numbers or not?


Say we have $\frac{dy}{dx}=e^x$, then it is solved by taking $dx$ to right hand side of the equation and integrated.  My question is if $\frac{d}{dx}$ is an operator, then how do can take $dx$ to right? What is the explanation and reason behind this mathematically and intuitively?

I see an equation like this:  $$y\frac{\textrm{d}y}{\textrm{d}x} = e^x$$  and solve it by "separating variables" like this:  $$y\textrm{d}y = e^x\textrm{d}x$$ $$\int y\textrm{d}y = \int e^x\textrm{d}x$$ $$y^2/2  = e^x + c$$  What am I doing when I solve an equation this way?  Because $\textrm{d}y/\textrm{d}x$ actually means  $$\lim_{\Delta x \to 0} \frac{\Delta y}{\Delta x}$$  they are not really separate entities I can multiply around algebraically.    I can check the solution when I'm done this procedure, and I've never run into problems with it.  Nonetheless, what is the justification behind it?  What I thought of to do in this particular case is write  $$\int y \frac{\textrm{d}y}{\textrm{d}x}\textrm{d}x = \int e^x\textrm{d}x$$ $$\int \frac{\textrm{d}}{\textrm{d}x}(y^2/2)\textrm{d}x = e^x + c$$  then by the fundamental theorem of calculus  $$y^2/2 = e^x + c$$  Is this correct?  Will such a procedure work every time I can find a way to separate variables?


I'm working through the Spivak Calculus book, and am having some difficulty with the following problem. Assume that $f$ is a second differentiable function, $f(0) = 0$, $f(1) = 1$, and $f'(0) = f'(1) = 0$. Prove that $\exists c\in [0,1]$ such that $|f''(c)|\geq 4$. The hint that the text provides is prove that either $f''(x) > 4$ for some $x\in [0, \frac{1}{2}]$ or $f''(x) < -4$ for some $x\in [\frac{1}{2}, 1]$.   Using the Mean Value theorem, it's easy enough to prove that that $\exists c_1\in (0,1)$ and $f'(c_1) = \frac{f(1) - f(0)}{1-0} = 1$.   From here, you can apply MVT to $f'$ on $[0,c_1]$ and $[c_1, 1]$ giving  $\exists c_2\in (0,c_1)$ where $f''(c_2) = \frac{1}{c_1}$  and  $\exists c_3\in (c_1, 1)$ where $f''(c_3) = \frac{-1}{1-c_1}$.   From here, using the assumption that $c_1 \leq \frac{1}{4}$ yields $f''(c_2) \geq 4$ or $c_1 \geq \frac{3}{4}$ yields $f''(c_3) \leq -4$.   However, I am unsure of what to do if $\frac{1}{4} < c_1 < \frac{3}{4}$. I have been told that Cauchy's Mean Value Theorem (sometimes called the Generalized Mean Value Theorem) is the way to go concerning this problem, but I'm unable to make it work. Any thoughts would be greatly appreciated.

Suppose $f:[a,b]\to \mathbb R$ has derivative up to order $2$, and  $f'(a)=f'(b)=0$.  Prove there is  a point $c$ at $(a,b)$ such that  $$ |f''(c)|\geq 4\frac{|f(b)-f(a)|}{(b-a)^2}. $$    If it was factor 2, not 4, then I could use a Taylor expansion with Lagrange residue.


I have windows installed on my 500 GB hard disk which contains of 5 partitions. One for system drive and rest four for data. I want to format and remove all the 5 partitions and convert that to following three partitions:   30 GB Ubuntu Gnome 13.04. 2 GB Linux - Swap. 50 GB Windows 7. Rest windows ntfs partitions.   I have a bootable Windows 7 Ultimate DVD, a bootable Ubuntu Gnome 13.04 flash Drive. I don't wish to backup any data that I have I want to remove all the partition and install both the OS from scratch. I read many articles but each one has a different method some suggesting to use GParted, and some others to install Ubuntu first and then Windows etc.  Please suggest me a step by step detailed guide or reference to complete the task.

I want to reinstall Ubuntu, but I also want all information and settings to disappear. So everything looks like the first time I installed it. Is it possible to do so via Terminal? Or what are the steps I should follow?


I am reading an example off a grammar book.   Snow white smiled at the dwarves and me/I.   "Me" or "I" should I choose and in which situation should I use me or I?

In this case what is correct?        Keep Tom and I updated.      or         Keep Tom and me updated.      I understand that me is an object pronoun. And therefore I feel the second option is correct.  Especially, because I would say "Keep him updated" and also "Keep me updated". Instead of "Keep he updated" or "Keep I updated". But something about saying "Keep him and me updated" feels wrong.  However I am not sure, because several people have told me that in this case I is the correct option because it is being used in conjunction with a name (Tom) and not a pronoun. Is that correct?


I've been reading a lot trough different articles about dark-matter and dark-energy and how they could explain observations such as the acceleration of the expansion of the universe or the gravitational pull of galaxies.  But what I ask myself is why? Why were these objects introduced in the first place? Why did physicists jump to conclusion saying this was another kind of unknown matter (which seems to me as a giant leap), and what are the reasons that made them follow this lead? Couldn't we consider that matter "simply" has exotic properties at large scales, just like it has at microscopic scales, which seems more fitting to me.   Are their any leads or theories that try to explain these phenomena without introducing  the concept of dark-matter/energy?

Is there any physics theory that either groups together gravity and dark energy/dark matter or eliminates dark energy/dark matter by modifying standard understanding of gravity or any force? If so, is there any theory that still matches with all correct predictions of standard physics theories?


Anyone who's played with bar magnets knows that if you bring a bar magnet close to another tilted at some angle off axial to the other magnet, the one you're not holding will immediately flip to line up with the other that you're holding.   This would mean that every single tiny magnet sent in to the SG apparatus no matter the angle would immediately flip in to a vertical orientation in line with the applied field and be sent in a straight line through the apparatus, resulting in a single clump at the center.  Yet in most animations of the Stern Gerlach experiment (like this one here ), and indeed in explanations of the classical expected outcome of the experiment, we see the tiny magnets maintain their orientation throughout the trajectory through the magnetic field, and this is used as an argument as to why the tiny magnets are evenly distributed at the other end.  This has always bothered me why this is not reconciliated with our childhood experiences of playing around with bar magnets. Please note that I am NOT talking about the actual result of the experiment wherein the electrons formed two clumps one at the top and one at the bottom. I'm asking about the part where they explain the classical expectation of an even distribution.  My classical expectation is for only a single clump, right in the center because they all rotate line to up immediately entering the field and have equal magnetic forces up and down.   What is wrong with my expectation?

My understanding of the Stern–Gerlach experiment is that neutral (0 total charge) particles are sent through a non-homogeneous magnetic field, with the expectation that the field will push that particle's path higher or lower on a detector because of the collective spin of that particle. While the detector can detect particles in a two-dimensional surface, the results of the experiment are that particles appear in only two localized areas directly above the path of the particle stream, or directly below the path of the particle stream - spin up or spin down. The conclusions from these measurements are that the particle, when measured, will always have about the same magnitude.  Why does this not follow from classical mechanical theory related to magnetism? If you shot a magnet through a similar apparatus, I would expect the magnet to be rotated to align with the magnetic field in some way which, at high enough field strengths relative to the mass of the magnet, would cause us to measure basically the same magnitude as if the magnet entered the apparatus pre-aligned with the field.  How is my explanation incorrect?


Its very easy to pull a logic gate or transistor circuit of the internet for example and begin to understand how it represents physical bits, by either having 5V across the circuit or below 3.3V. But I was wondering what are some of the methods for representing qubits from a hardware perspective.  I have already looked on Wikipedia and find the explanation to be very abstract and vague.

I understand how normal logic gates operate and are implemented using digital circuits and electronics but I wad wondering how qubits are physically implemented.   In other words is a physical qubit a mechanical structure or an electronic circuit or optical circuit or something else.  There's often alot of information online about qubits and how they are different from normal bits but I have never seen any information about how they are possibly physically implemented.


I would like to know the code for grep to check for two matches one after the other. For example I have the following text from one of the search files:  @<TRIPOS>MOLECULE   ← pattern 1532                ← ID 17 17 SMALL NO_CHARGES   I need to find the exact match of the ID which is always located one line below pattern and then retrieve the file name from which ID was located.  I used the following command:  grep -Pzo '@<TRIPOS>MOLECULE'(?:.*\n)*?\K1532' filename   but I got files containing 1532 as well as for 153284. I need code for exact ID match.

How would you perform a grep for text that appears on two lines?   For example:  pbsnodes is a command I use that returns the utilization of a linux cluster  root$ pbsnodes node1     state = free     procs = 2     bar = foobar  node2     state = free     procs = 4     bar = foobar  node3     state = busy     procs = 8     bar = foobar   I want to determine the number of procs that match nodes that are in state 'free'. So far I have been able to determine the "number of procs" and "the nodes in free state", but I want to combine them into one command that shows all free procs.   In the above example, the correct answer would be 6 (2+4).   What I have  root$ NUMBEROFNODES=`pbsnodes|grep 'state = free'|wc -l` root$ echo $NUMBEROFNODES 2  root$ NUMBEROFPROCS=`pbsnodes |grep "procs = "|awk  '{ print $3 }' | awk '{ sum+=$1 } END { print sum }'` root$ echo $NUMBEROFPROCS 14   How can I search for every line that reads 'procs = x', but only if the line above it reads 'state = free?


I recently came across this definition: Let $(X,d)$ be a metric space and $A$ be a nonempty subset of $X$. For each $x\in X$ we define a distance from $x$ to $A$ by the equation  $d(x,A)=\inf\{d(x,a) | a\in A\}$  I would guess that such a function will be continuous. But is there an easy and rigorous way to prove it?

Let $(X,d)$ be a metric space. How to prove that for any closed $A$ a function $d(x,A)$ is continuous - I know that it is even Lipschitz continuous, but I have a problem with the proof:  $$ |d(x,a) - d(y,a)| \leq d(x,y) $$ for any $a\in A$ - but we cannot just replace it by $|d(x,A) - d(y,A)|\leq d(x,y)$ since the minimum (or infimum in general) can be attained in different points $a\in A$ for $x$ and $y$, so we only have that $$ |d(x,A)-d(y,A)|\leq d(x,y)+\sup\limits_{a,b\in A}d(a,b) $$ which does not mean continuity.