The following Lagrangian density describes a charged scalar field. Determine the global U(1) symmetry. Make this global symmetry local, give the Lagrangian density and show that this is Gauge invariant. The Lagrangian density is given by: $$L = \partial_\mu \psi \partial^\mu \psi^* - \frac{1}{2}m^2|\psi|^2 - \frac{1}{4}\lambda|\psi|^2.$$  My first idea was to perform the following transformation (because it is mentioned we are dealing with U(1) invariance): $$\psi \rightarrow e^{i\theta}\psi$$ $$\psi^* \rightarrow e^{-i\theta}\psi^*$$ $$\partial_\mu \psi \rightarrow D_\mu \psi = (\partial_\mu + iqA_\mu)\psi$$ and $$\partial_\mu \psi^* \rightarrow D_\mu \psi^* = (\partial_\mu - iqA_\mu)\psi^*$$ However I think this is what you have to do to obtain a local symmetry out of the global one. I have no idea how to find the global one. In short my questions are:  How do you find the global U(1) symmetry for a given Lagrangian density? Is the way to determine the local symmetry out of the global U(1) symmetry achieved by transforming in the following way: $\psi \rightarrow e^{i\theta}\psi$, $\psi^* \rightarrow e^{-i\theta}\psi^*$, $\partial_\mu \psi \rightarrow D_\mu \psi = (\partial_\mu + iqA_\mu)\psi$ and $\partial_\mu \psi^* \rightarrow D_\mu \psi^* = (\partial_\mu - iqA_\mu)\psi^*$? Is every Lagrangian density where you performed the transformation given in 2. Gauge invariant? If not, how can you check whether the Lagrangian density is Gauge invariant?  Thanks in advance!

The following Lagrangian density describes a charged scalar field. Determine the global U(1) symmetry. Make this global symmetry local and give the Lagrangian density. The Lagrangian density is given by: $$L = \partial_\mu \psi \partial^\mu \psi^* - \frac{1}{2}m^2|\psi|^2 - \frac{1}{4}\lambda|\psi|^2.$$  My first idea was to perform the following transformation (because it is mentioned we are dealing with U(1) invariance): $$\psi \rightarrow e^{i\theta}\psi$$ $$\psi^* \rightarrow e^{-i\theta}\psi^*$$ $$\partial_\mu \psi \rightarrow D_\mu \psi = (\partial_\mu + iqA_\mu)\psi$$ and $$\partial_\mu \psi^* \rightarrow D_\mu \psi^* = (\partial_\mu - iqA_\mu)\psi^*$$ However I think this is what you have to do to obtain a local symmetry out of the global one. I have no idea how to find the global one. In short my questions are:  How do you find the global U(1) symmetry for a given Lagrangian density? Is the way to determine the local symmetry out of the global U(1) symmetry achieved by transforming in the following way: $\psi \rightarrow e^{i\theta}\psi$, $\psi^* \rightarrow e^{-i\theta}\psi^*$, $\partial_\mu \psi \rightarrow D_\mu \psi = (\partial_\mu + iqA_\mu)\psi$ and $\partial_\mu \psi^* \rightarrow D_\mu \psi^* = (\partial_\mu - iqA_\mu)\psi^*$?  Thanks in advance!


I have create some sort of Template I'm using for my reports. The Data shown in those document is collected by a script running on a webserver.   I was wondering if there is an appropriate method for creating the whole reports via scripting. My first intention was to simply replace strings withing the .texfile but this seems to be a very dirty method.  I'm considering writing my own tool which should be capable of setting some sort of variables within the .tex file. Maybe in combination with a package created for this purpose. The final goal would be, to run everything as a web-service giving you the ability to simply download the finished report.  Are there any Tools which are already doing this?

I'm using Tex Live 2009 on Debian squeeze. I can upgrade if I really, really  have to, but I'd rather not. I was wondering if it would be possible to do the following.  Given some data in a (relational) database, can I extract it and automatically format it in a LaTeX table, so one would not need to manually recreate the LaTeX table if the data changes? Could one do such a thing with Lua? One would normally use a suitable language database adaptor for this, and I see Lua has . I'd like to use PostgreSQL. I'm currently using version 8.4.  Solutions not involving Lua are also fine. Just to be clear, I don't know anything about Lua and my knowledge of LaTeX programming is also extremely skimpy. I'm looking for a recipe which I can adapt if necessary. While this is not really important for my current use case, it seems like a useful general technique if possible.


I am working on this logical proof for class and trying to either prove or disprove that an irrational to an irrational power is also irrational. Please don't answer the problem for me but I'm completely stuck on how to begin. Any hints would be appreciated.

Can an irrational number raised to an irrational power be rational?  If it can be rational, how can one prove it?


I have a requirement that create a script name say ./123.sh when given a path to directory it should print the file or files with minimum, maximum and average file size . eg  $> ./123.sh /usr/share Minimum file size: 1024     /usr/share/lala.txt     /usr/share/koko.txt Maximum file size: 100234     /usr/share/somewhere/else/test.tar.gz Average file size: 5034   My code :  dir="$1"  if [ $# -ne 1 ] then     echo "please pass arguments"  exit 0 fi   if [ -e $dir ] then printf "minimum file size: %s\n\t%s\n" \  $(du $dir -hab | sort -n -r | tail )  printf "maximum file size: %s\n\t%s\n" \  $(du $dir -ab | sort -n | tail -1)  printf "average file size: %s" du $dir -sk | awk '{s+=$1}END{print s/NR}' else echo " directory doesn't exits" fi  if [ -d "ls -1A -- $dir" ] then echo " directory is empty " fi   If I execute my script with ./123.sh the output should be:   "please pass arguments".  similar to script with arguments ./123.sh hdkjflkjds  "please pass correct arguments".  Similar to script with arguemnts ./123.sh /usr/share The output should display.  $> ./123.sh /usr/share     Minimum file size: 1024         /usr/share/lala.txt         /usr/share/koko.txt     Maximum file size: 100234         /usr/share/somewhere/else/test.tar.gz     Average file size: 5034   Finally If I execute the script with arguments(i.e empty directory path) say /usr/bin  $./123.sh /usr/bin  It should display:  "Directory is empty".  Rather its showing for me an error like this.  $> ./123.sh /usr/bin         Minimum file size: 1024             /usr/bin/lala.txt             /usr/bin/koko.txt         Maximum file size: 100234             /usr/bin/somewhere/else/test.tar.gz         Average file size: 5034   can anyone check my code fidn out the mistake what I have done.

I have a requirement, if I execute a script ./123 with an arguments of empty path, say /usr/share/linux-headers-3.16.0-34-generic/.tmp_versions(this directory is empty). It should display "directory is empty"  My code is:  #!/bin/bash dir="$1"  if [ $# -ne 1 ] then     echo "please pass arguments"  exit fi  if [ -e $dir ] then printf "minimum file size: %s\n\t%s\n" \  $(du $dir -hab | sort -n -r | tail -1)  printf "maximum file size: %s\n\t%s\n" \  $(du $dir -ab | sort -n | tail -1)  printf "average file size: %s" du $dir -sk | awk '{s+=$1}END{print s/NR}' else    echo " directory doesn't exists" fi  if [ -d "ls -A $dir" ]  then     echo " directory is  empty" fi   I have an error displays like, if I execute the script name ./123 /usr/src/linux-headers-3.16.0-34-generic/.tmp_versions (this directory is empty).  minimum file size: 4096     /usr/src/linux-headers-3.16.0-34-generic/.tmp_versions maximum file size: 4096     /usr/src/linux-headers-3.16.0-34-generic/.tmp_versions average file size: 4   instead of showing output only "directory is empty" its shows the above output  The below output has to be display if I exceute the script with correct arguments( I mean with correct directory path). say ./123 /usr/share  minimum file size: 196         /usr/share     maximum file size: 14096         /usr/share     average file size: 4000   my expected output is: ./123 /usr/src/linux-headers-3.16.0-34-generic/.tmp_versions  directory is empty.


I understand  the definition of  limit. I can use it to prove things, but I still  don't  get the motivation behind it.

I am having a hard time grasping the definition of a limit. I initially learned this loose definition of a limit:  $\lim\limits_{x \to a}f(x)=L$ iff $f(x)$ approaches L when $x$ approaches $a$ from both directions.    Then i learned the epsilon delta definition, which states the following:  $\lim\limits_{x \to a}f(x)=L$ iff for any $\epsilon > 0$ there exists some $\delta>0$ where if $0<|x-a|<\delta$ then $|f(x)-L]<\epsilon$  The way i think about this definition(please correct me if I'm wrong) is that for any given range $\epsilon$ around L, we can find some range $\delta$ around x such that the function evaluated at those points will be within $\epsilon$ of L. However i don't understand how that statement is the same thing as saying:  $\lim\limits_{x \to a}f(x)=L$ iff $f(x)$ approaches L when $x$ approaches $a$ from both directions.


After finishing the "A Refreshing Rescue" Quest, Bottle & Cappy started visiting my Vault. What are their effects, other than the happiness boost? And how does the happiness boost behave?

So I ran a mission and rescued Bottle & Cappy. They now show up randomly, and I've seen some people's happiness rise, one in particular went from 10% to 75%.  Now one of my quest runners (basically my Avatar in the game, so I keep a close eye on him). He recently died, and on revival, his happiness has dropped to 10%. Now, since he's one of my primary quest runner, he doesn't get assigned to a room.   So will Bottle & Cappy cheer him up while he's wandering around the vault?


I'm a native English speaker (from Ireland) and to this day I'd hesitate in saying "wife-beater" when referring to a sleeveless shirt. It seems to be much more common in the U.S.  Where did this term come from and why?  gave conjecture that apparently it's from how people are dressed as they are arrested on the TV show "Cops" and/or men who commit domestic violence, but I find that really unconvincing to lead to such widespread usage while also not maintaining the negative connotation.   And how is it so commonly accepted without implying the more literal meaning? I just don't understand how it became natural usage and something people ultimately say without needing to clarify or lose a straight face.

I was a li'l nonplussed to find out that the word  can mean other things besides "a man who beats up his wife". Its definition reads:        One who (usually as a repeated practice) beats one’s wife, or a husband prone to violence   A kind of sleeveless shirt, often but not exclusively worn as an undershirt.   (uncountable, UK, slang) Stella Artois, a brand of lager beer.       reckons that sense 2 is American and originates "apparently from the association of such a garment with men who commit domestic violence". It does not register the UK slang. I'm guessing that Stellas also have an unfortunate association with domestic violence.  Are these alternative senses popular in their respective countries or are they perhaps nonce words that have lingered on? Any idea how these disparaging associations came about? I expect that the brewers of Stella Artois are none too happy about it.


I have a dynamically populated array of strings in C++:  string** A;   it is populated like this:  A = new string*[size1];   and then:  for (unsigned int i = 0; i < size1; i++) {     A[i] = new string[size2];     for (unsigned int j = 0; j < size2; j++)     {         A[i][j] = whatever[j];     } }   elsewhere, I want to find out the dimensions (size1 and size2). I tries using this:  sizeof(A[i]) / sizeof(A[i][0])   but it doesn't work. Any ideas ?  Thanks

I've allocated an "array" of mystruct of size n like this:  if (NULL == (p = calloc(sizeof(struct mystruct) * n,1))) {  /* handle error */ }   Later on, I only have access to p, and no longer have n. Is there a way to determine the length of the array given just the pointer p?  I figure it must be possible, since free(p) does just that. I know malloc() keeps track of how much memory it has allocated, and that's why it knows the length; perhaps there is a way to query for this information? Something like...  int length = askMallocLibraryHowMuchMemoryWasAlloced(p) / sizeof(mystruct)   I know I should just rework the code so that I know n, but I'd rather not if possible. Any ideas?


The question is simple, should I write  "In this section..." or "In this Section"  "In this chapter..." or "In this Chapter"  ?

If I have the following sentences, which version is correct:   This chapter provides.... or This Chapter provides....   Note the capitalisation of 'c'.   Chapter 1 provides.... Chapter One provides...   Note the use of numbers   This model was discussed in Chapter One This model was discussed in chapter one This model was discussed in Chapter 1 This model was discussed in chapter 1   Note the use of capitalisation and numbers in the last part of the sentence.  Many thanks.


I'm trying to solve a matrix equation Ax=b with numpy.linarg.solve() A = np.array([[1, 1], [15,10]]) b = np.array([12,170]) sol = np.linalg.solve(A,b) print(sol)  the result is [10.  2.]  this is right answer but, when I run the code below, print(sol[0], sol[1])  I get 10.000000000000002 1.999999999999998  why are they different?

Consider the following code:   0.1 + 0.2 == 0.3  ->  false   0.1 + 0.2         ->  0.30000000000000004   Why do these inaccuracies happen?


Me and 9 other employees made calls to people who have donated this year thanking them for their donation. I have a csv file of all people that called, who they called, and what was said on the call. I would like to import these interactions into salesforce to the corresponding donor accounts. I did a test import of one of the interactions to make sure that it will be imported the way we want. I imported it into the "task" object with the task subtype as "call" and this is what it showed on the donors account(See photo 1). I would like the upload to look this way (see Photo 2). This example was done manually and not via an import. But, as you can see it shows who called and what they talked about as soon as you click on the account. It's not until I click the blue "Call" hyperlink button when I am only able to see who called and what was said on the call. I would like this information displayed as soon as I go to the account. Could someone please help me with this? Is this possible via importing or will I have to do each one manually?

I am using the Service Console in Lightning Experience, and using the Chatter Feed component on the Case layout to display updates to the Case.  If I use the "Log a Call" Quick Action from the Chatter publisher, these calls are displayed in the Chatter feed.  This is the desired behaviour.  However, if I insert a Log a Call record related to the Case any other way - e.g. using the Developer Console, or my CTI system's custom components - the call does not display in the feed.  If I query the record, it looks exactly the same as the record that is created with the Quick Action.  It just seems that the Chatter post is never made in this situation.  I have checked my Feed Tracking settings:   Task has Enable Feed Tracking and Subject checked Case has All Related Objects checked   How can I enable calls created with a custom component (part of a CTI system) to display in the case feed?


I want to show that : $$\int_{0}^{\infty}\ln^2\Big(e^{-x}+1\Big)dx=\frac{\zeta(3)}{4}$$ I have tried substitution like $y=e^{-x}$ it gives : $$\int_{0}^{1}\frac{\ln^2(y+1)}{y}dy=\frac{\zeta(3)}{4}$$ Next I was working on the power series : $$\ln^2(1 + x) = \Big(\sum_{k=1}^{\infty}\frac{(-1)^kx^k}{k}\Big)^2 ,\quad|x|<1$$ And now I'm stuck because I don't know how to make zeta appear. Thanks in advance .

The definite integral  $$\int_0^1\frac{\log^2(1+x)}x\mathrm dx=\frac{\zeta(3)}4$$  arose in my answer to . I couldn't find it treated anywhere online. I eventually found two ways to evaluate the integral, and I'm posting them as answers, but they both seem like a complicated detour for a simple result, so I'm posting this question not only to record my answers but also to ask whether there's a more elegant derivation of the result.  Note that either using the method described in  or substituting the power series for $\log(1+x)$ and using  $$\frac1k\frac1{s-k}=\frac1s\left(\frac1k+\frac1{s-k}\right)\;$$  yields  $$ \int_0^1\frac{\log^2(1+x)}x\mathrm dx=2\sum_{n=1}^\infty\frac{(-1)^{n+1}H_n}{(n+1)^2}\;. $$  However, since the corresponding identity without the alternating sign is used to obtain the sum by evaluating the integral and not vice versa, I'm not sure that this constitutes progress.


If energy is proportional to mass, and temperature is proportional to energy density, does it mean there is a certain absolute maximum temperature which can never be exceeded? With further energy added to the system simply increasing its mass without affecting the temperature anymore?

If temperature makes particles vibrate faster, and movement is limited by the speed of light, then I would assume that temperature must be limited as well. Why is there no limit?


I'm using TeXnic Center, but I'm having an issue with getting my figures where I want them. I've used [h!] etc but when I write something else it will put it before and partially after my figures, i.e. not where I want it. Is there a way I can ensure my text is where I want it?

How to influence the position of float environments like figure and table in LaTeX?   This is a general question and should collect useful answers for all users. I hope we can use this as a reference


I am currently developing a Indie RPG that I hope to Kickstart next year. What is the best way to promote it? (I know this is a common question)  Currently I have found Google+ communities the best, and I'm using  to upload snippets of my work. I am directing people to email me if they are interested in beta testing.  Is there anything I am missing? What is it?

I am working on a tabletop RPG (SteamDICE) that uses lots of online integration (web-based and mobile devices), but to kick start the project to the next stage, we need supporters, backers and feedback. Even a great project is worthless, if nobody knows it.  What are good strategies to promote a new game?


I am using the following code to register a menu for my theme. In functions.php I have written the following:  register_nav_menu( 'header-menu', __( 'Header Menu' ) );   When going into wp-admin >appearance > menus, the menu is not showing up.  Can anyone telll me what I am doing wrong?

Please help with menu registeration:  I have followed this guide (http://codex.wordpress.org/Navigation_Menus) step by step.  Added the following code to functions.php:  function register_my_menus() {   register_nav_menus(     array('header-menu' => __( 'Header Menu' ) )   ); }  add_action( 'init', 'register_my_menus' );   But the guide says that this will make the menu appear in the Appearance -> Menus admin screen in the "Theme Locations" box as "Header Menu".  When I go to Appearance -> Menus everything is greyed out and there is no option of "Theme Locations"


I have a directory in my Cent OS machine where the users would drop in in all their files. I want to find out which user is dropping the large files in the folder.   Day by day this increases & would want to know the large files. Any command for that as I do not wish to check them manually.

I am trying to find the largest file in a directory recursively. If there is a subdirectory inside of that directory the function needs to go inside that directory and check to see if the largest file is there. Once the largest file is found the output is displayed with the relative path name and the name and size of the largest file.  EX:  dude@shell2 (~...assignment/solutions) % bash maxfile.sh ~/test class/asn dude.h.gch: 9481628   This is what I have:  #!/bin/sh clear  recursiveS() {     for d in *; do         if [ -d $d ]; then             (cd $d; echo $(pwd)/$line; du -a; recursiveS;)         fi     done } recursiveS   I have been stuck for a while now. I cannot implement this by pipelining a number of existing Unix tools. Any ideas would be nice!


Is there an easier way to break out of nested loops than throwing an exception? (In Perl, you can give labels to each loop and at least continue an outer loop.)    for x in range(10):     for y in range(10):         print x*y         if x*y > 50:             "break both loops"   I.e., is there a nicer way than:  class BreakIt(Exception): pass  try:     for x in range(10):         for y in range(10):             print x*y             if x*y > 50:                 raise BreakIt except BreakIt:     pass

Given the following code (that doesn't work):  while True:     #snip: print out current state     while True:         ok = get_input("Is this ok? (y/n)")         if ok.lower() == "y": break 2 #this doesn't work :(         if ok.lower() == "n": break     #do more processing with menus and stuff   Is there a way to make this work? Or do I have do one check to break out of the input loop, then another, more limited, check in the outside loop to break out all together if the user is satisfied?


I recently updated to 13.10 and it broke all my opencv stuff (impossible to compile or run previous programs that were ok on 13.04).  Cuda wasn't installed anymore, nor were the nvidia drivers.  So I tried to install them again (did it in 13.04). I tried all the suggestions here:  That is, trying to install from:   sudo ./NVIDIA-Linux-x86_64-331.20.run   It didn't work but I could recover from the low graphics mode issue. After enabling the proper repository I tried:  sudo apt-get install nvidia-331   It didn't work either. Finally   sudo apt-get install nvidia-current-updates-dev   This got me totally stuck; I now can't get out of low-graphic mode.   I've checked and tried:      What else can I try?

Note: This is an attempt to create a canonical question that covers all instances of "low-graphics mode" error that occurs to a user, including but not limited to installation of wrong drivers, incorrect or invalid lightdm greeters, low disk space, incorrect installation of graphics card like ATI and Nvidia, incorrect configuration of xorg.conf file while setting up multiple monitors among others. If you are experiencing the "low-graphics mode" error when trying to login but none of the following answers work for you, please do ask a new question and then update the answers of this canonical question as and when your new question gets answered.   When I try to boot into my computer, I am getting this error:  The system is running in low-graphics mode Your screen, graphics cards, and input device settings could not be detected correctly. You will need to configure these yourself.   How do I fix the failsafe X mode and login into my computer?  Answer index:


Ok So I have multiple pieces of text in the sky and they are falling down on a rigid body plane (the floor) and it's set to passive not active.  The problem is I don't want ALL of the text to hit the floor at the same time.  The 3D text is set as rigid too and it's set as active (so it falls).  The way I've gotten text to hit the floor at different times is by simply varying the heights of the text falling (text closer to the passive rigid plane will hit first).    I don't like this though.  I wish there was some way using keyframes etc. that I could change from passive to active so I could control exactly when the 3D text would start falling.    Is there any way to do that?  Thanks guys

I'd like to have a group of debris fall from a ceiling onto the floor, but not have them drop all at the same time. Is there a way to set a keyframe that dictates when the object enters the simulation? For example, object 1 starts falling on frame 0, object 2 on frame 5, object 3 on frame 24, etc.


High school physics student here, so please bear with me for a moment.  I know that light waves oscillate, but I don't know how. In textbooks and diagrams they're portrayed as wavy lines traveling through space, but I don't think most light waves oscillate in perfect sine waves like that (unless they're polarized).  At first I thought they oscillated in sort of a "spring" shape, like a three-dimensional sine wave, but I later found that that's another kind of polarized light called circular polarization. What I imagine now is the wave going all over the place while retaining the same amplitude and period, like a ball bouncing along in an infinitely long cylinder, but of course I have no idea if that's actually the case.  So what do light wave oscillations look like?

What does a light wave look like?   The only models I can seem to find online are 2D waves, they just look like sin() graphs.  I have seen the models of the two components of "light waves" (electric field and magnetic field) and they are represented on a 3D Cartesian coordinate system, but they are still just two 2D waves.    Surely light isn't really FLAT like this is it?   I guess I have always assumed it pules out in all directions greater then lesser as it travels, giving off the shape that you see during a sonic boom:    I have drawn what I picture to be a 3D model of the electric field of a light wave as it travels from left to right:   (cone image from: )  Is this an accurate representation of what the 3D radiation emitting from a light beam looks like, like a 3D wave?  (Obviously it would be more wavey, using a 3D cone graphic to create this diagram caused the edges to look spiked and sharp, a better object to use would have been something like a bullet (3D parabola) but I'm not the best with photoshop).    Also, if this is a somewhat accurate model of light wave pulsing in 3D, what does the magnetic wave look like in model form? Do they just overlap with possibly a slightly larger or smaller amplitude but the same maxima and minima locations along t (x-axis in my model)


I know that $ a\cdot\left(\frac1a\right)=1$  as long as $a$ is not $= 0$,  but when we divide $(\frac a0)$ is $=$ we say it's undefined.   why is it really undefined? what's the big conspiracy here.

Why does $x$ divided by zero not equal $x$? After all, $x$ is not being divided by anything.


Let $a$ be a postive integer and let $A=\{a,a+1,a+2,\ldots,a+9\}.$ Show that there exists some $i$ such that for any $j\neq i$ we have $(a+i,a+j)=1$

Given any $10$ consecutive positive  integers , does there exist one integer which is relatively prime to the product of the rest ?


In the below code I need to execute the newUrl:     ...   How to make it?

I need to do an  request in JavaScript. What's the best way to do that?  I need to do this in a Mac OS X dashcode widget.


I used to see conditions like  if (something == 0){do it}, but  now I've met this sentence in iOS_Book   if (nil == s)   Is this the same as if (s == nil) and if not, what is the difference?

I noticed for a while now the following syntax in some of our code:  if( NULL == var){    //... }   or  if( 0 == var){   //... }   and similar things.  Can someone please explain why did the person who wrote this choose this notation instead of the common var == 0 way)?  Is it a matter of style, or does it somehow affect performance?


Let $X$ be a scheme and $j:Z\subseteq X$ be a closed subscheme. Let $\mathcal{F}$ be a sheaf of modules over $X$. Show that \begin{equation*} j_{*}j^{-1}\mathcal{F}_{x}=\left\{\begin{matrix}\mathcal{F}_{x} & \text{ if $x\in Z$}\\0 & \text{otherwise}\end{matrix}\right. \end{equation*} I think I can show that $j_{*}j^{-1}\mathcal{F}_{x}=0$ if $x\notin Z$ and $j_{*}j^{-1}\mathcal{F}_{x}=\mathcal{F}_{x}$ if $x$ is contained in $Z^{o}$ (the largest open subset of $Z$), but what do I do if $x\in Z\setminus Z^{o}$?

Given a continuous function $f:X\to Y$ of topological spaces, I'm trying to understand exactly what is the inverse image sheaf, I have read a particular property $(f^{-1}G)_x=G_{f(x)}$, where $G$ is a sheaf on $Y$. How can I get that identity on stalks if the left one is a stalk on a sheaf over $X$, and the right on is over $Y$?  I see this:  $(f^{-1}G)_x=\{[U,s], x\in U\subset X, s\in f^{-1}G(U)\}=\{[U,s], x\in U\subset X, s\in colim \{G(V), f(U)\subset V\}\}$  and   $(G)_{f(x)}=\{[V,s], f(x)\in V\subset Y, s\in G(V)\}$  So how can this two of this classes be equivalent if they are on different topological spaces? or it is only an isomorphism?.  Sorry for the "colimit" word, I look for a command but did not found one.  Appreciate any help.


I am writing an article that is focus on websites and web applications. I also need to refer to the rest software products. But I don't know how to properly name them. I could say "non-web software", but it sounds awkward. I also thought about "desktop software", but apparently, this is not inclusive because non-web software also contains server software, mobile software, etc. Could you please share your opinions and suggestions? Thank you!  The context: I am using this in the computer science field. More specifically, I want to talk about websites and web application vulnerabilities (e.g. SQL injection, XSS ...) versus non-web software vulnerabilities (e.g. buffer overflow, ...).

I am writing a cover letter and I would state my experience in both web application and "normal programs". "Normal programs" sounds so bad, what is a good term that I can use without delve into technical details?


How to insert movie in Palin Tex?  % Plain TeX \input media9.sty  \includemedia[addresource=cube.mp4, flashvars={source=cube.mp4&autoPlay=true &loop=true},passcontext  ]{\includegraphics[height=0.45\linewidth]{cubeposter}}{VPlayer9.swf}}  \bye

I am attempting to find out how to embed a flv video in a pdf file created using plain TeX and pdfTeX.  I was successful at manually (via Adobe Acrobat's menu: Tools->Multimedia->Video Tool) embedding a flv video clip into an existing pdf.  Then examined the pdf file in a text editor (vim) to see if I could figure out the code that needed to be added to embed a video.  Although I was able to identify some of the lines associated with the embedding, I am clueless as to how to achieve the embedding using plain TeX and pdfTeX.  Would appreciate any pointers.  Thanks.  PS:  @AlexG 's response does give me what I was looking for.  However, I do have a follow up question.  I attempted to write the follow-up as a comment, but was not able to format the follow-up properly.  So here it is:    Toward the end of the code, what's the need for the "\setbox0=..." and the "\hbox to ..." lines?  Commenting these two lines did not seem to affect the solution:  top    %\setbox0=\hbox{  }\immediate\pdfxform 0%    \vbox to 25.6mm{%   \pdfannot width \videowidth depth \videoheight height 0pt {     /Subtype/RichMedia     /BS <</W 0/S/S>>     /Contents (embedded video file:\videofile)     /NM (rma:\videofile)     /AP <</N \the\pdflastxform\space 0 R>>     /RichMediaSettings \the\pdflastobj\space 0 R     /RichMediaContent \rmcontent\space 0 R   }}%   %\hbox to \videowidth {\vbox to \videoheight {}\hss}%    bottom     The above ending results in the video showing up placed vertically between the words top and bottom.


I am making a drop down list inside an attribute table of car makes, but want to have a list of models from the respective maker populate when I select a make.  Example: I select Ford in my CAR_MAKE field My CAR_MODEL field would populate with models that Ford makes.

Is there a way to create attribute subdomains in ArcGIS with clauses?  For example, if I'm editing a line feature class of pipes, I create a domain for the pipe type to be either plastic or metal. I want to setup another domain field "Rusted" with a yes/no value. When editing the data in ArcMap, if the pipe is metal, I should get a yes/no coded value option on the "Rusted" field. If it is plastic, I want the "Rusted" field to calculate N/A or perhaps give me other options.


I have two classes one is:   public class Emp {     String name;     static int bankVault;     }   and the other one is:  public class TestEmp { public static void main(String[] args) {     Emp emp1 = new Emp();     Emp emp2 = new Emp();     emp1.bankVault = 10;     emp2.bankVault = 20;     System.out.println(emp1.bankVault);     System.out.println(emp2.bankVault);     System.out.println(Emp.bankVault);     } }   The output is:  20 20 20   Is this because of the static word? Shouldn't the first System.out.println return 10?

Duplicate:     I've read  already.  What does the "static" keyword in a method do?  I remember being told that static != clingy...but that is pretty much all I know about this keyword.


I would like to create a job which sends an email alert when my server disk space goes beyond a specific threshold value.Since my data files are bigger there is very little free space on disk partitions.     Is is possible to write a Query which checks all the disks for the   free disk space and give an email alert if the disk space goes below   the set threshold value?

I am quite new to SQL Server. I would like to collect database disk space metrics for the SQL Server instance as a whole.  I have found a code sample that can collect disk space information per database.  IF OBJECT_ID('DISK.dbo.disk_activity') IS NOT NULL     DROP TABLE disk_activity  CREATE TABLE disk_activity (        servername NVARCHAR(100)     ,  database_id INT PRIMARY KEY     , name NVARCHAR(MAX)     , data_used_size DECIMAL(18,2)     , log_used_size DECIMAL(18,2) )  DECLARE @SQL NVARCHAR(MAX)  SELECT @SQL = STUFF((     SELECT '     USE [' + d.name + ']     INSERT INTO DISK.dbo.disk_activity (servername, database_id, name, data_used_size, log_used_size)     SELECT           (SELECT @@SERVERNAME AS "Server Name") AS SERVER_NAME         , DB_ID()         , DB_NAME()         , SUM(CASE WHEN [type] = 0 THEN space_used END)         , SUM(CASE WHEN [type] = 1 THEN space_used END)     FROM (         SELECT s.[type], space_used = SUM(FILEPROPERTY(s.name, ''SpaceUsed'') * 8. / 1024)         FROM sys.database_files s         GROUP BY s.[type]     ) t;'     FROM sys.databases d     WHERE d.[state] = 0     FOR XML PATH(''), TYPE).value('.', 'NVARCHAR(MAX)'), 1, 2, '')  EXEC sys.sp_executesql @SQL   However, I would like to collect the metrics across the entire server, i.e. total disk space allocated for all databases, total disk space used, total disk space free, and percentage of disk space used.  How should I modify the above script or are there other options available?


Basis: In the clone spell, it states clearly that      The clone is physically identical to the original and has the same personality, memories, and abilities, but none of the original’s equipment.   while simulacrum does not have this text. Simulacrum does state, however, that     Otherwise, the illusion uses all the statistics of the creature it duplicates, except that it is a construct.   The 5e SRD definition of "statistics" also refers to that as its "stat block", which consists of features like its type, race, ability scores, features, and notably, its alignment. And according to the suggested post (), it only makes mention of alignment without addressing personality or memories and does not provide me with a satisfactorily specific answer.  By the language of clone and true polymorph as examples, does a sim'd creature's statblock include its current knowledge/memories and personality?

Many features and rules refer to a creature's "game statistics".  For example,  says:     The target's game statistics, including mental ability scores, are replaced by the statistics of the new form.   and Possess Corpse, an ability of a , says:     It otherwise uses the target's game statistics, gaining access to its knowledge and proficiencies but not its class features, if any.   Sometimes it instead just refers to "statistics" as in the description for a character with lycanthropy in the Monster Manual:     A character who becomes a lycanthrope retains his or her statistics except as specified by lycanthrope type.   What all is included in a creature's "game statistics" or "statistics"? Where in the rules is this defined?  Note that the term is used interchangeably between things intended for PCs and things intended for monsters and other creatures so answers should cover all those possibilities.


I want to show that this series converges $$\sum_{n=1}^{\infty} \frac{i^n}{n}.$$ It is easy to see that it is not absolutely convergent. No use looking at the radius of convergence either.  Can Someone help me?

$$\sum_{n=1}^\infty \frac{i^n}{n}$$  I'm not sure how to approach this series to find if it converges/diverges because of the $i^n$. I tried using the comparison test comparing it with $\frac{1}{n}$ and the ratio test, but didn't get anywhere. How would you approach this and look at series of this form or how to look at $i^n$ in an infinite series?


After .cls file changes,  \includegraphics[scale=0.5]{img/GoalHierarchyMetaModel.png} command gives the following error.  ! Package keyval Error: scale=0.5 undefined.  See the keyval package documentation for explanation. Type  H <return>  for immediate help. ...                                                l.6 ...[scale=0.5]{img/GoalHierarchyMetaModel.png}    can be accessed from google drive in .  main_e.tex is the working one, main_m.tex outputs error above. Only difference between those files is documentclass.   main_e.tex uses  \documentclass[conference]{IEEEtran} main_m.tex uses \documentclass[chaparabic,ceng,phd,12pt,oneandhalf]{metu}

Here is my document :   \documentclass[12pt]{book}  % must-have packages \usepackage[turkish]{babel} \usepackage[utf8]{inputenc} % This package will support Turkish chars % must-have packages  \usepackage[a4paper,left=2.5cm,right=2cm]{geometry} \usepackage{graphicx} \usepackage{listings}  % settings \setcounter{secnumdepth}{0} % settings  \begin{document}  \framebox{\includegraphics[scale=0.5]{./images/image_3.png}}  \end{document}   When I try to build a pdf out of this file I received bunch of errors. here is one of them :      Missing \endcsname inserted   ...graphics[scale=0.5]{./images/image_3.png}}   When I remove the babel package, it runs smoothly. Even when I change the language to another language, it runs as well.  What is happening here?


The c:svg element in the following code is causing an error on rerender     "rerender threw an error in 'markup://c:svg' [Cannot read property 'parentNode' of undefined]       Failing descriptor: {markup://c:svg}"   The element is in code here:  <button onclick="{!c.favouriteProject}">     <c:svg class="{!'button-icon' + (projectData.favourite ? ' favourite' : '')}"          xlinkHref="/resource/slds100/assets/icons/utility-sprite/svg/symbols.svg#favorite"     />     {!projectData.favourite} </button>   projectData.favourite updates correctly, but causes the svg to need re-rendering as it is coloured by the favourite class. I am using a custom SVG component as described in a trailhead module somewhere, namely:  svg.cmp  <aura:component >   <aura:attribute name="class" type="String" description="CSS classname for the SVG element" />   <aura:attribute name="xlinkHref" type="String" description="SLDS icon path. Ex: /assets/icons/utility-sprite/svg/symbols.svg#download" />   <aura:attribute name="ariaHidden" type="String" default="true" description="aria-hidden true or false. defaults to true" /> </aura:component>   With a custom renderer, svgRenderer.js:  ({     render: function(component, helper) {         //grab attributes from the component markup         var classname = component.get("v.class");         var xlinkhref = component.get("v.xlinkHref");         var ariaHidden = component.get("v.ariaHidden");          //return an svg element w/ the attributes         var svg = document.createElementNS("http://www.w3.org/2000/svg", "svg");         svg.setAttribute('class', classname);         svg.setAttribute('aria-hidden', ariaHidden);         svg.innerHTML = '<use xlink:href="'+xlinkhref+'"></use>';         return svg;     } })   I am at a loss to what is causing this error: can anyone explain?

I am building data table, here is html code from browser before rerendering table. I use actionFunction with rerender attribute. The problem is that svg disappears after rerendering.  Before rerender:                Sort         Account Name
             <svg aria-hidden="true" class="slds-icon slds-icon--x-small slds-icon-text-default slds-is-sortable__icon">                 <use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="/resource/1454076265000/SLDS01201/assets/icons/utility-sprite/svg/symbols.svg#arrowdown"></use>             </svg>
               	   After rerender:                Sort         Account Name

      	   How to solve this? The response of request for rerender in Chrome dev tools looks like this:     Maybe the issue is that xmlns="http://www.w3.org/2000/svg" is missing?


I'm trying to display a list of categories sorted by name and all posts of each category inside it. Like this:   Category A  Post B Post F Post Z Category B  Post A Post C Post G Category C  Post D Post E Post H    I managed to display categories list, but it is only sorted by post names, like this:   Category B  Post A Post C Post G Category A  Post B Post F Post Z Category C  Post D Post E Post H  This is my code:    $args = array('post_type' => 'projetos'); $my_query = new WP_Query( $args ); if( $my_query->have_posts() ) {     while ($my_query->have_posts()) : $my_query->the_post(); ?>     <?php foreach((get_the_category()) as $category) {echo $category->cat_name . ' ';} ?>
     <a href="<?php the_permalink() ?>"><?php the_title(); ?>
     <?php     endwhile; }  wp_reset_query();  ?>      How can i sort it properly?

I am looking for a solution that allows me to print the following:  Cat 1        Cat 2        Cat 3  Post 1       Post 1       Post 1  Post 2       Post 2       Post 2  Post 3                    Post 3                            Post 4   EDIT  I am looking for something that will only require one database query! So if you have a foreach in your code followed by a new WP_Query then that is not what I am looking for (I am planning to put this onto my website's homepage).


I have a Swiss passport and an American passport. My American passport is expired. So I am going home in 2 weeks to Switzerland and I am asking if I can come back, with a Swiss passport, to the United States?

I am a dual citizen. I have both a US passport and a non-US passport. I live in the US. My US passport is currently being processed for renewal. I am unsure whether I will receive my passport in time for a trip that I have scheduled. Could I use my non-US passport to leave the US and return? I have never entered the US with my non-US passport. There is no immigration leaving the US but I still need to scan my passport for ticketing. Will the airline refuse me a ticket? I know that in this situation returning with a non-US passport can be problematic as well, but will I be able to leave at all? Note that I am traveling to a country which neither of my passports are from.


How can I install the BoolTool?  The  lead me to  but don't tell me whether to use "BoolTool 0.1.rar - BoolTool 0.2 release" or "BoolTool 0.2 rar - BoolTool 0.2" (and those names are confusing). The instructions are also unclear in other ways. For example, "5. Save in somewhere as "BoolTool.py" if it's not"—does that mean manually change the extension to ".py"?  A step-by-step list with no assumption that I know Github or ".rar" or "Raw" or ".zip" or ".py" would be very helpful. Thanks!

There is this addon that was built called Window Generator 2. It can be . However, when I go to the download link it shows up in a new tab as a bunch of code.  How can I download and use this addon in Blender?


Im currently working on a PCB design, where I will have 6 layers  The stackup will be:   Top signals   GND layer   Signal 3   Signal 4   Powerlayer   Bottom signal     Right now I have an full Ground plane on layer 2, but should i also use copper fill connected to GND on the other 5 layers to shorten the GND return path as much as possible?  The design is filled with digital sensors sampling at a 1MHz or 2. - Only impedance that is important is my wire to the wifi antenna, which of course will follow the rules to get 50 Ohm impedance.

I have a 6-layer board where the internal 4 planes are +15,GND,VCC,-15.  I was wondering if there was any advantage to doing a copper pour on the top and bottom layers?  I would probably leave them floating as I don't want to use micro-vias to say tie it to GND?    Is this actually a bad idea?  I.e. floating copper=antenna.  Would it be just as acceptable to have 4 layer board with the top layer having copper pour to VCC and the bottom having a pour to GND and keep the two internals as +-15?  Note that this is for a fairly low speed circuit which has some analog and digital parts.


The latest  has:   no DeletionDate column no PostsWithDeleted table   but it does contain deleted posts.  This makes it hard to decide if posts are deleted or not.  I think I could extract that from the PostHistory table Deleted and Undeleted events, but that is much more inefficient.  Please either:   add a DeletionDate column. I prefer this method as it makes things easier to query. add a DeletionDate column, removed deleted posts, and create a PostsWithDeleted table. This is exactly what the SEDE does now, so at least things would be uniform. But from the query writer point of view, this method is just more complicated.   Maybe SEDE and dump got out of sync because the current dump it too old?  Add a more recent one pleaase :-)

I like to use  to view usage stats for some of the sites, however deleted posts are not included on Data.SE and I think this skews the numbers quite a bit, particularly on sites with a lot of deletions. Would it be possible to include some limited data about deleted posts in Data.SE to make statistical queries more accurate? You could clear the non-public data fields of deleted posts, such as Posts.Title, Posts.Body, and Posts.OwnerUserId to address privacy concerns explained . You could even leave the PostId set to 0 since I know SE doesn't want to provide users with a way of searching deleted questions. The data I would mostly be interested in is CreationDate, LastActivityDate, PostHistory (date closed, date reopened, date deleted, etc), and the fact there was a deleted question in the first place. Up/Down votes, Score, Tags, and View/Answer/Favorite count would also be preferred. This would make the statistical queries accurate, while still removing the information not meant to be visible to the public.


I was using lists in a program, but I don't understand this following behavior. I have begun to understand mutability and how it affects variable assignment, but I do not see the problem here:  class Test:     def __init__(self, list_n):         list_a = list_n[:]         list_b = list_n[:]         print(list_a is list_b) # Prints False         print(list_a is list_n) # Prints False         print(list_b is list_n) # Prints False          list_a[0][0] = 1         print(list_a) # Both of these print [[1,0,0][0,0,0][0,0,0]]         print(list_b)  def main():     list_n = [[0,0,0],[0,0,0],[0,0,0]]     test = Test(list_n)        if __name__ == '__main__': main()   Both list_a and list_b seem to still point to the same list, even though I thought I took the necessary measures to prevent that from happening.

I occasionally see the list slice syntax used in Python code like this:  newList = oldList[:]   Surely this is just the same as:  newList = oldList   Or am I missing something?


I understand that $\sum\limits_{i=0}^{\infty} x^i$ is $1/x-1$ and I know that $\sum\limits_{i=0}^{\infty} i\cdot x^i$ is $x/(x-1)^2$ but the $i^2$ in the original problem throws me off and I don't know how to differentiate to get it. Can someone show me the solution?

I think I'm supposed to use calculus somewhere but I'm completely lost.


My 3 year old daughter is fully potty/toilet trained apart from wearing a nappy for bedtime. She had constipation recently which was very painful for her. This has cleared now, but she is still refusing to sit on the potty or toilet and holding in her wee until it literally burst out of her. I have asked if she wants to wear a nappy and she refuses that as well. Please help!!!

Our son is going to be 3 years old. Lately, he had constipation and he doesn't eat much. Now he holds back his stool because he had a rash, but now it is really hard for us to make him poo as he cries a lot. We tried to make him in Indian style toilet so it's easy for the opening but to no vail.  People have told us to try many things few of them are   Melting butter into his milk olive oil in milk milk castor oil orange juice tummy rub lactoloose solution Mix  into water and give in morning Currently we are giving him    Now his routine. I am very strongly opposed to ice cream as he use to consume at least 1 in summers, Ice vans and in home, he use to have corner yogurt every morning because he "wouldn't eat". Again I oppose it because a healthy breaky habit is what we have to make him get used to. Not pre-processed food like sugary yogurt, ice cream or sausages because "he would eat something". But now I strongly opposed his ice cream and sausages habit because I am very advocate for natural food. We thought it was due to full fat (blue cap) milk too, so we changed it to semi milk (green), though there was a small progress but nothing really changed.   He doesn't eat anything "fully" and a lot of his food goes to waste. Sometimes, he does eat fruit like strawberry but he evades everything saying no. The doctors aren't too concerned because they say as long as he has liquid going in, it's all good but my wife wants to make him do poo everyday. Whenever he hides behind door it means he is trying to poo but doesn't really and it goes on and on.  Now it has become an everyday when he feels like poo is coming, my wife rushes him to sit down in squat position but he cries and doesn't stop. Same thing with making him sit on toilet seat.   What can we do? His taste has developed too much towards ice creams, chocolate or juices. My wife has stopped his ice creams, chocolate a lot as we had arguement over it. Again I am opposed to those things except for juices.TBH it hurts me to see him in pain.  Sidenote - I believe that his wrong eating habits have lead him to this point, where I had stood firm but he always got away with his mum or granny.


On  question, 's user profile picture does not render correctly for me. It renders like this:        It seems that only the 32px version is rendering incorrectly:              This question was also raised in the past, but it was  although it is now still broken.

In , you may see something odd: a peeking duck.    I've just recently uploaded this new profile picture of mine. I checked it after the upload and everything's fine. After a few hours, I opened my profile and there it is, the duck has somehow become afraid of the people viewing it.  Is this a bug, a feature, or is it just the duck?  I am about to re-upload my profile pic, but I've decided to drop first this topic to meta.  And if you're curious,  is the original picture.    ADDITIONAL: I've used the non-gravatar way to upload the picture.  ADDITIONAL 2: The problem only shows in the profile view. No problem in chat, less info profile view, and in the questions and answers.  UPDATE: Re-uploaded picture. Status normal (for now, at least).


For some reason, every time I go to SO after being at one of the other sites and ask a question, I almost always get negative results. I ask just about the same way on every site, and on just about every site I go to, I get at least a little bit of reputation. That isn't the case on SO, though. Why is this? Also: please look at my  on SO; is there something going on that I'm unaware of? My questions didn't get any attention for almost a month, and then they all get downvoted (in waves, each after I asked a question on SO Meta).

Why is insulting other users and giving sarcastic comments such a huge part of the culture on SO? It's the complete opposite of projects like Wikipedia where everybody is exceedingly friendly and helpful.  For example: This response comes from a user with 13k reputation to a question about an interview problem:     There are a fair number of undergraduate CS students who can see this solution       immediately, and it seems they were looking for those students.      If you have any ambition as a C++ programmer, and aren't already intimately       familiar with the data structures and algorithms provided by the STL, you       should learn them now. It seems your competition already has.   This was in response to a genuinely extremely difficult interview problem that did not even ask for a solution using the STL. This seems to me like an unnecessarily unfriendly thing to say. This is just one example of what I think is a major trend.


I wrote a simple c application and test on centos 6.5, the code as below  int main(int argc, char *argv[]) {     fprintf(stderr, "%s\n", argv[1]);     return 0; }   when I run the app with ./test $, then the print value is $, but if I run with ./test $$, the print value changed to 119688, is any special meaning of $ in linux, I found it works correctly on windows.

I once read that one way to obtain a unique filename in a shell for temp files was to use a double dollar sign ($$).   This does produce a number that varies from time to time... but if you call it repeatedly, it returns the same number.  (The solution is to just use the time.)  I am curious to know what $$ actually is, and why it would be suggested as a way to generate unique filenames.


I want to convert pictures into a video. Version = ffmpeg-4.3-win64-static I keep getting this error on Frame 865 of 17311 Running through powershell as Admin. ./ffmpeg.exe -r 30 -f image2 -start_number 10002 -i ./G0%06d.JPG -c:v libx264 -pix_fmt yuv420p video.avi ./ffmpeg.exe -r 30 -f image2 -start_number 010002 -i ./G0%6d.JPG -c:v libx264 -pix_fmt yuv422p video.avi

Why am I getting this warning and how to fix it? Essentially, I want to convert a video to a jpg every 4th frame with the same resolution as original video.  [jalal@goku vid2]$ ffmpeg -i debate_vid2.mov -r 0.25 images_%08d.jpg ffmpeg version 2.6.8 Copyright (c) 2000-2016 the FFmpeg developers   built with gcc 4.8.5 (GCC) 20150623 (Red Hat 4.8.5-4)   configuration: --prefix=/usr --bindir=/usr/bin --datadir=/usr/share/ffmpeg --incdir=/usr/include/ffmpeg --libdir=/usr/lib64 --mandir=/usr/share/man --arch=x86_64 --optflags='-O2 -g -pipe -Wall -Wp,-D_FORTIFY_SOURCE=2 -fexceptions -fstack-protector-strong --param=ssp-buffer-size=4 -grecord-gcc-switches -m64 -mtune=generic' --enable-bzlib --disable-crystalhd --enable-gnutls --enable-ladspa --enable-libass --enable-libcdio --enable-libdc1394 --enable-libfaac --enable-nonfree --enable-libfdk-aac --enable-nonfree --disable-indev=jack --enable-libfreetype --enable-libgsm --enable-libmp3lame --enable-openal --enable-libopenjpeg --enable-libopus --enable-libpulse --enable-libschroedinger --enable-libsoxr --enable-libspeex --enable-libtheora --enable-libvorbis --enable-libv4l2 --enable-libx264 --enable-libx265 --enable-libxvid --enable-x11grab --enable-avfilter --enable-avresample --enable-postproc --enable-pthreads --disable-static --enable-shared --enable-gpl --disable-debug --disable-stripping --shlibdir=/usr/lib64 --enable-runtime-cpudetect   libavutil      54. 20.100 / 54. 20.100   libavcodec     56. 26.100 / 56. 26.100   libavformat    56. 25.101 / 56. 25.101   libavdevice    56.  4.100 / 56.  4.100   libavfilter     5. 11.102 /  5. 11.102   libavresample   2.  1.  0 /  2.  1.  0   libswscale      3.  1.101 /  3.  1.101   libswresample   1.  1.100 /  1.  1.100   libpostproc    53.  3.100 / 53.  3.100 Input #0, mov,mp4,m4a,3gp,3g2,mj2, from 'debate_vid2.mov':   Metadata:     major_brand     : qt       minor_version   : 0     compatible_brands: qt       creation_time   : 2017-03-10 02:45:46   Duration: 01:36:50.03, start: 0.000000, bitrate: 785 kb/s     Stream #0:0(und): Audio: aac (LC) (mp4a / 0x6134706D), 44100 Hz, stereo, fltp, 95 kb/s (default)     Metadata:       creation_time   : 2017-03-10 02:45:46       handler_name    : Core Media Data Handler     Stream #0:1(und): Video: h264 (Main) (avc1 / 0x31637661), yuv420p(tv, bt709), 334x360 [SAR 1:1 DAR 167:180], 685 kb/s, 30 fps, 30 tbr, 600 tbn, 1200 tbc (default)     Metadata:       creation_time   : 2017-03-10 02:45:46       handler_name    : Core Media Data Handler       encoder         : H.264 [swscaler @ 0x1bb4240] deprecated pixel format used, make sure you did set range correctly Output #0, image2, to 'images_%08d.jpg':   Metadata:     major_brand     : qt       minor_version   : 0     compatible_brands: qt       encoder         : Lavf56.25.101     Stream #0:0(und): Video: mjpeg, yuvj420p(pc), 334x360 [SAR 1:1 DAR 167:180], q=2-31, 200 kb/s, 0.25 fps, 0.25 tbn, 0.25 tbc (default)     Metadata:       creation_time   : 2017-03-10 02:45:46       handler_name    : Core Media Data Handler       encoder         : Lavc56.26.100 mjpeg Stream mapping:   Stream #0:1 -> #0:0 (h264 (native) -> mjpeg (native)) Press [q] to stop, [?] for help frame= 1454 fps= 25 q=1.6 Lsize=N/A time=01:36:56.00 bitrate=N/A dup=0 drop=172847     video:28470kB audio:0kB subtitle:0kB other streams:0kB global headers:0kB muxing overhead: unknown [jalal@goku vid2]$


If $F$ is a finite field, show that $|F|=p^r$, for $p$ prime and $r>0$ integer.  I know that $p$ is zero in this field since $p$ is characteristic. So the kernel of this will be any multiple of of $p$. But am confused how to go from here. Don't fields have the requirement that they need to be prime. So wouldn't $p$ divide $p^r$ so it could not be a field?? Any help would be appreciated. Thank you

Let $F$ be a finite field. How do I prove that the order of $F$ is always of order $p^n$ where $p$ is prime?


I want to start learning Java, and I tried to download jdk and also other stuff that is helpful with Java, but I cant find the exact command to install oracle Java through terminal or in any other way. How can I do that?

I want to install Oracle's JRE and to update to the latest version with the Software Updater when they released. Is there a Ubuntu package that is provided by Canonical or Oracle?  Before release Java 7, I followed  to install Java 6.  But it doesn't work for Java 7. There is no package sun-java7-xxx. How can you install Java 7?


I have a google sheet with rows that have some date values and other info to place on a gCal.  Date 9/4/2019 9/6/2019 9/5/2019      I am trying to run a loop that will only pull dates that are equal to a futureDate (which is today plus three days, currently 09/05/2019)  If I use the <= or => it works fine.  Pulls the correct dates and places them on my calendar.  I can't get the equal to futureDate to work.  I have spent hours thinking it has something to do with the date format but then the <= should not work either.  What am I missing here??  var today = new Date(); var futureDate = new Date(); futureDate.setDate(today.getDate()+3);  for(var i = 0; i<data.length; i++){      if(data[i][11] == futureDate) {       cal.createEvent(data[i][0], data[i][1], data[i][2], {location: data[i][3], description: data[i][10]}).setColor(data[i][5]);  //This one works and returns all dates that are not equal to futureDate if(data[i][11] <= futureDate) {       cal.createEvent(data[i][0], data[i][1], data[i][2], {location: data[i][3], description: data[i][10]}).setColor(data[i][5]);    I need only 09/05/2019 to return currently because today is 09/02/2019. (today + 3 days)

Can someone suggest a way to compare the values of two dates greater than, less than, and not in the past using JavaScript? The values will be coming from text boxes.


I have a class template which defines a type inside it:  #include <boost/array.hpp>  template <typename T, int N> class MyFunct { public:   typedef boost::array<T,N> FArray;   MyFunct(); };   Now I have another class template. The thing that makes this class particular is that it is supposed to work only with types that define, inside of them, a type called FArray. Do not ask why please, there is a reason for this.  template <typename F> class MyClass { public:   MyClass() {     F::FArray a = F::FArray();   } };   And I use this:  int main(int argc, char** argv) {   MyClass< MyFunct<double,10> > m; }   When I have this situation the compiler gets mad telling me that double has no member called FArray. What's happening?

In templates, where and why do I have to put typename and template on dependent names? What exactly are dependent names anyway?    I have the following code:  template <typename T, typename Tail> // Tail will be a UnionNode too. struct UnionNode : public Tail {     // ...     template<typename U> struct inUnion {         // Q: where to add typename/template here?         typedef Tail::inUnion<U> dummy;      };     template< > struct inUnion<T> {     }; }; template <typename T> // For the last node Tn. struct UnionNode<T, void> {     // ...     template<typename U> struct inUnion {         char fail[ -2 + (sizeof(U)%2) ]; // Cannot be instantiated for any U     };     template< > struct inUnion<T> {     }; };   The problem I have is in the typedef Tail::inUnion<U> dummy line. I'm fairly certain that inUnion is a dependent name, and VC++ is quite right in choking on it. I also know that I should be able to add template somewhere to tell the compiler that inUnion is a template-id. But where exactly? And should it then assume that inUnion is a class template, i.e. inUnion<U> names a type and not a function?


The description for a long rest states:  A long rest is a period of extended downtime, at least 8 hours long, during which a character sleeps for at least 6 hours and performs no more than 2 hours of light activity, such as reading, talking, eating, or standing watch. If the rest is interrupted by a period of strenuous activity - at least 1 hour of walking, fighting, casting spells, or similar adventuring activity - the characters must begin the rest again to gain any benefit from it.  Which of the following interpretations is correct in regards to what is considered strenuous activity? a)  at least 1 hour of walking at least 1 hour of fighting at least 1 hour of casting spells  b)  at least 1 hour of walking fighting casting a spell  Personally, I think option b) is correct, because option a) allows for silly shenanigans. For example, assuming a combat encounter lasts 10 rounds - that is, 1 minute in game time - then it would be possible to have 59 encounters and still benefit from the long rest.

In the latest campaign, we're still around the third level, but every single night we've spend in the wild so far, we were interrupted by hard combat encounters (as in DMG-worded "hard"), forcing us to use our resources (like HP, spell slots, Ki, once-per-day stuff) and not restoring any of those lost the previous days. I feel like the , as it lasts four to six rounds, so we usually say that we'd like to resume our rest but the answer is always "you've been interrupted, your rest is over, you can't restart any until dusk". So the only real long rests we could have always were in town.  We've always used watch-turns, and being interrupted in the first night of the campaign, we now always spend one hour to find a safe place to rest and we make that intent very clear to the DM. But yet, kobolds, goblins, ghouls and gnolls always find us in the middle of the night, but never when we travel for ten hours during the day (which is comparable to "fast travel" in his own word). Once on the second day in the wild, we were faced to a deadly encounter (as in DMG-worded "deadly") which we survived only by fleeing. And we're kind of forced to get back to the deadly encounter, which is more than one day away from the nearest town.  We're five players and I'm the only one with PnP RPG experience... from ten years ago. I don't remember being this resourceless. We asked if it was a survival campaign and the answer was that it was only a normal introduction campaign found on the Internet that he spiced up a bit. We've also asked if we did anything wrong and the answer was that we followed the normal story.  The DM is mastering his second campaign (the first one is still ongoing, but with veteran players). The DM also plays a lot of survival campaigns as a player.  Is this situation normal? If yes, why? If not, what should I say to the DM?  Note that I'm fully aware of the "long rest" rule as written on page 186 of the PHB. This is why I encouraged my team to say that we resume our rest. (thanks Bloodcinder)


I am trying to port Python 2 to Python 3, but I am having trouble importing Glade:  import gtk.glade  ImportError: cannot import name glade, introspection typelib not found   Any idea how to fix this?  Thanks

I have Ubuntu 14.04 with python-2.7 and python-3 support. I am porting my python application from python-2.7 to python-3. I have example.py file which is importing below modules. and I #!/usr/bin/python3 as python evn variable.  import gtk, gobject, time, sys, os, subprocess, signal   **ImportError: No module named 'gtk'**   I am getting above error, when trying to run with python3.  Any idea what is missing here?


So I was solving a previous year question paper and stumbled upon the following question- $${\lim_{n\to {\infty}}}\biggl(\tan x+\frac{1}{2}\tan \frac{x}{2}+\frac{1}{2^2}\tan \frac{x}{2^2}+\frac{1}{2^3}\tan \frac{x}{2^3}+{\cdots}+\frac{1}{2^n}\tan \frac{x}{2^n}\biggl)$$ The only limit with $\tan$ that I have learnt is ${\lim_{x\to 0}}\frac{\tan x}{x}=1$. I have tried the following with no success- 1)Representing $\tan x$ in terms of $\tan \frac x2$   2)Simplifying into $\sin x$ and $\cos x$   I do not want a complete solution but would greatly appreciate a hint on how to simplify the series.

Question:  If $0 < x < \frac{\pi}{2}$ and $f_k(x) = \tan(x)+\frac{1}{2}\tan(x/2)+ ...+\frac{1}{2^k}\tan(x/2^k)$.  In Sigma Notation: $$f_k(x) = \sum_{n=0}^k \frac{1}{2^n}\tan\frac{x}{2^n}$$  Find $$\lim_{k\to \infty}f_k(x)$$  I'm not quite sure how to take the limit of a sequence, I've never seen this before, If someone could help me solve this it would be greatly appreciated.


1a.  This football team won the league championship 3 times over the last 5 years.   1b.  This football team won the league championship 3 times during the last 5 years.   1c.  This football team won the league championship 3 times in the last 5 years.      2a.  This football team has won the league championship 3 times over the last 5 years.   2b.  This football team has won the league championship 3 times during the last 5 years.   2c.  This football team has won the league championship 3 times in the last 5 years.      3a. He achieved great success over the last 5 years.   3b. He achieved great success during the last 5 years.   3c. He achieved great success in the last 5 years.      4a. He has achieved great success over the last 5 years.   4b. He has achieved great success during the last 5 years.   4c. He has achieved great success in the last 5 years.   For these sentences, we have three choices for the preposition.  How do we choose?  Does the tense of the sentences (past vs. present perfect) influence the choice?

Microsoft has steadily improved its operating cash flows in the past three years. Microsoft has steadily improved its operating cash flows in the last three years. Microsoft has steadily improved its operating cash flows for the past three years. Microsoft has steadily improved its operating cash flows for the last three years. Microsoft has steadily improved its operating cash flows for the past three years. ("for" omitted) Microsoft has steadily improved its operating cash flows for the last three years. ("for" omitted) Microsoft has steadily improved its operating cash flows during the past three years. Microsoft has steadily improved its operating cash flows during the last three years. Microsoft has steadily improved its operating cash flows over the past three years. Microsoft has steadily improved its operating cash flows over the last three years.  Which of them are idiomatic and preferred? Are they interchangeable?


as a part of script I'm trying to copy a file from remote site. But got an error. To me that sounds bit strange as everything sounds ok:  #aaa="/path/to/some file with spaces(and brackets).txt" .... #scp user@example.com:"$aaa" /test/ bash: -c: line 0: syntax error near unexpected token `(' bash: -c: line 0: `scp -f /path/to/some file with spaces.txt'   upd: problem with brackets...

When using SSH to connect rsync to a remote server, how do you escape spaces and such in the remote path? A simple backslash escapes the space for the local bash prompt, but on the remote machine the space is then being read as a break in the path, thus marking the end of that path.  So when I do rsync -avz /path/to/source/some\ dir/ user@host.tld:/path/to/dest/some\ dir/ what happens is that the remote server is reading that as just /path/to/dest/some/ and since it can't find that destination remotely, because the actual destination is "some dir" rather than just "some".  If I try the same command and escape the backslash and the space to get past the local bash prompt and maintain the backslash for the remote server (three backslashes total: /path/to/dest/some\\\ dir/), it does indeed send the backslash to the remote server, but the remote server then interprets the path as /path/to/dest/some\/ rather than /path/to/dest/some\ dir/ still stripping the space and the characters after it.  If I try to wrap the path with quotes, it behaves pretty much the same way, effectively cutting the path off at the space. So it too only works to get past the local bash prompt.  Initially I was using a path that had a " - " (space-hyphen-space) segment in it, and the remote server was returning an error rsync: on remote machine: -: unknown option which is what started this whole space-escaping endeavor in the first place.   So what must I do to get this working properly with the remote server, without having to remove the spaces or other erroneous characters like hyphens from the remote path?


The following quotes are from . It seems to me that they all use "they" for a generic person. For example, in the Chesterfield's example: "If a person is born of a . . . gloomy temper . . . they cannot help it.", "a person" appears to be singular but it represents any person. It is essentially plural.  'Tis meet that some more audience than a mother, since nature makes them partial,  should o'erhear the speech."— Shakespeare, Hamlet (1599);  "If a person is born of a . . . gloomy temper . . . they cannot help it."— Chesterfield, Letter to his son (1759);  "Now nobody does anything well that they cannot help doing"— Ruskin, The Crown of Wild Olive (1866); "Nobody in their senses would give sixpence on the strength of a promissory note of the kind."— Bagehot, The Liberal Magazine (1910);  "I would have every body marry if they can do it properly."— Austen, Mansfield Park (1814);  Caesar: "No, Cleopatra. No man goes to battle to be killed." Cleopatra: "But they do get killed" —Shaw, Caesar and Cleopatra (1901);  "A person can't help their birth."— W. M. Thackeray, Vanity Fair (1848);  "When in the Course of human events, it becomes necessary for one people to dissolve the political bands which have connected them with another . . ." —United States Declaration of Independence;  My question Is the use of singular they in the following passage grammatically correct?  Someone was approaching my room. I could see that they were alone judging from their footsteps. They knocked on my door. I didn't answer. They knocked again. I still didn't answer so they left.

Is there a pronoun I can use as a gender-neutral pronoun when referring back to a singular noun phrase?  Each student should save his questions until the end. Each student should save her questions until the end.


When I type firefox in terminal, it starts Firefox but the terminal "hangs".  What is happening behind the scenes?  Can I open Firefox from terminal and keep on using the same terminal tab for other things without closing Firefox?

On the CLI, sometimes a command I type takes a while to complete, and sometimes I know when that's about to happen. I'm a bit confused on "backgrounding" and such in Linux.  What is the most common (or user-friendly way) of telling the CLI that I don't want to wait, please give me back my prompt immediately. And if it could give me a progress bar or just busy-spinner, that would be great!


Verify that if $n > 1$, the unbounded function $u = \log \log \left(1+\frac 1{|x|}\right)$ belongs to $W^{1,n}(U)$, for $U=B^0(0,1)$.   This is PDE Evans, 2nd edition: Chapter 5, Exercise 14.  In order to show that $u \in W^{1,n}$, where $W^{1,n}$ is a Sobolev space containing the function $u$ itself and its first-order derivative.  Differentiating $u=\log \log\left(1+\frac 1{|x|}\right)$, I obtain (and please verify if you would like) $$u_{x_i}=\frac 1{\log \left(1+\frac 1{|x|}\right)}\frac 1{1+\frac 1{|x|}} \frac{x_i}{|x|^2}.$$  Given $u'=v$ in the weak sense, should I show, according to definition, that $$\int_{B(0,1)} u \phi' \, dx = -\int_{B(0,1)} v\phi dx$$ for all test functions $\phi \in C_c^\infty(U)$? The integration by parts formula comes to my mind here.    Or, should I be employing material from Section 5.6 (Sobolev inequalities) of the textbook? In particular, they discussed on page 280 the borderline case $p=n$, which mentions:     The borderline case p=n. We assume next that $$p=n.$$ Owing to Theorem 2 (page 279) and the fact that $p*=\frac{np}{n-p}\to+\infty$ as $p \to n$, we might expect $u \in L^\infty(U)$, provided $u \in W^{1,n}(U)$. This is however false if $n>1$: for example, if $U=B^0(0,1)$, the function $u=\log \log\left(1+\frac 1{|x|}\right)$ belongs to $W^{1,n}(I)$ but not to $L^\infty(U)$.

The entire problem statement is:  Let $n>1$ and let $U=B(0,1)\subset\mathbb{R}^n$. Show that $u:U\to\mathbb{R}$ given by  $$u(x)=\ln\left(\ln\left(1+\frac{1}{|x|}\right)\right)$$ is in $W^{1,n}(U).$  My attempt at the proof is as follows:  To show that $u\in W^{1,n}(U)$ it suffices to show that $|Du|\in L^{n}(U)$. Consider $$u_{x_i}=\frac{1}{\ln\left(1+\frac{1}{|x|}\right)}\frac{1}{1+\frac{1}{|x|}}|x|^{-2}\frac{x_i}{|x|},$$ which simplifies to, $$u_{x_i}=\frac{1}{\ln\left(1+\frac{1}{|x|}\right)}\frac{1}{1+\frac{1}{|x|}}\frac{x_i}{|x|^3}.$$ Thus, $$|Du|=\frac{1}{\ln\left(1+\frac{1}{|x|}\right)}\frac{1}{1+\frac{1}{|x|}}\frac{1}{|x|^2}$$ which can be manipulated to, $$|Du|=\frac{1}{\ln\left(1+\frac{1}{|x|}\right)}\frac{1}{1+|x|}\frac{1}{|x|}.$$  Moreover, since $U=B(0,1)$ we can bound the second term from above which gives, $$|Du|\leq\frac{1}{\ln\left(1+\frac{1}{|x|}\right)}\frac{1}{|x|}$$  Thus, we can instead show that $$\int_U\left(\frac{1}{\ln\left(1+\frac{1}{|x|}\right)}\frac{1}{|x|}\right)^n<\infty.$$  Converting this into polar coordinates we have with $r=|x|$, $$\int_0^R\int_{\partial B(0,r)}\left(\frac{1}{\ln\left(1+\frac{1}{r}\right)}\frac{1}{r}\right)^n\,dSdr=\int_0^R\left(\frac{1}{\ln\left(1+\frac{1}{r}\right)}\frac{1}{r}\right)^n\int_{\partial B(0,r)}dSdr$$ Note that $\int_{\partial B(0,r)}\,dS=n\alpha(n)r^{n-1}$, which is the surface area of $B(0,r)$. Thus, we have then $$n\alpha(n)\int_0^R\left(\frac{1}{\ln\left(1+\frac{1}{r}\right)}\frac{1}{r}\right)^nr^{n-1}\,dr=n\alpha(n)\int_0^R\left(\frac{1}{\ln\left(1+\frac{1}{r}\right)}\right)^n\frac{1}{r}\,dr$$  And so this is where I get stuck in the problem, since I don't how I can evaluate that last integral to show it's finite.  Thank you for any help or feedback!


I know $m$ ,$n$ are two positive integer numbers such that $m\mid n$. If $p$ is a prime number, I want to show $p^m-1\mid p^n-1$.

Let $a\ge 2$ be an integer. Show that for positive integers $m,n$, we have $a^n - 1$ divides $a^m - 1$ if and only if $n$ divides $m$.   I am having trouble showing this. I've seen a similar problem on here but it only shows one direction for the proof. I would like to see both directions.  This is what I have so far: Let $m = nq + r$, then $a^m - 1 = a^{nq + r}- 1 = a^{nq}a^r - 1 = a^{nq}a^r - a^r + a^r - 1 = a^r(a^{nq} - 1) + a^r - 1$. Since $0\le r\lt n$, $r = 0$ then $a^m - 1$ = $a^{nq} - 1$ so $a^m$ = $a^{nq}$ . Thus $m = nq$ hence $n\mid m$.


I read these novels in the late 80s or early 90s. In each book, they had to find one of a collection of things, which may have been rings, to do something or other like save the universe or whatever. They had the technology to transform someone to another form to match whatever was the dominant species of the current novel's target planet was, but for some reason, I think they could only transform once, so much drama ensued in choosing who would be the one transformed.  As another clue, my grandma bought me my first book in the series (not the actual first) because it had "Pirates" in the title, because she thought I would like a book about pirates, not realizing it was a deep-space science fiction series. I did like the series as an early teen, but I can't remember what it was and don't have my childhood library available to me.

I'm looking for a series of books that deals with humans escaping Earth and having a mother ship full of humans who are being sent throughout the universe to different planets. The ship can transform the humans into whatever type of alien the planet holds. One set of sisters is transformed to cow-like aliens and sent to spy on that planet. All the while the group that's taken the mother ship full of human colonizers is trying to evade/escape the government people from Earth.    The 9 or 10 humans who steal the colonizing ship drop a couple of humans (transformed to whatever the indigenous species is) to the planet to spy...the end result is to try and overthrow the Earth government.  The humans that the colonizing ship transform to aliens cannot be turned back into humans ever again so when they take on the assignment to spy they do so knowing that they won't ever be able to be humans again.


I'm aware that the use of \usepackage[T1]{fontenc} is advised to prevent a lot of inconveniences on the output. However, it makes my font too light, which I confirmed by generating a pdf with the same source text without the fontenc package.   This is my preamble   \documentclass[10pt, oneside, twocolumn, notitlepage]{article}  \usepackage{sectsty} \usepackage[T1]{fontenc} \usepackage[utf8]{inputenc} \usepackage[brazil]{babel} \usepackage[a4paper,margin=1.5cm]{geometry} \usepackage{graphicx} \usepackage{amsmath} \usepackage{amssymb} \usepackage{caption} \usepackage{float} \usepackage{siunitx}    I use miktex on windows to compile. How do I solve it?   Sorry if I'm not presenting some relevant information or if the answer is obvious, I know nothing of the programming aspects of the typesetting system.  Thanks!

I am using TeXstudio to edit Latex and create pdf files. The text is not smooth in the pdf files created by TeXstudio in my computer. When I zoom in, it will be   But if I use my friend's computer to generate the pdf files, it will be like below when I zoom in to see    Both computers have Windows 7 as OS, same Version of TeXstudio. What settings should I change to make the text smooth?  Edited:  I created two pdf files from same .tex files by TeXstudio in my and my friend's computers. The files can be downloaded in below link


Does the Stone Spirit have any vulnerabilities? I have both Hawkes, Isabela and Varric in my party. I don't have any tanks with me. Does the Stone Spirit have any weaknesses (ice, fire, etc.)?

Does anyone have any tips or hints on how to beat the Ancient Rock Wraith in the Deep Roads? I've tried battling him a few times and even hiding from his super AoE attack, I still get ground down by the minions, and then he nukes 2 of my team.  I'm running Hawke - Daggers Rogue Varric - Archer Rogue Merrill - Elemental Anders - Elemental + Heal    I think that I really needed to take a tank, but I ideally don't want to have to restart the Deep Roads section.  Does anyone have any tips on how to beat this boss?


Let $f$ be a polynomial with degree $n$, also $$\int_{0}^1 f(x)x^kdx=0,k=1,2, \cdots ,n$$ Prove that  $$\int_0^1 f^2(x)dx=(n+1)^2\left(\int_0^1 f(x) dx\right)^2$$ My first step is to subtract zero from the left of the equation.  $$\begin{aligned} \int_0^1 f^2(x)dx&=\int_0^1 f^2(x)dx-\sum_{k=1}^n\int_0^1 a_k x^k f(x)dx\\ &=\int_0^1 f(x)\left(f(x)-\sum_{k=1}^n a_k x^k\right)dx\\ &=a_0 \int_0^1f(x)dx \end{aligned}$$ Then  $$a_0=(n+1)^2\left(\int_0^1 f(x) dx\right)\quad\text{or}\quad \int_0^1 f(x) dx=0$$ I doubt that this is not true because the integral of an arbitrary polynomial is a constant only related to $a_0$. But this is possible. Could you show a better idea and give a proof? Thanks.

Suppose $P(x)$ is a polynomial of degree $n \geq 1$ such that $\int_{0}^{1}x^{k}P(x)\,dx = 0$ for $k = 1, 2, \ldots, n$. Show that $$\int_{0}^{1}\{P(x)\}^{2}\,dx = (n + 1)^{2}\left(\int_{0}^{1}P(x)\,dx\right)^{2}$$   If we assume that $P(x) = a_{0}x^{n} + \cdots + a_{n - 1}x + a_{n}$ then we can easily see that $$\int_{0}^{1}\{P(x)\}^{2}\,dx = a_{n}\int_{0}^{1}P(x)\,dx$$ and therefore to solve the given problem we need to show that $$\int_{0}^{1}P(x)\,dx = \frac{a_{n}}{(n + 1)^{2}}$$ Direct integration of the polynomial gives the expression $$\frac{a_{0}}{n + 1} + \frac{a_{1}}{n} + \cdots + \frac{a_{n - 1}}{2} + a_{n}$$ and simplifying this to $a_{n}/(n + 1)^{2}$ does not seem possible. I think there is some nice "integration by parts" trick which will give away the solution, but I am not able to think of it.


How do i find the linear factors from which the polynom: $$ x^2+i $$ Is built from. I remember that every polynom above the complex can be represent as linear factors, but how do i do that in my example?

Square root of number -1 defined as i, then what is the square root of complex number i?, I would say it should be j as logic suggests but it's not defined in quaternion theory in that way, am I wrong?  EDIT: my question is rather related to nomenclature of definition, while square root of -1 defined as i, why not j defined as square root of i and k square root of j and  if those numbers have deeper meanings and usage as in quaternions theory.


How would one print out to console, or iterate for each event listener that is attached to specific DOM element? I have tried using .eventListenerList but I am getting undefined.

I have a page where some event listeners are attached to input boxes and select boxes. Is there a way to find out which event listeners are observing a particular DOM node and for what event?  Events are attached using:    Event.observe; DOM's addEventListener; As element attribute element.onclick.


Example;   \begin{equation*}   \begin{aligned}     1 + 2 = 3 \\[3mm]     3 + 1 = 4 \\[3mm]     4 + 1 = 5   \end{aligned} \end{equation*}   I find that I'm often adding the [3mm] to the ends of equation lines so that the spacing isn't so tight between lines, but is there a way to set this for    a particular equation instance  globally for equations   I can't seem to find this out.   edit  this worked   \begin{equation*}   \addtolength{\jot}{12pt}   \begin{aligned}     1 + 2 = 3 \\     3 + 1 = 4 \\     4 + 1 = 5   \end{aligned} \end{equation*}

Is there a way to consistently increase the vertical spacing between equation lines in a gather (or gather*) environment from amsmath?  Specifically, I want to produce something like  \begin{gather*} a = b \\[2ex] c = d \\[2ex] e = f \end{gather*}   without having to write [2ex] at the end of each equation line.  I can think of some hacks that redefine \\ to automatically add the spacing, but is there some cleaner/better way to achieve this?


I'm developing a Burp Suite extension.  I have a class BurpExtender, it has public static field.  public class BurpExtender implements IBurpExtender, IContextMenuFactory{      private IBurpExtenderCallbacks callbacks;     public static PrintWriter stdout;     public static IExtensionHelpers helpers;     ...     @Override         public void registerExtenderCallbacks(IBurpExtenderCallbacks callbacks) {              this.callbacks = callbacks;             this.helpers = callbacks.getHelpers();             PrintWriter stdout = new PrintWriter(callbacks.getStdout(), true);              callbacks.setExtensionName("REQUESTSENDER");             callbacks.registerContextMenuFactory(BurpExtender.this);             stdout.println("Registered");          }      public List<JMenuItem> createMenuItems(final IContextMenuInvocation invocation) {         List<JMenuItem> menuItemList = new ArrayList<JMenuItem>();         JMenuItem item = new JMenuItem(new MyAction());         menuItemList.add(item);         return menuItemList;     }   and in this file i have another class MyAction:  private class MyAction extends AbstractAction{     public MyAction(){         super("Name");     }       public void actionPerformed(ActionEvent e) {         //Here i want to use BurpExtender.helpers, but i cant figure out, how to.         //BurpExtender.stdout doesnt work here. Dunno why, NullPoinerException.     } }   I had another solution, when i tryed to do smth like JMenuItem item = new JMenuItem(new AbstractAction("123") {...} result it the same

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'd be greatly appreciative of an idiom/phrase that depicts a subject (e.g. a governmental organisation) that acts surprisingly passive in relation to a given situation.  Context: The governmental organisation seem to be just observing without taking any concrete actions, while you would expect them to take action since it should be of vital importance to them.  Thank you in advance.

What would you call a person that just stands by and won't act? Is kind of acting like a spectator when in reality that person should do something?  I know there is a word for this because I knew what it was a few hours ago but now I can’t remember it.


Hi so im trying to do this pig latin code in which the first letter is deleted from a words and sent to the end of the word while adding an "ay" to the end result. I have finished all my code in which it should output the right result except my problem is with actually outputting the code. I get an error message right after the user inputs the sentence.   Here is my code:  package piglatin;    import java.util.Scanner;    public class PigLatinTest {  public  static String str;  public static String[] words;   public static String[] printLatinWords()  {      System.out.println("Enter a Sentence: ");        Scanner scanner = new Scanner(System.in);        str = scanner.nextLine();        words = str.split(" ");        //System.out.println(words);        return words;  }   public static String[] printPigLatinWords()   {     for (int i = 0; i < words.length; i++) {         char firstLetter = words[i].charAt(0);         words[i] = words[i].substring(1);         words[i] = words[i] + firstLetter + "ay";         //System.out.println(words[i]);         //If you want the words to be in the same line, then this could help                  instead of System.out.println:         System.out.print(words[i] + " ");     }     return words;   }  public static void main(String[] args)  {     words = printLatinWords(); }    }    /*    Enter a Sentence:      Hello from the other side       */


I have a relation $f$ defined as   $$ f=\{(x, y) \mid y=\sqrt{x} \;\text { and }\; y, x \in \Bbb R\} $$  Now this relation is a function.  But how? A function is a relation whose every element in domain have only one image in codomain. Now if I have $4$. Then  \begin{align} \sqrt{4}=\pm 2 \end{align}  So I have two ordered pairs whose second element is square root of first element:  \begin{align} (4,2) \quad \text { and } \quad(4,-2) \end{align}  Now you can observe that 4 has two images. Therefore relation $f$ must not be a function. But it is! How this is possible?

It is perhaps a bit embarrassing that while doing higher-level math, I have forgot some more fundamental concepts. I would like to ask whether the square root of a number includes both the positive and the negative square roots.  I know that for an equation $x^2 = 9$, the solution is $x = \pm 3$. But if simply given $\sqrt{9}$, does one assume that to mean only the positive root? And when simply talking about the square root of a number in general, would one be referring to both roots or just the positive one, when neither is specified?


I'm reading a book, and I found a sentence where I don't understand the grammar. It seems as the writer wants to write a statement, but uses the structure of a question. The sentence is highlighted in the following paragraph:     In the first ten paragraphs, he touted his engineering skills, including his ability to design bridges, waterways, cannons, armored vehicles, and public buildings. Only in the eleventh paragraph, at the end, did he add that he was also an artist. "Likewise in painting, I can do everything possible," he wrote.      Isaacson, Walter. (2017) Leonardo da Vinci.   Shouldn't that sentence start with "he added" instead of "did he add" since it's not a question? If it's correct, is it something people usually use when they speak, or is it more like something you would find in books?

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.


I have tried to write a template class. It seems that when I write the constructor in classname.cpp not in classname.h, then it could be compiled correctly.  Could someone explain this to me?

Quote from :     The only portable way of using templates at the moment is to implement them in header files by using inline functions.   Why is this?  (Clarification: header files are not the only portable solution. But they are the most convenient portable solution.)


I'm trying to patch some bidi footnote commands (\@footnotetext, \@LTRfootnotetext, and \@RTLfootnotetext) in biblatex.  The footnote patching commands in biblatex occur in an AtEndPreamble macro in biblatex.sty.  And I'm trying to use #1 as a hook in \patchcmd.  This is a combination which fails, and I'm looking for ideas as to the best way around the problem.  MWE:  \documentclass{article} \usepackage{etoolbox} \usepackage{bidi} \tracingpatches \newtoggle{blx@footnote} \makeatletter \AtEndPreamble{%   \patchcmd\@footnotetext     {#1}     {\toggletrue{blx@footnote}#1}     {\def\patchresult{success}}     {\def\patchresult{failure}}}% \makeatother \begin{document} \patchresult \end{document}   \@footnotetext is defined this way in bidi:  \long\def\@footnotetext#1{%   \footdir@write   \footdir@fntext{\bidi@footdir@footnote}%   \stepcounter{footdir@label}%   \footdir@fntext{\bidi@footdir@footnote}%   \footdir@toks{#1}%   \footdir@toks\expandafter     {\the\expandafter\footdir@toks      \expandafter \zref@labelbyprops      \expandafter{\thefootdir@label}{abspage}}%      \expandafter\footdir@ORG@bidi@footnotetext      \expandafter{\the\footdir@toks}}   This is in order to fix issue #412 in biblatex. See

Consider the following example of a patch using  and a dummy macro \abc:    \documentclass{article} \usepackage{etoolbox}% http://ctan.org/pkg/etoolbox \newcommand{\abc}[2]{#1\ #2}% Magic macro \begin{document} \abc{A}{B}  % \patchcmd{<cmd>}{<search>}{<replace>}{<success>}{<failure>} \patchcmd{\abc}{#1}{#2}{}{}% \abc{A}{B} \end{document}   If I want to maintain good programming practice, I'm encouraged to put \patchcmd in the document preamble (separating structure from content) and only trigger it with a different macro, say \patchabc:  \documentclass{article} \usepackage{etoolbox}% http://ctan.org/pkg/etoolbox \newcommand{\abc}[2]{#1\ #2}% Magic macro \newcommand{\patchabc}{%   % \patchcmd{<cmd>}{<search>}{<replace>}{<success>}{<failure>}   \patchcmd{\abc}{#1}{#2}{}{}% } \begin{document} \abc{A}{B}  \patchabc% Patch \abc \abc{A}{B} \end{document}   However, the above does not work since #1 and #2 inside \patchabc is assumed to reference its arguments while \patchabc has none. How can I write a macro that acts like a switch (and is cleaner in terms of the programming) that patches another macro's use of its own arguments?


I know that the below code will give the greatest value in an Array, but why?  public class Practice {   public static int greatest(ArrayList<Integer> list) {   int greatest = list.get(0);   for(int i: list){     if(i > greatest){         greatest = i;     } }  return greatest; }  public static void main(String[] args) {      ArrayList<Integer> list = new ArrayList<Integer>();      list.add(3);      list.add(5);      list.add(2);      list.add(7);      list.add(8);  System.out.println("The greatest number is: " + greatest(list)); } }   If it is comparing the first value indexed in the list to another value that is greater than it while looping, wouldn't it would choose 5 instead of 8? How does it know to choose 8 instead of 5?  Thank you very much.

Consider:  List<String> someList = new ArrayList<String>(); // add "monkey", "donkey", "skeleton key" to someList     for (String item : someList) {     System.out.println(item); }   What would the equivalent for loop look like without using the for each syntax?


I have created a database and tables in it. Now i want to view the databases and tables from android device and not emulator in eclipse. How do i do that?

If your application requires a database and it comes with built in data, what is the best way to ship that application? Should I:   Precreate the SQLite database and include it in the .apk? Include the SQL commands with the application and have it create the database and insert the data on first use?   The drawbacks I see are:   Possible SQLite version mismatches might cause problems and I currently don't know where the database should go and how to access it. It may take a really long time to create and populate the database on the device.   Any suggestions? Pointers to the documentation regarding any issues would be greatly appreciated.


I'm very new to Linux. I thought having a GUI would be nice, but it is using too much RAM so I'd like to just use the regular terminal for now. I have Ubuntu 12.04 server with XFCE installed.  How can I uninstall all GUI related packages and everything that came with them?

I installed few environments that I wanted to try out on Ubuntu 12.04, but none of them worked at all. It could be that I installed them all at the same time, meaning the OS didn't get a chance to work everything out, but either way, they didn't work. I would now like to remove them.   The one's that I installed are Xubuntu/Xfce, Lubuntu/LXDE, Kubuntu/KDE, Fluxbox, OpenBox, cinnamon, and MATE. I installed them. Everything seemed to have been working properly until I actually tried to use the shells and nothing loaded at all. Except for Fluxbox, I think that one worked. I want to know of any way to repair or perhaps just remove the packages entirely. I might have already removed them because I did the apt-get remove command on all of them, but they were still in the list on the login screen.


Let $a^n, a^m \in (a^k)$ for some positive integer $k$. Then $k \mid n, m.$ Hence $k \mid \operatorname{gcd(n, m)}$.  How is it possible? Let $k = 6, n = 12, m =24.$ Context:  Let $H$ be the smallest subgroup of $(a)$ s.t. $a^n, a^m \in H$. Prove that $H = (a^{\operatorname{gcd(n, m)}}).$ Proof: Since $G$ is cyclic, $H$ is cyclic. Hence $H = (a^k)$ for some $k \in \mathbb N.$ Since $a^n, a^m \in H,$ then $k \mid n,m.$ Hence $k \mid \operatorname{gcd(n, m)}.$ Thus $a^{\operatorname{gcd(n, m)}} \in H.$ Hence $(a^{\operatorname{gcd(n, m)}}) \subset H.$ Also, since $a^{\operatorname{gcd(n, m)}} \mid n, m$ then $a^n, a^m \in (a^{\operatorname{gcd(n, m)}})$. Since $H$ is the smallest subgroup of $(a)$ containing $a^n, a^m$  and $a^n, a^m \in (a^{\operatorname{gcd(n, m)}})$, we conclude that $H = (a^{\operatorname{gcd(n, m)}}).$

If $c$ is a common divisor of $a$ and $b$ then $c$ divides the greatest common divisor of $a$ and $b$.  What can we use to prove this?


How can I get Pidgin to connect to my Facebook chat? It says UserName@chat.facebook .com/disabled Not Authorized ...  Please help, if you can.

Good day to all!  I've been trying to use Empathy for Facebook chat for quite some time now but whenever I try to enable it, I get the "Applications can no longer access your Facebook online account blah, blah, blah..." and so I tried going to Online Accounts and then grant access.  But whenever I click the button to grant access, it reverts back to "off" after maybe three seconds. What's happening and how can I solve this?  P.S. I already tried using Pidgin but I still get the same error.  Sometimes I get the "authorization failed" error as well.  Also, I can log into my FB account using my web browser.


If the radical of a Lie algebra is zero, we call it semi-simple. In the lecture notes that I'm following its stated that for any arbitrary Lie algebra (over a field with characteristic zero and finite dimensional) $\mathfrak{g}$ we have, $\mathfrak{h}:=\mathfrak{g}/\mathrm{rad}(\mathfrak{g})$ semi-simple. I have trouble seeing why.   I need to show that $\mathrm{rad}(\mathfrak{h})=0$. I think we can use the fact that if $\mathfrak{I}$ is a solvable ideal of $\mathfrak{g}$ such that $\mathfrak{g}/\mathfrak{I}$ is solvable, then $\mathfrak{g}$ is solvable, but I'm not really sure how...

I found the following statement in Humphreys' book, 'Introduction to Lie Algebras and Representation Theory', in the first chapter, section 3.1:  "Notice that for arbitrary (Lie algebra) L, $L$ / Rad$L$ is semisimple."  And as substantiation of the statement he cites the proposition "If $I$ is a solvable ideal of a Lie algebra $L$ such that $L/I$ is solvable, then $L$ itself is solvable" which was proven earlier. I could prove the proposition that he's referring to but I could not, after hours of trying, see how the statement follows from the proposition. I'd much appreciate some help on this.