I have a question which i could not figure out the answer to, it was the hardest of them all that i got and i couldnt figure it out, its a proof of fibonaccis serie using matrixes and i need som help  The question: The Fibonacci Numbers are recursively defined as $f_0 = 1$, $f_1 = 1$ and $f_{n+2} = f_{n+1} + f_n,$ for all $n ≥ 0$. Set $M = \binom{1\quad1}{1\quad0}$ and consider the powers $M, M^2, M^3,$ ... of this matrix. Prove that $M^n = \binom{f_n\quad f_{n-1}}{f_{n-1}\quad f_{n-2}}$ for all $n ≥ 2$. Powers of a matrix are the products $M^0 = I,\quad M^1 = M,\quad M^2 = M*M,\quad M^3 = M*M*M, . . . .$  can someone help and show me how to do this please? the proof


Eclipse launcher shortcut in Ubuntu 18.04

I successfully installed Eclipse oxygen and created a launcher Eclipse.desktop file by reading some tutorials.   Whenever I launch Eclipse from this launcher, it successfully launches. But I want it in the dock or favourites for ease. When I try drag and drop, it just doesn't work. After launching Eclipse there is no Keep in favourites option too.   How to solve this.


I want to know about usage of "start + action" and "stop + action". Which one of followin are correct or preferred? For ex.  When shall I start working? When shall I stop working?  Or  When shall I start to work? When shall I stop to work?  Does it depend on a context or on the action itself? Are there any rules that I can apply to phrases contain "start" and "stop"? Or maybe there are some differences in meaning?


Set the same height of the splits with tikz

I am not able to get the figure with the same height (10 cm). When a division is split in more parts the height, apparently increases. How to fix this?  Here is a reproducible example.  \documentclass[a4paper]{scrbook} \usepackage[hmargin=2.5cm,vmargin=2.5cm]{geometry} \usepackage[utf8x]{inputenc}  \usepackage{caption} \usepackage{latexsym} \usepackage{amssymb} \usepackage{amsmath} \usepackage{subcaption}   \usepackage{calc} \usepackage{tikz} \usetikzlibrary{shapes.geometric, arrows,positioning,shapes,calc,arrows}  \newcommand\Textbox[2]{%     \parbox[c][#1][c]{2.3cm}{\centering#2}}  \begin{document}  \begin{figure}     \begin{subfigure}[b]{0.32\textwidth}         \centering         \resizebox{\linewidth}{!}{          \begin{tikzpicture}         \node (h1) {\textbf{Text I}};         \node[draw,         align=center,         text width=2.5cm,         %minimum height=7cm,         draw=red!50,         rectangle split,          rectangle split parts=3, below of= h1,yshift=.5cm,         rectangle split part fill={gray!30, blue!20, green!15},         anchor=north east]{\textbf{Tit A}             \nodepart{two}\Textbox{6.7cm}{Cir 1\\67\% }              \nodepart{three}\Textbox{3.3cm}{Cir 2\\33\%} };         \node[draw,         align=center,         text width=2.5cm,         %minimum height=7cm,         draw=red!50,         rectangle split,          rectangle split parts=4, below of=h1,yshift=0.5cm,         rectangle split part fill={gray!30, blue!15, green!15,green!30},         anchor=north west]{\textbf{Tit B}             \nodepart{two}\Textbox{4.6cm}{Cir 1\\ 46\%}               \nodepart{three}\Textbox{3cm}{Met \\30\%}               \nodepart{four}\Textbox{2.4cm}{Let\\24\%} };         \end{tikzpicture}         }     \end{subfigure}     \begin{subfigure}[b]{0.32\textwidth}     \centering     \resizebox{\linewidth}{!}{         \begin{tikzpicture}         \node (h1) {\textbf{Text II}};         \node[draw,         align=center,         text width=2.5cm,         %minimum height=7cm,         draw=red!50,         rectangle split,          rectangle split parts=3, below of= h1,yshift=0.5cm,         rectangle split part fill={gray!30, blue!20, green!15},         anchor=north east]{\textbf{Tit A}             \nodepart{two}\Textbox{3.3cm}{Part 1\\33\% }              \nodepart{three}\Textbox{6.7cm}{Part 2\\67\%} };         \node[draw,         align=center,         text width=2.5cm,         %minimum height=7cm,         draw=red!50,         rectangle split,          rectangle split parts=5, below of=h1,yshift=0.5cm,         rectangle split part fill={gray!30, blue!15, green!15,green!30,yellow!15},         anchor=north west]{\textbf{Tit B}             \nodepart{two}\Textbox{3.3cm}{Cr1 \\ 33\%}               \nodepart{three}\Textbox{2.5cm}{Cr2\\25\%}               \nodepart{four}\Textbox{2.2cm}{Cr3\\22\%}             \nodepart{five}\Textbox{2.0cm}{Cr4\\20\%} };         \end{tikzpicture}     }     \end{subfigure}  \end{figure}  \end{document}   Thanks for any help!


Getting a command block with command inside

I have gotten commands into command blocks before with the /setblock. For whatever reason, this does not want to work even though this is the command. /setblock -477 6 1146 minecraft:command_block{Command:"/summon falling_block ~ ~2 ~2 {BlockState:{Name:"minecraft:command_block"},Time:1,TileEntityData:{Command:"say hi",auto:1b},Time:1}"} it gives me an error any suggestions


Using a paper under review as writing sample for PhD application

I am submitting a PhD application, for which I am required to include a writing sample; either a publication or a class report. I don’t have publications but I have a submitted paper authored by me and my advisor which I already submitted to a conference but was not yet accepted (results are due in 2 months).   I was thinking of submitting this paper for admissions as a writing sample because I think that it is well written. I know that I have to get my advisor’s permission.  In case my advisor agrees, is doing that appropriate? My yet to be accepted paper will be reviewed by professors in the department I am applying to.


Easiest process for me to apply textures, created externally, to my models

For the first time I'm working with an artist who is going to be creating the textures for the models I create in Blender.  Up till now I had been building the models and the texturing them myself using pre-built textures from websites.  My question is: What is the easiest process for me to apply the textures our artist creates to my model?  Should I give the artist the UV Map from my model, or should I just get textures from the artist and fit them to the UV Map?  Basically I have no idea how this process works in a professional environment.


Perl one liner working with >> but not >

I'm running the following command to add line numbers:  perl -pe '$_ = "$. $_"'   I can append the results to a file with:  cat test.txt | perl -pe '$_ = "$. $_"' >> test.txt   But if I try to replace the current contents the file ends up blank:  cat test.txt | perl -pe '$_ = "$. $_"' > test.txt   Why is this?


About this question marked as duplicate, I wasn't asking about how to encode in the original question, the encoding was the answer to the question though.  In my php I've filled an array with data from a database (each object in the array is the row, stored as another array). I'm calling echo json_encode($json); so I can grab it through android but it doesn't output anything. I can call each array and every column like echo $json[#][#]; and get the expected result, so I know the arrays are filled. How do I get it all out there so people can touch it with their greedy little fingers?  php:  <?php     $host="HOST";     $username="USER";     $password="PASS";     $db_name="DATABASE";      $con=mysql_connect("$host", "$username", "$password")or die("cannot connect");     mysql_select_db("$db_name")or die("cannot select DB");     $sql = "SELECT * FROM Table WHERE Column = 1";     $result = mysql_query($sql);     $json = array();     if(mysql_num_rows($result))     {         while($row=mysql_fetch_assoc($result))         {             $json[] = array($row['col1'], $row['col2'], $row['col3'], $row['col4'], $row['col5'], $row['col6']);         }         echo json_encode($json);     } ?>    SOLVED The problem was with UTF8, on some columns that have text, occasionally specail characters are used (in this case, Å, Ä and Ö). Thanks to commenter @meda that suggested I use utf8_encode($row[col]) everything's fine.


Determinant of a block matrix using row operations

Consider an $n \times n$ matrix of the form $$ A = \begin{pmatrix} M & P \\ 0 & N \end{pmatrix} $$ with $M \in \Bbb K^{r \times r}$, $P \in \Bbb K^{r \times s}$, and $0 \in \Bbb K^{s \times r}$ is the zero $s \times r$ matrix, $n = s+r$. Show that $$\det(A) = \det(M) \cdot \det(N)$$   I know that I have to approach this question by changing $M$ and $N$ into upper triangular matrix, but how do I do this? I am only allowed to use row operations. Thanks in advance. Similar questions aren't showing the row operations method.


unicode-math replaces \not by the number "6"

The following MWE yields the attached picture:  \documentclass{article}  \usepackage{fontspec} \usepackage{amsmath,amssymb} \usepackage{unicode-math}  \begin{document} With \LaTeX{} commands: \begin{gather*}   A \not= B\\   A \not\le B\\   A \not\lesssim B\\   A \not\approxeq B \end{gather*}  With Unicode characters:  \begin{gather*}   A \not= B\\   A \not≤ B\\   A \not≲ B\\   A \not≊ B \end{gather*} \end{document}     Why is \not replaced by 6?  I tried using a Unicode combining long solidus overlay instead, but that doesn't work at all:  \begin{gather*}   A ≠ B\\   A ≰ B\\   A ≴ B\\   A ≊̸ B \end{gather*}


I recently bought a new laptop, and have updated it to El Capitan. I have started working on an old paper, which compiled just fine on my last laptop, and cannot get the bibliography to compile.   I am using TexShop. I can compile the main file (in XeLaTeX). but when I try to compile the bibliography I get this error message: "The program bibtex does not exist". The console does not generate any text whatsoever.   I've looked around online but can't find anyone else who seems to have had this exact problem. I'm assuming it's not with my code, as I can compile it on my old machine, but something to do with how TeX Shop has loaded on my new computer?   Any suggestions would be greatly appreciated!  the relevant bibliography code:  \usepackage[style=apa]{biblatex} \addbibresources{MyFile.bib}


Debug logs not working for Site Guest Users (Force.com sites) after the Winter 17 release

Recently our team has noticed that turning on the Debug Logs for a Site Guest User has stopped working. Prior to the Winter 17 release, if you turned on Debug Logs for a Site Guest User, logs appear like they do for any other user.   I couldn't find any relevant information in Google on this topic, and finally got an answer from Salesforce Tech support, so I am posting it here.


How did you know when to say "thing haveth or something"?

I have been watching Hocus Pocus and wondered how people in the 1800s knew when to add eth on the end of words.


Why does Win 10 Desktop Window Manager use so much memory 5+GB

Why does Windows 10 Desktop Window Manager consume so much memory? What is it doing with all that RAM? I have 16 GB of RAM and DWM is consuming 5+GB of it.


Is it experimentally verified that the neutrinos are affected by gravity?

If neutrinos (or any other particles) wasn't affected by gravity that would contradict the general theory of relativity. I'm convinced that the postulate of the equivalence between inertial mass and gravitational mass is adequate, but not totally convinced that it is the truth.   From my dialectical point of view there are no total unity. In every distinction there is a gap to explore. What is supposed to be identical will be found split complex when examined more closely.  And therefor I would like to know if it's experimentally verified that the neutrinos are affected by gravity?


How do i see which softwares are installed in ubuntu?

How can i get a list of my installed applications?


Thread with array of structures returns SIGSEGV (Segmentation fault error)?

i am creating a thread that will captures  packets and will store some information in a structure "flow" for each packet. i am using static array of "flow" type structures. but when i run the program it retuns SIGSEGV error. here's the structure "flow":  typedef struct flow {     unsigned int s_port;     unsigned int d_port;     char s_addr[20];     char d_addr[20];     int spi;     short total;      short data[10000];     struct timeval prev_t;     double ipt[10000];      flowParam info;     char status[100];  }flow;   note that flowParam is another structure whose object info is included in "flow". i also run program by commenting it but got same result...  and here's the main program:  int main() {     pthread_t tid;      int err = pthread_create(&tid, NULL, Capture, NULL);         if (err != 0){             perror("\ncan't create capturing thread");             exit(-1);         }         else             printf("\nCapturing thread created!\n");      pthread_join(tid, NULL);     printf("Finished!!");     return 0; }  void* Capture() {     flow Register[5000]; /* flow Register */     //counter Counter[5000];      pthread_exit(NULL);  }   interestingly, when i use another structure "counter" and make its array in thread, it does not give such error.  typedef struct counter {     char s_addr[20];     char d_addr[20];     }counter;   i tried to my best to solve this issue but could not find any clue.any help???


function foldersize($path) {   $total_size = 0;   $files = scandir($path);    foreach($files as $t) {     if (is_dir(rtrim($path, '/') . '/' . $t)) {       if ($t<>"." && $t<>"..") {           $size = foldersize(rtrim($path, '/') . '/' . $t);            $total_size += $size;       }     } else {       $size = filesize(rtrim($path, '/') . '/' . $t);       $total_size += $size;     }   }   return $total_size; }  function format_size($size) {   $mod = 1024;   $units = explode(' ','B KB MB GB TB PB');   for ($i = 0; $size > $mod; $i++) {     $size /= $mod;   }    return round($size, 2) . ' ' . $units[$i]; }  $SIZE_LIMIT = 5368709120; // 5 GB  $sql="select * from users order by id"; $result=mysql_query($sql);  while($row=mysql_fetch_array($result)) {   $disk_used = foldersize("C:/xampp/htdocs/freehosting/".$row['name']);    $disk_remaining = $SIZE_LIMIT - $disk_used;   print 'Name: ' . $row['name'] . '
';    print 'diskspace used: ' . format_size($disk_used) . '
';   print 'diskspace left: ' . format_size($disk_remaining) . '

'; }     Any idea why the processor usage shoot up too high or 100% till the script execution is finish ? Can anything be done to optimize it? or is there any other alternative way to check folder and folders inside it size?


How to replace a Acer Chromebook with Ubuntu?

I have an Acer Chromebook with model-number CB3-132-C971 and it will be reach end of support in June 2022. I don't want to throw this computer away. Is it possible to install Ubuntu on this computer with an ISO-file?  How do I remove Chrome-OS totally and install Ubuntu instead? what are the steps?


Beamer content disappears when notes are shown besides slides

I have finally encountered an exciting TeX-related problem to post here: Using beamer slides with notes, certain parts of my slides disappear in the main slide when the option \setbeameroption{show notes on second screen=right} in combination with the pgfpages package is used.  When i disable the option / only compile the slides without notes, the output is fine. However, using the option, the main slide view is missing text inbetween two itemize-environments as well as an equation.  This is my MWE:  \documentclass{beamer}  \usepackage{pgfpages}  \setbeameroption{show notes on second screen=right}  \begin{document}  \begin{frame} \begin{itemize} \item content \item more content \end{itemize} \note{a note} \pause aaaand \begin{itemize} \item content \item more content \end{itemize} \begin{equation} A \mathbf{x} = \mathbf{b} \end{equation} \end{frame}  \end{document}   My question is: How can I make the annoted slides show the content that disappears when the notes are shown?    What I find exciting about his problem in particular is that for the preview above the nodes, the content missing from the slide is shown!


Why are our planets in the solar system all on the same disc/plane/layer?

I always see pictures of the solar system where our sun is in the middle and the planets surround the sun. All these planets move on orbits on the same layer. Why?


MySQL runs fine for weeks or days, and then suddenly and without any user action, all attempts to connect begin failing. This is /var/log/mysqld.log:  160916 14:42:01 [Note] /usr/libexec/mysql55/mysqld: ready for connections. Version: '5.5.51'  socket: '/var/lib/mysql/mysql.sock'  port: 3306  MySQL Community Server (GPL) 160930 03:05:51 mysqld_safe Number of processes running now: 0 160930 03:05:52 mysqld_safe mysqld restarted 160930  3:05:53 [Note] /usr/libexec/mysql55/mysqld (mysqld 5.5.51) starting as process 8961 ... 160930  3:05:53 [Note] Plugin 'FEDERATED' is disabled. 160930  3:05:54 InnoDB: The InnoDB memory heap is disabled 160930  3:05:54 InnoDB: Mutexes and rw_locks use GCC atomic builtins 160930  3:05:54 InnoDB: Compressed tables use zlib 1.2.8 160930  3:05:54 InnoDB: Using Linux native AIO 160930  3:05:54 InnoDB: Initializing buffer pool, size = 128.0M InnoDB: mmap(137363456 bytes) failed; errno 12 160930  3:05:54 InnoDB: Completed initialization of buffer pool 160930  3:05:54 InnoDB: Fatal error: cannot allocate memory for the buffer pool 160930  3:05:54 [ERROR] Plugin 'InnoDB' init function returned error. 160930  3:05:54 [ERROR] Plugin 'InnoDB' registration as a STORAGE ENGINE failed. 160930  3:05:54 [ERROR] Unknown/unsupported storage engine: InnoDB 160930  3:05:54 [ERROR] Aborting  160930  3:05:54 [Note] /usr/libexec/mysql55/mysqld: Shutdown complete  160930 03:05:54 mysqld_safe mysqld from pid file /var/run/mysqld/mysqld.pid ended   What causes this, and how can I deal with it?


Do I need a visa for 23 hour layover in London to visit the city?

I have a 23-hour layover in London. I have a valid US visa. Which UK visa do I need for sightseeing during the layover time?


Suppose that $f$ is an entire function satisfying $f(2z)=\frac{f(z)+f(z+1)}{2}$. Show that $f$ is constant.

I've been working old qualifying exam problems from my university. I've been struggling with the following:  Suppose $f$ is an entire function with the property that $f(2z)=\frac{f(z)+f(z+1)}{2}$ for all $z$. Prove that $f$ must be a constant function.  Here are my thoughts Write $f(z)=\sum_{n=0}^{\infty}c_nz^n$. Then \begin{align*} 2\sum_{n=0}^{\infty}c_n2^nz^n&=\sum_{n=0}^{\infty}c_nz^n+\sum_{n=0}^{\infty}c_n(z+1)^n\\ &=\sum_{n=0}^{\infty}c_nz^n+\sum_{n=0}^{\infty}\sum_{k=0}^{n}c_n\binom{n}{k}z^k. \end{align*} By equating the coeffients of the power series, we have $$ c_n2^{n+1}=c_n+\sum_{k=0}^{\infty}c_k\binom{k}{n}, $$ or $$ c_n2^{n+1}=2c_n+\sum_{k=n+1}^{\infty}c_k\binom{k}{n}. $$ Thus $$ (2^{n+1}-2)c_n=\sum_{k=n+1}^{\infty}c_k\binom{k}{n}. $$ Furthermore, \begin{align*} (2^{n+1}-2)c_n-(2^{n+2}-2)c_{n+1}&=\sum_{k=n+1}^{\infty}c_k\binom{k}{n}-\sum_{k=n+2}^{\infty}c_k\binom{k}{n+1}\\ &=c_{n+1}(n+1)+\sum_{k=n+2}^{\infty}c_k\left(\binom{k}{n}-\binom{k}{n+1}\right) \end{align*} However here I am stuck. I realize that these equations should contain everything needed to solve this problem, but I don't see how to use them. Are there any easier ways to approach this problem? Any help is greatly appreciated. Thank you.


What is the industry standard to installing ubuntu in a windows machine?

I have before installed ubuntu alongside windows but I had to format that drive so both ubuntu and windows were gone so I wanna know if its recommendable and if its even possible to install ubuntu in a separate hard drive that will live inside my computer say disk f: and only install ubuntu there by itself nothing more while having disk c: for windows only.Will I have to always go to bios bootsetting to tell my pc I wanna boot from disk f or c? or I can use the dual install option and somewhere in the settings will tell me to install ubuntu in disk f: while still keeping the dual bootable screen that comes by default?(I have not attempted this for fear i will mess up and install ubuntu in c rather than f by itself) or should I just install in an external ssd running in wither usb c or 3.0 .Please tell me what is the most recommendable way to run ubuntu or how you run it to avoid having the issued I had.


Is there a way to disable a laptop's internal keyboard?

A week ago, I spilt the contents of my cup onto my laptop keyboard. Half of the keys no longer work, except one! The letter Q which is very active regularly.  This is very disturbing as I work.  Is there a way to disable the internal keyboard of a laptop?  Is it possible with xmodmap?


When an electron revolves around a nucleus, It uses its energy in form of kinetic energy and so it release energy and then moves . It means that it release energy continuously, Otherwise, if it does not release energy(in form of Kinetic energy) continuously. Then its motion around nucleus is not possible.Please make me understand this concept?


Google Photos Backup DNG file with low quality

Using the desktop google photos sync app, JPG files sync with resolutions like 2992x2000, and  NEF files like 3008x2000.  But with DNG files, only 1024x683?  Tried to download the file to see if it's a preview, but it doesn't seem so. Any idea why this happens only with DNG files, and how to resolve this issue?  Thanks in advance!


How do I mount an ext4 partition as my user account so I wouldn't require root access to r/w on it? I used -o uid=flint,gid=flint on the mount command but I keep getting   mount: wrong fs type, bad option, bad superblock on /dev/sda7,        missing codepage or helper program, or other error        In some cases useful info is found in syslog - try        dmesg | tail  or so   Another thing, I want avoid using udisks for now as it doesn't let me mount to my specified mount point name.


TikZ: \pgfmathresult problem inside (:\pgfmathresult) coordinate

After reading , I was playing around to make a command to create a TikZ command with two inputs like this:  \documentclass[10pt,a4paper]{article}  \usepackage{tikz} \usetikzlibrary{calc}  \begin{document} \centering  \newcommand{\mitsubishi}[2]{ % #1 = radius % #2 = position x,y \pgfmathparse{2.966/7} \pgfmathparse{#1*\pgfmathresult}  \filldraw (#2) circle(#1 cm); % plate  \foreach \angle in {0,120,240}{ \filldraw[white,rotate=\angle] (#2)--++(60:\pgfmathresult)--++(120:\pgfmathresult)--++(-120:\pgfmathresult)--cycle; } }  \begin{tikzpicture} \mitsubishi{2}{0,0} \end{tikzpicture} \end{document}   but I have problems with the command \pgfmathresult inside the \filldraw command.  Why?


If $a$ and $b$ are positive real numbers, then $a+ b \ge 2 \sqrt{ab}$.  Can you guys help me with this problem? I'm still trying to learn how to do proving and I don't really know how to start or complete this problem.


How to stop postgres from autostarting during start up

I have postgresql 8.4 installed on my desktop. It keeps starting on bootup because I think I used default settings.   so I issue /etc/init.d/postgresql stop everytime and sometimes i keep forgetting  It has folder paths as,  /etc/postgresql/8.4/main /usr/lib/postgresql/8.4   There are a lot of configuration files and if someone can tell me where to look and what to change, that will be great.   Thanks.


Let $a,b,c\in\mathbb{R}^*_+$, $abc=1$.  How can i show that $\left(a-1+\frac{1}b\right)\left(b-1+\frac{1}c\right)\left(c-1+\frac{1}a\right)\leq1$ ?  I got $\left(ab-b+1\right)\left(bc-c+1\right)\left(ca-a+1\right)\leq abc=1$, but i can't go any further ...  If i expand it :   $2-ab-\frac{b}a-c-ac-\frac{a}c-b+2a+\frac{2}a-bc-\frac{c}b-a+2b+\frac{2}b+2c+\frac{2}c-4$  Which gives using $c=\frac{1}{ab}$ :   $5ab-\frac{b}a-\frac{1}{ab}-a^2b+\frac{1}a+b+\frac{1}b-2$


I've flagged many posts for link-only answer when the user posts only a link with no explanation (e.g., to documentation). However, some users return after the fact (I've seen 3-4 hour delays in the past) to add some example code. If my flag still says "active," as in it hasn't been reviewed yet, shouldn't I be able to delete it?


I came across this funny proof-  $$4$$ $$=4+\frac 92-\frac 92$$ $$=\sqrt{(4-\frac 92)^2}+\frac 92$$ $$=\sqrt{16+\frac{81}{4}-36}+\frac 92$$ $$=\sqrt{25+\frac {81}{4}-45}+\frac 92$$ $$=\sqrt{(5-\frac 92)^2}+\frac 92$$ $$=5-\frac 92+\frac 92$$ $$=5$$  I suspect,that the error is in the second line where operation on negative is done before positive violating $BODMAS$ rule.But,$\sqrt{(4-\frac 92)^2}=4-\frac 92$ and the similar solving continues.So, where is the real error? Thanks for any help!!


Difference Between CSS and XPATH ?  Which is the best locator in selecting Elements in selenium?  If Xpath is the better why? why should we use Xpath instead of CSS?  If CSS is the better why? why should we use CSS instead of Xpath ?  What are the advantages of both Xpath and CSS ?  What are the Disadvantages of both Xpath and CSS?


The true or false question states: "True of False: Every 3-dimensional subspace of $ \Bbb R^{2 \times 2}$ contains at least one invertible matrix."  Here the $ \Bbb R^{2 \times 2}$ represents the space of all two by two matrices. It seems like this is true, but I am not sure how to prove or disprove the statement. (If such is true, then it's easy to see that every 3-dimensional subspace of $ \Bbb R^{2 \times 2}$ contains infinitely many invertible matrices)


I am writing a scientific research paper. As is common in the field, I am about 2000 words over the limit for submission, and I am trying to cut words. "Patient-specific" in its hyphenated form is only counted as one word, but I do not want to use it incorrectly. When is it appropriate to use "patient-specific" vs. "patient specific"? In most cases I am using the phrase as an adjective, such as "patient-specific anatomy".


I have "unknown PCI device" in Windows 7 device manager. What can it be?

I have just performed a fresh installation of Windows 7 Home Premium 64 bit on my lenovo e330 laptop. I managed to successfully download and install most of its drivers, but still, a "PCI Device" appears under "other devices" in the device manager.  What could it be? How can I check what is missing?


Generate unique integer with 8 digits in java

I'm trying to figure how to approach with generating unique integer with 8 digits in java. The biggest problem is that it gives you a limited permutation, and also the clustered env. Any suggestion is welcome.  Regards


Run commands on system shutdown/reboot/logout

I would like to run certain aliases and simple commands when system shuts down or reboots or when I simply log out of system. This would help a lot as I usually forget about shutting down vagrant ( vagrant halt ) and some other terminal commands. Do we have some kind of bash files or scripts so I can achieve this on Ubuntu 14.04.


For some reason when I reference something in my text, it also gives the type of object referenced (like Tabel 1, instead of just 1). I understand, that this is not standard latex behavior, but I do not explicitly load packages, that should alter this. I guess, one of the packages I use silently does this.  Here is my MWE:  \documentclass[12pt, english, parskip, a4paper]{scrartcl}  \usepackage[journal=angew]{chemstyle}   % loads chemscheme, graphicx  \begin{document}     \begin{table}[h]         \caption{Test}         \begin{tabular}{c}             Test \\          \end{tabular}         \label{tab:test}     \end{table}      Look at Table~\ref{tab:test}. \end{document}   This will print      Look at Table Table 1.   How can I get rid of this? Thanks!


Is it possible to delete SEDE queries from our account history?

As the title says. There's a history of all our queries and it would be good to be able to delete the lousy queries and keep the useful ones.   Is there a way to do this?


Did the Ring Bearers and Gimli die in Valinor?

A  on a recent question stated     The Undying Lands doesn't prevent mortals from dying so, in fact, [Frodo] died... maybe sixty years (or more, if his life was prolonged) after the end of the story.    If this is correct, Gimli certainly would have died.  Is there any direct reference to his death (preferably with age)? Failing that, what canon states or implies that mortals will still die there?  The Undying Lands might not prevent death, but the One Ring seems to. Gollum lived for over 500 years because of it. Bilbo, Frodo, and Sam all aged slowly before making their way to Valinor, even after the Ring's destruction.  My impression was that because of the Ring's influence they were expected to live forever, and their residence in Valinor served not only to make them comfortable, but also (perhaps even moreso) to protect them from becoming wraiths due to the Ring's effect.   So, did the Ring Bearers live until the End of Days in Valinor, or did they eventually expire, and at what age? Were they mortal once again because the Ring's power had been broken by its destruction, or the magic of the Undying Lands, or did the Valar themselves reverse it?  I'd also appreciate canonical references to age at death if it did happen.


I am doing research on reverse engineering. I am able to decompile .net dll files with reflector. But in reflector we can't decompile c++ dll files. Is there any other decompiler available to decompile c++ dll Files?


N cannot be partitioned into a finite number of arithmetic progressions

N cannot be partitioned into a finite number of arithmetic progression with distinct steps except the trivial case $\{1,2,...\}$  The hint told me to consider: $$\sum_{n\in N}z^n=\sum_{i=1}^r\frac{z^{a_i}}{1-z^{d_i}}$$ and I figured out for some $j$ we have  $a_j=1$, but I don't know how to prove $d_j=1,r=1$


Why is itemStateChanged on JComboBox is called twice when changed?

I'm using a JComboBox with an ItemListener on it. When the value is changed, the itemStateChanged event is called twice. The first call, the ItemEvent is showing the original item selected. On the second time, it is showing the item that has been just selected by the user. Here's some tester code:  public Tester(){      JComboBox box = new JComboBox();     box.addItem("One");     box.addItem("Two");     box.addItem("Three");     box.addItem("Four");      box.addItemListener(new ItemListener(){         public void itemStateChanged(ItemEvent e){             System.out.println(e.getItem());         }     });      JFrame frame = new JFrame();     frame.getContentPane().add(box);     frame.pack();     frame.setVisible(true); }   So when I changed the Combo box once from "One" to "Three" the console shows:  One Three   Is there a way I can tell using the ItemEvent maybe, that it's the second item (ie. the user selected item)? And if someone can explain why it gets called twice, that would be nice too!  Thanks


Is there any issue with LAN-card in ubuntu?

Will Ubuntu 14.04 will work if desktop is already fitted with LAN card?


Wulfgar won't teach me Unrelenting Force's final word after Arngeir accepts the Horn of Jurgen Windcaller

I am seeing this bug in Skyrim where Wulfgar doesn't respond though you found the Horn of Jurgen Windcaller.   I've returned the Horn to Arngeir, but he doesn't stand in the circle with the other Greybeards. I've noticed from videos where this is working that he is part of the circle.  Various attempts and workarounds I've tried:   Gate-related   Walked or sprinted through the gate and closed it  Replayed and closed the gate immediately after learning Whirlwind  System-related   Current on all patches (as of March 2, 2012) Deleted character and related Skyrim files in case any files were corrupt Reloaded multiple times before and after returning the horn  Additional (frustration-driven) attempts   Attacked the Greybeards, left the area, and snuck until forgotten Completed side quests before returning Slept and tried multiple times (16 or so)    Despite what I try, replaying up to the same spot gives me the same bug.  Does anyone know of a workaround aside from the closing the gate or reloading an earlier manual or autosave game?  I am playing on Xbox 360.


AUCTex: Math mode started with ‘\[’ cannot be closed with dollar in cases*

I have the following code: \[   \begin{cases*}     1& if    \end{cases*} ...  after the if, I want to type a dollar sign but get the error message "Math mode started with '\[' cannot be closed with dollar". I am unsure how to fix this. EDIT: Clarifications  I want to type a dollar sign to enter into math mode. Note that the cases* environment expects text after the ampersand. The error message mentioned is an AUCTeX error (shows up in the *Messages* buffer)---it doesn't allow me to type the dollar sign character into the Emacs buffer.


Apply force to one end of a rod in space: why not purely translational?

Why does applying force to a rod in space (or any other isolated systems) on one end leads to both translational and rotational motion?    Here's my logic: suppose there is a rod in space. We magically apply force on one end, perpendicular to the rod. From Newton's second law of motion: $$F_y=ma_{cm,y}.$$ The only force acting in the $y$-direction is $F$, so $a_{cm}$ must equal to $F/m$. Consequently, the rod purely translates as a whole and it doesn't rotates. There is no net external torque because the end of the rod is accelerating linearly along with the center of mass.   The answers to  assumes that there is torque, which I can't see why there should be.


Meta sites in "Your Communities" display different reputation

While using the top bar to navigate across communities, I noticed that the reputation displayed on meta sites on that list does not match the one of their corresponding main sites:    I have noticed on past situations that reputation gained takes a bit to "update" on the display on Meta sites (that is, if you gain rep on SO, for example, it will take some time for you to see your updated rep on MSO).  However, I have never noticed this behavior here, on the Sites List of the top bar. Furthermore, the "delay" here seems to be more severe, as the "outdated" rep showed is of several days ago (for example, I turned 3k on SO almost exactly a week ago, but the rep shown on MSO is still <3k).  Any idea what could be causing this behavior?    Update: 2 months later this persists: my main site rep updates correctly but their corresponding meta rep remains the same as in the image above.     Update: As per Catija's  I removed the site (MSO) and put it back in, but it didn't update the rep.   However, after removing one site (TWP Meta), waiting at least a day, and then adding it back I see that although the reputations still don't match, the number displayed did changed a bit (previously 29,924 but now 33,112):


"Unable to find a medium containing a live file system"

I've installed Ubuntu on my laptop, but when I open Ubuntu, it says the following message (initramfs) Unable to find a medium containing a live file system  Can anyone help?


how to select the best non-linear model that represents the data?

I have developed different non-linear models, all of them follow the following formula: y=b0 + b1*(x1)^b2 + b3*(x2)^b4 where y is the dependent variable;x1 and x2 are independent variables;b0, b1, b2, b3, and b4 are the estimated regression coefficients. different values of b0, b1, b2, b3, and b4 have been estimated with different R-square and adjusted R-square. All estimated regression coefficients in all models are positive, the range of all estimated values are between 0.001-5 the difference only in the combinations of regression coefficient values in the models. by example : model 1 : y= 2.5 + 0.01*(x1)^2 + 0.2*(x2)^0.5 model 2 : y= 2.3 + 0.005*(x1)^3 + 0.25*(x2)^0.4 I estimated the regression coefficients based on the Gauss-newton method and by assuming different initial values for the regression coefficient for each run (model). how to select the best model based on anything except R-square? how to determine the goodness of fit for these models?


Allow author of accepted answer to delete it in certain circumstances

I made a mistake today.  I . (A C# question, no less. My head is truly hanging in shame.) Unfortunately, by the time this was pointed out, the answer had already been accepted.  Another answer has been posted which is correct. It has more votes than mine, and mine has some downvotes (still a balance of upvotes, but...) Unfortunately because the answer has been accepted, I can't delete my answer. I've edited it so that it's correct - it won't mislead anyone any more - but I'd far rather delete it to let the original correct one float to the top.  In this case I suspect it won't be a real problem - the question author is reasonably regular, so hopefully he'll transfer acceptance to another answer reasonably soon. However, I can easily foresee situations where this wouldn't happen.  Could I suggest that the author of the accepted answer should be able to delete it, if the answer has received some threshold of downvotes (e.g. 3)? Deleting the answer straight away would have been preferable to editing it to be correct, effectively duplicating the effort already put in by Luis Filipe in this case.  I understand the "we don't want to lose value" argument for not letting a question author delete their own question after it's had good answers, but if an answer has received downvotes (so at least some of the community think it's harmful) and the answer's author thinks it should be removed, I think that should override the questioner's choice.


There is this theorem that states: If $\alpha$ is an ordinal, then there is a limit ordinal $\mu$ with $\alpha < \mu$. The definition of limit ordinal is just "an ordinal which is a limit", but a better reformulation of this definition is: Let $\lambda$ be a non-zero ordinal. $\lambda$ is a limit ordinal if and only if for all ordinal $\alpha$, if $\alpha<\lambda$ then $\alpha^+<\lambda$. ($\alpha^+$ is the successor ordinal of $\alpha$) I don't understand how that theorem makes sense, the book I'm reading gives the proof as an exercise (which I can't do) so I can't even see why it's true. If for example I have the ordinal $1=\{\emptyset\}$ what is a limit ordinal for this? Is it $\omega$ for example (or $2\omega$, $3\omega$ etc)? Is this what it means?


Let $G$ and $H$ be abelian groups. Show that the product $G\times H$ is also abelian. I have already proved, that for groups $G$ and $H$ finite groups, then the direct product $G\times H$ is cyclical if and only if $G$ and $H$ are cyclical. However, here I get confused because cyclic groups should be a subset of all abelian groups.


Find the Value of $\sin^2A + \sin^2B + \sin^2C$ given the following data.

If $2\tan^2A\tan^2B\tan^2C + \tan^2A\tan^2B + \tan^2B\tan^2C + \tan^2C\tan^2A = 1$, then find the value of $\sin^2A + \sin^2B + \sin^2C$.  My attempt  1). I tried to multiply both sides by $\cos^2A\cos^2B\cos^2C$ in given. Then took common but after that, I didn't get what to do next  2). I tried to relate the given with $(ab+bc+ca)^2,$ but it also didn't work...  I could only think of these two ways but nothing worked for me...


Differentiate Between free/trial (developers, sandbox) orgs vs Production Orgs?

Using the Organization object we can differentiate between Production or Sandbox orgs using IsSandbox. Is there any programatic way to differentiate between a Developer Free Org vs a typical Production Org?  I see there is Organization.OrganizationType with following values, but it holds value as followings   Enterprise Edition (dev org created from partner portal) Developer Edition (typical dev org)   Is there any easy and deterministic way to differentiate between Production and Developer Edition orgs?


When (if ever) is is acceptable to use an indefinite article immediately in front of an adjective?

What's the rule for using a/an before an adjective?  I am asking this question because my high school professor is teaching us that  we shouldn't use a/an before an adjective. With some 'exceptions' like "Picasso was a famous painter."   Now that sounds very strange to me because I am used to saying "It's a beautiful day.", not "It's beautiful day.", or "It's a small dog.", not "It's small dog". My professor also pointed out that "Picasso was a famous painter." was some kind of exception because "a" is used before an adjective. My professor also told me that this sentence is correct : "A mouse is an animal. It's small animal."  Like I said, for me, It's a very strange claim that we shouldn't use "a" or "an" before an adjective. What should I say to my professor? I would like your professional opinion about this.  Thanks.  Notice: This question isn't about 'a' vs 'an'. Read the question before marking it as a duplicate.


I have a Nikon D750 with a Nikkor 28-300mm VR lens. I am an absolute newbie and I've been trying to capture a reasonably good picture of the moon. But no matter what I try, the pictures are never sharp.  I've tried mounting the camera (by the camera, not the lens) on a tripod, set the shutter release to remote or timer (2s) and tried taking several shots at varying shutter speeds (10s to 30s) and ISOs (1600 to 6400) with the maximum aperture (f/5.6 I believe) at 300mm. But no matter how I take the photo, the moon always looks a bit blurred.  I tried with VR turned on and off, on my lens. What am I doing wrong?   Any help is appreciated.


Why is a microwave oven equipped with a waveguide?

In a microwave oven, the magnetron connects to the waveguide.  Magnetrons produce microwaves, which are guided into the cooking chamber by waveguides. Why don't we directly connect the magnetron to the cooking chamber?


I am experienced the following issue: after hibernation (using command sudo systemctl hibernatein a terminal or the menu on the right top of Ubuntu desktop) I get a black screen (Even though all devices seem to work. The fan works!) and I am forced to reboot the OS because resume failed and I can't back to a "saved state". The content in etc/polkit-1/localauthority/50-local.d/com.ubuntu.enable-hibernate.pkla is:      [Re-enable hibernate by default in upower] Identity=unix-user:* Action=org.freedesktop.upower.hibernate ResultActive=yes  [Re-enable hibernate by default in logind] Identity=unix-user:* Action=org.freedesktop.login1.hibernate;org.freedesktop.login1.handle-hibernate-key;org.freedesktop.login1;org.freedesktop.login1.hibernate-multiple-sessions;org.freedesktop.login1.hibernate-ignore-inhibit ResultActive=yes   Additional info: Ubuntu version: 16.04LTS  Kernel version:   uname -r 4.13.0-26-generic   Graphic info:   udo lspci | grep -E 'VGA|Display' [sudo] password di michele:  00:02.0 VGA compatible controller: Intel Corporation 2nd Generation Core Processor Family Integrated Graphics Controller (rev 09) 01:00.0 VGA compatible controller: Advanced Micro Devices, Inc. [AMD/ATI] Whistler [Radeon HD 6730M/6770M/7690M XT] (rev ff) michele@michele-ubuntu:~$ sudo lshw -c display | grep driver        configuration: driver=i915 latency=0   CPU info:  sudo lscpu [sudo] password di michele: Architecture: x86_64 CPU op-mode(s): 32-bit, 64-bit Byte Order: Little Endian CPU(s): 8 On-line CPU(s) list: 0-7 Thread(s) per core: 2 Core(s) per socket: 4 Socket(s): 1 NUMA node(s): 1 Vendor ID: GenuineIntel CPU family: 6 Model: 42 Model name: Intel(R) Core(TM) i7-2630QM CPU @ 2.00GHz Stepping: 7 CPU MHz: 1995.561 CPU max MHz: 2900,0000 CPU min MHz: 800,0000 BogoMIPS: 3991.12 Virtualization: VT-x L1d cache: 32K L1i cache: 32K L2 cache: 256K L3 cache: 6144K NUMA node0 CPU(s): 0-7 Flags: fpu vme de pse tsc msr pae mce cx8 apic sep mtrr pge mca cmov pat pse36 clflush dts acpi mmx fxsr sse sse2 ss ht tm pbe syscall nx rdtscp lm constant_tsc arch_perfmon pebs bts rep_good nopl xtopology nonstop_tsc cpuid aperfmperf pni pclmulqdq dtes64 monitor ds_cpl vmx est tm2 ssse3 cx16 xtpr pdcm pcid sse4_1 sse4_2 x2apic popcnt tsc_deadline_timer aes xsave avx lahf_lm epb pti tpr_shadow vnmi flexpriority ept vpid xsaveopt dtherm ida arat pln pts   Why does the resuming fail?  Thanks in advance for your help.


In last days my apache is being attacked by many connections from proxies. I've identified the source but could not block the attack effectively.  The attacker seems to be using pyloris or a variation of this to attack my apache on port 80.  I installed nginx and varnish but not enough to support the extra load.  I also added a rule in iptables to drop packets that contain the string "X-Forwarded-For" but does not block all the proxies.  Does anyone have a suggestion?


Showing a recursive sequence isn't bounded $a_{n+1}=a_n+\frac 1 {a_n}$

Show the sequence isn't bounded: $a_1=1$, $a_{n+1}=a_n+\frac 1 {a_n}$.   Proof by contradiction: Let $M>0$ such that $\forall n: |a_n|< M$.   Let $\epsilon >0 $ and for some $n=N, \epsilon: a_N=M-\epsilon<M $ pluging that in the recursion: $a_{N+1}=M-\epsilon+\frac 1 {M-\epsilon}>M>M-\epsilon$. Contradiction.  I wondered if I could suppose about the boundary that $\forall n: |a_n|\le M$ ? The proof would basically be the same only I could drop the epsilon.


Line break (\n) in return statement of a method

I am trying to use Line breaks (\n) in return statement. But it doesn't work. \n gets printed in the return statement. I am not using any VF Page. I am trying this in my webservice class.  Below is the method structure.  global static string createNewCase() {     //...     return 'FIELDS :' + '' + response.fields + '/\n' +         'MESSAGE :' + '' + response.message +         'STATUS CODE :' + '' + response.statuscode; }   I tried by adding '/\n' this also did not work. Please help in how to do this. I tried to search for this. But all I get is the example of VF page and controller where escape=False is specified in controller.  I have tried the code mentioned in the  link for reference and made changes. Still it is not working.


What is the policy on OP deleting the posted question?

There was a  on Stack Overflow that I was following because I was trying to troubleshoot the issue and was interested to know the answer.   The question seemed perfectly fine to me (and there were no downvotes either), and there were a few others along with me trying to figure out the problem. However, all of a sudden the OP decides to remove the question.   Now I am deprived of the opportunity to find out the answer, and I cannot recreate the problem and try to solve it myself.   So I'm just wondering if there is/should be any policy on OPs deleting their posted questions in such circumstances.


In the book 'Calculus the Early Transcendetals' at page 776 (7th edition) they give that the period of a  with length $\text{L}$ that makes a maximum angle $\theta_0$ with the vertical is: $$\text{T}_{\left[\text{s}\right]}=4\sqrt{\frac{\text{L}}{\text{g}}}\int_{0}^{\frac{\pi}{2}}\frac{1}{\sqrt{1-\sin^2\left(\frac{\theta_0}{2}\right)\sin^2(x)}}\space\text{d}x$$  Questions:  Does this formula work, for any pendulum? How did they get this formula (hint to derive the given formula)?


How can i differentiate between log2(2^5910-1) and log2(2^5910)? Both are giving 5909.9999999999

I was working with numbers up to 2100000. I am stuck at this point. Some of the numbers are not giving correct result as in the title:  >>> math.log(2**5910, 2) 5909.99999999999 >>> math.log(2**5910-1,2) 5909.99999999999 >>> math.log(2**5910+1,2) 5909.99999999999   How can i differentiate between log2(2^5910-1), log2(2^5910), log2(2^5910+1)? What I want is the characteristic of log2(n) to be exactly correct and I don't care about preciseness of mantissa. But it should give an integer in case of perfect power or atleast tell its a perfect power or not. Currently I am using this function:  def log(n):     c=int.bit_length(n)-1     m=0.5     if(2**c==n):m=0     return c,m


Let $z_0$ be a point in an open set $U \subset \mathbb{C}$.  Let $f,g:U \to \Delta(0,1)$ where $g$ is a bijection such that $g(z_0)=0$ and $g'(z_0)\neq 0$. Suppose that $f(z_0)=0$, then $|f'(z_0)|\leq |g'(z_0)|$  I am not even sure how to start this.  I was assuming Schwarz lemma.


Login directly to terminal instead of GUI

First: I'm obviously not talking about logging in and then automatically launching Terminal.app.  In , you used to be able to type >console in the username field on the login screen and go directly into a command line terminal session.  I haven't done it in years until the other day. However, now, when I try it, my computer just locks up. I can't cancel, and it never sends me to a terminal session.  Is it even possible to do this anymore? If not, does anybody know when it was removed? It seems odd that typing >console would cause the machine to lock up if it wasn't recognizing it in some way.


What is the origin of “Get a hold of the short/wrong end of the stick”?

I know this is a duplicate, of this question:  but none of the answers are can be considered fact. I propose this answer:  The  was a technique which became common in medieval Europe, which was constantly short of money (coins) and predominantly illiterate, in order to record bilateral exchange and debts. A stick (squared hazelwood sticks were most common) was marked with a system of notches and then split lengthwise. This way the two halves both record the same notches and each party to the transaction received one half of the marked stick as proof. Later this technique was refined in various ways and became virtually tamper proof. One of the refinements was to make the two halves of the stick of different lengths. The longer part was called stock and was given to the party which had advanced money (or other items) to the receiver. The shorter portion of the stick was called foil and was given to the party which had received the funds or goods. Using this technique each of the parties had an identifiable record of the transaction. The natural irregularities in the surfaces of the tallies where they were split would mean that only the original two halves would fit back together perfectly, and so would verify that they were matching halves of the same transaction. If one party tried to unilaterally change the value of his half of the tally stick by adding more notches, those notches would not be on the other tally stick and would be revealed as an attempted forgery. The split tally was accepted as legal proof in medieval courts and the Napoleonic Code (1804) still makes reference to the tally stick in Article 1333. Along the Danube and in Switzerland the tally was still used in the 20th century in rural economies. The person with the short end of the stick was in a bad spot because they were in debt to the person holding the longer side.  Source: Virtual Exhibitions in Informatics  An image of a medieval tally stick, courtesy of Wikipedia   Medieval English  (front and reverse view). The stick is notched and inscribed to record a debt owed to the rural dean of Preston Candover, Hampshire, of a tithe of 20d each on 32 sheep, amounting to a total sum of £2 13s. 4d.


Looking for a story about a time traveller talking to his younger self

I'm looking for a story about a man able to travel in time. Every time he visits the past, he instructs his younger self about how to be successful in life, gaining more experience following each subsequent trip. However, the very last time he talks to his past self he is so insistent that his younger version refuses to do anything useful in his life, feeling too much pressure.   This is probably a short story by a well-known author, since I read about it in a newspaper, on TV, or on the radio.


How, specifically, does the difficulty level affect the game?

I understand what the game already tells you in the general sense... it changes enemy damage, resistances, and chance of legendary monsters appearing.  But, specifically, how does the difficulty level affect the game? Is going from Normal to Hard a 5% increase in damage? 50%? 200%? Are there any additional things changed that aren't mentioned. Does Survival mode add any extra mechanics, or is it just even bigger numbers than Very Hard?


I have the following UTF-8 data in my database:  ããƒ€ãƒ³ãƒ’ãƒ«  In japanese:  ダンヒル  The field and the database are set to utf_8_general_ci. I can't figure out how to display the proper japanese characters in my html. Here's what I did so far with no success:  <?php mb_internal_encoding('UTF-8'); mb_http_output('UTF-8'); header('Content-Type: text/html; charset=UTF-8'); ?>   Also, in my html header, I set the charset to utf-8:  <meta charset="UTF-8">   Database connection is mysqli, set_charset is set to utf-8.  Note that using this , I managed to encode my string to the proper japense characters.  Any help, would be appreciated, thanks!


This section is from the .     In physics, work is done on an object when energy is transferred to   the object. In other words, work is done when a force acts on   something that undergoes a displacement from one position to another.   Forces can vary as a function of position, and displacements can be   along various paths between two points. We first define the increment   of work $\text dW$ done by a force $\mathbf F$ acting through an infinitesimal   displacement $\text d\mathbf r$  as the dot product of these two vectors:   Is it simply just a very small displacement?


Can I extend mathematical induction to real numbers?

Here is my rather simple idea. I will treat the set of real numbers as a set of discrete continuities, each separated by an Epsilon ball that tends to 0.  So, let's say P(b) is true. We then assume P(k) is true, and prove that P(k+e) is true, where e goes to zero.  I just want to know if this is a valid technique or not because our teacher said that mathematical induction can only be applied to discrete structures, but I see no difficulty in treating a continuous system as a set of infinitesimal discrete quantities. Mak


Is it true you should never put a comma after "then"? Please explain

I would like to know what the rule is, if there is one, behind the use of commas after all sequence words except then. I have seen "then" written both with a comma and without one, but I remember reading somewhere that you never put a comma after the word "then". is this true?  Examples:   -First, we went to the movies. Then we ate dinner. Finally, we went home.  -Outline your paragraph. Then write your thesis statement.


I am trying to align text at the bottom of a Div and the Middle of a Div.  The CSS attribute  vertical-align:text-bottom; seems to do nothing?  I have 3 divs and would like to center the div xrLabel1 and the other div xrLabel5 to put the text at the bottom.  I have included some sample code.  Thanks  <!DOCTYPE html>               <link type="text/css" rel="stylesheet" href="format.css"/>         <title></title>

xrLabel2

xrLabel1

xrLabel5

         The CSS file format.css  .TopMargin { position:absolute; left:0px; top:0px; height:92px; width:650px; background-color:#808080; color:#000000; }  .xrLabel2 { position:absolute; left:225px; top:17px; height:67px; width:99px; background-color:#FFFFFF; color:#000000; text-align:center; vertical-align:text-middle; font-family:Times New Roman ;font-size:9.75pt;text-decoration:underline; }  .xrLabel1 { position:absolute; left:367px; top:8px; height:75px; width:99px; background-color:#FFFFFF; color:#000000; text-align:right; vertical-align:text-bottom; font-family:Times New Roman ;font-size:9.75pt;text-decoration:underline; }  .xrLabel5 { position:absolute; left:75px; top:8px; height:75px; width:99px; background-color:#FFFFFF; color:#000000; text-align:center; vertical-align:text-top; font-family:Times New Roman;font-size:9.75pt; }


What is the plural form of "whitespace"?

I ask this because Firefox suggested that whitespaces is not a valid word; rather it gave me whitespace or white spaces.


The day before yesterday I reviewed  in  (I have > 2K rep there).  I clicked on “Improve Edit”, made some more changes, and saved (submitted) them.  All the changes were made (both the ones “suggested” by  and mine), and  shows two revisions — #5, by Chema, and #6, by me — made at the exact same time.   The issue is that revision #5 is shown as having been reviewed by the Community user, with no indication that I did an Improve Edit:          unlike the normal way it looks when I improve an edit:         Also, I looked at my editing stats, and they were the same before and after:        [Scott has approved 1267 edit suggestions and rejected 750 edit suggestions and improved 289 edit suggestions] Normally the third number (improved ___ edit suggestions) would go up by one. Also, it does not appear in my Review history ( → “Activity” → “all actions” → “reviews”) or .   This happens on a recurring, but occasional (irregular, irreproducible), basis.  For example, see , , and .  I did “Reject and Edit” on all three, but I didn’t “get credit” for .


How to prove $\mu(X \cup Y) \geq \mu(X) +\mu(Y) $ for this measure.

Let $\mu$ be the Lebesgue outer measure I want to prove $\mu(X \cup Y) = \mu(X) +\mu(Y) $ so far I have used properties of this measure to show $\mu(X \cup Y) \leq \mu(X) +\mu(Y) $ so what remains is to show $\mu(X \cup Y) \geq \mu(X) +\mu(Y) $ however I am unsure how to proceed. All I have that I have yet to use is that $X,Y$ are subsets of real numbers and that they are disjoint and non empty.  Any help??


To what extent are flying lessons provided at Hogwarts?

Flying lessons would be starting on Thursday — and Gryffindor and Slytherin would be learning together.   In Harry Potter and the Philosopher's Stone, Chapter Nine - The Midnight Duel Harry's first -     At three-thirty that afternoon, Harry, Ron, and the other Gryffindors hurried down the front steps onto the grounds for their first flying lesson.   (and only) flying lesson is described. During this single lesson Harry discovers that he has a tremendous natural ability to fly on a broomstick and is made Seeker of the Gryffindor Quidditch team.  Flying lessons are never mentioned again in the first book, and as far as I recall, not a single other time in the entire seven books. Harry clearly didn't require them but there were a lot of other students who would have benefited from them, including Hermione.  What amount of tutoring is actually available for those wishing to learn to fly at Hogwarts? Are flying lessons mandatory for first years? Do they continue in subsequent years as well?


Explainer, Refiner, and Illuminator badges are not awarded when it takes more than 12 hours to approve an edit

The Explainer, Refiner, and Illuminator badges descriptive text says:     Edit and answer [1/50/500] questions (both actions within 12 hours, answer score > 0)   But this .  It appears that the behavior is really based on when your edit is approved, not when the edit is made.  Is this a feature or a bug?


Ubuntu 14.04, Upgrade Path for Final Beta -> Release?

I need to build out a new server with long term support.  Ubuntu 14.04 LTS is in Final Beta. See .  I'm OK with using a Final Beta before the Release build is released. But I'm not clear if there's an upgrade path from the alphas and betas to release. (If there's no upgrade path, I'd prefer not to use it since this includes a mailbox migration).  Question: will there be an upgrade path from 14.04 Final Beta to 14.04 Release?  Note: this could be a duplicate of  If the process for 14.04 is the same as previous, then its a duplicate. However,  does not appear to discuss it.


Adjusting display geometry in a virtual machine?

Running 11.04 beta in a Parallels 5.0 virtual machine, but this question will apply to any virtualization software.  Parallels 5 Linux tools (guest additions) don't work for 10.10 and 11.04 and I don't want them. I like how the VM is integrated as is. The only thing that needs tuning is the screen geometry.  None of the options in the Systems -> Preferences -> Monitors fit my display perfectly. I need it at 1080 x 1920 (9:16) or 1920 x 1080 (16:9).  Many different resolutions work (see screen-shot bellow), among which are:   1680 x 1080 (too narrow horizontally and a bit too short vertically) 1920 x 1200 (perfect horizontally, but a bit too tall vertically)   How can I adjust the screen resolution (display/monitor size) manually?  What I tried so far  $ cvt 1920 1080 # 1920x1080 59.96 Hz (CVT 2.07M9) hsync: 67.16 kHz; pclk: 173.00 MHz Modeline "1920x1080_60.00"  173.00  1920 2048 2248 2576  1080 1083 1088 1120 -hsync +vsync $ sudo xrandr --newmode "1920x1080"  173.00  1920 2048 2248 2576  1080 1083 1088 1120 -hsync +vsync xrandr: Failed to get size of gamma for output default  $ cvt 1080 1920  # 1080x1920 59.96 Hz (CVT) hsync: 119.26 kHz; pclk: 176.50 MHz Modeline "1080x1920_60.00"  176.50  1080 1168 1280 1480  1920 1923 1933 1989 -hsync +vsync $ sudo xrandr --newmode "1080x1920"  176.50  1080 1168 1280 1480  1920 1923 1933 1989 -hsync +vsync  $ sudo xrandr -q xrandr: Failed to get size of gamma for output default Screen 0: minimum 640 x 480, current 1920 x 1200, maximum 1920 x 1200 default connected 1920x1200+0+0 0mm x 0mm    1920x1200       0.0*     1600x1200       0.0      1680x1050       0.0      1400x1050       0.0      1280x1024       0.0      1440x900        0.0      1280x960        0.0      1280x800        0.0      1024x768        0.0      800x600         0.0      640x480         0.0     1920x1080 (0x11d)  173.0MHz         h: width  1920 start 2048 end 2248 total 2576 skew    0 clock   67.2KHz         v: height 1080 start 1083 end 1088 total 1120           clock   60.0Hz   1080x1920 (0x11e)  176.5MHz         h: width  1080 start 1168 end 1280 total 1480 skew    0 clock  119.3KHz         v: height 1920 start 1923 end 1933 total 1989           clock   60.0Hz   The 2 new resolutions do not show up in the Monitor Preferences GUI:   Trying Takkat's Solution  Here is what I do and get:  $ gtf 1920 1080 60 -x    # 1920x1080 @ 60.00 Hz (GTF) hsync: 67.08 kHz; pclk: 172.80 MHz   Modeline "1920x1080_60.00"  172.80  1920 2040 2248 2576  1080 1081 1084 1118  -HSync +Vsync  $ sudo xrandr --newmode "1920x1080_60.00"  172.80  1920 2040 2248 2576  1080 1081 1084 1118  -HSync +Vsync  $ sudo xrandr --addmode default 1920x1080_60.00  $ xrandr  xrandr: Failed to get size of gamma for output default Screen 0: minimum 640 x 480, current 1680 x 1050, maximum 1920 x 1200 default connected 1680x1050+0+0 0mm x 0mm    1920x1200       0.0      1600x1200       0.0      1680x1050       0.0*     1400x1050       0.0      1280x1024       0.0      1440x900        0.0      1280x960        0.0      1280x800        0.0      1024x768        0.0      800x600         0.0      640x480         0.0      1920x1080_60.00   60.0     I also tried gtf 1920 1080 60 -x.  In both cases I can't switch to that resolution and get:   Could not set configuration for CRTC 262     All the other resolutions work.


I want to publish my app as free app on Salesforce AppExchange. I have already joined ISV partner portal through  and selected "AppExchange Partner Program". And I have read in salesforce packaging guide that for releasing the app I only need to register on partner portal which I had already done.


How is the Fez number cipher intended to be solved?

Every walkthrough/guide/faq I've found for FEZ just has the answer to the number cipher, but not the steps you're supposed to take to solve it on your own. How is it intended to be solved?


How do you get to level 36 in Candy Crush Saga?

After half a weekend spent on conquering Candy Crush Saga levels, I have finally arrived at level 36. Unfortunately, there seems to be a "barrier" of sorts to start playing this level, with two options:   Ask your Facebook friends for help Buy a ticket for $0.99   While option #2 is extremely cheap, I'm curious what option #1 entails. I am personally extremely annoyed when I get enormous amounts of requests from Facebook applications and I don't want to annoy my friends this way. While I know selecting option #1 sends a request to my Facebook friends, what happens after that?


How to find the limit of cos(2x)/x as x approaches zero

Basicly the title. I know it's easy but I can't figure it out. [Edit] Not a duplicate has a 2x instead of x.


customise bibliography style of multi bibliography

I have two bibliographies in my document. I am using multi bib. I displayed the two bibliographies in two separate list using the following code. But I need to customise the citations of one of them to be [S1] and the other one to be numeric citaton [1]  % arara: pdflatex % arara: bibtex: { files: [ mydoc, PS ] } % arara: makeindex % arara: pdflatex % arara: pdflatex  \documentclass{article} \usepackage{multibib} \newcites{PS}{Primary Studies}  \usepackage{url} \usepackage[utf8]{inputenc} \usepackage[english]{babel}  \usepackage[titletoc,title]{appendix} \usepackage{afterpage}  \begin{document} \section{Main body text}  reference 1 [1] primary study 1 [S1]   \bibliographystyle{IEEEtran} \bibliography{template_latex_bibliography-bib}  \begin{appendices} \section{List of Primary studies} \bibliographystylePS{IEEEtran} \bibliographyPS{mydoc-primarystudies-bib} \end{appendices}  \end{document}


Real Analysis - Prove a set is countable

I am asked to prove the following question:  For each finite set of real numbers, $F$, define $\sum F$ to be the sum of all the numbers in $F$.  For each set $P$ of positive real numbers, define $\sum P=\sup\{\sum F: F\text{ is a finite subset of } P\}$.  Suppose $P$ is a set of positive real numbers such that $\sum P < \infty$. Prove that $P$ is a countable set.  My attempt (just a sketch proof):  Suppose $P$ is uncountable, $\exists \epsilon_1 > 0$, s.t. $$ P_1 = [\inf P + \epsilon_1, \sup P]\cap P $$ is uncountable. Pick $a_1 \in [\inf P, \inf P + \epsilon_1] \cap P \in P$, such a $P$ must exists due to greatest lower bound property.  Now $P_1$ is uncountable, $\exists \epsilon_2 > 0$, s.t. $$ P_2 = [\inf P_1 + \epsilon_2, \sup P_1]\cap P_1  $$  is uncountable. Pick $a_2 \in [\inf P_1, \inf P_1 + \epsilon_2]\cap P_1 \in P$. Carry on this process (this should be formalized using induction), we can find  $$ a_1 \leq a_2 \leq a_3 \leq ... $$ with $a_n > 0$ and $a_n \in P$ for all $n$.  Now $\sup\{\sum F_n: F_n = \{a_1,...,a_n\}, n \in \mathbb{N}^+\} = \lim_{n \to \infty}\sum_{i = 1}^n a_i > \lim_{n \to \infty}na_1 = \infty$. This means that $\sum P = \infty$ since $\{\sum F_n: F_n = \{a_1,...,a_n\}, n \in \mathbb{N}^+\} \subset \{\sum F: F\text{ is a finite subset of } P\}$.  I think my proof is a bit clumsy but is it correct?


double math and boolean check gives erroneous answer

Take this c++ code:  double d = 0.3028 + 0.0028; cout << d << endl; if (d == 0.3056)     cout << "match" << endl; else     cout << "not a match" << endl;   Why is the output "not a match"?


Why Air bubble are always sphere in shape?

Everyone of us had noticed air bubbles once in his life. They are Sphere in shape. But I want to know why the are sphere in shape, instead of any other shape.


There are several minecarts around town that are "out of order" including near the blacksmith, the mines, and the bus stop. At what point do you get the chance to fix them if ever?


Show that the polynomials with coefficients in a prime ideal form a prime ideal in the polynomial ring

We are given that -  1) R is a commutative ring with unity. 2) I is a prime ideal of R.  We have to show that I[x] is a prime ideal of R[x].  MY PROGRESS SO FAR  My progress, so far, is simply that I multiplied two arbitrary polynomial from R[x] that give an arbitrary polynomial of I[x] and tried to show that since ALL the constants belong to I, somehow, since the constants are formed by product, i.e, either of the constants must belong to I.  For example   last constant = ab We must have either a in I or b in I Then I did a similar thing to the second last constant. However, I could never say with guarantee that one particular side belongs to I.


1970s SF story of aliens on earth farming brains for use in war machines - anyone read it and remember what it was called?

The aliens were often disguised as pretty women and the protagonist goes underground to battle them but is overpowered and ends up waking up as an alien tank on another world. He manages to telepathically wake up other brains in neighbouring tanks and they use their new fighting abilities to overpower the aliens and send word back to Earth warning them of the farming operations.


What is Bayesians' equivalence of sample size determination?

Under the frequentist framework, one can use power analysis to determine sample size for a given effect size, significance level, and power. How are similar questions answered under Bayesian framework?


Can't use graphical interface after installing Ubuntu 14.04 server

After installing 14.04 server, how could I get out from terminal and go to graphical?


Could we show $1-(x-\frac{x^3}{3!}+\frac{x^5}{5!}-\dots)^2=(1-\frac{x^2}{2!}+\frac{x^4}{4!}- \dots)^2$ if we didn't know about Taylor Expansion?

Suppose that humanity haven't discovered Taylor Series Expansion of trigonometric functions or of any function that would help us on this. Which means we are not allowed to replace the given infinite series sums with the corresponding $\sin x$ and $\cos x$ functions.  Could we still show that the following identity is true for all real $x$?  $$ 1 - \left( x - \dfrac{x^3}{3!} + \dfrac{x^5}{5!} - \dfrac{x^7}{7!} + \dots \right)^2 = \left( 1 - \dfrac{x^2}{2!} + \dfrac{x^4}{4!} - \dfrac{x^6}{6!} + \dots \right)^2 $$


Are there any web sites that store deleted questions?

Are there any websites (not associated with the owners, of course!) that store and/or keep track of deleted questions and/or answers, like Deletionpedia does to Wikipedia, and YouTomb does to YouTube?


getting 404 error trying to upgrade outdated 19.10 to 20.10

404  Not Found [IP: 91.189.91.123 80] Err:22  eoan Release my file is using http://old-releases.ubuntu.com/ubuntu eoan Release  but when I enter the link there is no eoan release  right now im trying to upgrade outdated ubuntu how should I change the sudo -i gedit /etc/apt/sources.list


Do drywall cracks pose any risk for further damage?

I recently discovered a fairly long (~2 foot) crack in my drywall within my home. Aside from the aesthetics, is there any negatives associated with leaving a drywall crack alone for an extended period of time? Of course I will eventually fix it up, but does delaying this fix pose any risk for further damage? Edit: The property is basically brand new. It is a condo that was constructed in 2019. The crack (image attached) is about 2-3 feet long. From top to bottom, it starts off jagged like a normal drywall crack but then suddenly becomes very straight near the window frame. The area right at this crack-type transition is raised off the wall. Don't know the exact dimension of the raise, but it is obvious in sight if you are close and very obvious running your finger over it. I do not know what would be in the wall here since it is a perimeter wall.


Is there a name for the type of photography or layout where items are arranged on a grid?


How much time does it take to take a move and immediate action when falling out of combat?

My character has a  that contains a wand of .   Taking the wand out of the haversack is a move action. Activating the wand is an immediate action.  How many seconds would it take once he starts falling for a character to take the wand out of his haversack and activate the spell?   If it's easier to answer another way: how many feet would he fall before being able to activate the wand and stop his fall? As a reference, .   A similar question is asked , but I've read that thread carefully and I don't see a clear answer to my question. Having read that, I do not know what the answer is.


Is there a way to run an update and upgrade in one command?

So, is it possible to update and upgrade without running:  sudo aptitude update && sudo aptitude upgrade   Meaning, is there one command that can do both?


Add a "Reject and Flag Original Post" button to Suggested Edit Review Queue Interface

TL;DR  I am requesting that a button be added to the Suggested Edit Review Queue interface to reject an edit and flag the post that the edit was made on.  Background  I started working through the Suggested Review Queue recently, and I've noticed that there are often edits made on posts that should just be deleted or closed. I feel that time spent "polishing turds" is wasted, both for the editor and edit reviewers. I currently handle these by rejecting the edit, visiting the original post, and flagging the question myself.  This three-step process occurs regularly enough that I think it should be made easier.  Therefore, I am requesting that a button be added to the Suggested Edit Review Queue toolbar for flagging posts. I also suggest that this button reject the edit by default, with a message similar to the following:     This edit was made on a post that should have been flagged for deletion or closing.   There is a related discussion on Meta Stack Overflow .  Expected Impact  Pros     Reviewers can get through the queue a little bit faster by reducing the amount of navigation required to help maintain site quality   Having the option more easily accessible will encourage reviewers to consider deleting posts that are not up to site quality standards     Cons   If edit reviewers find it easier to flag posts, the number of posts getting sent into the Low Quality Post and Close Vote queues may increase   My response: We as a community seem to have already decided that the cost of review effort is worth the benefit of having a cleaner site. I believe that this feature request coincides with that sentiment. Additionally, the user that suggested the edit will see this new reason for why their edit was rejected, which will discourage them from making further edits on unsalvageable posts, reducing the size of the Suggested Edit Review queue.   Adding a flag option may muddle the scope of what edit reviewers are supposed to do   My response: I agree with the assertion made by  answer, which is that the purpose of edit reviews is to just the quality of the edit, not the quality of the overall post. However, I am not trying to imply that edit reviewers should necessarily begin judging the original post. But if, in the course of judging the review, it becomes obvious that the whole post is garbage, then I think flagging the post is a reasonable action and we should encourage that behavior.  Side Note I do not have 3k reputation on any site, so I don't know exactly how the close vote and delete vote interfaces work. For users over 3k, I would suggest that the "Reject and Flag Original Post" button be replaced with a "Reject and Vote to Close Original Post" or "Reject and Vote to Delete Original Post" button, or something similar.  Conclusion  I acknowledge that flagging/deleting/closing original posts is beyond the scope of the Suggested Edit Review Queue, but I think it is a useful behavior that we should encourage in edit reviewers by making it easier.


Can I get Windows 10 back that has gone while I am rebooting?

While I was dual booting with the USB I got structed with screen containing only "-"   blinking  on the screen. I have nearly waited for 30 min. It did not work. I turned on the PC again my Windows 10 was degraded to Windows XP, how it's possible?  But the Windows XP does not contain anything, totally blank  but the data is present. I can't access the Windows XP also as it is only blank again. I tried to boot the system with pendrive it has worked and I gone through the process after the process i.e. the booting is completed and I successfully installed Ubuntu but after restarting this line is displaying      To reboot the device press any key or insert a boot device to boot   The main thing while I am booting Ubuntu is  the other space in my disk is filled with Windows 10 and XP while partitioning but while reacting I can't get both of them.   I can't get the OS to run. Can you help me in this regard and what are the steps to take and to get the Windows 10 again?


appSettings vs applicationSettings. appSettings outdated?

I've got some questions about two ways to save settings in the web.config.  Appsettings: Look in web.config  <appSettings>  <add key="key1" value="value1"/>  <add key="key2" value="value2"/> </appSettings>   Usage in code-behind:  ConfigurationManager.AppSettings["key1"];   ApplicationSettings/ Properties (autogenerated by using the 'properties'-tab in the project) Look in web.config  <applicationSettings>     <Projectname.Properties.Settings>         <setting name="TestEnvironment" serializeAs="String">             <value>True</value>         </setting>     </Projectname.Properties.Settings> </applicationSettings>   Usage in code-behind:  Properties.Settings.Default.TestEnvironment   So, what's the difference between these two storage possibilities of settings in the web.config? As far as I can see, a downside of the appSettings is that you have modify the web.config yourself and the appSettings are not strong typed, where as the applicationSettings are.  Both are replaceable within a web deployment project.  As far as I am concerned, there is no use for appSettings. Am I missing something here? Which is the historically seen older one?


Finding number of relations on a set with 3 elements

How do I find find out how many non reflexive relations X on the set P = {1, 2, 3}?  I know $2^{n^2 - n}$ returns how many reflexive relations there on a set. Do I subtract that from something to get my result?


I have a existing schema in my database called SCOTT, how can I create a new schema with exactly the same privileges which SCOTT schema is having?   Is there any create like or some command to create schema like SCOTT?  Thanks


As more-or-less a Ruby monoglot, this has never been clear to me... The answers to  explain how type-safety functions in Swift (and generally, I am guessing), but doesn't answer 'why'? Surely there is some performance or security benefit, but what is it exactly? Or is the benefit purely the strictness of the value later on -- the developer has the benefit of knowing some function will definitely perform (.each on an Array, for instance) or when run.   What trade-offs am I unknowingly adopting when I do this in, say, Ruby  x = Float.new x = 3 x = "a" x = [a, "a", ['a'], {a: 'a'}]   versus what benefits am I receiving in it's equivalent in Swift:  var v: String var x = 3 var y = "a" var z = [   a,    "a",    ['a'],    ['a': 'a'] ]   ?  Apologies if this is too basic or redundant -- I didn't find a similar question searching SO.


How to delete custom taxonomy terms in plugin's uninstall.php?

I am writing my plugin's uninstall.php file and would like it to delete any terms that were created in the plugin's custom taxonomy.  In the plugin's uninstall.php file I am using this:  // Delete all custom terms for this taxonomy $terms = get_terms('custom_taxonomy'); foreach ($terms as $term) {     wp_delete_term( $term->ID, 'custom_taxonomy' ); }   The problem seems to be that the custom taxonomy isn't registered at this point, so get_terms returns an error for "invalid taxonomy", thus I can't delete the custom terms in this manner, which seems the most straightforward way to do so.  If the custom taxonomy isn't registered when uninstall.php is called, how can I have it so that my plugin is able to clean up it's custom data?  Any help is greatly appreciated.  Thanks.


Material Sync from external .blend file UI

UPDATE: I reorganized the code in a way that now it runs and does what is meant to do when opening the file explorer. But still I fail on having the directory path on the UI. I have this script made by stephen_leger over BlenderArtist which does what I need, now I need to add the file path in the UI, and I found another script (sorry don't remember the author) which does exactly what I want. The problem right now is how to combine both so when I hit the Sync button it loads the file that is set in the file path. Can anyone please shed some light on this? This is the UI that I'm looking after:  Here is the code updated:     import bpy     import os          from bpy.props import StringProperty, BoolProperty     from bpy_extras.io_utils import ImportHelper     from bpy.types import (Panel,                            Operator,                            AddonPreferences,                            PropertyGroup,                            )               class OT_TestOpenFilebrowser(Operator, ImportHelper):         """Sync materials from older file"""         bl_idname = "object.sync_mats_from_file_operator"         bl_label = "Sync Materials"         bl_options = {'REGISTER', 'UNDO'}              filter_glob: StringProperty(             default='*.blend',             options={'HIDDEN'}         )                      def execute(self, context):             """Do something with the selected file(s)."""                  filename, extension = os.path.splitext(self.filepath)                                      library_path = self.filepath             # get mat names available in library             with bpy.data.libraries.load(library_path) as (data_from, data_to):                     available = set(data_from.materials)                  old_mats = {mat.name: mat for mat in bpy.data.materials if mat.name in available}                  # assign temp name to old materials             for name, mat in old_mats.items():                 mat.name = "{}_tmp".format(name)                  # load from library             with bpy.data.libraries.load(library_path, False, False) as (data_from, data_to):                 data_to.materials = list(old_mats.keys())                  # replace or remove temp name             for name, mat in old_mats.items():                 new_mat = bpy.data.materials.get(name)                 if new_mat is None:                     mat.name = name                 else:                     mat.user_remap(new_mat)                     bpy.data.materials.remove(mat)                          return {'FINISHED'}               class SomePanel(Panel):         """Creates a Panel in the Object properties window"""         bl_space_type = 'VIEW_3D'         bl_region_type = 'UI'         bl_category = "TEST CATEGORY"         bl_label = "Material Sync"         bl_idname = "TEST"              def draw(self, context):             layout = self.layout                  box = layout.box()             row = box.column()             row.operator("object.sync_mats_from_file_operator")               def register():         bpy.utils.register_class(OT_TestOpenFilebrowser)         bpy.utils.register_class(SomePanel)               def unregister():         bpy.utils.unregister_class(OT_TestOpenFilebrowser)         bpy.utils.unregister_class(SomePanel)               if __name__ == "__main__":         register()  Thanks in advance, Juan


Existence of a Noncontinous $f$ Satisfying $f(a+b) = f(a)+f(b)$

Dose there a function $f: \mathbb{R} \to \mathbb{R}$ satisfying  $f(a+b) = f(a)+f(b)\quad\forall a,b\in\mathbb{R}$ But not of the form $f(x)= \lambda x$ ?  Such $f$ must necessarily be discontinuous


Properties of composition of fields extensions in Galois Theory.

Problem. Let $K$ and $L$ be subfields of a common field, both which contain a field $F$. Prove the following statements. (a) If $K = F(X)$ for some set $X \subset K$, then $KL = L(X)$. (b) $[KL:F] \leq [K:F][L:F]$. (c) If $K$ and $L$ are algebraic over $F$, then $KL$ is algebric over $F$. (d) Prove that the previous statement remains true when $``$algebraic$"$ is replaced by $``$normal$"$, $``$separable$"$, $``$purely inseparable$"$, or $``$Galois$"$.  For (a). If $K = F(X)$, since $F \subset L$ and $KL = K(L) = L(K)$ we should have $KL = L(X)$. For (b). I tried two different ways:  Take $\lbrace \alpha_{i} \rbrace$ a basis for $K$ and $\lbrace \beta_{j} \rbrace$ a basis for $L$. How to find a basis for $KL$ from these? The product generates $KL$? I still get a little confused with the $``$appearance$"$ of elements of $KL$ (maybe, this is a problem in (c)).  Write $[KL:F] = [KL:L][L:F]$ and try to show that $[KL:L] \leq [K:F]$. Intuitively this seems right, but I couldn't prove   For (c). Take $\alpha \in KL$, so exists $k_{1},...k_{n}; k'_{1},...,k'_{m};l_{1},...,l_{n};l'_{1},...,l'_{m}$ such that $$\alpha = \frac{k_{1}l_{1} + ... + k_{n}l_{n}}{k'_{1}l'_{1} + ... + k'_{m}l'_{m}}.$$ Since $k_{i}, k'_{j} \in K$ and $l_{i}, l'_{j} \in K$, they are algebraic, then $\alpha$ is algebraic, because the set of algebraics is a field. This make sense? For (d). I have not tried it yet. Since I have not resolved the previous ones, I do not think it makes sense to try to.  I think my difficulty in this problem is due to the fact that I have not understood very well how to explicitly say who the elements of $KL$. I would like any hint! Thanks for the advance.


I want to show $\underset{n \to \infty}{\lim} (1+\frac{x}{n^2} )^n=1 \; \forall x \in \mathbb{R}$. But my solution only works for $x\leq 0$: $$\underset{n \to \infty}{\lim} (1+\frac{x}{n^2} )^n= \underset{n \to \infty}{\lim} (1-\frac{(-x)}{n^2} )^n=\underset{n \to \infty}{\lim} (1-\frac{\sqrt{-x}}{n} )^n(1+\frac{\sqrt{-x}}{n} )^n=e^{-\sqrt{-x}}+e^\sqrt{-x}=e^0 =1$$ The problem is, I cant use the $\exp$ identity with complex numbers because we only showed it for Reals. Is there a way to avoid the problem?


Can connecting of AC adaptor first into device, then into mains pose a risk of voltage spike?

Manuals of several various electronic devices I came across recommend connecting their AC adaptor first into the device, then into mains. I always thought the reverse order is safer because I thought that connecting into mains can send a voltage spike into already connected device. Are power supplies (adaptors of laptops or other electronics) designed in a way that there is no risk of harm to their device when connecting? Are both connecting orders equally safe in these terms?


Path to current desktop backgrounds in Windows 10?

There is another question on here that allows users to find the path to their current background image through a cmd command.    In Windows 10 this no longer works. It only returns the first image in the folder, it does not change with the backgrounds as they transition. I need a similar command that returns the path(s) to the current image on the desktop background(s) that actually works in Windows 10 if one exists.


Can't boot in Windows and can't run boot-repair after update to ubuntu 14.04

After update to 14.04 I can't boot in Windows 8 and in GRUB I have only 3 options instead of 7 I had previously. Also I tried to repair boot but I can't. Running: sudo add-apt-repository ppa:yannubuntu/boot-repair && sudo apt-get update returns me:   W: Failed to fetch http://ppa.launchpad.net/yannubuntu/boot-repair/ubuntu/dists/trusty/main/binary-amd64/Packages  404  Not Found   W: Failed to fetch http://ppa.launchpad.net/yannubuntu/boot-repair/ubuntu/dists/trusty/main/binary-i386/Packages  404  Not Found   E: Some index files failed to download. They have been ignored, or old ones used instead.


Seeking methods to solve: $\int_0^\infty \frac{\ln(t)}{t^n + 1}\:dt$

Seeking Methods to solve the following two definite integrals:  \begin{equation} I_(n) = \int_0^\infty \frac{\ln(t)}{t^n + 1}\:dt \qquad J(n) = \int_0^\infty \frac{\ln^2(t)}{t^n + 1}\:dt \end{equation}  For $n \in \mathbb{R},\:n \gt 1$  The method I took was to take the following integral:  \begin{equation}  \int_0^\infty \frac{t^k}{\left(t^n + 1\right)^m}\:dt = \frac{1}{n}B\left(m - \frac{k + 1}{n}, \frac{k + 1}{n} \right) \end{equation}  Where: $0 \leq k \lt n$. Here let $m = 1$.   with respect to $k$ and taking the limit as $k \rightarrow 0^+$ (via the ), i.e.   \begin{align} \lim_{k \rightarrow 0+} \frac{d}{dk} \left[ \int_0^\infty \frac{t^k}{t^n + 1}\:dt \right] &= \lim_{k \rightarrow 0+} \frac{d}{dk} \left[\frac{1}{n}B\left(1 - \frac{k + 1}{n}, \frac{k + 1}{n} \right) \right] \\ \lim_{k \rightarrow 0+}  \int_0^\infty \frac{t^k \ln(t)}{t^n + 1}\:dt  &= \lim_{k \rightarrow 0+}  \left[\frac{1}{n^2} B\left(1 - \frac{k + 1}{n}, \frac{k + 1}{n}\right)\left[\psi^{(0)}\left(\frac{k + 1}{n} \right) - \psi^{(0)}\left(1 - \frac{k + 1}{n} \right)\right] \right] \\ \int_0^\infty \frac{\ln(t)}{t^n + 1}\:dt&= \frac{1}{n^2} B\left(1 - \frac{1}{n}, \frac{1}{n}\right)\left[\psi^{(0)}\left(\frac{1}{n} \right) - \psi^{(0)}\left(1 - \frac{1}{n} \right)\right] \\ &=- \frac{\pi^2}{n^2}\operatorname{cosec}\left(\frac{\pi}{n}\right)\cot\left(\frac{\pi}{n} \right) \end{align}  Which is our expression for $I_n$. Taking the same approach but differentiating twice with respect to $k$ we arrive at our expression for $J_n$:  \begin{equation}  J(n) = \int_0^\infty \frac{\ln^2(t)}{t^n + 1}\:dt = \frac{\pi^3}{n^3}\operatorname{cosec}\left(\frac{\pi}{n} \right)\left[\operatorname{cosec}^2\left(\frac{\pi}{n}\right) + \cot^2\left(\frac{\pi}{n}\right) \right] \end{equation}  And in fact we may generalise:  \begin{equation}     \int_0^\infty \frac{\ln^p(t)}{\left(t^n + 1\right)^m}\:dt = \lim_{k\rightarrow 0}\frac{d^p}{dk^p}\left[\frac{1}{n} B\left(m - \frac{k + 1}{n}, \frac{k + 1}{n}\right)\right] \end{equation}  Where $p \in \mathbb{N}$  This method however was just an extension of another integral. I'm curious, if I had just started with $I_n, J_n$ what alternative methods could be used?


I have a Series in pandas consisting of empty lists.  >>> s = pd.Series( [[]] * 20, index= range(0,20) )  I want to add tags to certain elements by index.   >>> for i in [1,3,5,7,11]: ...     s.loc[ i ].append('prime')   but this is what I keep getting:  >>> s 0     [prime, prime, prime, prime, prime] 1     [prime, prime, prime, prime, prime] 2     [prime, prime, prime, prime, prime] 3     [prime, prime, prime, prime, prime] 4     [prime, prime, prime, prime, prime] 5     [prime, prime, prime, prime, prime] 6     [prime, prime, prime, prime, prime] 7     [prime, prime, prime, prime, prime] 8     [prime, prime, prime, prime, prime] 9     [prime, prime, prime, prime, prime] 10    [prime, prime, prime, prime, prime] 11    [prime, prime, prime, prime, prime] 12    [prime, prime, prime, prime, prime] 13    [prime, prime, prime, prime, prime] 14    [prime, prime, prime, prime, prime] 15    [prime, prime, prime, prime, prime] 16    [prime, prime, prime, prime, prime] 17    [prime, prime, prime, prime, prime] 18    [prime, prime, prime, prime, prime] 19    [prime, prime, prime, prime, prime] dtype: object   Which is not what I want.    I would like it to be like this:  >>> s 0     [] 1     [prime] 2     [] 3     [prime] 4     [] 5     [prime] 6     [] 7     [prime] 8     [] 9     [] 10    [] 11    [prime] 12    [] ...   I've been banging my head against the desk for an hour on this.  Total pandas newb.   UPDATE  The following works as expected.   s = pd.Series( [[]] * 20, index= range(0,20) ) >>> for i in [1,3,5,7,11]: ...     s.loc[ i ] = s.loc[ i ] + ['prime']   I will eventually want multiple 'tags' on each index, this is a fall back for the moment.  I still would like to know why the append doesn't work.


How to connect to WPA2/PEAP/MSCHAPv2 enterprise wifi networks that don't use a CA_Certificate, like Eduroam

My university uses WPA2 Enterprise encryption for students to login their wireless. In NetworkManager I have keyed in everything that they needed   Security : WPA & WPA2 Enterprise  Authentication : Protected EAP (PEAP) CA certificate is not needed PEAP version : Automatic Inner authentication : MSCHAPv2 Username and Password are correct.   Everytime I try to connect, I get a window asking me to input my password over and over again


I am attempting to update a custom Callable Contacts field on the Account object. The trigger will look at all contacts associated with an account, and contacts that have phone numbers will be included in the custom field. Contacts without phone numbers will not be counted. My solution was to basically look at all of the contacts associated with the account, and if any of their phone fields are not null I add them to a list. So far all of my logic appears to work. When I system.debug the callableContacts list, the list size is the correct number of contacts. When I use system.debug(myContact.Account.Callable_Contacts__c);...the result is null even though it should be an integer value. I am having trouble assigning the size of that list to the custom field on the account record. Please advise. trigger CallableContacts on Contact (after insert, after update, after delete) { List<Account> accList = new List<Account>(); if (trigger.isInsert || trigger.isUpdate) {     for (Contact myContact : Trigger.new) {         if (myContact.Id != null) {             List<Contact> acctFromRelatedContact = [SELECT   Id,                                                              AccountId,                                                              Account.Callable_Contacts__c,                                                              Account.Industry                                                                                FROM   Contact                                                      WHERE   Id = :myContact.Id                                                      LIMIT   1];             system.debug(acctFromRelatedContact);             List<Contact> callableContacts = [SELECT    Id                                                  FROM    Contact                                                WHERE    (Phone != null                                                   OR     AssistantPhone != null                                                   OR     HomePhone != null                                                   OR     OtherPhone != null)                                                  AND    AccountId = :acctFromRelatedContact.get(0).AccountId];             system.debug(callableContacts.size());             accList = [SELECT Id,                               Account.Callable_Contacts__c                          FROM Account                         WHERE Id = :myContact.AccountId];             system.debug(accList);             system.debug(myContact.Account.Callable_Contacts__c);                          if (myContact.Account.Callable_Contacts__c != null) {                 for (Account acc : accList) {                     myContact.Account.Callable_Contacts__c = callableContacts.size();                                         }                 update accList;                                 }                           }                                          } }  }


As far as every question I've seen concerning "what is $\sum_{k=1}^nk^p$" is always answered with "Faulhaber's formula" and that is just about the only answer.  In an attempt to make more interesting answers, I ask that this question concern the problem of "Methods to compute $\sum_{k=1}^nk^p$ without Faulhaber's formula for fixed $p\in\mathbb N$".  I've even checked this  without finding what I want.  Rule #1: Any method to compute the sum in question for arbitrary $p$ is good, either recursively or in some manner that is not in itself a closed form solution.  Even algorithms will suffice.  Rule #2: I don't want answers confined to "only some values of $p$".  (A good challenge I have on the side is a generalized geometric proof, as that I have not yet seen)  Exception: If your answer does not generalize to arbitrary $p$, but it still generalizes to an infinite amount of special $p$'s, that is acceptable.  Preferably, the method is to be easily applied, unique, and interesting.  To start us off, I have given my answer below and I hope you all enjoy.


I have created some blocks of a specific type, in Drupal 8, and I want to import them into the cloned instance.  There is no core import feature available. How can I achieve the task?  They don't get imported by the configuration synchronization; if you try, you will get the error     This block is broken or missing. You may be missing content or you might need to enable the original module.   and no listing in custom block library.


How to set the reference in numeric style with field order which authoryear has, but don't change the style of footcite?

I use \footcite command to add  my references and style=numeric and citestyle=authoryear in my document. So far everything is fine, besides I need to put the "year" field directly after the "author" field. I have tried different ways mentioned here, but either the style of footnote would be changed, or the style doesn't meet the requirement in references.  well, let the MWE talk:  \documentclass{article} \usepackage[%     backend=biber,     style=numeric,     citestyle=authoryear,     doi=true,     url=true     ]{biblatex}  \usepackage{filecontents}  \begin{filecontents}{test.bib}     @book{Foo,         title={Book title1},         author={Author1 AB},         year= {Year1},     }     @book{Bar,         title={Book title2},         author={Author2 AB},         year= {Year2},     } \end{filecontents}  \addbibresource{test.bib} \begin{document}  text\footcite{Foo}, and text\footcite{Bar}   %\nocite{*}  \printbibliography  \end{document}   So, how can I reorder the fields and keep the rest styles as they were?  p.s. The reason why I use authoryear style in the footnote is that the readers could have a rough idea about the citation when they are reading the paper in a print version. I have attached a screenshot blow:   If there is only a number like 1 or 2, like:    it wouldn't make much sense for the readers, would it?  Hope this could explain why I am trying to bring a little more info in the footnote about the citation.   Below a new MWE with an enumerate env added in the preamble (sorry, seems I don't have enough reputation to post more than 2 links...):  documentclass{article}  \usepackage[%         backend=biber,         style=authoryear,         %citestyle=authoryear,         labelnumber=true,         doi=true,         url=true         ]{biblatex}  \defbibenvironment{bibliography} {\enumerate{} %{\list{} {\printfield[labelnumberwidth]{labelnumber}} {\setlength{\leftmargin}{\bibhang}% \setlength{\itemindent}{-\leftmargin}% \setlength{\itemsep}{\bibitemsep}%     \setlength{\parsep}{\bibparsep}}} %\renewcommand*{\makelabel}[1]{\hss##1}} {\endenumerate} %{\endlist} {\item}  \usepackage{filecontents}  \begin{filecontents}{test.bib}     @book{Foo,         title={Book title1 whatever whatever whatever and tuff tuff         and gong gong},         author={Author1, AB and Author2, CD and Author3, EF},         year= {Year1},     }     @book{Bar,         title={Book title2},         author={Author2, AB},         year= {Year2},     } \end{filecontents}  \addbibresource{test.bib} \begin{document}  text\footcite{Foo}, and text\footcite{Bar}   %\nocite{*}  \printbibliography  \end{document}     Now I have a perfect footnote and numbered entries in references part, but how can I add a pair of square bracket to the numbers which exactly numeric style does?