This is really a yes-no question, and I am hundred percent certain that the answer is "yes". I simply have not found it written directly anywhere.  True, the Axiom of Choice is independent of ZF if we do not consider AC a part of ZF. But the question is: Let us restrict AC to $\Bbb R$ and just claim that whenever I have a subset of $\mathscr P(\Bbb R)\setminus\{\emptyset\}$, this subset has a choice function. Is this statement AC$\big|_{\Bbb R}$ independent of ZF?

Possible Duplicate:          Is possible to construct a Choice function for a collection of nonempty subsets of $X=\{0,1\}^\omega$? (Without AC)  Attempt:  We know an explicit injection $f\colon \mathbb{N}\to X$ is so easy to construct it, I think that a possible choice function $c$ is one which $c(X)=f(1)$, $c(X\setminus\{f(\{1,\ldots,n\})\} )=f(n+1)$, but I don't know how extend it (and I don't know if is possible to do) to all collection $P(X)\setminus\{\emptyset\}$.  This exercise comes from Munkres Topology chapter 1 section 9


I am using a function to covert number value in words. that is working fine but have a bug in some values like 33,030. this display as (Thirty Three Thousand Three) But should be (Thirty Three Thousand Thirty). But same function do correct like this value 2,778 this show correct (Two Thousand Seven Hundred Seventy Eight) function is as below.        function convertNumberToWord($num){         $decones = array(          '01' => "One",          '02' => "Two",          '03' => "Three",          '04' => "Four",          '05' => "Five",          '06' => "Six",          '07' => "Seven",          '08' => "Eight",          '09' => "Nine",          10 => "Ten",          11 => "Eleven",          12 => "Twelve",          13 => "Thirteen",          14 => "Fourteen",          15 => "Fifteen",          16 => "Sixteen",          17 => "Seventeen",          18 => "Eighteen",          19 => "Nineteen"          );      $ones = array(          0 => " ",         1 => "One",              2 => "Two",          3 => "Three",          4 => "Four",          5 => "Five",          6 => "Six",          7 => "Seven",          8 => "Eight",          9 => "Nine",          10 => "Ten",          11 => "Eleven",          12 => "Twelve",          13 => "Thirteen",          14 => "Fourteen",          15 => "Fifteen",          16 => "Sixteen",          17 => "Seventeen",          18 => "Eighteen",          19 => "Nineteen"          );      $tens = array(          0 => "",         2 => "Twenty",          3 => "Thirty",          4 => "Forty",          5 => "Fifty",          6 => "Sixty",          7 => "Seventy",          8 => "Eighty",          9 => "Ninety"          );       $hundreds = array(          "Hundred",          "Thousand",          "Million",          "Billion",          "Trillion",          "Quadrillion"          ); //limit t quadrillion       $num = number_format($num,2,".",",");       $num_arr = explode(".",$num);       $wholenum = $num_arr[0];       $decnum = $num_arr[1];       $whole_arr = array_reverse(explode(",",$wholenum));       krsort($whole_arr);       $rettxt = "";     foreach($whole_arr as $key => $i){       if($i < 20){      $rettxt .= $ones[$i];     }   elseif($i < 100){      $rettxt .= $tens[substr($i,0,1)];      $rettxt .= " ".$ones[substr($i,1,1)];    }   else{      $rettxt .= $ones[substr($i,0,1)]." ".$hundreds[0];      $rettxt .= " ".$tens[substr($i,1,1)];      $rettxt .= " ".$ones[substr($i,2,1)];      }    if($key > 0){      $rettxt .= " ".$hundreds[$key]." ";    }     }   $rettxt = $rettxt." (SAR)";   if($decnum > 0){    $rettxt .= " and ";  if($decnum < 20){      $rettxt .= $decones[$decnum];     } elseif($decnum < 100){      $rettxt .= $tens[substr($decnum,0,1)];      $rettxt .= " ".$ones[substr($decnum,1,1)].' Halalal ';   }  $rettxt = $rettxt;     }   return $rettxt; }   Help please

In PHP, is there an easy way to convert a number to a word? For instance, 27 to twenty-seven.


How can I write the character _ in an \fbox?  \fbox{PART one_Part two}   Doesn't work.

How can I produce the text Word_one_two in LaTeX?  I tried:  Samp\_Dist\_Corr   But, it doesn't quite look right. Also, I want it in the typewriter font, so actually, I'm doing:  \texttt{Samp\_Dist\_Corr}   I find it looks a bit like the underscore is merging in to the bottom of the "D", but maybe it's just because of the typewriter D?


Relativity holds that energy and mass are equivalent via the equation $E=mc^2$ also I know in quantum mechanics we talk about electrons jumping into bigger orbitals if they gain just the right amount of energy, or electrons emitting light and cascading down into lower energy levels, as in the laser phenomenon of population inversion. Either way the energy of the electrons is changing which changes its relativistic mass.  Back in relativity we have nuclear reactions converting mass into radiation and vice versa. So both theories seem to be talking about the same thing. Some how or other the massless photon is able to condense into ordinary matter. What I'm interested in is what that looks like. Is matter just a bunch of dead photos? Are they perhaps waves that somehow got tangled up and they are interfering with each other photon in the nucleus so that they sort of orbit each other?  Another thing that's always confused me is when to use what theories where. My chemistry teachers seem to switch back and forth arbitrarily between relativity and QM to explain various phenomenon.

I was watching the Cosmos documentary where Neil deGrasse Tyson explained how certain energy photons get absorbed by an atom, which causes the electrons of that atom to climb into a higher energy state.  He then says that an atom produces a photon when those electrons drop to a lower energy state, but that we don't know why this happens. I understood that as 'we don't know what triggers this to happen'.  Is that true? And if so, are there any feasible theories that explain this phenomenon?


I read a book as a kid about a world some 1000 years from now (I think), in which there is all sorts of magic. I think the book follows a kid who travels between towns with a mentor discovering the magic. At some point in their journey they pass through a decrepit city with ancient monsters in it that were created by technology; they fight a massive monster that I remember being described as having too many arms and being furry and as tall as the buildings. Other identifying things about this story are that at some point later in the book they go into the land of the angels/sirens/something like that, and have to go through without opening their eyes or something, to get to their destination.  I think of this monster scene often in my aesthetic thinking about how to design worlds, and I really want to find it again and see what it was I remembered and liked so much about it.

I really want to reread a book I read years ago. I can't remember the title, but I remember that for most of the book it just appears to be a classic fantasy book, but part way through the main character finds a ruined city and a robot, and it turns out it is a post-apocalyptic future several millennia after a nuclear war. Does anyone know what book this is? I really want to read it again.  As a side note, it could be by Philip K. Dick, but I'm not positive on that one.


im using Ubuntu 18.04.2 LTS want to install Win 10 along side im using a 500 GB hard disk with: 4 GB swap . primary------------ 150 MB /root .primary--------------- 345 MB /home . primary-----------  plz ive searched internet and found answers but im confused on how to use Disk Utility to create a C-partion for win, also should i creat another partion for my files or my /home partion is enough ? also what is Grub ?

I have Ubuntu on my laptop. Now I want install Windows 7 in a dual-boot. How can I do this? I can't lose my Ubuntu files, and I'm afraid that I might break . Go  for UEFI only!


I can't find any place to download Ubuntu Gnome 14.04 LTS in alternate ISO version.  Doesn't it exist ?

I would like to download the alternate installation ISO for the current release, Ubuntu 13.10 Saucy Salamander, but I can't find it on the releases.ubuntu.com website. Aren't alternate ISOs provided anymore?  I need the alternate ISO because Xorg crashes on recent versions of Ubuntu when using old SIS on board graphics.  In fact, I just patched Ubuntu sources and generated a custom package for the xserver-xorg-video-sis driver on my PPA to try fix this problem, after installing with the minimal ISO.


$x$ is a positive real number.  $n,\, k$ are positive integers.  I tried showing this by assuming an integer $t$ such that ${x} + t/n < 1$ and ${x} +(t+1)/n > 1$ , where $t \in [0, n-1]$ is an integer.     I got $$\sum = n[x]+(n-1-t) + [x]$$ can't go any further.

I'm doing some exercises on Apostol's calculus, on the floor function. Now, he doesn't give an explicit definition of $[x]$, so I'm going with this one:     DEFINITION Given  $x\in \Bbb R$, the integer part of $x$ is the unique $z\in \Bbb Z$ such that $$z\leq x < z+1$$ and we denote it by $[x]$.   Now he asks to prove some basic things about it, such as: if $n\in \Bbb Z$, then $[x+n]=[x]+n$  So I proved it like this: Let $z=[x+n]$ and $z'=[x]$. Then we have that  $$z\leq x+n<z+1$$  $$z'\leq x<z'+1$$  Then $$z'+n\leq x+n<z'+n+1$$  But since $z'$ is an integer, so is $z'+n$. Since $z$ is unique, it must be that $z'+n=z$.  However, this doesn't seem to get me anywhere to prove that  $$\left[ {2x} \right] = \left[ x \right] + \left[ {x + \frac{1}{2}} \right]$$  in and in general that   $$\left[ {nx} \right] = \sum\limits_{k = 0}^{n - 1} {\left[ {x + \frac{k}{n}} \right]} $$  Obviously one could do an informal proof thinking about "the carries", but that's not the idea, let alone how tedious it would be. Maybe there is some easier or clearer characterization of $[x]$ in terms of $x$ to work this out.  Another property is $$[-x]=\begin{cases}-[x]\text{ ; if }x\in \Bbb Z \cr-[x]-1 \text{ ; otherwise}\end{cases}$$  I argue: if $x\in\Bbb Z$, it is clear $[x]=x$. Then $-[x]=-x$, and $-[x]\in \Bbb Z$ so $[-[x]]=-[x]=[-x]$. For the other, I guess one could say:  $$n \leqslant x < n + 1 \Rightarrow  - n - 1 < x \leqslant -n$$  and since $x$ is not an integer, this should be the same as $$ - n - 1 \leqslant -x < -n$$  $$ - n - 1 \leqslant -x < (-n-1)+1$$  So $[-x]=-[x]-1$


I'd like to have a tikzpicture (actually several) appear inside a node of another tikzpicture. I already know that I can use savebox for that, the problem is: When I change the fontsize of a node inside of this nested picture it causes TeX to exceed its stack size, giving the following error:  TeX capacity exceeded, sorry [input stack size=5000].  It works if I leave the font size at normal, so that seems to be the root of the problem. However, as I do want the text in the node to be smaller, that's not a solution... I've searched for an hour now to find a solution, but am pretty much stuck. Increasing the stack size to 50000 didn't work, neither did putting extra braces anywhere. Does anyone have an idea why this eats all of my save stack?  MWE:  \documentclass{article} \usepackage[utf8]{inputenc} \usepackage{tikz}  \usetikzlibrary{positioning}  \begin{document} \begin{tikzpicture}     \node (1) {$x$};      \newsavebox\MyBox     \begin{lrbox}{\MyBox}         \begin{tikzpicture}             \node (1) {\scriptsize $y$};         \end{tikzpicture}     \end{lrbox}      \node[right=of 1] (2) {\usebox\MyBox}; \end{tikzpicture} \end{document}   As said, it works fine, if I remove the \scriptsize. I do know of course, that the MWE can be done differently (read: without the savebox), the thing I actually want to do however would require a lot of rewriting to be done differently, so I'd prefer to find a solution to this problem...

If I have two tikzpictures drawn:  \documentclass{article} \usepackage[margin = 1in]{geometry} \usepackage{tikz} \usetikzlibrary{decorations.pathmorphing,calc,shapes,shapes.geometric,patterns} \begin{document}  \tikzset{treetop/.style = {decoration={random steps, segment length=0.4mm},decorate},trunk/.style = {decoration={random steps, segment length=2mm, amplitude=0.2mm},decorate}}  \begin{tikzpicture} \foreach \w/\f in {0.3/30,0.2/50,0.1/70} { \fill [brown!\f!black, trunk] (0,0) ++(-\w/2,0) rectangle +(\w,-3); } \foreach \n/\f in {1.4/40,1.2/50,1/60,0.8/70,0.6/80,0.4/90} {    \fill [green!\f!black, treetop] ellipse (\n/1.5 and \n); } \end{tikzpicture}  \begin{tikzpicture} \shade[bottom color=cyan!60!black, top color=blue!20!white] (0,0) rectangle (10,10); \end{tikzpicture}  \end{document}     How could I use the first tikz picture within the second? Can I define the first picture as some variable and then place this variable within the second picture and have the option of defining its exact location (x,y) and its size? For example, if I wanted to place the tree in the middle of the rectangle (5,5) but make the size of the tree half its current size. How would I do this


I made this using a combination of LaTeX and powerpoint. I was wondering how it can be made purely in LaTeX code?

I am trying to creating a logo that resembles this one shown below, but I do not know the best way of going about it. I know of a fonts package that may be useful, but not sure how to overlay the letters on top of each as so. Would anyone know a neat way of accomplishing this?  Picture of Logo:


It is well-known that in an integral domain that is not a UFD, elements can have different decomopositions into irreducibles, that do not just differ by units. But in all examples I know, usually only two such decompositions are given. Is it possible for an element to have infinitely many non-equivalent decompositions?

Consider the factorization into irreducibles of $6$ in $\mathbb{Z}[\sqrt{-5}]$. We have $6=2 \times 3$ and  $6=(1+\sqrt{-5}) \times (1-\sqrt{-5})$, i.e. $2$ distinct factorizations. And,  $$6^2=3 \times 3\times2\times2$$ $$=(1+\sqrt{-5}) \times (1-\sqrt{-5}) \times (1+\sqrt{-5}) \times (1-\sqrt{-5})$$ $$=(1+\sqrt{-5}) \times (1-\sqrt{-5})\times3\times2.$$ More generally, $6^n$ will have $n+1$ distinct factorizations into irreducibles in $\mathbb{Z}[\sqrt{-5}]$ by a simple combinatorial argument. But, can we construct a ring in which there exists an element that has an infinite number of distinct factorizations into irreducibles? To make life harder, can we construct an extension of $\mathbb{Z}$ in which this happens? I have been thinking about this for a while and have managed to find no foothold.. Any help is appreciated.


In a document containing theorems with proofs and floating objects, LaTeX automatically places the floating object between the theorem and its proof (because the proof is on the next page). Is there a way to tell LaTeX not to place floating objects between the theorem and the proof.

Given following situation:  \begin{figure}[ht!]     ... \end{figure} \begin{equation}     ...     \end{equation} Some one-line text. \begin{eqnarray}     ...     ... \end{eqnarray}   how can I make sure that the float doesn't get placed between the equation and the equation array? Also the part to protect goes over two pages, if that's of any importance.


The software center in Ubuntu 12.04 had an option to sync software between computers with Ubuntu One (see ). Is there any way to achieve this in Ubuntu 20.04?

Is there any software to sync files-folders and software between two PCs? For example if I install program 'A' to my desktop I want to be installed to my laptop as well if I have synchronized these two. I want the same with my files and folders. If I change something to my desktop I want the changes to effect my laptop too(I exclude Ubuntu One as a solution).  Thanks for your time and patience!


So I understand that the == checks for equality in the reference number (the address of objects in memory). And the .equals() checks for the content of the objects.  String s = "test"; String s2 = "test";   I'm creating two different string objects but yet, I get the following:  s == s2;  //true, I dont know why, aren't s and s2 two different objects with              different internal values s.equals(s2); //true, which I understand

I've been using the == operator in my program to compare all my strings so far. However, I ran into a bug, changed one of them into .equals() instead, and it fixed the bug.  Is == bad? When should it and should it not be used? What's the difference?


How to use LIMIT function in SQL Server?  I need  to create a pagination using SQL Server data and I need to fetch the data using $start and $pagesize.  This is the query used:    SELECT *    FROM Customers    LIMIT $start, $pagesize;

What is the best way (performance wise) to paginate results in SQL Server 2000, 2005, 2008, 2012 if you also want to get the total number of results (before paginating)?


Does a non-EU citizen living in UK as spouse of UK national with permanent residence permit need health insurance for a short stay Schengen visa?

I am a South African citizen living in the UK 22 years with indefinite leave to remain.  Do I need Schengen travel insurance to go to Portugal if I'm covered by the NHS in the UK?


I have been struggled with the following problem.  Suppose that $f$ is differentiable on $(0, \infty)$. If we have $\lim_{x \rightarrow \infty} f(x) = c_1$ and $\lim_{x \rightarrow \infty} f'(x) = c_2$, where $c_1 c_2$ are two constants.  Can we get $c_2 = 0$？ If not could you please show me a counterexample?

I've been trying to solve the following problem:  Suppose that $f$ and $f'$ are continuous functions on $\mathbb{R}$, and that $\displaystyle\lim_{x\to\infty}f(x)$ and $\displaystyle\lim_{x\to\infty}f'(x)$ exist. Show that $\displaystyle\lim_{x\to\infty}f'(x) = 0$.  I'm not entirely sure what to do. Since there's not a lot of information given, I guess there isn't very much one can do. I tried using the definition of the derivative and showing that it went to $0$ as $x$ went to $\infty$ but that didn't really work out. Now I'm thinking I should assume $\displaystyle\lim_{x\to\infty}f'(x) = L \neq 0$ and try to get a contradiction, but I'm not sure where the contradiction would come from.   Could somebody point me in the right direction (e.g. a certain theorem or property I have to use?) Thanks


Just downloaded and started using the SE app for Android. It's pretty good, though I still prefer typing on a keyboard. But one thing I discovered was that even if I'm logged into my account, and can ask questions and vote, somehow when I suggest an edit I get a little red drop down on the top of the screen that says  This account is not allowed to suggest edits.  Why is that? It can't be because I have <2000 rep, because at that point it's not called suggesting edits anymore......what's going on? (Google Play tells me I have the most up-to-date version of the app; I am using Jelly Bean, 4.2.2) written on my android tablet, using the app Edit: This question is a , . Suggesting duplicates/related questions is not something the app does, either......

I edited a question, on Stack overflow and when submitting preview, got red bar telling me my account isn't allowed to make suggested edits.  On the Sandbox android question it works fine, but that is editing an answer to my question.   The message I receive is:     Account is not allowed to suggest edits   Are the rules for suggested edits different for Android app?


A lot of times, i try to import a python file as a module in interactive mode, but i notice an error in one of the functions, so i have to go and fix it, then i have to quit() python in interepter and re open it, then re-import the module which takes a good amount of time in my very slow pc, And if i notice another error then it is just a tudious task.  How can i delete a module from the python interepter without completely deleting it (allowing it to be re imported later) without restarting 'python'?

I have a long-running Python server and would like to be able to upgrade a service without restarting the server. What's the best way do do this?  if foo.py has changed:     unimport foo  <-- How do I do this?     import foo     myfoo = foo.Foo()


What hotkey should I use to quickly add "Viewer" node marked on the screenshot and preview result of my currently selected node?

I made a complicated nodes setup for a material using Cycles.  Is there an easy simple way to peek at the data passing through any node, to view it as an image?  I desire something like an oscilloscope, where I can touch a probe to any point of the circuit and see what kind of signal is there.  In Blender Internal, I could make many Output nodes and hook them up anywhere, and they'd show the data as a texture on a sphere, cube, Suzanne or whatever.  There doesn't seem to be anything like this for Cycles nodes.  Example of using Output to monitor textures along the "circutry".  (This is not any sensible texture; just messing around with BI nodes.)


I recently passed my CompTIA core 2 exam but there was a specific part of a question i was unsure about. It was simple disk partitioning in disk management but then it went on to say "The new partitions must be formatted to ensure that users files can be secured from other users and that the disk must be configured to account for future redundancy. Does anyone know how i should of done this within disk management?

i need a way to format a partition so that it is secure from other users on my pc. Also how  can i configure a disk in disk management to account for future redundancy?


I have three lists: [A, B, C], [1], [x,y].  How to generate the following with python:  [A,1,x], [A,1,y], [B,1,x], [B,1,y], [C,1,x], [C,1,y]

How can I get the Cartesian product (every possible combination of values) from a group of lists?  Input:   somelists = [    [1, 2, 3],    ['a', 'b'],    [4, 5] ]   Desired output:  [(1, 'a', 4), (1, 'a', 5), (1, 'b', 4), (1, 'b', 5), (2, 'a', 4), (2, 'a', 5) ...]


Is there any word or phrase to describe that nagging feeling you get when feels like you have forgotten something?  Edit : German words are welcome too!  Edie Edit : i see  i dont find any of  the answers satisfactory, i m moving this to German SE

Is there a word (or short phrase) that describes the sinking feeling that one is forgetting something, but but doesn't know what the "something" is?  For example, I'm looking for a word that describes the following feeling: Leaving to go on holiday, and two hours into your journey you feel sure you have left something important at home but just can't think what it is.


I wish to produce the underscore ("_") character without any significant slowness from an unused function key.  I'm intrigued by  provided by username Danny last year.  If a modification of the code they wrote is possible for my needs, I'd be grateful for anything you can offer (I don't know code myself).  I am not interested in fee-based software i.e. Keyboard Maestro if there's a way to do this natively or through shareware.  Thanks in advance! Edit: I should add, I'm using an external 104-key keyboard, and F16 is the key I'd like to configure to trigger the underscore.  Thanks!

I used to use  to remap Right Alt to Right Control (as an Emacs user I use Control MUCH more that Alt) but updating to Sierra broke this.  Downgrading is not an option.  How do I manually remap keys in Sierra?  I specifically would like to remap Right Alt to Right Control.


Does the Joker ever say, directly or indirectly, that he loves Harley Quinn? I know people say that he doesn't and he just uses her, and on the other half their relationship is described as mad love, but does the Joker ever say anything to confirm feelings for Harley Quinn? (I'm not looking for a sign of affection, just him actually saying he loves her or has strong feelings for her)

The Joker seems to care little about anything other than himself (and to some extent, Batman), whereas Harley Quinn is quite literally mad for the Joker.  Has the Joker ever shown any genuine concern or affection towards Harley?    I would prefer sources, if any, from comics.


In my log output I get the following 5 warnings:  Overfull \hbox (1.18692pt too wide) detected at line 81  []\T1/lmr/m/sc/10.95 100  \hbox(6.90094+0.0)x16.97252 .\glue 0.0 plus 1.0fil .\pdfcolorstack 0 push {0 g 0 G} .\T1/lmr/m/sc/10.95 1 .\T1/lmr/m/sc/10.95 0 .\T1/lmr/m/sc/10.95 0   Overfull \hbox (1.18692pt too wide) detected at line 82  []\T1/lmr/m/sc/10.95 100  \hbox(6.90094+0.0)x16.97252 .\glue 0.0 plus 1.0fil .\pdfcolorstack 0 push {0 g 0 G} .\T1/lmr/m/sc/10.95 1 .\T1/lmr/m/sc/10.95 0 .\T1/lmr/m/sc/10.95 0   Overfull \hbox (1.18692pt too wide) detected at line 83  []\T1/lmr/m/sc/10.95 100  \hbox(6.90094+0.0)x16.97252 .\glue 0.0 plus 1.0fil .\pdfcolorstack 0 push {0 g 0 G} .\T1/lmr/m/sc/10.95 1 .\T1/lmr/m/sc/10.95 0 .\T1/lmr/m/sc/10.95 0   Overfull \hbox (1.18692pt too wide) detected at line 84  []\T1/lmr/m/sc/10.95 100  \hbox(6.90094+0.0)x16.97252 .\glue 0.0 plus 1.0fil .\pdfcolorstack 0 push {0 g 0 G} .\T1/lmr/m/sc/10.95 1 .\T1/lmr/m/sc/10.95 0 .\T1/lmr/m/sc/10.95 0  ) \tf@toc=\write5  \openout5 = `output.toc'.    I tried to solve this warnings, but I cannot find where these overfull \hboxes are. On lines 80-84 there is no text in my texfile. Now I removed some text from my source file (around 150 pages) in order to identify where the 5 warnings come from. I managed to make them disappear by deleting some random parts of my text, but this did not answer my question. Also deleting some completely other random text, could remove the warnings. And this included lines which clearly did not produce a bad box. Because of this strange behaviour I cannot provide a minimal working example. Maybe you can tell me from my log file where the warnings come from. I am sure that there are no particular lines in my tex which produce these warnings, but it is more a global error coming from my settings.

Some of the page numbers listed in my table of contents are long roman numerals. For some reason, these long page numbers get pushed into the right margin.   Here is a screenshot of the table of contents. Note that the "xviii" page number gets pushed into the right margin, creating a black "warning blot".     How can I fix this? Below is some minimal code that recreates this problem:  \documentclass[12pt,draft,letterpaper]{report} \usepackage{tocloft}  \begin{document}  \pagenumbering{roman}  % PROBLEM: In the table of contents here, the abstract's page number is pushed %          into the right margin. \tableofcontents \newpage .  \section*{Acknowledgements}\addcontentsline{toc}{section}{Acknowledgements}  Here are the acknowledgements.  % a bunch of blank pages, to place the abstract on page xviii \newpage . \newpage . \newpage . \newpage . \newpage . \newpage . \newpage . \newpage . \newpage . \newpage . \newpage . \newpage . \newpage . \newpage . \newpage .  \chapter*{Abstract}\addcontentsline{toc}{section}{Abstract}  This is the abstract.  \end{document}


Consider $R^{\omega}$ in the uniform topology. Show that $x$ and $y$ lie in the same component of $R^{\omega}$ if and only if the sequence  $x - y = ({x_1 -y_1 , x_2 - y_2, .......})$ is bounded.  How to prove this?  My Try : By uniform topology We can not have a separation in $R^{\omega}$. Because we can not have separation on $R$.  I don't know I am wrong or right. Any help will be highly appreciated. Thank You.

This question can also be found in , but because of dull brain I could not understood that One line proof.  Let $\mathbb{R}^{\omega}$ be the set of all (infinite) sequences of real numbers. Determine whether $\mathbb{R}^{\omega}$ is connected or not in the uniform topology. Basis elements of uniform topology are $B_{\rho}(x,\epsilon)=\{ y\mid \rho(x,y)<\epsilon \}$, where $\rho(x,y)=\sup\{ \min(d(x_\alpha,y_\alpha),1)\mid \alpha \in \mathbb{Z} \}$  From the answer in the link, I understood that it is not connected. What I found: Note that $B_{\rho}(x,1)=\overline{B_{\rho}(x,1)}$. So I need to find $x_1,x_2\in \mathbb{R}^{\omega}$ such that $B_{\rho}(x_1,1)\cap B_{\rho}(x_2,1)=\phi$ How to find such $x_1$ and $x_2$?


I am working on a problem$^{(*)}$ on Lebesgue integral looks like this:     Given that both $f_n$ and $f$ are integrable, $f_n \longrightarrow f$ a.e., and $\int|f_n| \longrightarrow \int |f|$. Show that    $$\int |f_n - f| \longrightarrow 0.$$   To me, the question "makes sense" since $\int |f_n - f| \longrightarrow 0$ implies $\lim_{n \to \infty} \int |f_n - f| = 0,$ and $|f_n - f|$ is approaching zero as $n$ is approaching infinity, therefore the integral is approaching zero. But I do not know how to say it mathematically.  Any help or hints would be very much appreciated. Thanks for your time.    (*) Richard F. Bass' , 2nd. edition, chapter 7: Limit Theorems, exercise 7.5, page 57.

Let $1\leq p < \infty$. Suppose that    $\{f_k\} \subset L^p$ (the domain here does not necessarily have to be finite),  $f_k \to f$ almost everywhere, and  $\|f_k\|_{L^p} \to \|f\|_{L^p}$.    Why is it the case that $$\|f_k - f\|_{L^p} \to 0?$$   A statement in the other direction (i.e. $\|f_k - f\|_{L^p} \to 0 \Rightarrow \|f_k\|_{L^p} \to \|f\|_{L^p}$ ) follows pretty easily and is the one that I've seen most of the time. I'm not how to show the result above though.


I am a student of Indian nationality, currently pursuing my bachelor's in Electronics and Communication Engineering. I wish to pursue a Ph.D. and later a career in astronomy (with an inclination to Radio Astronomy) and have done relevant research internships and projects in the same. However, I have no publications in this area. Alongside this, I have worked on research in antenna engineering with a professor in my institute and we have published 2 papers in international conferences. My query is: for graduate admissions, will my research papers in antenna engineering have any value and consideration or are only research papers in Astronomy looked out for?

I am a economics major undergraduate student who will apply for grad schools in the coming semester. I think I have quite a strong research experience in mathematical statistics (asymptotic statistics to be specific), but, unfortunately, not much in economics itself. So I am curious if economics departments in graduate schools will care about my research experience in statistics?  Maybe a broader question is if grad schools care about applicants' research experience in a different (maybe even unrelated) field at all? I guess in my case statistics and economics are still quite correlated, but what about other more distant combinations of target departments and previous research experience?


I was recently working on something in Pathfinder and I was wondering about circumstances where it would be more favorable to automatically fail on the check then to have any success.   An example would be you somehow managed to steal the wizards overpower wand and you want to roll a nat 1 to prevent the item from being used for the next 24 hours. Yes, the UMD skill under retry does state "You cant try to activate it for the next 24 hours" but in the event that a DM rules that the item itself cant activate for 24 hours then its still helpful.  The final questions:   If you roll better then what you need, are you allowed to choose a worse result for the skill check? Would there be some kind of reverse check (as in you need to roll well to do poorly)? Would they get some kind of counter check or save? How much would this depend on it being a DM ruling?    This was what I was working on previously, in specific the activate someone elses magic items at range and failing (so they either explode, target someone else, or cant activate for 24 hours)      This question is very similar to mine but as it concerns Fly (3.x/PF) and mine focuses more on UMD (PF).

This comes up to me in the context of the 3.x/PF/d20 Fly skill, even when I simply read about it: Can you intentionally fail a Fly skill check, or any other skill check for that matter, if you, or your character for that matter, decides that the effects of failing the check are what is desired in the situation?  Example:  Take a a shapeshifted Draconian cruising at high altitude, with a few friends on his back who have some means of breathing air supply, whether it be mundane or magical.  Now lets say that the air supply goes kablooie, similar to a decompression or all-packs-trip in an airliner.  For the sake of the folks on his back -- if not himself, depending on if dragon forms need supplemental air to fly at such high altitudes, the Draconian has to lose altitude, and fast.  Considering that by RAW, a Fly check failure leaves yourself falling, would saying "I initiate a rapid descent" be enough to treat the next Fly check as an intentional failure, or would you have to roll a 'reverse' Fly check, where failing the check gives you the desired outcome of a rapid descent, and succeeding leaves you stuck at altitude?  P.S. I added the rules-as-written tag because a RAW answer is highly desired here, albeit not mandatory.  I can already mostly figure it out from a simulationist standpoint, but that answer involves going in-depth into airline flying and non-normal procedures.


I have Dell Inspiron N4050 i5 2gb. Am running dual boot (Ubuntu 14.04 along with Win7). As I am a new user (more specifically learner).  In Ubuntu am facing several issue regarding the performance. Response time for any operation is very high. And during browsing whenever am watching any video it's always getting hanged. Please help regarding system performance.  I am not able to install many of the software and updates, it's giving following error:  dpkg: error processing package linux-image-3.13.0-32-generic (--remove):  subprocess installed post-removal script returned error exit status 1     Errors were encountered while processing: linux-image-extra-3.13.0-32-generic linux-image-3.13.0-32-generic E: Sub-process /usr/bin/dpkg returned an error code (1)

What are your tips for improving overall system performance on ubuntu? Inspired by this  I realized that some default settings may be rather conservative on Ubuntu and that it's possible to tweak it with little or no risk if you wish to make it faster.  This is not meant to be application specific (e.g. make firefox load pages faster), but system wide.  Preferably 1 tip per answer, with enough detail for people to implement it.  A couple of mine would be:   Install  (via Software Center or sudo apt-get install preload); Change  value - "which controls the degree to which the kernel prefers to swap when it tries to free memory";   What are yours?  PS: Since this is not intended to have a unique answer but rather, several useful tips, I'm making this community wiki out-of-the-box.


Find all the functions in $\mathbb{R}$, satisfying the given equation  $(x+y)(f(x)-f(y)) = (x-y)f(x+y)$ for all $x,y$ in  $\mathbb{R}$.  I tried to find something like a pattern that would become a constant. If I simplify, I get      $xf(x)-xf(x+y)-xf(y)=yf(y)-yf(x+y)-yf(x)$ What should I do now? Is this going to help? Thank you.

Find all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ such that $$(x+y)(f(x)-f(y))=(x-y)f(x+y)$$  My attempt:   If $x=-y \not = 0$ then $0= 2x f(0)$ so $f(0)=0$.   Suppose for the sake of contradiction that $f(x)=f(x+\epsilon)$ for some $x$ and $\epsilon>0$. Let $y=x+\epsilon$. Then $$0=\epsilon \cdot f(2x+\epsilon)$$ therefore as $2x+ \epsilon$ can take any real value $f$ is either strictly increasing or strictly decreasing or $f(x)=0 \; \; \forall \; \;x \in \mathbb{R}$.   Note that $f(x)=ax$ is a solution $\forall \; \;a \in \mathbb{R}$. Thanks so much for any help!


I am currently using 18.04.   I wanted to install signal for desktop and I got this code from the site to install on Debian:  curl -s https://updates.signal.org/desktop/apt/keys.asc | sudo apt-key add - echo "deb [arch=amd64] https://updates.signal.org/desktop/apt xenial main" | sudo tee -a /etc/apt/sources.list.d/signal-xenial.list sudo apt update && sudo apt install signal-desktop   Since doing that I can't use APT; whatever I do I get the same error:  E: The "sudo" type is unknown in line 2 of the source list /etc/apt/sources.list.d/signal-xenial.list E: The source list could not be read. Go to the configuration of the repositories to fix the problem. E: _cache-> open () failed, please report.   I've tried to find solutions online but they want me to use the sources.list and I am not aware of how to navigate there.  My question has been closed as a duplicate but I can't get to grips with the sources.list; it's empty and I don't know how to manipulate it.  I cannot install or do anything because everything I want to do is stopped by the error:  Ignoring the file "some-ppa.list.save.1" in the directory "/etc/apt/sources.list.d/" because it has an incorrect file extension. Ignoring the file "some-ppa.list.save.1" in the directory " /etc/apt/sources.list.d/" because it has the incorrect extension.  The repository 'http://ppa.launchpad.net/baitsart/voice-commands/ubuntu bionic Release' does not have a Release file. Updating from such a repository can not be done securely, and is therefore disabled by default. See apt-secure (8) manpage for repository creation and user configuration details. The repository 'http://ppa.launchpad.net/grasch-simon- listens / simon / ubuntu bionic Release 'does not have a Release file.

Every once in a while I see users having issues to update due to errors like this:  E:Type 'ain' is not known on line 1 in source list /etc/apt/sources.list.d/some-ppa.list'   with varying types/line numbers/source list files (often after removing a PPA).  How can such an error be fixed?


Triangle ABC is an equilateral triangle and P is an arbitrary point inside it. The distance from P to A is 4 and the distance from P to B is 6 and the distance from P to C is 5. How to find the side of an equilateral triangle from this information?  $$\frac{a^2+x^2-y^2}{2xa} = \frac{\sqrt{3}}{2}\frac{a^2+x^2-z^2}{2xa}+\frac{1}{2} \sqrt{1- \Big(\frac{a^2+x^2-z^2}{2xa}\Big)^2}$$  @Aditya  based from that equation where did you get   that square root of 3 over 2 ....up to   ...... plus one half then square root of 1 minus something and so on.. pls explain further

Triangle $ABC$ is an equilateral triangle and $P$ is an arbitrary point inside it. The distance from $P$ to $A$ is $4$ and the distance from $P$ to $B$ is $6$ and the distance from $P$ to $C$ is $5$. How to find the side of an equilateral triangle from this information?


I currently use the following to delete all emails that contain EXAMPLE  sed -i '/EXAMPLE/d' newname.csv   However that deletes lines that have EXAMPLE in any of the columns. I want it to only delete lines that contain EXAMPLE in the second column. Columns are separated with tabs. (example below)  pa**s-***c.com  support@n**.com George Ka*****os    Athens  Athens  1****   GREECE   Due to tab problems none of the below that I have tried work, so alternatively I will cover to .txt and columns look like this  "pak**o.asia","jav***vip@live.com","T**iq Ja**id","Rajan Pur","punjab","33***0","PAKISTAN"

How can I manipulate field-based data from the commandline? For example   How can I print only lines whose Nth field is foo? How can I print only lines whose Nth field isn't foo? How can I print only lines whose Nth field matches foo? How can I change field N to foo?   Is there a standard approach or toolset that facilitates manipulating field-based data on *nix systems?


Every airline I've been on has an ashtray in the bathrooms, ironically right below the sign that says no smoking in the bathrooms.     If it's prohibited to smoke on airlines, and (in theory) you can't bring a lighter on the plane anyway, what's the point of the ashtray? If it's for cigarettes smoked before security, there are plenty of garbage cans and ashtrays outside of airports.

Airplane bathroom:       Why are there ashtrays in the bathrooms on nonsmoking flights?


As explained  (emphasys mine):        You can instantly close as a duplicate any question that was originally asked with a tag you have a gold badge for.      But golden tag badge owner can insta-close questions not originally tagged with a tag they own a golden badge for, as long as the question is tagged with one at the time they vote to close: .   : question is tagged with ,  and  by OP; The question is not tagged with ; : tags are not edited; : ,  and  are removed; , ,  are added by muru;  by heemayl, gold  badge owner, as a duplicate of . But the tag was added by muru during revision #3.   muru is also a gold  badge owner, but it's not clear whether muru voted before or after having edited the post: so it might be either that the check is not done at all or that the only thing checked is whether the user closing the question is not the same user that added the tag.

The help center tells us the dupehammer works with :     A question can be closed as duplicate with a single vote from a moderator or a user who has earned a gold tag badge in one of that question's original tags.   That, however, is :      First, we now look at the question's current tags instead of its original tags, unless you were the one that edited them (either by doing it yourself, or by approving an edit from someone else).   Please update the help center to reflect the change.


I'm trying to prove that $n! > n^2$ for $n\geq 4$ by use of mathematical induction, but I get to the inductive step and get lost. But I'm struggling with the inductive step as expected.

How can I show that $n^2<n!$ for all $n\geq 4$ Step 1 For $n=1$, the LHS=$4^2=16$ and RHS=$4!=24$. So LHS$<$ RHS. Step 2 Suppose the result be true for $n=k$  i.e., $k^2<k!$ Step 3 For $n=k+1$ $(k+1)^2=k^2+2k+1$ What will be the next step?


I have seen many new users posting comments as an answer, which is wrong. Some new users have good knowledge but they can't add comments because they don't have 50 reputation.    I agree that some users post comments that are not related to the topic; to deal with that, other users can raise "not an answer" flags.  My question is: Why don't we provide a limit of 1 or 2 comments to the new users on a daily basis?  To help new users write more useful comments the community can give some suggestions to the new user in additional comments.  I read , but it doesn't prevent many new users from writing comments in the answer section because they need more information in order to offer an answer.   Suggestions:   New users should be permitted a limited number of comments. The community can give suggestions to a new user for avoiding wrong comments.  The comments become visible after a review and acceptance by another user with enough reputation.

Users with less than 50 reputation points cannot write comments on questions and answers that they don't own.  Why does this limit exist? But I want to contribute now. What should I do instead? But I can't write a good answer without more information! Shouldn't I be allowed to post comments if I have reputation on a different site? But I saw a new user posting a comment! How did they do it? Why do I need 50 reputation to comment on my own post?   See also:    in the Help Center


I would like to insert brackets around a sum to signal the number of terms inside like we sometimes do in mathematics. I drew a picture:     The bracket can be either on top or bottom. Is there any way to do this in LaTeX?

I'm trying to put a nice square bracket over a complex text, it should look like an \overline but with ending like  \ulcorner and \urcorner. The presence of \overrightarrow and \overleftarrow makes me believe that is possible to decorate the end of the \overline bar.  I know the existence of \overbrace, but I need a square bracket; moreover, \overbrace takes too much vertical space


I know that for the exponential function $e^x$ that the derivative will equal $e^x$ itself. But why? And also what is the significance of that?  Is that what gives $e$ its power? The rate of change of $e$ as it grows to the power of $x$, is $e^x$ itself. I get that the function doesn't produce $e^x$, that merely the rate at which its changes between $e^x$ and $h$ as $h \to 0$. But the intuition as to why and what is the significance to math eludes me. Mind you, I understand the math behind it, just not the intuition. For example, I understand this entire post  but why  I understand the math behind this post . But I'm looking for an analogy.

As the title implies, It is seems that $e^x$ is the only function whoes derivative is the same as itself.  thanks.


I have number "000001B6" (hexadecimal). I want to convert hex "000001B6" to integer or byte,  then search result number in array of byte to check if this number exists in array or not.  How can i do that in C#, such that:  byte[] temp = new byte[20];  number = 000001B6 // convert number to integer or byte then search result number in array

How do you convert between hexadecimal numbers and decimal numbers in C#?


I am trying to show in the following equality that the left hand side equals the right hand side. I tried expanding out the summation but that didn't get me anywhere. Could somebody provide a hint? Thanks!  $\sum\limits_{k=0}^{n}\binom{n}{k}=(1+1)^n$

I'm well aware of the combinatorial variant of the proof, i.e. noting that each formula is a different representation for the number of subsets of a set of $n$ elements. I'm curious if there's a series of algebraic manipulations that can lead from $\sum\limits_{i=0}^n \binom{n}{i}$ to $2^n$.


I have two particles on the sensor of my Sony a6000. Both are round and about 0.3 mm in diameter.  The spots are only noticeable in bright areas and are easy to remove with Capture One's spot removal tool.  I looked up ways to clean my sensor and tried these:   Blowing the particles carefully away with a hand blower Using the built-in clean mode   The particles didn't budge, though. I have thought about using a swab after reading about that but I'm anxious about damaging my sensor.  Am I safe to touch my sensor lightly with a swab to remove these particles?

I've got a couple of spots of dust on the sensor of my Canon 20D. A rocket blower isn't shifting them, and I'm ridiculously scared of some of the more direct methods for cleaning sensors — what methods/systems have you tried, and how successful have they been?


I'm in need of deploying the same software over and over on multiple systems.  How can I build a .deb file from apt-get packages like ia32-libs in Ubuntu so I don't have to download this software on each and every system?  (and wait while doing so and consuming bandwidth?)

I have a friend who has got a computer that is not connected to the Internet. Is there any way to install software offline easily?


public static void main(String args[]) throws IOException{     String line = null;     File newfile = new File("/home/aoblah/Documents/Metaphor/June12/X");     File ex = new File("../June13/Test ID=ru002.txt");     BufferedReader in = new BufferedReader(new FileReader(ex));     PrintWriter wr = new PrintWriter(newfile);     while((line = in.readLine()) != null){         id = ex.getName();         id = id.substring(0, id.indexOf("."));         if(line.matches("^Sentence: [\\d]$")){             sen_count ++;         }         if(line.contains(":Sentence:")){             res_count ++;     }      }      Sentence[] sen = new Sentence[sen_count];     Results[] res = new Results[res_count];      in = new BufferedReader(new FileReader(ex));      sen_count = res_count = 0;      while((line = in.readLine()) != null){         if(line.matches("^Sentence: [\\d]$")){             line = line.trim();             a = line.split(": ");             sen[sen_count].sentence_number = a[1];             System.out.println(sen[sen_count].sentence_number);         }     }   }   public class Sentence{     public String sentence_number;      public String sentence;     public Sentence(){         this.sentence = null;         this.sentence_number = null;     }  Above is the structure and a string "1" is assigned to sen[0].sentence_number where I receive a null pointer exception. The pattern is extracted and when I assign the value of part of the pattern to a simple string, it works fine. The exception occurs when I assign it to the class member. It says that the value I am assigning it to, is referenced on a null variable. How do I fix this?  Thanks.

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


So I currently have this string: "//..\Desktop\vine.png" However, to use it when loading an image I need the \ to be \\ , so:    "//..\\Desktop\\vine.png"  path = "//..\Desktop\vine.png" image = bpy.data.images.load(path)   I've tried using  bpy.path.abspath(path)   however this is what it throws back at me:    For some reason it changes the "v" to "x0b" and doesn't change the last \ to a \\  Anyone have any ideas why this might be? Or any other methods to change the \ to \\

What's the best way to get the full directory of the current Blender file in Python?  It should be cross-platform.


I have run into this bug several times now and I can replicate it easily across all devices. If I post 3 images using the image tool on any of the mobile app platforms, the first tag always changes what image it is supposed to display. Since that's hard to explain, I took 3 random images and attached them to this question. Then, took a screenshot of before.         Hit preview... And chaos erupts. The first image always changes to a different number than it should be.        I've replicated this on both Android and iOS.

When using the Stack Exchange App for Android, I encountered a problem when uploading multiple images to the same post.  After uploading a single image, the image Markdown is inserted normally, e.g.:  ![enter image description here][1]     [1]: http://i.stack.imgur.com/Cbh1m.jpg   As I upload more images, the list of URLs at the bottom of the post should be appended to. After uploading the above in a new post, I tap to place the cursor at the end of the first line, enter a newline and the toolbar reappears. I then upload a second image with this result:  ![enter image description here][1] ![enter image description here][2]     [1]: http://i.stack.imgur.com/Cbh1m.jpg   [2]: http://i.stack.imgur.com/V5nXV.jpg   Now I edit the image descriptions, to make sure I can keep track of all my images, place the cursor at the end of the second line and enter a newline. The edit box contains:  ![a black circle of utter blackness][1] ![the best planet earth clip art ever][2]      [1]: http://i.stack.imgur.com/Cbh1m.jpg   [2]: http://i.stack.imgur.com/V5nXV.jpg   I then upload a third image. What's interesting is that as the screen reloads, for an instant I see the best planet earth clip art ever replaced by more image markup, so the second line is this:  ![![enter image description here][2]][2]   But only for a moment. Then the screen updates, and the edit window is left in this state:  ![the best planet earth clip art ever][2] ![the best planet earth clip art ever][2] ![enter image description here][3]     [1]: http://i.stack.imgur.com/Cbh1m.jpg   [2]: http://i.stack.imgur.com/V5nXV.jpg   [3]: http://i.stack.imgur.com/6Ra5w.jpg   I correct the first line and insert a line break after the third line in preparation to upload the first image again (I really love blackness). Before uploading, the edit window looks like this:  ![a black circle of utter blackness][1] ![the best planet earth clip art ever][2] ![a fast computer][3]      [1]: http://i.stack.imgur.com/Cbh1m.jpg   [2]: http://i.stack.imgur.com/V5nXV.jpg   [3]: http://i.stack.imgur.com/6Ra5w.jpg   After uploading:  ![a fast computer][3] ![the best planet earth clip art ever][2] ![a fast computer][3] ![enter image description here][4]      [1]: http://i.stack.imgur.com/Cbh1m.jpg   [2]: http://i.stack.imgur.com/V5nXV.jpg   [3]: http://i.stack.imgur.com/6Ra5w.jpg   [4]: http://i.stack.imgur.com/ILUCC.jpg   Now, instead of adding a newline, I position my cursor at the end of the third line. The toolbar isn't visible so I insert a space and then delete it. I upload another copy of the third image from this position adjacent to other image markdown, and now the result is:  ![a fast computer][3] ![the best planet earth clip art ever][2] ![a fast computer][3]![enter image description here][4] ![enter image description here][4]      [1]: http://i.stack.imgur.com/6Ra5w.jpg   [2]: http://i.stack.imgur.com/V5nXV.jpg   [3]: http://i.stack.imgur.com/6Ra5w.jpg   [4]: http://i.stack.imgur.com/jG0fk.jpg   [5]: http://i.stack.imgur.com/ILUCC.jpg   Notice:   The new image, the fifth I have uploaded, goes in as image [4]. Not a problem, so far, but: The previous image description is still linked to image [4], now a different URL; and The first URL in the list has been overwritten by the URL of the third image, which happens to be immediately adjacent on the line where I inserted the most recently-uploaded image.   Reproduced at the time of this question revision, with the following specs:   Device: Moto G 2013 OS version: 4.4.4 App version: 1.0.57


I'm given the hint that $||f(x)||=1$ can be written as $||f(x)||^2=1$, and that the chain rule may be helpful, but I'm still not sure how to proceed. Can someone point me in the right direction?

$R(t) \cdot R'(t) = 0$, which is what every source I can find tells me. Even though I understand the proof I don't understand the underlying concept. If $R(t)\cdot R'(t) = 0$, then $R'(t)$ is orthogonal to $R(t)$, right?   But you use the same derivative to find the tangent of a curve. Then somehow if you differentiate the tangent itself, you get the normal to the curve.  I really can't wrap my head around this. Could someone help me understand?


I have list of url(near about 50k) of images in text file which I want to download.  Is there anyway I can download it in async way using wget command or any other way, by reading it from text file.

I have a command, let say php process.php. I want to run 1000 instance of this command to test load caused on the server. How can I do this?  Things to note:   Ctrl+C should terminate all instance at once It is going to run on a single core processor so no need of advance feature like multi-threading. Nice to show current number of running instance on top Commands should output in the same terminal Commands requires no input


What is the English idiom for Russian "режет глаз" which literally can be translated as "hurts the eye"? In Russian, it is used when there is something, a thing, which does not fit to the whole picture and immediately attracts attention in the negative sense.

What's the opposite of eye candy?  I heard someone say, "Eye broccoli," but that's not very accurate to those of us who love broccoli. Any other ideas?


I want the top panel of Ubuntu 18.04 to show the date, DOW and time.  I tried following this link  but now all I get is a long unintelligible string of letters and numbers.  Anybody have any experience with this?

On previous versions I had the date displayed. Now it just shows the current day but not the day's number or the month.   Is there a way to customize the clock or tray/taskbar more in GNOME shell on Ubuntu 17.10 and later?


When I include multiple pictures produced in Inkscape and saved as pdf+latex in one page I get the warning:  pdflatex> pdfTex warning: pdflatex.exe (file D:/..... .pdf): PDF inclusion: multiple pdfs with page group included in a single page"   I found almost nothing via google.  Has somebody an idea?

I updated TeX Live to the Ubuntu Quantal version (2012.20120611-4) and I suddenly got this warning:     PDF inclusion: multiple pdfs with page group included in a single page   This is a minimal example for which I get the warning:  \documentclass{book} \usepackage{graphicx} \begin{document}   \includegraphics{image1}    \includegraphics{image2} \end{document}   Both images have been produced by the export PDF feature of Inkscape and contain simple line drawings (no fancy stuff).  I have been looking on the Internet, but only found others with this problem and did not found any solutions:   In the  they did not seem to understand/recognise the problem. And told the OP to go to the MikTeX groups, but it is not a MiKTeX specific problem as it is also happening with TeX Live and other distributions. At  they were looking into the use (and versions) of MS Office products. Also not the cause as I am not using MS Office to produce PDFs.   During my search if found the PDFTeX code () that spawns this warning, maybe it is of some help in understanding what is happening?  if (pdfpagegroupval == 0) {      // another pdf with page group was included earlier on the same page;     // copy the Group entry as is     pdftex_warn("PDF inclusion: multiple pdfs with page group included in a single page");     pdf_newline();     pdf_puts("/Group ");     copyObject(&dictObj); } else {     // write Group dict as a separate object, since the Page dict also refers to it     pageDict->lookup((char *) "Group", &dictObj);     if (!dictObj->isDict())         pdftex_fail("PDF inclusion: /Group dict missing");     writeSepGroup = true;     initDictFromDict(groupDict, page->getGroup());     pdf_printf("/Group %d 0 R\n", pdfpagegroupval); }   Does anyone have an idea what is happening, whether it is serious and how I could get rid of these warnings?


How can I gather (proper) food in the Nether? By "proper", I mean  any food excepting Rotten Flesh.

I just joined a multiplayer server and want to make a village in the Nether.  Is it possible to create farms for growing food and trees there? If so, how  could I go about doing it?


For example, in Ubuntu 14.04, dpkg -l bind9 outputs:  ||/ Name            Version                      Architecture                 Description +++-===============-============================-================================================ ii  bind9           1:9.9.5.dfsg-3ubuntu0.15     amd64                        Internet Domain Name Server   The version, 1:9.9.5.dfsg-3ubuntu0.15, looks like it is comprised of many pieces of information. How many sections are there in this Version field, and what are the meanings of them?  From some vague webpage, some conclusions which also needed further confirmation:   1 in 1:9.9.5.dfsg-3ubuntu0.15 - epoch 9.9.5.dfsg - upstream-version,  dfsg in 9.9.5.dfsg--- see  3ubuntu0.15 - debian-revision 3 in 3ubuntu0.15 - see  #debian-revision (thanks to @Rinzwind)   To be solved:   ubuntu0.15 in 3ubuntu0.15? 0.15 in 3ubuntu0.15?

Each package name is in the form: package-XubuntuY*_amd64(i386)  So my questions are:   What does the X stand for? What does the Y stand for?   for example binutils_2.22-6ubuntu1.3_amd64  What is the meaning of the numbers 6 and 1.3


I am working in a jee maven project that needs to make a JDBC connection to SqlServer, using windows authentication.  To achieve that, I need to have the "sqljdbc_auth.dll" in my java.library.path .  I tried multiple solutions, none of them worked: maven_surefire_plugin to modify the property path. System.setProperty("java.library.path", "..."): this changed the property, but the connection didn't succeed telling me that the driver isn't configured for integratedSecurity connection. Add the dll to a lib folder in Web_Inf & set the "Native Library_Path" of the maven dependency sqljdbc. Add the dll to the bin folder in the "wildfly" server: gave me an exception: Exception Access Violation (fatal)  I appreciate any help, thank's in advance.

I am currently investigating how to make a connection to a SQL Server database from my Java EE web application using Windows Authentication instead of SQL Server authentication. I am running this app off of Tomcat 6.0, and am utilizing the Microsoft JDBC driver. My connection properties file looks as follows:  dbDriver              = com.microsoft.sqlserver.jdbc.SQLServerDriver dbUser                = user dbPass                = password dbServer              = localhost:1433;databaseName=testDb dbUrl                 = jdbc:sqlserver://localhost:1433   I have zero problems with connecting to a SQL Server database in this fashion when using SQL Server authentication.  Is there any way I can retrieve the credentials of the user's Windows Authentication and use that authentication for SQL Server?  UPDATE: I know in ASP.net there is a way to set up Windows Authentication for access to the webapp, which is exactly what I am looking for, except I want to pass that token off to SQL Server for access to the database.


One of the strings I want to pass into a function contains {0}, which is a placeholder escape character in c#.  What is the correct syntax to get c# to ignore this?  i tried encasing it in single quotes ('), but no good

How can brackets be escaped in using string.Format? For example: String val = "1,2,3" String.Format(" foo {{0}}", val);  This example doesn't throw an exception, but it outputs the string foo {0}. Is there a way to escape the brackets?


According to conservation of energy,energy can neither be created nor be destroyed then where did the energy come from? Because there is no creation of energy we can't create

The simplistic undergrad explanation aside, I've never really understood what energy really is. I've been told that it's something when converted from one kind of something to another kind, or does some "work", as defined by us, but what is that something?  Moreover, if the total amount of energy in the universe is finite and we cannot create energy. Then, where did it come from? I've learned from thermodynamics where it goes, but where does it come from?  I know this sounds like something trivially simple, but there is so much going on in the physical universe and I just can't grasp what it is. Maybe it is because I lack the mathematical understanding that I can't grasp the subtle things the universe is doing. Still, I want to understand what it is doing.  How do I get to the point of understanding what it's doing?  (Note: What prompted me to ask this was . I'm afraid that it just puzzled me further and I sat there staring at the screen for a good 10 minutes.)


Scans of a SD card in Windows PC lead to chains of clusters with similar numbers. Does this point to decfective SD card rather than to other possible causes (bad card reader, problems with flashcard reader driver or with disruptive apps)?  chkdsk E: /f /offlinescanandfix /r ------------------- I'll Keep only substantial lines here. -------------------- Windows is verifying file allocations... Windows replaced bad clusters in file \Android\data\com.cleanmaster.mguard\files of name 1. Windows replaced bad clusters in file \.android_secure\com.booking.forsamsung-2.asec of name 57251. ------------------- I'll leave out file names now. -------------------- of name 57252. of name 57254. of name 57255. of name 60913. of name 60229. of name 60230. of name 61026. of name 61028. of name 61029.   One month later, after new series of Android system-wide crashes ...similar numbers again:  of name 57254.   <----- exact match - this one was listed before of name 59843. of name 60226. of name 60227. of name 60228. of name 60231. of name 60232. of name 60233. of name 60235. of name 60236.   The puzzling thing is that 0 KB in bad sectors is always reported at the end of each scan:  192219136 KB total disk space.  62334336 KB in 18750 files.    321664 KB in 2510 indexes.         0 KB in bad sectors.   <--------------       384 KB in use by the system. 129562752 KB available on disk.   If the card was defective, why 0 KB is reported? Moreover, values of rows 2-6 sum up to total disk space in row 1. This would indicate that the card is NOT considered defective.  Could it be a software issue (crash during write) causing this weird ?

I recovered all the files from my corrupted  today.   What should I do with it now?    Reformat and continue using it or throw it away and buy a new one   Here's the details on the card and how it got corrupted, if that matters:    16 GB  card () I had it for seven months I used it like a hard drive for my  netbook (but no programs stored on the card) The SD card stores documents, video, images, and MP3 files I am not sure how it corrupted; I started the netbook one day to find the card corrupted The netbook used  operating system at the time of corruption


From the help center:        You can accept an answer without awarding a bounty to it.   You can award a bounty on an answer without accepting it.      The question is why? Isn’t the bounty system used to get attention to a specific question so it gets answered? Why would anybody accept an answer and provide bounty to another one? Can you give me an example?

I placed a bounty on one of my questions, and I'm thinking of accepting one answer but awarding a bounty to another. Is this possible and is it socially acceptable? (Re the former, , but re the latter it seems a bit of a strange thing to do.) Roughly speaking, my reasoning is that one of the answers that came in after I placed the bounty shows a lot of effort and tackled some specific issues that I raised, using skills I didn't have. But another, earlier answer might be a nicer summary answer.


In (American) movies I have often heard people say     You OK?   You ready?   instead of      Are you OK?   Are you ready?   I doubt this is proper English. Or is it? Is it colloquial only? Is it only American "slang"?

Anyone have an extra apartment there?   This quote is from an English native speaker. Why "anyone have"?  This could be an elliptical question, but I'd expect native speakers to ask a question using an affirmative sentence as in:     Anyone knows what happened?   Here is the full quote:     Friends. Hi! Sitting here on a Friday night brainstorming honeymoon   options with David. Who has ideas?!? Where is a great place to visit   at the end of March? We have ideas all over the place. One option we   are thinking about Paris ... anyone have an extra apartment there?   If it is an elliptical question, what do you think is more common in everyday spoken English? Elliptical or questions in affirmative forms?  Edit:  Thanks to everyone for answering. I was looking for  when I came across this quote which serves as a real world example:     In Reply to: (Correcting omission) posted by R. Berg on February 25,   2003      : : : Anyone know the origin of the idiom or phrase "Throw the book at   em." I realize it means prosecute someone to the fullest extent of the   law, a law enforcement term, but does anyone really know where it came   from and when it first began being used?


I want to use adduser USER (USER is a user name), but this asks me many questions like full name and address. I want a script which types the return key automatically and skip those questions. For example, I execute ./myadduser.sh USER and myadduser.sh call adduser USER and input return to all questions. Is there a great way to do this? I am thinking about Ubuntu 14.04.  Sorry, I made a mistake. Input return not to all questions since I have to input password which cannot be return. Is it possible to input return to all questions except questions about password?

I'm trying to inject keystrokes into the input daemon so as to simulate typing from a Bash script. Is this possible, and if so, how can I make it happen?


I am trying to prove that $\sum_{k=1}^n (2k)^2 = \frac{2n(n+1)(2n+1)}{3}$. I managed to do the base case but I am stuck at the inductive step. Am I doing it wrong? This is what I need to prove: $$2^2 + 4^2 + \cdots + (2n)^2 = \frac{2n(n+1)(2n+1)}{3}$$ Here is the working I did. I feel that I did something wrong but I am not sure which portion. Show $k+1$ is true: $$2^2 + 4^2 + \cdots + (2k)^2 + (2(k+1))^2 = \frac{2(k+1)((k+1)+1)(2(k+1)+1)}{3}$$ $$\frac{2k(k+1)(2k+1)}{3} + \frac{3(2(k+1))^2}{3} = \frac{2(k+1)((k+1)+1)(2(k+1)+1)}{3}$$

I encountered the following induction proof on a practice exam for calculus:  $$\sum_{k=1}^nk^2 = \frac{n(n+1)(2n+1)}{6}$$  I have to prove this statement with induction.  Can anyone please help me with this proof?


Although reasonably experienced with ArcGIS I am a bit of a newbie with Network analyst. I have a situation in which things work Ok with the tutorial data but not with mine!  I am trying to determine an 8km road distance from a set of hospitals in East Africa. I have some roads data that I can build into a network. As far as I can see there is full connectivity. If I work using detailed polygons  (which is what I want) I get this.    So the "service area does not go along roads A,B and C, which I would expect it to. and how on earth does it think I am going to get to Point D!!.  Using generalised polygons I get this:    Now I have lost the slightly anomalous point D, but the services area still does not traverse roads A and B.  I am using ArcGIS 10.2 for Desktop.

I created a simple service layer polygon in network analyst (ArcGIS Desktop 10.2) with no hierarchies set in the street network. Now I don't understand why is this polygon created along some particular streets?   Why isn't is properly spread out? For example, why doesn't the polygon cover the areas/streets I have marked in red? Obviously those marked areas are also within 1 km.  The impedance is 1 km and 2 km respectively.   The streets are also well connected individual line elements as you can see the junctions.


How do you convert the WGS coordinate to latitude and longitude?

I'm working with  that has X Y coordinates. They are akin to '3672187.92698000, 534175.72095400'.  I would like to convert them to longitude latitude so they are more like '-90.097017, 29.963176'.  I've seen this  however I don't have that software. I was able to download and install  but I am unfortunately perplexed by its complicated interface. Would like to do the conversion with it, if possible.


I preferentially use  for writing scientific papers and appendix.   I'm borrowing \ell from kpfonst.sty, following , because \ell in mathpazo.sty is a bit less fitted with other symbols with mathpazo.  Question: how can I borrow \varg from pxfonts.sty to use it with mathpazo.sty?

Is there a general way to change the font of a particular symbol without switching packages?  For example, suppose I'm using Computer Modern for my entire document, but I want the "subset" operator to look as it does in mathabx.  How can I redefine it to appear in this way?


Imagine a  theoretical superhard steel cylinder pointed towards the moon , 1 cm in radius and 380,000 km long, traveling at 1km per hour towards the moon. Parallel to this cylinder, 1 meter away we have a magnetic cylinder of equal dimensions, not moving. If we pushed the magnetic cylinder "down" towards  the moving steel cylinder, causing the steel cylinder to stop, would both the earth side and the moon side stop at the same time? Would this pulse be a faster than light morse code machine?

Is it possible for information (like 1 and 0s) to be transmitted faster than light?   For instance, take a rigid pole of several AU in length. Now say you have a person on each end, and one of them starts pulling and pushing on his/her end.   The person on the opposite end should receive the pushes and pulls instantaneously as no particle is making the full journey.  Would this actually work?


I am trying to change the name of the "Appendices" part in my Table of contents to the dutch word "Bijlagen".  So far I have this, but the word "Appendices" still appears in my table of contents:      \documentclass[11pt]{report} \usepackage[toc,page]{appendix} \renewcommand\appendixname{Bijlage} \renewcommand\appendixpagename{Bijlagen} \renewcommand\contentsname{Inhoudsopgave}  \begin{document} \tableofcontents  \chapter{Eerste hoofdstuk} \chapter{Tweede hoofdstuk}  \begin{appendices} \renewcommand{\thechapter}{\arabic{chapter}} \chapter{Eerste bijlage} Text eerste bijlage. \chapter{Tweede bijlage} Text van tweede bijlage. \end{appendices}  \end{document}

I have the following document:  \documentclass[11pt,a4paper,twoside]{book}  \usepackage[spanish,activeacute]{babel}  \usepackage[titletoc]{appendix}   \begin{document}    \setcounter{tocdepth}{2}    \setcounter{secnumdepth}{3}    \tableofcontents    \chapter{First chapter}    \begin{appendices}    \addappheadtotoc    \appendixpage    \clearpage    \chapter{Some name}    \label{label1}    blah blah   \end{appendices}  \end{document}   this gives in the ToC:  Apéndice Appendices....................60 Apéndice A. Some name..................63   and in the body of the document:  Appendices (page skip) Apéndice A Some name  blah blah    The TOC shows "Apéndice Appendices" and I need it to show "Apéndices" (note the "s" at the end of that word; it's not the same word that the first one currently in the TOC) Also in the body of the document it shows "Appendices" (in english) and I also need it to say "Apéndices" (in spanish), ie: the same word that should be displayed in the TOC. This looks like a babel issue to me. Is there a way not to have to give each appendix a name? This is done with the \chapter{Some name} command, but I'd like the name of Apéndice A to be just that: Apéndice A. This way the ToC would look like (assuming the 1st point is fixed):  Apéndices........................60 Apéndice A.......................63   and the body of the document:  Apéndices (page skip) Apéndice A  blah blah   Is there any way to do this?     I think a hack to accomplish the 2nd point would be to combine @murray's answer with not giving a name to the chapter. This is, this line \chapter{Some name} would have to be replaced by:  \chapter[]{}   It's not pretty but I think it gets the job done. If anybody knows of a more elegant way to do this, please let me know.


During high-school and college I modeled all dynamic mechanical systems with displacement, velocity and acceleration. This was more than enough to address the systems and determine their behavior in the time domain for a certain external stimulation.  However, some part of my intuition keeps on telling me that further derivation past the second order of the displacement should also play a role, that is, the derivative of the acceleration should also be important when talking about dynamic systems.  For example, I feel completely different when accelerating smoothly but steadily harder (I get gradually pressed into my seat, as the derivative of the acceleration is small), compared to when I brake very hard (I go from no acceleration to full acceleration). ().  I know this is a weird question, but somehow I fail to reason about it and none of my text-books even mentions deriving the acceleration.

When I got more into physics, I started asking myself if just like acceleration represents the growth of speed, something else could also represent the growth of acceleration itself. And it came that is exists and is called jerk. Before I thought about this, I thought that acceleration was the highest derivative that made sense on physics.  My question is, why can we perform accurate calculations without account for jerk? I never needed it in a single physics class! I've also read that it is seldom used.  Also, while position, speed and acceleration seem familiar to me due to everyday experience, why doesn't jerk seem familiar to me? I never tell someone when driving a car "you're jerking too much", whereas I could say "you are accelerating too much".  Is it that jerk has little influence because it is almost constant? Even if it is not, what about higher order derivatives? Why don't derivatives higher than acceleration have much influence on calculations? We perform a lot of reasoning in everyday life without resorting to it!


I’m stuck at this point where me and my teammate working on the master branch and we both pushed the code but I didn’t pull the changes and again pushed the code so here i’m now I can’t pull or push the code.. what should i do?

I want to resolve merge conflicts in my Git repository. How to do that ?


Fisher's method and Stouffer's approach (z-transform) for meta-analysis roughly follow the same scheme:   take the p-values from some different experiments on the same hypotheses apply to them some monotonic transformation sum the transformed values together check the result against some well-known distribution.   Now, my question is: what is the rationale for step 2? P-values are (under the null hypothesis) uniformly distributed over [0,1]. The sum of $n$ p-values hence already tends to a normal distribution (and the approximation is fairly good already for small values of $n$).  This is not just a theoretical curiosity. The p-values I am working with come from Mann-Whitney tests (but many other examples could be made). There is a strictly positive probability (under the null, but also under my H1) that the (one-tailed) p-value for a given test is 1. If this happens, the aggregated p-value according to the Z-transform method is also 1 (unless there was some test which yielded a p-value of 0 - let us assume this is not the case), simply because the normal distribution has $cdf(c)=1$ for $x \to + \infty$. And this is true whatever the number of p-values we are aggregating! To make an extreme example, if one p-value is 1, the other 100 are 0.1% and I know that a p-value of 1 has a 10% of probability to arise by chance, my intuition is that the null hypothesis should be rejected - instead the aggregated p-value is 1.  What is wrong with just summing up the p-values, and then comparing them to the appropriate normal (or Irwin–Hall, or even a discrete version of it, if it's a matter of accuracy) distribution?!  Even in cases in which the above problem does not arise, I fail to see why extreme p-values should be given higher importance: and if there is a reason, then how much importance should be given to them (i.e. how the specific transformations used at step 2 can be justified).

I recently learned about Fisher's method to combine p-values. This is based on the fact that p-value under the null follows a uniform distribution, and that $$-2\sum_{i=1}^n{\log X_i} \sim \chi^2(2n), \text{ given } X \sim \text{Unif}(0,1)$$ which I think is genius. But my question is why going this convoluted way? and why not (what is wrong with) just using mean of p-values and use central limit theorem? or median? I am trying to understand the genius of RA Fisher behind this grand scheme.


If I enter [tag:X] on meta.stackoverflow.com, it is rendered as a link to tag X on stackoverflow.com.  Similarly if I post [tag:X] on chat, it is interpreted as a link to that tag on the SE site associated with that chat room.  I would like to be able to link to a tag on any SE site, not necessarily the one associated with that chat room.  E.g. I would like to be able to include  in a chat message associated with another site such as  and have it link to the corresponding tag wiki in stackoverflow (not unix.)  As far as I know the closest you can get at the moment is <kbd> elements inside links (e.g.  ) but that does not work in chat and does match the style of "real" taglinks.  Any chance of extending the markup syntax to permit this?

The tag  and meta-tag  syntax generate much nicer looking results than merely surrounding your tag with [square brackets].    However, they only work when you're talking about the site you're on.  On Area51, in Chat, and on Meta sites, this is frequently not the case, leading to attempts at syntax like [[tag:failure]](https://superuser.com/questions/tagged/failure), which produces:    Hmm, must be some subtle syntax thing:   : [tag:failure](https://superuser.com/questions/tagged/failure) []: [[tag:failure](https://superuser.com/questions/tagged/failure)] : [tag:[failure]((https://superuser.com/questions/tagged/failure))] : [tag:failure] : [tag:failure][1] \n\n [1]: https://superuser.com/questions/tagged/failure : [more text is a [tag:failure] too](https://superuser.com/questions/tagged/failure)   I give up!  How can I create a link to a tag on another site with tag markdown?


The problem is:  Show, assuming AC, that any Cartesian product of ﬁnite sets is either ﬁnite  or uncountable (can’t be countably inﬁnite).  My thought is: Finite product of finite sets is finite. This can be readily proved. Countably infinite product of finite sets is uncountable. This can be seen from the infinite sequence of 0 and 1. Uncountable product or with more than two elements is also uncountable. Trivially any Cartesian product of a set with only one element is finite. Then I'm done.  But I didn't use the ac. There should be a formal proof with ac. How to use ac? Please give me a hint.

let $A_i=\{0,1\} \forall i \in \mathbb Z^+$ and $A^{\omega}= \prod _\limits{i \in \mathbb Z^+}A_i$ thus $A^\omega=\{(a_i)|a_i=1,2 \forall i\in \mathbb Z^+\}$ now here is my problem  let $(\underline x_n)_{n \in \mathbb Z^+}$ where $\underline x_n=(x_{nk})_{k \in \mathbb Z^+}$ be a sequence in $A^\omega$. Define $\underline y=(y_n)_{n \in \mathbb Z^+}$ by $y_n=1-x_{nn}$ for all $n \in \mathbb Z^+$ a) Show that $\underline y \in A^\omega $ and $\underline y \neq \underline x_n$ for all $n\in \mathbb Z^+$ b) $\mathbf{using}$ $\mathbf{a)}$ show that $A^\omega$ is not countable  I did the a) part. And I can prove the part b) $A^\omega$ is uncountable by using diagonal argument. but here i should use the part a). my attempt was first, I suppose $ A^\omega$ is countable. then there exists a bijection from $f:\mathbb Z^+\to A^\omega$. then I can list out all elements in  $A^\omega$. then since I should use a) I have to find a connection between this list and $\underline x_n$s. I am stuck here.


The phrase "Doesn't do nothing" is often used when a person actually means,  "Doesn't do anything."   Should I avoid using this phrase? Generally, I would, but in my context, I want to negate what I had said previously.  Example:  I wrote that clicking a button does nothing. Later on, I found out that it does do something, so I want to write that I was wrong and that it, in fact, doesn't do nothing but does x.  Is it okay to write it like this or should I avoid it because people commonly misuse this phrase to mean the opposite?

How can you explain that this double negation is not a double negation? Is there a rule in English about this kind of sentence?  PS / Do I have to mention Pink Floyd Copyright ? :-)  Edit : Since there are a lot of Pink Floyd related explanation, I'll bring a Freddy Mercury one : "I don't have time for no monkey business", which I also understand as "I don't have time for monkey business". Am I right ?


I'm trying to build an entropy function from the scratch as asked by my leader. I have a dataset Ttrain, with many variables, sex being one. I'm having to extract the categories(male and female), and then calculate the probabilities and entropy subsequently, in a loop using the following code:  def entropy3(c):     import math     u=c.unique()     a=[]     b=[]     z=[]     for i in range(len(u)):         a=Ttrain[(c==u[i]) & (Ttrain.survived==1)].survived.count()         b=Ttrain[(c==u[i]) & (Ttrain.survived==0)].survived.count()         p=a/(a+b)         q=b/(a+b)         z=-(p)*math.log(p,2)-(q)*math.log(q,2)         return z   Now, when I run print(entropy3(Ttrain.sex)), I get 0.85, which is the entropy for the category female. Which means the loop does not iterate to the other category. Will be grateful if somebody could point out where am I going wrong. I'm very new to programming so please excuse any conceptual errors.

The canonical way to return multiple values in languages that support it is often . Option: Using a tuple Consider this trivial example: def f(x):   y0 = x + 1   y1 = x * 3   y2 = y0 ** y3   return (y0, y1, y2)  However, this quickly gets problematic as the number of values returned increases. What if you want to return four or five values? Sure, you could keep tupling them, but it gets easy to forget which value is where. It's also rather ugly to unpack them wherever you want to receive them. Option: Using a dictionary The next logical step seems to be to introduce some sort of 'record notation'. In Python, the obvious way to do this is by means of a dict. Consider the following: def g(x):   y0 = x + 1   y1 = x * 3   y2 = y0 ** y3   return {'y0': y0, 'y1': y1 ,'y2': y2}  (Just to be clear, y0, y1, and y2 are just meant as abstract identifiers. As pointed out, in practice you'd use meaningful identifiers.) Now, we have a mechanism whereby we can project out a particular member of the returned object. For example, result['y0']  Option: Using a class However, there is another option. We could instead return a specialized structure. I've framed this in the context of Python, but I'm sure it applies to other languages as well. Indeed, if you were working in C this might very well be your only option. Here goes: class ReturnValue:   def __init__(self, y0, y1, y2):      self.y0 = y0      self.y1 = y1      self.y2 = y2  def g(x):   y0 = x + 1   y1 = x * 3   y2 = y0 ** y3   return ReturnValue(y0, y1, y2)  In Python the previous two are perhaps very similar in terms of plumbing - after all { y0, y1, y2 } just end up being entries in the internal __dict__ of the ReturnValue. There is one additional feature provided by Python though for tiny objects, the __slots__ attribute. The class could be expressed as: class ReturnValue(object):   __slots__ = ["y0", "y1", "y2"]   def __init__(self, y0, y1, y2):      self.y0 = y0      self.y1 = y1      self.y2 = y2  From the :  The __slots__ declaration takes a sequence of instance variables and reserves just enough space in each instance to hold a value for each variable. Space is saved because __dict__ is not created for each instance.  Option: Using a  (Python 3.7+) Using Python 3.7's new dataclasses, return a class with automatically added special methods, typing and other useful tools: @dataclass class Returnvalue:     y0: int     y1: float     y3: int  def total_cost(x):     y0 = x + 1     y1 = x * 3     y2 = y0 ** y3     return ReturnValue(y0, y1, y2)  Option: Using a list Another suggestion which I'd overlooked comes from Bill the Lizard: def h(x):   result = [x + 1]   result.append(x * 3)   result.append(y0 ** y3)   return result  This is my least favorite method though. I suppose I'm tainted by exposure to Haskell, but the idea of mixed-type lists has always felt uncomfortable to me. In this particular example the list is -not- mixed type, but it conceivably could be. A list used in this way really doesn't gain anything with respect to the tuple as far as I can tell. The only real difference between lists and tuples in Python is that lists are , whereas tuples are not. I personally tend to carry over the conventions from functional programming: use lists for any number of elements of the same type, and tuples for a fixed number of elements of predetermined types. Question After the lengthy preamble, comes the inevitable question. Which method (do you think) is best?


The goal is to find all ideals of $\mathbb{Z}_n$.  First of all, I would like to know wheter this is a set of all congruence classes modulo $n$ or a set stricted to $\{0, 1, ..., n-1 \}$ with modular arithmetics? Because I do not know which one is easier to work with.  Secondly, besides trivial ideals i.e. $\{0\}, \mathbb{Z}_n$ how do I find others? I do know that it will be somehow connected to the primes dividing $n$ and such ideals will be maximal, but what with other integers being composite of prime divisors of $n$?  Would be grateful for any hints to start with because I know something in theory, but I have trouble with writing this down.

The task is to find all ideals of ${\mathbb{Z}_n}$, where $n$ is   positive integer, greater than one.   My effort  Let $I$ be an ideal of ${\mathbb{Z}_n}$. It is obvious that $I$ is an additive subgroup of ${\mathbb{Z}_n}$. Consider $G$ as an additive subgroup of ${\mathbb{Z}_n}$. Then $G$ is a cyclic additive subgroup generated by $\left\langle d \right\rangle $, where $d \mid n$. We know that for a finite cyclic group of order $k$, every subgroup's order is a divisor of $k$, and there is exactly one subgroup for each divisor. It follows that all ideals of ${\mathbb{Z}_n}$ are of form $\left\langle {{d_1}} \right\rangle ,\left\langle {{d_2}} \right\rangle , \ldots \left\langle {{d_i}} \right\rangle $, where ${d_1},{d_2}, \ldots ,{d_i}$ are positive divisors or $n$.   Questions  Is my proof correct?


I am looking for a book for a first month at a new job.   Where can I ask questions like this?

Stuff like polls, recommendations based on subjective constraints, puzzles, webcomics etc. do not belong on the serious main SE sites, where professionals should be considered at work and having just a few spare minutes ("code's compiling") to answer questions, so they should not be distracted by such things. However, I'd also like to have a home for these things still using the SE engine. For the reason I mentioned before, this needs to be a separate place though. Let's call it four.[sitename-here].com.


When I'm installing some software, it requires me to enter name and company. Then the 'default' name which 'was' same as my account name (of Windows 7) appears. The account name was misspelled, so I recently changed it (including folder name and registry) I think I completed all the steps to change the account name. But old name still appears when installing a software. How can I change this to my new account name?

how do I change the registered name in Windows 7 to my own name?


From what I've searched, it looks like there's only one way to install CPAN in Ubuntu, installing build-essential. Which brings in other dependencies like gcc and g++, which I don't want to install. Is CPAN actually in build-essential? If not is there a way to install CPAN so that we don't have to bring in other dependencies build-essential brings.

I am trying to use CPAN, but I am running into an issue. First I did sudo apt-get install perl. It says it's there. I typed cpan install automatically yes sudo which indicated as done, and I can get into cpan. I downloaded the .pl I wanted to use on CPAN, pointed to the directory, and tried perl file.pl. I am presented with this message:  Can't locate CAM/ODF.pm in @INC (@INC containes /etc/per/ /usr/local/lib/perl/5.14.2 /usr/local/share/perl/5.14.2 /usr/lib/perl5 /usr/share/perl5 /usr/lib/perl/5.14/ .usr/share/perl/5.14 /usr/local/lib/site_perl .) at file.pl in line 7   I downloaded CAM-PDF-1.59.tar.gz, double clicked, and tried placing the contents in /usr/local/lib/pkgconfig, but I am getting you don't have the right permissions.  How should I install CPAN on Ubuntu 12.10 (Quantal Quetzal) to use in the terminal? Where am I going wrong?


So as I say in the title I have this very big, annoying problem. On my new PC (HP Omen 2020, i7-10750h, Nvidia RTX 2070, 16GB RAM) when I connect an external hard drive (precisely an WD My Passport Ultra, 3TB) I get occasionally mouse and keyboard freezes. Practically, the system becomes unusable. The mouse and keyboards works, they even show in device manager, but from time to time (too often) they "freezes": mouse pointer freeze, and it won't respond to my input, and keyboard too, if I type something it will not respond. First I thought this was a behaviour due to bad drivers, or something related to my new PC, the fact that it has USB 3.1 ports. But then I've noticed that this fact happens only when I connect my WD Hard Disk (which is USB 3.0) to my pc. I've tried some stuff online, suggesting to update drivers, change some windows settings, but with no success. My guess is that the hard disk and the mouse-keyboard does interfere with each other in some ways. I guess that it's a software problem, at driver levels maybe, not a physical one. When the mouse doesn't respond, I've tried to use the touchpad on the notebook, and it does work. So it's not a windows freeze, it's just the device (mouse-keyboard-receiver) that doesn't respond. The mouse and keyboard are from Logitech, bot connected with the Unifiying receiver (a wireless receiver they provide for the mouse and the keyboard). Model: MX Anywhere 2S for the mouse, K360 for the keyboard. Please, help me solve this problem, monday I start taking my engineering class lessons from MS Teams, and I need my pc up and running and well responsive (I need to access data from the hard disk while I take classes). PS: I've seen that there are some other questions like this in the forum, but none of them seems to provide a solution to the problem. I would also change the external hard drive in the future, but I need to know that the problem with this one won't show with another hard drive, or other devices. I've already sent this very same post to Microsoft community, I really need help with this thing otherwise it will be a problem following my online classes. Thank you if you will try to help me EDIT: On the notebook in question I have 4 USB 3.1 Ports, with two ports on each side, and a single Type-C Thunderbolt port (I'm not counting that one cause both the hard disk and the logitech receiver are USB 3.0 type A connectors). I've already tried switching USB port, connecting the WD Hard Disk to another port, doing the same on the logitech receiver, and I've even tried putting them one on the left side and the other to the right side, to minimize "interference" as someone suggested. But nothing, I still got this problem, which seems driver-related. Hope this will give more info (I've edited the question cause they tagged the previous one as "incomplete", hope this is enough information)

so as I say in the title I have this very big, annoying problem. On my new PC (HP Omen 2020, i7-10750h, Nvidia RTX 2070, 16GB RAM) when I connect an external hard drive (precisely an WD My Passport Ultra, 3TB) I get occasionally mouse and keyboard freezes. Practically, the system becomes unusable. The mouse and keyboards works, they even show in device manager, but from time to time (too often) they "freezes": mouse pointer freeze, and it won't respond to my input, and keyboard too, if I type something it will not respond. First I thought this was a behaviour due to bad drivers, or something related to my new PC, the fact that it has USB 3.1 ports. But then I've noticed that this fact happens only when I connect my WD Hard Disk (which is USB 3.0) to my pc. I've tried some stuff online, suggesting to update drivers, change some windows settings, but with no success. My guess is that the hard disk and the mouse-keyboard does interfere with each other in some ways. I guess that it's a software problem, at driver levels maybe, not a physical one. When the mouse doesn't respond, I've tried to use the touchpad on the notebook, and it does work. So it's not a windows freeze, it's just the device (mouse-keyboard-receiver) that doesn't respond. The mouse and keyboard are from Logitech, bot connected with the Unifiying receiver (a wireless receiver they provide for the mouse and the keyboard). Model: MX Anywhere 2S for the mouse, K360 for the keyboard. Please, help me solve this problem, monday I start taking my engineering class lessons from MS Teams, and I need my pc up and running and well responsive (I need to access data from the hard disk while I take classes). PS: I've seen that there are some other questions like this in the forum, but none of them seems to provide a solution to the problem. I would also change the external hard drive in the future, but I need to know that the problem with this one won't show with another hard drive, or other devices. I've already sent this very same post to Microsoft community, I really need help with this thing otherwise it will be a problem following my online classes. Thank you if you will try to help me EDIT: On the notebook in question I have 4 USB 3.1 Ports, with two ports on each side, and a single Type-C Thunderbolt port (I'm not counting that one cause both the hard disk and the logitech receiver are USB 3.0 type A connectors). I've already tried switching USB port, connecting the WD Hard Disk to another port, doing the same on the logitech receiver, and I've even tried putting them one on the left side and the other to the right side, to minimize "interference" as someone suggested. But nothing, I still got this problem, which seems driver-related. Hope this will give more info


In the original paper, I was under the impression that the RF couldn't really overfit.  However, in practice I'm seeing that increasing 'ntree' sometimes increases test set error. Is this due to randomness, or is there an optimal level for 'ntree'? Right now, I'm only using cross-validation to choose the optimal 'mtry'.  I am using R and the randomForest package implementation.

Software implementations of random forest classifiers have a number of parameters to allow users to fine-tune the algorithm's behavior, including the number of trees $T$ in the forest. Is this a parameter that needs to be tuned, in the same way as $m$, the number of features to try at each split (what Leo Breiman calls mtry)?