If $X$ is a Hausdorff Space and there are 2 disjoint compact sets $A,B\subset X$, we want to prove $\exists V,U \subset X, V \bigcap U=\emptyset $ S.T. $A\subset U, B\subset V$.($U,V$ are open sets)  My idea is as follows:  We choose arbitray 2 points, $x_1\in A, y_1\in B$ and by definition of compactness, we can find a neighborhood of $x_1$ and $y_1$, denoted as $U_1,V_1$ S.T. $U_1\bigcap U_2=\emptyset$. By the same algorithm, we will have $U=\{U_1, U_2,...\},V=\{V_1,V_2,...\}$. So, what I want to ask is that are $U,V$ still disjoint?  If it is then problem solved.

I want to show that any two disjoint compact sets in a Hausdorff space $X$ can be separated by disjoint open sets. Can you please let me know if the following is correct? Not for homework, just studying for a midterm. I'm trying to improve my writing too.  My work:  Let $C$,$D$ be disjoint compact sets in a Hausdorff space $X$. Now fix $y \in D$ and for each $x \in C$ we can find (using Hausdorffness) disjoint open sets $U_{x}(y)$ and $V_{x}(y)$ such that $x \in U_{x}(y)$ and $y \in V_{x}(y)$. Now the collection $\{U_{x}: x \in C\}$ covers $C$ so by compactness we can find some natural k such that  $C \subseteq \bigcup_{i=1}^{k} U_{x_{i}}(y)$   Now for simplicity let $U = \bigcup_{i=1}^{k} U_{x_{i}}(y)$, then $C \subseteq U$ and let $W(y) = \bigcap_{i=1}^{k} V_{x_{i}}(y)$. Then $W(y)$ is a neighborhood of $y$ and disjoint from $U$.  Now consider the collection $\{W(y): y \in D\}$, this covers D so by compactness we can find some natural q such that $D \subseteq \bigcup_{j=1}^{q} W_{y_{j}}$.  Finally set $V = \bigcup_{j=1}^{q} W_{y_{j}}$, then $U$ and $V$ are disjoint open sets containing $C$ and $D$ respectively.   What do you think?


I'm having trouble figuring out what to do here, I'm supposed to find this limit:  $$\lim_{x\rightarrow0} \frac{x\cos(x)-\sin(x)}{x^3}$$  But I don't know where to start, any hint would be appreciated, thanks!

find the limit without l'Hôpital and Taylor rule :  $$\lim\limits_{x \to 0} \frac{x\cos x- \sin x}{x^3}=?$$  My Try :  $$\lim\limits_{x \to 0} \frac{x\cos x- \sin x}{x^3}\\=\lim\limits_{x \to 0}\frac{x\cos x \sin x- \sin x\sin x}{x^3\sin x}=\\\lim\limits_{x \to 0}\frac{x\sin 2x- \sin^2 x}{2x^3\sin x}=$$?  what now ?


Difference  between should, must, can, may in a conversation and a sentence.

I'm a native English speaker and I've been doing some research into English grammar for a programme I'm working on. However, on looking into modal verbs, I've only just come to appreciate how subtle and complicated they are.  What is the difference between these sentences? What possible different response might one have to each?        I can go to the cinema tonight.   I could go to the cinema tonight.   I may go to the cinema tonight.   I might go to the cinema tonight.      Granted, the first of these looks more like a statement of ability or possibility than the three that follow. But in what ways does it differ from the others, since all suggest ability and possibility? And crucially, what distinguishes the other three.  Perhaps it's a matter of tone, of context, of the speaker... The question may appear quite simple but I haven't found a satisfactory answer elsewhere.    looked quite useful in that it covered levels of confidence and certainty but it was talking about the potential state of something rather than the possibility for the person who is speaking. Are there any differences in that sense?   looked at these verbs used in question form (e.g., differences between 'Can I...?' and 'May I...?') but I'm not so interested in that for now.  Any thoughts appreciated.


I downloaded Ubuntu through BitTorrent.  Then I downloaded Oracle VirtualBox.  I've found a few different guides online but it keeps failing.  I'm not understanding what to do with the iso file once I've downloaded it and saved into my downloads.  Can anyone give me some good advice?  I'm running Windows 10 on my laptop.

I would like to know if anyone can help me with installing Ubuntu on VirtualBox


As far as I know, there are no special conditions other than this is a space with only real numbers. I'm not sure how to move forward with the problem. I know that $x^2 = |x|^2$ but I don't know how to make use of that.  $2|xy|≤ x^2 + y^2$

I am having issues solving these problems: I tried using $(|a|+|b|)^2 \geq 0$ and $(|a|-|b|)^2 \geq 0$ but I am having problems constructing the proof. I need to gain some intuition on how to proceed.     Show that for $a,b\in (-\infty,+\infty)$,   the following inequalities apply:   a) $2|ab| \leq a^2 + b^2$  b) $|a|+|b| \leq \sqrt {2}(a^2+b^2)^{1/2}$


Error message:  LaTeX Error: Unknown graphics extension: .eps"   Graphics command:  \begin{figure}[t]   \includegraphics[ ]{graphics/"new checkers order M 0200.eps"}  \end{figure}   Unsuccessful variants:    \includegraphics[ ]{graphics/"new checkers order M 0200"}    \includegraphics[ ]{graphics/"new checkers order M 0200".eps}    File header:  \documentclass[conference]{worldcomp}  \usepackage[hmargin=.75in,vmargin=1in]{geometry} \usepackage[american]{babel} \usepackage[T1]{fontenc} \usepackage{times} \usepackage{caption}  %%% Recommended to use for better results and compatible with the worldcomp.cls \usepackage{textcomp} \usepackage{epsfig,graphicx}   %%% <========== \usepackage{xcolor} \usepackage{amsfonts,amsmath,amssymb} \usepackage{fixltx2e} % Fixing numbering problem when using figure/table*  \usepackage{booktabs} \usepackage{colortbl}   Using TeXShop v 3.51 with Typeset flags LaTeX and PdfTex. Distribution: TeXLive-2014, Intel 64.  The PDF versions from Mathematica have inferior typesetting and EPS fixes the problem. How can I use the EPS files?  ====== addendum: EPS vs PDF  The top figure is the eps version, notice the label for the dependent parameter. In the subsequent PDF version the letter "a" collides with the absolute value operator.

There several types of graphics files. In no particular order .jpeg .eps .pdf .png .tif .jif (and no doubt others). Some work with latex, dvips and some work with pdflatex. How am I supposed to know which?  Just to confuse matters, metapost produces .eps but I can use these with pdflatex as long as I put in a four line incantation.  Can anyone explain this?


This is the exact opposite question of . My kids both have Android tablets and are playing Minecraft PE. They want me to join them on their PE world from my Windows PC over our LAN. Is this possible? If not with the PC version of Minecraft, is there a way to emulate the Android version on the PC?

My kids are playing Minecraft on 2 PCs, creative mode.  They are connected by the way of one of them starts a single player game on the other one than joins that game over the LAN.  Can I, using Minecraft PE on my iPad, join their game as well?


I have been researching the electron flow which goes from negative to positive in a battery. Since ground the returning point in a circuit, shouldn't ground be the positive terminal?

For the sake of not incorrectly connecting my power supply and damaging my board I'm going to ask a relatively dumb question. Is ground on my board the negative terminal on my battery? Explicitly should I connect the ground to the negative terminal of the battery?


This is a question from TIFR GS $2011$.But I think this is a stupid question or the question is not precise.This question asks if given $A,B$ matrices of order $3\times 3$ ,and $A$ invertible,there exists any $n\in \mathbb Z$ such that $A+nB$ is invertible.My simple answer would be yes,because $n=0\in \mathbb Z$ and $A+nB=A+0B=A$ which is of course invertible as $A$ is invertible.  Can someone help me to figure out if this question is stupid or the question should be made precise.If it the latter case,then one may write the precise version.I am also looking for a proof of this problem with linear transformations.  Also can someone suggest similar or more general results related to this problem?

If $A$ and $B$ are $3\times 3$ matrices and $A$ is invertible, then can we say that there exists an integer $n$ such that $A+nB$ invertible?  I was trying to show this by choosing $n$ such that eignevalues of $A+nB$ are non-zero. In the case where $B = I$ we can find the eigenvalues of $A+nB$ that would be $\lambda + nB$ (though I am not certain about its proof). This choosing of $n$ such that $\lambda$ is not equal to $-n$ times an eigenvalue of $B$ will serve the purpose. But I am not sure about general $B$. What if I take arbitrary matrices $A$ and $B$.


Is there a difference in how calloc() treats the count and the size parameters?  For example:  // calloc() parms are "count", then "size" ptr1 = calloc( 1, 20 ); ptr2 = calloc( 20, 1 );   The obvious assumption is that internally it multiplies the two to get the total number of bytes, and really doesn't care which is the count and which is the size.  But is that true?  Is there a subtle difference between the two parameters that makes it so we should be careful which one we pass in as the count versus the size?  (Yes, I know calloc can detect overflow by using 2 parms while malloc() cannot, but that doesn't answer my question.)

I'm a beginner C programmer, and I assumed that this would be the case, but would like some affirmation if possible.  If they are the same, why not just take one argument instead?


This is what I have so far. It is not lining up properly when I run the code.         \begin{adjustbox}{max totalsize={.9\textwidth}{.6\textheight},center}     \begin{tikzpicture}[ every edge/.append style = {-Straight Barb, thick,                             shorten >=1mm, shorten <=1mm},                         ] \matrix (tree) [matrix of nodes,                 nodes={circle, draw, minimum size=3mm, inner sep=0mm},                 column sep=2cm, row sep=1cm                 ] {                   & $C_{i+1,j+1}$    \\ $C_{i,j}$       &$C_{i+1,j}$  \\                  & $C_{i+1,j}$  \\     }; \draw[->] (tree-3-1) -- (tree-1-3) node{}; \draw[->] (tree-3-1) -- (tree-3-3) node{}; \draw[->] (tree-3-1) -- (tree-5-3) node{};     \end{tikzpicture}     \end{adjustbox}   \end{frame}

Grid line doesn't have to be included     \documentclass[10pt]{beamer}  \usetheme{default}  \usepackage{graphicx}  \usepackage{amssymb,amsmath}  \usepackage{tikz}  \usetikzlibrary{matrix}  \usepackage{adjustbox}  \usepackage{caption} \ usepackage{subcaption}   \setbeamercolor{title}{fg=black}  \setbeamercolor{subtitle}{fg=gray}  \setbeamercolor{footlinecolor}{fg=white,bg=green}  \setbeamertemplate{footline}[text line]{% \parbox{\linewidth}{\vspace*{-10pt} \textit{Where Wall Street Goes to School} \hfill \insertpagenumber} } \setbeamertemplate{navigation symbols}{} –  \begin{tikzpicture}[>=stealth,sloped][scale=0.8]  \matrix (tree) [matrix of nodes, minimum size=0.25cm, column sep=2cm, row sep=1cm, ]  { & $C_{i+1,j+1}$ \\ $C_{i,j}$ &$C_{i+1,j}$ \\  & $C_{i+1,j-1}$ \\   };  \draw[->] (tree-3-1) -- (tree-1-3) node [midway,above] {};  \draw[->] (tree-3-1) -- (tree-3-3) node [midway,above] {};  \draw[->] (tree-3-1) -- (tree-5-3) node [midway,below] {};  \end{tikzpicture}  \end{adjustbox} –


I'm not sure if it's proper to ask this question on Stack Overflow itself, but I'm really eager to find a good Stack Overflow app for my iPhone and Android phone, so I can login to my Stack Overflow and ask/answer questions. I tried a few but none is perfect, some can't support iOS 7 perfectly, others don't support login. Can anyone help?

I like using Stack Overflow (or any other Stack Exchange sites) and was wondering if there was an app I could install on my phone or other device that would allow me to use the site on-the-go or straight from my desktop.  Some systems to consider:   Windows 8 Android iPhone/iOS   What are some apps that I could install to my computer or phone to enhance my Stack Exchange experience?


I have came across several articles that mentioned that advise on not to store monetary value as decimal, but use integer instead. The reasoning that it does not store actual value and will cause some rounding difference/errors. But i have yet ever participate in any project that use an integer datatype for monetary value in database storage.  My question is:  1) Is there any solid business use case/scenario/example of using decimal datatype (19, 4) on monetary value that will result in rounding issue? As so far i had yet to experience the above mentioned issue.  2) As we all know that fiat currency have range of decimal place of 0 to 3 depending on countries.  Imagine now that we have a system that accepts fiat currencies transfer based on configuration configured in currencies config table.  Is it common to implement a decimal constraint for each currency during insert or we leave it to application level to deal with that?  TransactionLog -------------- CurrencyID UserIDFrom UserIDTo TransactionDateTime CurrencyAmount (decimal(19, 4)

I am working on a multi-currency application. For the purpose of simplifying this question, we will not be considering currency conversion (hence I have deliberately left AsAt : datetime out of the equation). In a number of places I need to store monetary values (e.g. 1.23 USD). I understand that I need to store both the amount (1.23), and the currency (CurrencyID with FK to Currency table having ISOAlpha3Code = USD). My question is, how should I best encapsulate and isolate these two data from the other columns in the table (TableX) to which the monetary value relates?  As I see it, I have three options:   I store two columns in TableX, one being the Amount (numeric(p,s)) and one being the CurrencyID (FK). I add an XOR check constraint on the two columns to TableX. (DBMS dependent) I create a CLR UDT (or equivalent) representing Currency, storing both Amount and CurrencyID. I store one Currency type column on TableX containing the monetary value. I create a MonetaryAmount table with three columns: MonetaryAmountID (surrogate PK), CurrencyID (FK), and Amount. I add MonetaryAmountID (FK) to TableX.   I dislike #1 because I have used this pattern before and nobody has understood that the two data are part of the one complex datum; also, it's not normalized. I dislike #2 because it breaks 1NF, it is DBMS specific, and it will likely be difficult/expensive to enforce referential integrity on Currency. I'm rather ambivalent towards #3 - it feels over-engineered and will probably be computationally expensive, but it is correctly normalized.  #3 also has the added complexity of whether to place a unique constraint on the (CurrencyID, Amount) combination, thereby making it an ad-hoc reference table and better normalizing it. I believe it would be best not to do this, as whilst MonetaryAmounts may correlate, they are distinct in nature.  Any experience you can share (or alternatives you can suggest) would be appreciated. I would especially like to hear from genuine database architectural gurus.


I was trying to derive the following formula $$\arctan(x)+\arctan(y) = \begin{cases}\arctan\left(\dfrac{x+y}{1-xy}\right), &xy < 1 \\[1.5ex]  \pi + \arctan\left(\dfrac{x+y}{1-xy}\right), &x>0,\; y>0,\; xy>1 \\[1.5ex]  -\pi + \arctan\left(\dfrac{x+y}{1-xy}\right), &x<0,\; y<0,\; xy > 1\end{cases}$$  I proceeded this way  $$\tan{(A+B)}= \frac{\tan{A}+\tan{B}}{1-\tan{A}\tan{B}}$$ $$\arctan(\tan{(A+B)})=\arctan\bigg(\frac{\tan{A}+\tan{B}}{1-\tan{A}\tan{B}}\bigg)$$ $$A+B=\arctan\bigg(\frac{\tan{A}+\tan{B}}{1-\tan{A}\tan{B}}\bigg)$$ $$\tag*{$\frac{-\pi}{2}<A+B<\frac{\pi}{2}$}$$ $$A=\arctan(\tan A)$$ $$\tag*{$\frac{-\pi}{2}<A<\frac{\pi}{2}$}$$ $$B=\arctan(\tan B)$$ $$\tag*{$\frac{-\pi}{2}<B<\frac{\pi}{2}$}$$ $$\arctan(\tan A) + \arctan(\tan B)=\arctan\bigg(\frac{\tan{A}+\tan{B}}{1-\tan{A}\tan{B}}\bigg)$$ $$\tan A=x$$ $$\tan B=y$$ $$\arctan(x) + \arctan(y)=\arctan\bigg(\frac{x+y}{1-xy}\bigg)$$  Now from here ownwards I don’t know how It gets converted to 3 different definitions. You’re help will be highly appreciated.

I know $$g(x) = \arctan(x)+\arctan(y) = \arctan\left(\frac{x+y}{1-xy}\right)$$  which follows from the formula for $\tan(x+y)$. But my question is that my book defines it to be domain specific, by which I mean, has different definitions for different domains:  $$g(x) = \begin{cases}\arctan\left(\dfrac{x+y}{1-xy}\right), &xy < 1 \\[1.5ex]  \pi + \arctan\left(\dfrac{x+y}{1-xy}\right), &x>0,\; y>0,\; xy>1 \\[1.5ex]  -\pi + \arctan\left(\dfrac{x+y}{1-xy}\right), &x<0,\; y<0,\; xy > 1\end{cases}$$  Furthermore, When I plot the function $2\arctan(x)$, it turns out that the book definition is correct. I don't understand how such peculier definition emerges. Thank you.


I want to create a play() method with Track in the method parameters but I can't do this in my controller class as the play is an action and actions can't have parameters (or it must be an ActionEvent).  So I thought of creating another class to apply play logic instead and just pass to this method in the new class instead of doing everything there.  @FXML private void play() {     play.setText("Pause");     Track selectedTrack = playingTable.getSelectionModel().getSelectedItem();      if (selectedTrack != null && selectedTrack != playingTrack) {         player.stopSong();         player = new TrackPlayer(selectedTrack);         playingTrack = selectedTrack;         player.playSong();     } else {         switch (player.getStatus()) {             case READY:                 player.playSong();                 break;             case PLAYING:                 player.pauseSong();                 play.setText("Play");                 break;             case PAUSED:                 player.playSong();                 play.setText("Pause");                 break;             default:                 System.out.println("Wtf?");         }     }     updateInfo(); }   This is my play() method now inside my controller class (which is working correctly). I want to change it so I can do the following  if(selectedTrack != null) {     manager.play(selectedTrack); } else {     System.out.println("Track not selected / null"); }   manager being another class which would have the following method  public void play(Track track) {     controller.setPlayTxt("Pause");      if (track != null && track != playingTrack) {         player.stopSong();         player = new TrackPlayer(track);         playingTrack = track;         player.playSong();     } else {         switch (player.getStatus()) {             case READY:                 player.playSong();                 break;             case PLAYING:                 player.pauseSong();                 controller.setPlayTxt("Play");                 break;             case PAUSED:                 player.playSong();                 controller.setPlayTxt("Pause");                 break;             default:                 System.out.println("Wtf?");         }     } }   However whenever I click on a song (that is not null) and press play I get a NullPointerException on the line manager.play(selectedTrack);  Why? I know that the object is not null, and have checks for it, and this is the exact same way I do it originally (which works) but when I change this to be a pass to another class I get NullPointerException.

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?


What's the risk of using PSU that is underpowered? Is there risk to the device drawing the power?  I have a TPLINK AC1900 Onhub Router. It is missing the PSU (12VDC, 3A)  I have a 12VDC 2A. I think the only risk is that I'll blow the PSU ( I guess it might heat up as well. Perhaps dangerously??).  The PSU is a leftover, so I don't mind the risk of blowing it.  But... perhaps there's some risk to the OnHub as well? -Clay

Power supplies are available in a wide range of voltage and current ratings.  If I have a device that has specific voltage and current ratings, how do those relate to the power ratings I need to specify?  What if I don't know the device's specs, but am replacing a previous power supply with particular ratings?  Is it OK to go lower voltage, or should it always be higher?  What about current?  I don't want a 10 A supply to damage my 1 A device.


We have a custom module mymodule that has the following structure. It basically has a configuration object that we are using in a mymodule_preprocess_node() call to do some logic and display certain output.   When the module is uninstalled, we noticed that configuration files are not deleted. How would we delete the configurations on uninstall?  What we were thinking, but not sure if that is correct or if we are missing any steps.    function mymodule_uninstall() {   \Drupal::configFactory()->getEditable('mymodule.settings')->delete(); }

I'm writing a custom module for Drupal 8. It defines a field storage configuration object, in a file called modules/mymod/config/install/field.storage.bloom_stem.bs_twitter_ac.yml.  The problem is that this is not removed when I uninstall the module; it is apparently left behind because, when I re-install the module, I get a crash.   drush -y pm-uninstall mymod drush cr drush -y en mymod      exception 'Drupal\Core\Config\PreExistingConfigException' with message 'Configuration objects (field.storage.bloom_stem.bs_twitter_ac) provided by mymod already exist in active configuration'   So it seems I need to some how manually remove this configuration object. Do I need to provide some more code that deletes it when the module is uninstalled?


I'm using a Dell Inspiron 5590, it came with Windows, I want to install Ubuntu instead. I downloaded the 18.04.5 image file and made a bootable USB device with Rufus following the . The problem is, when booting, the USB device doesn't show in the Boot Options. What I've tried:  Tested in USB ports 3.0 and 2.0 Tested flash drive in another notebook (It works) Tested with and without Secure Boot. Tried two "builds" of the bootable USB: Partition scheme: MBR + Target system: BIOS or UEFI AND with Partition scheme: GPT + Target system: UEFI (non CSM).  Also:  I'm not looking to dual boot this, just linux is fine. USB Boot Support is enabled I didn't tried with Legacy Boot, because the BIOS says that this mode is not supported in the platform. Contacted Dell before purchase to be sure the hardware was compatible with Linux. (Also contacted the Dell support for help, useless in this case) BIOS is up to date.  What else can I try in order to have my bootable USB to be recognized by the Boot Manager?

This question is asked often in Ask Ubuntu, sometimes with few hints about the situation.   Please provide a list of possible reasons to help troubleshoot the problem.


Of course, there's the issue of loading times. That's why putting javascript at the end of the HTML has always been recommended.  However, are there cases where this shouldn't be done? Are there any disadvantages to this method?

When embedding JavaScript in an HTML document, where is the proper place to put the <script> tags and included JavaScript? I seem to recall that you are not supposed to place these in the <head> section, but placing at the beginning of the <body> section is bad, too, since the JavaScript will have to be parsed before the page is rendered completely (or something like that). This seems to leave the end of the <body> section as a logical place for <script> tags.  So, where is the right place to put the <script> tags?  (This question references , in which it was suggested that JavaScript function calls should be moved from <a> tags to <script> tags. I'm specifically using jQuery, but more general answers are also appropriate.)


Ethics:  I started really programming 94 days using Mathematica. I learned with 2 friends and SO. I asked 74 questions yet all answered with generosity.   Sometimes I feel guilty only "asking". Then I thought that it depends on what others do.    Data:  I would be greatly interested to see some data of users behavior in that regard. From always asking to always answering, how are users distributed? This, along with data on time spent on SO, votes attributed, etc.  I would then like to see how that compare to Wikipedia Editors/Readers statistics.

I have used the websites of SO a lot the past few months because I am busy with a large scale web project. I feel I get better answers here on SO than when I just do a Google search, maybe because I can be more specific here with my problem, and the responses are really fast.  Occasionally when I am not working I try to answer some questions, but the question almost always has an answer which is 'as good as' or 'better' than the answer I would supply.  So my question/answer ratio is about 20/1 something, if not more. When I look at my profile page I see a bucket-load of questions and almost nothing I answered myself.  Is this considered bad behaviour? I can see that this looks a little egoistic.  : One devoted to one's own interests and advancement.


I am trying to attach my Vf page which is rendered as pdf to the Files section. But the error " Too many nested getContent calls." is being thrown. The code is as follows: VF Page (Only starting) <apex:page action="{!attachOfferPDF}"        standardController="Quote__c"        extensions="QuotePDFController"        readOnly="true"              applyHtmlTag="false"             sidebar="false"             showHeader="false"             cache="true"             renderAs="pdf">  Apex Controller: public with sharing class QuotePDFController { public PageReference rtn; public static string recursion = 'false' ; public string parId; public quote__c quotesRecords {get;set;} public Quote_header__mdt quotesHeaders {get;set;}  public QuotePDFController(ApexPages.StandardController standardController){     quotesRecords = new Quote__c();     parId = standardController.getId();         system.debug('parid '+parId);     quotesRecords = [select Id,Name, (SELECT Id,    Product_Name__c,DifficultyLevel__c,Product__r.Name,Level_Course__c,Onetime_Fee__c,OS__c,Vlab_Configuration__c,PerHourCost__c,PerChallengeEvaluationFee__c FROM Quote_Line_Items__r) FROM Quote__c where Id = 'a071y0000015mwEAAQ' limit 1];           } public void attachOfferPDF() {               if ( recursion == 'false'){         recursion = 'true';         system.debug(recursion);         PageReference pdfPage = Page.QuoteGeneration;         Blob pdfBlob = pdfPage.getContentAsPDF();         Attachment a = new Attachment(parentId = 'a071y0000015mwEAAQ', name='Rahul' + '.pdf', body = pdfBlob);         insert a;         system.debug('id is '+a.id);     }} }  Not able to figure why this error is being thrown.

I have a Visualforce page that renders perfectly as a PDF that I'd like to attach to an opportunity record and to attach to an email.  Whenever the code gets to getContent(), I keep getting an error saying      Too many nested getContent calls   Below, you can see the code is very simple.  Just pulls data to fit into the VF page in the substitution blanks then tries to create the PDF.  Looking at the debug log, the call to getContent() only happens once.  I'm stumped!  Thanks for your ideas...  public with sharing class GenerateThankYouLetterAsPDF {   // a handful of fields that are {!field} substitutions on the VF page     public id oppID {get; set;}     public string giftAmount {set; get;}     public string giftDate {set; get;}     //  etc...       public GenerateThankYouLetterAsPDF() {         id oppID = id.valueof( ApexPages.currentPage().getParameters().get('id') );               // set the values of field substituions           string filename = 'donation.pdf';          // Generate the PDF          PageReference pdf = ApexPages.currentPage();         system.debug ('calling getContent...');         blob b = pdf.getContent();   }                 }


I am trying to read from rockyou wordlist and write all words that are >= 8 chars to a new file.  Here is the code -   def main():     with open("rockyou.txt", encoding="utf8") as in_file, open('rockout.txt', 'w') as out_file:         for line in in_file:             if len(line.rstrip()) < 8:                 continue             print(line, file = out_file, end = '')         print("done")  if __name__ == '__main__':     main()   Some words are not utf-8.  Traceback (most recent call last):   File "wpa_rock.py", line 10, in <module>     main()   File "wpa_rock.py", line 6, in main     print(line, file = out_file, end = '')   File "C:\Python\lib\encodings\cp1252.py", line 19, in encode     return codecs.charmap_encode(input,self.errors,encoding_table)[0] UnicodeEncodeError: 'charmap' codec can't encode character '\u0e45' in position 0: character maps to <undefined>  Update  def main(): with open("rockyou.txt", encoding="utf8") as in_file, open('rockout.txt', 'w', encoding="utf8") as out_file:     for line in in_file:         if len(line.rstrip()) < 8:             continue         out_file.write(line)     print("done")  if __name__ == '__main__':     main()```   Traceback (most recent call last):   File "wpa_rock.py", line 10, in <module>     main()   File "wpa_rock.py", line 3, in main     for line in in_file:   File "C:\Python\lib\codecs.py", line 321, in decode     (result, consumed) = self._buffer_decode(data, self.errors, final) UnicodeDecodeError: 'utf-8' codec can't decode byte 0xf1 in position 933: invali d continuation byte

When I try to print a Unicode string in a Windows console, I get an error . UnicodeEncodeError: 'charmap' codec can't encode character .... I assume this is because the Windows console does not accept Unicode-only characters. What's the best way around this? Is there any way I can make Python automatically print a ? instead of failing in this situation? Edit:  I'm using Python 2.5.  Note: @LasseV.Karlsen answer with the checkmark is sort of outdated (from 2008). Please use the solutions/answers/suggestions below with care!!  is more relevant as of today (6 Jan 2016).


My niece gave me a Windows 7 laptop which has Short DST Failed errors on startup. Can I use a flash drive to install Ubuntu on this laptop so that I can use it?

I would like to see a full how-to guide on how to install Ubuntu.


I am optimising a website based on PageSpeed Insights guidelines. And one of the points is to Leverage Browser Caching.  And in this case - for the third party resources - like Google Analytics and Tag Manager. I already added this code to .htaccess file: # Expires headers <IfModule mod_expires.c> ExpiresActive on  ExpiresDefault                          "access plus 2 days"  # cache.appcache needs re-requests in FF 3.6 ExpiresByType text/cache-manifest       "access plus 0 seconds"  # Your document html ExpiresByType text/html                 "access plus 0 seconds"  # Data ExpiresByType text/xml                  "access plus 0 seconds" ExpiresByType application/xml           "access plus 0 seconds" ExpiresByType application/json          "access plus 0 seconds"  # Feed ExpiresByType application/rss+xml       "access plus 1 hour" ExpiresByType application/atom+xml      "access plus 1 hour"  # Favicon (cannot be renamed) ExpiresByType image/x-icon              "access plus 1 week"  # Media: images, video, audio ExpiresByType image/gif                 "access plus 1 month" ExpiresByType image/png                 "access plus 1 month" ExpiresByType image/jpeg                "access plus 1 month" ExpiresByType video/ogg                 "access plus 1 month" ExpiresByType audio/ogg                 "access plus 1 month" ExpiresByType video/mp4                 "access plus 1 month" ExpiresByType video/webm                "access plus 1 month"  # HTC files ExpiresByType text/x-component          "access plus 1 month"  # Webfonts ExpiresByType application/x-font-ttf    "access plus 1 month" ExpiresByType font/opentype             "access plus 1 month" ExpiresByType application/x-font-woff   "access plus 1 month" ExpiresByType application/x-font-woff2  "access plus 1 month" ExpiresByType image/svg+xml             "access plus 1 month" ExpiresByType application/vnd.ms-fontobject "access plus 1 month"  # CSS and JavaScript ExpiresByType text/css                  "access plus 1 year" ExpiresByType application/javascript    "access plus 1 year"  </IfModule>  What should I add to this code? And what is the recommended period for browser caching for Google Analytics and Google Tag Manager?

Google Pagespeed recommends caching resources for at least a week under "". I've done it for internal files but I was wondering if something could malfunction if I did the same to social media files:   http://connect.facebook.net/en_US/all.js (20 minutes) http://platform.twitter.com/widgets.js (30 minutes) https://apis.google.com/js/api.js (30 minutes) https://apis.google.com/js/plusone.js (30 minutes) https://www.gstatic.com/swiffy/v7.1.1/runtime.js (50 minutes) http://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js (60 minutes) http://pagead2.googlesyndication.com/pagead/osd.js (60 minutes) https://oauth.googleusercontent.com/…e:rpc:shindig.random:shindig.sha1.js?c=2 (60 minutes) http://stats.g.doubleclick.net/dc.js (2 hours)   The numbers in parenthesis indicate current expiration time.


Hy, I wrote the code below and I don't understand why it's not working. For example for today (04.04.2020) dayOfWeek should be 7, but the result is 2….      Calendar calendar = Calendar.getInstance();     calendar.set(2020, 4, 4);     int dayOfWeek = calendar.get(Calendar.DAY_OF_WEEK);     System.out.println(dayOfWeek); //this print 2 on the console

In java.util.Calendar, January is defined as month 0, not month 1. Is there any specific reason to that ?  I have seen many people getting confused about that...


Since every trade has a buyer and a seller, I don't understand when people say buyer volume is X or seller volume is Y (if seller volume is different from buyer volume). Where are these numbers coming from?

I often hear/read technical analysts looking at volume and price action on a chart and claiming that there are "more buyers than sellers" or vice versa.  Since every trade requires a buyer and a seller, how can volume/price signify more of one than the other?  What does that actually mean?  When I hear that there are "more buyers," I get the impression they actually mean more "professional" or "institutional" buyers, but I could just be imagining that meaning.  But wouldn't this "more buyers" situation actually represent a smaller number of large buyers placing multiple orders? (and those orders would be matched by a larger number of smaller investors on the other side of the trade?)  Maybe I have my assumptions backwards and "more buyers" is what they say when they actually mean "more retail buyers and less institutional buyers"?  Or maybe the expression has nothing to do with number of buyers/sellers at all and is just some arbitrary technical analysis situation?  What situation is it that they're trying to describe?  If the "smart money" traders had placed larger orders, then there would have to be equally large sellers on the other side of that large trade, right?  I know trades often get broken up, but if the trades had been broken up it would be equivalent to "large traders placing multiple orders" scenario described above.  If the trades were not broken up, then there would not be an imbalance in the "number" of "smart" vs. retail buyers/sellers, right?  UPDATE/EDIT: I usually see this stated in reference to technical indicators such as RSI.  I don't typically hear people saying "there are more buyers than sellers" in the situations you guys are describing with more unfilled orders on one side of the (potential) trade (though that would make more sense if that was what they were talking about).  See for example:


I am defining 3 classes in C++ and trying to make maximum use of Curiously recurring template pattern (CRTP). I am using VS 2017.   Code:   `  template<typename Outer> class OuterClass <Outer, uint32_t> {     using datatype = uint32_t;  static uintptr_t GetAddr(void const volatile* const ptr) {             auto const addr1 =            get_addr();             auto const addr_virtual =     ptr;             auto const baseAddr =         Outer::base_addr;             uintptr_t const addressCalcd = uintptr_t(baseAddr) + uintptr_t( addr_virtual - addr1 );         return addressCalcd;     }; };  template<typename Outer> class OuterClass <Outer, uint64_t> {     using datatype = uint64_t;  static uintptr_t GetAddr(void const volatile* const ptr) {             auto const addr1 =            get_addr();             auto const addr_virtual =     ptr;             auto const baseAddr =         Outer::base_addr;             uintptr_t const addressCalcd = uintptr_t(baseAddr) + uintptr_t( addr_virtual - addr1 );         return addressCalcd;     }; };  template<typename Inner, typename Outer> struct InnerClass {      GetAddVal CastVl()  const volatile {      uint32_t addrl = uint32_t(Outer::GetAddr(static_cast<const volatile R*>(this)));         return VAL_CAST{ addrl };     }     operator Outer::datatype() const volatile {         return RegBlock<Outer, Outer::datatype>::readReg(*this);     }     operator Outer::datatype() const {         return RegBlock<Outer, Outer::datatype>::readReg(*this);     }     void operator=(Inner const  & x) volatile;     void operator=(const Outer::datatype x) volatile; };   The errors are in the InnerClass. Firstly,   uint32_t addrl = uint32_t(Outer::GetAddr(static_cast<const volatile R*>(this)));  is perfectly fine. I can refer to the static class Outer::GetAddr no problem.   However, I cannot refer the typedef'd    operator Outer::datatype() const volatile {  Error: C2833 "operator qualified-name" is not recognized operator or type  This is also an error for :    void operator=(const Outer::datatype x) volatile;   C2805  binary "operator =" has too few parameters.  Why can I refer to static classes using the :: and not anything typedef'd ? Should I consider nesting the "InnerClass" inside the "OuterClass" ? Ideally I don't want to have nested classes at all.

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


As we all know Stirling Approximation is giving us an approximate value of factorial, aka   $\Gamma(x + 1)$.  $\sqrt{2\pi n}(\frac{n}{e}) \approx n!$  But what if we have equations with factorials. In this case we are allowed to use Stirling approximation in order to simplify our problem. But how can we find the exact value of this equation?  $ \sqrt{2\pi n}(\frac{n}{e}) = g(n)\\ g(n) \in \mathbb{R} $

The factorial function cannot have an inverse, $0!$ and $1!$ having the same value. However, Stirling's approximation of the factorial $x! \sim x^xe^{-x}\sqrt{2\pi x}$ does not have this problem, and could provide a ballpark inverse to the factorial function. But can this actually be derived, and if so how? Here is my work:  $$ \begin{align} y &= x^xe^{-x}\sqrt{2\pi x}\\ y^2 &= 2\pi x^{2x + 1}e^{-2x}\\ \frac{y^2}{2\pi} &= x^{2x + 1}e^{-2x}\\ \ln \frac{y^2}{2\pi} &= (2x + 1)\ln x - 2x\\ \ln \frac{y^2}{2\pi} &= 2x\ln x + \ln x - 2x\\ \ln \frac{y^2}{2\pi} &= 2x(\ln x - 1) + \ln x \end{align} $$  That is as far as I can go. I suspect the solution may require the Lambert W function.  Edit: I have just realized that after step 3 above, one can divide both sides by e to get  $$\left(\frac{x}{e}\right)^{2x + 1} = \frac{y^2}{2e\pi}$$  Can this be solved?


I saw these two sentences from a book called "The Art of Racing In The Rain" (I love it!!) and I don't see any verb inside, could anyone explain what's the grammar behind? "Peripheral vision, seeing things you’ve never seen before. Kinesthetic sensation, driving by the seat of the pants." Hope my question is clear enough. Thank you guys in advance:)))

I have seen some debate on EL&U about whether or not sentence fragments are acceptable to use, and under what circumstances.  I am not of the persuasion that they should be used, but if I must concede that they are permissible to use, I would like to know the rules that render them acceptable. For instance, it seems that most "acceptable" sentence fragment constructions function in a similar way to pronouns: they refer back to an antecedent.  With pronouns, the antecedent is a noun, and with sentence fragments, the antecedent is a subject-verb group.  Here is an example to clarify:  "The dog bit the child five times.  Every day."    While I would prefer to solve the issue by using a dash ("The dog bit the child five times – every day"), how would one who allows sentence fragments justify the construction?  What are general rules by which one can determine the acceptable construction of sentence fragments?  My intuition tells me that not even fragment-lovers would accept constructions such as "The dog bit the. Child five. Times every day." . . . on what grounds would such constructions not be acceptable?  To state it positively, on what grounds does one determine the grammatical acceptability of a sentence fragment group?  By "sentence fragment group" I am revealing a presupposition that a sentence fragment derives necessary contextual data from a nearby complete sentence.


Usually when I write an answer I explain each section of my code separately and then add a link to a JSFiddle demo at the end. For example take a look at :  Now with the introduction of  I would like to replace my JSFiddle links with stack snippets. However it seems that you cannot split your stack snippets into multiple sections. It would be nice if this were possible. It would be even better if you could arrange the sections in any order. The order in which the snippets should be rearranged could be specified in the language comment. For example: <!-- language: lang-js snippet: 2 --> <!-- language: lang-js snippet: 1 --> <!-- language: lang-js snippet: 3 -->  Currently the only other way I can split my code into multiple sections and use stack snippets is to duplicate the code (and rearrange and merge the sections) into a stack snippet at the end of the answer, which is okay: I can say “Here is the code put together.” However this method has the disadvantage that if I change some code in my section then I need to make the same change in my stack snippet. It would be nice if I only needed to make the change in one place.

Sometimes only 10 lines of 100 are relevant to the question/answer, the other  90 are setup.  Is there a way to hide 90 those in lines in the answer?


2013 Mac Pro with 2.7Ghz 12 core E5 + dual D300 macOS 10.15.3 beta Blender 2.82 beta Blender Benchmark 2.80  Blender by default doesn't recognize my GPUs as rendering devices.    I have tried Radeon ProRender, it sort of works, but crashes way too often (from every few seconds to every few minutes), it also limits the numbers of available shaders to about half.   Shaders when Cycles selected as renderer:   Shaders when ProRender selected as renderer:   So at this point, it's not really usable...  Then today, when I tried Blender Benchmark for the first time, I realized it actually recognized my GPUs! Although only one of the 2 GPUs was working during the benchmark, but it totally recognized them.    Now here's my question, assuming Blender Benchmark uses the same rendering engine as Blender, is there any way to get Blender itself to recognized my GPUs as rendering devices?  Thank you in advance for your kind help!

Hello I just got the AMD Radeon RX Vega 56 (blackmagic eGPU Pro) yesterday  plugged it in to my brand new Mac mini (Mojave), it shows up in the menubar and as an alternative as a render engine,. My question is, can I use this eGPU for cycles renders? (Blender 2.80)  Very grateful for your responses.


Earth rotates about its axis and also revolves around the Sun at the same time. So why Earth is considered as an inertial frame in Newtonian Physics. So technically, I'm effectively asking why the Earth-centered, Earth-fixed () frame is considered an inertial frame?

In many practical applications, one can consider the Earth-Centered Inertial () reference frame approximately as an inertial reference system, though strictly speaking, it is non-inertial.   Is there any quotable reference, where this claim is supported by a detailed estimation how small the effects are that one neglects if one considers the Earth's frame as inertial?


As I undersand in thermodynamics, a gas with an equation of state $f(V,T,p)=0$ will need only 2 variables (e.g $V$ and $p$) to determine its state.  Regarding this question:    if we fix the entropy $S$ and the volume $V$, the state of gas can still change. Why is that possible? If $f(T,p)_V=0$ and $S(T,p)_V=S$ fixed, then is it not true that the state of gas is fixed?  I know I'm wrong somewhere, please correct me.

Just like classical potential, it's stated that equilibrium is obtained when the corresponding thermodynamics potential reaches the minimum. Explicitly, according to , in particular:  When the entropy (S ) and "external parameters" (e.g. volume) of a closed system are held constant, the internal energy (U ) decreases and reaches a minimum value at equilibrium. When the temperature (T ) and external parameters of a closed system are held constant, the Helmholtz free energy (F ) decreases and reaches a minimum value at equilibrium. When the pressure (p) and external parameters of a closed system are held constant, the enthalpy (H ) decreases and reaches a minimum value at equilibrium. When the temperature (T ), pressure (p) and external parameters of a closed system are held constant, the Gibbs free energy (G ) decreases and reaches a minimum value at equilibrium.  There is something confuse me here. Take the first claim for example. If we have the formula: $dU=TdS-pdV$ then when $S$ and $V$ are held constant, is it not clear that $dU=0$ for whatever changes occurring? Furthermore, if there are $two$ fixed parameter, is it not true that the state of system is fixed? (assuming there is a state formula $f(T,p,V)=0$). It seems like I'm really misunderstanding some concepts of the thermodynamics potential. Can someone give me a clear explanation for my confusion?


Suppose i have system of equtions $x=a_imodm_i$ for  $1≤i≤n$ and it might be possible that for distinct $i,j$ such that  $1≤i≤n$ and $1≤j≤n$ and $gcd(m_i,m_j)≠1$ . I have read various answers on web and this website related to this , but most of the time they don't prove it completely . I wanted to know about the cases when it can be solved and when not and how to solve it if it can be , all of the these things with proof.

Let a system of three linear congruence equations in integers be given;      \begin{cases}x\equiv b_1\mod c_1\\ x\equiv b_2\mod c_2\\ x\equiv b_3\mod c_3\\ \end{cases}   with $c_1,c_2,c_3\in\mathbb Z_{+}$. Show that, if every pair of congruence equations admits solutions, then the entire system admits solutions.    Now, if every pairs admits solutions, then for example $b_1\equiv b_2\equiv a\mod \gcd(c_1,c_2)$ for some $a$ then;   $x-a\equiv b_1-a\mod c_1$  $x-a\equiv b_2-a\mod c_2$  replacing $x$ by $x':=\frac{x-y}{\gcd(c_1,c_2)}$, we obtain:  $x'\equiv b_1'\mod c_1'$  $x'\equiv b_2'\mod c_2'$  and since $\gcd(c_1,c_2)=1$ by Chinese Remainder Theorem we have a unique solution $\mod{c_1'c_2'}$, so $x\equiv (\gcd(c_1,c_2)x'+a)\mod{\operatorname{lcm(c_1',c_2')}}\quad(1)$  We can do it with another pair (take $2$nd and $3$rd, since we know that such a pair admits solutions;  $x\equiv(\gcd(c_2,c_3)x''+a')\mod{\operatorname{lcm(c_2',c_3')}}\quad(2)$  Now how can I show that for the pair $(1)$ and $(2)$ also solutions exist ?


In general, most Japanese manga are not colored, except for title page or centre color pages, rarely. However, most Korean manhwa manage to colour their works while maintaining a good standard of art, also in their weekly deadlines.

Lately, I been reading quite some more manwha cause of their good stories. But I can't help but notice that manwha use a lot more colored pages, sometimes even fully colored volumes. Or just all pages color, why are color pages more commonly used in manwha then  manga? Is there a specific reason for this?


For instance, in  the cells in the tag column contain not parsed tags if at least one question's tag is not Latin only:

Run the following SEDE query: . All the tags except kyūjitai-and-shinjitai, renyōkei, あれ, and たい-form get auto-linkified. These happen to also be the only four tags that contain characters outside the standard set of allowed characters [a-z 0-9 + # - .]. It would be nice if these would auto-linkify too. (I imagine this is even more applicable for other language sites like  - if you , you find that well over half the tags don't linkify because they contain Cyrillic characters.)


How to enable Contact to allow login on SF org .  I think this was available in classic but could not find in Lightning LEX

I know that in the Winter release the "Log in to Community as User" button was added to Lightning. I did look at other pre-existing topics for this subject and none of those answers resolved the issue for me.  I am a System Admin and I have access to the button when viewing a Contact.  Our core users do not, however (but they do in Classic, so I know they have permissions).  Things I checked based on other topics:   They have "Manage External Users" permissions. They have Read/Edit on Accounts. Their Role is in the same Sharing Groups that my role is in. The buttons are being displayed on all of our page layouts for the Contact object.


i have been running around in circles with this situation, i already tried all the answers that i found in stackoverflow and tried to use linkify aswell but with no success, can't make it work and i would rather NOT have to use any Javascript libraries, jquery, mootools etc...  So here is what i am trying to achieve;  I have a comment section for each of my posts and i want that each time a user posts a url in his comment:
 Nice, here is the respective link that you were asking for: www.linkforanywebsite.com
   turns into this:
 Nice, here is the respective link that you were asking for: www.linkforanywebsite.com
   Any guide/jsfiddle working example are very appreciated  Thank you for your time and help!

I am using the function below to match URLs inside a given text and replace them for HTML links. The regular expression is working great, but currently I am only replacing the first match.  How I can replace all the URL? I guess I should be using the exec command, but I did not really figure how to do it.  function replaceURLWithHTMLLinks(text) {     var exp = /(\b(https?|ftp|file):\/\/[-A-Z0-9+&@#\/%?=~_|!:,.;]*[-A-Z0-9+&@#\/%=~_|])/i;     return text.replace(exp,"$1");  }


In Harry Potter, what makes a wizard a wizard and a witch a witch? Apparently, wizards can be both men and women. But I'm not sure if men can be witches. So in this universe what is the distinction?  According to the sci fi stack exchange :     "Wizard" can be used for males and females.   According to this question:      Well, when Hagrid describes Muggles to Harry as "non-magic folk" it   might imply that 'magic' is a collective term used to describe witches   and wizards. An example sentence might be, "All the non-magic folk to   the right, the magic to the left." Also, 'magic' is the word I've most   commonly seen/heard as used to describe the genetic attribute that   makes a person a witch or wizard. Either a person has the magic gene   or they don't.   Because magic means both witches and wizards, this means there is a difference. Women can be wizards and in history men can be witches.  Therefore there is a difference between the magic abilities of witch and wizard.  I'm not seeing the clear definition though of what makes one or the other. The question related to a term for both wizards and witches, however, reports it as two separate entities, therefore there exists a distinction between witch and wizard, in the Potterverse anyway, but what makes one or the other according to J.K. Rowling I have not found an explanation that she gives.

When writing questions and answers here about the Harry Potter series, I often need a word for "someone who's not a Muggle". People often refer to "the wizarding world" as opposed to the Muggle word, so "wizard" would be one choice - but it seems slightly sexist to exclude witches in that way. On the other hand, "witch or wizard" is a bit cumbersome, much longer than the simple word "Muggle".  Is there a sensible word to use which is neither sexist nor cumbersome, that makes a good equivalent to "Muggle"? What would JK Rowling say to fill in a sentence such as this:     Muggles use technology, while [...] use magic.


I'm trying to code a webapp similar to  but simpler. I've checked blender documentation but being a developer not a modeler/3d artist i couldn't find answer to this.   Is it  possible to render a single frame of a scene using command line interface with given variables like a color of a surface or the camera angle?   Or can you point me to a direction i can achieve this kind of task.   Thanks in advance.

Is there any way to get blender to render on systems without a GUI?  Over the network on systems with a GUI?  I know of a service that will let you buy virtual servers that are charged by the hour, not the month, allowing to purchase extra performance on demand very cheaply!  The question itself is OS-agnostic, but in this case you can essentially respond in a any OS you would like.


I wrote a simple lightning component to launch from a quick action on a detail page from the SF1 iOS mobile app. This will launch a deep link to a 3rd party app. The mobile URL is stored in a field on the object that launches the quick action. When pulling in the URL field, it keeps saying the attribute inspection is undefined. I wanted to know if I am pulling in the fields correctly using the force:recordData component. The component and controller are below: Component: <aura:component implements="flexipage:availableForRecordHome,force:lightningQuickActionWithoutHeader, force:hasRecordId">       <aura:attribute name="inspection" type="Object" />     <force:recordData aura:id="recordLoader"     recordId="{!v.recordId}"     fields="Id, Mobile_URL__c"     targetFields="{!v.inspection}"     />       <aura:handler name="init" value="{!this}" action="{!c.doInit}" />   </aura:component>  Controller: ({     doInit: function (component, event, helper) {           var urlEvent = $A.get("e.force:navigateToURL");         urlEvent.setParams({             "url": "{!v.inspection.Mobile_URL__c}"         });         urlEvent.fire();           setTimeout($A.getCallback(function () {             var dismissActionPanel = $A.get("e.force:closeQuickAction");             dismissActionPanel.fire();         }), 5);     } })

Is there a way we can get the value from force:RecordData on init ? I am getting the onclick event of a button.  <aura:handler name="init" value="{!this}" action="{!c.doInit}"/>     <aura:attribute name="recordId" type="String"/>      <aura:attribute name="showButton" type="Boolean" default="false"/>     <aura:attribute name="Opportunity" type="Object"/>        <aura:attribute name="parentOpp" type="Object"/>     <aura:attribute name="oppLoadError" type="String"/>     <force:recordData aura:id="oppRecordLoader"                       recordId="{!v.recordId}"                       fields="Id,                               Name,                               AccountId,                               Cohort_Sem__r.End_date__c,                               LeadSource,                               Staff_Referral_Detail__c,                               lead_source_detail__c"                       targetRecord="{!v.Opportunity}"                       targetFields="{!v.parentOpp}"                       targetError="{!v.oppLoadError}"                       />   JS:  doInit: function(component, event, helper) {                     var opp = component.get("v.parentOpp");                   console.log('Name Value: '+ opp.Name);     }   Error:     Action failed: c:createIWSRecord$controller$doInit [Cannot read   property 'Name' of null] quickActionHandlerHelper.js failed to create   component - forceChatter:lightningComponent


I just reviewed a proposed edit on a SO question. At first it seemed that the edit was just just "how to" to "how-to". So I rejected the edit. However, my mistake turned out to be that there also was a change to a hyperlink in that edit which was relevant and should be approved. Is there any way to undo my rejection and approve the edit instead?

I (and probably many other people) have accidentally clicked the wrong button in reviews. For example, I just clicked the Leave Open button when I wanted to click Close. I think many people have done this. I think an ability to undo this would be appreciated.


I'm trying to display data in JSP by a servlet but I get a null object after getting the parameter:  This is my doGet function in the servlet:  protected void doGet(HttpServletRequest request, HttpServletResponse response) throws ServletException, IOException {     PrintWriter out = response.getWriter();       EntityManagerFactory emf = Persistence.createEntityManagerFactory("AdministracionWeb");      StudentManager sm = new StudentManager();     sm.setEntityManagerFactory(emf);      List<Student> result = sm.getAllStudents();     // result contains a correct value     //out.println(result);     request.setAttribute("stList", result);           request.getRequestDispatcher("students.jsp").forward(request,response); }   And this is how I read the result:  <%     List<Student> stList = (List<Student>) request.getAttribute("stList");     // stList here is null (why???)     Student st = new Student();     for (int i = 0; i < stList.size(); i++){         st = stList.get(i);      ... %>   Thanks in advance!!

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?


The below code produces a NullPointerException when I run it. Which is weird because shouldn't the setup() method be ran before the tests?  If I instantiate the AirJourney class within the test method the JUnit test passes without any problems. What am I missing?  private AirJourney journey;      @Before     public void setup()     {         journey = new AirJourney(4, 800, "A", "B");     }      @Test     public void testCorrectCostIsProduced()     {         assertEquals(32000, journey.calculateCostOfJourney());     }


I had a folder that I had pinned to my quick access and that folder has now been deleted. It is still pinned under my quick access but I cannot seem to get rid of it. I tried clearing the File Explorer History and that did nothing. I also tried following all of the steps in  but nothing has worked. Is there any way to get this folder out of the way? I have Windows 10. Is it possible that onedrive has something to do with it? (just a thought, I'm clearly no expert haha) Update: When following step 4 of the article, I do not have a folder titled Microsoft. I am not sure if this is because an update and/or the article is dated, but the last step no matter what I did I could not find an Automatic Destinations folder in File Explorer. Is there another place this could be, or is it possibly called something else? Update #2: I tried step 4 again, and it seems to have worked this time. How weird technology can be. Thank you for the help!!

I have a link to a deleted folder in "quick access" (frequent folders). However, I cannot remove it, because when I try to "unpin" it I get an error "Location is not available".  Somewhat related to "", but with no applicable answer.


Let $k\subset K$ be a normal extension of fields of characteristic $p>0$ with $G=\text{Aut}_k(K)$ (the automorphisms $\varphi\colon K\to K $ with $\varphi|_k = \text{id}\colon k\to k$). Show that the extension $k\subset K^G$ is purely inseparable.   So we have $k\subset K^G\subset K$ with $k\subset K$ normal, which implies that $K^G\subset K$ is normal as well. How are purely inseparable extensions and normal extensions related?

I need to prove the following:     Let $L/K$ be a normal field extension. Denote by $H=\operatorname{Aut}(L/K)$ the Galois group of the extension, and by $L^H$ the fixed field of $H$ in $L$. Prove that $L/L^H$ is separable, and that $L^H/K$ is purely inseparable.   For now, we tried to use the fact that an extension $M/F$ is separable (purely inseparable) if the number of homomorphisms $\phi:M\to \overline{M}$ that preserve $k$ is $[M:F]$ ($1$). We did not manage to conclude any results, and moreover this works only for finite extensions. How should we proceed?


Let $f$ be a function defined $[0,1]$ with the following property: For every real number $y$, either there is no $x$ in $[0,1]$ for which $f(x)=y$ or there are exactly two values of $x$ in $[0,1]$ for which $f(x)=y$ .  EDIT:  Prove that there are infinite discontinuities in this interval  I found a possible solution  but I am not able to comprehend the answer on the page as probably it uses high concepts of graph theory.   Could anybody please give a simpler solution?  Thank you for your help.

This is from Apostol's Mathematical Analysis.  Let $f$ be a function defined in $[0, 1]$ such that for each real number $y$ either there is no value of $x \in [0, 1]$ such that $f(x) = y$ or there are exactly two such values of $x$. Prove that a) $f$ must be discontinuous on $[0, 1]$. b) $f$ has an infinite number of discontinuities in $[0, 1]$.  Long back I had tried to solve the problem. I reasoned for a) as follows: Suppose that $f$ is continuous and let $m, M$ be its minimum and maximum values on $[0, 1]$. Clearly if $m = M$ then $f$ is constant and clearly for every $x \in [0, 1]$ we have $f(x) = m = M$ which contradicts given property of $f$. So we must have $m < M$. Clearly there are now four distinct points $a, b, c, d$ in $[0, 1]$ such that $f(a) = f(b) = m, f(c) = f(d) = M$. By checking possible linear orderings of $a, b, c, d$ I could find a find a value of $y \in (m, M)$ for which there exist more than 2 values of $x$ such that $f(x) = y$. However this approach looks very clumsy and I suspect much simpler and easier proof is possible. Part b) seemed bit complex and my only guess was that probably $f$ was discontinuous on each subinterval of $[0, 1]$ but I could not prove this claim (may be the claim is wrong!). Perhaps there is a simpler solution to this part of the problem. Apostol's also asks to provide an example of such a function. Any hints on the overall problem will be appreciated.  Update: After looking at Marc's answer, I think I have found a way to show that there are infinitely many discontinuities. Earlier the solution was a part of the question itself but it made the question look quite lengthy hence I moved it to a separate answer.


The Great Gatsby by F. Scott Fitzgerald     1) Whenever you feel like criticizing any one," he told me, "just remember that all the people in this world haven't had the advantages that you've had."     Why "told me" and not, "said to me"? I was taught "say" to attach to quote, and "tell" in another situation.       2) He didn't say any more but we've always been unusually communicative in a reserved way, and I understood that he meant a great deal more than that.     Why "say" and not "tell"?

I really get confused when to use say and when to use tell. Which is appropriate in the following:   What did he tell? / What did he say? What are you saying? / What are you telling?


I'm facing a problem to delegate an event on click on new element created in jQuery.  My HTML:
Add row
 <form class="form-horizontal" id="list-items">

                     Item number 1

                     ...

 </form>   My JS:  $('.panel-heading').click(function(){     if($(this).next('.panel-collapse').hasClass('in')) {         $(this).next('.panel-collapse').removeClass('in');     }     else {         $(this).next('.panel-collapse').addClass('in');     } });  $('#add').click(function() {     var newRow = $('.item').eq(0).clone();     $('#list-items').append(newRow); });   My problem is when a new element is create, I can't click it to open its content.  Could your please help me in it.  Thanks.

I have a bit of code where I am looping through all the select boxes on a page and binding a .hover event to them to do a bit of twiddling with their width on mouse on/off.  This happens on page ready and works just fine.  The problem I have is that any select boxes I add via Ajax or DOM after the initial loop won't have the event bound.  I have found this plugin (), but before I add another 5k to my pages with a plugin, I want to see if anyone knows a way to do this, either with jQuery directly or by another option.


Is there any diff. if I submit my site to google with www or without www?  Which is best way to submit from above?

After having read various articles on this site about WWW or Non-WWW website setup, ,  and , and after having setup a correct redirection rule in .Htaccess to at least eliminate duplicate contents (currently the non-www solution (e.g. http://example.com) I have a feeling that my site rank less since I changed this.   My confusion was strengthened by these two opponents:     &     Could the change of www.example.com >> http://example.com have a factual impact on ranking?  say either is better or worse. Are they holding information back?  I am confused fellow folks...  As much as I would like to separate facts from fiction, I am aware that not all the good valid information is written. Not on google webmaster site and perhaps not elsewhere. If so it seems out of date!  Does or does not a WWW domain impact SEO/rank better than its NON-WWW version? (Given that you have setup a proper redirect to avoid duplicates and go with one)


Let $f:\mathbb R\to\mathbb R$ $f$ is derivable in all of $\mathbb R$.      Let $\displaystyle\lim_{x\to\infty}(f(x)-f(-x))=0$      Show that there exists $x_0\in\mathbb R$ such that $f'(x_0)=0$.   From intuiton I see that $f$ is an even function because $f(x)=f(-x)$ so it can either be like for example $f(x)=x^2$ which has an extramum point where $f'(x_0)=0$ or $f(x)=c, \ c\in\mathbb R$ which is also an even function and the derivative is always 0.   I'm not really sure how to formally prove it.  Note: we can't use integrals.

Given $f:R \to R$, $f$ is differentiable on $R$ and $\lim_{x \to \infty}(f(x)-f(-x))=0$. I need to show that there is $x_0 \in R$ such that $f'(x_0)=0$  I am trying to prove it by contradiction .... so i assume there is no $x_0 \in R$ such that  $f'(x_0)=0$ this means this function is strictly monotonic because the derivative "respects" the mean value theorem so it cannot be negative and positive without passing a zero value ....  (from what i understand the derivative function of a continuous/differentiable functions isn't necessarily continuous but it still respect the mean value theorem i think it's called darboux's theorem )  now from $\lim_{x \to \infty}(f(x)-f(-x))=0$ ,we get $\lim_{x \to \infty}f(x)=\lim_{x \to \infty}f(-x)$  now the last step is the contradiction its very intuitive and even maybe obvious that we can't get $\lim_{x \to \infty}f(x)=\lim_{x \to \infty}f(-x)$ for strictly monotonic function but i cant think of a formal way to prove it .


Find all integer solutions for the equation $$x^2+7=2^n$$ where $n$ is a positive integer. Now as we can see that whenever $x$ is a solution of the equation $-x$ is also the solutions of the equation so we can assume that $x\geq 0$ Now writing the equation as $$x^2=2^n-2^3+1$$ and as $x$ is odd So we can write $x=2^mt+1$ such that $t$ is a positive integer and gcd$(t, 2)=1$ So for $n\geq 5$ our equation becomes $$2^{2m}t^2+2^{m+1}t+1=2^n-2^3+1$$ $$=>2^{m+1}t(2^{m-1}t+1)=2^3(2^{n-3}+1)$$ Now as gcd$(t, 2)=1$ So we get $m+1=3=>m=2$ and $$2^{n-3}-1=2^{m-1}t^2+t$$ $$=>2^{n-3}-1=2t^2+t$$ $$=>2^{n-3}-2t^2=t+1$$ $$=>2(2^{n-4}-t^2)=t+1$$ So we get $$2(2^{\frac{n-4}{2}}+t)(2^{\frac{n-4}{2}}-t)=t+1$$ Now $$t+2^{\frac{n-4}{2}}\geq t+1$$ So we get $2^{\frac{n-4}{2}}=1$ $=>n=4$ which is not possible as $n\geq 5$ So the given equation has no integer solutions for $n\geq 5$ Also $n=1, 2, $ does not give a solution But $n=3$ gives $x=-1$ and $x=1$ as the solution and $n=5$ gives $x=-5$ and $x=5$ as the solutions of the given equation Is this correct?

This came up while solving another ENT problem. I want to ask when is: $$2^n -7 \text{ where } n\geq 3$$ a perfect square? Specifically, I also wanted to know what would be the solutions when $n$ is odd? How should I solve this?  I can check that $n=3, 4, 7$ are solutions but cannot find more. As it is of the form $4k+1$, it doesn't help as well.


In earlier Ubuntu versions I would :  sudo apt-get install numlockx sudo sed -i 's|^exit 0.*$|# Numlock enable\n[ -x /usr/bin/numlockx ] \&\& numlockx on\n\nexit 0|' /etc/rc.local   But starting from version 16.10 there is no file rc.local, so how to I enable numlock in version 17.04 without desktop environment?  Update: I created rc.local file as described , then executed commands mentioned earlier and now numpad works when I connect over SSH. For it to work in VirtualBox I added  lines to rc.local:  # Turn Numlock on for the TTYs: for tty in /dev/tty[1-6]; do     /usr/bin/setleds -D +num < $tty done   And now everything works!

I am setting up quota on my Linode server running Ubuntu 16.10, and I get the following error      Cannot stat() mounted device /dev/root: No such file or directory   So to fix this, I reached  for the fix which is done by adding   ln -s /dev/xvda /dev/root /etc/init.d/quota restart   to the /etc/rc.local. But Ubuntu 16.10 doesn't uses rc.local anymore instead uses . What is the alternative for rc.local, How can I run the above commands on startup?  Also I enabled the service using systemctl enable rc-local.service but it didn't work for me. Any lead would be appreciated.


I have a problem with my router (Networking) and was wondering where would be a good place to ask my question? Obviously not on stackoverflow =).   Sorry this question is short.

Where can I ask questions regarding   Networking Cisco CCNA/CCNP/CCIE IP subnetting


Do we have a well defined mathematical expression denoting the size of a fundamental particle with no internal structure (electron for example) ? If we do, how does it fit in with the uncertainty principle ? And if we don't then what exactly do the experiments reveal claiming radius of electron is of the order $10^{-18} m$ or something like that ? Also in this particular case, does this mean that the probability of the electron being within that radius is 1 and zero outside ? A proper clarification would be very helpful.

I am wondering if the mass density profile $\rho(\vec{r})$ has been characterized for atomic particles such as quarks and electrons. I am currently taking an intro class in quantum mechanics, and I have run this question by several professors. It is my understanding from the viewpoint of quantum physics a particle's position is given by a probability density function $\Psi(\vec{r},t)$. I also understand that when books quote the "radius" of an electron they are typically referring to some approximate range into which an electron is "likely" to fall, say, one standard deviation from the expectation value of its position or maybe $10^{-15}$ meters.  However it is my impression that, in this viewpoint, wherever the particle "is" or even whether or not the particle "had" any position to begin with (via the Bell Inequalities), it is assumed that if it were (somehow) found, it would be a point mass. This has been verified by my professors and GSIs. I am wondering if its really true.  If the particle was truly a point mass then wherever it is, it would presumably have an infinite mass density. Wouldn't that make electrons and quarks indistinguishable from very tiny black holes? Is there any practical difference between saying that subatomic particles are black holes and that they are point masses? I am aware of such problems as Hawking Radiation although at the scales of the Schwarchild radius of an electron (back of the envelope calculation yields $\tilde{}10^{-57}$ meters), would it really make any more sense to use quantum mechanics as opposed to general relativity?  If anyone knows of an upper bound on the volume over which an electron/quark/gluon/anything else is distributed I would be interested to know. A quick Google Search has yielded nothing but the "classical" electron radius, which is not what I am referring to.  Thanks in advance; look forward to the responses.


I'm a bit confused with the variable scope of Python. Perhaps because of being used to the convention of C++, I always made some mistakes in variable scope of Python. For example:  in C++:    int main(){     int i = 3;     for (int j = 0; j <= 3; ++j){         i += 1;     }     cout << "i = " << i << endl;     cout << "j = " << j << endl; //Error, out of 'for' scoping.     return 0; }   But in Python:    i = 3 for j in range(1,4):     i += 1 print j               # j = 3, nothing wrong for i in range(5,7):     j += 1 print i               # i = 6, changed by operation in for loop   This is just a simple example, and I'm not going to list other differences. Could anyone please give a detailed explanation of their differences in scoping.

What exactly are the Python scoping rules?  If I have some code:  code1 class Foo:    code2    def spam.....       code3       for code4..:        code5        x()   Where is x found?  Some possible choices include the list below:   In the enclosing source file In the class namespace In the function definition In the for loop index variable Inside the for loop   Also there is the context during execution, when the function spam is passed somewhere else. And maybe  pass a bit differently?  There must be a simple reference or algorithm somewhere.  It's a confusing world for intermediate Python programmers.


Let $G$ be a finite abelian group and $x$ be an element of maximal order. Can $G$ be written as an internal direct product $G = \langle x\rangle\times K$ for some normal subgroup $K$? To me it seems like a trivial intersection of the subgroups may not always hold.

If $g\in G$ is an element of maximal order in a finite abelian group $G$ then exists $H\leq G$ such that $G=\left<g\right>\oplus H$  Attempt: Using fundamental theorem I know that $G=C_{n_1}\times\cdots\times C_{n_k}$ where $n_i|n_{i+1}$. With some work I proved $|\left<g\right>|=n_k$, so $C_{n_k}\cong \left<g\right>$. Then $G\cong H\times \left<g\right>$, but this is not an equality.


I need to plot these values against time. Y are prices of an stock index and X are given in dates. When I highlight both the columns and insert line graph. The graph turns out wrong. Not sure why. Need some guidance.  Y 55.86 56.4831183 56.79287172 56.15020358 56.54651172 57.17813626 57.74751614 57.99484875 57.81842842 57.82525099  X 19620702 19620703 19620705 19620706 19620709 19620710 19620711 19620712 19620713 19620716   The graph looks like this:

In Microsoft Excel 2010, I'm trying to draw a line graph with three different lines.  I've got the graph looking the way I want, with one exception: Excel is treating my X-axis column like text labels, rather than data points along the X-axis.  As a result, the gap between 0-85, 100-120, and 300-750 are all the same.  How can I get Excel to treat these as numbers and space them accordingly along the X-axis?  Here is what I have so far:    In the Format Axis dialog box for the Horizontal Axis, I've got the format selected as "Number" with 0 decimal places:    And in the Axis Options tab, I've got the "Interval between labels" selected as "Automatic," and the "Axis Type" selected as "Automatically select based on data":


Firstly excuse my english, I have one question. Protected modifier expose to all classes in the same package and to all subclasses in different packages. Isn't it useless? when you have it in your package with class with main method it act like public, and if you have it in different package with all subclasses you don't have to use any modifier becauce any modifier expose only to package, am i right?

In Java, are there clear rules on when to use each of access modifiers, namely the default (package private), public, protected and private, while making class and interface and dealing with inheritance?


I had downloaded Unity 8 on Ubuntu 16.04 LTS and after I log into it, only a black screen shows up, when I hit Ctrl + Alt + F1, some sort of command line opens, and there I type my username and pass and then type startx, then only my desktop wallpaper can be seen, without any status bar, and the cursor is a cross-hair, a can use terminal, I can make folders and open them but there is nothing except those windows, no launcher and no status bar.  Please help! I installed Ubuntu for unity 8!

When I login, nothing happens.   I am presented with my desktop wallpaper.    No Dash, no Launcher, nothing.


Are there any good Linux applications for drawing electro fittings? I haven't been able to find any...Usually these fittings are drawn in the Autocad software.

Just that. By good I mean something at the level of SolidWorks, AutoCAD, or similar. This is a complete limitation for me (and many others) to use Ubuntu.


Hey i am searching for a program that can add a password too a folder with just right mouse click i am really lazy i already know there are lots of encryptions program but which one integrate well with the ubuntu interface

Is there a way to encrypt a folder, which is not in Home (/home/user/) but even in a different partition, so only my user can access/read contained files?  Alternatively, I would like to understand if it is possible to turn a complete ext4 partition into an encrypted volume, which would be mounted at user login.  If possible, I would like to make the change without reinstalling Ubuntu.  My PC has (mount output):  /dev/sda1 on / type ext4 (rw,errors=remount-ro) /dev/sda3 on /home type ext4 (rw) /dev/sda4 on /home/igor/Personale type ext4 (rw)   sda4 is the partition containing folders I would like to protect.


I would like detail instructions on How to Install GUI on Ubuntu server 15.10

Trying to run a Ubuntu server for the first time... But everything is in a terminal. Is there a way to switch to a GUI?


Using myscript mydir/* I don't understand why bash is processing only the first element with the code below. #!/bin/bash  files="$1"  for f in "$files"; do   echo "Processing $f" done  What do I miss so that I can process a list of files given as an argument to the script?

I have a complex command that I'd like to make a shell/bash script of.  I can write it in terms of $1 easily:  foo $1 args -o $1.ext   I want to be able to pass multiple input names to the script. What's the right way to do it?    And, of course, I want to handle filenames with spaces in them.


So I need to solve $\begin{pmatrix} 1 &2\\  1 &2 \end{pmatrix}X=\begin{pmatrix} -1 & -5\\  -1 &-5 \end{pmatrix}$. I took $X=\begin{pmatrix} a &b \\   c& d \end{pmatrix}$ and I got that $a+2c=-1$ and $b+2d=-5$. What do I do now or do you have any method to solve this and find values for $a,b,c,d$?  P.S. Determinants are $0$ so you can not use the inverse.

I need to find $X$ from   $$\begin{pmatrix} 1 & 2\\  -3 &-6  \end{pmatrix} X \begin{pmatrix} 1 &2 \\  -1 &-2  \end{pmatrix}=\begin{pmatrix} 2 &4 \\  -6 & -12 \end{pmatrix}$$  I wrote $X$ as   $$X=\begin{pmatrix} a & b\\  c &d  \end{pmatrix}$$  and I got $a+2c-b-2d=2$ but I do not know what to do next. Please help.


def f(L):  if L == []:   return 0  return (f(L[0]) if type (L[0]) == list else 1) + f(L[1:])  I'm having a bit of trouble determining big O for recursive functions. I have a feeling this function is O(n*m) where n is the length of the list L and m is the length of list elements in list L. Am I correct or is this function just O(n)?

Most people with a degree in CS will certainly know what . It helps us to measure how well an algorithm scales.   But I'm curious, how do you calculate or approximate the complexity of your algorithms?


Edit 2: Tried to make the question clearer by adding a graph  Edit: Please note: This is not a duplicate of another question I asked earlier (). The difference being that in the other question, $x$ and $y$ are correlated and hence their distributions are not independent -- i.e. $f_{X,Y}\neq f_Xf_Y$. Here, I am assuming that the two variables are independently distributed, but that the probability that I want to compute (i.e. the upper bounds of the interval) is a function of the other variable $a=u(Y), \ \ b=v(X)$.   I'm new to the site so please accept my apologies for asking anything to obvious.  I've got two independent continuous random variables $X$ and $Y$ with pdf's $f_X$ and $f_Y$, such that the joint density function is given by $f_{X,Y}$ and the joint cdf by $F_{X,Y}$.  I am looking for the joint probability $Prob(X \leq a,Y \geq b)$, where each variables' cut-off point is a function of the other variable, i.e. $a=u(Y)$ and $b=v(X)$. Essentially I need to integrate where the interval is dependent on the random variables:  $$\int^a\int_b f_{X,Y}(x,y)\,dy\,dx$$  Graphically, I am looking for the blue area:    which (I believe) should come down to $F_{X,Y} (a,y)-F_{X,Y} (a,b)$, but $a$ and $b$ depend on $X$ and $Y$, respectively.  Is there a way to find an analytical solution to this problem? Many thanks in advance even for a small hint. Much appreciated!

I've got two random variables, $x$ and $y$, where $x=u(y)$ and $y=v(x)$. How do I find the joint density of the two variables?   The eventual purpose is to find the integral  $\int^a\int^b f(x,y) dydx$,  where $f(.)$ is said joint density function.  This question is related () but I'm still a bit confused by the answer. I am indeed effectively looking for $Prob(x \leq a, y \leq b)$ but don't understand how I can get there without knowing the PDF first.  Any advice is much appreciated. Thanks a lot in advance!


Given an element $a\in\mathcal A$ which is self-adjoint, it is easy to prove that $\|a^2\|=\|a\|^2$, from $\|a^2\|=\|aa^*\|=\|a\|^2$. This can be generalised to say that $\|a^{2^k}\|=\|a\|^{2^k}$.  What about the other powers? Can you have for example $\|a^3\|\neq \|a\|^3$ for a self-adjoint $a$? If so, what is an example of an operator that does this?  This doesn't seem to be possible in a finite-dimensional Hilbert space, as if $A$ is a self-adjoint operator then $A^n=\sum_k \lambda_k^n u_k u_k^*$ with $\lambda_k\in\mathbb R$ its eigenvalues, and thus $$\|A^n\|=\max\{\lambda_k^n\}=(\max\lambda_k)^n=\|A\|^n.$$

Does anyone have a reference for the fact that if A is a normal operator on a Hilbert space the $\|A^n\|=\|A\|^n$? I have managed to prove this fact using a hint on another question, but I need an actual bibliographical reference, please help.


I have 64-bit Ubuntu and Eclipse 64-bit for an older project. In 32-bit I tried to run it, but it doesn't work (swt)... so I decided to download a tarball of Eclipse 32-bit (with JVM 32-bit integrated). All fine, but so far I cannot seem to run it. Do you have any ideas?    4 drwxrwsr-x  9 wouter wouter   4096 Feb 16  2012 .   4 drwxr-xr-x  6 wouter wouter   4096 Mai 20 07:50 ..   4 drwxrwsr-x  2 wouter wouter   4096 Feb 16  2012 about_files  20 -rw-rw-r--  1 wouter wouter  18909 Feb  8  2012 about.html  92 -rw-rw-r--  1 wouter wouter  94179 Feb 16  2012 artifacts.xml   4 drwxrwsr-x  4 wouter wouter   4096 Feb 16  2012 configuration   4 drwxrwsr-x  2 wouter wouter   4096 Feb 16  2012 dropins  64 -rwxr-xr-x  1 wouter wouter  62814 Feb  8  2012 eclipse   4 -rw-rw-r--  1 wouter wouter    408 Feb 16  2012 eclipse.ini   4 -rw-rw-r--  1 wouter wouter     59 Feb  8  2012 .eclipseproduct  20 -rw-rw-r--  1 wouter wouter  16536 Feb  8  2012 epl-v10.html   4 drwxrwsr-x 38 wouter wouter   4096 Feb 16  2012 features  12 -rw-rw-r--  1 wouter wouter   9022 Feb  8  2012 icon.xpm 260 -rwxr-xr-x  1 wouter wouter 266168 Feb  8  2012 libcairo-swt.so  12 -rw-rw-r--  1 wouter wouter   8951 Feb  8  2012 notice.html   4 drwxrwsr-x  5 wouter wouter   4096 Feb 16  2012 p2  40 drwxrwsr-x 22 wouter wouter  36864 Feb 16  2012 plugins   4 drwxrwsr-x  2 wouter wouter   4096 Feb 16  2012 readme wouter@laptop-wouter:~/Downloads/eclipse$ ./eclipse bash: ./eclipse: No such file or directory wouter@laptop-wouter:~/Downloads/eclipse$ sudo ./eclipse sudo: unable to execute ./eclipse: No such file or directory

I installed Ubuntu 14.04 and the current Android development SDK, which contains 32-bit executables. I found that I cannot run those 32-bit binaries. Trying to start them from bash gives me an error: $ ./adb bash: ./adb: No such file or directory  It is there though: $ ls -al ./adb -rwxrwxrwx 1 thomas thomas 1231255 Jan 17 13:31 ./adb $ file ./adb ./adb: ELF 32-bit LSB  executable, Intel 80386, version 1 (SYSV), dynamically linked (uses shared libs), for GNU/Linux 2.6.8, not stripped.   Same symptom for all the other 32-bit tools in the Android SDK. In olden days one could just install 32-bit libraries on 64-bit Ubuntu to get 32-bit support, but that does not seem to work anymore. How do I run 32-bit apps on a 64-bit Ubuntu distribution?


Various people have advocated centering independent variables in regression, on the grounds that the intercept then refers to a sensible point (the mean of each IV) rather than the often impossible case that all the IVs are 0.  But does this really help?  First, the intercept is often not of interest.  Second, the mean of the variables depends on the particular data set.  Third, that means that, if you want to interpret the intercept, you need to know the mean of each IV.  So, I'd say that this reason for centering is not a good one. (There are some other reasons for centering which I am not discussing here).  Am I missing something?

In some literature, I have read that a regression with multiple explanatory variables, if in different units, needed to be standardized.  (Standardizing consists in subtracting the mean and dividing by the standard deviation.)  In which other cases do I need to standardize my data?  Are there cases in which I should only center my data (i.e., without dividing by standard deviation)?


And I’m back with more fontspec trouble. Recently, I asked a question about how to access a particular character variant using fontspec (). ’s solution — to put a newer version of the font in my local texmf tree then call mktexlsr and luaotfload-tool -u -f — worked wonderfully for a time, and then broke later the same day.  Now I am unable to load any OpenType features, not even small caps. Here’s a minimal example:    \documentclass{article} \usepackage{fontspec} \setmainfont{Junicode}   \addfontfeatures{      Script={Latin},     Numbers={OldStyleOff, Proportional}, }  \begin{document}     1. a/b \addfontfeatures{StylisticSet={10},Numbers={Lowercase,Proportional}}     2. a/b      3. \textsc{a/b} \end{document}   When I ask for the same features with another software (I think MS Word generates its own small caps, so I’m using Publisher), everything is fine:     Similar problems persist even with system fonts e.g. Cambria or Candara.  I don’t know whether it’s useful information or not, but just in case, the log file flags up the following warnings,  luaotfload | cache : Lookup cache loaded from C:/Users/MyName/AppData/Local/ MiKTeX/2.9/luatex-cache/generic/names/luaotfload-lookup-cache.luc. luaotfload | aux : no font with id -1 luaotfload | aux : no font with id -1 luaotfload | aux : no font with id -1 luaotfload | aux : no font with id -1  Package fontspec Info: Font family 'Junicode(0)' created for font 'Junicode' (fontspec)             with options [Ligatures=TeX]. (fontspec)               (fontspec)              This font family consists of the following NFSS (fontspec)             series/shapes: (fontspec)               (fontspec)             - 'normal' (m/n) with NFSS spec.: (fontspec)             <->"Junicode:mode=node;script=latn;language=DFLT;+tlig;" (fontspec)             - 'small caps'  (m/sc) with NFSS spec.:  (fontspec)             - 'bold' (bx/n) with NFSS spec.: (fontspec)             <->"Junicode/B:mode=node;script=latn;language=DFLT;+tlig; " (fontspec)             - 'bold small caps'  (bx/sc) with NFSS spec.:  (fontspec)             - 'italic' (m/it) with NFSS spec.: (fontspec)             <->"Junicode/I:mode=node;script=latn;language=DFLT;+tlig; " (fontspec)             - 'italic small caps'  (m/itsc) with NFSS spec.:  (fontspec)             - 'bold italic' (bx/it) with NFSS spec.: (fontspec)             <->"Junicode/BI:mode=node;script=latn;language=DFLT;+tlig ;" (fontspec)             - 'bold italic small caps'  (bx/itsc) with NFSS spec.:   LaTeX Info: Redefining \rmfamily on input line 37. luaotfload | aux : no font with id -1  Package fontspec Warning: Font "Junicode" does not contain requested Script (fontspec)                "Latin".   Package fontspec Warning: OpenType feature 'Numbers=LowercaseOff' (onum) not (fontspec)                available for font 'Junicode' with script '' and (fontspec)                language 'Default'   as well as a further number of the type below.  Package fontspec Warning: OpenType feature 'Variant=10' (ss10) not available (fontspec)                for font 'Junicode' with script 'CustomDefault' and (fontspec)                language 'Default'.   I’m really baffled here, especially since the problem appears to be restricted to my machine. Does anyone know what could be going on?  Edit: This is a known issue with luatex 1.10.1 in MiKTeX. See  and .

I need to use the font Constantia and thus compile my document with LuaLaTeX using \usepackage{fontspec}(Editor is TeXStudio). As I do not like the OldStyle numbers, I use \setmainfont[Numbers=Lining]{Constantia}. So far, this worked perfectly, but since I updated MikTeX yesterday I get the error:   OpenType feature 'Numbers=Uppercase' (lnum) not(fontspec) available for font 'Constantia' with script(fontspec) 'CustomDefault' and language 'Default'.   Here is a MWE:  \documentclass{scrreprt} \usepackage{fontspec} \setmainfont[Numbers=Lining]{Constantia}  \begin{document}  1234567890  \end{document}   It produces the following output:    The font itself can't be the problem, as I tested it in Word where I can change the behavior:    Thank you in advance for your help.


I often hear people use the word "Ecology" when i think they mean "biology." This got me wondering: are the words ever interchangeable, or are these people really just that frequently using the wrong word?   My understanding is biology is the broader study of life while Ecology is the more specialized study of life interacting with other stuff (life + earth).

What precisely is ecology? How does it differ from biology? Because I never studied biology after high school, please explain as if I were 10 years old. I only know that ecology is a subset of biology I tried some dictionaries but they  didn't  adequately discriminate. I tried to find an explanation from a scientist: the following appears to claim that only ecology concerns some organism's external interactions with other entities? But how? Biology must also? For example, suppose that someone studies prions' interactions with humans, and not just prions. Then this is biology, not ecology? : by  ,   So what makes us fully fledged marine ecologist different from our biologist counterparts?  Well, I think that marine ecology is even cooler than marine biology because as marine ecologists we link what we know about the biology of a given species with other plants/animals and the environment as well. [...] If we were splitting hairs, ecology is technically a form of biology, but I felt the need to write this post given how passionately I see some researchers stating that they are in one camp or another. [...]  But as an ecologist (albeit a biased one!) what gets me excited isn’t just finding out how the amazing plants and animals we find in the ocean work, but how they interact with each other and their environment, explaining why we see certain species in some places and not others!


I still have not grasped the intuitive reason for adding a coefficient for each degree in denominator when doing partial fraction integration. For example  $\int_a^b  \frac {R(x)}{(x+2)^3} $ , we need to do  $\frac {A}{(x+2)^1} + \frac {B}{(x+2)^2} + \frac {C}{(x+2)^3}$.   Why?

1) First, why are powers of linear factors repeated?  For example, $(x+1)^2$ gets $\frac{A}{(x+1)}$ and $\frac{B}{(x+1)^2}$   2) Why does a quad factor like $x^2+1$ get a term $\frac{Cx+d}{x^2+1}$  Looking for an example that shows WHY you need a linear term above the quadratic, and WHY you need to repeat the factors.


My Blender started acting wierd after I bought a brand new graphics card, because the old one fried. The geometry in viewport is all glitched, but what is more wierd when I look at it through camera or render it, everything is fine. Here are examples, in the first picture I have enabled backface culling and in the second one I deleted everything, and created brand new cube also I have disabled backface culling. For some reason backface culling reduces the flickering but it is still present.      The graphics card is Radeon RX 580 with 8GB of memory if it helps in any way.  I have tried reinstalling blender, I made sure that my graphic card's drivers are up to date. I tried every method from Window Draw Method in user settings.The card's fine, I don't see any glitches anywhere else just in blender viewport. I would appriciate any suggestions cause I looked through various forums and couldn't find anyone with similiar problem. Thanks in advance.

I have recently started using blender and one of the models I'm working on has dark shadows along edges. I started this model from scratch. I can't remember them being there when I first started the model, but I had trouble joining areas together and think I've pressed something I shouldn't have. However, there are so many options I'm not sure what I did.  Here is an image of what I mean   The one on the left has the shadow. As a test I started a new model, which is on the right in the image, and as you can see it doesn't have any shadows.  Also, occluded vertices partially show through the model. Occlusion doesn't work properly.   In orthogonal view small darkened triangles appear along the the edges.    I don't really want to start the model again from scratch so any ideas on how to remove this shadow would be great. Thanks.


I have windows Vista and XP I downloaded Ubuntu 21.04 and Ubuntu 20.04.2.0 LTS burnt both to dvd but could not find a front end to install on my computer. What do I need to do?

I would like to see a full how-to guide on how to install Ubuntu.


As you may know, OpenVPN is vulnerable to the heartbleed attack. However, I can't find any guide online on how to fix it. The only source I've found is this:    Is just doing (in Ubuntu)   apt-get update; apt-get upgrade; apt-get dist-upgrade  enough to make sure that my OpenVPN is safe? I can confirm i have this version of openSSL:  # dpkg-query -l 'openssl' ii  openssl                                   1.0.1-4ubuntu5.12                         Secure Socket Layer (SSL) binary and related cryptographic tools   Thanks

Is OpenVPN UDP vulnerable to heartbleed?   I need to decide if I'm going to rebuild some servers, but they are very carefully firewalled; 1194/TCP is one of the firewalled ports (yay whitelist!).   1194/UDP is used (mission critical).


I'm working on the following problem:     Prove that $\mathbb{Z}$ and $\mathbb{Q}$ are not isomorphic as groups.   Here is my attempt at a solution:  If $\mathbb{Z} \cong \mathbb{Q}$, then there must exist a bijective homomorphism $\varphi: \mathbb{Z} \to \mathbb{Q}$. Consider $\varphi(x) = x$. Clearly, this is a homomorphism as it is the identity map. Moreover, it is also clearly injective. However, it fails to be surjective since there exist elements of $\mathbb{Q}$ that are not mapped to by $\varphi$ (like $3/2$ or $1/4$). Hence, since $\varphi$ is an injective homomorphism, but not surjective, we see that there cannot exist a bijection between $\mathbb{Z}$ and $\mathbb{Q}$. Thus, $\mathbb{Z} \not \cong \mathbb{Q}$.  Could anyone critique this solution? Am I on the right path?

Is my proof below correct? What specific property of rationals did I exploit in my proof? It looks like the property I exploited is the following: Given any positive rational, I can always write it as sum of arbitrary number of positive rationals, whereas given any positive integer I cannot write it as a sum of arbitrary number of positive integers. Has it got to do with the fact that $\mathbb{Q}$ is a field?       Problem Prove that the additive groups $\mathbb{Z}$ and $\mathbb{Q}$ are not isomorphic.   Solution Let there exist an isomorphism between $\mathbb{Z}$ and $\mathbb{Q}$. Now consider the element $1_{\mathbb{Q}}$. We then have $\phi(1_{\mathbb{Q}}) = z \in \mathbb{Z}$. Since $\phi$ has to be a bijection, $z$ cannot be zero, since $\phi(0) = 0$.  Now consider the element $\left(\dfrac1{z+1}\right)_{\mathbb{Q}}$. We now have $$z = \phi(1_{\mathbb{Q}}) = \phi\left(\underbrace{\left(\dfrac1{z+1}\right)_{\mathbb{Q}} + \left(\dfrac1{z+1}\right)_{\mathbb{Q}} + \cdots + \left(\dfrac1{z+1}\right)_{\mathbb{Q}}}_{z+1 \text{ times }} \right) = (z+1) \phi\left(\left(\dfrac1{z+1}\right)_{\mathbb{Q}}\right)$$ However, there is no element in $y \in \mathbb{Z}$ such that $(z+1)y = z$.    First update  Actually I realize that I complicated it unnecessarily. Instead, we can do like this. Since $\phi$ is an isomorphism, we have $\phi(q_{\mathbb{Q}}) = 1_{\mathbb{Z}}$ for some $q \in Q$. However, $$\phi(q) = \phi(q/2+q/2) = 2\phi(q/2)$$ And there is no $y \in Z$, such that $2y=1$. Hence, $\phi(q/2)$ remains unmapped.    Thanks