I have this code in mssql:  SELECT     t1.Id,     t2.Id,     t1.QuantityIn,     t1.PriceIn,     t2.QuantityOut,      (If (t2.QuantityOut - t1.QuantityIn)=0          THEN t2.QuantityOut      Else t2.QuantityOut - t1.QuantityIn ) AS Quant,      t2.PriceOut  FROM t1  LEFT JOIN t2 ON t2.Id = t1.Id   In software MsSql Server Management Studio error is      Incorrect syntax near the keyword 'If'.   What is the correct syntax for 'if' in my case?  Thank you!

How do I perform an IF...THEN in an SQL SELECT statement?  For example:  SELECT IF(Obsolete = 'N' OR InStock = 'Y' ? 1 : 0) AS Saleable, * FROM Product


I had Ubuntu 16 and Windows 10 installed and coexisting peacefully. On boot, the past and wise me had configured the computer so that it would give me a choice on whether I would like to boot Ubuntu or Windows, on a timer that would start Ubuntu by default if 30 seconds without input passed. But the last Windows 10 update has disabled the possibility of booting Ubuntu altogether. What I have tried:  I entered the power options on Windows 10 and disabled fast boot I have shutdown the computer while pressing shift, then pressed F2 on boot to access the BIOS menu. There I have checked that indeed my first boot option is Ubuntu, and I have also tried disabling a fast boot option there was there in the BIOS menu.  I do not know what else to try. How can I return the boot configuration to its behaviour pre update?  UPDATE:  I have tried running bcdedit /set {bootmgr} path \EFI\ubuntu\grubx64.efi from the console with admin rights. When I load, now I see a scary screen saying  Secure Boot Violation. Invalid signature detected. Check secure Boot Policy in setup   I have also tried booting from a live USB. Got into BIOS menu using F2 on boot, then when I launch the boot override... I get the same scary message as above.

After I ran Windows 10 update this afternoon my partition table broke... I had dual boot with Windows 10 and Ubuntu 14 with Grub as the boot loader. The error that came up was "Error no such partition, Entering rescue mode... grub rescue>". I googled it,  about the boot-repair ISO, installed it on a USB, ran the repair, got this report, but still no luck:    Now the boot skips Grub entirely and goes to Windows boot manager which fails with "The boot configuration data for your PC is missing or contains errors". So now instead of dual boot I have zero boot. Thanks Microsoft.  Anyway can you guys help me interpret the disk info in the pastebin link? I don't remember my partition configuration but I believe Ubunut had slightlty less disk space than Windows. Questions I have:   Is the Ubuntu partition still there? Could it be the one named "Extended"? (sda4) Where would GRUB be? Gone? Can it be reinstalled? how?   I don't really care about the Windows partition anymore, but it would be nice to rescue Ubuntu.


I remember seeing this movie, it could even have been a TV series, in the early 1980s but the movie, or TV series, was clearly older probably '70s.  It seemed to be European.  I can't remember the name. The plot was about a computer that becomes sentient, and starts controlling humans by implanting a chip in the backs of their heads.  It aimed to control all of humanity.  Some people are aware of this and try to stop it.

I am trying to recall the name of TV-series that was aired in the 70s (possibly only in selected European countries?). IIRC it was a French production. The bad guy was using some kind of mind control devices. He was gradually getting more and more people as followers to his pacifist ideology (it was the cold war era, and pacifism might have struck a chord even without mind control).  His modus operandi was to send a dozen or so (mind-controlled) cronies to surround a new victim. They would form a square around the helpless target, forcing him to walk into a building, where mind control devices were surgically installed.  The protagonists were trying to organize a resistance movement. IIRC they failed, as the bad guy had good intelligence about their plans.


In hybrid encrytion, I still see that some site's use RSA in their https connection, so now I wonder, why do they not use ECC instead of RSA, ECC requires less computational power and encrypt's and decrypt's faster (atleast that's what I read). I know that there have been smiliar question's about this but none of these answered specfically why rsa is still used. The only two reasons what I can think of is that some hardware may not support it or that there are some web administrators that are being to lazy to upgrade, but im not sure if that is the case. I hope someone could explain this to me and shed some light on it :) .

I recently ran across elliptic curve crypto-systems:    (Brown University)  (Wikipedia)  (IEEE)  (RSA.com)   It seemed to me to be great alternative to RSA as the de-facto cryptosystems to be used in banking and financial systems and in the public key infrastructure for certificates, but is not used! If someone can explain why this is not done, it would be very helpful. A comparison between traditional RSA and an elliptic curve cryptology would be helpful.  To begin with:  Advantage of RSA:   Well established.   Advantages of elliptic curve:   Shorter keys are as strong as long key for RSA (see the IEEE paper) Low on CPU consumption. Low on memory usage.


I wanted to install wine, but then it gave me this message:  "To install wine, this package has to be removed:  Nvida opencl driver and icd loader library"  can anyone help me with this? and how can I remove this package?

I am looking for a step by step instruction to guide me in the ways of installing, configuring and debugging many of the issues new users have when dealing with Wine in Ubuntu.  What is the recommended way of installing Wine, some of the key issues that it has and how to solve them?  If I have a specific problem with an App in Wine, how do I go about solving it? What are the recommended steps to ensure that I can fix a problem related to an app I wish to use?


I am writing a document in English that contains words and passages in ancient greek. XeLaTeX seems ideal to this purpose because one doesn't need to mark the text. Loading polyglossia and choosing English helps with the hyphenation.   The default font does not contain Greek letters, so I use fontspec and load CMU Serif as it is my preferred font.   However, with these settings I get the upper line:   but what I want is the second line. Please note, how they differ in the characters β (beta) and λ (lambda).  I do get the second line when adding the command   \setmainfont[Script=Greek]{CMU Serif}   to the preamble. I don't understand what the difference is: my choice of font is CMU Serif in any case. Additionaly, is this the correct way to get my preferred result?  Here's a MWE:  % !TEX TS-program = XeLaTeX \documentclass[a4paper,12pt]{article}  % font setup \usepackage{fontspec} \setmainfont{CMU Serif} \setsansfont{CMU Sans Serif} \setmonofont{CMU Typewriter Text} \setmainfont[Script=Greek]{CMU Serif}  \usepackage{polyglossia} \setdefaultlanguage{english} \setotherlanguage[variant=ancient]{greek}  \begin{document} This is my text! This is my Greek: ἀλλὰ τοῦτο μὲν ἔσβεσεν. \end{document}

I've tried to use Computer Modern Unicode (version 0.7.0) with XeLaTeX to write greek letters.  However, using the following code in TeXLive 2012 or 2014, the shapes of "βγλθωχ" seem different with those provided in the document   \documentclass{article} \usepackage{fontspec} \setmainfont{CMU Serif} \begin{document} βγλθωχ \end{document}     Bottom: greek letters provided in the document  But I got the shapes same with those in the document, using the following code with polyglossia.  \documentclass{article} \usepackage{polyglossia} \setmainlanguage{greek} \setmainfont{CMU Serif} \begin{document} βγλθωχ \end{document}   I cannot figure what I am doing wrong.


I have been advised to download cuda and I downloaded nvidia cuda version 6.5,yet the cycle compute showed none. what should I do?  Help me please.  I'm using windows 7  im trying to enable graphics card nvidia geforce 320

I want to enable GPU rendering, but there is no option in User Preferences > System:    Why is this? How can I get cycles to render using my GPU?


I am fetching some results from three different tables Orders, OrderDetails and Customers. I am trying to combine two fields OrderDetails.ProductCode and OrderDetails.Quantity into one and group the results by OrderID.   What I am getting is  OrderID ProductCode Quantity Email 1       A           2        john@gmail.com 1       D           1        john@gmail.com 2       E           5        warren@gmail.com 3       B           3        david@gmail.com 3       F           1        david@gmail.com   This is what I want  OrderID ProductCode_Quantity Email 1       A_2, D_1             john@gmail.com 2       E_5,                 warren@gmail.com 3       B_3, F_1             david@gmail.com   My current query is  SELECT Orders.OrderID, OrderDetails.ProductCode, OrderDetails.Quantity, Customers.EmailAddress FROM Orders JOIN OrderDetails ON Orders.OrderID = OrderDetails.OrderID JOIN Customers ON Orders.CustomerID = Customers.CustomerID

I'm trying to migrate a MySQL-based app over to Microsoft SQL Server 2005 (not by choice, but that's life).  In the original app, we used almost entirely ANSI-SQL compliant statements, with one significant exception -- we used MySQL's group_concat function fairly frequently.  group_concat, by the way, does this: given a table of, say, employee names and projects...  SELECT empName, projID FROM project_members;   returns:  ANDY   |  A100 ANDY   |  B391 ANDY   |  X010 TOM    |  A100 TOM    |  A510   ... and here's what you get with group_concat:  SELECT      empName, group_concat(projID SEPARATOR ' / ')  FROM      project_members  GROUP BY      empName;   returns:  ANDY   |  A100 / B391 / X010 TOM    |  A100 / A510   So what I'd like to know is: Is it possible to write, say, a user-defined function in SQL Server which emulates the functionality of group_concat?   I have almost no experience using UDFs, stored procedures, or anything like that, just straight-up SQL, so please err on the side of too much explanation :)


I am encountering a problem while installing the wireless driver in my ubuntu 20.04 version also facing the same issue with (Ubuntu 18.04).   I have gone through .  These are the steps which I am following:  git clone https://github.com/lwfinger/rtlwifi_new.git cd rtlwifi_new git checkout extended sudo make install sudo modprobe -r rtl8723de sudo modprobe rtl8723de   But while executing the the sudo make install, I am getting this error:  make -C /lib/modules/5.4.0-28-generic/build M=/home/username/rtlwifi_new modules make[1]: Entering directory '/usr/src/linux-headers-5.4.0-28-generic'   CC [M]  /home/username/rtlwifi_new/rc.o /home/username/rtlwifi_new/rc.c:336:11: error: initialization of ‘void * (*)(struct ieee80211_hw *, struct dentry *)’ from incompatible pointer type ‘void * (*)(struct ieee80211_hw *)’ [-Werror=incompatible-pointer-types]   336 |  .alloc = rtl_rate_alloc,       |           ^~~~~~~~~~~~~~ /home/username/rtlwifi_new/rc.c:336:11: note: (near initialization for ‘rtl_rate_ops.alloc’) cc1: some warnings being treated as errors make[2]: *** [scripts/Makefile.build:275: /home/username/rtlwifi_new/rc.o] Error 1 make[1]: *** [Makefile:1719: /home/username/rtlwifi_new] Error 2 make[1]: Leaving directory '/usr/src/linux-headers-5.4.0-28-generic' make: *** [Makefile:85: all] Error 2    The output of lspci -knn | grep Net -A3; rfkill list:  08:00.0 Network controller [0280]: Broadcom Inc. and subsidiaries BCM43142 802.11b/g/n [14e4:4365] (rev 01)     DeviceName: Broadcom BCM43142 802.11bgn 1x1 WiFi Adapter + BT 4.0 combo adapter     Subsystem: Hewlett-Packard Company BCM43142 802.11b/g/n [103c:2230]     Kernel driver in use: wl 0: phy0: Wireless LAN     Soft blocked: no     Hard blocked: no 1: brcmwl-0: Wireless LAN     Soft blocked: no     Hard blocked: no 2: hci0: Bluetooth     Soft blocked: no     Hard blocked: no

I'm having serious problems installing the Broadcom drivers for Ubuntu. It worked perfectly on my previous version, but now, it is impossible.   What are the steps to install Broadcom wireless drivers for a BCM43xx card?  I'm a user with no advance knowledge in Linux, so I would need clear explanations on how to make, compile, etc.    lspci -vnn | grep Network showed:   Broadcom Corporation BCM4322 802.11a/b/g/n Wireless LAN Controller [14e4:432b]      iwconfig showed:  lo        no wireless extensions. eth0      no wireless extensions.   NOTE: Answer below is updated every time new information is added and confirmed working.


I'm using a wooden pickaxe, and that might be the problem, I can mine coal and flint, but nothing else. Can someone help please?  (edit) I was using nothing to mine down a staircase, when I stumbled upon a cave, keep in mind this is in single player. And I cannot mine the diamonds, the redstone, the gold, nothing. it just doesn't give it to me. can someone please help me understand why this is happening? I just can't get it to work. I want my gold...

I am on Peaceful mode, and I am using a Wooden Pickaxe. Whenever I mine Iron Ore, it just disappears. Am I doing something wrong?


Please help as I am getting null pointer exception in the method onEndCall, Please refer to the below code  public class GET_END_DETAILS extends Thread implements EndCallInterface  {  public String strCallId= ""; public String strVxmlServerIp= ""; public String strCli= ""; public String strDnis= ""; public String strCallStDateTime=""; public String strCallEndDateTime="";  public Connection conn;  public CallableStatement SQLStm; //public ResultSet rs=null; public int res;  public CallEndAPI callEndAPI;  Thread t;  public void onEndCall(CallEndAPI callEndAPI) throws AudiumException{     try{   //          SETTING CALL END DATE TIME          DateFormat dateFormat = new SimpleDateFormat("yyyy/MM/dd HH:mm:ss");//24hrs         Date date = new Date();         strCallEndDateTime=dateFormat.format(date);          callEndAPI.addToLog("Call End Time : ", strCallEndDateTime);          callEndAPI.setSessionData("S_CALL_ENDDATETIME", strCallEndDateTime);          strCallId= callEndAPI.getSessionData("CallID").toString();          callEndAPI.addToLog("CallID : ", strCallId);          strVxmlServerIp= callEndAPI.getSessionData("S_VXMLSERVER_IP").toString();          callEndAPI.addToLog("Vxml Server IP : ", strVxmlServerIp);         strCli=callEndAPI.getSessionData("S_ANI").toString();          callEndAPI.addToLog("CLI : ", strCli);           strDnis=callEndAPI.getSessionData("S_DNIS").toString();          callEndAPI.addToLog("DNIS : ", strDnis);          strCallStDateTime=callEndAPI.getSessionData("S_CALL_STARTDATETIME").toString();            callEndAPI.addToLog("Call Start Time : ", strCallStDateTime);          //callEndAPI.addToLog("Call End :", "Call ID=" + sCID );                callEndAPI.addToLog("Starting the Java Thread to insert values into EWT table","");              t.start();             }catch (Exception e){         callEndAPI.addToLog("Call End Exception: ", e.getMessage().toString());      }   }  public void run(){      try{         callEndAPI.addToLog("Inside run() method","");         Class.forName("com.microsoft.sqlserver.jdbc.SQLServerDriver");         conn = DriverManager.getConnection("jdbc:sqlserver://172.18.150.154;user=ivr_user;password=aircel123;database=AircelInterimReport");         //Statement SQLStm= conn.createStatement();          //String sSQL="insert into CALL_END_DETAILS_EWT (CALL_ID,VXMLSERVER_IP) values ('" + sCID + "','" + sVxmlIP + "')";          String sSQL="{call LOG_CALLEND_DETAILS_EWT(?, ?, ?, ?, ?, ?)}";          SQLStm= conn.prepareCall(sSQL);          SQLStm.setString(1, strCallId);         SQLStm.setString(2, strVxmlServerIp);         SQLStm.setString(3, strCli);         SQLStm.setString(4, strDnis);         SQLStm.setString(5, strCallStDateTime);         SQLStm.setString(6, strCallEndDateTime);          callEndAPI.addToLog("Call End : ", "Insert Statement " + sSQL);         res =SQLStm.executeUpdate();          callEndAPI.addToLog("","Values inserted to EWT SQL table successfully");             /*int res;         res=Call_Log_EWT(sCID,"172.18.150.66" , "121313", "4555");          if(res>0)             callEndAPI.addToLog("Call End API", "Database Connection successfull and Table Record Count is : " + res);          else             callEndAPI.addToLog("Call End API", "Database Connection failed");*/      }catch(Exception e){         callEndAPI.addToLog("Exception occured",e.getMessage().toString());     }   finally {     try     {          conn.close();          SQLStm.close();      }     catch(SQLException sqlEx)     {         callEndAPI.addToLog("SQL Exception while closing connection : "  , sqlEx.getMessage().toString());     } }   } }

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


I can't save my animation as a .mov and thats the only thing that plays on my mac.  Is there a way that i can add file formats such as .mov

In the past, Blender (at least the Mac version) has had the ability to encode video files as .mov, the format used by Quicktime Player. However, with Blender 2.79 this feature seems to have vanished, for both the Internal and Cycles render engines. The release log happens to have the entry "Video encoding settings have been simplified, along with the addition of a Constant Rate Factor (CRF) mode" which I suppose could be the cause.  Does anyone know what happened—whether it is the aformentioned reason or something else—and how to export videos as Quicktime .mov in Blender 2.79?


is anything else supposed to be here? I am using Ubuntu gnome and my keyboard is unresponsive for encryption password. Do I need any more modules, and if so where do I add them.  # List of modules that you want to include in your initramfs. # They will be loaded at boot time in the order below. # # Syntax:  module_name [args ...] # # You must run update-initramfs(8) to effect this change. # # Examples: # # raid1 # sd_mod

I need to add these modules because my usb keyboard is not working when I try to type my encrypted password. usbcore uhci_hcd ehci_hcd usbhid  I guess I need to add these to /etc/initramfs-tools/modules, but where exactly do i add them. Here is the modules file: # List of modules that you want to include in your initramfs. # They will be loaded at boot time in the order below. # # Syntax:  module_name [args ...] # # You must run update-initramfs(8) to effect this change. # # Examples: # # raid1 # sd_mod  Where am I supposed to add it here, and am I doing the right thing (is it safe)?


I have a domain name and have added the Gmail MX records to it. I understand I can use the Send mail as for sending mail and the POP3 for receiving, but I currently don't have a mail server and I would rather just have Google Mail receive my domain emails through an alias.  Is there a way I can have my regular @gmail.com also receive mail from my personal domain?

I use my own domain for email, so that I can use multiple email addresses when shopping online, subscribing, etc.  These are all redirected to Gmail.  I have created some addresses under that domain for use when sending in Gmail.  What I would like to do is send mail without the need to register each address separately, or create a new email address in "Google Apps for your domain".  Is there a method to register the whole domain with Gmail so that I can send email in this way without needing to verify a new address?  [Original answers suggested Google Apps for your domain.  I didn't known about this, and I think it will be useful for me, but it doesn't obviously allow this feature.]


I wanted to create a play/pause button on my webpage that flips between play/pause when clicked. I used the on function to create a click event to trigger the song play and pausing. However, the first click does everything as expected, preventing the default action of refreshing the page, but when clicking the same button after it's been switched to a pause button, it does not prevent the default action. I have tried using preventDefault() for both of them and even stopPropagation() and return false, which still doesn't work. I am assuming this has to do with something with using replaceWith() and possibly removing events or something but I am not sure how all of this works.  I have also tried repurposing this for other functions like a mute button and having the pause play first with everything working fine on the first click but not the second.   play = $('#play'); pause = $('#pause');  play.on('click', function(e) {         e.preventDefault();         song.play();         $(this).replaceWith('');         container.addClass('containerLarge');         cover.addClass('coverLarge');      });      pause.on('click', function(e) {         e.preventDefault();         song.pause();         $(this).replaceWith('');     });

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.


I am using pdflatex (shell-escape is enabled) with auto-pst-pdf, psfrag and chemnum to replace tags in eps-files for auto-numbering molecules in my B.Sc. thesis. It went fine until this week, when I got the errors: GPL Ghostscript 9.53.3: Unrecoverable error and The error does not occur without the auto-pst-pdf package but I haven't found alternatives for my intention. I tested a MWE and there is no error with an eps-file. With an png-file I get a ghostscript-error: \documentclass{scrbook}  \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc}                \usepackage{             caption,             graphicx,       libertine,     lmodern }  \usepackage{psfrag} \usepackage[runs=2,crop=off,cleanup=]{auto-pst-pdf} \usepackage{chemnum}  \begin{document} plain text \begin{figure}     \includegraphics{test.png}  \end{figure} plain text with \cmpd{1} \end{document}  However if I reduce my "original" thesis.tex to the packages above and even if I don't include no eps-files (even if I only have my titlepage) I get the errors named above. I also tried to save my document in another directories but it didn't change anything. How can this be? Can it be a dvi2ps or ps2pdf error? Update: There was a pst-pdf-Update, but it didn't fix my error. However I managed to copy an error log directly from Texstudio. It seems to abort creating the pdf-graphics after some time (not always after the same image). Error-log when I use both png- and eps-graphics This is dvips(k) 2020.1 Copyright 2020 Radical Eye Software (www.radicaleye.com) ' TeX output 2020.10.12:1150' -> main-autopp.ps dvips: Font Helvetica used in file pics/Chatt-Disprop.eps is not in the mapping file. [...] dvips: Font Helvetica used in file pics/PNP-TMS/PNP-TMS_Ligand.eps is not in the mapping file. dvips: Font Helvetica-Bold used in file pics/PNP-TMS/PNP-TMS_Ligand.eps is not in the mapping file. <c:/texlive/2020/texmf-dist/dvips/base/tex.pro>  <c:/texlive/2020/texmf-dist/dvips/config/alt-rule.pro> <c:/texlive/2020/texmf-dist/dvips/l3backend/l3backend-dvips.pro> <c:/texlive/2020/texmf-dist/dvips/pstricks/pstricks.pro>  <c:/texlive/2020/texmf-dist/dvips/pstricks/pst-algparser.pro>  <c:/texlive/2020/texmf-dist/dvips/pst-tools/pst-tools.pro>  <c:/texlive/2020/texmf-dist/dvips/pstricks/pst-dots.pro>  <c:/texlive/2020/texmf-dist/dvips/psfrag/psfrag.pro>  <c:/texlive/2020/texmf-dist/fonts/enc/dvips/libertine/lbtn_76gpa5.enc>  <c:/texlive/2020/texmf-dist/fonts/enc/dvips/libertine/lbtn_25tcsq.enc>  <c:/texlive/2020/texmf-dist/dvips/base/texps.pro>  <c:/texlive/2020/texmf-dist/dvips/base/special.pro>  <c:/texlive/2020/texmf-dist/dvips/base/color.pro>  .  <c:/texlive/2020/texmf-dist/fonts/type1/public/libertine/LinBiolinumTB.pfb> <c:/texlive/2020/texmf-dist/fonts/type1/public/libertine/LinLibertineT.pfb> [1  <./pics/Chatt-Zyklus.eps>  ] [2  <./pics/Chatt-Disprop.eps>  [...] <./pics/PNP-Cy/PNP-Cy_Ligand.eps>  ] [22  <./pics/PNP-Cy/Komplex.eps>  ] [23  <./pics/PNP-TMS/PNP-TMS_Ligand.eps>  ]    GPL Ghostscript 9.53.3: Unrecoverable error, exit code 1  system returned with code 1 system returned with code 1  Prozess endete mit Fehler(n)

this is my first time here but I will try to do my best. My document stopped compiling and I was able to boil it down to the following MWE. Basically I need chemnum (and therefore auto-pst-pdf) to replace temporary markers in my chemical schemes (all .eps files). Chemmacros seems to break this because if I comment it out, the document compiles just fine. \documentclass{article}  \usepackage{graphicx} \usepackage{chemnum} \usepackage{auto-pst-pdf} %\usepackage{chemmacros}  \begin{document}  Hello World...      \begin{figure}         \includegraphics{picture.eps}     \end{figure}          \begin{figure}         \includegraphics{picture2.png}     \end{figure}   \end{document}  From the log: ------------------------------------------------- auto-pst-pdf: Auxiliary LaTeX compilation ------------------------------------------------- This is pdfTeX, Version 3.14159265-2.6-1.40.21 (TeX Live 2020) (preloaded format=latex) entering extended mode system returned with code 256   Package auto-pst-pdf Warning:      Creation of 00_preamble-autopp.dvi failed. This warning occured on input line 128.   Package auto-pst-pdf Warning:      Could not create 00_preamble-pics.pdf. Auxiliary files not deleted. This warning occured on input line 128.  ------------------------------------------------- auto-pst-pdf: End auxiliary LaTeX compilation -------------------------------------------------  I think it has something to do with ghostscript or related. This was tested on a fresh install on Xubuntu. I can supply log files of a failed and of a working compilation. If anything is needed, please tell me and I will try to provide. Best regards, Phil PS: I was able to reproduce the error with these files:


Let $a_n=1-2^{\frac{-1}{n}}$, $b_n=\frac{1}{n^p}$. If $p=1$, then if I want to compare $\sum_{n=1}^{\infty}a_n$ with $\sum_{n=1}^{\infty}b_n$, does it converge or diverge by comparison? To answer this question, I think it's obvious that $b_n$ diverges, without a doubt. But the real question is am I able to draw this conclusion from comparing it with $b_n$? I know that sometimes these comparison tests do not work, so this is the main problem that i am concerned with.

Let $a_n=1-2^{\frac{-1}{n}}$, $b_n=\frac{1}{n^p}$. Does $\sum_{n=1}^{\infty}a_n$ converge or diverge when compared to $\sum_{n=1}^{\infty}b_n$ if $p < 1$? My answer to this is that it diverges, since $b_n$ diverges if $p<1$, and by a comparison test $a_n$ does as well. Is this correct? Thank you.


The system goes slow or seems to stop, screen then goes to black and white and laptop is unusable, but usually recovers after a few minutes.   During this outage disk read/write light is on constantly. HTOP shows no excess CPU usage but has 46 instances of usr/lib/firefox/firefox some with -contentproc.......  previous updates to software have had errors.   I would like to simply re-install 16.04 to see if this solves the problem but can't find simple instructions on how to do this.

Recently I installed Ubuntu 12.10 x64 Server Edition on my PC. Unfortunately, I attempted to install a lightweight desktop but due to the fact that I have an old graphics card, the PC does not perform so well. I am thinking of re-installing an Ubuntu version but I do not want to lose the contents in my home folder. Is there any way to do that with a Live CD?


I am unable to change my volume using cd d: in command prompt using administrator rights. After typing this it just reopens c drive for me instead of opening d drive.  Edit   I came to a little solution that open the d drive using cd /d d: command but it is unable to open the e drive.

This may be a silly question, and I think I have looked elsewhere to find the answer...  Might be a path issue, but when I open the command line and type from the C:\>: cd D:\  I cannot get to the D drive.  Even if I type: cd D:\<folder name>  The command.exe will auto-complete the line with the tab key, so it knows where I'm at.  It just doesn't print to screen the result or actually get me there.  This problem exists for the network drives as well. Now, if I use the chdir (cd) command like this: chdir D: or cd d: I get the print out of the D:\ below the command but it still says I'm in the C:\. I feel like I'm missing something simple.


So, I would like to prove the following: $$\forall n,k\in\mathbb{N}_0, n\geq k+1: \sum_{i=0}^{k}{{n-i-1}\choose {k-i}}={n\choose k}$$ First of, i exploited trivial symmetry of the binomial coefficients to obtain: $$\sum_{i=0}^{k}{{n-i-1}\choose {k-i}}=\sum_{i=0}^{k}{{n-i-1}\choose {n-k-1}}$$ Now I proceeded by induction on $n$. The base step: ($n=k+1$): $$\sum_{i=0}^k{{k-i}\choose 0}=k+1={{k+1}\choose 1}={{k+1}\choose k}$$ But now here in the inductive step, I'm quite unsure how to proceed $$\sum_{i=0}^k{{n-i-1}\choose {n-k-1}}={n\choose k}$$ (the premise) and this should follow: $$\sum_{i=0}^k{{n-i}\choose{n-k}}={{n+1}\choose k}$$ All i managed to do was to "simplify" by symmetry: $$\sum_{i=0}^k{{n-i}\choose{n-k}}=\sum_{i=0}^k{{n-i}\choose{k-i}}$$ But from here i have no idea, would you please suggest further steps and how should i proceed from here?

Prove that for every $n \ge m \ge 1 , \sum_{k=0}^m{n-k \choose m-k}={n+1 \choose m}$    I've tried saying that the RHS represents the number of binary series with m "1" 's and n+1-m "0"'s, but I couldn't find out what k represents at the LHS. Thanks


Let $R$ be commutative ring $R$ with a multiplicative identity $1$. Suppose $p(x)=a_{n}x^{n}+\cdots a_{1}x+a_{0} $ is a polynomial in $R[x]$.   Prove that each $a_0,a_{1},\dots,a_n$ is a nilpotent element in $R$ if and only if $p(x)$ is nilpotent in $R[x]$.   Here is my attempt at the forward direction.   $(\Rightarrow)$ Suppose each $a_0,a_{1},\dots,a_n$ is nilpotent in $R$. Then $a_{i}^{n_{i}}=0$ for each $a_{i}$ and for some positive integer $n_{i}$. Let $N=\prod\limits_{i=0}^{n}n_{i}$. Then $[p(x)]^{N}=0$ which shows that $p(x)$ is nilpotent in $R[x]$.  I think this is correct, but I'm not positive. I couldn't find any concrete examples of a polynomial ring which contains more than one nilpotent element.   For the $(\Leftarrow)$ direction, I was thinking that I should use induction on the degree of $p(x)$. If this is the wrong approach, then I could use some advice on how to prove this.

Let $R$ be a commutative ring.  The nilradical $\text{nil}(R)$ is the set of all nilpotent elements, and it is the intersection of all the prime ideals of $R$.  Is the following true in the polynomial ring? $$\text{nil}(R[X])=(\text{nil}(R))[X]$$  Any polynomial in the right hand side has all its coefficients nilpotent in $R$, hence also in $R[X]$, and therefore it is nilpotent in $R[X]$ as the sum of nilpotent elements.  The other inclusion is not clear to me.  Is there a counterexample?


I am beginning the "History of Sexuality" and wanted to ask to what degree should I take what Foucalt states about historical events in any of his works as accurate? From my understanding from looking online Foucalt does something similar to Nietzsche's Genealogical method. By this I understand that he takes a general outline of commonly held beliefs about history and performs a cultural analysis. Is my understanding correct?? Thanks in advance.

I have only recently heard about philosophical ideas of Michel Foucault from a friend of mine. His claims, those concerning madness for example, sound iconoclastic to me. After looking up some relevant facts I found that a significant proportion of historical claims he made were based on biased material, which presented information that was only partially accurate. That is to say, some of his assumptions -- assumptions underpinning his historiographical (or genealogical) method -- were NOT true, or, at least, not based on solid enough evidence.    Then why should we pay attention to him? Is it forgivable in philosophy to make statements based on biased premises? (It is not in mathematics, which is my field of study.) If this is not the case then what part of Foucault's work is still relevant to us today?  Note: If this question is deemed inappropriate or in need of appropriation, moderators please do so. I am no expert in philosophy or this website.


I have a problem understanding theorem 2.14 of Rudin's Principles of Mathematical Analysis. The theorem is the following:  $\textbf{Theorem 2.14:}$ Let $A$ be the set of all sequences whose elements are the digits $0$ and $1$. This set is uncountable. The elements of $A$ are sequences like $1,0,0,1,0,1,1,1,...$  $\textbf{Question:}$ Why there is not a $1$-$1$ mapping of the set $A$ to the set of all the positive integers? I  would think that every positive integer (denoted by $J$ by Rudin) can be represented by an element of $A$ by using the binary representation. So each number is $$J_n = \sum_{i=0}^\infty s_{ni}2^i  $$ where $s_{ni}$ is the $i^\text{th}$ element of the sequence $s_n$ (using zero-based numbering). Then, if $A\sim J$, shouldn't $A$ be countable? Rudin mentions this theorem implies that the set of all real numbers is uncountable, so I understand this sequences actually represent real numbers and not the natural numbers, but why? I know my logic has at least one mistake (likely a huge blunder), but what is it?

I will use binary.  I claim to have a bijection $f \colon \mathcal{N} \to \left[ 0, 1 \right)$ where $\mathcal{N}$ is the set of natural numbers $\left\{ 0, 1, 10, 11, 100, \dotsc \right\}$ as follows:  $$ \begin{array}{l|l} x \in \mathcal{N} & f(x) \in \left[ 0, 1 \right)\\\hline 0 & 0.0 \\ 1 & 0.1 \\ 10 & 0.01 \\ 11 & 0.11 \\ 100 & 0.001 \\ 101 & 0.011 \\ 110 & 0.101 \\ 111 & 0.111 \\ 1000 & 0.0001 \\ \hspace{.6em}\vdots & \hspace{.9em}\vdots \end{array} $$  It's basically the .  I claim to have everything on this list.  Diagonalization?  Go ahead!  Constructing a number that differs from $f(i + 1)$ in its $i$-th fractional digit yields $0.11111\!\ldots = 0.\overline{1}$ which is $1$, and that should not be on the list anyway!  Why does this not work? I think it has something to do with integers supposedly not having infinite digits, while reals supposedly do.


THIS IS NOT A DUPLICATE FOR  as i'm already using the ON function, but it doesn't work :  I'm trying to delete dynamically created elements.  Everytime a user make a search, a tag with the keyword is added containing an X button to delete this tag (it's add to the .tags div) :

      <input type="search" class="searchfield" />       <button class="searchbutton">add tag</button>
   The problem is, when i click on the X button, the on("click" function is never executed! (i never get the alert) :  $( document ).ready(function() {      $(".searchbutton").click(function(){         addTag($(".searchfield").val());     });      $(".removeTag").on("click", function(){         alert("yes");     }); });  function addTag(search) {   $(".tags").append("
" + search + "<button class='removeTag'>X</button>
"); }   Check the demo here  you have to make a search to see the added tag  I use jQuery 1.9.1  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.


I'm only on my third day of trying out Blender after hearing about 2.8 changing the workflow. I followed the classic donut tutorial and now I wanted to try a simple project of my own.  I'm trying to use a boolean modifier difference operation to remove an object from a cylinder. I imported a SVG and solidified it and turned it into a mesh as the object I would like to remove out of the cylinder, but it's not working as expected. I suspect the SVG is the weird part because I can remove a sphere from a cube and it works as expected.  In the cylinder object mode using X-Ray, I can see that the shape is cut into the object but the face between the two objects is still there. In smooth shading mode you can see a hint of the process. I haven't seen this problem in any other question about booleans, including the ones this question is marked as a duplicate of. It doesn't even show up/cut the shape out.      The only time I've seen it work correctly is if I'm in edit mode for the SVG Shape and I've hidden it from viewport but I can't do anything from there. The shading is weird, but it removes the geometry how it should.    I've tried searching around but I'm not quite solid on 3D terms yet, and it's talked about normals, limited dissolve, merge by distance, etc. I've tried a bunch of things suggested but I can't seem to figure it out after a few hours.

I tried to manipulate a cube with the Boolean modifier. I tried to cut out an edge of the cube with a cylinder. Also, the shading result looks awful in FLAT SHADING mode, so I turned on SMOOTH SHADING.   Has anyone an idea how to achieve a better result. (I also cut out a Sphere first, this made the result less awful).   I used Blender Internal and rendered with smooth shading for smoothness.  Using flat shading looks okay, except the "round" cutouts :/  Face normals are okay.  First image is smooth shading.    EDIT: User Pisurquatre suggested the EdgeSplit modifier, works perfect to me (Maybe a little tweaking here and there):


I had been inactive on the homepage for a while - unsure of the exact time - and when I switched my filter from the default recommended to favorite tags, I received the "That's a miss" no results page.     Obviously, pressing F5 resolves the problem and generates a list of questions with my favorite tags.

When I click the filter favorite tags it often doesn't show anything. After a while, some new questions ping in, but the original list is empty:        There really should be questions on SO with those tags...


I'm newbie in SalesForce development and need to get access to community pages using the User-password login. I already got access with this flow using a common user to authenticate. In this case, I'm using a CORS server to avoid use the security token.  I need to use the REST API to integrate with a mobile application, but reading about it, I could't get more detailed information.  If somebody already done that, please help me. If it's not possible, I'll try another solution, but I need access the communities using the REST API.  I changed the URL to the community login, as explained in docs. But I receive an error:   {"error":"unsupported_grant_type","error_description":"grant type not supported"}   My server is allowed to access using the User-Password flow with the following CURL requisition:  curl https://<login server>/services/oauth2/token --request POST --data "grant_type=password&client_id=<client_id>&client_secret=<client_secret>&username=<username>&password=<password_without_security_token>" -H "X-PrettyPrint:1"   Regards, Alexandre

I am trying to implement  and below is my code and debug log - any help is appreciated.  Http httpProtocol = new Http();    HttpRequest request = new HttpRequest(); request.setHeader('Content-Type', 'application/json;'); request.setEndPoint('https://test.salesforce.com/services/oauth2/token'); request.setMethod('POST'); String strbody = '{"grant_type":"Password", "password":"MY PASSWORD + TOKEN", "username":"SANDBOX USER NAME",  "client_secret":"secret",   "client_id":"Client id from remote setttings"}'; request.setBody(strbody); HttpResponse response = httpProtocol.send(request); String jsonInput = response.getBody(); system.debug('jsonInput===>'+jsonInput);   Debug log -   15:55:38.068 (68324000)|SYSTEM_METHOD_ENTRY|[5]|System.HttpRequest.setMethod(String) 15:55:38.068 (68346000)|SYSTEM_METHOD_EXIT|[5]|System.HttpRequest.setMethod(String) 15:55:38.068 (68350000)|STATEMENT_EXECUTE|[6] 15:55:38.068 (68356000)|HEAP_ALLOCATE|[6]|Bytes:357 15:55:38.068 (68381000)|VARIABLE_ASSIGNMENT|[6]|strbody|"{\"grant_type\":\"Passw (337 more) ..." 15:55:38.068 (68387000)|STATEMENT_EXECUTE|[7] 15:55:38.068 (68407000)|SYSTEM_METHOD_ENTRY|[7]|System.HttpRequest.setBody(String) 15:55:38.068 (68440000)|SYSTEM_METHOD_EXIT|[7]|System.HttpRequest.setBody(String) 15:55:38.068 (68445000)|STATEMENT_EXECUTE|[8] 15:55:38.068 (68478000)|SYSTEM_METHOD_ENTRY|[8]|System.Http.send(APEX_OBJECT) 15:55:38.068 (68568000)|CALLOUT_REQUEST|[8]|System.HttpRequest[Endpoint=https://test.salesforce.com/services/oauth2/token, Method=POST] 15:55:38.483 (483258000)|HEAP_ALLOCATE|[EXTERNAL]|Bytes:219 15:55:38.483 (483399000)|CALLOUT_RESPONSE|[8]|System.HttpResponse[Status=Bad Request, StatusCode=400] 15:55:38.483 (483424000)|HEAP_ALLOCATE|[8]|Bytes:96 15:55:38.483 (483444000)|SYSTEM_METHOD_EXIT|[8]|System.Http.send(APEX_OBJECT) 15:55:38.483 (483615000)|VARIABLE_ASSIGNMENT|[8]|response|"System.HttpResponse[Status=Bad Request, StatusCode=400]"|0x1b22c3f1 15:55:38.483 (483627000)|STATEMENT_EXECUTE|[9] 15:55:38.483 (483666000)|SYSTEM_METHOD_ENTRY|[9]|System.HttpResponse.getBody() 15:55:38.483 (483742000)|HEAP_ALLOCATE|[9]|Bytes:81 15:55:38.483 (483751000)|SYSTEM_METHOD_EXIT|[9]|System.HttpResponse.getBody() 15:55:38.483 (483780000)|VARIABLE_ASSIGNMENT|[9]|jsonInput|"{\"error\":\"unsupporte (61 more) ..." 15:55:38.483 (483786000)|STATEMENT_EXECUTE|[10] 15:55:38.483 (483794000)|HEAP_ALLOCATE|[10]|Bytes:13 15:55:38.483 (483980000)|HEAP_ALLOCATE|[10]|Bytes:94 15:55:38.483 (483999000)|SYSTEM_METHOD_ENTRY|[10]|System.debug(ANY) 15:55:38.484 (484025000)|USER_DEBUG|[10]|DEBUG|jsonInput===>{"error":"unsupported_grant_type","error_description":"grant type not supported"}


Need help how can I work on ubuntu but also have windows?

I need my pre-installed version of Windows 7 (or any other version of Windows), how could I install Ubuntu without erasing it?


Which one is correct sentence? I'm asking how many times I need to use 'will' in a sentence?  One day I will have so many cars that I will not even remember how many cars I will have.  One day I will have so many cars that I don't even remember how many cars I have.   Should I use 'will' again and again?

I just would like to know if this sentence would be grammatically correct and in which cases should I use it:  I don't know when he is back instead of he will be back . I know the rule with when "no will" in most cases but we can say" please let me know when it will be available or when it is available"  If that's not correct let me know why please


Decompose ${\mathbb{Z}_n}^{*} / ({\mathbb{Z}_n}^{*})^2$ into a direct sum of cyclic groups,  Where $({\mathbb{Z}_n}^{*})^2 = \left\{a^2 \ : \ a \in {\mathbb{Z}_n}^{*} \right\}$,  A) when $n$ is an odd prime $p$,  B) when $n$ is a product of two distinct prime $p$, and $q$.  I think that they are just $\mathbb{Z}_2$.  Since, if $n=p$ an odd prime, ${\mathbb{Z}_p}^{*} = \left\{ 1, \ 2, \ ... , \ p-1\right\}$, then $({\mathbb{Z}_p}^{*})^2 = \left\{ 1^2, \ 2^2, \ ... . \ (\frac{p-1}{2})^2 \right\}$.  Then ${\mathbb{Z}_p}^{*} / ({\mathbb{Z}_p}^{*})^2 \cong \mathbb{Z} _2$  Similarly, if $n = pq$ for distinct prime $p$ and $q$, ${\mathbb{Z}_{pq}}^{*} = \mathbb{Z}_{(p-1)(q-1)}$.  And if $m \in \mathbb{Z}_{pq}^{*}$, then should $pq-m$ be too.  Clearly, their squares modulo $pq$ is exactly same. So $(\mathbb{Z}_{pq}^{*})^2$ should be $ \mathbb{Z}_{\frac{(p-1)(q-1)}{2}}$.  So is this case, $\mathbb{Z}_{pq}^{*} / (\mathbb{Z}_{pq}^{*})^2 \cong \mathbb{Z}_2$.  It seems to me, then, no matter what $n$ is, $\mathbb{Z}_{n}^{*} / (\mathbb{Z}_{n}^{*})^2 $ is congruent to $\mathbb{Z}_2$.  Where have I done wrong thing? What is wrong?

Let $\mathbb{Z}_n ^*$ be the set of all units in $\mathbb{Z}_n$  and $(\mathbb{Z}_n ^*)^2$ = $\{ a^2 | a \in \mathbb{Z}_n ^*\} $  Then,  decompose the factor group  $\mathbb{Z}_n ^* / (\mathbb{Z}_n ^*)^2$  1.when $n$ is an odd prime  2.when $n$ is a product of two distinct odd primes $p, q$  I solved the first as following: In $\mathbb{Z}_p$, since $x^2=(p-x)^2$ holds, the order of $(\mathbb{Z}_n ^*)^2$ is exactly the half of that of $\mathbb{Z}_n ^*$.  Thus, the answer is $\mathbb{Z}_2$.  However the second is more complicated. I didn't know that. Please help me to solve this.


I am planning to install an Ubuntu system in my laptop computer.  After downloaded an Ubuntu image file, how can I use it with USB stick? Do I have to make the USB bootable? If it is so, how can I make it?

How do I make an Bootable Ubuntu USB containing the the latest version of Ubuntu?  For completeness, how would I be able to do this on Ubuntu, Windows, OS X or another Linux distro?


Consider this code:  \documentclass{article} %\usepackage[latvian]{babel}                                                                                \usepackage{tikz} \usetikzlibrary{angles, quotes} \begin{document} \begin{tikzpicture}   \coordinate(A) at (0, 0);   \coordinate(B) at (1, 1);   \coordinate(C) at (1, 0);   \draw   pic [draw, "$\theta_{p}$" font=\tiny] {angle=A--B--C}; \end{tikzpicture} \end{document}   If I uncomment the line   %\usepackage[latvian]{babel}      I get an error:  (/usr/local/texlive/2018/texmf-dist/tex/latex/latexconfig/epstopdf-sys.cfg)) ! Missing \endcsname inserted. <to be read again>                     \theta  l.12     "$\theta_{p}$" font=\tiny]                                     {angle=A--B--C};   What is the problem and how to fix it?     The solution proposed by @marmot works in an article. Now, consider the same example in beamer:  \documentclass{beamer} \usepackage[latvian]{babel} \usepackage{tikz} \usetikzlibrary{angles, quotes, babel} \begin{document} \begin{frame}   \begin{tikzpicture}     \coordinate(A) at (0, 0);     \coordinate(B) at (1, 1);     \coordinate(C) at (1, 0);     \draw   pic [draw, "$\theta_{p}$" font=\tiny] {angle=A--B--C};   \end{tikzpicture} \end{frame} \end{document}   We get a similar problem even when using tikz library babel:  (/usr/local/texlive/2018/texmf-dist/tex/latex/translator/translator-theorem-dic tionary-English.dict) (./latvianpres.nav) ! Missing \endcsname inserted. <to be read again>                     \theta  l.13 \end{frame}

I am preparing lecture notes in Turkish, and I have a digram for mathematical modelling procedure. But I cannot produce a good output for the following code. When I remove the first three packages, I get my desired output. However, I need to have keep them in my document. Would you help me in this direction?  \documentclass[10pt,notheorems]{beamer}  \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} \usepackage[turkish]{babel}  \usepackage{tikz} \usetikzlibrary{positioning,shapes,arrows}  \hypersetup{bookmarksdepth=4,bookmarksnumbered=true,bookmarksopen=true}  \usetheme{Warsaw} \usecolortheme{seahorse}  \begin{document}  \begin{frame}[fragile]{}{}  \begin{figure}   \centering   \begin{tikzpicture}     \node (rwp) [draw,fill=blue!20,text centered,minimum height=2em,rounded corners] {Ger\c{c}ek ya\c{s}am problemi};     \node (mm) [right=2cm of rwp,draw,fill=purple!20,text centered,minimum height=2em,rounded corners] {Matematiksel model};     \node (mc) [below=2cm of mm,draw,fill=green!20,text centered,minimum height=2em,rounded corners] {Matematiksel \c{c}{\i}kar{\i}m};     \node (rwq) [below=2cm of rwp,draw,fill=red!20,text centered,minimum height=2em,rounded corners] {Ger\c{c}ek ya\c{s}am tahminleri};     \path [draw,->] (rwp.east) -- node [above] {Form\"{u}lasyon} (mm.west);     \path [draw,->] (mm.south) -- node [right] {\c{C}\"{o}z\"{u}m} (mc.north);     \path [draw,->] (mc.west) -- node [below] {Yorum} (rwq.east);     \path [draw,->] (rwq.north) -- node [left] {Kontrol} (rwp.south);   \end{tikzpicture}   \caption{Modelleme s\"{u}reci}\label{s2ss2fig1} \end{figure}  \end{frame}  \end{document}


I know there are "guidelines" out there for how to handle floating Back to Top buttons, but I haven't found hard data or studies showing that users measurably prefer to use a Back to Top button rather than scroll. Has anyone done any studies or know of analytics to show proportion of users leveraging Back to Top over scroll? Asking because in my anecdotal design experience I've only ever added a floating Back to Top button at the insistence of a client without any usability data to back up the requirement. Now I need to introduce another feature that also performs best as a bottom-right floating button (Chat), but I would love to evidence studies demonstrating that Back to Top is worth nixing.

I'm talking about links or buttons at the bottom of the page or screen simply linking to the top of the website.  Is there any data on that? Are they used more frequently on long pages? What about mobile?  I know that , but I don't know if people actually know this and I also don't know if it works on Android and WP7.


While learning about asymptotes and holes in rational functions in Precalculus, I came across a problem that shouldn't happen, but I don't understand. Something just doesn't add up in my head... Here we go:  Let f(x)=1. Since $\frac aa=1$ and $a*1=a$, obviously $a={a*b \over b}$. Let $b=(x-1)$. We can multiply f(x) by 1, technically, by saying that: $$f(x)=1={x-1 \over x-1}$$ However, a bit of precalc knowledge shows us that ${x-1 \over x-1}$ has a vertical asymptote at x=1, and an x-intercept at x=1 as well. This means that the graph has a hole, or is undefined at, x=1. (Because plugging in 1 for x yields a denominator of 0, which is undefined.) However, this is absurd because the graph of $f(x)=1$ obviously has no holes, anywhere. Somehow, multiplying this extremely simple function by something equivalent to 1 makes it undefined at a particular point...  Whaaaaa...?  EDIT: I realize that the above function does not have a vertical asymptote. However, my statement was referring to the fact that it appears to have both a vertical asymptote and an x-intercept at the same x-value, which means that it has neither of those things, just a hole.

$$\lim _{x\rightarrow 5}\frac{x^2-25}{x-5}  = \lim_{x\rightarrow 5} (x+5)$$  I understand that to evaluate a limit that has a zero ("hole") in the denominator we have to factor and cancel terms, and that the original limit is equal to the new and simplified limit. I understand how to do this procedurally, but I'd like to know why this works. I've only been told the methodology of expanding the $x^2-25$ into $(x-5)(x+5)$, but I don't just want to understand the methodology which my teacher tells me to "just memorize", I really want to know what's going on. I've read about factoring in abstract algebra, and about irreducible polynomials (just an example...), and I'd like to get a bigger picture of the abstract algebra in order to see why we factor the limit and why the simplified is equal to the original if it's missing the $(x-5)$, which has been cancelled. I don't want to just memorize things, I would really like to understand, but I've been told that this is "just how we do it" and that I should "practice to just memorize the procedure." I really want to understand this in abstract algebra terms, please elaborate. Thank you very much.


After seeing a question on Stack Overflow that had 7 answers, all of which practically said the same thing (not word for word, but the general answer as a whole, although some of the answers were more helpful), I thought that something should be done, but what?  Should we flag the least helpful answers? Downvote? Nothing?

I'm taking a look at  (now removed), which all seem to be pretty much the same.  Should any be downvoted/flagged, and if so, which ones?


I was wondering about the following modelling problem, but I can't think of an appropriate way to solve it.   Imagine two variables without a linear relationship, but a one increases, the variability of the other increases.   In this case, while there is no relationship between the variables, we might assume we don't know anything, but we do know that a lower score in x means the range of values for y is much smaller.  So it not true that we know nothing. So it seems like we could build a model with some explanation for how variation changes, which is a better model that no relationship  Below is some R code showing what I mean. The application I have in mind for this is slightly more complicated, but I am unsure if I can even pass this hurdle.   What kinds of methods are available to solve this kind of problem?   set.seed(123) df = data.frame(   y = rnorm(1000, mean = 0, sd = 1:1000),   x = 1:1000  ) plot(df$x, df$y)

As a motivating example, consider this hypothesis: A friend and I were discussing how it might be the case that, the more one person is given control in the process of making a movie, the higher the variance of the quality of that film. The more hands that go into making a film, the safer of a bet it is—but the less likely it will be that it is great.  Here are some simulated data that could characterize this hypothesis:  set.seed(1839) x <- runif(1000, 0, 100) y <- rnorm(1000, 0, x) dat <- data.frame(x, y)  library(ggplot2) ggplot(dat, aes(x = x, y = y)) +   geom_jitter() +   theme_light() +   labs(y = "Quality of Film",         x = "Amount of Artistic Control in One Person")     Note that here, I am not interested in predicting the expected value, but the expected variance of $y$ from $x$.  I am familiar with how one can create models for both location and dispersion in beta regression and how one can create models for both location and scale in conditionally heteroskedastic truncated regression.  However, is there a way to model conditional heteroskedasticity in an ordinary least squares regression like this? Are there regression models that exist where one can model the variance of $y$ as a function of $x$? When I try looking for these models, I usually end up with people wanting to use sandwich estimators or weighted least squares or something.  I don't want to treat heteroskedasticity as a problem with the data, but something to be explicitly modeled as a function of predictors $X$. Is there a way to do this with linear regression?


Hello I am using ubuntu server and I am getting an error when I try to use sudo:   sudo: unable to resolve host ira: Resource temporarily unavailable  I have looked this error up and people say its something with /etc/hosts/  Here is mine:   127.0.0.1       localhost.localdomain   localhost ::1             localhost6.localdomain6 localhost6  # The following lines are desirable for IPv6 capable hosts ::1     localhost ip6-localhost ip6-loopback fe00::0 ip6-localnet ff02::1 ip6-allnodes ff02::2 ip6-allrouters ff02::3 ip6-allhosts    What is wrong with this file? Also what could cause this? was it someone changing this file by hand or is it the system that did it?  Thanks, Ira.

And when I tried the following commands /etc/hostnames and /etc/hosts, it says:  bash: permission denied.


I have no idea what the difference between these are. I have heard that they have the same meaning, but how do they?

I know several questions were asked about the difference between "going to" and "will". Based on several answers (see, for instance, ,  and ), I understood that "will" is more spontaneous and "going to" is used with more planned actions.  So, it seems that everything is pretty fine. However, in , Kosmonaut has an answer in which he states: "Let's say that tomorrow you will walk your dog from 7 - 8 AM".  On the one hand, you probably planned to walk your dog long before and thus I should use "Let's say that tomorrow you're going to walk your dog from 7 - 8 am".   On the other hand, since I'm saying "let's say...", I'm deciding right now (thus, unplanned) that you will walk your dog. So, even though in this hypothetical situation you made a plan, I'm in a more spontaneous mood deciding right now that that's what you will do tomorrow, and, thus, I should use "will".  Which one (if any) of the above explanations is right?


I made a bash file "my_sh.sh". by default it has no x permission:  -rw-rw-r-- 1 amin amin 37 Mar 12 00:45 my_sh.sh   But I could run it without any problem or warning! Why?  amin@ubuntu:~/newDIR$ bash my_sh.sh

I can seem to run scripts (.sh) with and without them being set as executable. So where exactly this matters?


Recently top-bar started to feature indicator with number of pending reviews [actually it seems that it shows number of suggested edits approvals only, not sure]. That's good.  But why does it appear even after I have exceeded daily review limit? It's distracting, especially as it appears/disappears very frequently.  Is it a [kind-of] bug or does it have a purpose that I'm missing?

Now that I've reached 2k on Stack Overflow, I get access to the "Suggested Edits" review queue.  Although I only have 20 edits per day, the "suggested edit awaiting" icon in the top bar is always there and it bothers me a lot!  My suggestion is to apply one of three solutions:   Remove the suggested edits icon when we reach the maximum (50) edits Remove the Highlight (orange) on the suggested edits Remove the suggested edits part when we click on it   What do you think?


I write three similar demos and compile them with   gcc -S 1.c -o 1.s   these demos diff in one line :   //  1.c , get 1.s 1 #include <stdio.h> 2 int main() 3 { 4    int a[2]={111,222}; 5    int j=0; 6    printf("%d ",0[a]);  // another two are a[j] and j[a] 7    return 0; 8 }   I use vimdiff to view assemble demo  in .s files, a[j] and j[a] is the same.  there are three different line in 0[a]  ; main in 0[a] , file 1.s .loc 1 5 0 movl    $111, -16(%rbp) movl    $222, -12(%rbp) .loc 1 6 0 movl    $0, -20(%rbp) .loc 1 7 0                             movl    -20(%rbp), %eax              | no these two line   cltq                                 | in a[j] and j[a] movl    -16(%rbp,%rax,4), %eax        movl    %eax, %esi movl    $.LC0, %edi movl    $0, %eax call    printf    I learn 8086 and intel assemble last year, several days ago find AT&T and feel a little strange. In 1.s ,ctlq extend rax to 64bit , and $0 doesn't need that. Is that right?  The problem is , after compiled to .s file, a[j] and j[a] is the same,does gcc compiler recognize the base address(pointer a) and the offset (j) ? a and j are both in memory,how can gcc get eax and ebp? Check their type?

As Joel points out in , in  (aka: K & R), there is mention of this property of arrays in C: a[5] == 5[a]  Joel says that it's because of pointer arithmetic but I still don't understand. Why does a[5] == 5[a]?


Can I install Ubuntu on a blackberry passport?

With the announcement of the Ubuntu Phone OS I'd like to know what phone (and tablet) models are supported at this time.  Note from foss & Oli: We are making this the master question for all future "Will this work on <insert random tablet/phone/device here>?!" questions


I've been tasked with gathering performance metrics on a few database servers that have one TempDB data file.  It seems prevailing wisdom is to have one TempDB data file per core up to a certain point.  Both servers in question have 4 CPUs, so we're going to add three more on each.  My question is which performance metrics should I gather to get a solid depiction of where my servers are at?  I want to gather data pre-change and post-change for comparison.

The article  suggests that I should split tempdb into a number of files equal to the number of cores. So for 4 cores you get 4 files.      By having the larger number of files, you can increase the number of   physical I/O operations that SQL Server can push to the disk at any   one time. The more I/O that SQL Server can push down to the disk   level, the faster the database will run. With standard databases, SQL   Server can cache a large amount of the data that it needs into memory.   Because of the high-write nature of the tempdb, the data needs to be   written to the disk before it can be cached back up into memory.   Though it sounds good in theory, is it really that good as a general optimisation? Is it something that may only apply for specific systems where IO is very high?


I don't know how to calculate the following modulo: $$321^{654} \mod 1013$$  Are there some easy way to do this?

What is the fastest way (general method) to calculate the quantity $a^b \!\mod c$? For example $a=2205$, $b=23$, $c=4891$.


I have a VM that I share/synchronize daily over a NAS, so size is of high importance.  The image is stored as a single VMDK file, which is ~31GB in size. However, so far as I can tell, it doesn't need to be that large.  The VMWare Player settings suggest that ~21.5GB is unused, and the output of df suggests that around ~13GB is used (assuming this includes swap) when it's actually running.  I have tried both defragmenting the disk, as well as compacting the disk, in the VMWare settings - both operations complete almost immediately.  How can I shrink this VM down to a more manageable size? When it was split across multiple files (there were ~30 of them) prior to my converting it to a single file, it still took up roughly the same amount of space.  I've tried using the vmware-vdiskmanager.exe program, and it took ~5 minutes to both defrag (-d) and then shrink (-k) the image, but it went from 32.4GB to 32.1GB. Not a huge difference.  Note that the size of the VMDK file (in Windows Explorer) was measured after the machine had been powered down.

I created an image of a Windows Server 2008 system using the free VMware Player and set the maximum hard drive size to 100GB. I then gave those image files - 30GB at the time - to a server hosting company. A few weeks later I asked them for a copy of them back; the image should not have changed much in size, but the files I got back were the full 100GB size.  I am not a VMware expert at all, so I have two questions:   How/why did they expand the whole dynamic disk? Is there any way I can somehow shrink this image down to the size that actually contains data?   I tried the VMware converter, and it can't seem to read my image (vmdk) file; it just outputs a generic error.


In my html code I have this inline script (no src)     How can I then insert the div into the DOM with javascript such that it appears right after the script tag, so it ends up looking like this

   The main thing is I want a solution that avoids using id's, class's and attributes to try to do a lookup. Is there a way I can do something like getting the current script node and then a insertAfter method?  Thanks

How can I reference the script element that loaded the javascript that is currently running?  Here's the situation. I have a "master" script being loaded high in the page, first thing under the HEAD tag.  <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"  "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> <html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en"> <head> <script type="text/javascript" src="scripts.js"></script>   There is a script in "scripts.js" which needs to be able to do on-demand loading of other scripts. The normal method doesn't quite work for me because I need to add new scripts without referencing the HEAD tag, because the HEAD element hasn't finished rendering:  document.getElementsByTagName('head')[0].appendChild(v);   What I want to do is reference the script element that loaded the current script so that I can then append my new dynamically loaded script tags into the DOM after it.  <script type="text/javascript" src="scripts.js"></script> loaded by scripts.js--><script type="text/javascript" src="new_script1.js"></script> loaded by scripts.js --><script type="text/javascript" src="new_script2.js"></script>


I'm trying to install ubuntu from a USB stick. I did it on my old computer, using the same stick, but this time I've replaced 14.05 with 16.04. I've tried choosing both the try ubuntu without installing and install ubuntu options. I get the loading screen, but then I get into initramfs:  BusyBox v.1.22.1 (Ubuntu 1:1.22.0-15ubuntu1) built-in shell (ash)  Enter 'help' for a list of build-in commands.  (initramfs) unable to find a live medium containing a live file system  I've tried formating the USB again and checking that I have the 64-bit desktop version. Any ideas?

I am trying to boot Ubuntu on my computer.  When I boot Ubuntu, it boots to a black screen.  How can I fix this? Table of Contents:


Consider $N$ independent random variables $X_{1}, X_{2}, \ldots, X_{N}$ such that \begin{equation} X_{i} \sim \Gamma\left(1, \frac{1}{N}\right), \end{equation} for $i \in [N]$. Let \begin{equation} Y = \sum_{i=1}^{N} X_{i}. \end{equation} I am trying to find the joint PDF $$f_{\left(X_1, X_2, \ldots, X_{N-1}\right)|Y=1}(x_{1}, x_2, \ldots x_{N-1}).$$ Can we conclude from our given information that the joint PDF is the PDF of a $\text{Dirichlet}(1, 1, \ldots, 1)$ distribution?  answer tackles a similar question, but I am not sure how the answer concludes that the Beta marginals imply a joint distribution which is a Dirichlet (as a comment states, the marginals contain insufficient information about the joint). In other words, my confusion with the question I linked to is this: Is it true that, for this case at least, the distribution for the random variable $\frac{X_i}{X_1+\cdots+X_{N}}$ is the same as the distribution for the random variable $X_{i} | X_1+\cdots+X_{N} = 1$? If so, just out of curiosity, how general is this result? Does it hold for any distribution and any random variable?

Let $X_1,\dots,X_{k+1}$ be mutually independent random variables, each having a gamma distribution with parameters $\alpha_i,i=1,2,\dots,k+1$ show that $Y_i=\frac{X_i}{X_1+\cdots+X_{k+1}},i=1,\dots,k$, have a joint ditribution as $\text{Dirichlet}(\alpha_1,\alpha_2,\dots,\alpha_k;\alpha_{k+1})$   Joint pdf of $(X_1,\dots,X_{k+1})=\frac{e^{-\sum_{i=1}^{k+1}x_i}x_1^{\alpha_1-1}\dots x_{k+1}^{\alpha_{k+1}-1}}{\Gamma(\alpha_1)\Gamma(\alpha_2)\dots \Gamma(\alpha_{k+1})}$.Then to find joint pdf of $(Y_1,\dots,Y_{k+1})$ I can not find jacobian i.e.$J(\frac{x_1,\dots,x_{k+1}}{y_1,\dots,y_{k+1}})$


Im making c++ && sfml game for my teacher. I need to make game class naturaly I make constructor and destructor, but I cant figure out what methods should game class contain. curently it has these : init() - init all variables and other stuff (before I moved to c++  I was making games in HTML,JS but I never used OOP there. So I have no exp. doing games like this)

Generally, what are the core things that one should do in the game loop, and what are some things that one shouldn't do in the game loop?


I want to know how many rows in result set after executing the particular query  ResultSet rs = ps.executeQuery();   how get the size of rs??? thanx in advance

Shouldn't this be a pretty straightforward operation? However, I see there's neither a size() nor length() method.


I have two uniformly dirstributed random variables $$r_1 = \mathcal{U}(0,1)$$ and $$r_2 = \mathcal{U}(0,1)$$. I am looking for the probability distribution of $$max\{r_1, r_2\}$$. Is there any known distribution?

I have a question. Let's suppose that the two random variables $X1$ and $X2$ follow two Uniform distributions that are independent but have different parameters:  $X1 \sim Uniform(l1, u1)$  $X2 \sim Uniform(l2,u2)$  If we define X3 as the maximum of X1, and X2, i.e., $X3 = max(X1, X2)$, what kind of distribution would it be? It is certainly not a uniform and I can calculate the cumulative probability, i.e., $p(X3 <= a)$, because $p(X3 <= a) = p(X1 <= a) p(X2 <= a)$. But, I wonder if there exists any density function that can model X3.


I'm told that it's possible that $Cov(x_i, \epsilon_i) = 0$ and $E[\epsilon] =0$ yet $E[\epsilon | X] \neq 0$ but I haven't been able to find an example. My professor proposed $\epsilon_i = x_i^2$ where $x_i \sim \text{uniform}(-1,1)$ but I realized that this fails $E[\epsilon_i] = 0$. If we got rid of the assumption $E[\epsilon]=0$ than this satisfies $Cov(x_i, \epsilon_i) = 0$ yet $E[\epsilon | X] \neq 0$ but the task is to include $E[\epsilon]=0$.  The suggested pages do not provide a concrete example. @Whuber provides a nice image which appears to be of $\epsilon_i = x_i^3$ where $x_i \sim \text{uniform}(-2,2)$ but this doesn't work out: Let $\epsilon_i = x_i^3$ where $x_i \sim \text{unif}(-2,2)$. We have: \begin{align}     \begin{split}         E[\epsilon_i] &= \int_{-2}^2 \frac{1}{4} x_i^3 dx \\                        &= \frac{1}{16} x_i^4 \Big|_{-2}^2 \\                        &= \frac{1}{16}((2)^4 - (-2)^4) \\                        &= 0     \end{split} \end{align} But for the covariance, we have: \begin{align}     \begin{split}         Cov(\epsilon_i, x_i) &= E[\epsilon_i,  x_i] + E[\epsilon_i]E[x_i]\\                               &= E[(x_i^3)  x_i] + 0E[x_i] \\                                &= E[x_i^4] \\                               &= \int_{-2}^2 \frac{1}{4}x^4 dx \\                               &= \frac{1}{20}x^5 \Big|_{-2}^2 \\                               &= \frac{1}{20}(2^5 - (-2)^5) \\                               &\neq 0     \end{split} \end{align} Am I mistaken?  Professor gave me a solution which was just demeaning the variable. (Should have thought of doing that sooner.) Let $\epsilon_i = x_i^2 - E[x_i^2]$

Let $x$ and $\epsilon$ are two random variables. If $$Cov(x, \epsilon)=0$$ and $$E[\epsilon]=0,$$ can that lead to $E[\epsilon|x]=0?$


I was reading the Wikipedia page of , and according to it,  cupboard is pronounced /ˈkʌbərd/ and not /ˈkʌpbɔːrd/.  I see why the /b/ is merged into the /p/ sound, making cupboard sound like "cu-board", but it seems very strange to me that the /ɔ/ is reduced to just /ə/ sound.   Is "cupboard" really pronounced as /ˈkʌbərd/?

According to Google at least, the word "cupboard" originated in late Middle English as denoting a board that held cups. Since then, the word has evolved to mean a kind of cabinet.  My question is, given its origin and spelling, why do we pronounce "cupboard" with a silent "p"? Has the pronunciation simply evolved because "cup-board" is too awkward to say, or is there a deeper pronunciation rule that I'm not aware of?


Let $\{f_n\}_{n=1}^\infty$ be a sequence of holomorphic functions in a domain $D\subset \mathbb C$ which converges uniformly on a compact subsets to $f$ with $f\not\equiv 0$. If a point $a\in D$ is a zero of $f$, prove that $a$ is a limit point of zeros of $f_n$ for $n\geq n_0$ for some positive integer $n$.         Someone gave me a hint, but I forgot it.

I do not know how to proof following question:  Let $D$ be a domain in $C$.  ${{f}_{n}}$ be a sequence of holomorphic functions on $D$ that converges uniformly locally to a function non-constant $f$. Show that for each $z\in D$, there is a sequence ${{z}_{n}}\to z$ as ${{f}_{n}}({{z}_{n}})=f(z)$ for all sufficiently large $n$.  Actually, I know that I should use an assumption such as: ${{f}_{n}}({{z}_{n}})\ne f(z)$  Therefore, there is compact set    that  $\left\| {{f}_{{{n}_{k}}}}({{z}_{{{n}_{k}}}})-f(z) \right\|>\varepsilon $  Then I think I have to use Montel theorem, but I do not know how to show the contradiction.


If $A$ is an arbitrary element of the general linear group $GL(2, q)$, is there a way to determine the order of $A$ without having to compute matrix powers?  The "brute force" method works fairly well. There are $q (q + 1) (q - 1)^2$ elements in $GL(2, q)$. At worst, you could check all divisors of this. Using  it's possible to limit the search to the divisors of $q(q - 1)$ and $(q - 1)(q + 1)$. However, I am slightly unsatisfied at having to compute the order this way.

There's a particular property of the elements of $\mathrm{GL}(2,q)$, the general linear group of $n\times n$ matrices over a finite field of order $q$, that I don't understand.  I know that the order of $\mathrm{GL}(2,q)$ is $(q^2-1)(q^2-q)=q(q+1)(q-1)^2$, since there are $q^2-1$ possible vectors for the first column, excluding the $0$ vector, and $q^2-q$ possible vector for the second column, excluding all multiples of the first.  So the order of any element must divide $q(q+1)(q-1)^2$ by Langrange. However, there is a further detail that      any element of $\mathrm{GL}(2,q)$ must have order dividing $q(q-1)$ or $(q-1)(q+1)$.    Is there a reason why one can narrow down the order to divide one of those smaller factors of $q(q+1)(q-1)^2$? Thanks!


Can anyone offer an intuitive description of a   that admits no ? I know they exist, but am unsure if there is any path to some level of understanding aside from total immersion in the original papers.

In 1960, Kervaire found the first example of a PL-manifold which does not admit a smooth structure. Since then, I understand that there are many examples of non-smoothable manifolds that can be built. My question is: Which is the "easiest" non-smoothable manifold? Easiest in the sense that among all the non-smoothable manifolds, this manifold has the easiest construction process.  Thanks everyone for your help !!  Cheers...


I have a python script that does incorrect math. here it is:  from random import randint while 1==1:     try:         exp = input()         if exp=="1+1":             print("=3")         else :             answer = exp             while answer == exp:                 answer = randint(0, exp+10)             print(answer)     except Exception as e:         print(e)         print(259)   when i run it, I get an error:  Traceback (most recent call last):   File "/Users/the_name_of_my_home_folder/Documents/the name of the file.py", line 1, in <module>     from random import randint ImportError: bad magic number in 'random': b'\x03\xf3\r\n'   I am using python 3.5.1 on a mac.

What's the "Bad magic number" ImportError in python, and how do I fix it?  The only thing I can find online suggests this is caused by compiling a .py -> .pyc file and then trying to use it with the wrong version of python. In my case, however, the file seems to import fine some times but not others, and I'm not sure why.  The information python's providing in the traceback isn't particularly helpful (which is why I was asking here...), but here it is in case it helps:  Traceback (most recent call last):   File "run.py", line 7, in <module>     from Normalization import Normalizer


I am taking a course in general topology. And I am struggling with the following exercise:     Let $\mathbb{R}$ be the set of all real numbers. Prove that each of the following subsets of $\mathbb{R}$ is a topology.      i) $\mathscr{T}$ consists of $\mathbb{R},\emptyset$, and every interval $(-n,n)$, for $n$ any positive integer.   Definition of topology:   $X,\emptyset\in\mathscr{T}$ If $\{x_\lambda:\lambda\in\Lambda\}\subseteq\mathscr{T}$, so that $\bigcup_{\lambda\in\Lambda}^{}x_\lambda\in\mathscr{T} $ If $A,A'\in\mathscr{T}$ then $A\cap A\in\mathscr{T}$   1) The first definition is checked once $\mathbb{R},\emptyset\in\mathscr{T}$  2) The second definition is the one I do not know how to tackle. It seems straight-forward to mw that the union of any $(-n,n)$ belongs in the topology. However I do not know how to write a proof about it.  Question:  How should I write a proof of the second axiom?

I'm doing exercise from "Topology without tears book", page 27, exercises a and b.   First one (a) reads as follows. "Let $\mathbb{R}$ be the set of all real numbers. Prove that each of the following collections of subsets of $\mathbb{R}$ is a topology.  a. $\tau_1$ consists of $\mathbb{R}$ , $\emptyset$ and every interval $(-n;n)$ for $n$ any positive integer  b. $\tau_1$ consists of $\mathbb{R}$ , $\emptyset$ and every interval $[-n;n]$ for $n$ any positive integer"  To prove this I noticied that     $S_n=(-n;n) \in \tau_1 \; \forall n \in \mathbb{N}$ by definition.   $S_{n_1} \subset S_{n_2} \; \forall \; n_1 < n_2, n_1,\;n_2 \in \mathbb{N}$   From 2 it follows that    $S_{n_1} \cap S_{n_2} = S_{n_1} \; \forall n_1 < n_2 $  $\bigcup_{i=1}^{i=n} S_i = S_n \in S_{n+1} $   Sience intersection of any two sets is in $\tau_1$ and union of any number of sets is also in $\tau_1$ and noticing that $S_n \subset \mathbb{R} \; \forall n \in \mathbb{N}$ I can state that $\tau_1$ is a topology of $\mathbb{R}$  Is this proven right? I have the following question. Exercise b is very similar to exercise a - the only difference is that now $[-n; n]$ is a closed interval. I think that I still can use the same prove for this case too, but not sure - does closed interval $[-n;n]$ changes anything?


How to disable window grouping while Alt-TAB?

When I use ALT+TAB to cycle through my apps I would like to have icons for all my open browsers. I use the ` (Grave or the key above TAB) but I really find that hard to use.  Anyway I can just use ALT+TAB only?


Prove that $\Bbb Z[\sqrt{2}, \sqrt{3}]$ does not equal $\Bbb Z[\sqrt{2} + \sqrt{3}]$.   This is homework. I want to prove that these are different sets. The first set is the smallest ring containing the integers and the two radicals separately. The second is the smallest ring containing the integers and the sum of the two radicals. Unfortunately I cannot find any similar proofs to learn from. I've been trying to show that the second set does not contain the square roof of $6$, for instance, or the square root of $3$. We haven't looked at what the second set might contain. We've only looked at adjoining a single radical and not the sum of radicals on class.  If someone could solve a similar example or give me a crucial insight, that would be great.

Motivated by the positive answer to the following question:      I'm curious about whether ${\Bbb Z}[\sqrt{2}+\sqrt{3}]=\Bbb{Z}[\sqrt{2},\sqrt{3}]$ is also true, where ${\Bbb Z}[\alpha]$ denotes the smallest subring of ${\Bbb C}$ which contains $\alpha\in{\Bbb C}$. It suffices to know whether $\sqrt{2}\in{\Bbb Z}[\sqrt{2}+\sqrt{3}]$ is true or not. With some manipulation one can get $$ 2\sqrt{2}\in {\Bbb Z}[\sqrt{2}+\sqrt{3}].  $$ It seems no hope to get $f(x)\in\Bbb{Z}[x]$ such that $$ f(\sqrt{2}+\sqrt{3})=\sqrt{2}, $$ which is equivalent to $\sqrt{2}\in{\Bbb Z}[\sqrt{2}+\sqrt{3}]$. But I don't have a proof. How should I go on?


I am writing a book and I want to show the formats of equation numbering; I mean, I want to tell the students that they can put the numbering at the beginning or at the end of the formula's line in their documents such as papers or assignments.  So, in an example, I want to bring equation numbering in the right side of the equation and in another example I want to show the equation number in the left side of the equation at the beginning of the line. I did try the following answers but they change the numbering format in the whole document. How can I do it locally?      This is what I tried based on a  to my question and it's linked question with use of the amsmath package:    %pdflatex \documentclass{article} \usepackage[leqno]{amsmath}  \makeatletter \newcommand{\leqnomode}{\tagsleft@true} \newcommand{\reqnomode}{\tagsleft@false} \makeatother  \begin{document} \reqnomode \begin{align}\tag{1} \frac{{{\partial ^2}u}}{{\partial {r^2}}} + \frac{1}{r}\frac{{\partial u}}{{\partial r}} - \frac{u}{{{r^2}}} = \frac{1}{{{c_1}^2}}\frac{{{\partial ^2}u}}{{\partial {t^2}}} \end{align} \\[-10pt] \leqnomode \begin{align}\tag{1} \frac{{{\partial ^2}u}}{{\partial {r^2}}} + \frac{1}{r}\frac{{\partial u}}{{\partial r}} - \frac{u}{{{r^2}}} = \frac{1}{{{c_1}^2}}\frac{{{\partial ^2}u}}{{\partial {t^2}}} \end{align} \end{document}     However, when I was writing my file first, I was not using the amsmath package because in my document I had only two equations just as examples. I was not aiming to write complicated mathematical equations to use that package. So, I am looking for an easy way to make such equation's tag.

I'd like to know if it is possible switch between the leqno and reqno options in the same document keeping the numbering of the equations. Namely i use the reqno option (default for amsmath and the standard article class), but i want that some equations are numbered by the left side (as if I had relied the leqno option) and the others no.  I'd like a commands as \leqnomode and \reqnomode to change the position of \tag in anywhere of the document.  Is this possible?


I know this is an elementary question, however I am really lost as to where to start.  Since both $\mathbb{R}$ and $\mathbb{C}$ are finite-dimensional I think the inner product will be completely determined by the basis $\{1\}$.   I am not sure where to go from here.

This is a question of the book Linear Algebra of Kenneth Hoffman.  Describe explicitly all inner products on $\mathbb{R}$ and on $\mathbb{C}$.  I think that if $<,>$ is one inner product on $\mathbb{R}$ (or $\mathbb{C}$) then $< ,>=K[,]$, where $[,]$ is the standard inner product. Is that correct?


I have access to a Linux CentOS box.  (I can't use crontab sadly)  When I need to run a task everyday I have just created a infinite loop with a sleep.  (it runs, sleeps ~24 hours and then runs again)  #!/bin/sh   while : do     /home/sas_api_emailer.sh |& tee first_sas_api  sleep 1438m done   Recently I have a task that I need to run at a specific time everyday 6:00 am (I can't use crontab)  How can I create an infinite loop that will only execute @ 6:00 am?

I want my bash script to sleep until a specific time. So, I want a command like "sleep" which takes no interval but an end time and sleeps until then.  The "at"-daemon is not a solution, as I need to block a running script until a certain date/time.  Is there such a command?


This is probably a nonsensical question, but I'm having trouble wrapping my head around it. I'm thinking of the classic scenario where a stationary observer is watching a spaceship move horizontally. It makes perfect sense to me that a beam of light bouncing up and down will appear to move more slowly vertically, since it has to also move horizontally. This produces the time dilation effect. However, I don't see why this same dilation factor has to apply to a beam of light moving horizontally. This is the way that I have seen length contraction derived. It sounds peculiar, but couldn't there be a different time dilation factor for objects moving horizontally versus vertically on the spaceship? edit: I believe this can be explained by thinking about a beam of light moving diagonally on the spaceship, but I'll leave the question up in case someone has a better explanation.

I have seen and understood the classical thought experiment where you imagine a "light clock" sending a light ray between two mirrors while moving in a perpendicular direction to the lights direction in the reference frame of the clock, as shown here:    What I don't understand is that the formula for an observers perceived time, $\Delta t'$, of the clock is derived from the Pythagorean theorem which only works because the light is being reflected in a direction perpendicular to the direction of the velocity of the clock (from the clock's point of view). If the clock reflected the light in the same direction as it was itself moving, that is in the animation above the clock would be flipped 90 degrees "laying down", then it would still be a clock because it would still have a fixed period but I don't see how one would derive the same result for how a bystander perceives the clock:    $$\Delta t' = \dfrac{\Delta t}{\sqrt{1-(v/c)^2}}$$  I am asking this because in the example I've seen of length contraction, the clock was moving in the same direction as the light was being reflected, but in the derivation of the equation of the contraction effect they still used the formula for time dilation, which was derived when the clock was "standing" as in the animation above.


I recently created a Public folder for my user on samba. I have it set up so that anyone can access it on my network(it's just me and a couple other computers). How do I prevent the other computers from dumping huge amounts of data into that folder, and thus exceeding the amount of space the drive holds. e.g. Someone dumps 200GB of garbled text onto a 50GB drive. I guess what I am asking is "how to limit a folders capacity?".

I have a simple set-up with just one public share on my configuration file. How can I restrict its size?


I am a mathematician who specialises in algebraic geometry and algebraic topology. I am looking for a good textbook on the standard model that gears towards readers with more of a math rather than a physics background. Any suggestions?

I know classical physics, quantum mechanics, special relativity, and basic nuclear physics. I would like to get into some particle physics.   Where can I find a good introduction? It might be useful to segment books by whether they require quantum field theory or not.


I would like to write the code to forecast the status. The status 0 means non-active, 1 means active. I would like to predict the future month (e.g 2016/6/1), the status should be "0" or "1".    What algorithm could be used in such a situation?  date       status 2016/1/10   0 2016/1/19   0 2016/2/2    1 2016/2/10   1 2016/3/1    0 2016/4/2    1 2016/4/3    0 2016/5/4    0 2016/5/5    1

I have a binary time series with 1 when the car is not moving, and 0 when the car is moving. I want to make a forecast for a time horizon up to 36 hours ahead and for each hour.   My first approach was to use a Naive Bayes using the following inputs: t-24 (daily seasonal), t-48 (weekly seasonal), hour of the day. However, the results are not very good.  Which articles or software do you recommend for this problem?


If my opponent has an abundance of other creatures including  out, can I play cards like , , or the new  to get around my opponents creatures? Since they each target all of certain types of creatures and not the individual creature itself?  Or would Hexproof prevent this since the cards don't target ALL creatures?

Note: this is intended to be a canonical question about whether or not a spell or ability targets so there are multiple sub-questions.   Can Hexproof or Shroud save my creature from ? What about a  that was cast for it's Overload cost? Does shroud prevent me from using the Monstrosity ability of a creature, or from giving it more counters with Proliferate? Can I cast an Aura Enchantment on one of my creatures with Shroud, or an opponent's creature with Hexproof? Or can I use the Equip ability to attach an equipment to one of my creatures with Shroud? Will 's ability trigger when my opponent plays ? And will I have to sacrifice my  if my opponent casts ? Will Shroud or Hexproof prevent an opponent from choosing me with 's ability? Will Hexproof keep one of my creatures from being affected by ? If an Aura or Equipment is attached to a creature with Hexproof, does the Hexproof protect the attached permanent?


As i read, the GC method will be called automatically during run time and all the unused object's memory will be deallocated. If everything is done by automatically then what is the use of forcefully calling GC() method.

The general advise is that you should not call GC.Collect from your code, but what are the exceptions to this rule?  I can only think of a few very specific cases where it may make sense to force a garbage collection.   One example that springs to mind is a service, that wakes up at intervals, performs some task, and then sleeps for a long time. In this case, it may be a good idea to force a collect to prevent the soon-to-be-idle process from holding on to more memory than needed.   Are there any other cases where it is acceptable to call GC.Collect?


I'm not used to that kind of p-value form as I don't know how to interpret it...  It's usually shown a p-value with stars (significant codes) on its sides  Can anyone help? How to read if the variable significant or not...?

After taking a statistics course and then trying to help fellow students, I noticed one subject that inspires much head-desk banging is interpreting the results of statistical hypothesis tests.  It seems that students easily learn how to perform the calculations required by a given test but get hung up on interpreting the results.  Many computerized tools report test results in terms of "p values" or "t values".  How would you explain the following points to college students taking their first course in statistics:   What does a "p-value" mean in relation to the hypothesis being tested?  Are there cases when one should be looking for a high p-value or a low p-value? What is the relationship between a p-value and a t-value?


I have a Sony Xperia M device with Android 4.3 the official support for the device was stopped in 2015-16. Now is that possible to update the android version to 5 or 6?  If yes, how? I tried many sites but it is very tricky to understand for a beginner like me.  My main question is will the Android 5 app work on my device after upgrading?  EDIT: I will be great if you reopen the question I have something to share with people who came across this same issue or question in future.

This Community Wiki question is designed to be the "canonical question" for questions asking how to upgrade one's device to a new Android version.   I want to get a newer version of the OS for my Android device. How can I do that?  See also:


I am trying to compare a string (ignoring case) against a specified element in a vector string (I don't want to see if the string exists anywhere in the vector, only if it exists at the specific index).    I have not been successful using a string compare as I normally would.  Any help would be appreciated.

What is the best way of doing case-insensitive string comparison in C++ without transforming a string to all uppercase or all lowercase?  Please indicate whether the methods are Unicode-friendly and how portable they are.


I cant download anything from Ubuntu software center, it hangs on updating cache then its telling me "failed to download repository information". Linux I understand suppose to be a straight forward OS with no hiccups, but lately its been giving me headaches and I just only installed it 5 days ago. I looked up similar problems but nothing comes close to fixing it. Any suggestions or fixes ?

Since migrating to a true install and upgrading to 12.04 I have had several problems that seem to relate to the Ubuntu Software Center. Hanging at applying changes and blank screen on screen lock only when it is running, for instance.  My question is: Can I safely uninstall and reinstall Ubuntu Software Center and could this possibly fix those problems or are they just bugs I have to wait for updates for?


Made a button to add "links" to "richTextBox".  "Links" are added not to the text, but from above "richTextBox".   Question How to make the "links" added to the text based on the current code or based on another solution?     LinkLabel link = new LinkLabel();         link.Text = "*** LINK ***";          // link.LinkClicked         link.LinkClicked += new LinkLabelLinkClickedEventHandler(this.link_LinkClicked);          // data         LinkLabel.Link data = new LinkLabel.Link();         data.LinkData = @"C:\";          // link         link.Links.Add(data);         link.AutoSize = true;         link.Location =             this.richTextBox1.GetPositionFromCharIndex(this.richTextBox1.TextLength);          // richTextBox1         this.richTextBox1.Controls.Add(link);         this.richTextBox1.AppendText(link.Text + "   ");         this.richTextBox1.SelectionStart = this.richTextBox1.TextLength;

When I add www.stackoverflow.com into my RichTextBox and run the program it is shown in blue and as a hyperlink yet when I click it nothing happens. How can I fix this?


Prove that there are infinitely many prime numbers of the form $6n-1$. I proved that there are infinitely many prime numbers but I couldn't bring it in the form given in the question. While proving it, I was getting $6n+1$ not $6n-1$.

The proofs given on other sites weren't that clear and used different methods that I have yet to learn.    Prove that there are an infinite number of primes of the form 6n+1.  The hint that was given was: Let p = p1, p2, ..., pk + 1, where p1 = 2, p2 = 3,...pk are the first k primes.  Show that p is prime.  (p1 means p sub 1, p2 means p sub 2, and pk is p sub k.  Wasn't sure how to write it on this.)    Can someone explain this hint on how they came about of p1 = 2, p2=3, etc, and prove this please?    Also, how would the proof change if the form changed?  ("Prove that there are infinite number of primes of the form....")


Installed ubuntu and it was showing low graphics so updated by the command   sudo apt-get install fglrx    as told in     Now screen shows only blank screen.with x shape pointer.What to do now?  My laptop hp n003tx

I am trying to boot Ubuntu on my computer.  When I boot Ubuntu, it boots to a black screen.  How can I fix this? Table of Contents:


please help me, i don't know what wrong with this regular expression.
\s*\s*Ціна[\s[:alpha:]\,\.]*:\s*<\/strong>\s*(\d+[\s\d]*.\d*)\s*грн[\s[:alpha:]\,\.]*<\/div> Without g flag i have 1 match, but with g flag no matches Below part of searching text
Ціна продажу: 5 734 600.00 ГРН

Is there a quick way to find every match of a regular expression in Ruby? I've looked through the Regex object in the Ruby STL and searched on Google to no avail.


How is it possible that I can password lock my terminal. I do not want anybody but me in the terminal. I want it so like when I start up the terminal, it will ask for a password, and if the password is incorrect, it will exit out, or maybe ask again. What are my possible ways I can do this?

I want to restrict an application being opened under ordinary privileges. Only root shall run the application, so that contents wont be seen by others and they wont change anything.


I've searched here, Google, Wikipedia, etc. without luck. I would have read this book after about 2004 but probably more than 5 years ago.  As best I recall the book has a near-future setting, but most people wear augmented-reality goggles as part of their daily life.  If you travel through a city, you can see advertising overlaid on blank walls that's published to everyone, but you can also subscribe to specific channels of overlays; how the city appeared in a specific era, for example, or how it was represented in a famous game/movie.  Some people publish AR travelogues, marking up reality for other people to view.  There is also widespread use of 3D printing technology, something of a maker culture.  The protagonists are recruited/instructed to recover some MacGuffin - something dangerous in the wrong hands, like a bottle of radioisotopes or the like.  I think this takes place somewhere in the western US.  As they chase leads, they discover that hidden in the real world, there are hidden economies.  You need to have correctly-programmed goggles even to see them; the economies function using various game-type economic/social systems and perpetuate themselves by printing their own goggles to control access.  This part of the novel takes place in the EU, I think.  The protagonists eventually manage to track their target to a ship (I recall it being in the North Atlantic) and there's a fight which ends with them tossing the MacGuffin into the ocean.  I'd like to re-read this book, since I'm very interested in how the hidden economies/secret societies worked.  If I'm not conflating a completely different story, there was even a secret society that functioned by passing around copies of a book, and rigorously following the instructions in that book.  (The implication was that the book itself was somehow an intelligent agent processing itself by means of its followers.)

I think this novel came out in the 2000s.  There are many cultures that live close together but are very different, for example some pretend to be pre-industrial.  One of the main characters is a youth who grew up in a pretend pre-industrial society and is now exploring the rest of the solar system? ring-world?   Each culture experiences their own reality that is defined by a ruleset.  One of the rulesets becomes aggressively self-propagating and this is the problem that drives the plot.  At some point a tumbling house, just a normal house, is used to travel across space.


As the title says: the vacuum packed salmon fillets have been sitting in a turned off fridge for quite some hours. The packs only felt a little cooler than the room temperature of +/- 20 degrees Celsius (68℉). They have been put in a working fridge immediately after finding out. If they weren't vacuum packed, I'd have thrown them away already.  Can I still safely eat them if they do not smell bad, or should I throw them out?

If I left food out of the refrigerator for some period of time, is it still safe? If I left it out too long, can I salvage it by cooking it more?


I know photon is an electromagnetic wave and are generally massless and therefore cannot exert a gravitational force, however I know energy can wrap the space around it so I'm confused. I think I'm mistaken somewhere so please help, thanks.

In general relativity, light is subject to gravitational pull.  Does light generate gravitational pull, and do two beams of light attract each other?


Sorry guys I just have a quick question. I am trying to figure out why program won't print out "Your item is a moose" when the user enters animal at the first prompt and then puts yes at the second prompt. Any help would be great thanks      public static void main(String[] args) {     // TODO Auto-generated method stub       String Answer1;     String Answer2;      // Read in how much cash the user has     Answer1 = JOptionPane.showInputDialog("Question 1: Is it an animal, vegetable, or mineral");     Answer2 = JOptionPane.showInputDialog("Question 2: Is it bigger than a breadbox");       if (Answer1 == "animal" && Answer2 == "yes") {         JOptionPane.showMessageDialog(null, "Your item is: A Moose");     } }   }

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