I have been trying to find a generalized relationship between Von Neumann Entropy and Purity of a quantum state?  there is a discussion of a specific case for a qubit and a more general case of a multi-level system but, I believe these are relations for the system in a given state basis. Is there a to work this out some way in which we can keep this in a basis-independent formalism.

Given a density matrix $\rho$, its linear purity is $\mathrm{Tr} \rho^2$, its von Neumann entropy is $-\mathrm{Tr} \rho \log \rho$. Knowing one how do I calculate the other?  Edit:   My thought is that the linear purity and the von Neumann entropy are a parallel set of benchmarks for mixedness. Their inter-conversion should be like unit conversion.  See it this way, as a state goes from a pure state to a maximally mixed state, $\mathrm{Tr} \rho^2$ goes from $1$ to $0$, and $-\mathrm{Tr} \rho \log \rho$ goes from $0$ to $\log d$, like two rulers. A point on one should correspond to a point on the other.


I am trying to install python 3.6 idle. I have used sudo apt-get install python3.6 but keep getting the same error:  Reading package lists... Done Building dependency tree Reading state information... Done E: Unable to locate package python3.6 E: Couldn't find any package by regex 'python3.6'   Please help

When I try to install any package through the command line, I get an error.   $ sudo apt-get install <package> Reading package lists... Done Building dependency tree        Reading state information... Done E: Unable to locate package <package>   Can anyone help me on this?


Right now I use a backpack to hold all of my supplies including spare tubes, pump, patch kits, tools, my change of clothes for work, etc.  This is the backpack I use:    It's about as comfortable as a backpack can get without getting into the hiking backpacks with frames. Altogether I would say it weighs no more than 10 lbs max. The muscles in my back get slightly irritated during my commute.  Would it be more comfortable to use a rear cargo rack on my bike instead? Will adding more weight to the bike change how the bike rides and feels?  EDIT: After doing some research I came across  that explains the different methods of carrying your gear on commutes and how it affects your body. It's worth a look.  EDIT #2: Having tried both for a couple of weeks now, I can say that (for me personally) the backpack is the better way to go given the relatively light weight I have to carry.  If you do use a backpack, make sure that the straps are tightened enough so that it's positioned higher up on your back and to the point to where there is little to no movement on your back. This makes a world of difference when it comes to comfort.

Probably, another debatable question from my side.  When carrying items while riding, like water bottle, repair kits, pumps, or other stuffs that you might need, What is the best option.... to carry them?   On your cycle at saddle bag, handlebar bags, or pannier bags or etc.  or, On backpacks, like hydrant pack, or simple travel pack.   While loading on cycle, it will increase the weight of the bike, thus affect a lot of things, like speed, traction, more reactive on corners. Like while using pannier bags.. it will increase rear weight, making it difficult on uphill.   Also while loading on backpack, it will tire you down fast if its a big load, decreases your flexibility, agility & etc.  So what is right way to do it?  Update:  The type of ride I generally, go to are commuting, mountain biking, & trailing. And the items I generally carry are   Commuting: Water bottle(x2), Laptop (17"), books, copies, repair kits, hand pump, few other accessories. Mountain Biking & Trailing: Water bottle(x2), repair kits, extra tubes, hand pumps, candybars & few other accessories


If $M$ is a $3\times3$ matrix, where M'M=I and $\det(M)=1$, then prove that $\det(M-I)=0$  By the information given I know that given matrix is orthogonal. How can prove the above determinant zero?

$M$ is a $3 \times 3$ matrix such that $\det(M)=1$ and $MM^T=I$, where $I$ is the identity matrix. Prove that $\det(M-I)=0$  I tried to take $M$ $=$ $$ \begin{pmatrix}         a  &b & c \\         d & e & f \\         g & h & i         \end{pmatrix} $$   but its expansion is too long.


You toss a fair coin with sides $K$ and $Z$ infinitely often. What is the probability of the event that the pattern $KKK$ occurs before $ZKZ$ ?  I did the following: Let $(Z_n)_{n\in\Bbb N_0}$ be i.i.d. with $\Bbb P (Z_1 = K) = 1/2 = P (Z_1 = Z)$. We define the Markov chain $X_n$ by $$X_n = (Z_n , Z_{n+1} , Z_{n+2})$$ and $\alpha := \text{Uniform}(\{K,Z\}^3)$ and the entry times $T_A := \inf\{n\geq 0 : X_n \in A\}$ for $A\subset \{K,Z\}^3$. Writing in short forms, we are interested in $$\Bbb P _\alpha( T_{KKK} < T_{ZKZ})$$ We can define the function $f(z) = P _z( T_{KKK} < T_{ZKZ})$ and calculate by the first step method   $f(ZKZ) = 0$ $f(KKK) = 1$ $f(ZZZ) = f(ZZK)$ $f(ZZK) = \frac 1 2 f (ZKK)$ $f(ZKK) = \frac 1 2 + \frac 1 2 f(KKZ)$ $f(KKZ) = \frac 1 2 f(ZKK)$ $f(KZZ) = \frac 1 2 f(ZZZ) + \frac 1 2 f(ZZK)$ $f(KZK) = \frac 1 2 f(ZKK)$   Combining 5. and 6. yields $f(KKZ) = \frac 1 3$ and this makes the full calculation of $f$ possible. Thus  $$\Bbb P _\alpha( T_{KKK} < T_{ZKZ}) = \frac 1 8 \sum_{z\in \{K,Z\}^3} f(z) = \frac 5 {12}$$  Is there a more elegant way to solve this?  Edit: I really ask for different approaches (not only one different from mine)

What is the probability of obtaining THT before HHH when a toss is tossed sequentially? Could someone solve using state diagram and law of total probability?


I pass 1(stdout)/2(stderr) to read system call but it still works fine. Then I pass 0(stdin) to write system call and find out it works too!  int main(int argc, char** argv){     char buf[1024] = "abcdefghi\n";      write(0, buf, 10);      char readbuf[1024] = {0};     // read(1, readbuf, 10); works too     read(2, readbuf, 10);     write(2, readbuf, 10);      return 0; }   output:  abcdefghi hey stdin  <-- I input this hey stdin   Confused, I thought it should be an error.   Experiement:   Then I tried redirecting fd 2.  $ ./a.out 2>/dev/null   this time both the read and 2nd write is not 'visible'. The output is  abcdefgi   So the stderr can be used for read?  I then close the stdout & stderr and make two copy of stdin:   int main(int argc, char** argv){     char buf[1024] = "abcdefghi\n";      close(1);     close(2);      dup2(0, 1);     dup2(0, 2);      write(0, buf, 10);      char redbuf[1024] = {0};     read(2, redbuf, 10);     write(2, redbuf, 10);      return 0; }   Again it works.   output:  abcdefghi hey stdin  <-- I input this hey stdin   So stdin can be used for write?  I need some explanation here.  Question  I want to know:  Why stdout/stderr can be used for read?  Why stdin can be used for write?  Is the three stream(stdin,stdout,stderr) internally one stream ?  If not, why am I getting this result?

According to , less reads navigation commands from stderr if it's not able to open /dev/tty.  This seems puzzling, since I've never seen anything write to another program's stderr stream, and I don't know how I would even accomplish that.  What is the purpose of stderr being open for both reading and writing? And if this is useful, how do I make use of it on modern systems? (Is there some arcane syntax to pipe something into stderr instead of stdin, for instance?)


When I add fields using the jQuery .after() function, the show/hide functionality does not work on those fields.  Here's a JSFiddle that demonstrates the issue:    The show/hide functionality works on the first row, but does not work on any rows added after that one. I think the code being written after the page has been loaded might be the issue, but I'm not certain. If that's the case, is there a work around other than hard coding a certain amount of rows?  Here's the code I'm working with:  CSS:  #Table {   font-family:"Trebuchet MS", Arial, Helvetica, sans-serif;   border-collapse:collapse; } #Table td, #Table th {     font-size:1em;     border:1px solid #98bf21;     padding:3px 7px 2px 7px; } #Table th {     font-size:1.4em;     text-align:left;     padding-top:5px;     padding-bottom:4px;     background-color:#A7C942;     color:#fff; } #Table tr.alt td {     color:#000;     background-color:#EAF2D3; }   HTML:

         #	         Cause

         1	                      <select name='report_cause2' id='report_cause2' class="report_cause">                 <option value='default'>-</option>                 <option value='other'>Other, Not Listed</option>             </select>
                 <input type="text" name="cause_detail_info" id="cause_detail_info" placeholder="Type cause here" size="48" maxlength="50" class="textbox required" value="" />

 <input type="button" id="btnAdd" name="btnAdd" value="Add More" class="button" />   jQuery:  var count_2 = 5; var table_count2 = 1;  $(document).ready(function () {      $('.cause_details').hide();     $('.report_cause').change(function () {          if ($(this).val() == 'other') {             $(this).parent().find('.cause_details').show();         } else {             $(this).parent().find('.cause_details').hide();         }      });      $('#btnAdd').click(function () {         count_2 = count_2 + 2;         table_count2 = table_count2 + 1;         $('#Table tr:last').after('
' + table_count2 + '	' +             '' +             '<select name=\"report_cause' + count_2 + '\" id=\"report_cause' + count_2 + '\" class=\"report_cause\">' +             '<option value=\'default\'>-</option>' +             '<option value=\'other\'>Other, Not Listed</option>' +             '</select>' +             '
' +             '<input type=\"text\" name=\"cause_detail_info' + count_2 + '\" id=\"cause_detail_info' + count_2 + '\" placeholder=\"Type cause here\" size=\"48\" maxlength=\"50\" class=\"textbox required\" value=\"\" />' +             '
' +             '
');     }); });

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.


Suppose someone ask a question, then in base of the answer I gave, he/she change the question to something else. Now the my answer is meaningless looking like a copy of a part of the question. What am I supposed to do? Should I delete the answer?

What should I do if a question has changed since I answered it? The other members vote my answer down because it actually doesn't answer the current question.  This kind of editing sometimes happens with  where the OP keeps adding new questions, making my pre-existing answer now incomplete.  But another pattern is when the OP asks an "XY problem" question, an answer points it out, and he changes the question to react to that.  Those answers now not only aren't answers but can look very tangential to people who don't review the edit history.


Is there a command where which I can input into terminal to list the users which have been created by a user or root? I don't want to use the GUI interface I'm wondering if there is a command.

I have set of users with root access.I want to know list of users who are all created by currently logged in user.  From below structure if user1 login to system , how to list user's like user11,user12.who are all created by user1.  RootUser  user1(Root Access)   user11(normal user created by User1) user12(normal user created by User1)  user2(Root Access) user21(normal user created by User2) user22(normal user created by User2)


Why do multiple people have to review an edit, when I have edit privileges anyway?  Should it not just automatically apply if I approve it?

I already have the "Edit Questions And Answers" privilege. Yet, if I approve someone else's edit, I'm told that more votes will be required before the edit is accepted.  This seems a bit peculiar to me, since I could just copy the edited version and paste it myself.


What SD card type and brand would be the fastest and most reliable for a Pentax K-01 DSLR camera?

Cameras rarely specify exactly what speed cards you should be using in them - I just checked the manual for my DSLR, and all it says is to use an SDHD card, and a "high speed" card should be used for recording video.  On the other hand, there are a number of different rating systems for memory card speed (33x! 150x! Class 2! Class 10!) and price seems to increase with speed.  Is there any way to test the maximum write speed the camera is capable of?  Are the read/write speeds documented anywhere?


Let $f$ be a holomorhic function on the open unit disk $D$. Suppose that there is an $r\in[0,1)$ such that restriction of $f$ to the annulus $$U=\left\{z\in C:r<\left|z\right|<1\right\}$$ is one-to-one. Prove that $f$ is one-to-one on $D$.  Firstly, $f$ is one-to-one if and only if derivative of $f(x)$ is not zero. So my aim is to use the boundary property of this function to prove the result. I tried Cauchy integral theorem. But it doesn't seem to work very well. Neither do the maximum and minimum principle.

Let $f: B(0,1) \rightarrow \mathbb{C}$ be holomorphic and suppose $\exists\ r \in (0,1)$ such that $f$ is injective in $A = \{z \in \mathbb{C} : r < |z| < 1\}$. Prove that $f$ is injective.  I tried using Rouché theorem, or the identity theorem, but I don't know what to do. Any hints? :)


Is there a way to align the view or a camera to be perpendicular to a specific face or object using it's normal? The thing I am trying to acheive, is to use the view to unwrap a face, so I can use it later for neighboring faces unwrap, but I'm trying to do this precisely, not by eying it.

I would like to align the view straight on to a face, perpendicular to the normal. How do I align the 3D viewport to the face of a mesh?


Description: I have want to structure my website into several pages using following css: .page {     height: 100vh; }  I add several pages to the website and on the last one I want a footer to appear on the bottom of the page, e.g.   .page {   height: 100vh;   background-color: cyan; }  footer {   position: relative;   width: 100%;   height: 100px;   bottom: 0;   background-color: #000; }
Page 1

Page 2

    What I've tried:  I've tried to set position: absolute (of footer) like in this answer:  I also tried to put a wrapper around the footer with height: 100%; I've also used min-height: 100vh instead of height with no effect  The question: How can I get the footer to the bottom of the page? PS: I don't know if it's relevant but I'm using Firefox v. 85.0.2 (64-bit) Edit: I want the footer to be inside the page, I use these pages to structure my website and the footer should appear on the bottom of the very last page.

Given the following HTML:

     Copyright Foo web designs

    I would like #copyright to stick to the bottom of #container. Can I achieve this without using absolute positioning?


I am looking for help, because I don’t know about computers much. I had to restart my notebook, and than my ubuntu won’t start and I don’t know what these things it is writing mean. If there is anyone who could help me with it I would be really happy.

I dual boot Ubuntu and Windows 7. I was browsing on FireFox in Ubuntu and all of a sudden I get some error message, so I rebooted.  Now when I try to boot into Ubuntu I get this message:  fsck from util-linux 2.26.2 /dev/sda6 contains a file system with errors, check forced. /dev/sda6: Inodes that were part of a corrupted orphan linked list found.  /dev/sda6: UNEXPECTED INCONSISTENCY; RUN fsck MANUALLY.         (i.e., without -a or -p options) fsck exited with status code 4 The root filesystem on /dev/sda6 requires a manual fsck  Busybox v1.22.1 (Ubuntu 1:1.22.0-15ubuntu1) built in shell (ash) Enter 'help' for a list of built-in commands.  (initramfs) _   How can I fix this?


I'm wondering how I can proof that for the following Ring $(R; +,-,0,\times,1)$ with $a \times a = a$ that $a + a = 0$.  How can I proof that? I just know about the lemma:  (i) $0(a) = a(0) = 0$  (ii) $(−a)b = −(ab)$  (iii) $(−a)(−b) = ab$  Many thanks in advance!!!  Kind regards

Im not sure what to do for this one, any help would be appreciated.


Since high school I was always confused by the concept of energy, in recent years I tried multiple times to understand what it actually is and I failed to grasp it from the common definitions (why does the joule have so many definitions on so many apparently unrelated physical phenomena?).  Recently I stumbled upon this quote from Feynman, addressing exactly what my problem was.     There is a fact, or if you wish, a law governing all natural phenomena   that are known to date. There is no known exception to this law – it   is exact so far as we know. The law is called the conservation of   energy. It states that there is a certain quantity, which we call   “energy,” that does not change in the manifold changes that nature   undergoes. That is a most abstract idea, because it is a mathematical   principle; it says there is a numerical quantity which does not change   when something happens . . . it is a strange fact that when we   calculate some number and when we finish watching nature go through   her tricks and calculate the number again, it is the same. It is   important to realize that in physics today, we have no knowledge of   what energy “is.” We do not have a picture that energy comes in little   blobs of a definite amount. It is not that way. It . . . does not tell   us the mechanism or the reason for the various formulas.   source: The Feynman Lectures on Physics Vol I, p 4-1   So my question is: Feynman died in 1988, do we today, 30 years later, have any better insights on what energy really is? does this quote still hold?

When lecturing about conservation of energy in the 1960s, Richard Feynman remarked:     It is important to realize that in physics today, we have no knowledge of what energy is. We do not have a picture that energy comes in little blobs of a definite amount. It is not that way. However, there are formulas for calculating some numerical quantity, and when we add it all together it gives “28” —always the same number. It is an abstract thing in that it does not tell us the mechanism or the reasons for the various formulas.    50 some years later, have we made any progress in terms of understanding the fundamental nature of what energy is?


First off I'm using Ubuntu 14.04  I was following this  to set up a Java JDK and at the end he uses   java -version   to see his current version number. The Version I installed was 1.8.0_66 but mine returns  java version "1.7.0_79" OpenJDK Runtime Environment (IcedTea 2.5.6) (7u79-2.5.6-0ubuntu1.14.04.1) OpenJDK 64-Bit Server VM (build 24.79-b02, mixed mode)   But when I check for the JAVA_HOME that seems to be correct  user@user:~$ $JAVA_HOME bash: /usr/lib/java/jdk1.8.0_66: Is a directory   Where have I gone wrong? The additional resource he uses in the video is  and I feel like step 5 is maybe where things are going haywire, even though I do update the file name version before I run the script.  Any ideas? Anything is much appreciated thank you.  After digging around online I ran the line  update-alternatives --config java   which returned with  There are 3 choices for the alternative java (providing /usr/bin/java).    Selection    Path                                            Priority   Status ------------------------------------------------------------ * 0            /usr/lib/jvm/java-7-openjdk-amd64/jre/bin/java   1071      auto mode   1            /usr/lib/java/jdk1.8.0_66/bin/java               1         manual mode   2            /usr/lib/jvm/java-6-openjdk-amd64/jre/bin/java   1061      manual mode   3            /usr/lib/jvm/java-7-openjdk-amd64/jre/bin/java   1071      manual mode  Press enter to keep the current choice[*], or type selection number:    I've tried entering in 1 and sudo 1 etc but the java version doesn't change. And it just redisplays the above code, without changing the default. How do I correctly enter this? If this is even how to do it. According to this I already had java installed in the jvm folder. Is it necessary to use the latest version of java or should I use this preinstalled version? I'm new to java so I'm not very experienced on what I need to be doing.

I followed all the instructions stated at this , but am encountering some problems with the last part of it.  I actually have version 6.22 of java and would like to update to version 6.30.  So after moving the extracted directory java-6-oracle into /usr/lib/jvm I do not know what to do, since the script that is pointed out in the answer above updates from java 5 to java 6.  For sake of clearness here is output if I do an ls in dir /usr/lib/jvm:  $ ls -l /usr/lib/jvm total 8  lrwxrwxrwx  1 root root   14 2011-07-12 15:18 default-java -> java-6-openjdk lrwxrwxrwx  1 root root   14 2011-07-12 12:19 java-1.6.0-openjdk -> java-6-openjdk  drwxr-xr-x 10 root root 4096 2012-04-12 12:06 java-6.31-oracle  drwxr-xr-x  7 root root 4096 2012-02-24 14:43 java-6-openjdk   What should I do now?    ADDED PART  Under the suggestion of @fossfreedom I ran the script anyway and actually it updated the java version.  In fact if I run command java -version output will be the following:  $ java -version java version "1.6.0_31" Java(TM) SE Runtime Environment (build 1.6.0_31-b04) Java HotSpot(TM) Server VM (build 20.6-b01, mixed mode)   There is still a problem, if Irun javac -version it gives me the old version installed:  $ javac -version javac 1.6.0_22   And if I use the tester at this  it will tell me that version is   Java Version 1.6.0_22 from Sun Microsystems Inc.   What's going wrong?  It seems that Java Runtime Environment has updated, but Java Compiler and Java plugin for browser have not.  How can I update them?    OTHER ADDED PART  sudo update-alternatives --config java will return following output  $ sudo update-alternatives --config java There are 2 choices for the alternative java (providing /usr/bin/java).    Selection    Path                                      Priority   Status ------------------------------------------------------------ * 0            /usr/lib/jvm/java-6.31-oracle/bin/java     1062      auto mode   1            /usr/lib/jvm/java-6-openjdk/jre/bin/java   1061      manual mode   2            /usr/lib/jvm/java-6.31-oracle/bin/java     1062      manual mode  Press enter to keep the current choice[*], or type selection number:   these makes sense with the fact that JRE is correctly updated to version 6.31, issues are on Java Compiler and Java browser plugin.  Any ideas?


WiFi is unable to turn on and connect to network. I have tried many options available on the Internet and nothing is working to allow my MacBook Pro to connect to a WiFi network.   When in System Report under the WiFi tab it states Airport Utility: Not Installed (as shown in attached picture).  When I try to delete the network and reinstall it the WiFi option is not available in interface/service name (as shown in pic.)  I attempted to reset NVRAM & SMC - this turned WiFi on for a few seconds allowed me to connect then it dropped again and I was not able to turn WiFi back on; so back to square one.   Any help fixing this would be greatly appreciated.  Running macOS Catalina - model A1278

I have a MacBook Pro 2009 running MacOS El Capitan. Recently the Wi-Fi has stopped working.   When I click on the Wi-Fi icon it displays the message "No hardware installed", but Ethernet still works.   Is there any way of fixing this by using a Wi-Fi dongle or something of the sort, if so do I need a specific dongle and how do I install it?


I want to remember one movie, it’s from the 80's or early 90's (or maybe even 70's), about a boy in wheelchair who eventually becomes cyborg.  There are also this guy's friends, one girl and one other guy who at the end of the movie shoots this cyborg with a crossbow, but cyborg catches the arrow and removes his mask to show who he is.  I'm sorry. I only remember this mess.  Thanks in advance.

I'm trying to find the name of a lower-budget science fiction film that was available for viewing on demands on MIT student cable in the late 1990s.  I suspect the film was made earlier in that decade, and it definitely seemed to have been influenced by RoboCop.  The plot involves characters is a somewhat dystopian near future.  One of the characters (named Hawkins, I think) is initially in a wheelchair, and that is interfering with his relationship with the woman he loves.  (He watches virtual reality simulations of himself having sex with her when he's alone at home.)  Maybe halfway through the movie, he decides there's no hope for their relationship, so he lets the bad guys turn him into a RoboCop-like cyborg.  I think he ends up fighting the other main characters, but I don't remember how the movie ends.  The film was clearly shot cheaply but competently.  The color palette was rather drab, I think, and there were few indoor sets.  It's possible that the film never got a normal release of any kind, since I don't know where the students at MIT cable got ahold of it.  So does anybody know what this film was?


Codeblocks have horizontal scrolling.  So, how can I print from StackOverflow to show all code?  Is there a way to turn horizontal scrolling off?  It's no good for mobility impaired users, anyway, so I'd prefer not to have it on my system.

I would like to make a suggestion for a Stack Overflow/Exchange complete Q&A printer-outer.   It would print out the full question, its answers, and  its comments, which the normal web-browser print does not do.


If I have the courage to read the umpteen pages on their site I may find the answer but it's far easier to ask a Lucky Backup user!! Does Lucky Backup do incremental backups or full backups after the first backup? I've now just (hopefully) set it to backup once a week. Will it then do another complete backup or simply add the changes since its' last backup? Thanks Garoolgan

This question exists because it has historical significance, but it is not considered a good, on-topic question for this site, so please do not use it as evidence that you can ask similar questions here.  While you are encouraged to help maintain its answers, please understand that "big list" questions are not generally allowed on Ask Ubuntu and will be closed per the .   Backup is incredibly important. Obviously there's no best backup tool, but a comparison of the options would be very interesting.   Graphical Interface? Command line? Incremental backups? Automatic backups? Install method: In standard repositories? PPA?


I have faced many time the NullPointerException in android. Some times I understand why the exception is thrown.  My Question is: Android applications are developed in Java and Java does not support pointers, then why is the exception called NullPointerException?

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


Is there a general rule whether to use the Verb + to infinitive or the Verb + ...ing format?  There are cases in which I can't decide which one to use. Like:  -They can't afford to go out very often.  -They can't afford going out very often. Or:  -I don't mind to wait.  -I don't mind waiting. Or:  -It was a nice day, so we decided to go for a walk.  -It was a nice day, so we decided going for a walk.

Some verbs are followed by ing, e.g. I enjoy swimming. We can't say I enjoy to swim. Likewise, some verbs are followed by to, e.g. I decided to make a plan.   Which particular verbs are followed by ing and to? Can you please provide a list for that?  Moreover, which verbs can be followed by both without having the meaning changed?


I landed in Paris on Long Stay Visa and I am planning to attend one international conference in Barcelona, Spain. Can I travel on Long Stay French Visa (Student).

I have requested for a French long term (Type D) student visa from a consulate in India. It's a national Type D visa and not a Schengen visa. My question is that can we still go to other Schengen countries on this visa? If not then can we get a Schengen visa from a consulate in France?


Facebook will not allow me to use "godjhavoc" as my username for my Facebook page.   The thing is, that username is no longer in use so I don't understand why Facebook won't let me use it.  Previously I used "godjhavoc" as my username for my personal page but I changed it to "ibraheempedro" so I figured "godjhavoc" would be available but it is not.  How do I use "godjhavoc" as my username for my Facebook page?

Do I have to re-register a new Facebook account to change my facebook.com/USERNAME?  Or are there any ways to change it?


Edit:  My question has been requested to close due to its apparent lack of clarity. My question is below under "Problem". If the information above it is redundant, please let me know in a comment. I will try my best to make my question as clear as possible.    I was looking at the equation $x^y=y$. If I want to isolate $x$, we would have $$x=y^{1/y}\stackrel{\small\rm{or}}{=}\sqrt[y]{y}.$$  Now let's consider $x^{x^y}=y$. I did not know how to do this, but I noticed something at first. If we let $x^y=y$, then this means $x^{x^y}=y\implies x^y=y$ by order of substitution. Notice that the same equation we substituted is in fact yielded; and, as mentioned previously, this equation would arrive at the fact that $x=y^{1/y}$. If we substitute this equation in, we obtain:  $$({y^{1/y}})^{(y^{1/y})^{y}}=y$$ which is clearly true.  But that means...  $$x^y=y\implies x^{x^y}=y\implies x^{x^{x^y}}=y\implies x^{x^{x^{x^y}}}=y\implies \cdots\tag1$$  It is now clear that we can look at this from a different perspective: if $x^y=y$ then similarly, $y=x^y$. We can substitute this on the LHS of the former equation, therefore resulting in that $x^{x^y}=y$. Clearly, this can be done ad infinitum, and this angle of looking at it is much easier to mentally grasp.  However.... if $x^y=y$ and $x^{x^y}=y$ then this means $x^y=x^{x^y}$ which doesn't make sense. Perhaps I am missing the part that $$x^y=x^{x^y}\color{red}{\iff x^y=y}$$ for otherwise we could let $x$ and $y$ be equal to anything, even each other, in the equation $x^y=x^{x^y}$ and quickly arrive at some problems.    Problem:  Now I have a problem when it comes to a certain substitution. If we can carry out the implications as shown in $(1)$ forever and ever, we will get the following equation:     $$x^{x^{x^{x^{x^{\,\,\style{display: inline-block; transform: rotate(60deg)}{\vdots}}}}}} =y.\tag2$$   Considering that $\sqrt[4]{4}=\sqrt{\sqrt{4}}=\sqrt{2}$ then one can quickly deduce from Eq. $(2)$ that $2=4$ which is clearly wrong. Let $y=2$ then $x=\sqrt{2}$. Let $y=4$ then $x=\sqrt [4]{4}=\sqrt{2}$. Thus $2=4$.  But since we just discussed the entire concept of this equation and there doesn't seem to be any flaws with it, why am I getting the absurd flaw now that $2=4$? Clearly I did something wrong with the substitution, but that's the easy part, so I believe I am overlooking something, something likely obvious $-$ but I don't understand!  May someone please correct me on this? Any help would be much appreciated (particularly hints).  Thank you in advance.

Out of boredom, I decided to recall the following equation:   $$x^{x^{x\cdots}} = 2.$$  Which, I simply rewrote like this:   $x^2 = 2$, and therefore $x = \sqrt{2}$.  Then I took a look at the more general form:  $$x^{x^{x\cdots}} = p.$$  I then concluded that $x = (p)^{\frac{1}{p}}$, and this was the solution set for all $p$. Then I thought for a while and determined that there are multiple values where this function equals the square root of $2$, so its not injective. However, this led to an awkward statemend based on the fact that $\sqrt{2} = (4)^{\frac{1}{4}}$. We deduce the following:  The equation $x^{x^{x\cdots}} = 2$ and the equation $x^{x^{x\cdots}} = 4$ have the same solution, namely $x = \sqrt{2}$. So we conclude that $2 = 4$.   I showed this to friend of mine, and he conjectured that there are no valid solutions for all $p > e$. To prove this, I tried writing the following:   I tried differentiating $f(x) = (x)^{(1/x)}$ and setting it equal to $0$ to find the maximum. I determined that there was a maximum at the point where $x = e$. Does this mean that the maximum possible solution $x$ for the infinite power is $e^{(1/e)}$ therefore showing that the maximum value for $p$ is indeed $p = e$?


I installed the Intel's graphics drivers from ;  After reboot, the GUI doesn't start and hangs with the text "starting version 219" on a black background.  I'm trying to install these drivers because I use the built-in GPU with a second display and I'm experiencing a terrible screen tearing effect.  My primary graphic card is an AMD Radeon 7000 series (not FGLRX). It had screen tearing too, which I solved using Compiz. The problem is that the second monitor still has this problem (with Compiz enabled).  Do these drivers work on Xubuntu 15.04 (or Ubuntu 15.04, which has the same problem)?  Could they solve the screen tearing on the second display?  Can I use both the Intel and the FGLRX drivers like I did on Windows?

My processor is Intel core i3 inside x64 bit and RAM is 4 gb. When I used Windows 7 Intel was successfully installing, but now I am using Ubuntu 14.04 and Intel Installer makes me crazy!!! I've tried to change lsb-release, but is doesn't help me. I tried to reinstall signature and Intel Installer, but everything is the same!  I heard  was on Ubuntu 14.10, but not on Ubuntu 14.04.1 LTS. If someone knows why I have this error please help me...


Regarding trying to destroy the Nikker's nest in Witcher 2: I'm trying to fire either drop the bomb I've already made bombs I can't figure out how to release it of trying on keyboard and with the gamepad.

In , I need to destroy all of the Nekker nests. I found my first Nekker nest, but when I try to destroy it, Geralt just says, "I've got to blow up this nest," and doesn't do anything.   So I assume that I need something to blow it up—what would that be?  Screenshot of a Nekker nest with the left-click "destroy nest" option:


I want to redraw this image using TikZ:   I've written this code so far:  \documentclass[tikz]{standalone}  \usetikzlibrary{intersections} \tikzset{help lines/.style={dashed, thick}}  \begin{document} \begin{tikzpicture}[scale=3] \clip (-2,-1.5) rectangle (1.5,1.5);    % draw x axis and small ticks at centers of circles   \draw[name path={xaxis}] (-2,0) -- (2,0);   \draw (-1.5,0.05) -- (-1.5,-0.05);   \draw (0,0.05) -- (0,-0.05);    % set coordinate of center of big circle   \coordinate (centerbig) at (-1.5,0);    % draw small circle and invisible big circle   \draw[name path={small circle}] (0,0) circle (1);   \draw[style=transparent,name path={big circle}] (-1.5,0) circle (2) {}; % just to get name for bigcircle    % calculate and name intersections of both circles and big circle with x axis   \draw [name intersections={of=small circle and big circle, by={first intersect, second intersect}}];   \draw[name intersections={of=big circle and xaxis, by={middle intersect}}];    % draw help lines of big circle   \draw[style=help lines] (middle intersect) arc (0:35:2);   \draw[style=help lines] (middle intersect) arc (0:-35:2);    % draw radius lines of big circle   \draw (centerbig) -- +(20:2);   \draw (centerbig) -- (second intersect);      % indicatior for diameter of small circle    \draw[thick,style = ->] (135:1.3) -- (135:1);    \draw[thick,style = ->] (-45:1.3) node[above right] {\(2 D\)} -- (-45:1);    % draw the section of big circle inside the small circle   \pgfsetlinewidth{1.5pt}   \pgfsetstrokecolor{black}   \pgfpathmoveto{\pgfpointanchor{first intersect}{south}}   \pgfpatharcto{2cm}{2cm}{1}{0}{0}{\pgfpointanchor{second intersect}{south}}   \pgfusepath{stroke} \end{tikzpicture} \end{document}     It yields this image:    As you can see, tthe indicator for the angle γ is missing.  To keep things tidy I am looking the an answer to another question:  How can I draw the arrows above the two lines reading vT and r?  (Answers to the other missing feature are also welcome...)

Is it possible to define in TikZ a new decoration or something like that, such that it is possible to write something like:  \draw[dim={text,above}] (A) -- (B); \draw[dim={text,below}] (C) -- (D);   or even better  \draw (A) dim[text,above] (B); \draw (C) dim[text,below] (C);   to get something like this:    It's important that the text is sloped.  If possible I would prefer the second syntax, because then I could easily combine such path's:  \draw (A) dim[text,above] (B) -- (C) -- (D) dim[text] (E) dim[text,below] (F) -- circle;


In the below sentence, does "taking the fifth" need to be in quotation marks?  A person may stay silent in order to avoid self-incrimination (commonly referred to as taking the fifth).  The style guide I'm working under does not allow for italics (it's reserved only for Latin/foreign terms). I like the way it looks without quotes, but just want to make sure that is okay.

I know, I know - similar questions have been asked before, but after reading so many answers here and elsewhere my intuitions have been scrambled and I have lost confidence in my normal practice...   Stylistics originally developed out of what was known in the past as 'rhetoric'.   Stylistics originally developed out of what was known in the past as "rhetoric".   Stylistics originally developed out of what was known in the past as rhetoric.   Normally (and throughout the previous hundred+ pages I have just proof-read) I would have favoured single quotation marks to indicate that I am mentioning rather than using a word.  I'm reluctant to introduce an inconsistency into my proofing, but somehow the single quotation marks look quite wrong in these sentences - the single quotation marks seem to suggest an unusual word or a non-standard use, whereas italics seems much more natural. Is there actually a subtle difference that I can't quite coax into consciousness? Or am I just tired...?  Similarly, 'philology', linguistics' and 'stylistics' in the following sentences (bolded just to highlight the words I am talking about):   During the nineteenth century rhetoric was incorporated into linguistics, which was known at that time as philology.   The emphasis shifted to other areas of language which all fall under the umbrella of linguistics. [Neither quotation marks nor italics for 'linguistics' in this sentence?]  After that, in the 1960s, the sub-discipline known as stylistics was born.


I am trying to get the scanner working on my Brother MFC295CN all-in-one, but Brother's website is so confusing that I can't figure it out to save my own life. Is there anyone who has done this successfully, and if so, can you explain how you installed it? Thanks:)

I have a brother DCP J125  I have downloaded and installed the scanner driver but Simple Scan shows that it couldn't detect any scanner.  I'm running on Ubuntu 12.10 32bits, the steps show in  do not work for me as I can't find the lib64 folder.  Can anyone help me?


I am new here and I don't really know how to post, so please forgive my mistakes. My question is this: Is a sentence like "everybody has to obey their own parents" nowadays completely acceptable under a grammatical point of view or it is still preferable, in written form, to use "everybody has to obey his/her own parents"? Thank you very much and sorry if this has been asked before.

Is this sentence grammatically correct?  Anyone who loves the English language should have a copy of this book in their bookcase.  or should it be:  Anyone who loves the English language should have a copy of this book in his or her bookcase.


I understand photons travel at light speed because they have no mass therefore they travel at the fastest possible speed, and at the speed of light time stops. If time is frozen at light speed how do photons vibrate/osculate/have wavelengths? Are photons not effected by time dilation, or is the wave frequency just a symbolic representation of how closely packed together the electric and magnetic fields are to each other?

I read with interest about Einstein's Theory of Relativity and his proposition about the speed of light being the universal speed limit.    So, if I were to travel in a spacecraft at (practically) the speed of light, would I freeze and stop moving?  Would the universe around me freeze and stop moving?  Who would the time stop for?


So I have an AsyncTask class to handle populating my RecyclerView. It works well but when it needs to be refreshed then it crashes with a NullPointerException. I kind of know why but then I can't do it because I am creating a new object and adding it to my list.  This is my code:    @Override         protected void onPostExecute(String s) {             try {                 userslist.clear();                 JSONArray jsonArray = new JSONArray(s);                 for(int i=0; i < jsonArray.length(); i++){                     ...                     UsersData usersData = new UsersData(var1, var2);                     userslist.add(UsersData);                 }                 cAdapter.notifyDataSetChanged(); // Culprit line, despite the list being deleted and added again in the try block             } catch (JSONException e) {                 e.printStackTrace();             }         }   I suspect is it something to do with the userslist.  This is my error logs:  java.lang.NullPointerException             at lukazs.newapp.UserInfo$GetUserList.onPostExecute(UserInfo.java:218)             at android.os.AsyncTask.finish(AsyncTask.java:741)             at android.os.AsyncTask.access$600(AsyncTask.java:197)             at android.os.AsyncTask$InternalHandler.handleMessage(AsyncTask.java:654)             at android.os.Handler.dispatchMessage(Handler.java:100)   EDIT: This is the method call where I populate the recyclerview:  public void populateRecyclerList(){     GetUserList getUserList = new GetUserList();     getUserList.execute(); }  @Override protected void onCreate(Bundle savedInstanceState) {     ...     setContentView(R.layout.usersdetails);      populateRecyclerList();     }   This is where cAdapter is initialised, in onCreate method:  RecyclerView.Adapter cAdapter; ArrayList<UserDetailsProvider> userslist = new ArrayList<UserDetailsProvider>();  @Override protected void onCreate(Bundle savedInstanceState) {     super.onCreate(savedInstanceState);     recyclerView = (RecyclerView) findViewById(R.id.recycleMusic);     cAdapter = new UserDefinedAdapter(userslist);     recyclerView.setAdapter(cAdapter);     populateRecyclerList(); }   EDIT: I have done something now, but the populateRecyclerList() is crashing in another AsyncTask class on onPostExecute. Basically, I want to repopulate the recyclerView after a user has been added. This is my code for the onPostExecute() method, where I am calling the populateRecyclerList() method:  @Override         protected void onPostExecute(String s) {            populateRecyclerList();         }   Maybe you are not meant to call this method here? But then how would I update the RecyclerView?

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 have a strange problem, and it involves my keyboard and a cat.  I have a computer in a shared office, and this is my machine. But there’s also a cat in the office, that likes to walk on keyboards. So every day when I come back to log-in, I see this :     I know I can unplug the USB at night, but I am looking for a quicker way. Is there a  less-manual way? I’d like to disable the keyboard easily, and re-enable upon coming back to office

Question for any programmer—and cat lover—working from his home office. So many times my keyboard is taken over violently by my two cats who think it’s the right place for a nap. And almost every time when they do this I’m was in this precious 100% concentration phases before I get interrupted.  I tried it with a burning an anti-mosquito coil under the desk but they got used to the smell pretty fast.  EDIT: And no I don’t want to keep the cats away completey from my room.


It's just a struct  #define _CRT_SECURE_NO_WARNINGS //def   #include<iostream> #include<conio.h>   using namespace std;   my struct  struct muncitor   {     int id;     char *nume;     float salariu;     char init_t;     bool fct_conducere;     int nr_calificativ;     int *calificativ; };   reading struct content  void read(muncitor m)  {      cout << "Id: ";     cin >> m.id;      cout << "numele: ";     char aux[20];     cin >> aux;     m.nume = new char[strlen(aux) + 1];     strcpy(m.nume, aux);      cout << "salariul: ";     cin >> m.salariu;      cout << "initiala: ";     cin >> m.init_t;      cout << "functie: ";     cin >> m.fct_conducere;      cout << "nr calificative: ";     cin >> m.nr_calificativ;     cout << m.nr_calificativ << " ";      m.calificativ = new int[m.nr_calificativ]; here is the problem      for (int i = 0; i < m.nr_calificativ; i++)     {         cout << "calificativul: ";         cin >> m.calificativ[i];     }  }  void main() {      muncitor m;      m.id = 1;     m.salariu = 1250;      read(m); //call void     _getch; }   Can't figure it out. The debug stops at m.calificativ = new int[m.nr_calificativ]; What is wrong? Please help me. A test is coming soon. I can't find a solution, so I'm asking here.

What is the difference between    a parameter passed by reference a parameter passed by value?   Could you give me some examples, please?


I am trying to do isometric pixel art on Illustrator. To this end, I am using a hex grid to draw simple cubes using the pen tool (as described in ). However, the anchor points tend to move by themselves. The result is : my cube is not a cube.  Details:  Here I put my first anchor point :    When I add the second one, the line moves down :    And this is the shape I get in the end :

TL:DR Smart guides aren't accurate - even though the snap, (end up causing more problems in the long run) is there a way to fix it?  Maybe there are some settings that I'm missing (need to be changed)    I use my smart guides all the time (and am overall pleased with them). I do have my issues with it, as explained here:  A lot of times, when I'm trying to make a bunch of triangles like this:    Done by making a triangle, cloning, flipping, rotating etc. Repeat until full  (Perfect) Snapping using Smart Guides    Ends up looking likebetween the triangles (Outline Mode)    Now I personally (with a strong attention to detail) will notice that there is something off after making just 1 or 2 triangles (Even before outline mode... strokes look oh so slightly thicker/off)   And then I check in outline mode... and sure enough:    Notice the line spaces (and this is in outline mode, so if I didn't notice it before, now it's sitting right in front of my nose)  The way I (seemingly) "fixed" the first image was by adding in a thick stroke outline so that masks out the difference, however, in a lot of my cases I don't want to have a stroke at all (and then you really notice the problems).


Good day.  I'm trying to discover which query is causing tempdb growing too much (around 100gbyte).  In my new company, people is using a lot of dynamic Excel files with various query.  I'm pretty sure that one of them is "guilty" for tempdb growing.  The only solution I've discovered is to restart sql server service (it delete and recreate tempdb). Is there a way to discover which query is allocating so much space ?  Thanks

I would like to know how to identify the exact query or stored proc which is actually filling up the transactional log of TEMPDB database.


I'm trying to use the makemap hash command, but even as root it says Permission denied. Command i'm trying to run:  sudo makemap hash /etc/mail/authinfo/gmail-auth < /etc/mail/authinfo/gmail-auth -bash: /etc/mail/authinfo/gmail-auth: Permission denied

Disclaimer: I'm pretty novice at sysadmin stuff.  I'm trying to set up port forwarding in an AWS EC2 instance, this has to be done in the command-line because I don't want to go in and edit anything, it has to be automatic (it's part of a build process).   sudo echo "net.ipv4.ip_forward = 1" >> /etc/sysctl.conf      Permission denied   The weird thing is I've been (successfully) using sudo for pretty much every command that required su privileges. If I do sudo su before the command (trying it out by hand in an ssh session), then it works.  Reasons behind this? Possible solutions that don't involve sudo su or manual edits?


When I try to suggest to make  a synonym of , I get an error message about a reverse synonym:    The reason seems to be that  has itself a synonym, . Both of those tags should be made synonyms of .

Recently the  (106) tag was created. It should be merged with  (385) tag. The  tag is more general and it is the older one, but should it be the one to live on? This seems disputable as I haven't heard of a virtual function which is not a method.


The Drupal 7 {system} table has a schema_version column. Its default value is -1 as indicated by the DESCRIBE system; MySQL command.  Sometimes an update function won't run if the module's schema_version is -1.  For instance, I have site that migrated from Drupal 6 to Drupal 7 quite some time ago.  Recently I found that a database column that should have been introduced by honeypot_update_7100() never ran.  I'm not sure whether or not the version of honeypot at the time of the migration contained that function.  After changing the schema_version to 0, update.php ran that update and the missing column was introduced.  See  for similar stories.  Is -1 treated specially?  Do all -1's potentially need to change to 0 for their update functions to run?

The problem is, it seems when I enable a disabled module, the module's schema version in the system table is automatically updated to the latest version supplied by hook_update_N.  So my current module with the schema version -1 is modified to 7106 when I enable the module, and no hook_update_N functions are run.   So when I come to the next step of running database updates, no hook_update_N functions are run because the module thinks it's already the correct version.  The only method I can see is to manually set the module version in hook_enable, however I'll then need to update the module code to remove the hook_enable to make sure it doesn't run if the module is ever re-enabled in the future, so obviously this approach is a bit dirty.  I'm hoping there's a better solution?


If  $\emptyset$ denotes the  empty set, what is $\langle \emptyset \rangle$ in a group?  Would it just be $\emptyset$? or none?

I have come across a problem in Durbin, Modern Algebra, that I am not quite convinced of the answer. The question states:       If $\emptyset$ denotes the empty set, what is $\langle\emptyset\rangle$ (in any group $G$)?   I searched for answers to this question for a while and the only one I could find stated:       $\langle\emptyset\rangle = \{e\}$ , the identity element.   I am not quite sure of the logic behind this answer and any hints or explanations would be thoroughly appreciated.


I have designed 3 tables as below: Table: Country Columns:  country(name of country), iso2_code, iso3_code, phone_code  primary key: country Table: State Columns:  state(name of state), country(fk from country table)  primary key: state, country Table: City Columns:  city(name of city), state(fk), country(fk)  primary key: city, state, country I have used composite keys as primary key for state & city tables. Is it bad design? Should I create auto-increment key for state & city tables & use them as primary key?

I want to know if composite primary keys are bad practice and if not, in which scenarios is their use beneficial? My question is based on this   Note the part about composite primary keys:  Bad Practice No. 6: Composite Primary Keys This is sort of a controversial point, since many database designers talk nowadays about using an integer ID auto-generated field as the primary key instead of a composite one defined by the combination of two or more fields. This is currently defined as the “best practice” and, personally, I tend to agree with it.  However, this is just a convention and, of course, DBEs allow the definition of composite primary keys, which many designers think are unavoidable. Therefore, as with redundancy, composite primary keys are a design decision. Beware, though, if your table with a composite primary key is expected to have millions of rows, the index controlling the composite key can grow up to a point where CRUD operation performance is very degraded. In that case, it is a lot better to use a simple integer ID primary key whose index will be compact enough and establish the necessary DBE constraints to maintain uniqueness.


Both programs stat and ls -l tell about the number of (hard) links to file(s).   Going under the assumption that one usually cannot create hardlinks for directories in Linux it confuses me to see outputs like this  $ ls / -l | grep etc drwxr-xr-x 163 root     root       12288 Oct 11 17:32 etc  $ stat /etc | grep Links Device: fc00h/64512d    Inode: 655361      Links: 163   Are there indeed 163 links to etc? I am confused and I would like to know what the number of links means with respect to directories?  I have tested that creating symbolic links does not have an influence to the number (which seems logic as the system would have hell of a job to keep track of all symbolic links)  Also I have tested that for regular files the number really reflects the hardlinks.

When I stat a directory I get a listing that tell me there are 5 links to the directory.  stat dir   My question is how do I get information (names and locations) to all these 5 links?


What does the bold phrase below mean? Why do they use the possessive? Why do they use the noun time?     Yes, but he's getting married in three months' time.    I have understood this sentence     Yes, but he's getting married in three months.

Are these expressions syntactically correct and semantically equivalent? What is general rules for "number-time noun" and "number time' noun" from semantic point of view?    "a day's work" vs "one-day work" "two days' notice" vs "two-day notice" "one year's pay" vs "one-year pay"     also see .


A tennis club has 40 members. They host a tournament playing single   (one verses one) matches. Every member of the club plays one match   with another member of he club, so twenty matches are held. (a) In how   many ways can this be arranged?   I was a little confused by the wording of this question in regards to the teams being 'arranged' but I was wondering if it is as simple as the number of ways to choose 20 different match setups, i.e number of ways to choose two different people out of 40. So tried:  C(40,2) and wasn't sure if I needed to multiply by the number of people: so C(40, 2) * 40. I also thought this could be a circular arrangement problem but wasn't sure.. Am I on the right track or way off here?

Apparently, there are $\frac{(2n)!}{2^nn!}$ ways to break $2n$ people into partnerships. Why?   An explanation reads that there are $2n!$ ways to line people up. If we just pair adjacent people in the line up, we would have overcounted. So we must divide by $2^n n!$.  My question is why do we divide by $2^n n!$ specifically to adjust for overcounting?  Furthermore, this problem can apparently be solved by taking a skip factorial of odd values:  $(2n-1)(2n-3)(2n-5) ... (5)(3)(1)$  Why is that so? What does this skip factorial have to do with the problem?


It seems that, given she has given her life for Harry, why not have become a ghost and helped Harry, or even 'mothered' him as much as a ghost could, too. If I were Harry, I think I would have preferred this to never knowing his mother. And I think that Lily herself should have preferred this to see her son grow up, even help protect him especially in a time of peril in the Wizarding World.

In Harry Potter and the Sorcerer's Stone, Nearly-Headless Nick and some other ghosts can visit the Hogwarts students, but why can't other deceased people - such as Harry's parents?


I have a file named test.sh:   #!/bin/bash -o pipefail echo "Running test" git diff HEAD^ HEAD -M --summary | grep delete |  cut --delimiter=' ' -f 5   When I try to run this script as:  ./test.sh   I get:  /bin/bash: line 0: /bin/bash: ./test: invalid option name   I ran cat -v test.sh to check if there are carriage returns or anything, but that doesn't seem to be the case. I can run the script if I just run it as bash test.sh. Grateful for any help, and lmk if I can provide more info!

I am wondering whether there is a general way of passing multiple options to an executable via the shebang line (#!).   I use NixOS, and the first part of the shebang in any script I write is usually /usr/bin/env. The problem I encounter then is that everything that comes after is interpreted as a single file or directory by the system.  Suppose, for example, that I want to write a script to be executed by bash in posix mode. The naive way of writing the shebang would be:  #!/usr/bin/env bash --posix   but trying to execute the resulting script produces the following error:  /usr/bin/env: ‘bash --posix’: No such file or directory   I am aware of , but I was wondering whether there was a more general and cleaner solution.    EDIT: I know that for  scripts, there is a way to achieve what I want, documented in  of the manual:   #!/usr/bin/env sh  exec guile -l fact -e '(@ (fac) main)' -s "$0" "$@"  !#   The trick, here, is that the second line (starting with exec) is interpreted as code by sh but, being in the #! ... !# block, as a comment, and thus ignored, by the Guile interpreter.  Would it not be possible to generalize this method to any interpreter?     Second EDIT: After playing around a little bit, it seems that, for interpreters that can read their input from stdin, the following method would work:  #!/usr/bin/env sh sed '1,2d' "$0" | bash --verbose --posix /dev/stdin; exit;   It's probably not optimal, though, as the sh process lives until the interpreter has finished its job. Any feedback or suggestion would be appreciated.


I'm trying to get my broadcom wireless adapter working, ubuntu MATE 18.04.  Running lshw -C network shows e.g.  product: BCM4321 802.11a/b/g/n logical name: wlp3s0 configuration: broadcast=yes driver=wl0 driverversion=6.30.223.271   Running  rfkill list all   Does not show my wireless being soft or hard blocked.  Running lspci shows that my hardware is Broadcom Limited BCM 4321 802.11 a/c/g/n (rev 05)  So the proprietary driver seems to be installed, hardware is fine AFAICT, but running sudo iwlist wlp3s0 scan yields no results, and the 'wireless networks' option on the network applet is greyed out. I don't hide my SSID, it just seems like I can't connect to any networks. Wrong driver perhaps? How can I tell?  Also, the computer is a 2009 Mac Mini if that matters.

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 am traveling to Jamaica via a US port. Since Jamaica has on arrival visa for Indian citizens, do I need a transit visa for the USA? My next flight from the USA is 4 hours later.

In Europe usually you don't need to go through immigration to change planes (unless you are entering/exiting Schengen). Is it the case in the US as well? May I catch a connecting flight on one of the US airports if I don't have US visa?


I'm using Python to create a Bezier curve programmatically. bpy.ops.curve.primitive_bezier_curve_add() bpy.ops.curve.subdivide(number_cuts=4)  The code above works fine in the console, but not in my script. I get the error message: bpy.ops.curve.subdivide.poll() failed, context is incorrect I've tried both primitive_bezier_curve_add(), and ...add(enter_editmode=True). Same result. Using Blender 2.83.2 NOTE: I am able to use this as a workaround: bpy.context.scene.objects["BezierCurve"].data.splines[0].bezier_points.add(count = 4)

I keep on getting context errors in the Blender Python API.  I don't understand the issue of the context in the API, how do I know which is the correct context?   Thanks!


I am designing an application where I have a list of items. Some have been added by "You" (the user) and some have been added by your colleagues (everyone else)  To show who has added the item I show the name of the person that added it.  For the items you have added instead of the name I show "You".  But then the question arose. When referring to the user of the application should I use "You" or "Me"

Some user interfaces feature titles such as:   My documents My photos My previous orders   While others opt for:   Your documents Your photos Your previous orders   Are their any guidelines addressing which is more suitable to pick in different situations? Is one more preferable than the other?


I use the bellow less code to let the con-order width 80%:  .con-order {      height: 100%;     width: 80%;     overflow: hidden;   the html code is like bellow:

       <Alert type="warning" show-icon closable>     ...   it bellow like this, I want the content move center.    I tried use text-align: center; but the content become odd.  It become like this, I don't want this:    I want all move to center, not all content align center.

How can I horizontally center a
 within another
 using CSS?

Foo foo


$R=k[x]/(x^n)$, $n>1$. Suppose $\operatorname{pd}_RM<\infty$, $M$ might not be finitely generated and $M$ might be uncountably generated. I want to show $M$ is free irregardless of non-finitely generated (i.e., either countably or uncountably generated).    I am aware that the previous post indicates a solution for finitely ranked free modules in the free resolution as . However in Eisenbud, there is no such guarantee.   I have two ideas on this.    I was referring to Eisenbud Commutative Algebra Exercise 4.11b to solve the problem for finitely generated case. However, there is no reason to assume $F_i$'s have finite rank. So this clearly does not work. See answers below Mariano Suárez-Álvarez's comments. The other way is to see $M$ as a limit of finitely generated modules $N_i$. I hope the free resolution is finite and finite rank for sure as it is artinian ring. However, it might not be guaranteed that $N_i$ being free where Mariano Suárez-Álvarez commented on this as well.

How to show a $k[x]/(x^n)$ module with finite free resolution is free?    Suppose we have a exact sequence $k[x]/(x^n)^{\oplus n_1}\to k[x]/(x^n)^{\oplus n_{0}}\to M\to 0$, how do we get information to show $M$ is free?


i have the package jdk-8u171-linux-x64.tar.gz  on my pc how to install it on Ubuntu 18.04 LTS

Since I upgraded to the latest version of Ubuntu, I cannot install the Java OpenJDK package needed to compile Android custom ROMs. When I run sudo apt-get install openjdk-7-jdk, the following error appears:  Reading package lists... Done Building dependency tree        Reading state information... Done Some packages could not be installed. This may mean that you have requested an impossible situation or if you are using the unstable distribution that some required packages have not yet been created or been moved out of Incoming. The following information may help to resolve the situation:  The following packages have unmet dependencies:  openjdk-7-jdk :  Depends: openjdk-7-jre (= 7u51-2.4.6-1ubuntu4) E: Unable to correct  problems, you have held broken packages.   How do I fix this problem?


Read it in the 90's. I remember one specific part where the inventor of the peeking mechanic has his Eureka moment, and has the presence of mind to give a thumbs-up/wave to the future, when they look back on his Eureka moment.  I also remember that they had computer screens that were like plastic cloth that they would just unfold on whatever surface was handy.  Sorry I don't have much more to go on.  Please and thank you!

I read a book a while ago in which a device is invented which opens up "tunnels" back through time. These tunnels cannot be traveled through, but can be used to view what happened in the past. I believe it starts out narrating the invention of the device, then skips ahead to after it is widely in use. There is another device created, a cloak of sorts,  which hides the user from the view of someone using the tunnel device. Does this ring a bell with anyone?


What's the point of having dwellers working in the warehouse? When you select a warehouse it says that Endurance is needed for that, but does it have effect in the game?

I've played Fallout Shelter for a while now and normally use dwellers with appropriate SPECIAL stats for each room (Strength in the reactor, Perception in the water supply, etc).  However, I have a question regarding Endurance. The only room which uses this is the storage room. It doesn't produce anything; it has no cooldown; it just does nothing...  Even if I just build and upgrade the warehouse, my stock capacity is increased. Is there any good reason for me to waste my dwellers by assigning them to storage rooms?


var x = [1, 2, 3, 4, 5, 6];  function change1(y) {   y[0] = 7;   y[1] = 8;   y[2] = 9;   y[3] = 10;   y[4] = 11;   y[5] = 12; } change1(x); console.log(x);  var z = [1, 2, 3, 4, 5, 6];  function change2(y) {   y = [7, 8, 9, 10, 11, 12]; } change2(z); console.log(z);    Output: 7,8,9,10,11,12 1,2,3,4,5,6  I am unable to understand in the above code why the change1() function can alter the passed array while the change2() function cannot. And why is the line break not working?

The primitive types (number, string, etc.) are passed by value, but objects are unknown, because they can be both passed-by-value (in case we consider that a variable holding an object is in fact a reference to the object) and passed-by-reference (when we consider that the variable to the object holds the object itself).  Although it doesn't really matter at the end, I want to know what is the correct way to present the arguments passing conventions. Is there an excerpt from JavaScript specification, which defines what should be the semantics regarding this?


I have two questions in the following explanation: "Consider the quotient ring $S/3=Z_3[x]/(3,x^{n-1}+x^{n-2}+...+1)$. The canonical S/3-representative of $a\in Z[x]$ is the unique polynomial $b\in Z[x]$ of degree at most $n-2$ with coefficients in $\{-1,0,1\}$ such that; $a\equiv b $ $(mod~(3, x^{n-1}+x^{n-2}+...+1))$. We write $\underline S3(a)$ for the canonical S/3 -representative of $a $.  We write $S3(a)$ when the choice of representative is not normative". Question 1: How do we take modulo of : (something) $(mod~(3, x^{n-1}+x^{n-2}+...+1))$ ? Do we first take (something) mod 3, then take $(mod~( x^{n-1}+x^{n-2}+...+1))$ of it afterwards? Question 2: What does normative mean in the context above?

Where does a layman go to get a basic understanding of AKS primality testing. I am not talking about the optimal choice of $r$ (which I am told is the hardcore number-theoretic part of the algorithm). I mean basic things, like what does $\bmod(n, x^r-1)$ mean (how can something be mod two things?) And what does binomial expansion have to do with anything?  I can't find anything in Wikipedia that is appropriate for my level.


my usb stick was containing som kind of virus which was visible and my little brother double clicked on it! and now my laptop is infected!! the virus opens several Firefox tabs and opens some websites as advertisement! the virus does this every 20 minutes whether the browser is open or not!! and it is driving me crazy. I dont know how to prevent it from opening tabs :(     I checked and there is no unwanted add-on or plugin on my browser! should I delete my browser?

What should I do if my Windows computer seems to be infected with a virus or malware?  What are the symptoms of an infection? What should I do after noticing an infection? What can I do to get rid of it? how to prevent from infection by malware?   This question comes up frequently, and the suggested solutions are usually the same. This community wiki is an attempt to serve as the definitive, most comprehensive answer possible. Feel free to add your contributions via edits.


I have a small function which uses one list to populate another.  For some reason, the source list gets modified.  I don't have a single line that manipulates the source list arr.  I am probably missing the way Python deals with scope of variables, lists.  My expected output is for the list arr to remain the same after the function call.  numTestRows = 5 m = 2 def getTestData():     data['test'] = []     size_c = len(arr)     for i in range(numTestRows):         data['test'].append(arr[i%size_c])         for j in range(m):             data['test'][i].append('xyz')  #just a 2x5 str matrix arr = [['a', 'b', 'c', 'd', 'e'], ['f', 'g', 'h', 'i', 'j']] print('Array before: ') print( arr) data = {} getTestData() print('Array after: ') print( arr)   Output  Array before:  [['a', 'b', 'c', 'd', 'e'], ['f', 'g', 'h', 'i', 'j']] Array after:  [['a', 'b', 'c', 'd', 'e', 'xyz', 'xyz', 'xyz', 'xyz', 'xyz', 'xyz'], ['f', 'g', 'h', 'i', 'j', 'xyz', 'xyz', 'xyz', 'xyz']]

I needed to create a list of lists in Python, so I typed the following: my_list = [[1] * 4] * 3  The list looked like this: [[1, 1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1]]    Then I changed one of the innermost values: my_list[0][0] = 5  Now my list looks like this: [[5, 1, 1, 1], [5, 1, 1, 1], [5, 1, 1, 1]]    which is not what I wanted or expected. Can someone please explain what's going on, and how to get around it?


Some binaries in Unix-Linux systems like ping or mount have a long argument. For example if we write ping -h in the terminal, one of the options is:  Usage: ping [-aAbBdDfhLnOqrRUvV64]   Is this long set of characters really an argument?

While researching another problem, I ,  locate something | xargs -I {} bash -c "if [ -d "{}" ]; then echo {}; fi"   that I wanted to learn more about.  So I ran man xargs and get the following output:  XARGS(1)                    General Commands Manual                   XARGS(1)  NAME        xargs - build and execute command lines from standard input  SYNOPSIS        xargs  [-0prtx]  [-E  eof-str] [-e[eof-str]] [--eof[=eof-str]] [--null]        [-d delimiter] [--delimiter delimiter]  [-I  replace-str]  [-i[replace-        str]]    [--replace[=replace-str]]   [-l[max-lines]]   [-L   max-lines]        [--max-lines[=max-lines]] [-n max-args] [--max-args=max-args] [-s  max-        chars]  [--max-chars=max-chars]  [-P max-procs] [--max-procs=max-procs]        [--interactive]      [--verbose]      [--exit]      [--no-run-if-empty]        [--arg-file=file]   [--show-limits]   [--version]   [--help]   [command        [initial-arguments]]  DESCRIPTION        This manual page documents the GNU version of xargs...   I am trying to get better at using documentation to learn about Linux programs, but that "Synopsis" section is intimidating to new users.  It literally looks like gibberish compared to man locate or man free.  So far, I understand that square brackets mean optional and nested brackets mean options in optional.  But how am I supposed to induce a valid command with that?  I am not asking for help with xargs here.  I am looking for help interpreting a man page to understand complicated commands.  I want to stop making Google-indexed web blogs and personal help from others my first approach to learning Linux commands.


Supposed we have $n = 15$ independent samples $X_1, X_2, ..., X_n$ from distribution $N(\mu, \sigma)$. Sample mean $\bar{X} = 2.4$ and sample variance $\hat{\sigma^2} = 0.55$  What's the 95% confidence interval of $\mu$ and $\sigma$?   I understand the 95% confidence interval of $\mu$ -- I can estimate the standard error by $\hat{\sigma} / \sqrt{n}$, then I can obtain the CI. But how do I calculate the CI of $\sigma$?   P.S. As you can tell this is more of an homework-ish question. I am self-studying  and this is on one of the practice exams. Unfortuantely they don't have solutions. In addition to answering this question, if someone can recommend another open course with solutions to homework/exams that would be appreciated too.

This is a very basic question. Why do we use a chi square distribution? What is the meaning of this distribution? Why is this the distribution used for creating a confidence interval for the variance?   Every place I google for an explanation just presents this a fact, explaining when to use chi, but not explaining why to use chi, and why it look the way it does.  Many thanks to anyone that can point me towards the right direction and that is - really understanding why I am using chi when I am creating a confidence interval for the variance.


I tried to solve a question in combinatorics and ended up with this sum:  $\sum_{t=0}^{r}\binom{ m-t}{r-t}$   when I give it to WolframAlpha it says it equals to  $\binom{ m + 1}{r}$ but gives no proof, can someone provide a discrete proof?

My question is:  show $$\sum_{k=0}^{m} \binom{n-k}{m-k}=\binom{n+1}{m}$$ $$n\geq m\geq 1$$ I tried to do this via induction and failed. there has to be another way of doing this.  We could either explain combinatorically that we are counting the same thing in 2 different ways, in this sense, we are counting the number of ways to choose $m$ elements from a set with $n+1$ elements.  Or we could try like me to prove it algebraically, both ways are valid...I'd like some help, or a push in the right direction.


A device I have that uses Ubuntu is stuck during the boot process displaying this message: /dev/nuve0n1p5: clean, 209898/64141336 files, 2921324/2560432 I'm new to linux systems so I am unsure what to do to get back onto the OS

dev/sda1: clean, 552599/6111232 files, 7119295/24414464 blocks   After I turn on my laptop this message appears. The system never boots, the message just stays there.


I generated an ANOVA table in R and every boxes are in number except the P value shows "3.387e-05". What does that really mean?

Hey all I asked this over  =) and I got a good answer but I still have no idea whats going on. I want to know how the expression got to the answer and maybe the math behind how it was reasoned.. the steps if you would be so kind. The likelihood is I don't understand the equation.   I'm not a big maths person please be gentle :p     For all those playing along at home I'm reading Absolute Java 5th   Edition by Walter Savitch (Chapter 2 Page 66).      The Expression  double d = 12345.123456789; System.out.printf("START%12.5e END %n", d);       The Answer  START 1.23451e+04END       I understand the basic principles of this printf method's arguments   for example I know the '%' represents the start of the parameters.   '12' is the number of spacing, '.5' is the times the decimal point   will move.... I see the decimal point has moved 4 places towards the   left... can someone explain the principles of e-notation. Also how   this expression came to this answer =).      As far as e-notation go's its meant to be scientific notation;      So like 5.89e-4 would mean 0.000589 (move the decimal place if minus   left if not move the decimal place right).


Electron is a particle with momentum $p$ and it spins up. Positron is its antiparticle having momentum $-p$ and it spins down. "A positron is an electron travelling backwards in time" said by Feynman. Therefore how an electron and positron annihilate producing photons since total momentum is $p-p=0$. Therefore how they produce photon with momentum?

Is it possible to create matter? In a recent discussion I had, it was suggested that with enough energy in the future, "particles" could be created.   It seems like this shouldn't be possible due to conservation but perhaps I could be wrong. Would any of you Physics masters care to elaborate?  (Note... I will understand the basics, I am by no means an expert.)


I am new to Python and to these forums.   My question is: How can I create a list of n Fibonacci numbers in Python?   So far, I have a function that gives the nth Fibonacci number, but I want to have a list of the first n Fib. numbers for future work.   For example:  fib(8) -> [0,1,1,2,3,5,8,13]

I had originally coded the program wrongly. Instead of returning the Fibonacci numbers between a range (ie. startNumber 1, endNumber 20 should = only those numbers between 1 & 20), I have written for the program to display all Fibonacci numbers between a range (ie. startNumber 1, endNumber 20 displays = First 20 Fibonacci numbers). I thought I had a sure-fire code. I also do not see why this is happening.  startNumber = int(raw_input("Enter the start number here ")) endNumber = int(raw_input("Enter the end number here "))  def fib(n):     if n < 2:         return n     return fib(n-2) + fib(n-1)  print map(fib, range(startNumber, endNumber))   Someone pointed out in my Part II (which was closed for being a duplicate - ) that I need to pass the startNumber and endNumber through a generator using a while loop. Can someone please point me in the direction on how to do this? Any help is welcome.    I'm a learning programmer and I've run into a bit of a jumble. I am asked to write a program that will compute and display Fibonacci's Sequence by a user inputted start number and end number (ie. startNumber = 20 endNumber = 100 and it will display only the numbers between that range). The trick is to use it inclusively (which I do not know how to do in Python? - I'm assuming this means to use an inclusive range?).  What I have so far is no actual coding but rather:   Write Fib sequence formula to infinite Display startNumber to endNumber only from Fib sequence.   I have no idea where to start and I am asking for ideas or insight into how to write this. I also have tried to write the Fib sequence forumla but I get lost on that as well.


The gravitational lensing evidence suggests the existence of massive and relatively dense regions of dark matter. However, if dark matter interacts only gravitationally, what would stop it from collapsing to a black hole of any size? For example, if there is a cloud of a dark matter gas of the mass of the Moon, and this cloud over time condenses under its own gravity down to the size of the Moon, then what would hold this object from quickly collapsing to a singularity with no electroweak of strong force to resist the collapse? Would the Pauli exclusion principle apply to dark matter to create a degeneracy pressure preventing the collapse?

I'm a complete layperson. As I understand, dark matter theoretically only interacts with the gravitational force, and doesn't interact with the other three fundamental forces: weak nuclear force, strong nuclear force, and electromagnetism.  Those are my understandings going in. If I'm wrong, please correct me. I've done some googling, and I haven't found anything confirming or denying that dark matter is affected by either of the fundamental nuclear forces.  So since dark matter only interacts with gravity, what causes any dark matter particle to be repelled from another? If they can pass freely through each other, and they are gravitationaly attracted to each other, why don't such particles clump together in a single 'point' in space?   It seems to me that particles occupying a single 'space' are philosophically not distinct particles, but I don't know how actual physics would play into this.  Edit , author's credentials unknown, but implicitly claims to be a physicist or astronomer, says "...[P]hysicists generally take all dark matter to be composed of a single type of particle that essentially interacts only through gravity."  Edit 2 The author is this , "Professor of Science on the physics faculty of Harvard University."


When Rey was left on Jakku, she faintly remembers seeing a starship leave Jakku.  We're given a little glimpse of the Starship in Star Wars: The Force Awakens.  Who owned that Starship?  As in, was it a First Order / Empire Starship or a "good guys" Starship?   Obviously this would be a huge clue into who left her there (maybe), but I do understand that there may not be an answer for it at this time.

The ship flying away from Rey in her flashback of being left on Jakku looks like one of the ships in the group that takes her away when she is captured.  If so, and it is a First Order ship that dropped her off, this is an interesting Easter egg.


I keep on hitting a road block in trying to solve this, especially when trying to prove it going from the right hand side to the left hand side.

Is this true?  If $A$ and $B$ are sets, then $A=\emptyset $ if and only if $B = A \bigtriangleup B$.  If $A=\emptyset$ then $B=\emptyset$ too?  Could someone help me please?


The question was: "If rolling two 6-sided dice what is the probability of getting at least one six? One third? Why or why not?"  In order to answer that I wrote a simulation in Python and the results are a pretty convincing NO.   The results:  Ser. 0 D1=6 16671 ; D2=6 16622 ; D1 AND D2 = 6 2721 ; D1 OR D2 = 6  30572 / 100000 Ser. 1 D1=6 16629 ; D2=6 16782 ; D1 AND D2 = 6 2739 ; D1 OR D2 = 6  30672 / 100000 Ser. 2 D1=6 16618 ; D2=6 16651 ; D1 AND D2 = 6 2754 ; D1 OR D2 = 6  30515 / 100000 Ser. 3 D1=6 16596 ; D2=6 16957 ; D1 AND D2 = 6 2792 ; D1 OR D2 = 6  30761 / 100000 Ser. 4 D1=6 16575 ; D2=6 16665 ; D1 AND D2 = 6 2822 ; D1 OR D2 = 6  30418 / 100000 Ser. 5 D1=6 16630 ; D2=6 16634 ; D1 AND D2 = 6 2759 ; D1 OR D2 = 6  30505 / 100000 Ser. 6 D1=6 16585 ; D2=6 16706 ; D1 AND D2 = 6 2809 ; D1 OR D2 = 6  30482 / 100000 Ser. 7 D1=6 16707 ; D2=6 16762 ; D1 AND D2 = 6 2811 ; D1 OR D2 = 6  30658 / 100000 Ser. 8 D1=6 16568 ; D2=6 16618 ; D1 AND D2 = 6 2694 ; D1 OR D2 = 6  30492 / 100000 Ser. 9 D1=6 16705 ; D2=6 16695 ; D1 AND D2 = 6 2826 ; D1 OR D2 = 6  30574 / 100000   So every result is I expected: 16% for either die to be six 2.7% for both dice to be six  except for at least one being six.  What bothers me is WHY? And how would I derive the result from formal probability without doing the simulation?

$11$ out of $36$? I got this by writing down the number of possible outcomes ($36$) and then counting how many of the pairs had a $6$ in them: $(1,6)$, $(2,6)$, $(3,6)$, $(4,6)$, $(5,6)$, $(6,6)$, $(6,5)$, $(6,4)$, $(6,3)$, $(6,2)$, $(6,1)$. Is this correct?


$\newcommand{\tr}{\operatorname{tr}}$Let $A$ be a complex $n\times n$ matrix such that $\tr(A^m)=0$ for each $m=1,\ldots,n$. Show that $A$ is nilpotent.  My attempt: Since $A$ is a complex matrix, there exists a diagonal matrix $D$ and a nilpotent matrix $N$ such that $A=D+N$. Furthermore, this decomposition is unique and $D$ and $N$ commute. So we wean to show $D=0$. Since $DN=ND$, $A^2=D^2+2DN+N^2\implies \tr(A^2)=\tr(D^2)+2\tr(DN)+\tr(N^2)$. Since $N$ is nilpotent, $N^2$ is nilpotent $\implies \tr(N^2)=0$. Also, since $D$ and $N$ commute, $DN$ is nilpotent, so $\tr(DN)=0$. Hence $0=\tr(D^2)=\lambda_1^2+\cdots+\lambda_n^2$, where $\lambda_1,\ldots,\lambda_n$ are the diagonal entries of $D$. This implies each $\lambda_i=0$ and so $D=0$, which completes the proof.  I'm a little unsure though because I didn't use the fact that $\tr(A^m)=0$ for $m>2$. Is my argument correct, or does someone see a flaw?

I would like to have a result similar to . Namely:      Let $R$ be a commutative $\mathbb{C}$-algebra, $A \in \mathcal{M}_n(R)$ such that $\mathrm{tr}(A)=\cdots=\mathrm{tr}(A^n)=0$. Does it follow that $A^n=0$?   I have no idea weather or not the analogy of eigenvalue exists for matrices over algebra so I can't simply generalize considerations from cited post. Any help will be appreciated.


I want to see all output even if it is huge. For example, running systeminfo via regular command line prompt in Windows will show everything with vertical scrolling. But when I'm invoking the same command in Far 3 I'm able to see just the end of information that fit in one screen.

Hi guys, how do I copy FAR-Manager's console output? For example when I use ping command I want to copy it's output text, but not image.  Oh, and I would like to do so with keyboard! :)


If my Ubuntu is installed in ext4, will everything I download and write there be worthless if I try to view it on Windows 10?  Is it possible to convert anything without losing it? Will I be able to copy bookmarks from Windows onto Ubuntu?

I have currently got Google Chrome and Firefox installed, but I want to switch to Firefox so I want to some how transfer my mass collections of bookmarks from Chrome to Firefox, so is there any way of doing this?  Perhaps if I export all my Google Chrome bookmarks into an HTML file, can I import them into Firefox then? Or is there any quick and efficient way of sort of manually transferring the bookmarks through the editing of Firefox files? Or any way at all of doing it? And is there any way of doing this without installing a third-party add-on?    OS Information:  Description:    Ubuntu 15.04 Release:    15.04   Package Information:  Google Chrome:  google-chrome-stable:   Installed: 42.0.2311.90-1   Candidate: 42.0.2311.90-1   Version table:  *** 42.0.2311.90-1 0         500 http://dl.google.com/linux/chrome/deb/ stable/main amd64 Packages         100 /var/lib/dpkg/status   Mozilla Firefox:  firefox:   Installed: 37.0.2+build1-0ubuntu0.15.04.1   Candidate: 37.0.2+build1-0ubuntu0.15.04.1   Version table:  *** 37.0.2+build1-0ubuntu0.15.04.1 0         500 http://gb.archive.ubuntu.com/ubuntu/ vivid-updates/main amd64 Packages         500 http://security.ubuntu.com/ubuntu/ vivid-security/main amd64 Packages         100 /var/lib/dpkg/status      37.0+build2-0ubuntu1 0         500 http://gb.archive.ubuntu.com/ubuntu/ vivid/main amd64 Packages


There are a lot of people telling how to make a bootable disc to other people who must understand a lot more than I do.  I try to read those answers and I say "OK, now tell me how to make bootable usb for dummies.  It would make Ubuntu much more popular if you did not need to be a computer hacker to figure out how to install it.  Why do you think Windows is popular?  You put in the disk and click install and 1 hour later you are surfing the web and emailing.  I need Ubuntu to be much easier to install than it is now!  Why not make a file to download that you copy to your USB then just reboot?  I would like to try an alternative to windows if someone could do a much simpler explanation to make a bootable USB, or even a bootable dvd.  Please help.  Thanks for your time!

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?


Suppose that a,b exist in $\Bbb R$ with $a < b$.  Show for every $x$ that exists in $(a,b)$, there exists $\epsilon\ > 0$ such that there is an $\epsilon$-neighborhood centered at $x$ that is contained in $(a, b)$.

First, the question I have is very similar to  question, but I hope it doesn't get closed as duplicate since I'm stuck nevertheless.  I'm trying to algebraically prove that an open interval is an open set. If I sketch it, as suggested by @rschwieb in the other question, then it seems quite obvious that this is indeed true. But I would like to be able to show it algebraically and after having looked at various sources found on the internet, I have decided to ask it here.  For definiteness, let us consider: \begin{equation} (c,d) = \{ x \in \mathbb{R} \mid c < x < d \} \end{equation} Furthermore, let $a \in (c,d)$, and recall that the $\epsilon$-neighborhood of $a$ is the set: \begin{equation} V_\epsilon (a) = \{ x \in \mathbb{R} \mid |x-a| < \epsilon \}  \end{equation} Now, if we take \begin{equation} \epsilon = \mathrm{min} \{ a-c,d-a \} \end{equation} then $a-\epsilon \geq c$ and $a+\epsilon \leq d$. Up until here I understand everything. But then I don't understand how we can conclude that $V_\epsilon (a) \subseteq (c,d)$? I'm sorry if this conclusion is really obvious (which it probably is), but for some reason I can't wrap my brain around it. Any help is much appreciated.


Janna's E is a shield that also grants the shielded champion bonus AD.   If a champion uses a skillshot and gains the shield after the skillshot is fired but before it hits an enemy, does the skillshot have the bonus AD or not?

For example: I'm playing Janna in bot lane with Caitlyn. Caitlyn begins channeling Ace in the Hole to finish off an enemy. Will the AD buff from my Eye of the Storm apply extra damage to Caitlyn's ultimate if I cast at after she begins channeling? Similarly, if I see Caitlyn rev up to shoot Piltover Peacemaker, can I boost her AD after the animation begins? (If I remember correctly, Piltover Peacemaker has a quick cast time, but the spell animation is rather long, so it may be a different circumstance from the first example.)  Basically, I want to know if the AD is calculated at the start of a cast, at the end of a cast, or when the ability actually creates and object on the battlefield.


When I zoom out in the view window, my object is not being shown entirely.    Can anyone help understand why this is happening and how to fix it?  My Hardware specification: i7 2.80GHz NVidia GTX 1050 4GB 8GB RAM Windows 10

I'm having an odd issue - When I try to zoom in on a detail using my MMB, the "camera" in the 3D view seems to be cutting off the exterior surface of my object and showing me the inside instead. I'd expect this behavior, but only when I was much more zoomed in.  If I zoom out a bit (one click on the scroll wheel) then I can see the exterior as I intend.  Is there any way to adjust this behavior?  Thanks!


I have a directory which has subdirectories (of arbitrary depth) that all have files, but have LaTeX (.tex) files as well. However, I do not want to go to each file and compile each separately. Is there a script to compile all of them at once from the top directory?

Is there a way to compile all tex files within a specific folder, from LINUX terminal, at once?   I would like to do this using pdflatex or lualatex in a way to create a pdf file for each distinc original tex file.   This question is not about creating individual tex files to form a single pdf file using \input or \include, at all.


When I prepare my cinnamon tea in hot water it produced a sludge at the bottom but I don't drink the sludge. Is there a way to make this tea so that there is no cinnamon remaining in the cup?

When you grind up cinnamon (say in a coffee grinder) and use it in a drink, it ends up producing this thick sludge.  You can only prevent the sludge from forming if you leave it very course.  Why does it turn to sludge?  I swear I once had a container of cinnamon that did not produce sludge.  Am I buying the wrong cinnamon?


I am trying to prove by double-counting that $$k2^{k-1} = \sum_{i=0}^{k} i\binom{k}{i}$$ where $n$ is a positive integer. I did it algebraically. However, the professor told me that I have to do this also by double-counting but I am not sure how to do this. Can someone help me?

I am trying to prove this binomial identity $\sum_{r=0}^n {r {n \choose r}} = n2^{n-1}$ but am not able to think something except induction,which is of-course not necessary (I think) here, so I am inquisitive to prove this in a more general way.  The left side of an identity occurs while solving another problem (concerning binomial theorem) so I am more interested in deriving the right side from the left side, else I have to remember it now onward.  EDIT: I am more interested in an algebraic proof rather than combinatorial argument or something involving calculus (however I liked  and  solution), hence I am removing the combinatorics tag.


:) I need some help with calculating the limit $$\lim_{n\to\infty}\dfrac{\ln(n!)}{n\ln(n)}.$$ I think that it's easy to see that we can find it using d'Alembert (square root) criterion, because, obviously, $\forall n\in\mathbb{N}_{\geqslant 2}:\phi_n>0$, where $\left(\phi_n\right)_{n\in\mathbb{N}_{\geqslant 2}},\,\phi_n:=\dfrac{\ln(n!)}{n\ln(n)}$, so I did the following observation: $$\dfrac{\ln(n!)}{n\ln(n)}=\dfrac{1}{n}\cdot\dfrac{\ln(n!)}{\ln(n)}=\dfrac{\dfrac{1}{n}\ln(n!)}{\ln(n)}=\dfrac{\ln(n!)^{\frac{1}{n}}}{\ln(n)}=\dfrac{\displaystyle\sqrt[n]{\ln(n!)}}{\ln(n)}=\displaystyle\sqrt[n]{\dfrac{\ln(n!)}{\ln^n(n)}}.$$ Ok. d'Alembert tells me that I should do the limit $$\ell:=\lim_{n\to\infty}\bigg\lvert\dfrac{x_{n+1}}{x_n}\bigg\lvert=\lim_{n\to\infty}\dfrac{x_{n+1}}{x_n},$$ where $\left(x_n\right)_{n\in\mathbb{N}_{\geqslant 2}},\,x_n:=\dfrac{\ln(n!)}{\ln^n(n)}$. We have, then: $$\ell=\lim_{n\to\infty}\dfrac{\ln[(n+1)!]}{\ln^{n+1}(n+1)}\cdot\dfrac{\ln^n(n)}{\ln(n!)}=\cdots=\lim_{n\to\infty}\left[\dfrac{\ln(n)}{\ln(n+1)}\right]^n\left[\dfrac{1}{\ln(n+1)}+\dfrac{1}{\ln(n!)}\right]$$ but what about the next?

I'm interested in the exact barrier of $$\ln(n!)= \Theta(n\ln(n))$$  and if it even exists.  This means, there is a $c_1, c_2$ , so that $$\ln(n!) \le  \Theta(n\ln(n) c_1$$  $$\ln(n!) \ge  \Theta(n\ln(n) c_2$$  or  $$0 \le \lim\limits_{n \to \infty}\frac{\ln(n!)}{n\ln(n)} \ge \infty$$  I could use de l'Hospital for the limit fraction, since it's $\frac{\infty}{\infty}$ but the derivate of $\ln(n!)$ causes problems. Also I don't know how I could prove the two statements above or how to prove them wrong. Any help is appreciated.


How to download graphics driver for Intel G41 express chipset in ubuntu 20.4?

Can someone help me out and explain or point me in the right direction on how to check video drivers and see if my video card running okay?  I had 10.04 installed on my Thinkpad r61 with Compiz Manager and life was great, until the machine took water damage. I bought an ASUS (X54H) since and am trying out 12.04, but the desktop just doesn't look right.  I always struggled with video driver installation. There are no proprietary drivers available in the hardware manager.  When I run lspci | grep VGA:  00:02.0 VGA compatible controller: Intel Corporation 2nd Generation Core Processor Family Integrated Graphics Controller (rev 09)   I will greatly appreciate your help. I want to use Linux more, but like I said video drivers appear to be my biggest concern. I have also tried 12.04 on my desktop PC, but again failed to configure video card, so switched back to Windows 7.


Let's suppose I'm in a while (1) loop calculating something, would it be possible to quit the whole application by pressing a certain key?  It's a C console application without threads.  I'm pretty sure it's not possible, but I'm a newbie so hey. I can only imagine beeing forced to press a key by some function like _getch() or similar. But then you have to wait until the user presses the key and the calculation cannot run meanwhile.

I'm trying to write a program in C (on Linux) that loops until the user presses a key, but shouldn't require a keypress to continue each loop.  Is there a simple way to do this? I figure I could possibly do it with select() but that seems like a lot of work.  Alternatively, is there a way to catch a ctrl-c keypress to do cleanup before the program closes instead of non-blocking io?


There are four maps in my program:  std::map< int, SigGen* > id_to_siggen_map; std::map< int, std::vector< double > > id_to_ticks_map; std::map< int, std::vector< double > > id_to_samples_map; std::map< int, QListWidgetItem* > id_to_item_map;   and I want to write a template function that, given an id, can delete from any of the above maps an entry corresponding to that id, i.e.  int id = 4; //could be any other id number delete_from_map(id, id_to_siggen_map); //deletes entry corresponding to id 4 from id_to_siggen_map delete_from_map(id, id_to_ticks_map); //deletes corresponding entry from id_to_siggen_map delete_from_map(id, id_to_samples_map); delete_from_map(id, id_to_item_map);    What I have so far:  template <typename T> void delete_from_map(int id, std::map< int, T > mymap){   for (auto it = mymap.begin(); it != mymap.end(); it++){      if(it->first == id){         mymap.erase(it);         break;      }   } }   However, attempts to compile give me undefined reference error for each of the four maps. The error looks like the following:  error: undefined reference to `void DVis::delete_from_map<QListWidgetItem*>(int, std::map<int, QListWidgetItem*, std::less<int>, std::allocator<std::pair<int const, QListWidgetItem*> > >)'   What am I doing wrong here?

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