For me, the modal/dialog window is positioned semi outside the screen. When resizing the window or opening the developer tools, the issue fixes itself. When resizing it back or closing the developer tools, the issue often reoccurs, but not always.  I'm using Linux with Firefox 55 for a bunch of add-ons that can still not be implemented in more recent versions. Not sure if anything changed in CSS vertical/horizontal alignment since then; positioning an element should be pretty compatible so I figured I'd report it and see if others can reproduce.

If I flag a comment now, it puts the dialog off the page:        It is only fixed by performing one of these actions:   Maximize window (if not already maximized) Restore window (if maximized)         I am running Windows and Firefox; also I tried Firefox in safe mode. I would be interested to see what testing was done on this beforehand - as this seems like a pretty glaring error. Please and thank you.    Inspired by the answer, the following CSS worked for me. It makes me sad to have to fix Stack Exchange CSS; I would figure this community over all others would get it right. Oh well.  aside {   transform: none !important; }


Is there a reason for this? Or is it an actual bug? I haven't received any downvotes recently, so that's not the issue.  Edit to include some questions from the comments below:  Re duplicate of : I haven't deleted any posts recently, nor have any posts of mine been deleted, as far as I can tell.     IIRC, I have downvoted an answer (or question) before (at some point in time), but I'm pretty sure it's been at least 6 months :D.  @Shadow Wizard said that maybe the answer I downvoted (-1) got deleted (+1), and then undeleted (-1).  That's possible, I guess (I had thought that they expire after a while and only mods can undelete, but I guess that's not the case).    Aannd it just happened again.  (Although as @Cai pointed out, I might have already gotten the +5 from this post so this might be a false positive (aha- see what I did there))

In the top bar, the green “achievements” number shows +14. But when I open the dropdown, I see four items totalling +20. Why does the total not match the sum of the items?    No lower entries were highlighted.


Suppose that X, Y, and Z are random variables. X and Y are positively correlated and Y and Z are likewise positively correlated. Does it follow that X and Z must be positively correlated?

I have a question regarding correlation inference. Consider, I have two sets of variables X and Y. For an x element of X I know the correlation to an unknown variable z. I also have the covariance matrix X and Y. Moreover, I know a set of (y1,y2,y3) element of Y, which model best my variable x. So how to infer the correlation of (y1,y2,y3) and z?  I need a function: f(corr(x,z), corr(x,(y1, y2, y3)), cov(X,Y)) --> corr((y1,y2,y3),z)  This might be a very simple question, but I have no idea how to do it or for what I can search in the literature.  Thank you in advance!


I want to use a font which contains glyphs for some common ligatures (fi, fl, ff, ffi, ffl) and actually needs them to avoid ugly collisions. However, for some reason they are not accessible via any OpenType feature or similar, but only through the respective Unicode characters. I do not want to tweak the font itself since I want my document to be compilable by others without supplying my tweaked font.  What I am now looking for is a way to emulate a normal ligature feature from within TeX (more precisely, XeLaTeX). For example, whenever the source contains fi, I want it to be rendered using the ligature glyph. I do not want to use the Unicode character for this ligature (ﬁ) in the source, nor do I want to use a custom command (such as \newcommand{\fi}{ﬁ}). Given, that regular TeX does something similar when rendering -- as “–”, I expect this to be possible.  I thought about using XeTeX’s inter-char tokens for this (see, e.g., the second half of ), but I could not get beyond inserting something in between the two characters. I am also aware of , whose answer is specific to LuaTeX, however.

I would like to add one char from otf font in xelatex as ligature. 'łł' = 'some char number in font' How make it? How tell for xelatex this char is a ligature of two letter 'ł' and 'ł'


I have purchased a ACM812a RFID reader and want to connect it to my PC via an ethernet cable. I thought it would just be a plug and play application but it is rather becoming a frustrating issue. The RFID reader manual or lack of there of, doesn't provide an IP address for the reader. So I have researched that I can use Winshark to ascertain the IP address of the reader. However even this software fails to extract the IP address of the reader, see picture below. The IP address of the computer is 169.254.106.15.    The reader application is shown in the picture below. From the picture, you can see the application requires an IP address and a port number. Can someone please help to get the IP address of the reader and how to get the port number so I can run the RFID reader application? (The 6000 port no. and 192.168.1.192 IP address is just a dummy that default when the application opens).  The reader RJ45 connector has 4 wires connecting to the RJ45 connector and my ethernet cable connecting the reader to the PC as 8 wires. Is this also an issue?   The model of the router is: B315s - 936 Huawei     Pictures of reader:

I have a Huawei WiFi router that has 4 ethernet ports. I have connected one of those to my laptop and connected another to device via an ethernet cable (RFID reader). I run the software Advanced IP scanner to scan all the devices on my network. But the connected device (RFID reader) fails to be detected by the software. The RFID reader is powered.   Can someone please explain to me why this frustrating network RFID reader fails to pick up on the software. As mentioned in my other post I want to know the IP address of the reader?


I have evaluated $\frac{d}{dx} x^x$ to be $x^x \left( log(x) + 1 \right)$ is that correct? Furthermore, what is $\int x^x dx$? Is that even possible? If not, why?

I'm trying to find $\int x^x \, dx$, but the only thing I know how to do is this:  Let $u=x^x$.  $$\begin{align} \int x^x \, dx&=\int u \, du\\[6pt] &=\frac{u^2}{2}\\[6pt] &=\dfrac{\left(x^x\right)^2}{2}\\[6pt] &=\frac{x^{2x}}{2} \end{align}$$  But it's certain that this isn't the correct way to evaluate that, and the answer must be wrong.


How do I show: $$\zeta {\space(3)} = \frac{5}{2} \sum_{n=1}^{\infty}{\frac{(-1)^{n-1}}{{{n^3}{2n\choose{n}}}}}$$ and if I want to generalize for any value of the zeta function what do I have to change, the $n^3$ term?

Apery's original proof that $$ \zeta(3) \equiv \sum_1^\infty \frac1{n^3} $$ is irrational starts from an alternating series  $$ \zeta(3) = \frac52\sum_1^\infty\frac{(-1)^{n-1}}{n^3\binom{2n}{n}} $$  There must be a way to see that those two series are equal, but I have tried various telescoping and other techniques and I just can't see it. Help me out:       Show (preferably by reasonably elementary means) that$$\sum_1^\infty \frac1{n^3}=\frac52\sum_1^\infty\frac{(-1)^{n-1}}{n^3\binom{2n}{n}}$$


Which of these is correct?  The mayor as well as his brothers is going to prison. The mayor as well as his brothers are going to prison.

My question arises from , where OP asks whether he should use the singular or plural verb form after "the title, as well as the tone,"  As luck would have it, when I searched Google Books for , I found...        ...and...        At the risk of having this question closed as just peeving, I feel that the first one should have been plural "err", because without the commas it seems to me both "the title" and "the tone" have more or less equal status as "joint" subjects of the verb, making it plural.  On the other hand, I feel the commas in the second example effectively demote "the tone" to "parenthetical" status (the clause is almost incidental). Since this encourages us think of "the title" as the primary subject, it should have been singular "derives".  I'm no great fan of "grammatical rules", but it seems weird to me that the only two relevant examples for this specific wording should both (in opposite ways!) contradict my inclinations.  What's going on?


When I copy a file, name.txt, in Windows Explorer and paste in the same directory, a new file appears.  Its default name is name - Copy.txt.  Is there a way to customize the default name for a new file which is a copy. For example, I'd like to have the copy be name_12345678.txt where 12345678 is a timestamp. Is it possible to achieve this using Windows' configuration and not with any 3rd party software?

On my Windows 7 machine, when I make a copy (Ctrl+C, Ctrl+V) of a file in the same folder I get the new file created with " - Copy" added to the file name:  1st copy: "foo.txt" -> "foo - Copy.txt". 2nd copy and so on: "foo.txt" -> "foo - Copy (2).txt".  Is there a way to change this naming pattern?  Particularly I'm interested in changing the naming from " - Copy (index)" to "_index", so that the files would be named foo_1.txt, foo_2.txt and so on.  I know there are 3rd party file managers that can do this, but I would like to know if there is a way to change this naming pattern in explorer.


Is there any easier way to create a polygon from the white empty space in: ? This space is associated with a municipality but the best i can do is this:   using the add polygon feature in QGIS, which as you can see is not great. Is there an easier way to completely cover this blank area and assign information to it?

I work with this polygon and try to find a way to create a new polygon from the empty gap (not distinguish it) in the middle of the polygon.  I succeed to do it with a "Difference" tool but used with another layer on the polygon and then using the difference tool.  I can also digitize the shape of the hole and create a new layer I seeking an automated way to do it and not doing in manually.   I read:        Is it possible to do it with a direct tool in QGIS 2.18.1, without the aid of another layer?


Please help! I have no idea how to start this problem / what to do to evaluate this.  For m>0 , let f(m) = $\sum_{r=1}^{m} \frac{m}{gcd(m,r)}$ . Evaluate f(m) in terms of the prime factorization of m.


My employer sends out lots of internal marketing and "aren't we great" emails that I don't read. I currently have a rule which moves the emails sent by the worst offenders to a CompanyName Spam folder in Outlook 2010.  Is there a way to have the emails delete after a period of time, lets say 30 days, without me having to do this manually? Ideally, I'd like a single rule to say: IF it's from joe.bloggs@CompanyName.com MOVE to CompanyName Spam AND after 30 days, move to deleted items folder.  I can make a rule to find emails within a particular absolute date range, but not a rolling relative date range (such as today - 30).  To make this even more complicated, if this could be done without VBA, that would be greatly appreciated (as I'm slow at using VBA and encoding)  Thanks,

I have a web application that sends me many emails that are only for notification purposes - and so, are not important. There can be a great deal of these per day, and I sometimes forget to delete them.    I am using a Microsoft Exchange mail server, and do not have administrator rights to it. Is there a way I can set up/configure from Outlook a procedure that deletes emails from a specific sender after an amount of time?


I'd like apt-get to default to using the -y option without me having to explicitly provide it.  Is this possible?

Is there a way to make apt-get install answer "yes" to the "Do you want to continue [y/N]?"?


There are plenty of good answers here about how reverse DNS works, but why is it used?  It seems that all reverse DNS proves is that the person sending the email has access to the DNS records for the IP. For an end user on a residential connection I find outgoing mail getting blocked by the SMTP server because there is no reverse DNS record. Since I am not trying to spoof some other domain, but using the domain for the SMTP server, how does this check add any security? It seems like the first check should be if there is a large volume of mail coming from the IP before considering rejecting.

I have heard that most spam filters use a reverse DNS lookup on the originating IP address of the sending SMTP server (or something like that) as part of the verification process.  I want to make sure my emails will pass this check.  How exactly can I verify that my emails are OK?  In researching it, I've noticed that if I look at the header of a valid email message coming from Gmail, I will see something like this:  Received: from mail-pz0-f185.google.com (mail-pz0-f185.google.com [209.85.222.185])         by mx.google.com with ESMTP id 10si2346996pxi.164.2009.07.22.22.26.19;         Wed, 22 Jul 2009 22:26:19 -0700 (PDT)   When I do an nslookup on 209.85.222.18, it responds with mail-pz0-f185.google.com, which is what I would expect.  If it responded with a different domain, then I assume that would indicate a problem and it would fail the check.  Is this what the reverse DNS lookup is all about or am I barking up the wrong tree?


at the moment i am trying to build a Java class which is able to creat a random Object.  I tryed it with Factory Pattern and the abstract Product Interface is like :  public interface ObjectFactory<T> {     T createObject(); }   but when i am trying to implement a concret generic Product it dosn't work. Here is the Code of my concrete Product:  public class GenericFactory implements ObjectFactory<T> {      @Override     public T createObject()     {         return new T();     }  }   IntelliJ says: "Cannot resolve symbol T"

I have got a template class as follows:  class MyClass<T> {     T field;     public void myMethod()     {        field = new T(); // gives compiler error     } }   How do I create a new instance of T in my class?


I purchased a ticket to Brussels via Amsterdam on KLM, with the Schiphol to Brussels-Midi portion on the Thalys.  The return portion of my itinerary is on Air France several days later.  This was done in good faith (i.e., not as a fare dodge) since I really do need to go to Brussels.  However, it now turns out that I have a meeting in Amsterdam the day I arrive.  I realise I am required to board the train to Brussels to fulfill the terms of my KLM ticket, and that I will need to get my ticket stamped on the Thalys in order to board my return flight.  What I want to know is where and when this takes place, since I need to return to Amsterdam. Will I need to ride the train all the way to Brussels, or can I get my ticket stamped and then disembark in Rotterdam or Antwerp?  Alternatively, is there any possibility of getting my KLM Thalys ticket issued for a later train, so that I can attend my meeting in Amsterdam before heading to Brussels?  NOTE: Some users have marked this question as duplicate.  Be assured that I read other Thalys/KLM questions others carefully prior to posting, but none of them address my key question: Where/when during the Thalys ride does the ticket get stamped?  This is important to anyone in my situation -- i.e., needing to return to Amsterdam after boarding the Thalys, but needing their ticket stamped to ensure their return itinerary is not cancelled.

I have a flight booked form Cairo to Amsterdam Schiphol via KLM and then a Thalys train from Amsterdam Schiphol to Brussels. As Brussels is not my final destination anyway I want to intentionally skip the train from Amsterdam airport to Brussels Midi. I have read many reviews about skipping a flight leg can lead to cancelling your entire flight but does the train booked with the flight included in this rule? What are the risks?


After having had , I came to wonder what bionic-updates actually was but could not find any documentation.  What is this distribution for? Is this some kind of "testing but not quite" for bionic?

In /etc/apt/source.list,  deb http://us.archive.ubuntu.com/ubuntu/ precise universe deb-src http://us.archive.ubuntu.com/ubuntu/ precise universe deb http://us.archive.ubuntu.com/ubuntu/ precise-updates universe deb-src http://us.archive.ubuntu.com/ubuntu/ precise-updates universe deb http://us.archive.ubuntu.com/ubuntu/ precise-backports main restricted universe multiverse deb-src http://us.archive.ubuntu.com/ubuntu/ precise-backports main restricted universe multiverse   I wonder what differences are between "precise" and "precise-updates" and "precise-backports" I only know "precise" means the code name of Ubuntu release 12.04. Thanks.


I`m fairly new to the sport and I see the people in my town half have clips and the other clipless pedals. Is there any advantage to using clipless  competitively or recreationally?

Other than not having to buy special biking shoes, is there any clear advantage to using pedal straps over clipless (aka clip-in or step-in) pedals?


A calculator is broken so that the only keys that still work are the $\sin$, $\cos$, $\tan$, $\cot$, $\arcsin$, $\arccos$, and $\arctan$ buttons. Assume that the calculator does real number calculations with infinite precision. All functions are in terms of radians, and you may assume all the values of $x$ below are positive. (a) Find, with proof, a sequence of buttons that will transform $x$ into $\frac{1}{x}$ . (b) Find, with proof, a sequence of buttons that will transform $\sqrt x$ into $\sqrt{x+1}$. (c) The display initially shows $1$. Prove that there is a sequence of buttons that will produce $\dfrac{3}{\sqrt{5}}$.  I got parts (a) and (b) pretty easily, but I can't figure out how to get (c).

A calculator is broken. The only keys that work are  $\sin, \cos, \tan, \cot, \arcsin, \arccos$, and $\arctan$ buttons. The original display is $0$. In this problem, we will prove that given any positive rational number $q$, show that pressing some finite sequence of buttons will yield $q$. Functions are always in radian form. (a) Find and prove that there exists a  sequence of buttons that will turn  $\sqrt x$ into $\sqrt{x+1}$.  For this, I got lucky and tried out $\sec (\arctan(x))$ on my calculator and got $\sqrt{x^2+1}$, so I just used the reciprocal and got $\cos (\arctan (x)) = \frac{1}{\sqrt{x^2+1}}$. However, how I can actually prove this?  (b) Prove that there exists a sequence of buttons that will yield $\frac{3}{\sqrt{5}}$.  I know that to go from $x$ to $\frac{1}{x}$ it is $\cot (\arctan (x))$, and I will have to use part a) to get to part b). How do I utilize this? I also know that $\sqrt{\frac{9}{5}}$ = $\frac{3}{\sqrt{5}}$, but after that, I'm stuck. Any hints?


I was reading about mathematical physics on a university website and they said "an education in theoretical physics is..." appearing to imply mathematical physics is theoretical physics. Is this the case? I want an education in theoretical physics or the closest thing to it. The problem is I live in New Zealand and the universities here don't teach it other than this one potentially.

I'm a huge fan of mathematical physics and I know what the formal definitions of those  two areas are, I've seen them. But I still get completely baffled when someone asks me to explain it simply. The difference is obvious to me, but I just can't seem to put it into words in a satisfying enough manner. So I'm asking you to help me...  What is the essential difference between  and ?  or if you prefer the rephrased version...  What was the motivation for introducing the name "mathematical physics" as a separate entity?  (It doesn't matter if you're one of those people who don't like labels, the thing is that we do have these two separated very often in academia.)


I use this php code to check the variable that I get from the URL to protect my Database from URL injection :  if(isset($_REQUEST["u_i"])) {//echo $_REQUEST["u_i"];exit; if(!is_numeric($_REQUEST["u_i"])) { //echo $_REQUEST["u_i"];exit; header('Location:index.php'); } else  {//echo $_REQUEST["u_i"];        $id_raw = trim(htmlentities($_REQUEST["u_i"])); $visitor_id = mysql_real_escape_string($id_raw); } }   I want to know what should I edit in this code to use it on the $_POST array variables (user input text not numbers) like (comments from users, text blocks) because I use this part to direct users to index if the url variable contain a text not number :  if(!is_numeric($_REQUEST["u_i"]))     {     //echo $_REQUEST["u_i"];exit;     header('Location:index.php');     }   so how could I check a variable which have text securely ?

If user input is inserted without modification into an SQL query, then the application becomes vulnerable to , like in the following example:  $unsafe_variable = $_POST['user_input'];   mysql_query("INSERT INTO `table` (`column`) VALUES ('$unsafe_variable')");   That's because the user can input something like value'); DROP TABLE table;--, and the query becomes:  INSERT INTO `table` (`column`) VALUES('value'); DROP TABLE table;--')   What can be done to prevent this from happening?


I installed OBS Studio:  sudo apt-get install obs-studio  Reading package lists... Done Building dependency tree        Reading state information... Done The following packages were automatically installed and are no longer required:   gir1.2-keybinder-3.0 libkeybinder-3.0-0 Use 'sudo apt autoremove' to remove them. The following additional packages will be installed:   libfdk-aac0 libluajit-5.1-2 libluajit-5.1-common libxcb-xinerama0 The following NEW packages will be installed:   libfdk-aac0 libluajit-5.1-2 libluajit-5.1-common libxcb-xinerama0 obs-studio 0 upgraded, 5 newly installed, 0 to remove and 0 not upgraded. Need to get 3,678 kB of archives. After this operation, 13.0 MB of additional disk space will be used. Do you want to continue? [Y/n]    I decided to remove it:  sudo apt-get --purge remove obs-studio Reading package lists... Done Building dependency tree        Reading state information... Done The following packages were automatically installed and are no longer required:   gir1.2-keybinder-3.0 libfdk-aac0 libkeybinder-3.0-0 libluajit-5.1-2   libluajit-5.1-common libxcb-xinerama0 Use 'sudo apt autoremove' to remove them. The following packages will be REMOVED:   obs-studio* 0 upgraded, 0 newly installed, 1 to remove and 0 not upgraded. After this operation, 11.6 MB disk space will be freed. Do you want to continue? [Y/n]    When removing it, I expect 13.0 MB of disk space to be freed because that is what the installation required, but I got 11.6 MB disk space freed instead: Why?

Why do apt-get install package and then apt-get remove package do not consume and clear almost exactly the same space? For example with the package "latex2html" one gets:  ubuntu:~$ sudo apt install latex2html Need to get 758 MB of archives. After this operation, 1,211 MB of additional disk space will be used. Do you want to continue? [Y/n] .... ubuntu:~$ sudo apt remove latex2html The following packages will be REMOVED:   latex2html 0 upgraded, 0 newly installed, 1 to remove and 92 not upgraded. After this operation, 5,578 kB disk space will be freed. Do you want to continue? [Y/n]


I am learning powershell, and am curious as to why the syntax Remove-Item does not put the file(s) in the recycle bin?  Where do these files go when you remove them, and are they recoverable?  I read the  article, but did not see anything in there that answered my question, so I ask here.

After reading the quote below on the Casey Anthony trial (CNN) ,I am curious about where deleted files actually go on a hard drive, how they can be seen after being deleted, and to what extent the data can be recovered (fully, partially, etc).  "Earlier in the trial, experts testified that someone conducted the keyword searches on a desktop computer in the home Casey Anthony shared with her parents. The searches were found in a portion of the computer's hard drive that indicated they had been deleted, Detective Sandra Osborne of the Orange County Sheriff's Office testified Wednesday in Anthony's capital murder trial."  I know some of the questions here on Super User address third party software that can used for this kind of thing, but I'm more interested in how this data can be seen after deletion, where it resides on the hard drive, etc. I find the whole topic intriguing, so any additional insight is welcome.


In oracle, how can i give grant to 'A' user to access 'B' schema?  Also, Is it possible to give, 'SELECT, EXECUTE AND VIEW' grant to A user on B schema?

I have two users Bob and Alice in Oracle, both created by running the following commands as sysdba from sqlplus:      create user $blah identified by $password;    grant resource, connect, create view to $blah;   I want Bob to have complete access to Alice's schema (that is, all tables), but I'm not sure what grant to run, and whether to run it as sysdba or as Alice.  Happy to hear about any good pointers to reference material as well -- don't seem to be able to get a good answer to this from either the Internet or "Oracle Database 10g The Complete Reference", which is sitting on my desk.


I have a model imported from SMD file, and all the faces of the mesh seem independent. When I move a single face, the faces around it do not warp (a hole appear in the mesh).  I wonder how I could make a unified mesh from all the independent faces ?   Thanks

I wrote an algorithm to randomly generate terrain and I am trying to load and edit my results with blender.  The problem is that when I load my terrain in blender, the individual triangles are not linked together.     You can see when I shrink/flatten a subset the the faces, the rest don't follow and deform as a single mesh.  I tried deleting the faces and edges and using F to create faces from the points, but it does not give usable results.    How can I go about solving this problem?


I am trying to compute the character of $\Lambda^k V$ and Sym$^k V$ for V an arbitrary representation of a group G. I already know how the characters look for $k=2$, but I cannot find a way to generalize that. My attempt would be to find a way to decompose $\Lambda^k V$ and Sym$^k v$ into powers of 2 and 1, but I am not sure that is possible. Does someone have an idea to solve that?

Does there exist some simple formulas for the characters $$\chi_{\Lambda^{k}V}~~~~\text{and}~~~\chi_{\text{Sym}^{k}V},$$ where $V$ is a representation of some finite group?  Thanks.


I am not an English language native, and as such, I may be less sensitive to the difference between open usage of neo-pronouns and plain bad English. In the light of the recent discussions, is it possible to provide grammar resources which I should rely on?  Which of the style guides (e.g. ) should I follow in general in this respect?

Please leave any feedback or questions about this FAQ on .     Two weeks ago, we  to directly address concerns over pronoun usage. We tried to anticipate likely questions, but… missed the mark by quite a lot. Based on Gareth McCaughan’s excellent post, “”, we’ve gone back to the drawing board and written a new FAQ that aims to address actual questions that have been frequently asked in these discussions.  If you read only one thing, the answer to question #1 under The Basics sums up our goals in publishing this guidance:     It would be rude to refer to a man as "she" or a woman as "he". Some people are neither male nor female and might, for instance, ask to be referred to as "they". When someone indicates what pronouns should be used to refer to them, please use the pronouns they state as you would others.   This is a learning process for most of us - from authors to readers to moderators to employees of Stack Exchange, Inc.  Let’s all try to approach this with good intentions and a willingness to learn from one another.  Big thanks to Gareth for leading by example here, and to everyone who has stepped up to ask and answer the important questions!  What's all this stuff about pronouns in The Code of Conduct?  The  has two direct references to pronouns:   “Use stated pronouns (when known).” “Prefer gender-neutral language when uncertain.”   What does all of this mean and how can I as a user understand and follow the CoC guidance?


I'm trying to add myself to the fuse user group but it doesn't look like the change is taking effect even though /etc/group looks correct after invoking addgroup or usermod.  I've tried both ...  sudo addgroup fjohnson fuse   and   sudo usermod -a -G fuse fjohnson   /etc/group shows the change  fuse:x:104:fjohnson   but I can't read   -rw-r----- 1 root fuse 215 Oct 16 10:39 /etc/fuse.conf   as   cat: /etc/fuse.conf: Permission denied   and groups(1) returns   fjohnson adm dialout cdrom plugdev lpadmin admin sambashare

I have the su executable with the following permissions:  bash-4.2# ls -la /bin/su -rws--s--- 1 root wheel 59930 Sep 14  2012 ./su   When I am logged in as a user, not in the wheel group and try to run su, I get an error, which is correct:  bash-4.2$ su bash: /bin/su: Permission denied   After that I add this user to wheel group from root:  bash-4.2# usermod -a -G wheel user   But for the same terminal session I still can't run su:  bash-4.2$ su bash: /bin/su: Permission denied   For the new sessions I can run su. How to allow to run su instantly after I added the user to the appropriate group?


Supposedly, $\frac1i=-i$. However, my simplification reaches another result: $$\frac1i=\frac{\sqrt1}{\sqrt{-1}}=\sqrt{\frac1{-1}}=\sqrt{-1}=i\text.$$ What's wrong with my process?

I know there must be something unmathematical in the following but I don't know where it is: \begin{align} \sqrt{-1} &= i \\\\\ \frac1{\sqrt{-1}} &= \frac1i \\\\  \frac{\sqrt1}{\sqrt{-1}} &= \frac1i \\\\  \sqrt{\frac1{-1}} &= \frac1i \\\\  \sqrt{\frac{-1}1} &= \frac1i \\\\  \sqrt{-1} &= \frac1i \\\\  i &= \frac1i \\\\  i^2 &= 1 \\\\  -1 &= 1 \quad !!? \end{align}


I use the following function to create a multidimensional list of shape dimension:  def create(dimensions, elem):     res = elem     for i in dimensions[::-1]:         res = [copyhelp(res) for _ in range(i)]     return res.copy()  def copyhelp(r): #when res begins as elem, it has no .copy() function     if isinstance(r,list):         return r.copy()     return r   So if I say mylist = create([3,3,2],0), I get    >> mylist   [[[0, 0], [0, 0], [0, 0]],    [[0, 0], [0, 0], [0, 0]],    [[0, 0], [0, 0], [0, 0]]]   Great. Now I use this function to change the value at an index given by a list index to v:  def replacor(array, index, v):     if not isinstance(array[0],list):         array[index[0]] = v     else:         return replacor(array[index[0]], index[1:], v)    Now when I do replacor(mylist, [1,2,0], '.'), I get this:    >> mylist   [[['.', 0], [0, 0], [0, 0]],    [['.', 0], [0, 0], [0, 0]],    [['.', 0], [0, 0], [0, 0]]]   I'm suspicious it has to do with array pointers, but I used copy() at every step, so I'm not sure where I went wrong. Clearly the issue is the way I define my first list, but I still don't understand why I'm getting this behavior since ints, bools, and strings are immutable.

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?


I have one dictionary, like the following:  adict = {'1': alist, '0': blist, '2': clist}   I want to perform some things, for all lists in adict except the list with the key '0'.  So I have tried:  for key in adict:     if key is not '0':         do something   but the test doesnot work, something is done in all cases, including the one that key=='0'.  I cannot figure out, what is wrong, any help?

My  has failed me.  In Python, are the following two tests for equality equivalent?  n = 5 # Test one. if n == 5:     print 'Yay!'  # Test two. if n is 5:     print 'Yay!'   Does this hold true for objects where you would be comparing instances (a list say)?  Okay, so this kind of answers my question:  L = [] L.append(1) if L == [1]:     print 'Yay!' # Holds true, but...  if L is [1]:     print 'Yay!' # Doesn't.   So == tests value where is tests to see if they are the same object?


I know that for a symmetric matrix, its eigenvector are orthogonal. But for a repeated eigenvalue for a symmetric matrix, why still its eigenvalue must be still orthogonal. I read somewhere that symmetric matrix can not have defective eigenvalue, so for a repeated eigenvalue with m multiplicity, we will still have m orthogonal eigenvector for it. Kindly please for your answer, can you show by taking a 3 by 3 matrix and show it.

A matrix is diagonalizable iff it has a basis of eigenvectors. Now, why is this satisfied in case of a real symmetric matrix ?


I want to serialize datacontract classes into XMl, but without the Namespaces.  I've added:  [DataContract(Namespace="")]   but I still get:  <Person xmlns:i="http://www.w3.org/2001/XMLSchema-instance"> <Title>Mr</Title> ... </Person>   Is there any way to stop this happening as I just want the clean xml to pass into a legacy component.

The code looks like this:   StringBuilder builder = new StringBuilder(); XmlWriterSettings settings = new XmlWriterSettings(); settings.OmitXmlDeclaration = true; using (XmlWriter xmlWriter = XmlWriter.Create(builder, settings)) {     XmlSerializer s = new XmlSerializer(objectToSerialize.GetType());     s.Serialize(xmlWriter, objectToSerialize); }   The resulting serialized document includes namespaces, like so:   <message xmlns:xsi=\"http://www.w3.org/2001/XMLSchema-instance\"      xmlns:xsd=\"http://www.w3.org/2001/XMLSchema\"      xmlns="urn:something">  ... </message>   To remove the xsi and xsd namespaces, I can follow the answer from .  I want my message tag as <message> (without any namespace attributes).  How can I do this?


As pointed out in a comment to the question this was about gfx.xrender.enabled. The answer can be found in the marked dupe, but it is easy to miss in all the noise talking about ssh and the X11 protocol. Direct link to answer:  My problem started happening about a month ago. I'm currently on Firefox 89.0.1. Up until this point, Firefox ran just fine over ssh -X. I'm running it from an Ubuntu machine (server) to an Ubuntu VM (client) and a different Ubuntu machine (server) to Windows 10 (client), both showing the same symptoms. It's not my hardware setup or -X as all machines are wired to a local gigabit switch and other applications (including Thunderbird) run just fine. They are a little slower than if I was running them on their own desktop, but perfectly usable. After it happened, Firefox is just .... slow. I'm using it with --no-remote and the actual window for Firefox appears in under a second. It then hangs there for about 2 minutes until the tabs become usable. The output in my ssh shell reads: $ firefox --no-remote & libGL error: No matching fbConfigs or visuals found libGL error: failed to load driver: swrast  (firefox:757486): GLib-GIO-CRITICAL **: 10:39:54.241: g_dbus_proxy_new: assertion 'G_IS_DBUS_CONNECTION (connection)' failed  (firefox:757486): GLib-GIO-CRITICAL **: 10:39:54.241: g_dbus_proxy_new: assertion 'G_IS_DBUS_CONNECTION (connection)' failed  (firefox:757486): GLib-GIO-CRITICAL **: 10:39:54.241: g_dbus_proxy_new: assertion 'G_IS_DBUS_CONNECTION (connection)' failed [GFX1-]: Failed GL context creation for WebRender: 0 [GFX1-]: FEATURE_FAILURE_WEBRENDER_INITIALIZE_UNSPECIFIED [GFX1-]: Failed to connect WebRenderBridgeChild. [GFX1-]: Fallback WR to SW-WR libGL error: No matching fbConfigs or visuals found libGL error: failed to load driver: swrast libGL error: No matching fbConfigs or visuals found libGL error: failed to load driver: swrast  but that doesn't look too different to what I had before. Can anyone please suggest anything that might speed it up? I'm not really looking for answers telling me that ssh -X is slow (it is, but it's acceptable to me on all other applications) or things to do with compression or cypher suites. My link is fine, except for Firefox.

I try to launch Firefox over SSH, using  ssh -X user@hostname   and then  firefox -no-remote   but it's very very slow.  How can I fix this? Is it a connection problem?


I'm having this problem for the first time. After rebooting my laptop I stuck with endless login loop (black screen shows up for 2 seconds and then it throws me back to login screen).   I didn't find Xauthority in my home folder. So I've created a new user and logged in - everything's fine except I can't login with my main user.  What should I check?

My Ubuntu is stuck in a login loop when trying to enter my desktop. When I login, the screen gets black and soon after that the login screen comes back.   I've read that the problem might be caused by an error depending on the graphics, here's my graphics card: ATI Radeon 7670M


In the olden days of DEC/HP VMS Vax Basic, there was a way to define a record's fields and "map" that definition to an open file. When a record was read, the fields defined in the map were populated for that record without coding the parsing and setting. It used to look like this:  MAP (Bec) STRING Owner = 30%, LONG Vehicle_number,    &           STRING Serial_number = 22% OPEN "VEH.IDN" FOR INPUT AS FILE #2%,                 &       ORGANIZATION SEQUENTIAL FIXED,                  &       MAP Bec, ACCESS READ INPUT "Which record do you want";A% WHILE (A% <> 0%)    GET #2%, RECORD A%    PRINT "The vehicle number is", Vehicle_number    PRINT "The serial number is", Serial_number    PRINT "The owner of vehicle";Vehicle_number; "is", Owner    INPUT "Next Record";A% NEXT CLOSE #2% END   I cannot find if there is anything similar in a .Net environment, specifically C#.

I'm trying to read binary data using C#. I have all the information about the layout of the data in the files I want to read. I'm able to read the data "chunk by chunk", i.e. getting the first 40 bytes of data converting it to a string, get the next 40 bytes.  Since there are at least three slightly different version of the data, I would like to read the data directly into a struct. It just feels so much more right than by reading it "line by line".  I have tried the following approach but to no avail:  StructType aStruct; int count = Marshal.SizeOf(typeof(StructType)); byte[] readBuffer = new byte[count]; BinaryReader reader = new BinaryReader(stream); readBuffer = reader.ReadBytes(count); GCHandle handle = GCHandle.Alloc(readBuffer, GCHandleType.Pinned); aStruct = (StructType) Marshal.PtrToStructure(handle.AddrOfPinnedObject(), typeof(StructType)); handle.Free();   The stream is an opened FileStream from which I have began to read from. I get an AccessViolationException when using Marshal.PtrToStructure.  The stream contains more information than I'm trying to read since I'm not interested in data at the end of the file.  The struct is defined like:  [StructLayout(LayoutKind.Explicit)] struct StructType {     [FieldOffset(0)]     public string FileDate;     [FieldOffset(8)]     public string FileTime;     [FieldOffset(16)]     public int Id1;     [FieldOffset(20)]     public string Id2; }   The examples code is changed from original to make this question shorter.  How would I read binary data from a file into a struct?


Is there anyway to do something like: testfor @p[score_snowball=0] {Inventory:[{id:"minecraft:snowball",Count:0b}]}" That works besides inverting: testfor @p[score_snowball=0] {Inventory:[{id:"minecraft:snowball",Count:1b}]} ? I wanna give player a snowball when they accidentally thrown one into a wall. Because when they throw it into a wall when they are too close to it, it doesn't get found by: testfor @e[type=snowball] and therefore doesn't give a snowball when it breaks. I also want the player to only have 1 snowball, everytime the snowball objective = 0. Setup:  Repeating + Always active cmd block with: testfor @p[score_snowball=0] and comp going to: give @p minecraft:snowball  Another Repeating + Always active cmd block with: testfor @e[type=snowball] and two comps, one going to: scoreboard players add @p snowball 1 and another going to cmd block that's inverted: scoreboard players set @p snowball 0

I know that you can use exclamation marks in Minecraft commands to check for an entity that does not have a specific tag. For example, you can use /kill @e[type=!Player] to kill all entities except for the player. I have, however, encountered two problems with using exclamation marks that I can't find a solution for.  For my first problem, I've set up a series of command blocks to summon shootable fireballs above the player’s head when a certain item is being held;  /scoreboard players add @a Fireball 1 {SelectedItem:{tag:{display:{Name:"Summon Fireball"}}}} /execute @a[score_Fireball_min=1,score_Fireball=1] ~ ~ ~ /summon Fireball ~ ~2.5 ~ {direction:[0.0,0.0,0.0]} /scoreboard players set @a Fireball 0   I used a comparator and a redstone torch so that the last command would activate when the first command would deactivate, that is, when the player is not holding the item.  The problem is, that when I move far away from the setup, the redstone stops working, leaving me unable to summon any new fireballs. Instead, I'm trying to use a command block to check when anything except for item is being held;  /scoreboard players set @a Fireball 0 {SelectedItem:{tag:{display:{Name:!"Summon Fireball"}}}}   I’ve either put it at the wrong place, or you simply can’t use exclamation marks in NBT tags. Could someone tell me where I should put the exclamation mark, or in the latter case, how I can check for anything except for a specific item?  Further, I’ve tried using exclamation marks to set the score of all entities, including the ones with a blank score, but except for the ones with a score of 2 or higher, to 0;  /scoreboard players set @e[score_arrows_min!=2] Arrows 0 /scoreboard players set @a Arrows 1 {SelectedItem:{tag:{display:{Name:"Rain of Arrows"}}}} /scoreboard players set @e[type=Arrow] Arrows 2 {inGround:1b}   The code does change the scores of entities without scores to 0, but it doesn’t exclude the arrows with a score of 2. Could anyone tell me what I’m doing wrong here?


I have found answers that say that gravity interferes with the oscillating electric and magnetic fields of the waves and others that say that since gravity is a bend in space-time, in which case the waves are bent because they travel in a linear pattern along space-time, so that when space-time bends, so does the wave.   Are either of these true and if so which one? If neither is true then why does it occur?   An accurate explanation of space-time would also be appreciated.

Light is clearly affected by gravity, just think about a black hole, but light supposedly has no mass and gravity only affects objects with mass.  On the other hand, if light does have mass then doesn't mass become infinitely larger the closer to the speed of light an object travels. So this would result in light have an infinite mass which is impossible.  Any explanations?


On Meta Stack Exchange, I've noticed two privileges that don't make any difference on this site, but that are still listed on the .  One of these is the  privilege. This privilege is irrelevant on meta since there still aren't any ads on meta, as stated in the help center:     Meta sites have no advertisements so this privilege is not relevant for them.   The other such privilege is the  privilege. This privilege is irrelevant to Meta Stack Exchange since this site itself is meta and has no other meta site associated to it.  However, both these privileges are listed on the privilege page of Meta Stack Exchange and can be tracked as the next privilege on the profile page. Is there any reason to this?

I just took a look at meta today and noticed something weird in the meta privileges. If you look at the meta privilege list, you can see that at . I know that there is no meta for meta, and the link they give you in the privilege page leads you to meta.stackexchange.com, right where you started. Why do they have this privilege? I have a feeling that this is a bad recursive joke. You must be  member of meta to get the privilege of being a member of meta! :)


Is there any way to 'copy' or 'export' Lubuntu to a USB-drive so I can use it on another PC without having to set it up ?

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?


I'm playing Minecraft and I'm not sure how to save my items/stuff when I die. I always lose my house and I found out I have to commit suicide to go back to my home. But then I can't find my items. This is always a problem for me! Please tell me the command for saving my items and for my house. My compass always points to the place where I spawn I don't understand I sleep at my house and I don't spawn there, is my compass broken?

I wandered too far to go look for sheep and now I'm on a completely different island.  How do I find my way back to my house?


At www.keylength.com, I found the following table of ECC field size and the corresponding RSA modulus recommended by NIST.   ECC Modulus  RSA Prime Size  160             1024  224             2048  256             3072  384             7680  512             15360  But NIST proposed P-192, P-224, P-256, P-384, P-521 curves. May I know what is equivalent RSA modulus for P-192 and P-521 curves?

§5.6.1 p.62–64 specifies a correspondence between RSA modulus size $n$ and expected security strength $s$ in bits:  Strength  RSA modulus size   80        1024  112        2048  128        3072  192        7680  256       15360   This works out to approximately $s \approx 4 n^{0.43}$ (but I have no idea whether my extrapolation means anything; strengths up to 112 are indexed on DES while strengths 128 and above are indexed on AES, i.e. the strength is the difficulty of brute-forcing the corresponding symmetric algorithm with the specified key size).  What are these numbers based on? Do they come from the expected complexity of the best known factorization methods? Or are they extrapolation from the amount of computation in specific factorization efforts such as for  (which “required more than $10^{20}$ operations”)?  (I'm asking for more precise information than .  has a nice history of RSA factorizations, but doesn't answer my question — is that what the strength estimates are based on?)


For a presentation I had to temprorary clear my Desktop , so I ran  mv Desktop Desktop1 after which desktop was cleared But after a reboot my HOME directory files started to appear in Desktop I tried to run  mv Desktop1 Desktop  and restarted the PC yet the problem wasn't solved I also noticed that the Desktop shortcut in Nautilus File manager's side panel too disappeared  How do I fix this?

As of now, my desktop has begun showing the contents of my home folder (~) instead of the contents of ~/desktop. I must have changed something, but I have no idea what, or what I was doing exactly when it happened.  How do I re-point gnome to the right folder?  I'm running Ubuntu 11.04.


I wish to know if anybody from here owns too a Gigabyte Aero 15 laptop and if he/she can control the fans. This laptop is from 2017, with a 7th gen. Intel Core i7-7700HQ and an Nvidia GTX 1060 with 6Gb. This is an awesome laptop, thin, compact, lightweight yet at the same time powerfull and a long-lasting battery life. I'm very happy with it, except that I can't control the fans when running Ubuntu, meanwhile this is possible under Windows 10. I want to know if it's possible to control the fans under Ubuntu since it gets pretty hot under some load using this OS. Except that quirk and some others: some Fn keys doesn't work at all, and when connecting an external monitor Grub does not show (I suspect this is a problem between Intel and Nvidia GPUs). I'm pretty happy using Ubuntu but if I could control the fans it would be perfect, the Fn keys problem can be easy to solve with mapping that function keys to another custom keyboard shortcut, and since I only use Ubuntu and Windows 10, it's easy to remember the Grub menu too. So my main issue are the fans. Could anyone guide to know if I can control the fans, please?  Thank you in advance!

How can I control the computer's fan speed?  On Windows there is a wonderful program called .


As i have multiple drop-downs in my form, I would like to retrieve the HTML id from one of the selected drop-downs. I have the following code for my drop-downs on change:  $("select[name$='product_type']").change(function(){}   when using console.log($(this).select());  i can see the selected drop-down id in the console;    What is the syntax for retrieving this id into a var?

Is there any way to get the ID of the element that fires an event?  I'm thinking something like:    $(document).ready(function() {   $("a").click(function() {     var test = caller.id;     alert(test.val());   }); }); <script type="text/javascript" src="starterkit/jquery.js"></script>  <form class="item" id="aaa">   <input class="title"></input> </form> <form class="item" id="bbb">   <input class="title"></input> </form>     Except of course that the var test should contain the id "aaa", if the event is fired from the first form, and "bbb", if the event is fired from the second form.


Purple lights has the highest frequency among all visible lights, while the red lights is the least frequent one. However, purple seems to be a mix of red and blue to human eyes, why?

When people are asked to match monchromatic violet light with an additive mix of basic colours, they (paradoxically) mix in red.  In fact, the CIE 1931 color space chromaticity diagram shows this effect begins at about 510nm (greenish-cyan), where people mix in no red.  From that point on, the higher the frequency of the light source, the more red they mix in.    This effect is reflected by the red curve of the , which has an additional bump in the area of blue light.  However, that curve does not match the actual spectral sensitivity of red cones.  So where does this additional perception of red at higher frequencies come from?


Let $E/F$ be a field extension and $a \in E$ ,$a$ algebraic over $F$. Prove that if the degree of the minimal polynomia of $a$ is an odd number then $F(a)=F(a^2)$.  The first step is to consider the extensions $F \leqslant F(a^2) \leqslant F(a)$.  We need need to show that $[F(a):F(a^2)]=1$  If  $[F(a):F(a^2)]=m>1$ then $m<n$ and $m=2k_0+1$ where $n=deg(irr(a,F))$($m$ cannot be an even number)and $[m/2]>k_0>1$.  So we have that $[F(a^2):F]=n/m=s$ for some $s<n$ is an odd number.  From the above  we see that  $deg(irr(a^2,F))=n/m=s$.  From this point i don't know how to proceed to derive a contradiction.  Can someone help me with this?

I have a question about simple field extensions.  For a field $F$, if $[F(a):F]$ is odd, then why is $F(a)=F(a^2)$?


The validation loss is decreasing very slowly and the accuracy after 100 epochs is significantly lower than the train accuracy. What seems to be the problem here and how can I fix it? Do I decrease the number of nodes in the hidden layer, or use dropout?

I'm training a neural network and the training loss decreases, but the validation loss doesn't, or it decreases much less than what I would expect, based on references or experiments with very similar architectures and data. How can I fix this?    As for question        to which this question is inspired, the question is intentionally left general so that other questions about how to reduce the generalization error of a neural network down to a level which has been proved to be attainable, can be closed as duplicates of this one.  See also dedicated thread on Meta:


I have Linux Mint on my computer and wondering how I can get Windows on here as well. I saw one saying to use Grub except I have no idea how to use it. Any ideas/suggestions?

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


I'm in the middle of writing my dissertation. I have created a search application using .net c#.  I need a way to accurately time the search.  I have heard of System.Diagnostics.Stopwatch but I have read that it wasn't accurate.  So my question is what is the most accurate way to time methods and how would you implement it?

How accurate is System.Diagnostics.Stopwatch? I am trying to do some metrics for different code paths and I need it to be exact.  Should I be using stopwatch or is there another solution that is more accurate.  I have been told that sometimes stopwatch gives incorrect information.


I'm fairly new to Blender and 3-D modeling in general.  I created my first model and was pretty proud of it.  However, when I finally thought about it and noticed it, I decided 400,000 faces may have been a few too many.  So to my question:  Does anyone have a basic set of rules and/or a guide they follow as they model that will help lead to proper technique and efficiently rendered models? Triangles vs Quads, when to (and not to) subdivide/subsurf, is there anything wrong with making a high-res version and decimating/shrinkwrapping after it's done?    Like I said, I'm a beginner so I want to make sure I'm doing things correctly and won't be forming a bunch of bad habits I will have to correct later.  So a step by step workflow, or tips on things to avoid, etc.  I've been doing a lot of research, but haven't found this type of information broken down well.  I don't necessarily need a large amount of detail - just a basic list to act as a guide of more things to research as I model.  (It is worth mentioning that most of my models will be used in a realtime application, so I am aware I have to get my polycount WAY down)

When I get an idea for something I'd like to make in Blender, I hit up Google for specifics, then blender SE when I get stuck.   I'm very overwhelmed by the immensity of Blender and I'm a little afraid that this self-directed approach is going to lead me to develop bad habits. Is there a "best practice" way of learning to use Blender?


I'm generally very picky about what my computer does - I'm disabling a lot of stuff that I don't like (i.e., different MS office, nvidia, creative stuff that tries to autorun), I constantly monitor my computer for all sorts of misbehaving programs.   My AV of choice is Kaspersky and I think I'm pretty secure from viruses because I never visit fishy sites like poker/porn, and never install programs from unconfirmed sources.  However, I have just randomly checked and it seems that after I freshly start my PC, about 1.5GB of 8GB RAM is already used up! In the Task Manager, "all user's processes" ticked of course, top users are explorer.exe at 73MB, SQL Server at 51MB and dwm.exe at 28MB. I've manually calculated total amount for all processes that are running, and came to a number of less than 400MB (had to round up everything to count only megabytes).  So, is it true that the system itself uses 1.1GB? Because I've googled and people report their PC uses only ~500MB memory when just started.   If no specific information is available, maybe someone could give me advice about how to find out what else uses RAM (except what is listed in Task Manager)? So I could track whatever is hogging that gigabyte of RAM.

I have 16GB of system RAM. On startup with no applications open except the task-manager Windows is using about 3gb of RAM. I looked in the processes tab, but nothing seems to be out of the ordinary. How can I find out why my Windows is using so much RAM.    all processes from all users      Reading from the poolmon it seems that my wireless broadcom driver is using about 0.4GB of of RAM. Even if I remove  it would still be using  2.6GB on start-up, which is still too much.      After reinstalling the wireless driver associated with the memory leak. I have a new screenshot and would like to confirm that it was indeed a memory leak.


I need to show that if the sum and the product of two complex numbers is algebraic, then each of then is algebraic.   We have that the extensions $Q(a+b)/Q$ and $Q(ab)/Q$ are finite, so the extension $Q(a+b,ab)/Q$ is finite.   Since $$[Q(a,b):Q]=[Q(a,b):Q(a+b,ab)] [Q(a+b,ab):Q],$$ it suffices to show that the extension $Q(a,b)/Q(a+b,ab)$ is finite, but I can't come up with an appropriate basis. Any ideas?

Let $\alpha, \beta \in \mathbb{C}$,  such that $\alpha + \beta$, and $\alpha\beta$ are algebraic. Show that $\alpha$ and $\beta$ are algebraic.   attempt: Suppose $\alpha, \beta \in \mathbb{C}$ such that $\alpha + \beta$, and $\alpha\beta$ are algebraic.  Let $\alpha + \beta$, $\alpha\beta$ are algebraic be algebraic over $F$. And let $\alpha, \beta \in K$, where $K$ is an extension of $F$.  then $\alpha + \beta $ and $\alpha\beta$ lie in the extension $K = F(\alpha,\beta)$, which is finite over $F$.  so $[F(\alpha, \beta) : F] = [F(\alpha, \beta): F(\alpha + \beta, \alpha\beta)][F(\alpha + \beta, \alpha\beta) : F] \leq 2[F(\alpha + \beta, \alpha \beta) : F] $, since $\alpha + \beta$ and $\alpha \beta$ are roots .   So $[F(\alpha + \beta) : F]$ is finite and in the extension $F(\alpha,\beta)/F$ the elements must be algebraic over $F$, then $\alpha , \beta$ are algebraic.  Can someone please verify this? Or help me give a better approach. Thank you!


I have been desperate to resolve this problem as I am not being able to install certain programs.   my computer says that I have broken packages:   The following packages have unmet dependencies:  python3-requests : Depends: python3-chardet (>= 2.2.1) but 2.0.1-1 is to be installed E: Unable to correct problems, you have held broken packages.   But when I check in synaptic manager i can't find any broken packages. I can't re-install python3-requests for some reason. And for some reason all the other steps to clean up unmet dependencies or broken packages such as sudo apt-get install -f, autoremove, upgrade, etc don't seem to work.   Please someone help!

Occasionally, when I'm installing stuff, I get an error like the following:  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:  package1 : Depends: package2 (>= 1.8) but 1.7.5-1ubuntu1 is to be installed E: Unable to correct problems, you have held broken packages.   How can I resolve this?


Most of you probably heard the phrase "gild the lily", which describes the act of trying to improve something that is already perfect. What I'm looking for is the opposite of that, is there a phrase/idiom that describes the act of trying to repair something that is ruined beyond repair? The phrase "beat a dead horse" comes to mind, but to me, it feels like it describes the act of carrying on trying to fix something when it's too late to do so.

It's on the tip of my tongue.  Example: "Replacing the hard drive of this computer would be [idiom]. It's going to fail completely soon enough."


Is there a sequence of unbounded closed intervals $J_1\supseteq J_2 \supseteq J_3 \supseteq \cdots$ such that $\bigcap _{n=1} ^{\infty} J_n = \emptyset$. By an unbounded closed interval I mean an interval of the form $[a,\infty) = \{x \in \mathbb{R} \mid x \ge a\}$.  My answer to the question is yes taking the sequence $[1,\infty),[2,\infty),[3,  \infty), ...$ because suppose $b \in  \bigcap _{n=1} ^{\infty} J_n$. Then there exists an interval in the sequence such the $b\lt a_i$ whereby $b \notin [a_i, \infty) $ hence $b $ cannot be in $\bigcap _{n=1} ^{\infty} J_n$. Therefore the intersection is empty.  Is my answer correct and if so is my reasoning correct? If not can you please provide the correct justification for the correct answer. Thanks in advance!

I've been trying to make sense of this in my head. I know that the nested interval theorem proves the following if the intervals are bounded, but what if they are unbounded? I apologize for my ignorance to type mathematical symbols on this editor.  Let I be a family of non-empty closed intervals, and suppose that I has the finite intersection property. Is it true that the intersection of all I is necessarily non empty?


How to take public transport from Monaco to Nice, and beyond to Vence please?

What's the simplest and cheapest way to get from central Nice, France to Monaco by public transportation?


It's about time that I figure this out. I can say with a pretty high confidence that I have experienced this issue in all consumer versions of Windows since XP.  I keep "Auto-hide the task bar" checked to maximize screen real estate. Every once in a while, the task bar will refuse to hide while individual windows will continue to act as if that option is checked (by falling under the task bar).  For years, I have fixed this by rebooting. Of course, I cannot predict the timing or frequency of the problem, so the process becomes burdensome.  I want to know how this can be fixed without rebooting. It has affected my on multiple machines using multiple versions of Windows, so I cannot be the only one who is bothered by it.  Can anyone help me solve this?

I have my Win 7 taskbar set to autohide but its often pops up... and just stays visible, obscuring the bottom of all other programs (since they are behaving correctly (as if the Task Bar isn't there b/c it's supposed to autohide).  Any way to force it to HIDE again?


I'm having an issue with the image that is displaying on the lockscreen, I'm currently running Version 21H1, Build 19043.899, Windows Feature Experience Pack 120.2212.3030.0. I go into the settings area and choose the image that I desire to see on the lockscreen, for some reason on the computer I'm typing this post on the 'selected' image fails to display & instead a different image that I really don't like displays. I have a different computer that's running the exact same version of windows 10 it all of my images get displayed properly. I'm to the point that I really don't know what to do next, in file explorer I have the settings set to show all of the 'hidden' settings that normally can't be seen. I know that there MUST be a way to correct my issue, but so far I haven't been able find it yet. David

Where, or what format, are the images used by Windows 10 when logged out or in lock-screen?  I searched the entire drive for *.jpg, *.bmp, *.png, and *.tif but the one I was looking for did not appear.  At first glance, , although not exactly a duplicate, appeared to have the path I wanted.  But when I went there, the pre-login image was there, but the lock-screen image was not.  (And contrary to the claim in that answer, the files there did have extensions.)  UPDATE: I just did a lockscreen, and got an image that IS in that directory, but earlier today, it was consistently an image of an interesting footbridge that is not in that directory.


We have a wire of length 28 meters and we have to form a circle and a square. What will be the maximum area and how?  Can we draw the circle?

A wire of length 12" can be bent into a circle, a square or cut into 2 pieces and make both a circle and a square. How much wire should be used for the circle if the total area enclosed by the figure(s) is to be: a) a Maximum b) a Minimum  What I've got so far is that the formula for the square is $A_s=\frac{1}{16}s^2$ and the circumfrance of the circle to be $P=12-c$ and area to be $A_c = \pi(\frac{P}{2\pi})^2$ where $c$ is the length of the wire for the circle and $s$ is the length of the wire for the square. Now I know I need to differentiate these formulas to then find the max and min they both can be, but what am I differentiating with respect to? The missing variable in each of the formulas? Also, once, I find the derivitives, what would my next steps be to minimizing and maximizing these? And did I set the problem up correctly? Thanks for any help


I have downloaded some roads in a section of Los Angeles from OpenStreetMap. I used overpassturbo.eu to generate the data, using the expression highway=primary. However, because these streets are broken into many segments (bridges, changes in speed limits, etc.), the street names repeat too much. Is there a way in QGIS, or elsewhere, to edit this data to remove some of these repeating street names? I have been looking for something in QGIS, but so far no luck.

I followed instructions in  to  to add directional arrows to the one-way streets on a map I'm creating.   I've currently created a marker line with the standard arrow marker but there are a lot of one-way streets (and one-way street segments). So even with just a marker on the centerpoint of each line, I get something like the below image    I'm worried that if I dissolve streets together by name, that the direction of their drawing might get muddled (and the labels point in the wrong direction).   Do tutorials exist for labelling one-way streets in QGIS?


I have a few questions about setting a variable equal to another variable in JavaScript.  Let's say we create an object, a and set b = a.  var a = {   fname: "Jon",   lname: "Smith",   age: 50 }  var b = a;   I understand that if we change one of a's properties b will also be changed because when we set b = a we don't clone a's data, but rather create a reference to a's data. For example if we set a.fname = "Sarah", the new value of b.fname will be "Sarah".  If we try to "clear" a though by setting a = {}, object b will remain unchanged. I don't understand why manipulating an object in this way produces a different result than in the 1st example.    Also I have a question about the following scenario.   var x = 10; var z = x;   If we then set x = 20, the value of z remains unchanged. Based on the behavior described in my 1st question, one would think that the new value of z would reflect the new value of x. Could someone please explain what I am missing here?  Thank You!

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 was wondering if there was, say, a "Spanish Stack Overflow." This would be the same as the Stack Overflow site, but people would ask and answer in Spanish. This way, the asker doesn't need a translator or knowledge of a foreign language to ask a question of the Stack Exchange community. Does something like this exist already, or could it be proposed in Area 51?  Note: This is NOT like Spanish Language Stack Exchange; questions there are about Spanish, but in English rather than about other topics, in Spanish.

Otherwise known as  必须用英语吗？(is English required?) ¿Necesito hablar en inglés? ?האם אני חייב לכתוב באנגלית Muss ich auf Englisch schreiben?  Do I have to use English when posting a question, an answer or a comment on a Stack Exchange site?


Let $G$ be a group and $a,b\in  G$ such that    $a^{-1}b^2a=b^3$ and $b^{-1}a^2b=a^3$. Then prove that $a=b=e$, where $e$ is the identity of group.   If we are able to prove $ab = ba$ then we are done. But i am unable to show that. Can we use somewhere that $\gcd(2,3)=1$, or if we write $b^2a=ab^3$ and $a^2b=ba^3$ then finding some relation between $a$ and $b$ to prove that.

Suppose $a$ and $b$ are elements of a group $G$. If $a^{-1}b^{2}a=b^{3}$ and $b^{-1}a^{2}b=a^{3}$, prove $a=e=b$.   I've been trying to prove but still inconclusive. Please prove to me.  Thanks very much for proof.


I'm working on a school project and I am a total beginner on this arduino stuff. So, I bought this led strip at  and used  to connect it and controll it with my Arduino. The thing is that I want to power up the led strip using another power source, so I bought 8x 1,5V AA batteries to power it up.     The idea is to upload the code to the Arduino and unplug the computer and use the Arduino to control my led strip. I was thinking of just using the power adapter which comes with the led strip from IKEA, it's an 12V DC power. It says on the arduino that 7-15V is okay for input voltage.   So is this okay? will I fry my arduino board? Note that I followed all the instructions on this tutorial above and it works perfectly, I just want to use it without my computer.

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


Definition 1: Given a Map $f: X \to Y$ between two topological spaces define the mapping cone $C_f$ as $(X \times I) \sqcup Y / \tilde{} $ with $(x,0) \tilde{} (x\prime{}, 0)$ and $(x, 1) \tilde{} f(x)$  Definition 2:  Given two Complexes $A: \dots  \to A^{n+1} \to A^n \to A^{n - 1} \to \dots $ and $B: \dots \to B^{n+1} \to B^n \to B^{n-1} \to \dots$ and a map $F: A \to B$ Note the degree shift by $n$ as $A[n]$ and the differentials of each complex by $d_A$ (or $d_B$)  Define the mapping cone of a complex as $C_f = A[1] \oplus B $ with differential $ \begin{pmatrix}  d_{A[1]} & 0 \\ f[1] & d_B\end{pmatrix} $.  I understand both definitions and have some geometric intuition for them. But I dont understand the connection between them. How is the second definition motivated by the first one?  bg, Johannes

I was reading some topics in Homological Algebra when I came across the concepts of cone of a map of complexes and cylinder.  My knowledge of Algebraic Topology is pretty basic so I only used these concepts in a pure algebraic setting. What is the motivation for this?   The shapes of a cone for example appears only in the simplicial context of Algebraic Topology or is it possible to "see" the cone in algebraic terms ?


I am unable to solve following proof by induction.   $$\sum_{k = n}^{m} \binom{k}{n} = \binom{m + 1}{n + 1}$$  Can you please help me ?  a) show that it is true for $n=m$  b) show that it is true for $(m+1,n)$  c) give proof why it works for all other values of $m,n$   Thanks.

Prove that $\binom{n+0}0 + \binom{n+1}1 +\binom{n+2}2  +\ldots+\binom{n+r}r  = \binom{n+r+1}r$ using combinatoric arguments.   (EDITED)  I want to see if I understood Brian M. Scott's approach so I will try again using an analogical approach.  $\binom{n+0}0 + \binom{n+1}1 +\binom{n+2}2  +\ldots+\binom{n+r}r  = \binom{n+r+1}r$ can be rewritten as $\binom{n+0}n + \binom{n+1}n +\binom{n+2}n  +\ldots+\binom{n+r}n  = \binom{n+r+1}{n+1}$  We can use the analogy of people lining up to buy tickets to see a concert. Let's say there are only $n$ number of tickets available for sale. "Choosing" who gets to attend the concert can be done in two ways.  The first way (the RHS), we have $n+1$ number of tickets for sale but $n+r+1$ people who wants to buy the tickets. Thus, there are $\binom{n+r+1}{n+1}$ ways to "choose" who gets to attend the concert.   The second way (the LHS) is to select the last person in line to buy the first ticket (I think this was the step I missed in my first attempt). Then, we choose $n$ from the remaining $n+r$ people to buy tickets. Or we can ban the last person in line from buying a ticket and choose the second-to-last person in line to buy the first ticket. Then, we have $\binom{n+r-1}n$ ways. This continues until we reach the case where we choose the $n+1$ person in line to buy the first ticket (banning everyone behind him/her from buying a ticket). This can be done in $\binom{n+0}n$ ways.   Therefore, adding up each case on the LHS is equal to the RHS.


How can I take a shapefile that has road segments and read it into a data structure in Python that I can use to get begin and end points with?   For example x, y to x2, y2.  It's not a large shapefile, just a one with roads for my county. I've previously worked with argisscripting at ArcGIS 9.3 but that was a couple years ago and now I'm rusty and using ArcGIS 10.1.   Any and all help is appreciated.  import arcpy  infc = "C:\\Users\\Jeff\\Downloads\\tl_2013_30063_edges\\tl_2013_30063_edges.shp"  for row in arcpy.da.SearchCursor(infc, ["OID@", "SHAPE@"]):     # Print the current line ID      print("Feature {0}:".format(row[0]))      #Set start point     startpt = row[1].firstPoint      #Set Start coordinates     startx = startpt.X     starty = startpt.Y      #Set end point     endpt = row[1].lastPoint      #Set End coordinates     endx = endpt.X     endy = endpt.Y   This is what one of the features looks like.  FID 16992  Shape   Polyline  STATEFP 30  COUNTYFP    063  TLID    205238472  TFIDL   217915003  TFIDR   217914215  MTFCC   S1400  FULLNAME    S 9th St W

How do I retrieve start and end point coordinates with ArcPy for a polyline feature class?   I expect to pass a segment identifier to a subroutine and have it pass back start and end coordinates. The Field Calculator method doesn't work for me, because I need the value for other calculations that can't be performed within it. (I also prefer not to change the data to store these coordinates as attributes.) I am attempting to calculate address ranging for a "center out" addressing scheme. The address value depends on the distance to the "county center".


Can you provide some real-world examples when problem can be more easily addressed using multiple inheritance rather than using composition or other alternatives?  When should one use multiple inheritance?  Why do some languages support multiple inheritance (C++, Python) and others don't (Java, Ruby)? I mean - based on what factors do creators of programming languages decide to include support for MI or not.

Can anyone think of any situation to use multiple inheritance? Every case I can think of can be solved by the method operator   AnotherClass() { return this->something.anotherClass; }


I have a question.  I'm developing a Data Warehouse, I retrieve the data from my reconciled level, this in order to keep updated my Data Warehouse, but i am not sure how to handle some numeric fields that have a null value.  I was thinking to replace it with some special numeric value like -1 for example, that never appear in my column list. But during the analysis process this value replaced by -1 they must not be considered.  Now my question is, is better leave the null numeric field to null, or replace it with some numeric value?

I remember reading this one article about database design and I also remember it said you should have field properties of NOT NULL.  I don't remember why this was the case though.  All I can seem to think of is that, as an application developer, you wouldn't have to test for NULL and a possible nonexistent data value (for instance, an empty string for strings).  But what do you do in the case of dates, datetime, and time (SQL Server 2008)?  You'd have to use some historic or bottomed-out date.  Any ideas on this?


Let $(X, M ,\mu)$ be an arbitrary measure space. Dominated convergence theorem requires some sequence of integrable functions  to converges to some function f almost everywhere.   However, if $f^n$ converges to some function $f$ 'in measure', then does the DCT still holds? I heard that the answer is yes, but can't figure out how to prove it. Could anyone show me how to prove it?

Wikipedia claims, if $\sigma$-finite the Dominated convergence theorem is still true when pointwise convergence is replaced by convergence in measure, does anyone know where to find a proof of this? Many thanks!  Statement of the theorem:  Let $\mu$ be $\sigma$-finite, $|f_n|\leq g$ and $f_n\rightarrow f$ in measure, then we must have  $\int f_n \rightarrow \int f$ and $\int|f_n-f| \rightarrow 0$


Let  $$f(x) := \| y - B x \|_2^2$$  where $y \in \mathbb R^k$, $x \in \mathbb R^n$, and $B \in \mathbb R^{k \times n}$. How to calculate the gradient of $f$ w.r.t. $x$?

In the proof of matrix solution of Least Square Method, I see some matrix calculus, which I have no clue. Can anyone explain to me or recommend me a good link to study this sort of matrix calculus?  In Least-Square method, we want to find such a vector $x$ such that $||Ax-b||$ is minimized.   Assume $r=Ax-b$  $\Rightarrow\|r\|^2=x^TA^TAx-2b^TAx+b^Tb$  $\Rightarrow \nabla_x \|r\|^2=2A^TAx-2A^Tb$  In the end we set the gradient to zero and find the minimized solution. I understand the whole idea, but I just don't know how exactly we did matrix calculus here, or say I don't know how to do the matrix calculus here. For example, can anyone tell me how we got those transpose in $\|r\|^2$(By what rule?) and how we got the gradient?(how do we take the gradient exactly in matrix format)?  I'll really appreciate if you can help me out. Thanks!


When I understand it correctly, a  curve composes of a lot of ratios of TPR and FPR. Each such ratio is gained, e.g., by scanning/investigating a parameter where the ratio is the result of the used classifier. In other words: I'm interested in how a classifier separates data points according to a frequency interval of 0-100 Hz. Hence I scan this frequency, record all the 101 ratios, put them into the plot and the ROC curve represents these datapoints, finally.  Wouldn't it be much more interesting when the frequency would be used as a third axis? Or is it implicit in the axis? But anyway, I think it would be easier to look at with a third axis?

Something that really confuses me with how ROC plots are generated is that, according to Wikipedia:  The ROC curve is created by plotting the true positive rate (TPR) against the false positive rate (FPR) at various threshold settings.  So the algorithm seems to be: Set a decision threshold for binary classification, e.g., a number between $[0, 1]$ that tells which data is labeled as $1$ or $0$. Run the trained classifier on your dataset. Calculate TP and FP, which is just based on the result of your classification. Then plot a point with coordinate (TP, FP) on a 2D plot. Repeat this process for....(?) many many times, until you get many points. Then linearly interpolate between these points to generate a 2D curve. Do I get this process correct?  So my question is: why isn't this naturally a 3D plot? The threshold parameter seems to be pretty important.  First of all, I cannot tell at any given plot on the ROC curve what the threshold was used. Are the points even plotted according some sorted order of these thresholds? I cannot tell.  Also, shouldn't the threshold be critical at creating your final classifier? The ROC curve should have a point that corresponds to the best threshold. But I don't know what that threshold is on this plot.  Finally, this is not related to the ROC plot per-se but just the entire concept. It seems pretty dumb to me to either use a very large or very small threshold. A decision threshold of $0$ or $1$ would not make any sense in creating a classifier, no?   It just doesn't seem to make sense to neglect this information.


Suppose we consider the following set  $$ X = \big\{ (p,q) : p \in \mathbb{Z} \ \text{and} \ q \in \mathbb{N} \big\}$$  Define the following relation $$(p_1,q_1) \sim (p_2,q_2) \iff p_1q_2 = p_2q_1$$  We can easily verify that this relation is both symmetric and reflexive. I am having trouble many with transitive. The issue that I am having is we can't really "divide". So what we assume is the following:  Suppose that $(p_1,q_1) \sim (p_2,q_2)$ and $(p_2,q_2) \sim (p_3,q_3)$. This means that the following equations are satisfied:  $$p_1q_2 = p_2q_1$$ $$p_2q_3 = p_3q_2$$   We would like to show that the following equation is satisfied: $$p_1q_3 = p_3q_1$$   I am kinda lost in how to do that?

Suppose you have:      $x=(p,q)$ and $y=(p',q')$ with $p, q \in \mathbb{Z}$ and $q \not = 0$ then $x \sim y$ if $pq'=p'q$ is an equivalence relation?   So I managed to show that its reflexivity and symmetry, but I am unable to prove that it's transitive.


Imagine a universe infinite in all directions with only one elementary particle moving through it (impossible, but suppose). Can one define time in this universe?

I am sorry if this question is silly; it′s just one of those things I wished I asked before leaving university.  If there were a static universe only as big as the size of two particles, say electrons, and there were one electron in it going back and forth from point A to point B: would time also go back and forth in the future (point B) and in the past (point A), or would it be considered to  go forward as it does for us? would it be possible to know how long that electron stayed at point A or point B, would it even make sense to ask? I guess what I am asking is: does time move forward only because there are so many particles moving in this enormous space that it is almost impossible they would all be back in the same position they held at least once before relative to each other? does time exist only as a consequence of a lot of particles and their position relative to each other, and the space for them, just like heat?


I would like to use star and crescent (U+262A) emoji in my document, even though I have read several articles in this environment, I couldnt realize how to do it. Please can anyone give me a hand? Thanks in advance

How do I enter Unicode characters in LaTeX?  What packages do I need to install and what escape sequence do I type to specify Unicode characters in an ASCII source file?


My application is based on MySQL database and it requires "MySql.Data.dll" file to run or else it will crash. Installing MySQL Connector on my computer will allow me to run it without previously mentioned file, only my application (standalone).   Is there a way to "inject" it(mysql.data.dll) to the application so there is no need to have additional files to run?  I'm using Microsoft's Visual Studio IDE.

Is it possible to embed a pre-existing DLL into a compiled C# executable (so that you only have one file to distribute)? If it is possible, how would one go about doing it?  Normally, I'm cool with just leaving the DLLs outside and having the setup program handle everything, but there have been a couple of people at work who have asked me this and I honestly don't know.


I am a complete beginner and I am trying to dual boot Ubuntu 20.04 with Windows 10. I have already made a bootable USB. When I try to boot from USB and before coming to the Ubuntu installer GUI it boots to a black screen with multiple errors.  I am using an old HP Pavilion G6 laptop with an Intel i3 processor, 4GB RAM and an SSD.

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


How to generate word document in Rails 2.3.5?  Is their any gem available?

Is there an easy way to create Word documents (.docx) in a Ruby application? Actually, in my case it's a Rails application served from a Linux server.   A gem similar to  but for  instead of PDF would be great!


I burnt Ubuntu 12.04 to a CD since that was the max it could hold. I've used the disc four times before, therefore it's not invalid.

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


Is it true the following  $ R \subset R^2$ ?  (If yes, I would like to see a rigorous proof.)

I think I've been confusing myself about the language of subspaces and so on.  This is a rather basic question, so please bare with me.  I'm wondering why we do not (or perhaps "we" do, and I just don't know about it) say that $\mathbb{ R } $ is a subspace of $\mathbb{ R }^2 $.  It's elementary to prove that the set $$ S:= \left\{ c \cdot \mathbf{x} \mid c \in \mathbb{ R }, \mathbf{x} \in \mathbb{ R }^2  \right\}$$ is a vector subspace of $\mathbb{ R } ^2$.  What is confusing me is that there seems to be an isomorphism between the set $S$ and $\mathbb{ R } $: \begin{align*} \varphi: S &\rightarrow \mathbb{ R }   \\  c \cdot \mathbf{x} &\mapsto c \\ \end{align*} If this is indeed true, as I believe it is having checked that $\varphi$ gives an isomorphism, wouldn't we say that $\mathbb{ R } $ is a subspace of $\mathbb{ R } ^2$? Any help sorting out this (language) problem will be greatly appreciated!


Is there anyone who knows how to compare two version strings in Java?  For example,  Compare : 1.0.3.1 & 1.0.4.1 Result : 1.0.4.1  Thanks in advance.

Is there a standard idiom for comparing version numbers?  I can't just use a straight String compareTo because I don't know yet what the maximum number of point releases there will be.  I need to compare the versions and have the following hold true:  1.0 < 1.1 1.0.1 < 1.1 1.9 < 1.10


How do I reset a for-loop while looping through a list? For example, I want the for-loop to reset i.e. (i=0 and j=1) when there are duplicates in a list .  In this piece of code, I want the duplicates removed and the for-loop reset when subsequent entries in the list are equal. For instance, we have   list1 = [east, west, west, east]   I want the resultant list1 to be equal to an empty list.   This is because, When both "west" entries are eliminated, this results in the list updating to [east,east]. Since this is also a duplicate, the result must hence be an empty list [].   j=1; for (int i=0;i<(list1.size()-1);i++){     if((list1.get(i)==list1.get(j))){         list1.remove(i);         list1.remove(i);         i=0;         j=1;     }else{         j++;     } }

We all know you can't do the following because of ConcurrentModificationException:  for (Object i : l) {     if (condition(i)) {         l.remove(i);     } }   But this apparently works sometimes, but not always. Here's some specific code:  public static void main(String[] args) {     Collection<Integer> l = new ArrayList<>();      for (int i = 0; i < 10; ++i) {         l.add(4);         l.add(5);         l.add(6);     }      for (int i : l) {         if (i == 5) {             l.remove(i);         }     }      System.out.println(l); }   This, of course, results in:  Exception in thread "main" java.util.ConcurrentModificationException   Even though multiple threads aren't doing it. Anyway.  What's the best solution to this problem? How can I remove an item from the collection in a loop without throwing this exception?  I'm also using an arbitrary Collection here, not necessarily an ArrayList, so you can't rely on get.


In Python, I am adding float numbers.   I have numbers  client_balance = 40360.7416622703 fund_manager_balance = 676.600516394647  uits= 6.72791159564433   here is my python code   def update_client_balance(self, record):     if record.client_id.account_name != ACCOUNT_MANAGER_NAME:         self.client_balance += record.units  def update_manager_balance(self, record):     if record.client_id.account_name == ACCOUNT_MANAGER_NAME:         self.fund_manager_balance += record.units   After execution of these functions I have   client_balance = 40360.7416622703 fund_manager_balance = 683.328427990291  Now I want to validate the result of these functions manually   so (client_balance + fund_manager_balance)(before function execution) -uits - (client_balance + fund_manager_balance)(after function execution)  By Value  40360.7416622703 + 676.600516394647 + 6.72791159564433 - (40360.7416622703 + 683.328427990291) = -0.00000000000727595761418343   It should give me Zero value but it's giving me -0.00000000000727595761418343  Please help me how I can solve this?

Consider the following code:   0.1 + 0.2 == 0.3  ->  false   0.1 + 0.2         ->  0.30000000000000004   Why do these inaccuracies happen?


What is the OS X modifier key symbol that looks like the control icon (^) but with the addition of a line over it?  Symbol:

On a Mac, symbols are often used for keys rather than names. In Adobe Indesign for Mac, the keyboard shortcuts for inserting various break characters are described using what looks like an up arrow / caret / chevron pointing into a flat horizontal line:     It's the symbol on the right I'm asking about.  After much searching, I found it on the far bottom right of the full-size Apple keyboard. It's the... enter-like key (?) in the bottom right of the numeric keypad.    So two related questions:   What's it called? Is it possible to trigger this key (for use in keyboard shortcuts) when using a keyboard without a numeric keypad (like a wireless keyboard or laptop keyboard)? If so, how?


Is any built-in tool in Lubuntu (or other Linux from Ubuntu family) allows restore operating system to brand-new snapshot with all default settings?

Ubuntu n00b here.  I have created several disasters of the first order already.  I am getting ready to try to install opera - it is a very long and arduous process.  I am afraid - no - I am absolutely certain that I will damage something important.  How do I create a system restore point?  Does such a thing exist?


Which of the above forms is "better" for running bash, python etc. scripts? Why can't I just do #!$(which foo)? Is it neccecery to specify full path to env? I gather from  answer, that the path /usr/bin/env is set in stone for all *nix-es, much more than /usr/bin/python3 for example. Is that so?

I notice that some scripts which I have acquired from others have the shebang #!/path/to/NAME while others (using the same tool, NAME) have the shebang #!/usr/bin/env NAME.  Both seem to work properly.  In tutorials (on Python, for example), there seems to be a suggestion that the latter shebang is better.  But, I don't quite understand why this is so.  I realize that, in order to use the latter shebang, NAME must be in the PATH whereas the first shebang does not have this restriction.  Also, it appears (to me) that the first would be the better shebang, since it specifies precisely where NAME is located.  So, in this case, if there are multiple versions of NAME (e.g., /usr/bin/NAME, /usr/local/bin/NAME), the first case specifies which to use.  My question is why is the first shebang preferred to the second one?


While we're waiting for the Android app to be repaired ...  The browser UI lets us set both most and least favorite tags, and set a filter to hide questions carrying the latter. In some stacks I found that quite useful as a way of focusing on the questions I could actually contribute to or learn from.  As far as I can tell, the app doesn't have that filtering capability, despite needing it more due to smaller screens.  I presume it's on the list for eventual implementation. But sooner would be nice.

On , this is my tag blacklist:        Note well that I have them set to hidden, because I would prefer not to see questions on this topic. Bridge players, don't take offence — I don't have problem with the game itself. I don't understand the game's mechanics, though, so I find questions about it incomprehensible, and I'd rather stick to just seeing questions I can understand.  I still see [bridge] questions galore on the Android app though. Could it be updated to pay attention to whether I have certain tags ignored and set to be hidden?


I got a new keyboard with function keys, but I have to hold the FN key to use the F1|F12 keys normally and not to change the volume, brightness, etc. How do I change this?

I do have a wireless Logitech K750 keyboard (silver Mac version) connected to a Lenovo ThinkPad (via the unifying USB receiver, together with a wireless Logitech mouse M705) and currently running Ubuntu 12.04.  By default the F-keys are mapped as multimedia/function keys, e.g. Play  /Pause. As I don't use them very often, I want the F-keys to behave like the "real" F-keys (F1-F12). How can I do that?  I know there is an option in the BIOS settings, but this only toggles the built-in keyboard of the notebook, not on my wireless keyboard.  I know there is a way to change this for the Apple wireless keyboard (), but there is no "parameters" directory in /sys/module/hid_logitech_dj/.  Any ideas? Or is there maybe a way to do this in a later Ubuntu version (13.04)?  UPDATE:  lsusb -d 046d: shows Bus 002 Device 005: ID 046d:c52b Logitech, Inc. Unifying Receiver  UPDATE 2: Thanks a lot for your help Lekensteyn. Finally  works just fine. In the "Known Issues" of Solaar it says that it does not work with the Nano Receiver. But I have one and it works just fine. Just don't forget to read the installation instructions and run the rules.d/install.sh script. It also recognized my M705 Mouse.


Recently I installed Ubuntu 17.04 in my Dell laptop, but WiFi does not work in Ubuntu (It works well in windows 7). I have already tried the following steps, but no luck.   sudo -H gedit /etc/NetworkManager/NetworkManager.conf   At the bottom of this file, copied and pasted the following:  [device] wifi.scan-rand-mac-address=no   then  sudo service network-manager restart   Output of lspci -nn -d 14e4  06:00.0 Network controller [0280]: Broadcom Limited BCM43142 802.11b/g/n [14e4:4365] (rev 01)   Output of iwconfig  lo        no wireless extensions. enp7s0    no wireless extensions.   How to solve this issue?

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 was trying to change my change directory in my unc path,while trying to access the network folder myself getting error :  CMD does not support UNC paths as current directories.   is it there any method to access unc directories through command prompt?

C:\> cd \\somewhere '\\somewhere' CMD does not support UNC paths as current directories.   What I usually do to get around this is to map that directory to a network drive and then I could easily access it from the command prompt.  But is there an easier way on how to get around this?


What do you call a person who craves danger? Like how a person who believes that the pursuit of pleasure is the most important thing in life is known as a hedonist.

I don't know of any nouns that describes a person who thrives under pressure. In basketball and sports in general, I know people who do well under pressure are called clutch. However, clutch would be an adjective. Are there any nouns that fit this description? If there are no nouns, what other adjectives have this meaning.


I am confused between precedence of operators and want to know how this statement would be evaluated.  # include <stdio.h>  int main() {   int k=35;     printf("%d %d %d",k==35,k=50,k>40);     return 0;   }   Here k is initially have value 35, when I am testing k in printf I think :   k>40 should be checked  which should  result in 0 k==35 should be checked and which should result in 1 Lastly  50  should get assigned to k and which should output 50   So final output should be 1 50 0, but output is 0 50 1.

Can it be assumed a evaluation order of the function parameters when calling it in C ? According to the following program, it seems that there is not a particular order when I executed it.   #include <stdio.h>  int main() {    int a[] = {1, 2, 3};    int * pa;      pa = &a[0];    printf("a[0] = %d\ta[1] = %d\ta[2] = %d\n",*(pa), *(pa++),*(++pa));    /* Result: a[0] = 3  a[1] = 2    a[2] = 2 */     pa = &a[0];    printf("a[0] = %d\ta[1] = %d\ta[2] = %d\n",*(pa++),*(pa),*(++pa));    /* Result: a[0] = 2  a[1] = 2     a[2] = 2 */     pa = &a[0];    printf("a[0] = %d\ta[1] = %d\ta[2] = %d\n",*(pa++),*(++pa), *(pa));    /* a[0] = 2  a[1] = 2 a[2] = 1 */  }


I need to prove that there is no rational number $\frac{p}{q}$ with:$\ |\sqrt{2}-\frac{p}{q}| \leq \frac{1}{5q^2}.$ I really don't know how to start because we didn't really learn how to solve equations with absolute in the lectures until now. We got a hint that we should somehow come to this: $\ |\sqrt{2}-\frac{p}{q}| \geq \frac{24}{50pq}$ and there would be a contradiction. As the title says, I only want to get some tips for solving it and not the solution. I want to know if it's just basic equation transforming or if there are other things to consider.

Prove that for for all $p,q\in \mathbb{Z}$, $q>0$ we have: $$ \left| \sqrt{2}-\frac{p}{q} \right| > \frac{1}{3q^2}. $$  To be honest, I do not know where to start - any help would be appreciated.


The  Sorcerer has the following feature:  Elemental Affinity Starting at 6th level, when you Cast a Spell that deals damage of the type associated with your Draconic ancestry, you can add your Charisma modifier to one damage roll of that spell. At the same time, you can spend 1 sorcery point to gain Resistance to that damage type for 1 hour.  This reads that it would only apply to one damage roll of a spell, meaning that spells such as  and  would only benefit from the first damage roll of that spell. Is this the correct assumption? If so, would it be too strong to rule that it applies on every separate instance of damage?

If a 6th level Sorcerer with Elemental Affinity (lightning) casts Witch Bolt, is only the inital bolt's damage is increased, or the damage of every one of them?  Elemental Affinity:     [...] when you cast a spell that deals damage of the type associated with your draconic ancestry, add your Charisma modifier to that damage.   Witch Bolt:     [...]  on each of your turns for the duration, you can use your action to deal 1d12 lightning damage to the target automatically.