I watched with interest the  which was fun.  They had a secondary list of vids of one was entitled .  Now I thought that black holes don't necessarily have to be dense, if they are very large.  The Swartzchild radius is  $$ r_\text{s} = \frac{2 M G}{c^2} $$  so if the mass-to-radius ratio exceeds  $$ \frac{M}{r} > \frac{c^2}{2 G} $$  you gotta black hole.  But it's only a single power of $r$ in the denominator.  This means, assuming a sphere, if the density exceeds  $$ \frac{M}{\tfrac{4}{3}\pi r^3} > \frac{3 c^2}{8 \pi G r^2} $$  you gotta black hole.  With $r^2$ in the denominator, it appears you wouldn't need a lotta density if the radius is large enough.  With  $ \frac{c^2}{2 G} = 6.7332 × 10^{26} \frac{\text{kg}}{\text{m}} $  and $ \frac{M}{r} = 4.5455 × 10^{27} \frac{\text{kg}}{\text{m}} $  (Numbers come from Wikipedia. This is including non-baryonic matter and energy, all which should have gravitational effect.)  It looks pretty close, but with these numbers the entire mass and energy of the observable Universe is contained in a radius smaller than the Swartzchild radius.  45.455 is bigger than 6.7332.  Couldn't an entire observeable universe be a black hole?  Wouldn't this be a different "type", a fifth type of black hole than the four described in the NOVA vid?

I was surprised to only recently notice that      An object of any density can be large enough to fall within its own   Schwarzschild radius.   Of course! It turns out that supermassive black holes at galactic centers can have an average density of less than water's.  Somehow I always operated under the assumption that black holes of any size had to be superdense objects by everyday standards.  Compare the Earth to collapsing into a mere 9mm marble retaining the same mass, in order for the escape velocity at the surface to finally reach that of light.  Or Mt. Everest packed into one nanometer.  Reading on about this , it increases proportionally with total mass.  Assuming matter is accumulated at a steady density into a spherical volume, the volume's radius will only "grow" at a cube root of the total volume and be quickly outpaced by its own gravitational radius.  Question: For an object the , what would have to be its diameter for it to qualify as a black hole (from an external point of view)?  Would this not imply by definition that:   The Earth, Solar system and Milky Way are conceivably inside this black hole? Black holes can be nested/be contained within larger ones? Whether something is a black hole or not is actually a matter of perspective/where the observer is, inside or outside?


I am tring to make bibliographig list in Bibtex with subtitles. For this I have the following minimal example:  \begin{filecontents}{minimal.bib}     @online{electronic1,         author = {A. Author},         title = {Funny website},         urldate = {2013-01-09},         url = {http://www.example.org},     },     @book{book1,     author = {B. Bthor},     title = {A Book of whatever},     date = {2012},     },     @article{article1,         author = {C. Cthor and D. Dthor},         title = {Writing interesting articles},         journaltitle = {The Journal of References},         date = {2010-12-01},     } \end{filecontents} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Optionen zum Layout des Buchs                                     %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     \documentclass[a4paper, 11pt     liststotoc,                 % Abb.- und Tab.verzeichnis im Inhalt     bibtotocnumbered     listtotoc     idxtotoc     bibtotoc ] {scrbook}      \usepackage[         natbib = true,         style  = alphabetic     ]{biblatex}   \addbibresource{Literatur.bib}  \setuptoc{toc}{numbered}  \usepackage[ngerman]{babel} \usepackage[ansinew]{inputenc}  \usepackage{graphicx} %%Zum Laden von Grafiken  \begin{document}  \title{Minimalbeispiel zur Literaturverwendungsstyl ausprobung} \author{Autor Anonymus}  \maketitle  \tableofcontents            % Inhaltsverzeichnis  \mainmatter                 % Vorspann (z.B. römische Seitenzahlen) \chapter{Einleitung}  Bei der Book-Klasse des KOMA-Script wird durch den Gliederungsbefehl \verb#\frontmatter# automatisch auf römische Seitennummerierung gewechselt und die Nummerierung der Kapitel unterdrückt. In der Regel sollte der Vorspann nur aus einem Kapitel -- dem Vorwort -- bestehen. \cite{Kuester 2010}  Der Vorspann endet für scrbook, wenn durch \verb#\mainmatter# der Hauptteil beginnt.   \appendix                       % Beginn des Anhangs \pagenumbering{Roman}  \newpage \addcontentsline{toc}{chapter}{Tabellenverzeichnis} \listoftables               % Tabellenverzeichnis  \newpage \addcontentsline{toc}{chapter}{Abbildungsverzeichnis} \listoffigures              % Abbildungsverzeichnis  \newpage \addcontentsline{toc}{chapter}{Literaturverzeichnis} \nocite{*} \printbibheading                    % print heading for all bibliographies \printbibliography[         nottype = online,               % Put here verything that is NOT of the type "online".                                                                         % The "electronic" type is just an alias to "online"          title={Quellen},     % title of the subbibliography         heading=subbibliography         % make bibliography go one sectioning level lower ] \printbibliography[         type=online,                    % Put only references of the type "online" here.         title={Online-Quellen},         heading=subbibliography ] \end{document}   I tried to compile 3 times, but it doesn't work. My problem is that the entries doesent seem to be printed out to the pdf.  If you can help me, I would be happy.

Running the minimal example  \documentclass{article} \usepackage{filecontents} \begin{filecontents*}{\jobname.bib} @ARTICLE{example,   author  = {Other, Anthony Norman},   title   = {Some things I did},   year    = {2014},   journal = {J.~Irrep. Res.},   volume  = {1},   number  = {1},   pages   = {1-10} } \end{filecontents*} \usepackage[backend=biber]{biblatex} \addbibresource{\jobname.bib} \begin{document} Hello\cite{example}. \printbibliography \end{document}   I get the warning There were undefined references.  I have read  and know that I need to run:   LaTeX Biber LaTeX   However, my editor is only set up to run BibTeX. How do I go about setting up my editor/IDE to be able to run Biber, and how do I run the LaTeX/Biber/LaTeX cycle?  Answers (sorted alphabetically by editor name)                    Answer guidelines   Each answer should be for one editor. If the editor is cross-platform, if possible give a single answer with notes covering the minor platform variations. Please edit the question to include new answers in the 'link list' Each answer should be 'stand alone', i.e. don't say 'It's almost the same as editor Y but ...' for the editor part Instructions for 'build tools' such as arara or latexmk are welcome but should explain how to set up the editor in question as not all editors allow simple addition of arbitrary tools


I was wondering, whether there are any problems that we already know are difficult to solve for a quantum computer, and that we could potentially use in cryptography, just as we do now with e.g. the factorization of integers?

Quantum computers are known to be able to crack  a broad range of cryptographic algorithms which were previously thought to be solvable only by resources increasing exponentially with the bit size of the key. An example for that is .  But, as far I know, not all problems fall into this category. On , we can read     Researchers have developed a computer algorithm that doesn’t solve problems but instead creates them for the purpose of evaluating quantum computers.   Can we still expect a new cryptographic algorithm which will be hard to crack using even a quantum computer? For clarity: the question refers to specifically to the design of new algorithms.


Let $f(z)$ be an entire function such that $|f(z)|\le C|z|$ where $C$ is a positive constant. Show there exists a $D$ which is a complex constant such that $f(z)=Dz$. I am trying to use a cauchy's estimate to show that $f''(z)=0$ but not sure how to go about this.

Let $f(z)$ be an entire function s.t $|f(z)|\leq M|z|$ ; $M>0$ is a constant then $f(z)$ Is polynomial of degree 1   My try $f(z)$ is entire so it can be written as a $\sum a_n z^n$  $$|\sum a_n z^n|\leq \sum |a_n||z|^n\leq M|z|$$  So $n=1$  Seems that the move $\sum |a_n||z|^n\leq M|z|$ is problematic


I added two photos in Latex. I want these two pictures to be placed next to each other. Note that two pictures are appropriate, not two sub-pictures in one picture. \begin{figure}[t]     \centering     \includegraphics[width=\linewidth]{figure/a.eps}     \caption{This is my first picture } \end{figure}  \begin{figure}[t]     \centering     \includegraphics[width=\linewidth]{figure/b.eps}     \caption{This is my second picture. } \end{figure}

How can I put two figures side-by-side? Not two sub-figures, but two actual figures with separate "Fig.: bla bla" captions.  A figure is supposed to spread over the entire text width, but I have two figures which are narrow and long, and I need to save the space in order to withstand the pages limit.


I wanted to restart my server so I did :  sudo service apache2 restart   It instead showed me the message below :  Job for apache2.service failed. See 'systemctl status apache2.service' and 'journalctl -xn' for details.   I then did systemctl -l status apache2.service and it came out with these results:      apache2.service - LSB: Apache2 web server    Loaded: loaded (/etc/init.d/apache2)   Drop-In: /lib/systemd/system/apache2.service.d            └─forking.conf    Active: failed (Result: exit-code) since Thu 2016-12-15 07:44:48 CST; 43min ago   Process: 31239 ExecStart=/etc/init.d/apache2 start (code=exited, status=1/FAILURE)  Dec 15 07:44:48 s87890 apache2[31239]: Starting web server: apache2 failed! Dec 15 07:44:48 s87890 apache2[31239]: The apache2 configtest failed. ... (warning). Dec 15 07:44:48 s87890 apache2[31239]: Output of config test was: Dec 15 07:44:48 s87890 apache2[31239]: apache2: Syntax error on line 216 of /etc/apache2/apache2.conf: Could not open configuration file /etc/apache2/conf-enabled/softaculous.conf: No such file or directory Dec 15 07:44:48 s87890 apache2[31239]: Action 'configtest' failed. Dec 15 07:44:48 s87890 apache2[31239]: The Apache error log may have more information. Dec 15 07:44:48 s87890 systemd[1]: apache2.service: control process exited, code=exited status=1 Dec 15 07:44:48 s87890 systemd[1]: Failed to start LSB: Apache2 web server. Dec 15 07:44:48 s87890 systemd[1]: Unit apache2.service entered failed state.   I looked at line 216 of /etc/apache2/apache2.conf and this is what I saw:  IncludeOptional conf-enabled/*.conf   I did journalctl -xn and it showed me :      - Logs begin at Tue 2016-12-13 16:17:11 CST, end at Thu 2016-12-15 08:11:24 CST. -- Dec 15 08:11:05 s87890 sshd[32074]: pam_unix(sshd:auth): authentication failure; logname= uid=0 euid=0 tty=ssh ruser= rhost=116.31.116.48  user=root Dec 15 08:11:07 s87890 sshd[32074]: Failed password for root from 116.31.116.48 port 61622 ssh2 Dec 15 08:11:10 s87890 sshd[32074]: Failed password for root from 116.31.116.48 port 61622 ssh2 Dec 15 08:11:12 s87890 sshd[32074]: Failed password for root from 116.31.116.48 port 61622 ssh2 Dec 15 08:11:12 s87890 sshd[32074]: Received disconnect from 116.31.116.48: 11:  [preauth] Dec 15 08:11:12 s87890 sshd[32074]: PAM 2 more authentication failures; logname= uid=0 euid=0 tty=ssh ruser= rhost=116.31.116.48  user=root Dec 15 08:11:22 s87890 postfix/smtpd[32032]: warning: hostname dedic858.hidehost.net does not resolve to address 91.200.13.20: Name or service not kn Dec 15 08:11:22 s87890 postfix/smtpd[32032]: connect from unknown[91.200.13.20] Dec 15 08:11:24 s87890 sudo[32065]: ejandra : TTY=pts/0 ; PWD=/home/ejandra ; USER=root ; COMMAND=/bin/journalctl -xn Dec 15 08:11:24 s87890 sudo[32065]: pam_unix(sudo:session): session opened for user root by ejandra(uid=0)   I already did an apache uninstall and then installed it again but still the same error persists. What could be wrong here?

Trying to restart apache from terminal using following command:   sudo service apache2 restart   when executing that command getting below error:  Job for apache2.service failed. See "systemctl status apache2.service" and "journalctl -xe" for details.   On excuting "systemctl status apache2.service" got below output   apache2.service - (null)    Loaded: loaded (/etc/init.d/apache2)    Active: failed (Result: exit-code) since Sat 2015-05-30 02:22:41 IST; 12s ago      Docs: man:systemd-sysv-generator(8)   Process: 4866 ExecStart=/etc/init.d/apache2 start (code=exited, status=1/FAILURE)   apache error.log  AH00489: Apache/2.4.12 (Unix) configured -- resuming normal operations AH00094: Command line: '/usr/local/apache2/bin/httpd'


I recently moved from Linux to Mac, and am missing a two pane file manager. I was thinking about along the lines of midnight commander, krusader (Linux) or total commander (Windows).  I installed midnight commander and am using it, but a GUI file manager would sometimes be handy.  Any suggestions for Open Source alternatives?

I'm looking for a graphical  fro OS X, for console Midnight Commander is ok.  I need two panels, function keys operations and preferably FTP and SCP support.  Also, it would be great to be free.


the output of sudo apt-get update command are below:  Hit:9 http://ppa.launchpad.net/ubuntu-mozilla-daily/ppa/ubuntu xenial InRelease Get:11 http://archive.ubuntu.com/ubuntu xenial-backports InRelease [102 kB]     Hit:12 http://ppa.launchpad.net/ubuntu-wine/ppa/ubuntu xenial InRelease         Hit:13 http://ppa.launchpad.net/webupd8team/brackets/ubuntu xenial InRelease    Err:14 http://dell.archive.canonical.com/updates xenial-dell InRelease            Could not connect to dell.archive.canonical.com:80 (91.189.89.6), connection timed out Fetched 306 kB in 2min 0s (2,551 B/s)                       Reading package lists... Done W: Failed to fetch http://dell.archive.canonical.com/updates/dists/xenial-dell/InRelease  Could not connect to dell.archive.canonical.com:80 (91.189.89.6), connection timed out W: Some index files failed to download. They have been ignored, or old ones used instead.

I've just purchased a Dell Precision 7520 with Ubuntu 16.04. I needed to reinstall the Ubuntu version with partitions for the root and home and now I want to install the Dell Repositories which this machine had on it originally. They were:  http://dell.archive.canonical.com/updates/ exnial-dell-crane-kbl public http://dell.archive.canonical.com/updates/ exnial-dell-crane-kbl public (source Code) http://dell.archive.canonical.com/updates/ exnial-dell public http://dell.archive.canonical.com/updates/ exnial-dell public (source Code)   How can I do this in the Software & Updates window (Other Software Tab)? I need to install some open software drivers which were in the Additional Drivers Tab (when I bought it).


I'm fond of old especially folk songs, but as a foreigner I often have troubles interpreting some phrases. Here is one from :  I'm going there to see my father I'm going there no more to roam I'm just a-going over Jordan I'm just a-going over home  Does "going over" here mean "going to", i.e. approaching to some goal? I can't find some dictionary article which can prove this - though I've seen some about "go over to smth" with similar sense.  Or can this be some archaic, or dialect-specific (Appalachian?) usage, but not "normal" for contemporary / everyday language?  Thanks in advance for guiding me!

Can someone explain the etymology of using over in expressions like come over to and go over to as in "pay a casual visit"?  Is there a source for the etymology of idiomatic expressions somewhere?


I have this habit of searching Jon Skeet and checking his reputation(inspires me). But when I searched it today, I found two Jon Skeet's as :    Hoping Jon Skeet doesn't have two accounts. :)    (EDIT: a moderator has reset the offending user's name and image, so they no longer show up as pictured above)  So this user is using name of famous Jon Skeet and using his picture too.  What should be done to these accounts? Can they be reported directly or is this OK to use name and picture of anybody?

What is done to prevent people from changing their display name to another persons', for example Jon Skeet, and then also changing their gravatar to match too?  In comments it seems there is no visible differentiator, and the differentiator in questions and answers is just reputation and badges.  This doesn't seem to be a problem for stackoverflow, but I'm just wondering what are possible safeguards against this?  EDIT: Also it doesn't even have to be deliberate, if two people just happen to choose the same display name, and they both participate in the same question/comment thread, that would be confusing right?


Give an example of a finite and infinite Boolean ring without unity.  I find difficulty to answer this question.Please help me.  Thank you in advance.

Let $(B, +, \cdot)$ be a non-trivial ring with the property that every $x \in B$ satisfies $x \cdot x = x$. How does one prove that such a ring $(B, +, \cdot)$ must have a unit element $1_B$? (Or, in case this is not true in general, what is a counterexample?)   BTW, I'm looking for an elementary proof, not requiring anything more than the definition of a ring, the definition of $(B, +, \cdot)$, and, if necessary, the easily shown facts that $x + x = 0$ and $x\cdot y = y\cdot x,\,\forall\, x,y \in B$.


I read somewhere that "if python can't find instance variable it will try to return value of the class variable having the same name"  eg  class Sample:     pi = 10   Now  x1 = Sample() x2 = Sample()  x1.pi         # returns 10 x2.pi         # returns 10  x1.pi = 20    # change the value of class variable x1.pi         # return 20 (OK) x2.pi         # still returns 10 :( Sample.pi     # returns 10 :(   What is happening??

Is it possible to have static class variables or methods in Python? What syntax is required to do this?


I'm trying to understand imaginary quadratic fields and the ideal class group seems to be really important, yet I cannot find a simple explanation of it and why it's important. I understand that it is related to unique factorization, yet I don't know why. If someone could give a simple explanation of it and maybe a simple example of it I'd really appreciate it.

Let $O$ be a Dedekind domain and $K$ its field of fractions. The set of all fractional ideals of $K$ form a group, the ideal group $J_K$ of K. The fractional principal ideals $(a) = aO, a \in K^*$, form a subgroup of the   group of ideals $J_K$, which will be denoted $P_K$. The quotient group   $$CL_K=J_K/P_K$$ is called the ideal class group of $K$.   This definition looks completely arbitary, I fail to see why the class group or the ideal class group is worth studying. So, why is the class group or ideal class group interesting? I've read that ideal class group "measures" how much unique factorization fails in a domain, but I don't understand how it does so.  This from Algebraic Number Theory by Neukirch.     The class group $C_K$ measures the expansion that takes place when we pass from numbers to ideals, whereas the unit group $O^*$ measures the contraction in the same process. This immediately raises the problem of understanding these   groups $O^*$ and $C_K$ more thoroughly.   I don't understand the above paragraph. What does it mean by  "the expansion that takes place when we pass from numbers to ideals"? And why should we even bother about such "expansion"?


So I have this function I created called isDateOverlapping. It takes in (of all type LocalDate):   Start Date 1 End Date 1 Start Date 2 End Date 2   What this function does is it tells me if the 2 date periods are overlapping or not.  For example if I have 1 period from 2019-06-15 to 2019-06-18 and another period from 2019-06-15 to 2019-06-12. It would return true because the 2 date periods overlap.  However my function doesn't seem to always return the right answer. Could you please help.  public boolean isDateOverlapping(LocalDate start1, LocalDate end1, LocalDate start2, LocalDate end2) {      if (start1.isAfter(start2) && start2.isBefore(start1)) {         return true;      } else if (end1.isBefore(end2) && start1.isAfter(start2)) {         return true;     } else if (start1.isAfter(end1) && end2.isBefore(start2)) {         return true;     }      return false;  }

Given two date ranges, what is the simplest or most efficient way to determine whether the two date ranges overlap?  As an example, suppose we have ranges denoted by DateTime variables StartDate1 to EndDate1 and StartDate2 to EndDate2.


Recently, when a user deleted his account on Lifehacks, his questions with negative scores and no accepted answers were deleted, including . However, some users .  I don't think it should have been deleted -- yes, the question had a negative score, no there wasn't an accepted answer....but there was an answer with a positive score. Why should positive score answers be deleted, ever?  In short:     Please protect positive score answers to deleted users' negative score questions from damaging deletion by the Roomba.

As I found out earlier today, users who are deleted . This goes against established conventions, for two reasons:  As moderators, we constantly tell users that we won't unilaterally delete questions that have upvoted answers.  Even our . See also .   This 'delete my user' process allows a user to get around this policy by simply deleting their own account. Since nothing stops them from creating another account, it's quite possible this harms our mission of keeping good content around. Also, it allows users to delete their own questions whose answers have received bounties, which can take away the bounty award; this behavior was recently prevented for normal question self-deletions. I propose that we make changes to the user deletion algorithm:  If a user is deleted and they have questions with upvoted answers, those questions are disassociated from the user's account instead of being summarily deleted. Questions without upvoted answers are treated like they are currently: they are deleted when the user is deleted.  This should be the same for destroyed users as well.


I use xev to debug x11 events for a window. I can filter events using grep, for example: xev -id windowid | grep FocusIn. I want to append time to each output from the above command (date +"%T.%N") . I need to know when each event occured. Is it possible ? How to achieve that ?  Edit1  Following command works:  xev -id windowid | awk '{ print strftime("%Y-%m-%d %H:%M:%S"), $0; fflush(); }'   but with grep there is no output:  xev -id windowid | grep FocusIn | awk '{ print strftime("%Y-%m-%d %H:%M:%S"), $0; fflush(); }'   When I use grep and ts there is also no output:  xev -id windowid | grep FocusIn | ts   How to fix that ?

I ended up writing a quick little script for this in Python, but I was wondering if there was a utility you could feed text into which would prepend each line with some text -- in my specific case, a timestamp.  Ideally, the use would be something like:  cat somefile.txt | prepend-timestamp   (Before you answer sed, I tried this:  cat somefile.txt | sed "s/^/`date`/"   But that only evaluates the date command once when sed is executed, so the same timestamp is incorrectly prepended to each line.)


It is well known (and the proof is simple) that $\det(AB)=\det(A)\det(B)$ when $A,B\in M_n(F)$ where $F$ field. But what about for $A,B\in M_n(R)$ where R is any arb. commutative ring? A field is distinguished from a com. ring by the presence of multiplicative inverses. I feel like this isn't a necessary condition for proving the determinant function is a homomorphism but I'm having a hell of a time trying to do so. How would I go about proving the above?

Given two square matrices $A$ and $B$, how do you show that $$\det(AB) = \det(A)\det(B)$$ where $\det(\cdot)$ is the determinant of the matrix?


After puzzling over this phrase for quite some time I came across the possible answers offered in this site.  The one that seemed to show the most promising solution was the longest entry, which included the possibility of there being a verb “to lam” meaning “to run.” I found just such a verb in the English Dialect Dictionary, a somewhat now forgotten, yet very useful, text.  I here provide the germane entry, from Vol. III, pp. 509-10:  “LAM...4. to run quickly. w. Yks 5 Whear’s tuh lamming tul! Ther wur a peeler after him - by Gow didn’t he lam!”  The above quotation - which seems to fit exactly the meaning of “lam” - as “running from the police” (i.e. a “peeler”) - comes from C.C Robinson’s  The Dialect of Leeds and its Neighbourhood, of 1861.

According to the Online Etymological Dictionary, lam means:     "flight," as in on the lam, 1897, from a U.S. slang verb meaning "to run off" (1886), of uncertain origin, perhaps somehow from the first element of lambaste, which was used in British student slang for "beat" since 1590s.    Does anyone know of any other explanations?


I don't want to use the same Apple ID on my new phone as on my old phone because it got messed up, however I don't want to have to buy each app twice. Is there a way I can without using the same Apple ID? Same goes for music.

I have two Apple IDs and would like to close one and move the apps from one to the other. Is this possible and how?


char *char_ptr = "anisha";     char char_arr[]= "anisha";  What is the "reason" that the contents of first memory location cannot be modified but the contents of second memory can?  Why is the first memory storage a constant string whereas the second one isn't?

The following code receives seg fault on line 2:  char *str = "string"; str[0] = 'z';  // could be also written as *str = 'z' printf("%s\n", str);   While this works perfectly well:  char str[] = "string"; str[0] = 'z'; printf("%s\n", str);   Tested with MSVC and GCC.


I have an object that is visible, and on frame 30 I'd like that object to be invisible, the same way you would hide an object with 'h' and un-hide it with 'alt+h'. Is there a way to achieve this without an material alpha?

lets assume we have an iron man pointing his hand to a target and shooting few frames later as shown in the picture below:    frame 0 to 10 he will point frame 11 to 15 he will shoot, which is just a long cube with one larger face to give idea or a laser projectile   how can I add the projectile cube only on frame 11? I don't what it to exist before that  thanks


This question is in regards to an existing thread: . I am facing an issue with regards to Part-IV / Figure 8 from the thread above. After assigning letter G to the volume, I tried executing cd /d g:. However, I get an error "Access is denied". I am unsure how to fix it, and proceed with rest of the steps mentioned in the thread above. Appreciate any help/advice.

OS: Windows 7. I want install Linux Ubuntu on portable external Hard Drive USB 2.0. I read a variety of methods, but I'm confused by contradictory advices and methods. Actually, installing Ubuntu on anything other than clean PC looks much more complicated than installing Windows. I need to have Ubuntu package + Python 2.7 + C compiler installed. My external hard drive is partially filled, I need to keep all files.   Will Ubuntu run entirely on external hardrive, without writing anythinhg to Windows system folders and to registry?  Can anyone post detailed guide how install Ubuntu on external hard drive?


I am practicing for my algebra qual and I would like to know if $\mathbb{Z}[2\sqrt{2}]$ is a PID. I had no intuition at first except the fact that $\mathbb{Z}[i\sqrt{2}]$ is a ED with norm $N(a+i\sqrt{2}b)=a^2+2b^2$.  I tried proving that $\mathbb{Z}[2\sqrt{2}]$ is a ED with norm $N(a+b2\sqrt{2})=a^2-8b^2$ using the standard proof for $\mathbb{Z}[i\sqrt{2}]$ and $\mathbb{Z}[i]$. This led nowhere.  This may not be a PID, but I'm not sure how to prove it. Any tips? Thanks in advance.

Why is not the polynomial ring $R[x]$ a unique factorization domain, where $R$ is the quadratic integer ring $\mathbb{Z}[2\sqrt{2}]$?    I'm trying to find a irreducible nonprime element or something but I don't know where to start.


I'm having some difficulty with this proof. I want to show  $ \sup (E_1 \cup E_2) = \max \{ \sup E_1, \sup E_2 \}$, where $E_1, E_2$ are two bounded, non-empty subsets of $\mathbb{R}$. Naturally, the supremum must exist by the least upper bound property.   I know by definition that $\sup (E_1 \cup E_2) \geq x \ \forall x \in E$ and that $\sup (E_1 \cup E_2) \leq \beta$ where $\beta$ is the set of all upper bounds for E. I know the first condition satisfies one of the conditions for the maximum, but my problem is that I don't know how to show that $ \sup (E_1 \cup E_2)$ is in an element of E.   As for $\max \{\sup E_1, \sup E_2\}$, I have proved that it is equal to a supremum by the following:     Let $\beta _0$ denote $\max \{\sup E_1, \sup E_2\}$. Assume $\beta$ is the set of upper bounds for E, and $ x \in E$. Then we have that:       If $x > \beta_0$, then by definition of upper bound $x \notin E$      If $\beta_0$ > $\beta$, then $\beta$ cannot be an upper bound since $\beta_0 \in E$      Therefore, $\beta_0 = \sup (\max \{\sup E_1, \sup E_2\})$   Again, this proof is incomplete because I have not shown that $\beta_0$ lives in the supremum of the union.

Let $A,B \subset \mathbb{R}$. Show that $\sup(A \cup B) = \max\{\sup A, \sup B\}$   Here's what I did so far:  Let $\sup A, \sup B$, and $\sup (A \cup B)$ denote upper bounds of $A,B$, and $A \cup B$, respectively. If $x \in A$, then $x \le \sup A$. If $x \in B$, then $x \le \sup B$. In either case, $x \in (A \cup B)$. So either $x \le \sup A$ or $x \le \sup B$. In either case, $x \le \max \{\sup A, \sup B\}$. So $\max \{\sup A, \sup B\}$ is the upper bound of $A \cup B$, which means $\sup (A \cup B) \le \max\{\sup A, \sup B\}$.  I do not know if there's a better way to go at it, but all I did was show the inequality. Can I do this, and show the reverse inequality? If so, how can I go about doing that?


I am using ubuntu 12.04 LTS (64bit) in 64 bit machine. But I want to use a 32-bit operating system (either 12.04 or 8.04), I tried to do it using bootable pen drive but it failed, while I have alreay changed my OS from 12.10 (64 bit) to 12.04 (64bit) using bootable pendrive. Any kind of help will work.

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


If I buy Minecraft on my laptop and I’m getting a new one at the end of the year can I get Minecraft on the new one I’m gonna get? I’ve seen people say this works but other people say it won't. I really want to play but I don't know if I’m going to have to buy it again and waste money?

I plan on buying a gaming PC as I expect to be able to get it around a year and I currently have a laptop that I play (a pirated version of) minecraft. I heard that minecraft broke out off of the "cringe culture", which convinced me to finally buy it (for now) and later buy the gaming PC, but...  The thing I'm wondering about is, if I buy minecraft on a laptop, will I be able to avoid the whole buying part when I'll get a gaming PC in the future?  Just want to know if I just need to re-download minecraft and log-in on my mojang account or (in the worst case) re-purchase minecraft and log-in on my mojang account...


Recently I started googling out old AD&D books, but I stumbled upon very strange mix-up in terms of edition naming convention. For example, the  has most of the Greyhawk book covers, but strangely enough, many times newer books are named  "AD&D" while older ones have "AD&D 2nd Edition" in the title. The same happens for Forgotten Realms listings, and other setting books too.  I've read somewhere that AD&D 1e and 2e had some small overlap in terms of releases, but it doesn't explain the scale of the issue and the examples below.  How am I supposed to know which AD&D books are actually for 2nd Edition, and which are for 1st Edition?  Even assuming the small overlap mentioned above and some reprints which I identified, I'm still finding books released 5+ years into the lifespan of 2nd Edition that still have the old 1st Edition logo.  Was the release schedule that insanely messy back in the days? Or did they drop the "2nd Edition" part of the logo for some reason? Or did something else happen there?  Examples of the problem:   Greyhawk Player's Guide (1998): Not a reprint (at least not of anything I can find); nearly 10 years into the 2nd Edition lifespan but with a 1st Edition logo. Also released long after other Greyhawk 2nd Edition content which makes it even more odd. The Scarlet Brotherhood (1999): Also not a reprint; also has 1st Edition logo.  TSR Silver Anniversary Collector's Edition (1999): On the first page, there is information that its content is updated for 2nd Edition, yet the cover still has the 1st Edition logo.   There are, of course, many more examples; the ones I found so far are mostly of setting-specific books (Forgotten Realms, Greyhawk, Dark Sun, etc.).

, each of which has loads of rules, source, and splat books.  But how do I know which edition the books I'm looking at are for?  A lot of the time the ones in hobby stores are wrapped up, or you'll buy from elsewhere that doesn't say in the description, and the covers just say D&D.  Is there a way to identify which edition of D&D the books I'm buying are for, either from the cover or some description in the book?  For the purposes of this question I'm asking about core rule books only. Eg. PHB, MM, and DMG. Hopefully the answer to this can be carried over to other books.


I went ahead and upgraded from Mint 17.2 to Ubuntu 15.10 on my Acer ES1-511-P1T9 with Bay Trail n3530 CPU and so far am having amazing performance over Mint 17.2 (almost 70-80% performance increase) however the system has started freezing.  It seems to be when hitting the 4gb+ of memory in use (8gb installed).  I've run a full memtest (about 3-4 hours) on the 8gb stick and am not seeing any errors.  I've read a few things about issues with the new Intel HD linux drivers causing issues, has anyone else seen this with the Bay Trail CPUs?  I'm hesistant to pull the 8gb and reinstall the 4gb as its such a pain removing the whole motherboard to do so lol if there is any chance that it's something else.  Edit:  Under 8.1 Pro x64 system is fully stable.  Under 15.04 system is fully stable however performance is horrible (actually worse than under Win8.1).  Fresh install of 15.10 yields a freeze usually within 10 minutes even with 0 applications running and wifi disabled.  This sucks :( I don't want to use Win8.1 lol

My system freezes completely at random, frequent intervals. I started to have the same problem in Ubuntu 14.04 but after recent upgrade to 16.04 there is no improvement, in fact it seems worse.  When it happens, it's impossible to do anything. I've tried everything in this thread:  but nothing works, I have to hard reset. I have read all the system logs and journalctl but there is never any information that could help diagnose the problem.  This is a dual-boot system with Windows 10 and there's no problem there, so it's not defective hardware.  My laptop has an Intel Bay Trail processor (Pentium N3540)


So I changed my name on my profile but when I go to it in the leaderboards, it still has my old name instead of my new one. Does anyone know how to fix this? Thanks!

I would like to change my Geometry Dash username. I know how, but will all my posted levels still have my old name and will changing the username negatively affect them?  I have changed my name and waited, but it still lists me as my old name when commenting, and viewing my name on levels. The only place it shows my updated name is when you are actually on my profile. Is there a way to get it to display my new name and not my old name?


Is it possible to call javaScript from <apex:commandButton> ...?

I have a custom search page for use in Customer Portal.  VF Page:    <form name="frmSearch">      <input type="text" name="keyword" id="keyword" value="{!portalSearchModel.searchTerm}" onkeypress="return noenter(event);" style="width:25%; height:25px;margin:0; padding: 0px 6px 0px;" placeholder="What are you looking for?" />      <input type="button" id="btnSearch" name="btnSearch" value="Search" onclick="searchTerm()" class="go-we3" />   </form>   <script type='text/javascript'>       function searchTerm(){         var searchTerm = document.getElementById("keyword").value;          var url="/apex/PortalSearch?s="+searchTerm;          window.location = url;          return false;     }          </script>   Is there a way to call this apex method in Controller on button click along with the JavaScript?      public void logSearchTerm(){         portalSearchModel.searches();         Search_Log__c sl = new Search_Log__c();          sl.search_term__c = portalSearchModel.searchTerm;         sl.user__c = UserInfo.getUserId();              insert sl;  }


Even though the field becomes infinite near the charge a gaussian surface can pass through the continuous charge distribution and have a finite value of flux. How?

The Electric field lines coming out of a charge are infinite, So the lines passing through a closed surface should be infinite , right?


While I was executing a C program in terminal I wrote:  gcc -o demo demo.c ./demo   Actually my doubt is why we write ./ before demo and what does it mean?

While executing a C program, a.out, using the Ubuntu terminal, why do I always need to type ./ before a.out, instead of just writing a.out? Is there solution for this?


I have a large amount of data associated with latitude/longitude in a database (currently housed in MS SQL Server).   For the data, I would like to use SQL to calculate the distance from a user derived lat long and then use this distance in an  (IDW) algorithm. I want to do this in SQL rather than inside of a GIS because the data is quite honestly large and complex and I have a tendency to not rely on ArcGIS to do these calculations.  I was wondering if there are SQL implementations of IDW algorithm out there that some could share.  As stated in the link above, IDW is NOT a distance calculator rather the IDW algorithm is an INTERPOLATION function which uses distance as an input.  Please remove the duplication status.

I've got a working PHP script that gets Longitude and Latitude values and then inputs them into a MySQL query. I'd like to make it solely MySQL. Here's my current PHP Code:  if ($distance != "Any" && $customer_zip != "") { //get the great circle distance      //get the origin zip code info     $zip_sql = "SELECT * FROM zip_code WHERE zip_code = '$customer_zip'";     $result = mysql_query($zip_sql);     $row = mysql_fetch_array($result);     $origin_lat = $row['lat'];     $origin_lon = $row['lon'];      //get the range     $lat_range = $distance/69.172;     $lon_range = abs($distance/(cos($details[0]) * 69.172));     $min_lat = number_format($origin_lat - $lat_range, "4", ".", "");     $max_lat = number_format($origin_lat + $lat_range, "4", ".", "");     $min_lon = number_format($origin_lon - $lon_range, "4", ".", "");     $max_lon = number_format($origin_lon + $lon_range, "4", ".", "");     $sql .= "lat BETWEEN '$min_lat' AND '$max_lat' AND lon BETWEEN '$min_lon' AND '$max_lon' AND ";     }   Does anyone know how to make this entirely MySQL? I've browsed the Internet a bit but most of the literature on it is pretty confusing.


I searched a lot and there are resources which point to e-bay and others but all that is third party.  I would like to buy JUST THE KEY for Windows 7 NOT the media, so I can make the already working copy of Windows 7 legal/activated.  Reason for this is to save some money. I have the media just give me the key, and only charge me for the key.

Does anyone know how to install a new serial on a working copy of Windows 7 - I get notified that my software is not genuine but cannot reenter the serial


I've recently had a stream of downvotes without comment on a number of my answers. I personally feel these answers are of objectively good quality and I fear I am being targeted out of spite.  Could someone please investigate?              I'm not sure who it is but the only person I've gotten into a tif was recenlty on this question, where I felt the answer was misleading and didn't answer the question.

I just noticed that I lost a bunch of points from my reputation score, and I used the "reputation" tab on my user profile page to try and track down the cause.  During my investigation, I noticed there was an unusual event of type "reversal". In the normal place of a question title, it says "voting corrected".     What does this mean, and what caused it?  Did I do something wrong? Why did I lose all of that reputation? Is the system punishing me for leaving too many good answers?  Is there any way to earn it back?


When simplifying an equation such as $x^4 + x^4$, I know the answer is $2x^4$, but what I don't understand is why don't you add the exponents along with the $x$? $x^4$ is $x \cdot x \cdot x \cdot x$, right? So why can't you simplify/add them, and have the answer be $2x^8$?

I am working on a problem and I am confused if exponents can be split up in the manner below.   $$x^{k+2} = x^{k+1}+x^{k+1} = 2x^{k+1} $$  I apologize if this is a simple question I tried to look up exponent rules but I couldn't find exponents + a number.


This is a question about JavaScript Prototype Chaining.  I've read some documentation about this, and the syntax doesn't really make much sense to me.    The way I've understood JavaScript Prototypes is essentially some syntactic candy that wraps around a function call which just adds properties to a new object named this.  Basically, turning what you might do in JavaScript without prototypes from this:  function PsuedoClass(arg0, arg1){     var this = {};      this.arg0 = arg0;     this.arg1 = arg1;      return this; }  var obj = PsuedoClass(0, 1);   into what we all know and love:  function PsuedoClass(arg0, arg1){     this.arg0 = arg0;     this.arg1 = arg1; }  var obj = new PsuedoClass(0, 1);   So naturally, the way one might expect to do inheritance in JavaScript would essentially to be call the constructor functions in a chain. It only makes sense, Apply all the properties from both PsuedoClasses into one object.  The whole obj.prototype thing just seems out of the blue to me. It seems to destroy the natural flow that JavaScript seems to lead you on. It would be much more intuitive if just using PsuedoClass.call(this, arg0, arg1); would be enough.  And it almost does, except then javascript's instanceof operator fails.  And there's more arguments than just increased readability that JavaScript's obj.prototype should be removed.  It simplifies the JavaScript Inheritance, reducing things from 2 lines to 1.  If they'd make PsuedoClass.call(this, arg0, arg1) cause this to be an instanceof PsuedoClass, it'd make it possible to do things like this:  function CustomRowClass(){     this.someCustomMethod = function(){} }  var tableRow = document.getElementById('myRow'); CustomRowClass.call(tableRow);  console.log(tableRow instanceof CustomRowClass); //returning true tableRow.someCustomMethod();   I'm really not trying to bash JavaScript as a whole here, I think the language does make a lot of sense in many ways, its just this Prototype chaining is not what I expected it to be, and it doesn't really make intuitive sense.   Am I missing something here, is there a way to understand this obj.prototype in an intuitive way? Everything about it just throws things off for me.  Or is there a simple way to use PsuedoClass.call(this, arg0, arg1); and get the desired instanceof behavior?

I'm not that into dynamic programming languages but I've written my fair share of JavaScript code. I never really got my head around this prototype-based programming, does any one know how this works? var obj = new Object(); obj.prototype.test = function() { alert('Hello?'); }; var obj2 = new obj(); obj2.test();  I remember a lot discussion I had with people a while back (I'm not exactly sure what I'm doing) but as I understand it, there's no concept of a class. It's just an object, and instances of those objects are clones of the original, right? But what is the exact purpose of this ".prototype" property in JavaScript? How does it relate to instantiating objects? Update: correct way var obj = new Object(); // not a functional object obj.prototype.test = function() { alert('Hello?'); }; // this is wrong!  function MyObject() {} // a first class functional object MyObject.prototype.test = function() { alert('OK'); } // OK  Also these  really helped a lot.


I have looked through some of the previous questions posted on this topic, and I think mine is different.   Is there a flaw in defining division by zero? For example, define   $\frac{a}{0} = \infty_a$   it would seem like things work now, for example,   $\frac{a/0}{b/0}=\frac{\infty_a}{\infty_b}=a/b$.   What could go wrong with this idea, or more specifically, is it defined in some branch of mathematics?

We add negative numbers and zero to natural sequence to make it closed under subtraction, the same thing happens with division (rational numbers) and root of -1 (complex numbers).  Why this trick isn't performed with division by zero?


I installed ubuntu 13.10 on my laptop but it won't boot into unity just command line and says running in low graphics mode. How do I fix this.  I have an HP 15-g029wm laptop with amd radeon hd 3330 graphics

Note: This is an attempt to create a canonical question that covers all instances of "low-graphics mode" error that occurs to a user, including but not limited to installation of wrong drivers, incorrect or invalid lightdm greeters, low disk space, incorrect installation of graphics card like ATI and Nvidia, incorrect configuration of xorg.conf file while setting up multiple monitors among others. If you are experiencing the "low-graphics mode" error when trying to login but none of the following answers work for you, please do ask a new question and then update the answers of this canonical question as and when your new question gets answered.   When I try to boot into my computer, I am getting this error:  The system is running in low-graphics mode Your screen, graphics cards, and input device settings could not be detected correctly. You will need to configure these yourself.   How do I fix the failsafe X mode and login into my computer?  Answer index:


Should you be lucky to visit the Seoul, you will be happy.   If you are lucky to visit the Seoul, you will be happy.      What is the difference between the two sentences in meaning? And what is the reason we change the order of the sentence 'you should' into 'should you'?

Should you be lucky to invite the Seoul,   If you are lucky to invite the Seoul,      What is the difference between the two sentences in meaning? And what is the reason we change the order from 'you should' into 'should you'?


Do I get the cards from the highest arena I was in if I get a chest from the shop

Will cards from a higher arena than you appear in the card shop, or will only cards from the arena you are in (or below) when it refreshes be available to purchase?


The question in the title is the following:  If $f : \mathbb{R}^n \to \mathbb{R}$ is differentiable and $f(0) = 0$, prove that there exist $g_i : \mathbb{R}^n \to \mathbb{R}$ such that $$f(x) = \sum_{i = 1}^{n} x_i g_{i}(x).$$   And the hint provided is the following: If $h_x(t) = f(tx)$, then $f(x) = \int_{0}^{1} h_x^{'}(t)dt.$  I followed the hint and got the result below, $$f(x) = \int_{0}^{1} \sum_{i = 1}^{n}x_i D_if(tx)dt.$$  Now I'd like to bring the sum outside due to linearity of the integral, but for that I need to show that the functions $h_i : \mathbb{R} \to \mathbb{R}$ defined by $h_i(t) = D_i f(tx)$ are integrable. How do I show this?   I know that there are differentiable real valued functions whose derivatives are not integrable, so I don't know if this result is true at all (by this I mean I think it's possible to slightly tweak such a function with non integrable derivative to get a counterexample). Am I right in thinking so? All the solutions I can find to this problem (for example, here: ) just expand the integral without considering integrability of the $h_i$s so I might be missing something basic here.  Any help is appreciated.

Problem 2-35 on page 34 of Spivak's Calculus on Manifolds states      If $f: \mathbb{R}^n: \to \mathbb{R}$ is differentiable and $f(0) =0$,   prove that there exist $g_i: \mathbb{R}^n \to \mathbb{R}$ such that   $f(x) = \sum_{i=1}^n x^ig_i(x)$.       Hint: if $h_x(t) = f(tx)$, then $f(x)  = \int_0^1 h_x'(t)$.   I understand the answer he wants, but hasn't he left out a hypothesis that would ensure $h_x'(t)$ is integrable? (For instance the continuity of $df$.)   Secondly, I'm wondering if this theorem is used anywhere. Perhaps in differential geometry it might be useful to write locally $f \in C^\infty (M)$ as $\sum_i g_i(x) x_i$ for some coordinates $x_i$.


I have just had my new PC delivered. I have a Macbook running and am now downloading the iso file. Do I need to follow the instructions on the  to create an OS X bootable usb and start the PC with it? Or is this only for installing Ubuntu on OS X machines? So what should I do in my case?

I have a netbook that I want to install Ubuntu onto. I do have a good Mac computer that I can make a bootable USB drive from, but I'm confused on how to go about making it.


The equation to be proved is: $\sum_{j=0}^n(-1)^j\dbinom{n}{j} = \dbinom{n}{0} - \dbinom{n}{1} + ... \pm \dbinom{n}{n}=0$  But if i take the base case ($n = 1$) i get  $\sum_{j=0}^n(-1)^j\dbinom{n}{j} = \dbinom{n}{0} - \dbinom{n}{1}$  But this evaluates to $\frac{n!}{0!n!} - \frac{n!}{1!(n-1)!}$  I don't think the above statement evaluates to zero. Could this be an error? The book is Spivak's Calculus and the problem is 2-3(e)(ii)

Let $n$ be a positive integer. Prove that   \begin{align} \sum_{k=0}^n \left(-1\right)^k \binom{n}{k} = 0 . \end{align}   I tried to solve it using induction, but that got me nowhere. I think the easiest way to prove it is to think of a finite set of $n$ elements, but I can't find the solution.


I am using a notebook without a CD burner and want to install Ubuntu. I could use an USB stick as an installation medium but I would like to do something different:   I would like to use my old PC and put the HDD from the laptop into it. Than make this HDD as a installation medium using a Ubuntu DVD (the old PC has a CD burner). In the next step I would like to put the prepared HDD into the laptop and install Ubuntu on the same HDD (from the same HDD). Is something like this possible?

I know that I can create/burn bootable CD/DVD or live USB and can boot/install from it. But suppose I am currently running GNU/Linux and I've ISO file of another GNU/Linux that I want to install on my hard disk, then Can I directly boot from ISO from hard disk and try/install that GNU/Linux operating system?


I thought game engine are something like Unity or Unreal. They have a editor with scene editor, some Physics library, some scripting editor and tools to improve the workflow of developer. Furthermore, I thought game engine should independent of the actually game.(i.e.) The game engine should not have any game logic in it.  However, I watched this game engine video and I am totally confused.  . In the game engine video, I don't see the game engine anywhere because it seemed as though the professor developed the game straightaway.  I hope someone can explain the exact difference between a game engine and the actual game.

I am new to Game Development, All I have developed is some 2d Games, using Game Maker by . There game development is much more easy, just as simple as Drag and Drop. But, Now I wish to evolve in Game Development, and wanna try some hands with the common programming languages like, Java, C++ or C. In order to achieve this, I came around the first topic, Game Engine. So, What is Game Engine.? That is a broad question, with various answers. I came out with some conclusion after reading various links,  Wikipedia: A game engine is a system designed for the creation and development of video games. The core functionality typically provided by a game engine includes a rendering engine for 2D or 3D graphics, a physics engine or collision detection (and collision response), sound, scripting, animation, artificial intelligence, networking, streaming, memory management, threading, localization support, and a scene graph.  It exists to abstract the (sometime platform-dependent) details of doing common game-related tasks, like rendering, physics, and input, so that developers (artists, designers, scripters and, yes, even other programmers) can focus on the details that make their games unique. Engines offer reusable components that can be manipulated to bring a game to life. Loading, displaying, and animating models, collision detection between objects, physics, input, graphical user interfaces, and even portions of a game's artificial intelligence can all be components that make up the engine.  Now what I understand is, Game Engine takes care of all the common work, like physics, loading etc... As far my question is concerned, what is a Game Engine (Programmatically)? Is it a Library? With pre-defined functions and classes, which can be inherited? Or what so ever, what is it?


I am trying to compile an (R) markdown document that includes a journal style file. The following line produces the following error:  \newcommand\@titlenote{} %! LaTeX Error: Command \@ already defined. %               Or name \end... illegal, see p.192 of the manual.   I'm not really familiar with macros so I don't know if this should be valid or not! I know that it is used later in the style file:  \let\footnote\thanks  {\fontsize{20}{22}\usefont{OT1}{phv}{b}{n} \@title \par {\small{\@titlenote}} } \vskip 1.5em {\@author \par} \end{minipage} \vskip 1em \par }   In case this isn't enough information, this is my full setup. This markdown in foo.Rmd  --- title: "The foo bar: a novel metal bar for holding fire doors" author: - name: Bar Baz   affiliation:    - Bar Institute   email: foo@bar.baz abstract: |   Lorem ipsum dolor. keywords: Foo, Bar, Baz output:    BiocWorkflowTools::f1000_article:     includes:       in_header: f1000_styles.sty urlcolor: Orange subparagraph: yes geometry: "hmargin=1.8cm,vmargin=2.2cm" ---  Lorem ipsum dolor.   where f1000_styles.sty is available .  This document can be built by running rmarkdown::render("foo.Rmd"). Sorry that it's a bit roundabout. This is as close to minimal as I managed.

Many LaTeX “hacks” begin with \makeatletter and end with \makeatother. What do these commands do?


I'm learning about conic sections as defined using focci. Every derivation I find for the hyperbola get's this definition out of the blue: $b²=c²-a²$ It totally looks like a triangle somewhere, but when I see $a$ and $c$ they are parallel and I cant find how to form a triangle from them. for example  it's just stated  Let's define $b^2 = c^2 - a^2$ and make the substitution into the equation.  With no explaination.  also justs states  Remove the square roots by suitable squarings and use the relation $b^{2}=c^{2}-a^{2}$ to obtain the equation of the hyperbola:  For reference, I'm defining $a,b,c$ as in the following image, where  $b$ is a distance along the $y$ axis  $a$ and $c$ are distances along the $x$ axis (to the vertex and focus respectively)    The question: why is the pythagorean theorem applied here, is there a sneaky triangle that can be defined? how/why does $c$ suddenly become a hipotenuse?

When I teach conics, I give a simple geometric argument for the Pythagorean relation for ellipses. (By "Pythagorean relation" I mean the fact that the square of the focal length $c$ is the difference of the squares of the semimajor and semiminor axes, i.e. $c^2=|a^2-b^2|$ for the ellipse defined by $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$.) The picture argument goes as follows: just draw the obvious isosceles triangle from the two foci to one of the two points at the end of the minor axis. We see two right triangles; in each, one leg is the focal length $c$ and the other leg is the semiminor axis, while the hypotenuse is the semimajor axis. The result follows from the Pythagorean theorem applied to this right triangle.  But when it comes to the Pythagorean relation for hyperbolas, I can't think of an equally convincing picture to draw. Instead I have to give a rather inelegant algebraic argument for the relation $c^2=a^2+b^2$ (for the hyperbola defined by $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$, with focal length $c$), directly from the definition of the hyperbola. The messy details are below.*  Now, obviously there is an asymmetry between the argument for the ellipse and the argument for the hyperbola: the ellipse argument is almost trivial and doesn't involve working straight from the locus definition, but the hyperbola argument is tedious and does require working straight from the definition. So, my question:     Is there an equally persuasive picture I could draw to convince high   school students of the Pythagorean relation for hyperbolas -- without having to get technical with points at infinity, say?   The natural triangle to draw is the right triangle with legs from the center to a vertex and from that vertex to an asymptote, which has legs of length $a$ and $b$; but then the problem becomes why the length along the asymptote should be equal to $c$. I doubt there is a purely (Euclidean) geometrical reason because this triangle lies on the asymptote, not on the hyperbola itself; I suspect some sort of limiting procedure will be required.    [*] The tedious algebraic details:     The foci lie at $(\pm c,0)$.   Say $a>b$. Then hyperbola is the locus of points $(x,y)$ such that       $$\left|\sqrt{(x+c)^2+y^2}-\sqrt{(x-c)^2+y^2}\right|=2a$$      Assume for simplicity the expression between the absolute value bars   is positive. (The algebra is even more tedious if we don't make such a   simplifying assumption.) Then moving the right root to the other side   and squaring gives      $$(x+c)^2+y^2=4a^2+(x-c)^2+y^2+4a\sqrt{(x-c)^2+y^2}$$      Simplifying gives      $$xc-a^2=a\sqrt{(x-c)^2+y^2}$$      and upon squaring again we have      $$x^2c^2-2xca^2+a^4=a^2(x^2-2xc+c^2+y^2)=a^2x^2-2xca^2+c^2a^2+a^2y^2$$      which reduces to      $$x^2(c^2-a^2)-y^2a^2=a^2(c^2-a^2)$$      Defining $b^2:=c^2-a^2$ brings the equation into the form   $x^2/a^2+y^2/b^2=1$, and the Pythagorean relation follows from the   definition of $b$.


I'm having trouble understanding the behavior of a WP_Post variable (and / or possibly the behavior of var_dump itself).  As far as I know, var_dump will inspect all data from a variable. From the PHP documentation:     This function displays structured information about one or more expressions that includes its type and value. Arrays and objects are explored recursively with values indented to show structure.    Then, why is it that var_dump($post) doesn't show metadata, whereas var_dump($post->metadata) does?  I've already read the offficial documentation, specially , as well as . I assume the explanation is there, in plain sight -- however, it's still unclear to me.   What's going on here? Is it some basic PHP behavior that I'm not aware? (I'm not sure if this question is because a lack of understanding how WordPress works or how PHP works. Sorry if this is the wrong site to ask).

I want to add additional items to the data returned as . So for every function/query that returns a WP_Post object I want my additional data added.  Example of returned result:  WP_Post (object) => [     // Default data returned by WP_Post     ID                  => int,     post_author         => string,     post_name           => string,     post_type           => string,     post_title          => string,     post_date           => string,     post_date_gmt       => string,     post_content        => string,     post_excerpt        => string,     post_status         => string,     comment_status      => string,     ping_status         => string,     post_password       => string,     post_parent         => int,     post_modified       => string,     post_modified_gmt   => string,     comment_count       => string,     menu_order          => string,      // Additional data I want to add     extra_data_1        => array,     more_data_key       => string,     another_added       => string ]   For example when the functions  or  are run they will return the WP_Post object along with my additional data.  I've tried finding the appropriate  but this has been unsuccessful.  I am hoping I can do something like:  // This is concept code add_action('pre_wp_post_return', function($data) {     $data->extra_data_1     = get_post_meta($data->ID, 'extra_data');     $data->more_data_key    = get_post_meta($data->ID, 'more_data', true);     $data->another_added    = get_post_meta($data->ID, 'another_data', true);      return $data; });   My reasoning is I am having to build a custom API for WP that uses a range of different core functions which return WP_Post objects. Being able to add my additional data in one place would prevent me from duplicating code.  I hope this is clear enough. Any help would be great!


I have three c++ files, sort.cpp defines a bubble sort function that takes an array, the length of the array and a function that is used to do the comparison. sort.h contains the function prototype inside a namespace. main.cpp is used to test the implementation.  sort.h:  #ifndef SORT_H #define SORT_H  namespace sort {     template <typename T>     void bubble(T*, int, bool (*)(T, T)); }  #endif   sort.cpp:  #include "sort.h"  template <typename T> void sort::bubble(T *array, int length, bool (*compare)(T, T)) {     while (length != 0) {         int newLength {0};         for (int i {0}; i < length - 1; ++i) {             if (compare(array[i], array[i+1])) {                 T temp {array[i]};                 array[i] = array[i+1];                 array[i+1] = temp;                 newLength = i + 1;             }         }         length = newLength;     } }   main.cpp:  #include <iostream> #include "sort.h"  bool larger(int x, int y) {     return x > y; }  int main() {     int arr[] {3, 5, 1, 3, 7, 2};     sort::bubble(arr, 6, larger);     for(const auto e: arr)         std::cout << e << ' ';     std::cout << '\n';     return 0; }   When I compile with g++ main.cpp sort.cpp -std=c++11 I get the error  Undefined symbols for architecture x86_64:   "void sort::bubble<int>(int*, int, bool (*)(int, int))", referenced from:       _main in main-767bbd.o ld: symbol(s) not found for architecture x86_64 clang: error: linker command failed with exit code 1 (use -v to see invocation)   Do I get the error because the compiler doesn't know which types I'm going to use when compiling sort.cpp? So the compiler doesn't generate any function off of the template and then the linker can't find it when I use it in main.cpp?  How can I solve this issue?

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


QueryRunner qr = new QueryRunner(C3P0Util.getDataSource());         qr.update("DELETE FROM course_access " +                 "WHERE user_id = ? " +                 "AND course_id NOT IN (?)", user_id, courseIdList);   String user_id  = "2" String courseIdList = "101,102,104,105,106,108,109" But the results are not correct only the result same as     DELETE FROM course_access WHERE user_id=2 AND course_id NOT IN (101)   The table structure looks like this  id  course_id  user_id 1    101          1 2    102          1 3    105          1 4    104          1 5    106          1 6    108          1 11   110          1 12   101          2 26   101          8 27   102          8 28   105          8 29   104          8 30   106          8 31   108          8 32   110          8 33   113          8 34   115          1 35   107          1 36   115          8 37   109          8 38   109          1 39   107          8 40   116          8 41   116          1 98   102          2 99   103          2 100  104          2 101  105          2 102  106          2 103  107          2 104  108          2 105  109          2

What are the best workarounds for using a SQL IN clause with instances of java.sql.PreparedStatement, which is not supported for multiple values due to SQL injection attack security issues: One ? placeholder represents one value, rather than a list of values.  Consider the following SQL statement:  SELECT my_column FROM my_table where search_column IN (?)   Using preparedStatement.setString( 1, "'A', 'B', 'C'" ); is essentially a non-working attempt at a workaround of the reasons for using ? in the first place.    What workarounds are available?


We all know that this refers to the actual instance of a class...but it seems to me that most people are not using it. So, should I be using it?  My thoughts about it are as follows: Since this refers to the actual instance of a class, it should be used to access any member of that class.    public void(String newValue) {         this.privateVariable = newValue;   }   This should guarantee that the value is not assigned to an object with the same name within the scope (which could also end up as undefined behavior, anyway). But, what if an underscore is used to separate private from non-private fields:    public voud(String newValue) {         _privateVariable = newValue;   }   this seems in that case a little redundant and unnecessary.  So, are there good reasons to use or not use this? Or am I just racking my brain about nothing?

I was curious about how other people use the this keyword. I tend to use it in constructors, but I may also use it throughout the class in other methods. Some examples:  In a constructor:  public Light(Vector v) {     this.dir = new Vector(v); }   Elsewhere  public void SomeMethod() {     Vector vec = new Vector();     double d = (vec * vec) - (this.radius * this.radius); }


Consider the equation $$\frac{d^2u}{dt^2}=c^2\frac{d^2u}{dx^2}$$ where c is some constant. Define new variables, $\sigma=x-ct $ and $\gamma=x+ct$. Now show that the equation becomes $$\frac{d^2u}{d\gamma d\sigma}$$  Can somebody explain what is happening here. I do not know what $u$ is nor what it is a function of. Would this have anything to deal with the wave equation in Physics?  This question is the same as to

I have the following question:    Show that if $z=x+ct$ and $y=x-ct$ then:  $$\frac{\partial^2 u}{\partial t^2}-c^2\frac{\partial^2u}{\partial x^2}=0\text{ implies } \frac{\partial^2 u}{\partial z \partial y}=0$$    If I had $u$ it would follow trivially I imagine, but I don't have $u$. It would seem that $u$ is linear in $t,x$ and since $t,x$ are linear in $y,z$ it seems logically consistent, but I am not sure what to do. Perhaps this is related to harmonic functions.  What should I first do to get this started?    Perhaps I notice that $c=\frac{z-x}{t} \text{ and } c=\frac{x-y}{t}$  and thus $\frac{z-x}{t} =\frac{x-y}{t}\implies x-y=z-x\implies 2x=y+z$


Define $a^2$ as $a * a, a^3 = a * a * a$, and for a positive integer $n, a^n= a * a * \cdots * a$ ($n$ copies of $a$).  (a) If $(G,*)$ is an abelian group, then show that $(a * b)^n = a^n * b^n$ for all positive integers $n$. (b) If $n$ is a positive integer, then show that $(a^n)^{-1} = (a^{-1})^n$.  By being an abelian group, commutative property w.r.t. $*$ is there.  (a) Need show that $(a * b)^n = a^n * b^n,\ \forall n\in\mathbb{N}$.  Stuck ...  (b) If $n$ is a positive integer, then show that $(a^n)^{-1} = (a^{-1})^n$. Unable to think of any approach.

If $ \langle G, \star \rangle $ is an abelian group, then for all $a, b \in G$, show that $(a \star b)^{n} = a^{n} \star b^{n}$.  I am stuck at the first step, unable to figure out how to start. I am just beginning on group theory, and know that an abelian group obeys commutativity, associativity, has an identity element, and each element is invertible. I am unable to figure out how to apply this for the proof. Any hints on how I should get started?


For the following question:  We call an undirected graph a basic graph if its adjacency matrix is such that all diagonal entries are zero and all off-diagonal entries are less than or equal to one. Let $G = (V,E)$ be a basic graph. We call any set of three distinct vertices $\{u,v,w\} \in V$ a trinity, if each pair of vertices in the set is connected by an edge.  I need to find an expression for the number of trinitys (made up term for this question) contained in a basic graph, in terms of the trace of an appropriate matrix and ended up obtaining the expression trace(A³)/6. Would this be correct?

The trivial approach of counting the number of triangles in a simple graph $G$ of order $n$ is to check for every triple $(x,y,z) \in   {V(G)\choose 3}$ if $x,y,z$ forms a triangle.   This procedure gives us the algorithmic complexity of $O(n^3)$.  It is well known that if $A$ is the adjacency matrix of $G$ then the number of triangles in $G$ is $tr(A^3)/6.$  Since matrix multiplication can  be computed in time $O(n^{2.37})$ it is natural to ask:  Is there any (known) faster method for computing the number of triangles of a graph?


i am in the process of creation of simple Document Map for the following C# source.  public class Person {     public string Name { get; set; }     public int Age { get; set; }      public string DoSomething(string x)     {         return "Hello " + x;     } }   The results should be presented in treeview or listview, in following manner:  Person -- Name -- Age -- DoSomething()   So, question is, is there a regex or library which handles C# source code?

Which parsers are available for parsing C# code?  I'm looking for a C# parser that can be used in C# and give me access to line and file informations about each artefact of the analysed code.


Question is as stated above. Can someone explain if (and how) $$\iint f(x)g(y)\,dx,dy=\int f(x)\,dx*\int g(y)\,dy$$  I found this website, but I don't get why they use $x\leq y\leq b$. It makes a bit more sense (in my mind), to have $0\leq y\leq x$, but I still don't undersand how to finish/solve this logic.

Can I argue that:  \begin{align} \left(\int_a^b f(x) \,dx\right) \left(\int_c^d g(y) \,dy\right) &= \int_a^b f(x) \int_c^d g(y) \,dy \,dx \\ &= \int_a^b \int_c^d f(x) g(y) \,dy \,dx \end{align}  since the same would be true for a product of finite sums?


I'm interested to split a larger, irregular polygon into smaller ones. I know the area of the resulting polygon, and I know that the line I want to split it by should be parallel to one of the sides of the original polygon (line AB in the image below).    I'm also curious if i can do this in one go. For example I have the big polygon (of 2400 sqm for example), and I know I want to split it as follows: (Division 1: 200 sqm, next one 140 sqm, next one 100 sqm, and so on) resulting in 10 new polygons of unequal area, but all of them having edges parallel to side AB of the original polygon.  I work in ArcMap 10.1, but I can use QGIS 2.4 as well if there is some plugin that might help me.

I have several thousand irregularly shaped polygons in a shapefile. I want to be able to split each polygon into three areas, and to specify what the size of those areas (they sum to the previous total area). It does not matter what the sub-polygon shape is, as this is for visualization purposes.  How can I go about doing this? Is there a standard algorithm that exists that I can use?    One approach I considered was to get all the points that make up the polygon. Then, I would join two randomly together using a straight line, split the polygon, then check if the area was within a satisfactory tolerance. If it was too small, I would change the point in one direction; if it was too large, I would change to a point in the opposite direction.


How can I write this formula:  1)  I have tried to use $ \stackrel {}{}$ but it does not give the right form.  And how to align these equations   2)  3)

Which book (free or otherwise) was the most useful to you when you started learning LaTeX?  I am frequently asked this question by friends who want to learn LaTeX, and I recommend the book which got me started, , but I feel that there might be better options around.  Also see .


I found out that Unity will be discontinued by Ubuntu so I want to know if there's an available replacement for it. I'm mainly interested in the universal menu bar at the top of Unity (like in macOS), is there another desktop environment that does this?

that it will drop Unity 7 from Ubuntu 18.04 onwards, reverting back to the Gnome desktop environment. I know all the larger desktop environments quite well, Gnome, KDE and Xfce; however, Unity is the one I am more comfortable with and on which I I feel more productive.   I would therefore like to know if there any desktop environments forked from Unity 7 that could be installed on Ubuntu. I understand we are still one year away from the shift, but it is never too early to test the alternatives and eventually choose a project to contribute to.


When there are same-name builtin, keyword and/or external command, what is the order in which the Bash shell decides which to run?  For example,    keyword time and external command time,  builtin printf and external command printf from coreutils.

If I execute the test command in bash, test(evaluates conditional expression) built-in utility is started:  $ type test test is a shell builtin $ type -a test test is a shell builtin test is /usr/local/bin/test test is /usr/bin/test $    However, as seen in output of type -a test above, there is another test in /usr/local/bin directory and yet another one in /usr/bin directory. How are executables ordered, i.e. are the built-in commands always preferred and then the rest of the commands depend on the directory order in $PATH variable? In addition, is it possible to change the order of the executables started, e.g. if I type in test, then /usr/bin/test is started instead of bash-builtin test?


I am going to home or house  explain difference between home and house with examples

Can you explain more?  I do not know when we can use them in the sentence.  Can we use them instead of each other?     They have a beautiful home.   They have a beautiful house.


I am using an Android One mobile phone. When I try to install apps via WiFi I get Error Code: 495, but, when I do the same via mobile data it's working fine.  When  follow the procedure mentioned in  I get a "Connection Time Out Error". If I try a second time I can see the "Installing..." indicator appear, but I don't see any downloading file information and finally I get the same Error Code: 495.  What could be the problem? How to solve this issue?

"Facebook" could not be downloaded due to an error. (495)   How do I solve this error?


The following data is coming from an ajax response and then I've appended it to the DOM.    <input name="new"       value=1 type="checkbox"       id="switchButton"       data-id="'+order.id+'"       data-toggle="toggle">          I used the follwoing method to sellect the checkbox value and toggle the state of the setButton div but it is not working. the jquery code is placed inside document ready function. $('#switchButton').click(function(){                 $('#setButton').toggle();             });  The div which i want to hide and show is as follow:
             <button type="button" name="button"></button>
  Note: When I do the functionality in JavaScript it works but it misses some clicks, say once it is clicked the button will be displayed but when click again it doesn't hide it and when clicked again it will hide it.

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


Running: Kubuntu 18.04 (os set to Japanese today)  However Firefox is still set to English, I went through the options on Firefox; there is an option to change preferred languages for viewing pages but how do I set the language for the UI?

Is it possible to change the language of a particular application so that when opened it shows in Spanish for example while the rest are in English?  I have Spanish and English installed in Ubuntu and am using English as the default one but I would like a way to change the language for a particular application without having to change the whole language of the system.


(B) According to some analysts, the gains in the stock market reflect growing confidence in the economy to avoid the recession, what many feared earlier in the year, rather to come   This is an excerpt from GMAT Question.  some instructor has given this response - * it appears that this choice is trying to substitute "what" for "which". that is not acceptable.   Can some one explain in detail why the usage of what is wrong here?  The whole complete sentence -   According to some analysts, the gains in the stock market reflect growing confidence that the economy will avoid the recession that many had feared earlier in the year and instead come in for a “soft landing,” followed by a gradual increase in business activity.   (A) that the economy will avoid the recession that many had feared earlier in the year and instead come    (B) in the economy to avoid the recession, what many feared earlier in the year, rather to come    (C) in the economy’s ability to avoid the recession, something earlier in the year many had feared, and instead to come    (D) in the economy to avoid the recession many were fearing earlier in the year, and rather to come    (E) that the economy will avoid the recession that was feared earlier this year by many, with it instead coming    Which one is correct. It is GMAT question.

Sometimes I can't see which clause fits the best. What "check-up" could be done to make sure which one is the right one?  For example,  1) He will do anything that is needed. or He will do anything what is needed.  2) They always ignore that is so obvious. or They always ignore what is so obvious.  3) All that I have is yours. or All what I have is yours.  My take is the correct ones are 1) that 2) that 3) what/that???  But I am not sure. I think it has to do something with different types or dependent clauses, but I don't know how to go about them in this case. Any suggestions?  Here is an interesting example  How do I know what I think, until I see what I say? VERSUS How do I know that I think, until I see what I say?  I think both are correct meaning two different things.


My question is how to prove that $f(x) = 4x(16 - x)(6 - x)$ has its maximum at point $x_0 = \frac{8}{3}$. I am trying to use arithmetic-geometric inequality, but I am unable to solve it.

Some people may carelessly say that you need calculus to find such a thing as a local maximum of $f(x) = x^3 - 20x^2 + 96x$.  Certainly calculus is sufficient, but whether it's necessary is another question.  There's a global maximum if you restrict the domain to $[0,8]$, and $f$ is $0$ at the endpoints and positive between them.  Say the maximum is at $x_0$.  One would have $$ \frac{f(x)-f(x_0)}{x-x_0}\begin{cases} >0 & \text{if }x<x_0, \\  <0 & \text{if }x>x_0. \end{cases} $$ This difference quotient is undefined when $x=x_0$, but mere algebra tells us that the numerator factors and we get $$ \frac{(x-x_0)g(x)}{x-x_0} = g(x) $$ where $g(x)$ is a polynomial whose coefficients depend on $x_0$.  Then of course one seeks its zeros since it should change signs at $x_0$.  Have we tacitly used the intermediate value theorem, or the extreme value theorem?  To what extent can those be avoided?  Must one say that if there is a maximum point, then it is at a zero of $g(x)$?  And can we say that without the intermediate value theorem?  (At least in the case of this function, I think we stop short of needing the so-called fundamental theorem of algebra to tell us some zeros of $g$ exist!)


I am unable to connect to a open hidden network (without password) The network is the following (from iwlist wlan0 scan)    Cell 0 - Address: 11:22:33:44:55:66                     Channel:5                     Frequency:2.### GHz (Channel 1)                     Quality=50/70  Signal level=-42 dBm                       Encryption key:off                     ESSID:""   What is the right wpa_supplicant.config to connect to this open hidden network?  In particular What is the key_mgmt field for this open network? (instead of WPA-PSK)  Wrong guess:  network={ ssid="11:22:33:44:55:66 scan_ssid=1 mode=0 proto=WPA2 key_mgmt=WPA-PSK pairwise=CCMP group=CCMP auth_alg=OPEN priority=1 psk="" }

I need to connect to a hidden network without password with wpa_supplicant:  iwlist <interface> scan  output:   Cell 02 - Address: 11:22:33:44:55:66                     Channel:1                     Frequency:2.412 GHz (Channel 1)                     Quality=67/70  Signal level=-43 dBm                       Encryption key:on                     ESSID:""                     Bit Rates:1 Mb/s; 2 Mb/s; 5.5 Mb/s; 11 Mb/s; 6 Mb/s                               9 Mb/s; 12 Mb/s; 18 Mb/s                     Bit Rates:24 Mb/s; 36 Mb/s; 48 Mb/s; 54 Mb/s                     Mode:Master                     Extra:tsf=##################                     Extra: Last beacon: 248ms ago                     IE: Unknown: ######                     IE: Unknown: ##################                     IE: Unknown: #####                     IE: Unknown: ##############                     IE: Unknown: ######                     IE: Unknown: ###############                     IE: IEEE 802.11i/WPA2 Version 1                         Group Cipher : TKIP                         Pairwise Ciphers (1) : CCMP                         Authentication Suites (1) : PSK                     IE: WPA Version 1                         Group Cipher : TKIP                         Pairwise Ciphers (2) : CCMP TKIP                         Authentication Suites (1) : PSK                     IE: Unknown: ###################   What is the wpa_supplicant configuration file needed to connect to this network?    Wrong guess:  network={     ssid=""     bssid=11:22:33:44:55:66  }


I'm new to Ubuntu. I know that windows has a feature that allows you to remove your USB flash drive without having to go to the drive, right click and choosing safely remove. This prevents you from corrupting your files if you quickly unplug your flash.  What I want to know is. Does Ubuntu have a similar feature? can I just unplug my USB devices and my files wont get corrupted or must I always go to the drive right click and chose safely remove?  Thank you.

How I can safely remove a USB external drive?  Ubuntu 12.10 does not come with this option, only to "Unmount" the disk, but not "Eject".    I have tried both USB sticks and with my external hard drive.


I have already seen all related questions but none of them worked.

So the new item, Elytra on 1.9 are supposed to make you glide. I have used them at my friend's house when we were playing snapshots but when the update came out, I tried them at my house and all that happened was I fell to my death. Does anyone know what I'm doing wrong and how I can fix it?


I understand what this C++ function does, but I don't understand why the return statement is written this way:  int intDivide(int num, int denom){   return assert(denom!=0), num/denom; }   There is only one statement here, because there is only one ; but the comma confuses me. Why not write:  int intDivide(int num, int denom){   assert(denom!=0);   return num/denom; }   Aside from "elegance" is there something to be gained in the first version?  What exactly is that comma doing anyway? Does it break a single statement into 2 parts such that essentially the above 2 versions are identical?


I'm currently learning about functions and I need a clarification regarding some basic concepts since every book I read seems to change something here and there.  The concepts of domain and codomain are quite clear and I have no issues about them. I have issues understanding the range and the image set.  First, I used to believe the range and the image set were much like the same thing. Now, after more reading it seems that range and image set are not exactly the same thing.  From what I have understood, the range is the image set of the domain. But I can have image sets of subsets of the domain (not equal to the domain) which will not be the range but just image sets of these subsets. Saying the same but differently, the range is always an image set, but an image set does not necessarily has to be the range.   My question is simple, is this understanding of the topic correct?

Can someone please explain to me in layman what each means? Perhaps with some examples with functions (inputs to outputs/numeric values in them)? Especially range, image, and preimage. So far this is my understanding:   Domain is basically the input $x$ in $f(x)$. Codomain is what $f(x)$ produces as an output such as $y$ when $f(x) = y$. Range sounds like codomain but with some restriction?  Image I have little understanding of but I think it is basically a relation between domain to codomain given that we take a subset of our function (Eg; it is the input to output process of our function given we put a restriction on the domain as $x$ can only go from $0$ to $1$).  Preimage is just walking backward on the "image" process? (Inverse image?) Going from our "subsetted" output back to our "subsetted" input?    I am very frustrated that I can't seem to grasp these basic concepts so I would greatly appreciate any help from anyone who can break this down for me and help me understand it without too much mathematical notation. Thank you!


I am using below code to dynamically add a chunk of html to a div using innerHTML property. Here is my html code:       <form>
<input type="date" name="arrival"/>

<input type="date" name="departure"/>

<input type="submit" value="Submit"/>
    </form>     After the closing body tag I am adding the following JavaScript,     I the above code, innerhtml mark-up is not being added, I can see that in view source. What could be wrong with this piece of code?

Is there a character in JavaScript to break up a line of code so that it is read as continuous despite being on a new line?  Something like....   1. alert ( "Please Select file    2. \ to delete" );


I encrypted my installation of Ubuntu 14.04 while installing it, later I switched the driver of my ATI Radeon HD 6970 to "fglrx-updates". After that I could only close but not open any programs. I guessed that a reboot would help and the Ubuntu cryptsetup login screen looked a lot more primitive (text based). Also I can't login any more. Error message "cryptsetup failed, bad password or options?"  I've done some research and apparently quite a few people face problems with those proprietary drivers, also while booting. For some the cryptsetup login screen looks different too, but I can't even get past the encryption. I'd prefer to not lose the installation, is there a different way than formating and reinstalling?

I activated disk encryption for my Ubuntu 15.10 64bit installation and get every time after entering the (correct) password the error message:  cryptsetup: unknown fstype, bad password or options?  But after few seconds (without any further interaction) this error message is replaced by the expected message:  cryptsetup: sda5_crypt set up successfully  That's it and the system is started.  Any suggestions what could be the problem? Is it merely cosmetic or serious?


Is there a function that will express any given number in words?  For example:  If a number is 1432, then this function will return "One thousand four hundred and thirty two".

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


Using Java tools,  wscompile for RPC wsimport for Document etc..   I can use WSDL to generate the stub and Classes required to hit the SOAP Web Service.  But I have no idea how I can do the same in REST. How can I get the Java classes required for hitting the REST Web Service. What is the way to hit the service anyway?  Can anyone show me the way?

With JSR 311 and its implementations we have a powerful standard for exposing Java objects via REST. However on the client side there seems to be something missing that is comparable to Apache Axis for SOAP - something that hides the web service and marshals the data transparently back to Java objects.  How do you create Java RESTful clients? Using HTTPConnection and manual parsing of the result? Or specialized clients for e.g. Jersey or Apache CXR?


I extracted CodeIgnitor to XAMPP's htdocs and when I tried to access index.php like this:     h t t p://127.0.0.1/ci/index.php   I get the following error message:     Access forbidden! You don't have permission to access the requested object. It is either read-protected or not readable by the server. Error 403......   How can I troubleshoot this problem?

This is a  about  the use of a *AMPP's stack.    I recently had a talk with some experienced people and they suggested to me not to use a WAMP stack, and instead install apache, mysql and php separately.  I don't understand why they have suggested this, though, so can anyone tell me?  Is there a particular disadvantage of WAMP, or a particular advantage to installing all of them separately?  Since a WAMP stack itself is composed of apache, mysql and php, then what's the difference between using the WAMP stack and installing them all separately?


I know that it is possible to check if a URL redirects, as mentioned in the following question and its answer.    using the following code:  eq = urllib2.Request(url=url, headers=headers) resp = urllib2.urlopen(req, timeout=3) redirected = resp.geturl() != url # redirected will be a boolean True/False   However, I have list of Millions of URLs. Currently it is discussed wether one of them is a harmful URL or redirects to a harmful URL.   I want to know if it is possible to check for redirect without opening a direct connection to the redirecting website to avoid creating a connection with a harmful website?

Looking at the source of urllib2 it looks like the easiest way to do it would be to subclass HTTPRedirectHandler and then use build_opener to override the default HTTPRedirectHandler, but this seems like a lot of (relatively complicated) work to do what seems like it should be pretty simple.


I wish to install Windows 7 on my mac. I had a copy of Win7 years ago, and I believe I allowed the automatic upgrade to Win10 to happen, on my current PC. Tonight I entered my old Win7 product key here:  ...and it validates, and allows me to download a Win7 disc image file.  Questions are... 1) Shouldn't that product key have expired for Win7? 2) Is there any scenario where my Win7 product key might be available to use (unassigned)?  Thanks for any advice in advance. I'm just trying to get a totally legal Win7 installation, wouldn't mind paying.

Many posts around that subject, but this case is a bit specific (I think) since it's not about a migration nor a cloning.   Initially Windows 7 on a 500GB HDD (OEM) then upgrade to Windows 10 (offered by Microsoft)   Now we have a brand new 550GB SSD and would like to install a fresh Windows  on it (and get rid of the old one on the HDD).   Do we have to install the initial (Win 7) or the upgraded (Win 10) on the SSD? What happens with the license, will Microsoft accept the license "transfer" automatically?   We'd prefer to install Windows 7, unless 10 is mandatory (or recommended).  Edit  Actually we'll go for win 10 since we need to switch languages after the install (thanks @Ramhound). Thus the question is back to the classical Win 10 reinstall, and is definitely a dupe . . .


I discovered last week that an elected moderator can modify a user's name. The user had a username that was clearly meant to insult one particular elected moderator. This was discussed in chat, and the moderator decided to make a minimal change to the user's username.   While it was funny to see this happen to an obvious troll, it did make me wonder. I'd have expected that only Stack Exchange personnel would have this kind of power.    So the question is - what else can a moderator do to my profile?    For example, can a moderator also completely rewrite the "About me" section? I can understand that under rare circumstances, material must be removed from these sections. But I would have expected that elected mods would only be able to make these things go black. Could they also completely rewrite it if they wanted to?

Some people have a diamond after their username (e.g. )    What special privileges do diamond moderators have? How can I become a diamond moderator? Who are the diamond moderators?  How many are there?      For more information, see  in the .     Note: not to confuse with certain Stack Exchange employees, for example  members or "community managers", who often have diamonds as well, but are not ordinary moderators.


In "The Wolverine", during the final battle, the Silver Samurai heats up his sword and cuts off Wolverine's Adamantium claws:                                  Then, after the Silver Samurai has been injured, Wolverine grows back his original bone claws:                                  But, in "Days of Future Past", Wolverine has his Adamantium claws again.  There was no real explanation as to how he got them back, as he still had his bone claws at the end scene where Magneto and Charles Xavier come to see him.  So what is the in-universe or out-of-universe explanation for Wolverine getting his Adamantium claws back?

"The Wolverine" movie is a prequel for "Days of Future Past" (because it shows DoFP related scenes on the after-credits).  So Wolverine has bone claws when The Wolverine movie ends, and on DoFP it has adamantium claws again, is there any explanation for this? maybe on the comics, or something?


I am trying to add to an array list using a passed in object, but I keep getting a nullpointer exception when executing the line "order.add(shape)" below.  public void addSquare(Square shape) {     System.out.println(shape.toString());      order.add(shape); }   How do I fix the exception? Do I need to initiate shape somewhere?

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


E: The repository 'https://download.docker.com/linux/debian focal Release' does not have a Release file.  N: Updating from such a repository can't be done securely, and is therefore disabled by default.  N: See apt-secure(8) manpage for repository creation and user configuration details.  I'm getting this error when I tried installing docker from . Anyhow, now I don't want it, but I can't find it anywhere in sources. I ran $ sudo nano /etc/apt/sources.list  but I cant find the docker repository to remove. How do I remove docker repository?

When updating, I get the following error message:   W: The repository 'http://ppa.launchpad.net/mc3man/trusty-media/ubuntu xenial Release' does not have a Release file.   Here, I find another statement on this error:   This recommends removing certain PPAs; and, I'm not sure if I should do that since it might mean not getting the updates that I need.    Is this what I should do?


I have a burn mark texture and the problem is that when I put it on a plane and adjust the UV mapping instead of there being one burn mark loads show up. How do I get only one?

Update  As of 2.76 there is a .    In Blender Internal there was an option to turn this off (called )  Is there a way to do this with Cycles? I know you can just scale your textures up with a transparent background, but you end up with textures much bigger than they need to be.  Is there a way to this, and if not, why not?


Someone commented one of my answers (on Arquade ) saying they down voted because of the lack of "freehand circles". Is this a joke?   Could someone explain it? I don't think they actually did down vote the answer (or if they did someone up-voted at the same time).   My answer did contain a picture with a square that I had inserted but it wasn't freehand.

Catchphrases and concepts that spread from person to person are known as [memes], which, courtesy the Internet, can now explode across the Earth like a highly contagious virus (hence "going viral"). As with their real-life counterparts, some infectious diseases are global (pandemic), while others are endemic to specific regions. Stack Overflow, and now even more predominantly Meta Stack Exchange, have seen more than their fair share of these pathological social constructs spread through the user base. They are now ingrained units of our collective culture as SOpedians (a term which I hate, by the way). Just as travelers' immune systems can be assaulted by new diseases in new places, new users are increasingly likely to be miffed by an ingrained meme and left sitting scratching their heads. I therefore propose that this space be used to document the memes endemic to Stack Exchange's culture. Each meme should be listed in a separate answer and I hope that we as a community will be able to provide greater context to each one. Please actually explain each meme in a way understandable to those not already in the know. Especially considering that a lot of these memes aren't really understandable to newer users who weren't around in the early years of the network, or are based on system features that no longer exist.  On other Stack Exchange sites          [memes]: