How is the passage of years measured in Game of Thrones?
What is a "year" in Westeros?
Orbit followed by a particle around Schwarzschild Black Hole $-1$ is a quadratic residue modulo $p$ if and only if $p\equiv 1\pmod{4}$ Is it logically correct to assert that the expectation of the momentum $$\langle \hat p \rangle=0$$ for any bound state because it is bound to some finite region? What is the physical interpretation of the fact that $$\langle \hat p \rangle=0$$ in an energy eigenstate $\psi_n(x,t)$  but $$\langle \hat p \rangle\neq0$$ in some superposition state $$\psi(x,t)=c_m\psi_m(x,t)+c_n\psi_n(x,t)~?$$ Here $\psi_n(x,t)$ the eigenstates of the Hamiltonian, for example, in the problem of particle in a box (say). Implementing a PIVOT query How can I pivot the following SELECT statement:           SELECT sc.CID,                 sc.CodeName     as OverviewText,                 scRAG.CodeName  as RAGStatusText             FROM StatusCode      sc LEFT OUTER JOIN ProjectOverview po               ON sc.CID          = po.ProjectOverviewCID              AND po.ProjectId    = 180 LEFT OUTER JOIN StatusCode      scRAG               ON po.RAGStatusCID = scRAG.CID           WHERE sc.SCID         = 18   Such statement yields the result set that follows:  CID OverviewText    RAGStatusText --- ------------    ------------- 153 Cost            Green 154 Requirements    Yellow 155 Schedule        NULL 156 Technical       NULL 157 Testing         NULL   But, I want it to return one single row with 10 values, as shown bellow:   ----------------------------------------------------------------------------------------------  | Cost | Green | Requirements | Yellow | Schedule | NULL | Technical | NULL | Testing | NULL |  ----------------------------------------------------------------------------------------------   Can I pivot on CID? Can I see why a package is installed? Cannot install Ubuntu in VirtualBox due to "this kernel requires an x86-64 CPU, but only detects an i686 CPU, unable to boot" error I was trying to install Ubuntu 12.04 in VirtualBox 4.2.12r84980. I see    this kernel requires an x86-64 CPU, but only detects an i686 CPU, unable to boot   But I am using a 64 bit Windows 8, and trying same .iso for trying Ubuntu. Then what is the problem? Trash icon and files have disappeared from the desktop after upgrade to Ubuntu 19.04 Can “zealot” have a positive connotation? A zealot is a person who is fanatical and uncompromising in pursuit of their religious, political, or other ideals.  I have never seen this word used with positive connotation, but could it (without causing raised eyebrows)? For example, “Gandhi was a zealot and should be admired by all who believe in non-violence.”  Also, do “zealous” and “zeal” carry the same connotation as “zealot”? Did J.R.R. Tolkien ever write a deeper connection between The Hobbit & Lord of the Rings: Fellowship of the ring? There seems to be a bit of a gap between The Hobbit and Lord of the Rings: Fellowship of the Ring. While we know the outcomes from The Hobbit to Lord of the Rings, we don't know what happened between them. Did Tolkien ever novelize this?  Connecting the two movies together, I've pieced the following sub-plots:   Saruman becomes corrupted by peering into the Palantír of Orthanc at some point after The Hobbit Gollum gets captured by Sauron's army Legolas leaves his homeland, in search of a ranger of some importance Tauriel is banished from her homeland Bilbo returns to the Shire, and finally relinquishes the one ring on his 111th birthday to Frodo   What doesn't seemed joined by the books or the two trilogy films:   How did a powerful white wizard like Saruman become enchanted/corrupted by Sauron What was Gollum doing before he was captured Where was Thranduil during the events of Lord of the Rings What happened to Tauriel during Lord of the Rings What happened to the remaining company of dwarves after The Hobbit Who now resides within Erebor What happened to Radagast during Lord of the Rings How to say that you have plans to go to the movies tonight (but you are not sure yet, maybe you will have a pizza)? I mean there are options:     I am going to the cinema tonight.   Way too much certainty in this. For me it means that you have already bought tickets, the least.     I am going to go to the cinema tonight.   Sounds a bit awkward.     I will go to the cinema tonight.   Sounds too formal to me. The following question is on my homework assignment that I cannot figure out:     Let U and V be independent random variables, each having a normal distribution with mean zero and variance one. Find the moment generating function of the random variable W = UV .   I have looked around online, and cannot find an answer to this question. In fact, the only answers I can find that even relate to the product of standard normal random variables are using techniques that we never covered in my class. We covered in class how to find the MGF for linear combinations of random variables, by W isn't linear, its a product of two normals. So that technique won't work.   What am I supposed to do? I am completely at a loss. I have tried multiplying the MGFs of U and V together, but that leaves me with something ugly that I can't reduce. Wine pollutes "Open With" application list The dialog box in question here is the one you get with the context menu option "open with other applications". Wine seems to have inserted more than a dozen or so entries for each application I install, which makes it a pain to find the correct application:     What can I do to remove the duplicates?     Update: Neither of the two solutions really work. The bug is interesting, but the symptoms does not match my problem (I'm not having problem with uninstalling applications, but rather the things that are inserted after installing them), and with the other one, all references to the Wine application are removed, which actually makes the problem worse (although it may be an acceptable solution if nothing else can be found). So this is still an open question; any takers? Earlier today, I was talking with my friend about some "cool" infinite series and the value they converge to like the Basel problem, Madhava-Leibniz formula for $\pi/4, \log 2$ and similar alternating series etc.  One series that popped into our discussion was $\sum\limits_{n=1}^{\infty} \frac{1}{n^n}$.  Proving the convergence of this series is trivial but finding the value to which converges has defied me so far. Mathematica says this series converges to $\approx 1.29129$.  I tried Googling about this series and found very little information about this series (which is actually surprising since the series looks cool enough to arise in some context).  We were joking that it should have something to do with $\pi,e,\phi,\gamma$ or at the least it must be a transcendental number :-).  My questions are:   What does this series converge to? Does this series arise in any context and are there interesting trivia to be known about this series?   I am actually slightly puzzled that I have not been able to find much about this series on the Internet. (At least my Google search did not yield any interesting results). Why cannot fermions have non-zero vacuum expectation value? Why do we say "try and" [verb] instead of "try to" [verb]? (E.g., "Try and call me tomorrow.") In written and standard semi-formal (and above) spoken English, one would use &quot;try to&quot;:  Try to be a better person. Try to get the fishhook out of my thumb, please. Try to find a pharmacy when you need one.  But in spoken English, we (Americans, at least) usually substitute &quot;try and&quot; for all those cases. &quot;Try to&quot; makes sense because the &quot;to&quot; begins the construction of an infinitive: &quot;try to be&quot;, &quot;try to do&quot;, &quot;try to act&quot; and so on. &quot;Try and&quot; on the other hand doesn't seem to make any sense. I'm curious how the &quot;try and&quot; crept in, and when. It's really tough to Google small words like these, so I'm not finding anything on the Web. Is it a contraction of something like &quot;Try hard, and ...&quot;? Note: I've seen  and it is somewhat related but doesn't tell me what I want to know. Edit Observe how, even on this site,  construction. Turning it on its head Note that you can't make a negative construction with &quot;try and&quot;:  It's raining. Try not to get wet. It's raining. Try not and get wet. [?]  Even adding do doesn't help. The following means something different from &quot;try not to get wet.&quot;  It's raining. Don't try and get wet.  Even use of to instead of and there means something else:  It's raining. Don't try to get wet.  &quot;Try not to get wet&quot; means try to stay dry. &quot;Don't try to get wet&quot; means avoid actively seeking out a soaking, and implies that a soaking might in fact be what you are looking for. MORE I just happened to notice a video from an editor for Merriam-Webster on this very topic, so I include the link here: . I have a requirement to implement an "Unsaved Changes" prompt in an ASP .Net application.  If a user modifies controls on a web form, and attempts to navigate away before saving, a prompt should appear warning them that they have unsaved changes, and give them the option to cancel and stay on the current page.  The prompt should not display if the user hasn't touched any of the controls.  Ideally I'd like to implement this in JavaScript, but before I go down the path of rolling my own code, are there any existing frameworks or recommended design patterns for achieving this?  Ideally I'd like something that can easily be reused across multiple pages with minimal changes. This question is a duplicate of  (but this question can't be marked as a duplicate because that question is on meta.stackoverflow.com, and this question is on meta.stackexchange.com).  I'm seeing a bug on stackoverflow.com. I'm not sure if the culprit is Stack Overflow, Google Chrome, or macOS.  (Below I refer to a "code box". By that I mean some text that begins with 4 spaces when editing a question or answer.)  When I hover over a code box that contains one long line of code, a horizontal scrollbar appears. When I stop hovering over the code box, very frequently (maybe 3 out of 4 times) the scrollbar does not disappear. Clicking elsewhere on the page also does not dismiss the scrollbar. The only way to dismiss it is to refresh the page.  ...After experimenting more, it appears to always happen if I enter the box from below, but not always when I enter from above. It seems to be triggered by hovering over the lower half of the box.  Also if I enter from the top and scroll to the right, then until I refresh the page again that scrollbox will behave normally (only show a scrollbar when scrolling, and disappear after). In that case the scrollbar also has a different appearance, being much less tall (maybe a quarter of the height of the code box rather than half as tall).  Further, if I get a box and scrollbar into that functional state and then hover over the lower part of the box for a bit, then sometimes eventually it will break and stay broken until refresh again.  And in any case hovering over the lower part of the box causes the scrollbar to get taller.  Here is a screenshot of the issue:        Google Chrome 71.0.3578.98 (Official Build) (64-bit)  macOS High Sierra 10.13.6  Here is a code box that repros the issue for me:  fooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo   Here is another:  foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo Expandably change letter case and use inside \csname, without a package I want to change the letter-case of a single character argument, and use that changed letter inside a \csname.  And I want to do it without an additional package.  For example, I want to pass a macro the letter {S}, and have it execute the macro \csname macros\endcsname, or pass it the letter {T}, and have it execute the macro \csname macrot\endcsname.    In my MWE, I show three approaches:   I didn't expect \lowercase to work, since I recall reading that it is not truly expanded until the last possible moment.  Surprisingly, it goes into an \edef okay, but it must not be truly expanded, because it breaks the \csname. I also formulated an approach where I used \numexpr to add 32 to the ASCII code of the argument and perform a \char upon that result.  Like \lowercase, it gives the appearance of being expandable, but it also fails inside the \csname. I finally achieve success with the stringstrings package.  Having written the package, I know the conversion was not pretty... essentially, it is an exhaustive 26-fold check of the form \if #1Aa\else\if #1Bb\else\if #1Cc\else...\fi\fi\fi, which has the virtue that it can be expandably placed into an \edef, and so it works.   There has to be a better way.  The MWE works only because I use the inefficiently calculated \tmp from METHOD 3 inside the \csname.  If I use \tmp from either of the two earlier methods, it breaks.  \documentclass{article} \usepackage{stringstrings} \def\macros{Expandably converted an S to a s} \def\macrot{Expandably converted a T to a t} \newcommand\convert[1]{%   %MAKE THE ARGUMENT LOWER CASE   1) LOWERCASE\\   \edef\tmp{\lowercase{#1}}% PRETENDS TO EXPAND, BUT FAILS IN \csname   Here is the ``expanded'' conversion: \tmp\\   % OR   2) ASCII CONVERSION\\   \edef\tmp{\expandafter\char\numexpr`#1+32\relax}% PRETENDS TO EXPAND, BUT FAILS IN \csname   Here is the ``expanded'' conversion: \tmp\\   % OR   3) STRINGSTRINGS PACKAGE\\   \caselower[q]{#1}\def\tmp{\thestring}% WORKS BUT USES A PACKAGE   Here is the ``expanded'' conversion: \tmp\\   %   Now use it in a csname: \csname macro\tmp\endcsname% } \begin{document} \convert{S}\par \convert{T} \end{document}       SUMMARY OF ANSWERS:  I have added egreg's code snippets into this MWE to produce a document (and not just terminal output), showing the methods put forth to this point:  \documentclass{article}  %%%%%%%%%%%%%%%%%%%%%%%%%%%% L3 APPROACH  \usepackage{expl3}  \ExplSyntaxOn \cs_set_eq:NN \Xexplower \tl_expandable_lowercase:n \ExplSyntaxOff  %%%%%%%%%%%%%%%%%%%%%%%%%%%% EGREG'S LESS HACKY SOLUTION  \def\explowerchar#1{%   \ifcase\numexpr`#1-`A\relax    a\or b\or c\or d\or e\or f\or g\or h\or i\or j\or k\or l\or m\or    n\or o\or p\or q\or r\or s\or t\or u\or v\or w\or x\or y\or z\else    #1\fi }  \def\explower#1{%   \doexplowerchar#1\relax }  \def\doexplowerchar#1{%   \ifx#1\relax   \else     \explowerchar{#1}\expandafter\doexplowerchar   \fi }  %%%%%%%%%%%%%%%%%%%%%%%%%%%% STEVE'S HACKY PACKAGE APPROACH  \usepackage{stringstrings}  %%%%%%%%%%%%%%%%%%%%%%%%%%%%  \def\macros{Expandably converted an S to a s} \def\macrot{Expandably converted a T to a t}  \begin{document}  \textbf{Steve's hacky approach}  \caselower[q]{S}\csname macro\thestring\endcsname\par \caselower[q]{T}\csname macro\thestring\endcsname  \textbf{egreg's less hacky approach}  \edef\lcstring{\explowerchar{S}}\csname macro\lcstring\endcsname\par \edef\lcstring{\explower{T}}\csname macro\lcstring\endcsname  \textbf{L3 approach}  \edef\lcstring{\Xexplower{S}}\csname macro\lcstring\endcsname\par \edef\lcstring{\Xexplower{T}}\csname macro\lcstring\endcsname  \end{document} Which repository source do I need to add to my sources.list to access the package firmware-linux-nonfree?  I am using Deb 6 testing 32 bit. Convergence test of the series $\sum\sin100n$ I need to prove that $$\sum_{n=1}^{\infty} {\sin{100n}} \; \text{diverges}$$ I think the best way to do it is to show that $\lim_{n\to \infty}{\sin{100n}}\not=0$. But how do I prove it?