The new  for 5e can infuse magic into weapons or shields, and use the infused item as a spell focus for material components. However, can you wave your focus for the somatic part of a spell as well?  Basically, I am curious whether an artificer can have a one-handed crossbow in one hand, and an infused shield in the other and still cast V, S, M spells.
If there is a wizard that, by some means, has acquired proficiency in the use of shields, can said wizard use his shield in one hand and his arcane focus quarterstaff in the other and still cast somatic component spells?  Since the quarterstaff has been crafted to also be an arcane focus, and the Sage Advice Compendium states that you can provide the somatic components of spells with the same hand wielding the arcane focus, in this case an arcane focus quarterstaff, could that wizard still be able to perform somatic component spells while using a shield in the other?  I understand War Caster is the feat that allows you to cast somatic component spells even while using a shield and weapon or two weapons in each hand, but is this a simple way around those rules seeing as this "weapon" is your arcane focus? I would like to believe it is not, but I'm not fully fluent in the ways of spellcasting.
PHP - Get rid of notation Defender of the Realm hat broken, or just badly worded? Description of the hat unlock requirement:     at least 5 flags dismissed as helpful and at most 20% of non-disputed flags declined   Does "dismissed" mean something unusual here, or is this hat not unlocking properly? I'm not sure if that means "since winter bash started" or "since your account was created": if the former, I've flagged 8 items so far today, of which 6 were marked "helpful" (the other two are still active; none have been disputed or declined). If the latter, the flag page indicates I've flagged 391 items (plus 6 for spam), of which 1 was declined (which incidentally, I assume that was by accident, given that the question was closed soon after for the reason I flagged it for), 1 was disputed (that one was legitimate), and 21 are still open. That is definitely way under 20%.  So what's up with that unlock?  edit: it appears to be the case (further edit: this has now been confirmed first-hand) that this hat unlock disregards any flags that are the flag equivalent of voting to close. I put forth that if this is intended behavior, well, it shouldn't be (if it's to equalize the playing field for over-3k-rep people, it should just also count votes-to-close. Though granted, I suppose in the scheme of things it really doesn't matter much, as it'll all go away in a couple weeks anyway. But dang it, I want to show off all the flagging I do! :p) I just updated my iMac to Mojave, and am still trying to setup my preferences.  I tried dark mode, but did not like it (half of me apps seem to ignore it anyway).  I switched to light mode, but this too has problems. The File Save dialog shows a list of Directories and existing files, but the latter are very light grey, almost indistinguishable from the background.    I have searched the Preferences menu, but can't seem to find any setting to set normal contrast levels like in High Sierra. How can I convert from a SID to an account name in C# I have a C# application that scans a directory and gathers some information.  I would like to display the account name for each file.  I can do this on the local system by getting the SID for the FileInfo object, and then doing:  string GetNameFromSID( SecurityIdentifier sid ) {     NTAccount ntAccount = (NTAccount)sid.Translate( typeof( NTAccount ) );     return ntAccount.ToString(); }   However, this does not work for files on a network, presumably because the Translate() function only works with local user accounts.  I thought maybe I could do an LDAP lookup on the SID, so I tried the following:  string GetNameFromSID( SecurityIdentifier sid ) {     string str = "LDAP://&lt;SID=" + sid.Value + "&gt;";     DirectoryEntry dirEntry = new DirectoryEntry( str );     return dirEntry.Name; }   This seems like it will work, in that the access to "dirEntry.Name" hangs for a few seconds, as if it is going off and querying the network, but then it throws a System.Runtime.InteropServices.COMException  Does anyone know how I can get the account name of an arbitrary file or SID?  I don't know much about networking or LDAP or anything.  There's a class called DirectorySearcher that maybe I'm supposed to use, but it wants a domain name, and I don't know how to get that either - all I have is the path to the directory I'm scanning.  Thanks in advance. sum pair of columns based on matching fields Need hint: Determine whether the series $\sum_{n=1}^{\infty}(\frac{n}{n+1})^{n^2}$ is convergent or divergent. Determine whether the series $\sum_{n=1}^{\infty}(\frac{n}{n+1})^{n^2}$ is convergent or divergent.  I've tried applying all the basic tests to no avail. I need to find out what the "trick" for this particular series is. Proving $\int_0^1 \frac{(\ln(x))^5}{1+x} \mathrm{d}x = -\frac{31\pi^6}{252}$ I would like to show the following identity:     $$\boxed{ I :=  \int_0^1 \dfrac{(\ln(x))^5}{1+x} \mathrm{d}x = -\dfrac{31\pi^6}{252} }$$     Here is what I tried. The change of variables $u=1/x$ yields $$I= \int_1^{\infty} \dfrac{(\ln(x))^5}{1+1/u} \dfrac{1}{u^2} \mathrm{d}u = \int_1^{\infty} \dfrac{(\ln(x))^5}{u^2+u} \mathrm{d}u$$ Then $z=u-1$ gives $$I = \int_{0}^{\infty} \dfrac{(\ln(z+1))^5}{z^2+3z+2} \mathrm{d}z $$ with $z^2+3z+2=(z+1)(z+2)$. I wanted to use contour integration like , but I was not sure how to proceed in this case. Anyway, the computations of the residues (of which "well-chosen" function? Maybe something like ?) seem to be difficult.  I believe that we can generalize to $\frac{(\ln(x))^n}{1+x}$, or maybe even more (e.g. $\frac{(\ln(x))^n}{ax^2+bx+c}$). Related computations are: , , , .  Thank you for your detailed help. This is from a problem seminar and I need help figuring out the solution.  Four bugs, $A,B,C,D$ are initially placed at the corners of a unit square. From a given initial moment, all four crawl simultaneously at one and the same speed $s&gt;0$, $A$ towards $B$, $B$ towards $C$, $C$ towards $D$, and $D$ towards $A$, with each heading at every instant along the line joining it with its target.  Find a system of differential equations describing the trajectory of $A$.  Do the bugs eventually all meet at the center of the square? If so, how long did it take?  My attempt so far: $\def\grad{\mathbf\nabla}$ $\newcommand{\norm}[1]{\left\Vert #1 \right\Vert}$ Call ${\vec x}_1,{\vec x}_2,{\vec x}_3,{\vec x}_4$  the positions in the plane of $A,B,C,D$ respectively. Then $$\grad {\vec x}_1 = \frac{{\vec x}_2-{\vec x}_1}{\norm{{\vec x}_2-{\vec x}_1}}s$$ $$\grad {\vec x}_2 = \frac{{\vec x}_3-{\vec x}_2}{\norm{{\vec x}_3-{\vec x}_2}}s$$  $$\grad {\vec x}_3 = \frac{{\vec x}_4-{\vec x}_3}{\norm{{\vec x}_4-{\vec x}_3}}s$$  $$\grad {\vec x}_4 = \frac{{\vec x}_1-{\vec x}_4}{\norm{{\vec x}_1-{\vec x}_4}}s$$  with ${\vec x}_1(0) = (0,0),\  {\vec x}_2(0) = (0,1),\ {\vec x}_3(0) = (1,1),\ {\vec x}_4(0) = (1,0)$.  I have noticed that the sum of the gradients is 0, but I don't know if that is helpful or not. Can someone help me figure this problem out? How to create & execute a script file A ring element with a left inverse but no right inverse? Can I have a hint on how to construct a ring $A$ such that there are $a, b \in A$ for which $ab = 1$ but $ba \neq 1$, please? It seems that square matrices over a field are out of question because of the determinants, and that implies that no faithful finite-dimensional representation must exist, and my imagination seems to have given up on me :) Comment hint not disappearing when I start to type comment If I click "add comment", the comment hint (placeholder; "Request clarification or add information.") is not a hint, but editable text. If I delete the text and click outside of the comment then the hint appears as it should and when I click back into the comment box the hint disappears as it should.   I am on Internet Explorer 10.0.7.  Am I just oblivious and this is how it has always been (having to delete the comment hint), or is this a bug? How to make this curly 'R' (ℛ)? Which package has a similar looking fancy R or does anyone know how to make one? (Note: the line underneath the R is just the notebook paper... this is from a scanned set of notes). Regex to match only letters I'm working on a new edition of a book which uses a very unusual style of bibliography: Entries are sorted in author-year fashion, but then numbered per author or group of authors, e.g.:  Milnor, J.:    1. Construction of universal bundles: I, Ann. Math., (2)63:272-284 (1956).    2. Construction of universal bundles: II, Ann. Math., (2)63: 430-436 (1956).    3. On manifolds homeomorphic to the 7-sphere, Ann. Math., (2)64: 399-405       (1956).    4. The theory of characteristic classes, mimeographed, Princeton University,       Princeton, N.J., 1957. Milnor, J., and M. A. Kervaire:    1. Bernoulli numbers, homotopy groups, and a theorem of Rohlin, Proc. Intern.       Congr. Math., 1958. Milnor, J., and E. Spanier:    1. Two remarks on fibre homotopy type, Pacific J. Math., 10: 585-590 (1960).   Citations are formatted as Milnor [3], and so on.  Is there any bibtex style for something strange as this? Or can this type of bibliography be created with biblatex without too much coding? The screenshot below says it all, really. The object is offset in both the X and the Z axes, though only the X axis says 1. No other modifiers are on it, no constraints, no locked axes, and I can't think of anything else that would affect this. How can I make it stop doing this? How can I reject all changes in a Linq to SQL's DataContext? On Linq to SQL's DataContext I am able to call SubmitChanges() to submit all changes.  What I want is to somehow reject all changes in the datacontext and rollback all changes (preferable without going to the database).  Is this possible? How do you reset timers? I tried out the clock setting cheat on a throw-away vault but somehow it also messed up my real one so now they both have 3000+ hours on radio station and 70d+ on returning wastelanders..   Any way to reset all the timers to default?  For some reason my phone refuses to change time at all anymore.. Is it wrong to place the  tag after the  tag? Checking from shell script if a directory contains files From a shell script, how do I check if a directory contains files?  Something similar to this  if [ -e /some/dir/* ]; then echo "huzzah"; fi;   but which works if the directory contains one or several files (the above one only works with exactly 0 or 1 files). Is there a better way to do optional function parameters in JavaScript? I've always handled optional parameters in JavaScript like this:  function myFunc(requiredArg, optionalArg){   optionalArg = optionalArg || 'defaultValue';    // Do stuff }   Is there a better way to do it?  Are there any cases where using || like that is going to fail?