The minimum amount of charge possible is that of quarks. But it also has mass. Why is there no charge without mass? Or is it there?
Are there any massless (zero invariant mass) particles carrying electric charge?  If not, why not? Do we expect to see any or are they a theoretical impossibility?
Essentially, I wonder that if X is a plural noun, should we use a plural or singular verb in a sentence such as "X are a subject that [verb] ..."? I believe that we should always use the singular verb form there (for example, "Eatable flowers are a subject that comes up ..."). However, I was surprised to find this sentence on the  page:     Eatable flowers are a subject that come up in almost all cooking classes eventually and I am a big fan of them.   as well as this on Google Books:     Tools are a subject that come up at our house from time to time.   I think they are typos, but I would like a double check to be sure. Story about encounter with hostile aliens This is a short story I read in the late 80s or early 90s in an anthology or collection.  Here are the plot points I remember:   A human spaceship encounters a ship with hostile aliens (HA). There may be friendly aliens (FA) on board the human spaceship A human (or perhaps FA) telepath scans the HA and finds they are hostile and bent on conquest of other races The captain and crew decide on a bluff: pretend they are from a large federation of many species, one so big the HA will become discouraged and drop their plans of conquest They invite one or more HA on their ship To pretend that there are many (more) races in their federation, they do things like put a fake control panel in the ships aquarium and claiming the fish in them are one of the races in their federation The HA can't conceive of multiple races cooperating and are convinced there must be some race on top controlling it all. If not, they can just be conquered one at a time This goes on for a little while until, seeing their plan isn't working (via their telepath) the humans change their plan so that when      the ship's cat (so far unseen by the HA) walks in the room, one of the humans loudly calls "The CAT!" causing everyone to stand rigidly at attention while the cat walks around more or less ignoring everyone and everything the way cats do. Having seen the "top dog" and the rigid discipline and fear he instills in everyone else, the aliens "realize" the humans are deluded into thinking all races are equal members in their 'federation", the cats are really in control of a huge empire, and they should not be messed around with. "No worthy mechs found" when trying to relay email to Gmail using Postfix I've been trying to configure email to forward to Gmail, using Postfix to relay email to smtp.gmail.com. However, I'm failing to get it to authenticate with smtp.gmail.com, which is a rather vital prerequisite to getting anything working…  The mail logs show only:  Oct 29 15:50:14 gsnedders-1 postfix/master[6596]: daemon started -- version 2.7.1, configuration /etc/postfix Oct 29 15:50:19 gsnedders-1 postfix/pickup[6598]: EBA1F78750: uid=1000 from=&lt;gsnedders&gt; Oct 29 15:50:19 gsnedders-1 postfix/cleanup[6603]: EBA1F78750: message-id=&lt;20111029145019.EBA1F78750@mail.gsnedders.com&gt; Oct 29 15:50:19 gsnedders-1 postfix/qmgr[6599]: EBA1F78750: from=&lt;gsnedders@gsnedders.com&gt;, size=324, nrcpt=1 (queue active) Oct 29 15:50:19 gsnedders-1 postfix/cleanup[6603]: F2D557874F: message-id=&lt;20111029145019.EBA1F78750@mail.gsnedders.com&gt; Oct 29 15:50:19 gsnedders-1 postfix/local[6605]: EBA1F78750: to=&lt;me@gsnedders.com&gt;, orig_to=&lt;me&gt;, relay=local, delay=0.04, delays=0.03/0.02/0/0, dsn=2.0.0, status=sent (forwarded as F2D557874F) Oct 29 15:50:19 gsnedders-1 postfix/qmgr[6599]: F2D557874F: from=&lt;gsnedders@gsnedders.com&gt;, size=454, nrcpt=1 (queue active) Oct 29 15:50:19 gsnedders-1 postfix/qmgr[6599]: EBA1F78750: removed Oct 29 15:50:20 gsnedders-1 postfix/smtp[6606]: warning: SASL authentication failure: No worthy mechs found Oct 29 15:50:20 gsnedders-1 postfix/smtp[6606]: F2D557874F: SASL authentication failed; cannot authenticate to server smtp.gmail.com[74.125.157.108]: no mechanism available   And the postfix config is:  relayhost = [smtp.gmail.com]:587  smtp_use_tls = yes smtp_sasl_auth_enable = yes smtp_sasl_password_maps = hash:/etc/postfix/sasl/passwd smtp_sasl_security_options = noanonymous  smtp_tls_eccert_file = smtp_tls_eckey_file = smtp_tls_security_level = may smtp_tls_CAfile = /etc/postfix/cacert.pem smtpd_tls_received_header = yes tls_random_source = dev:/dev/urandom smtpd_tls_security_level = may Determine the Galois group of $\mathbb{Q}(\sqrt{a+b\sqrt{d}})$ Suppose $L=\mathbb{Q}(\sqrt{a+b\sqrt{d}})$,($d$ and $a+b\sqrt{d}$ are square free algebraic integers) when is $L/\mathbb{Q}$ a normal extension? When does $Aut(L/\mathbb{Q})=\mathbb{Z}/4\mathbb{Z}$ or $Aut(L/\mathbb{Q})=\mathbb{Z}/2\mathbb{Z}\times \mathbb{Z}/2\mathbb{Z}$? Overfull box and broken pagination with page that contains only section headings How did Stannis's army get north of the wall? If Mance Rayder had to attack Castle Black to use the tunnel to get through the Wall and get out of the north, how did Stannis get his army across the Wall into the north without anyone knowing? If there was another way over the Wall wouldn't the wildings go that way too? Sum and Product of Infinite Radicals Why is setting a variable before a command legal in bash? I've just encountered several answers such as to  that use the construct:  while IFS=, read xx yy zz;do     echo $xx $yy $zz done &lt; input_file   where the IFS variable is set before the read command.  I've been reading through the  but can't figure out why this is legal.  I tried  $ x="once upon" y="a time" echo $x $y   from the bash command prompt but got nothing echoed. Can someone point me to where that syntax is defined in the reference that allows the IFS variable to be set in that way? Is it a special case or can I do something similar w/ other variables? An  is defined as $p = q\times d$ (for two point charges $\pm q$ separated by a distance $d$).    What is the physical meaning of this quantity?  Why does the direction of the electric dipole moment go from the negative charge to the positive charge? Another way of saying this, why electric dipole moment is a vector quantity? Finding the 1st three derivatives of a function and plotting all four curves Is there any efficient algorithm for finding subgroups of a given finite group? I am implementing an algorithm which finds every subgroup of given group.  Here's my algorithm.  Let $G$ be a group of order $n$ with elements $g_1,\cdots,g_n$.  Then I consider each $\langle g_i\rangle $ which are all cyclic subgroups of $G$.  Of course, if $\langle g_i\rangle =\langle g_j\rangle $, we append only $\langle  g_i\rangle $ into our result set.  We call all distinct subgroups of the form $\langle g_i\rangle $ to be the first-generation. (Note that the number of the first-generation subgroups is at most $n$.)  To get $(i+1)$-th generation from $i$-th generation inductively, we construct the subgroup $S$ from each two elements of $i$-th generation $S_1, S_2$ to be  $$S=\langle S_1,S_2\rangle .$$  Obviously, if generated subgroup is already in previous generations, we do not call it $(i+1)$-th generation, hence every subgroups of $G$ has the unique generation number.  We do this construction until the number of the typical generation subgroups to be $0$, since we get all subgroups of $G$.  This works perfectly to any groups, but unfortunately, it is not fast although I implemented additional steps to avoid repeated computation.  So I searched some other algorithms but they are all vague to understand.  One of the algorithm is called the cyclic extension algorithm, but I can not get it easily unless I have studied some backgrounds for this method.  If you have enough knowledge about the cyclic extension algorithm or some other algorithms, please give me an easy explanation. I am in undergrad. course of math dept. Thanks. Workflow for converting LaTeX into Open Office / MS Word Format Which choice of line-breaking parameters gives the minimum number of lines Georeferencing vector PDF/SVG/DXF linework using QGIS? I want to  create a small web application to visualize election results on a per poll site basis for my city. The result is going to be very similar to what has been done for Berlin . Hopefully this helps in understanding what I'm going for.  The election raw data on the scale I need is published and I know how to visualize this on the grounds of a shapefile with separate polygons lining out the election districts. My problem is - as you could probably guess - that something like this doesn't already exist.  What actually is published though, is a PDF file lining out the borders of the districts I'm interested in:   I'm not keen on redrawing the linework myself, so I'm looking for a way to make a shapefile out of this. Luckily, the PDf includes the linework as separate vector objects, I extracted these into a SVG file:   I already tried converting the SVG to a DXF and importing it into qgis 2.0.1. This actually works, but (as expected) places the vectors in the atlantic ocean and I can't find a way to edit it and fix this.  What can I do now to georeference these vectors with open source tools and finally produce a shapefile? Let $R$ be a commutative ring.  The nilradical $\text{nil}(R)$ is the set of all nilpotent elements, and it is the intersection of all the prime ideals of $R$.  Is the following true in the polynomial ring? $$\text{nil}(R[X])=(\text{nil}(R))[X]$$  Any polynomial in the right hand side has all its coefficients nilpotent in $R$, hence also in $R[X]$, and therefore it is nilpotent in $R[X]$ as the sum of nilpotent elements.  The other inclusion is not clear to me.  Is there a counterexample? How best to determine if an argument is not sent to the JavaScript function I have now seen 2 methods for determining if an argument has been passed to a JavaScript function. I'm wondering if one method is better than the other or if one is just bad to use?   function Test(argument1, argument2) {       if (Test.arguments.length == 1) argument2 = 'blah';        alert(argument2);  }   Test('test');   Or   function Test(argument1, argument2) {       argument2 = argument2 || 'blah';        alert(argument2);  }   Test('test');   As far as I can tell, they both result in the same thing, but I've only used the first one before in production.  Another Option as mentioned by :  function Test(argument1, argument2) {     if(argument2 === null) {         argument2 = 'blah';     }      alert(argument2); }   As per Juan's comment, it would be better to change Tom's suggestion to:  function Test(argument1, argument2) {     if(argument2 === undefined) {         argument2 = 'blah';     }      alert(argument2); } How to manage a redirect request after a jQuery Ajax call I'm using $.post() to call a servlet using Ajax and then using the resulting HTML fragment to replace a div element in the user's current page. However, if the session times out, the server sends a redirect directive to send the user to the login page. In this case, jQuery is replacing the div element with the contents of the login page, forcing the user's eyes to witness a rare scene indeed.   How can I manage a redirect directive from an Ajax call with jQuery 1.2.6? My Visual Studio (2008) Editor has stopped to underline Errors (this nifty wavy red lines). I can't really tell when, but it can be related to the installation of .Net Framework 3.5 SP 1 or the MVC Beta (which I guess is unlikely). Furthermore have I installed and uninstalled both CodeRush and Resharper for evaluation purposes (decided not to keep either one of them).  Does anyone know the problem and how to restore this functionality again? I have a question about using the phrase "some kind of _".  Is it incorrect to say "some kind of + plural noun"?     For example, is it wrong to say "are these rock-like things some kind of chocolates?"   I didn't use "kinds" and that kind of adds to my question. Is "kind" always plural, like "some kinds of chocolates"? Because although I'm using "some", it feels like "kind" shouldn't be a countable noun.  Anyway, I don't think I've heard of "some kind of + plural", but I think it makes more sense then using singular, since I think chocolates are countable. Please help! I need to build a list of files present in a directory but also pass in a file containing a list of directories to exclude.  I've seen the below suggestion but I've had no luck with it when it comes to the type flag:  find $dir_name $(printf "! -name %s " $(cat $exclude_file))   Is there a way I can do it or will I need to create the entire list and then work through it removing ones that partially match ones in the exclude directory.