How to set default footnote linespacing? Now for each footnote I have to write  \footnote{\onehalfspacing ...}   But I would like to set the line spacing once.  I guess its possible to use \renewcommand{\footnote}{...}. But I don't know how to redefine the command.
I'd like to "add to" an existing command by writing something like  \renewcommand{\somecommand}{\begin{something}\somecommand\end{something}}   but (not surprisingly) I get errors about being "too deeply nested".  Is there a way to take an existing command, add to it (by appending or prepending additional commands or text), and then have that "augmented" command replace the existing command?
Why is Git not found after installing OS X Lion? Given some potential $V$, we have the eigenvalue problem   $$ -\frac{\hbar^2}{2m}\Delta \psi + V\psi = E\psi $$   with the boundary condition   $$ \lim_{|x|\rightarrow \infty} \psi(x) = 0 $$   If we wish to seek solutions for   $$ E &lt; \lim_{|x|\rightarrow \infty}V(x), $$   I find textbooks like Sakurai and others assert that (without proof) set of all such eigenvalues $E$ that admits nontivial solutions is discrete, which gives us liberty to index them with natural numbers (principal quantum numbers). Can anyone help me with a little elaboration of this mathematical fact ? As a student of mathematics, I know that compact operators have discrete spectrums, so for the operator $ T : L^2 \rightarrow L^2 $given as  $$ T(\psi) = -\frac{\hbar^2}{2m}\Delta \psi + V\psi. $$   Are there methods to show that $T$ is compact? Or possibly other ways to establish discreteness of its eigenspectrum? Matrix in a matrix I would like to draw a matrix with top left, top right, bottom left and bottom right blocks. The top left should be a 3x3 matrix with numerical entries, the top right is 0, the bottom left is 0 and the bottom right is just a "single" entry uJ. Here is my attempt.    $ \left[ \begin{array}{c|c} [\begin{array{c|c|c} 0 &amp; 0 &amp; 2\mathrm tr(MM^{*}) \\ 0 &amp; 0 &amp; -ua \\ u &amp; -ua &amp; 0 \end{array}]     &amp;  0\\ \hline 0 &amp; uJ  \end{array}\right]. $    I would like to emphasize that the non-top-left entries are not just single entries, but blocks, so I do not want to just make a 4 by 4 matrix with vlines and hlines and additional 0's. Rate limit suggested edits We need a hard rate limit on suggested edits, to limit the damage someone can do with blasting the review queue with minor edit suggestions.  Case in point:  peppered the site with a whopping 133 tag-only edit suggestions in 2 hours and 15 minutes. That's one edit every minute on average, but towards the end he was entering a new suggestion every 20 seconds. He only stopped because a  drew enough rejections to have him banned from entering more.  If there was a limit to the number of suggested edits you can enter in a time period we could have stopped this guy earlier. No &lt;2k user needs to edit hundreds of tags across that many questions in 2 hours time.  Considerations   There are cases where a retag drive or tag burninate justifies editing a larger number of posts, but I'd be fine if such tasks were limited to people with 2k+ reputation. A retag or burninate job requires a minimal engagement with the community to know when they are justified anyway. The suggested edit review process, by itself, was clearly not enough to stop this barrage. It cannot be seen as a rate limiting measure, at least not as a sufficiently efficient one.  The vast majority of the edits made in the above example were too minor, leaving spelling, grammar and formatting mistakes in the post untouched. The user was going too fast to pay attention to such details anyway. Yet this user has 98 approved edit suggestions, but all but 6 or 7 I'd have rejected as too minor, so the review process itself is broken.   What should be limited   The number of review votes reviewers have is already limited; I burned through 20 reviews in short order just reviewing the suggestions from just this one user. Certainly the number of unreviewed suggestions should be limited to let reviewers catch up with a user like this. I'd say having 20 outstanding suggested edits pending review is plenty. Suggested edits should be made with some consideration; we don't want minor edits, so if you are suggesting more than 20 in an hour (that's 1 every 3 minutes) you are not improving posts anymore, you are gaming the system to gain reputation. Hyperref - Token not allowed Possible Duplicate:          The following code:  \subsection{The classes $\mathcal{L}(\gamma)$}   generates the errors:  Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref)                removing `math shift' on input line 1938.   Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref)                removing `\gamma' on input line 1938.   Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref)                removing `math shift' on input line 1938.   What do I have to do to keep \gamma in the subsection, so that it is also listed in the table of contents? Coming from a programming background, where should I start to learn web design? I'm a web developer mainly working in front end developing. My main fields are HTML5, CSS3 and Flash ActionScript 3.0.  Here in Iran, teamwork means nothing for most of the people, but I think it's the most important aspect of our work, especially in web design.   I have poor skills in graphic design and UI design. I always have to work with graphic designers for my websites. They are usually good and skilled designers. But they are all print designers and unfortunately they know nothing about the web and designing for it.  For example, one of the designers that I work with most of the time is a great designer and he won a couple awards for his logo and poster designs. However, he knows nothing about the web and most of my time is spent explaining to him how things work on the web, i.e. in what size he should work, using pixels instead of centimeters, and so on... After all he is a print designer, not a web designer. They often think everything is static and constant, not in motion.  So the best way to work around this is to improve my skills in graphical designing. I just want to be able to design good layouts, make good color selections, and etc for my websites. I do not want to design illustrations and do heavy graphical works. Just design websites with no Photoshop illustrations like posters and etc.  What do you do for your graphic works, and if you do them yourself, which books or references do you suggest I read? Where should I start? The well-known fable of an astronaut sending signals out to an external observer while falling toward an event horizon states that the time lapse between such signals becomes greater even if in the astronaut sends them out periodically (as judged in his inertial frame). When viewed from earth and weighing time-dilation due to the gravitational field of the collapsing star, how is it possible that a black hole can form in finite time (for any external observer) if it takes an infinite amount of time to "see" events occurring at the event horizon? Let $f: \Bbb C \to \Bbb C$ be an entire (analytic on the whole plane) function such that exists $\omega_1,\omega_2 \in \mathbb{S}^1$, linearly independent over $\Bbb R$ such that: $$f(z+\omega_1)=f(z)=f(z+\omega_2), \quad \forall\,z\in \Bbb C.$$Prove that $f$ is constant.   The intuition seems clear to me, we have the three vertices of a triangle given by $0$, $\omega_1$ and $\omega_2$. All points in the plane are one of the vertices of that triangle under a suitable parallel translation. The constant value will be $f(0)$, fine. Throwing values for $z$ there, I have found that $$f(n\omega_1) = f(\omega_1) = f(0)=f(\omega_2) = f(n\omega_2), \quad \forall\, n \in \Bbb Z.$$  I don't know how to improve the above for, say, rationals (at least). Some another ideas would be:   Checking that $f' \equiv 0$. I don't have a clue of how to do that. Write $w = a\omega_1+b\omega_2$, with $a,b \in \Bbb R$, do stuff and conclude that $f(w) = f(0)$. This approach doesn't seem good, because I only have a weak result with integers above. Finding that $f$ coincides with $f(0)$ on a set with an accumulation point. This seems also bad: the set on with $f$ coincides with $f(0)$ by which I found above is discrete.    Nothing works and this is getting annoying... And I don't see how analyticity comes in there. I'll be very thankful if someone can give me an idea.  (On a side note.. I know that this title is not informative at all. Feel free to edit if you come up with something better.) Let's consider a polynomial ring of single variable. One can define them informally by saying $P(X)=\sum_{i=1}^n a_n X^n$ while $X$ is an indeterminate variable. However, since mathematics is based on first-order logic, one can only talk about something that actually exists (as a set). So as its name says, indeterminate variable is not a sentence in $ZFC$. Nevertheless, we can formally define a polynomial ring $R[X]$ as a subset of $R^\omega$ whose support is finite. ($R$ is a commutative ring with unity) Just like a single variable, I want to know what would be the formal definition of a polynomial ring of several variables. What would be a formal definition? === I have figured out a candidate. That is,  Candidate for a &quot;Definition of a polynomial ring $R[X_1,...,X_n]$&quot;. ($R$ is a commutative ring with unity) Let $R[X_1,...,X_n]$ be the set of all functions $f:\omega^n \rightarrow R$ whose support is finite. Define $(f+g)(a,b,c)=f(a,b,c)+g(a,b,c)$ and $(f•g)(a'',b'',c'')=\sum_{a+a'=a''} f(a,b,c)•g(a',b',c')$ (Note that in this way, $+,•$ are well defined.) Then, it can be checked that $(R[X_1,...,X_n],+,•)$ is a ring.  Is this a formal definition of a polynomial ring? Stack Overflow 'review' button is slow, and test questions are slower In the last few weeks, the 'review' button at the top of stackoverflow.com has become very slow. I can count to 20 in some cases (but not always).   In a perhaps related phenomenon, I believe that test questions in the queue often trigger a level of extreme slowness all their very own. If I click on a queue, or 'next' after a review, and the periods sit there throbbing for a good long time, chances are that what will show up will be a review audit. I have data with a column containing a number value, and I want to divide the value of each feature by the total sum of all the values in the column (to get a percentage).  So I would like to know if there is some simple syntax in the QGIS field calculator to get the sum of a column, preferably without resorting to for loops and what not.    I have a shapefile where feature A has the value X in column B. How can I summerize the values for all features in column B in order to divide value X to get a percentage for each feature? Prove that 1/2 + 1/4 + 1/8 ....... = 1 I've often heard that instead of adding up to a little less than one, 1/2 + 1/4 + 1/8... = 1. Is there any way to prove this using equations without using Sigma, or is it just an accepted fact? I need it without Sigma so I can explain it to my little sister.  It is not a duplicate because this one does not use Sigma, and the one marked as duplicate does. I want it to use variables and equations. How does the eye perform the equivalent of white balance? Possible Duplicate:          How does the eye perform the equivalent of white balance? Why is the camera not able to replicate it? I have the following validation rule:  AND(  $Profile.Name &lt;&gt; 'System Administrator',  OR(  ISPICKVAL(PRIORVALUE(Level__c), "Archived"),  ISPICKVAL(PRIORVALUE(Level__c), "Closed")  )  )   This validation rule is on the opportunity object, and what I want to achieve is, if the picklist Level__c is either set to Archived or Closed, the opportunity record can only be edited by the System Administrator.  For some reason though, the validation rule also triggers, when I want to set the Level__c to Archived or Closed. But this is not what I want.   Any idea what's wrong with the validation rule? The value of $\lim_{n \to \infty}\int_{0}^{1}nx^ne^{x^2}dx$ The value of $\lim_{n \to \infty}\int_{0}^{1}nx^ne^{x^2}dx$ is _____ I tried by taking the odd $n$ values as in that case, the integral I suppose was easier to calculate. So, denote $I_n=n\int_{0}^{1}e^{x^2}x^ndx$, then we have : $I_1=\frac{e-1}{2},\\I_3=\frac{3}{2},\\I_5=5(\frac{e}{2}-1),\\I_7=7(3-e)$ Then I tried calculating (random) values using calculator as integration was getting cumbersome. $I_{31}=2.488$, $I_{51}=2.57$. I do not see any kind of recurrence so that I can find a general term for odd $n$. I also tried the method given . The idea was that since integral doesn't depend on $n$ considering $I(n)=\int_{0}^{1}e^{x^2}x^ndx$, then $I'(n)=\int_{0}^{1}x^n\ln(x)e^{x^2}dx$, but this also doesn't lead me to any conclusion as well. I believe I couldn't get to a proper approach to tackle this question. Can someone please help with the idea that involves in solving these type of questions? How to remove \n from a list element? Could someone please tell me what the symbol ringed in red represents?     I know it has ON Switch pointing to it, but the symbol has other lables in different parts of the document. Do file-extensions have any purpose (for the operating system)? I have been learning English for 7 years now, and I have read so many grammar books with rules, telling the difference between Present Perfect and Past Simple and I still find it hard to distinguish them.   On paper, it is easy, if it is not a certain (exact) time in the past without any time markers (yesterday, a month ago, etc) it is past simple. Yes, but outside the classroom it is really harder than this . I have heard many people speaking how they want to, mixing the tenses.   So, I will give these sentences which i have heard to be constructed differently, please, if someone can explain the difference to me.     Have you enjoyed the party? / Did you enjoy the party?      I have given the documents today. / I gave the documents today.      I have done this when I have revised it. / I did it when I revised it      What did you do today? / What have you done today ?   Is it possible to use past simple without mentioning a definite time in the past  (without the time markers)?     It has been 3 years since we moved house. / It has been 3 years since we have moved house.      I know him since we met each other/ I know him since we have met each other   Correct me if some of the sentences are grammatically wrong! I just made some minor edits to the text of .  I didn't edit the tags at all.  When I completed my edits, my edit showed as:    Now, I think those tags were present before I started my edit, and so were probably slipped in by the OP in their edit grace window.  I have no problem with that tagging, but I don't like seeing edits attributed to me that I didn't make.  So, what the heck?