Self-invoking function jQuery
What is the purpose of this? (function ($) { //function code here })(jQuery);
\pdfendlink ended up in different nesting level than \pdfstartlink pc ram memory 2x1GB or 1x2GB I don't know if it's the right place to ask but can somebody advise me for buying a ram memory for my computer.  I have a Dell Vostro 200 with 1GB of RAM and 667MHz. (2 x 512MB)  I want to buy raise the amount of RAM but I'm confused whether to buy 1 x 2GB or 2 x 1GB  I know it's the same for the available amount of memory but is ther a difference maybe in the clock speed so that 2 x 667MHz will be better than 1 x 667MHz. or maybe accessing one single memory slot will be faster and better than accessing two slots.  Please anyone helps. Continued fraction of a square root If I want to find the continued fraction of $\sqrt{n}$ how do I know which number to use for $a_0$? Is there a way to do it without using a calculator or anything like that? What's the general algorithm for computing it? I tried to read the wiki article but was overwhelmed and lost. I tried Googling but couldn't find a website that actually explained this question.  If anyone has a good site that answers these questions either, please let me know. Thanks! How do I get a block with data to place myself? Why isn't the gamma function defined so that $\Gamma(n) = n! $? As a physics student, I have occasionally run across the gamma function  $$\Gamma(n) \equiv \int_0^{\infty}t^{n-1}e^{-t} \textrm{d}t = (n-1)!$$  when we want to generalize the concept of a factorial.  Why not define the gamma function so that   $$\Gamma(n) = n!$$  instead?  I realize either definition is equally good, but if someone were going to ask me to choose one, I would choose the second option.  Are there some areas of mathematics where the accepted definition looks more natural?  Are there some formulas that work out more cleanly with the accepted definition? How can I underline a single word with LaTeX? Given a simple paragraph, how do I underline a word in that paragraph?  (Note: I post this here because it wasn't really obvious using google or this site and my TexNicCenter is somehow missing this highlighting option.) My (very simple) question to a friend was how do I prove the following using basic trig principles:  $\tan75^\circ = 2 + \sqrt{3}$  He gave this proof (via a text message!)  $1. \tan75^\circ$   $2. = \tan(60^\circ + (30/2)^\circ)$  $3. = (\tan60^\circ + \tan(30/2)^\circ) / (1 - \tan60^\circ \tan(30/2)^\circ) $  $4. \tan (30/2)^\circ = \dfrac{(1 - \cos30^\circ)}{ \sin30^\circ}$    Can this be explained more succinctly as I'm new to trigonometry and a little lost after (2.) ?    EDIT  Using the answers given I'm almost there:   $\tan75^\circ$    $\tan(45^\circ + 30^\circ)$   $\sin(45^\circ + 30^\circ) / \cos(45^\circ + 30^\circ)$   $(\sin30^\circ.\cos45^\circ + \sin45^\circ.\cos30^\circ) / (\cos30^\circ.\cos45^\circ - \sin45^\circ.\sin30^\circ)$    $\dfrac{(1/2\sqrt{2}) + (3/2\sqrt{2})}{(3/2\sqrt{2}) - (1/2\sqrt{2})}$   $\dfrac{(1 + \sqrt{3})}{(\sqrt{3}) - 1}$   multiply throughout by $(\sqrt{3}) + 1)$   Another alternative approach:   $\tan75^\circ$    $\tan(45^\circ + 30^\circ)$   $\dfrac{\tan45^\circ + \tan30^\circ}{1-\tan45^\circ.\tan30^\circ}$   $\dfrac{1 + 1/\sqrt{3}}{1-1/\sqrt{3}}$   at point 6 in above alternative $pq\mid pn^q+qn^p+kn$ for some $k,\,$ if $p,q$ are primes Which groups have precisely two automorphisms Which groups $G$ have precisely two automorphisms, i.e., precisely one non-trivial automorphism?  Examples: $G= C_3, \mathbf{Z},\ldots$.  I think $G$ has to be abelian. In fact, we have $ \vert G\vert \geq 3$. Therefore, if $G$ is not abelian, we have at least two non-trivial inner automorphisms.  If we can show that $G$ is cyclic the above examples are all of them. Prove that every terms of a sequence defined by a recurrence relation is a perfect square. I would like to draw a squiggly line with an arrow somewhere in the middle of it. TikZ has a pathmorphing decoration that draws a squiggly line and a markings decoration to place an arrow tip. So a solution would be to use them together:  \documentclass{article} \usepackage{tikz} \usetikzlibrary{decorations,decorations.pathmorphing,decorations.markings} \begin{document}  \begin{tikzpicture}  \draw[          decoration={snake},          decorate,          postaction={decoration={markings,mark=at position 0.6 with {\arrow{>}}},decorate}      ]         (0,0) -- (2,0); \end{tikzpicture}  \end{document}   Unfortunately this does not work and results in  ! Dimension too large. &lt;to be read again&gt;                     \relax  l.11         (0,0) -- (2,0);   I suspect there is an infinite recursion going on somewhere.  Is there a workaround? If not, is there a different simple solution to the problem?  (Note: This is probably related to my previous question ) Does COVID-19 have a case fatality rate of 41%? Is this formula correct? According to the data on the , as of 3rd February 2020 there were 17491 confirmed cases of COVID-19 globally, 536 total recoveries and 362 deaths. From my non-expert calculation this implies a mortality rate of:  (Nd / (Nd + Nr)) * 100 = 41%  where:  Nd is the total number of deaths, Nr is the total number of full recoveries.  This leaves 16593 people still suffering from the disease who have neither recovered or died.  This is in stark contrast to the publicly disseminated value of ~2% mortality, so have I made a mistake in my calculation or assumptions, or is COVID-19 much more dangerous than commonly claimed?    [After a helpful discussion in the comments, 'mortality rate' is not the correct term to use here, instead I should say ''.] Intersection of open affines can be covered by open sets distinguished in *both*affines Suppose $X$ is an arbitrary scheme and $U \cong \operatorname{Spec} A$ and $V \cong \operatorname{Spec} B$ are affine upon subsets of $X$.  It's not true in general that $U \cap V$ is affine, so if we want to prove basic results about general schemes (e.g. the stuff in section II.3 of Hartshorne), we need some technical means of understanding what goes on on the intersections of open affines.  I've heard that this can be done by covering $U \cap V$ with open sets which are distinguished in both $U$ and $V$, i.e. sets $W \subseteq U \cap V$ with $W \cong \operatorname{Spec} A_f \cong \operatorname{Spec} B_g$ for some $f \in A$ and $g \in B$.  I'm having trouble actually proving this.    So, questions:   Is this actually true? If so, how are these sets constructed? DES-X , computation load and storage Lately I've been seeing this cookie popup that blocks a lot of the screen.  When I try to do the &quot;manage cookies&quot; thing, all it shows me are several categories, with a green oval containing a black circle to the right of each.  Clicking on that oval makes it disappear.  Clicking on the same spot again makes it reappear.  But I see no indication as to which state is off or on. So how can I make this popup go away, never to bother me again?  Or failing that, could you at least provide some indication as to what those buttons do?  Like maybe simple text saying &quot;Off&quot; or &quot;On&quot;? How to give an image or video a TV screen effect? If $$S=\frac{1}{1+1^2+1^4}+\frac{2}{1+2^2+2^4}+\cdots+\frac{n}{1+n^2+n^4}\,$$ find the value of $14S$.  The question can be simplified to:  Find $S=\sum\limits_{k=1}^n\,t_k$ if $t_n=\dfrac{n}{1+n^2+n^4}$.  As $1+n^2+n^4$ forms a GP, $$t_n=\frac{n(n^2-1)}{n^6-1}\,.$$ But I can't figure out how to solve further. It would be great if someone could help. Prove that if $n$ is a composite, then $2^n-1$ is composite. Not sure if I'm doing this correctly but this is what I've done:  Assume that $n$ is composite and suppose $2^n-1$ is a prime for $n \gt 2$. Then, $2^n-1 = 2k$ for some $k \in \Bbb Z $, $\forall n$.  But this would be a contradiction since $n \gt 2$.  I'm not sure if this a correct proof.  EDIT: I realized that it's to prove $2^n - 1$ NOT $2^{n-1}$ so my attempt above is completely wrong. I have searched, but not found anything on this. I am looking for a functionality in bash, using a terminal.  Way back when, I had a user on a debian system, and a friend set me up with a convenient history search feature (I believe I used tcsh then), where I would type the beginning of a previous command, hit up-arrow, and it would do a search, based on the partial string.  E.g. if my history is:  ./script.pl ./script.pl arg1 cat output cat output | grep yada   And I type ., and press up-arrow, it would show me: ./script.pl arg1. Press it again and it would show ./script.pl, etc.  Very much like it would perform a grep on .bash_history. Is there a way to get this functionality? Is $\mathbb{R}^\omega$ endowed with the box topology completely normal (or hereditarily normal)?