Render is taking way too long
Why are my render times 30+ minutes, but other people's are ~3 minutes?
Is there a way to remove sites permanently from (my personal) Google search results? I regularly find sites that copy content from elsewhere (mailing lists, etc) while not providing any added value. Quite to the contrary, they are pretty heaped with ads.  I'd like to remove those sites as permanently as possible from my Google search results. Any ideas? Hadamard Product of $e^z-1$ Assuming the formulas $$\sin(z)=\frac{e^{iz}-e^{-iz}}{2i}\quad\text{and}\quad\frac{\sin(\pi z)}{\pi z}=\prod_{n=1}^\infty\left(1-\frac{z^2}{n^2}\right),$$ I want to find the Hadamard product of $e^z-1$. I think I've done the work correctly, but I end up having an extra factor of $2\pi i$ at the end (this is from Stein and Shakarchi's book and they list the answer for this particular problem). So, my work is \begin{align} e^z-1&amp;=e^{z/2}\left(e^{z/2}-e^{-z/2}\right)\\ \\ &amp;=e^{z/2}\left(e^{i(-iz/2)}-e^{-i(-iz/2)}\right)\\ \\ &amp;=2ie^{z/2}\left(\frac{e^{i(-iz/2)}-e^{-i(-iz/2)}}{2i}\right)\\ \\ &amp;=2ie^{z/2}\sin(-iz/2)\\ \\ &amp;=2\pi i ze^{z/2}\frac{\sin(-iz/2)}{\pi z}\\ \\ &amp;=2\pi i ze^{z/2}\frac{\sin\left(\pi(\frac{-iz}{2\pi})\right)}{\pi z}\tag{*}\\ \\ &amp;=2\pi i ze^{z/2}\prod_{n=1}^\infty\left(1-\frac{\left(\frac{-iz}{2\pi}\right)^2}{n^2}\right)\\ \\ &amp;=2\pi i ze^{z/2}\prod_{n=1}^\infty\left(1+\frac{z^2}{4n^2\pi^2}\right). \end{align}  The answer according to the book is $$e^z-1=e^{z/2}z\prod_{n=1}^\infty\left(1+\frac{z^2}{4n^2\pi^2}\right).$$Have I made a simple mistake in calculation, or are the two somehow compatible with each other?  Update: Thomas Andrews has pointed out a mistake in my infinite product formula. I've corrected that mistake.  $(*)$ The error occurs from this line to the next. Instead of multiplying and dividing by $z$, I should have multiplied and divided by $\frac{-iz}{2\pi}$. That would cause the appropriate cancellation. Selecting and manipulating CSS pseudo-elements such as ::before and ::after using javascript (or jQuery) Custom question lists April status update Previous posts:                           After a long hiatus, a new Custom Question Lists update is out with a fresh new design.  What's shipped?  If you are participating in the Custom Question List alpha (by ), you'll see some brand new UI components when viewing question lists:  New tab bar and editor    Based on your feedback, we decided to rethink the whole UI, removing some confusing and redundant components, and bringing back some much loved pieces.  The new design is closer to "the existing question lists with advanced options" than "a radically new experience".  Huge shoutouts to our new designer, , for making this new design possible and to  for picking up development while I was on sabbatical!  Some important notes for existing testers:   The summary is back in its rightful place next to the tab bar.  If bounty or unanswered filters applied, the summary provides a clearer explanation of what you're looking at, inspired by /unanswered. The "Filter" and "Sort" popovers are gone. Sort was too similar to the existing tabs, and Filter was a form in a popover. (how were you supposed to submit or cancel?)  Now there's a dedicated UI for filtering. The complex "Create" and "Edit" modals are gone.  Now you just configure your list with the same UI as if you were filtering and click "Save filter" when you're ready to save. You can preview your changes before updating a filter.  Editing a saved filter and clicking apply shows you your new options while remembering what filter you were looking at.  You can then click "Save filter" to either update your existing filter or create a new one. We handle responsive better.  The tab bar has been set up so it compresses more naturally on narrower browsers and mobile devices.   New sidebar widget    A new right-sidebar widget has been added, similar to Watched Tags, to give you more direct access to your saved lists.  This is where indicators will live in Phase 3 (which I swear we are actually going to ship).  Please give it a try.  If you have any questions, bugs, or feedback, you can reply to this post directly or add a new question with the  tag.  A wider alpha  Since we're nearing launch, we're expanding the alpha out to the whole network.  So feel free to try this out on any site you frequent, to help suss out any site-specific issues.  What's next?  As always, Phase 3 of this project is adding indicators for new content, now in the right sidebar widget.  There's increasing interest in this feature from Enterprise, so I do really expect this to ship and get out of Alpha sooner rather than later and this time, I mean it. How does a wizard or bard learn new spells? How to create a new object instance from a Type One may not always know the Type of an object at compile-time, but may need to create an instance of the Type.    How do you get a new object instance from a Type? Which is correct: "the below information" or "the information below"? I frequently see statements that refer to something later in the text that use a phrase such as "the below information". Is it more correct instead to say "the information below" (or "the following information")? In the sentence     What’s funny is Cat’s dry humour.   Wouldn’t it be better to put a comma after “funny”:     What’s funny, is Cat’s dry humour.   This question entails a (at the time of writing) heated discussion in the . Existence of a local geodesic frame Let $(M,g)$ be a Riemannian manifold of dimension $n$ with Riemannian connection $\nabla,$ and let $p \in M.$ Show that there exists a neighborhood $U \subset M$ of $p$ and $n$ (smooth) vector fields $E_1,...,E_n \in \chi (U),$ orthonormal at each point of $U,$ s.t. at $p,$ $\nabla_{E_i}E_j(p)=0.$  What I've found so far;  Let $V$ be a normal neighborhood at $p.$ Let $(W,x(x_1,...,x_n))$ be a local coordinate system at $p$ s.t. $x(W) \subset V.$  Let $\{X_i:=\frac{\partial}{\partial x_i}\}$ be the standard basis of $T_pM.$ By Gram-Schmidt, there exists an orthonormal basis $\{E_i\}$ of $T_pM.$ Consider the orthonormal frame $E_i(t),$ by parallel transporting $\{E_i(0)=E_i\}$ along a  a geodesic $\gamma :I \to M$ starting at $\gamma(0)=p$ and ending in $\gamma(1)=q,$ where $q \in V.$ This gives us an orthonormal frame at each point of $V.$ To satisfy the second condition, let $E_i(t)=\sum_{l}a_{li}X_l$ and  $E_j(t)=\sum_{s}b_{sj}(t)X_s.$ Then   $$\nabla_{E_i}E_j=\sum_{k}(\sum_{l,s} a_{li}(t)b_{sj}(t)\Gamma^k_{ls}+E_i(b_{kj}))X_k,$$  where $\Gamma^k_{is}$ are Christoffel symbols.   To have $\nabla_{E_i}E_j(p)=0,$ we must have $\sum_{l,s}a_{li}(0)b_{sj}(0)\Gamma^k_{ls}+E_i(b_{kj})(p)=0$ for each $k.$      How can I conclude the argument? Relationship between complex number and vectors How to overcome Acrobat Reader error 131 with a pdfLaTeX doc? I'm generating a PDF document with pdflatex (more precisely, latexmk invoked from TexMaker 3.4. My LaTeX install is TeXLive 20120719). I can read the document fine in Okular and Gmail's attachment preview, but a colleague that runs Acrobat Reader on Windows reports: "There was a problem reading this document (131)".  EDIT: The error disappears when using \usepackage[demo]{graphicx}, which puts black boxes instead of the real images. They are all PDFs, PNGs and JPGs. Instead of using demo, I added the code for a \demoincludegraphics command, which makes the file work in Reader when using it to replace the logo in the headers, as shown below. But enabling it (using \includegraphics instead of \demoincludegraphics) and removing everything else also works in Reader! There is some strange global interaction that makes the file appear broken to Reader when enabling all the graphics...  My code compiles fine, reason why I only attach the preamble and a simple text for a Minimal Working Example:  \documentclass[12pt,lettersize,twoside]{article}  \usepackage[utf8]{inputenc} \usepackage[spanish,es-tabla]{babel}   \usepackage[fixlanguage]{babelbib} \usepackage{amssymb,amsmath} \usepackage{graphicx}    \usepackage{array}    \usepackage{caption} \usepackage{subfig} \usepackage{rotating} \usepackage{booktabs} \usepackage{multirow} \usepackage{calc} \usepackage{stfloats} \usepackage{fixltx2e} \usepackage{url} \usepackage[colorlinks=true,linkcolor=blue,citecolor=red]{hyperref} \usepackage[all]{hypcap}  % Margins \usepackage[top=2cm, bottom=2cm, left=3cm, right=2cm]{geometry}  % Make header show up in the first page \makeatletter \renewcommand\maketitle{\par \begingroup     \renewcommand\thefootnote{\@fnsymbol\c@footnote}%     \def\@makefnmark{\rlap{\@textsuperscript{\normalfont\@thefnmark}}}%     \long\def\@makefntext##1{\parindent 1em\noindent             \hb@xt@1.8em{%                 \hss\@textsuperscript{\normalfont\@thefnmark}}##1}%     \if@twocolumn     \ifnum \col@number=\@ne         \@maketitle     \else         \twocolumn[\@maketitle]%     \fi     \else     \newpage     \global\@topnum\z@   % Prevents figures from going at top of page.     \@maketitle     \fi     \thispagestyle{fancy}\@thanks % was {empty} \endgroup \setcounter{footnote}{0}% \global\let\thanks\relax \global\let\maketitle\relax \global\let\@maketitle\relax \global\let\@thanks\@empty \global\let\@author\@empty \global\let\@date\@empty \global\let\@title\@empty \global\let\title\relax \global\let\author\relax \global\let\date\relax \global\let\and\relax } \makeatother  % Remove date field in title; Remove preceding vertical space \makeatletter \renewcommand{\@maketitle}{ \vspace{-3cm} \begin{center}% {\LARGE \@title}\\ \vspace{2mm}% {\@author} \end{center}% \par} \makeatother \makeatletter  % Demo includegraphic boxes \newcommand{\demoincludegraphics}[2][]{%   \setlength{\fboxsep}{-\fboxrule}% Remove frame separator/gap   \framebox{\rule{0pt}{100pt}\rule{150pt}{0pt}}% Framed box of 150pt x 100pt }  % Headers Config  \usepackage{fancyhdr} \pagestyle{fancy} \fancyhead{} \renewcommand{\headrulewidth}{0.4pt} \setlength{\headheight}{2.2cm}  \addtolength{\textheight}{-1.62cm} \fancyhead[LO,RE]{\demoincludegraphics[height=1.6cm]{logo-slogan}} \fancyhead[LE,RO]{}  % Footers Config \fancyfoot{} \renewcommand{\footrulewidth}{0pt} \fancyfoot[C]{\thepage}  % Notas al pie etiquetadas por simbolos   \renewcommand{\thefootnote}{\fnsymbol{footnote}}  \title{Doc Title} \author{My name}  \begin{document}  \maketitle  This is a test. It includes graphics and other floats.   \end{document}   EDIT: I found a workaround: Processing the generated pdf file through Ghostscript, as follows:   gs -dSAFER -dBATCH -dNOPAUSE  -sDEVICE=pdfwrite -sOutputFile=output.pdf input.pdf   where input.pdf is the file generated by pdfLaTeX, and output.pdf the one that will be readable by Adobe Reader and the rest of the PDF readers. This is Baby Rudin exercise 7 of Chapter 3. Prove that the convergence of $\sum{a_n}$ implies the convergence of $\sum{\sqrt {a_k} \over k}$ if $a_n \ge 0$.  Proof:  I will attempt to show that the cauchy criterion is met so $${\sum_{k=n}^m {\sqrt {a_k} \over k}} \le \epsilon $$ for all $n,m \le N_1$. Im disregarding the absolute value since its all positive terms.   Since $\sum{a_n}$ converges, we know that the $\lim \limits_{n \to \infty} a_n =0$ So there exists some $N_2$ such that for all $n \ge N_2$, $$   a_n \lt \ {{(m-n)}^2k^2(\epsilon)^2} $$ I am again disregarding the absolute values because its always positive Let N=max{$N_1,N_2$} then for all $n,m \ge N$ $$\sum_{k=n}^m {\sqrt {a_k} \over k} \le \sum_{k=n}^m {\sqrt {{(m-n)}^2k^2(\epsilon)^2} \over k} \le \sum_{k=n}^m{(m-n)(\epsilon)} = \epsilon $$  Maybe this is just crazy, should I just use Cauchy-Schwarz inequality and forget about this or could I possibly make this method work? how to run the dialog command with proccess Please look on my code – ( bash script )  I want to display both dialogs on the screen on the same time,   one dialog display the:  tail –f from - /var/log/proccess1.log  ,   and the second dialog display the:  tail –f from the file - /var/log/proccess2.log     but the sad fact is that I can display only one dialog and not both dialogs ( because when I run the first dialog , the second dialog will activate only if the first dialog will killed )   So I create process on the second dialog ( ….. ) &amp;    , in order to display both dialogs    But …. the second dialog create process number but not create the second dialog GUI , ( seems that when we create dialog with process , the process not send the dialog to standard output )  So how to  run the second dialog with process but send the dialog GUI to screen ? , or other solution in order to display both dialogs on screen  My code       #!/bin/bash       # this dialog will locate the tail box on the top of the screen      dialog --begin 15 10  --tailbox   /var/log/proccess1.log  13 125         # this dialog will locate the tail box down in the screen      ( dialog --begin 37 10  --tailbox   /var/log/proccess2.log    13 125 ) &amp; Can I disable pinch to show all open tabs in Safari? Where can I find Obsidian in the Pocket Edition? I have looked everywhere for lava or obsidian in 0.7.1. I've looked all the way from top to bottom and all around, in about a 100 block diameter, but I can't find any. Where can I get some? Function ereg() is deprecated Modify iPhone restrictions passcode Is there a way to change the restrictions passcode on an iPhone without restoring the phone? I haven't forgotten the passocde; I just want to change it. Derivation of the Partial Derangement (Rencontres numbers) formula I'm looking for the method by which the partial derangement formula $D_{n,k}$ was derived. I can determine the values for small values of N empirically, but how the general case formula arose still alludes me.  Any links/books or an explanation will be appreciated.  The formula is:  $D_{n,k} = {n \choose k}!(n-k)$  Links: What should I be teaching my two year old? My two year old daughter has never been to a daycare, so everything she knows is something that me, my husband, or her grandparents have taught her. She sees very little interaction with other kids her age, well, except for her 8 month old sister.   I am wondering what people, or even day care centers, teach two year olds. What do they do all day long? Presently, our daughter draws a lot - she has bathtub crayons, wax crayons for paper, and chalk for the driveway/sidewalk. She attempts to draw circles and lines. We try to teach her shapes and colors, and she has a rough idea of what they are. She plays with sand in the sandbox a lot, dumping sand all over her and her sister's head. She goes to her playhouse and uses the slide and the swing.   We sing songs together - the alphabet song or the numbers song. She is able to say the correct word when I say the phonic (i.e. if I say B, she'll say ball; if I say H, she'll say hat). She tries counting, but is still learning (she goes 1, 2, 6, 7, 8...). She enjoys building and destroying towers. We read books and I sing some nursery rhymes. She plays a toy piano and dances around to it. She plays with playdough, but most of the time it just ends up in crumbs everywhere.  She also watches TV - something I know most parents object to. She enjoys watching Dora, Finding Nemo, and Cinderella. She will sometimes watch LeapFrog phonics videos for alphabet and numbers.   I am not trying to give a resume for my daughter, but merely wondering is there something more that kids her age do? Is there something else that I should be teaching her? What do kids her age do at a daycare?   Thanks Is it appropriate to use the salutation "Dear All" in a work email? I have observed that in my work place, whenever a mail is sent to more than one person( like an information, meeting request or a notice etc.), the mail starts with the salutation "Dear All". This, somehow, doesn't seem correct to me. For me, a salutation should address the reader individually, at least in its singular form, as in "Dear Colleagues".  Am I correct in thinking that?