Size of printed photo
What resolution would be needed for a billboard advertisement?
Time-Stream Crossing and Forgetfulness In The Day of the Doctor, it's explained that the Doctor doesn't remember having interacted with himself, and if he interacts with a future version of himself, the younger version forgets.  But in Time Crash, 10th solves the problem of the TARDISes occupying the same space because he remembers himself doing it from when he was 5th.  If this is true, 5th wouldn't have wondered whether or not he was going to regenerate when he did.  Does the TARDIS occupying the same space with itself re-instate those memories? Or is it just possible that I'm asking a ridiculous question that will never have an answer because Doctor Who.  :D intuition on the fundamental group of $S^1$ I am familiar with the proof that the fundamental group of the unit circle $S^1$ is $\mathbb Z$, yet I couldn't develop intuition for why it is true. For example, why would I fail if I try to find homotopy from a path that circles $S^1$ once to the path that stays at one point all the time? What brakes the continuity of such a homotopy? I launch a batch which call a lot of scheduled job. But I reach the governor limit :     Maximum number of Apex classes scheduled concurrently : 100   I'm wondering what happens when this limit is reached. The next scheduled jobs are waiting the number of scheduled jobs is lower than 100 for being executed or are they all cancelled ?  And is there to way to manage the number of scheduled jobs to avoir reaching this limit ? For example wait before schedule a new job if we are near the limit. No Line Break in Author Command? It goes off the page! What word would describe someone who doesn't generally leave much of an impression on people? How to know whether Lagrange multipliers gives maximum or minimum? How to get a normal application menu in the top- or titlebar in Gnome How can I get grub2 to boot a different option only on the next boot? When one hears that something smells, one would generally assume that it smells bad.   Isn't there a word which wouldn't bring to mind the idea of a bad odor? For example, how would you describe pot-pourri (assuming you like the smell of pot-pourri)? If possible, I would like an adjective, or a word that could takes the place of an adjective. How do you detect where two line segments intersect? Contour integral of $\sqrt{z^2-1}$ on $|z| = 2$ I've been wrestling with this problem (available  ):  Evaluate the integral of $f(z) = \sqrt{z^2-1}$ around the circle $\{z: |z| = 2\}$, where the branch of the square root function is chosen so that $\sqrt{2^2-1} &gt; 0$.  I came up with the answer $$\int\limits_{|z| = 2} \sqrt{z^2-1} dz = \pi i$$ using the following argument, which seems a little like voodoo to me.  You notice that there are two points, at $z \pm 1$, where you might have to pick a branch of $log()$ to define the square root. Then, I convinced myself that as long as you exclude from your domain the real interval $-1 \le x \le 1$, the function $f(z)$ can be continuously defined (maybe the two branches somehow cancel?), and so is analytic on its domain.  Therefore you can shrink the contour of integration continuously using the Cauchy Closed Curve Integral Theorem, so that you wind up reducing it to the real integral $$2\int_{-1}^1 \sqrt{x^2-1} dx = \pi i$$  I'm not really sure the answer is correct, and I'm even less certain about the way I got it. I had a hard time convincing myself that $\sqrt{z^2-1}$ was not multi-valued on the domain. To try to get at that I tried $\sqrt{z^2-1} = \sqrt{z+1} \sqrt{z-1}$ and reasoned that the product makes the discontinuity disappear, using $$e^{\frac{\pi}{2}i}\cdot e^{\frac{\pi}{2}i} = -1 = e^{-\frac{\pi}{2}i}\cdot e^{-\frac{\pi}{2}i} $$ for the different branches of $log()$ you can choose.  I'd appreciate any input that would help me get a a better way to look at this.  Thanks!    EDIT  An attempt to use the Residue at infinity:  By substituting $z = 1/w$ you get \begin{eqnarray} \int\limits_{|z| = 2} \sqrt{z^2-1} dz &amp;=&amp; \int\limits_{|w| = 1/2} \frac{1}{w^2}\sqrt{\frac{1}{w^2}-1} dw \\ &amp;=&amp; \int\limits_{|w| = 1/2} \frac{1}{w^2}\sqrt{\frac{1-w^2}{w^2}} dw \\ &amp;=&amp; \int\limits_{|w| = 1/2} \frac{1}{w^3}\sqrt{1-w^2} dw \end{eqnarray} The integrand is analytic in $|w| \le 1/2$ except at $w = 0$, so we can apply the Residue Theorem. Near $w = 0$, $\sqrt{1-w^2} = 1 - \frac{1}{2}w^2 + \dots$, so the residue of $\frac{1}{w^3}\sqrt{1-w^2} $ at $w = 0$ is $-\frac{1}{2}$. Then the integral is $$\int\limits_{|z| = 2} \sqrt{z^2-1} dz = 2\pi i \cdot (-1/2) = -\pi i$$ I have a valid US passport. I will fly Jet Airways to Delhi airport with 9 hours of layover to change to another Jet Airways Flight to Abu Dhabi. Do I need a transit visa? I am having some issues with the hyperref package. I would like to create a Introduction chapter without a number so I use \chapter*{Introduction} and \addcontentsline{toc}{chapter}{Introduction} because I want it in the table of contents (see example).  But then the link in my PDF viewer gets it wrong and also the automatically created header is no longer correct (see picture). The table of contents shows the right page number (p.1) but the link is also wrong.   What is my mistake here?  \documentclass{scrbook}  \usepackage{hyperref} \usepackage{blindtext} \usepackage{glossaries}   \makeglossaries  \newacronym{eg}{e.g.}{% for example }   \begin{document}   \frontmatter  % abstract before the table of contents \chapter*{Abstract} \addcontentsline{toc}{chapter}{Abstract} \blindtext  \tableofcontents  % chapter with acronyms \cleardoublepage \phantomsection  \printglossary[type=\acronymtype] \addcontentsline{toc}{chapter}{Glossary}  \cleardoublepage \mainmatter   \phantomsection % \chapter{Introduction} % with this everything is correct but I don't want the number \chapter*{Introduction} \addcontentsline{toc}{chapter}{Introduction}  \blindtext  \pagebreak  \blindtext  % first chapter \chapter{Chapter1}  \gls{eg} \blindtext  \pagebreak  \blindtext   \end{document} How to handle OutOfMemoryError in Java? mathtools: \dddot cause the term to rise Optimal step size in gradient descent How to use a proxy on the command line? I can set my proxy username and password along with proxy settings in the proxy ui but these settings do not work on the command line. How can I use apps such as wget &amp; ping on the command line with a proxy?  Example Details:   username: 1234 pass: linux proxy: proxy port: 8080 Is there a word for colloquial forms of address? For example, "dude," "man," "buddy," "pal," etc, when used to stand in for someone's name.  "Hey, pal, how's it going?"  Is there a word for terms like these?  Or is "colloquialism" as close as we can get? How are answers with the same vote score sorted? How do I get a slanted \sum symbol? I want to use a slanted \sum symbol denoting a different meaning from summation. How do I get a slanted \sum symbol?