Best resolution for a 2x2m design in Photoshop ?
I need to print an image at a certain size. What dimensions and resolution should I use?
Balancing long table inside multicol in LaTeX I would like to put some longer tabular data inside the multicols environment while maintaining its balancing abilities. I have tried supertabular with the trick to redefine \newpage as columnbreak. This isn't good though, because the columns aren't properly balanced. Finally I ended up using \halign:  \documentclass[11pt, a4paper]{article} \usepackage[margin=3cm]{geometry} \usepackage{supertabular} \usepackage{multicol}  \def\shortlipsum{\par Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Ut purus elit, vestibulum ut, placerat ac, adipiscing vitae, felis. Curabitur dictum gravida mauris. Nam arcu libero, nonummy eget, consectetuer id, vulputate a, magna. Donec vehicula augue eu neque.\par}  \newcounter{entryno} \setcounter{entryno}{1} \def\tabline{Test &amp; \the\value{entryno} &amp; Description\addtocounter{entryno}{1}\\} \def\tablines{\tabline\tabline\tabline\tabline\tabline} \def\mybreak{\hrule width \columnwidth height 0pt \columnbreak}  \begin{document} \begin{multicols}{2} \shortlipsum \medskip  % % This doesn't balance the columns. Whole table ends up in the left column (it fits) % \begingroup\let\newpage\mybreak % \noindent\begin{supertabular*}{\columnwidth}{@{\indent}l l l} % \tablines\tablines\tablines\tablines\tablines\tablines % \end{supertabular*} % \endgroup  \begingroup\let\\\cr \noindent\halign{\indent#\quad&amp;#\quad&amp;#\hfil\cr \tablines\tablines\tablines\tablines\tablines\tablines} \endgroup  \medskip \shortlipsum \end{multicols} \shortlipsum \end{document}     I was wondering if I'm the only one using \halign to achieve this result. On the other hand supertabular leaves me with an undesired almost empty right column. How would you approach this problem? I was recently watching Episode 3 and a few clone wars episodes, and I found myself thinking during the opening battle between the Republic and General Grievous' forces above Coruscant, on a planet so densely populated where potentially thousands of inhabitants can be killed from a drifting capital class ship with a decaying orbit during space battles what defenses are in place?  Is there any instances of some form of emergency services that tractor beam chunks of debris to safe landing places or repulsor towers that can slow or suspend it until it can be taken apart safely? Even disintegration lasers or emergency force field generators like the types deployed on Hoth as they must have the energy output capable of sustaining it. This IS the galactic capital so must have some advanced tech at its deposal. Even now in our own development humans have certain preventative measures for all types of threats and ways of tracking them, plus responses or fall back plans. I've got about a billion rows of data in a table with a name and an integer in the range 1-288.  For a given name, every int is unique, and not every possible integer in the range is present--so there are gaps.  This query generates an example case:  --what I have: SELECT * FROM ( VALUES ('foo', 2),               ('foo', 3),               ('foo', 4),               ('foo', 10),               ('foo', 11),               ('foo', 13),               ('bar', 1),               ('bar', 2),               ('bar', 3)      ) AS baz ("name", "int")   I'd like to generate a lookup table with a row for each name and sequence of contiguous integers.  Each such row would contain:  name   --  the value of the name column start  --  the first integer in the contiguous sequence end    --  the final value in the contiguous sequence span   --  end - start + 1  This query generates example output for the above example:  --what I need: SELECT *  FROM ( VALUES ('foo', 2, 4, 3),               ('foo', 10, 11, 2),               ('foo', 13, 13, 1),               ('bar', 1, 3, 3)      ) AS contiguous_ranges ("name", "start", "end", span)   Because I have so many rows, more efficient is better.  That said, I only have to run this query once, so it isn't an absolute requirement.  Thanks in advance!  Edit:  I should add that PL/pgSQL solutions are welcome (please explain any Fancy Tricks--I'm still new to PL/pgSQL). How to avoid tripping over UTF-8 BOM when reading files I'm consuming a data feed that has recently added a Unicode BOM header (U+FEFF), and my rake task is now messed up by it.  I can skip the first 3 bytes with file.gets[3..-1] but is there a more elegant way to read files in Ruby which can handle this correctly, whether a BOM is present or not? I am trying to solve the following question which is Ex3 from Arthur Engel, Problem Solving strategies. Here is the question: $\sum_{k=1}^n k^3 {n \choose k}$ and asks to find the sum. I am sincerely having a hard time trying to figure out how to solve it and get $n^2 (n+3)(2)^{n-3}$. I would really appreciate if someone could show the step-by-step process. Thank you! Interpretation of log transformed predictor and/or response Link2SD not working completely This is an unproven proposition I've come across in multiple places.   Suppose $A$ is a commutative Noetherian ring, and $S$ a multiplicative subset of $A$. Then $S^{-1}A$ is Noetherian.  Why is this? I thought about taking some chain of submodules $$ S^{-1}M_1\subset S^{-1}M_2\subset\cdots $$ and pulling back to a chain  $$ M_1\subset M_2\subset\cdots $$ of submodules of $A$ which must eventually stablize. Is there more to it than this? I kind of wary of assuming all submodules of $S^{-1}A$ have form $S^{-1}M$ for $M\leq A$. How to import a module given its name as string? C++ 11 Thread initialization with member functions compiling error Can you 'exit' a loop in PHP? I have a loop that is doing some error checking in my PHP code. Originally it looked something like this...  foreach($results as $result) {     if (!$condition) {         $halt = true;         ErrorHandler::addErrorToStack('Unexpected result.');     }      doSomething();  }  if (!$halt) {     // do what I want cos I know there was no error }   This works all well and good, but it is still looping through despite after one error it needn't. Is there a way to escape the loop? How can I tell how long (more or less) it will take me to complete a game? Possible Duplicate:          I often want to know how long a game is so that I can decide whether or not to buy it, or even to decide if I've got enough free time available in the near-future to make it worth trying to play and complete over a weekend. Sometimes I even want to know just because I'm getting a little tired of the game and I want to have a sense of whether or not I'm nearing the end, so I can decide whether to tough it out or pack it in.  What are some good ways of determining how long a given game takes to complete, on average? What Application Indicators are available? This question exists because it has historical significance, but it is not considered a good, on-topic question for this site, so please do not use it as evidence that you can ask similar questions here.  While you are encouraged to help maintain its answers, please understand that "big list" questions are not generally allowed on Ask Ubuntu and will be closed per the .     I installed Ubuntu 11.04 on one of my systems and I am using the Unity interface. Unity is working quite well so far but I really miss panel applets for net speed, cpu temp, and system monitor.   These applets are useful for viewing quick info. Unlike 10.10, there is no other way to get this info onto the panel or unity launcher. There are solutions like screenlets and conky but they don't feel appropriate for a clean desktop look.  If you know one then please list out any third party indicators with links so that they can be found. Why are springs shaped the way they are? Why are springs coiled the way they are? Why not some other shape? Is the shape due to its elasticity or something? Automatically convert links to popular mobile pages (such as the mobile Wikipedia) to point to the corresponding regular pages This issue came up  on Worldbuilding:  If somebody is on a mobile device and wants to cite, e.g., Wikipedia, they usually insert a link to the  instead of the regular one. This is annoying for users with immobile devices, while it poses no benefit to users with mobile devices, who should get redirected to the mobile Wikipedia anyway.  I thus request that links to mobile versions of popular web pages are automatically converted to regular ones either in the post source or when rendering the page.  As  mentioned, an author may sometimes explicitly want to link to the mobile version of a webpage but as far as I can tell, this should be the exception. At least for Wikipedia, an automatic conversion would do much more good than harm, because it is very often cited as a resource. For example, until recently, there were at least 82 posts with links to the mobile Wikipedia on Worldbuilding alone (going by  edit spree to remove them) $\lim_{x \rightarrow \infty} \lim_{n \rightarrow \infty} f_{n}(x) = \lim_{n \rightarrow \infty}\lim_{x \rightarrow \infty}f_{n}(x) $ in case of uniform convergence of $f_{n}(x)$ to $f(x)$  I used this while I was given that $f_{n}(x)$ converges to $f(x)$ uniformly. Is this correct and I was also thinking to prove this! Let $K=F(x)$ be the rational function field over a field $F$ of characteristic $0$, let $L_1=F(x^2)$, and $L_2=F(x^2+x)$. How to show that $L_1\cap L_2 = F$? Decoupling caps, PCB layout I guess I've been somewhat ignorant when it comes to the finer details of pcb layout. Lately I've read a couple of books that try their best to lead me on the straight and narrow. Here is a couple of examples of a recent board of mine, and I have highlighted three of the decoupling caps. The MCU is a LQFP100 package and the caps are 100nF in 0402 packages. The vias connect to ground and power plane.     The top cap (C19) is placed according to best practices (as I understand them). The other two are not. I haven't noticed any problems. But then again the board has never been outside the lab.  I guess my question is: How big a deal is this? As long as the tracks are short, does it matter?  The Vref pins (reference voltage for the ADC) also have a 100nF cap across them. Vref+ comes from an onboard TL431 shunt regulator. Vref- goes to ground. Do they require special treatment like shielding or local ground?    EDIT    Thanks for great suggestions! My approach has always been to rely on an unbroken ground plane. A ground plane will have the lowest possible impedance, but this approach may be too simplistic for higher frequency signals. I've made a quick stab at adding local ground and local power under the MCU (The part is an NXP LPC1768 running at 100MHz). The yellow bits are the decoupling caps. I'll look into paralleling caps. The local ground and power are connected to the GND layer and the 3V3 layer where indicated.  The local ground and power are made with polygons (pour). It's going to be a major rerouting job to minimize the length of the "tracks". This technique will limit how many signal tracks can be routed under and across the package.  Is this an acceptable approach? Do eyeballs exhibit chromatic aberration? Fairly straightforward question. If not, why not?  I suspect that if they do, it is not perceived due to the regions of highest dispersion being in one's region of lowest visual acuity. Today I taught an introductory class of statistics and a student came up to me with a question, which I rephrase here as: "Why is the standard deviation defined as sqrt of variance and not as the sqrt of sum of squares over N?"  We define population variance: $\sigma^2=\frac{1}{N}\sum{(x_i-\mu)^2}$   And standard deviation: $\sigma=\sqrt{\sigma^2}=\frac{1}{\sqrt{N}}\sqrt{\sum{(x_i-\mu)^2}}$.   The interpretation we may give to $\sigma$ is that it gives the average deviation of units in the population from the population mean of $X$.   However, in the definition of the s.d. we divide the sqrt of the sum of squares through $\sqrt{N}$. The question the student raises is why we do not divide the sqrt of the sume of squares by $N$ instead. Thus we come to competing formula: $$\sigma_{new}=\frac{1}{N}\sqrt{\sum{(x_i-\mu)^2}}.$$ The student argued that this formula looks more like an "average" deviation from the mean than when dividing through $\sqrt{N}$ as in $\sigma$.  I thought this question is not stupid. I would like to give an answer to the student that goes further than saying that the s.d. is defined as sqrt of the variance which is the average squared deviaton. Put differently, why should the student use the correct formula and not follow her idea?  This question relates to an older thread and answers provided . Answers there go in three directions:   $\sigma$ is the root-mean-squared (RMS) deviation, not the "typical" deviation from the mean (i.e., $\sigma_{new}$). Thus, it is defined differently. It has nice mathematical properties. Furthermore, the sqrt would bring back "units" to their original scale. However, this would also be the case for $\sigma_{new}$, which divides by $N$ instead.   Both of points 1 and 2 are arguments in favour of the s.d. as RMS, but I do not see an argument against the use of $\sigma_{new}$. What would be the good arguments to convince introductory level students of the use of the average RMS distance $\sigma$ from the mean?