Equation labeling in latex
Custom cross-reference formats (e.g. "Equation 1" instead of just "1")
How does the twitter bot work? I heard that there was a twitter bot which automatically posted questions and asked for answers for specific questions on every site. How do they work? Is there an algorithm for doing this or is it purely random? I know that it doesn't tweet closed questions, but that's it. Four tasks in parallel... how do I do that? I have a bunch of PNG images on a directory. I have an application called pngout that I run to compress these images. This application is called by a script I did. The problem is that this script does one at a time, something like this:  FILES=(./*.png) for f in  "${FILES[@]}" do         echo "Processing $f file..."         # take action on each file. $f store current file name         ./pngout -s0 $f R${f/\.\//} done   Processing just one file at a time, takes a lot of time. After running this app, I see that the CPU is just 10%. So I discovered that I can divide these files in 4 batches, put each batch in a directory and fire 4, from four terminal windows, four processes, so I have four instances of my script, at the same time, processing those images and the job takes 1/4 of the time.  The second problem is that I lost time dividing the images and batches and copying the script to four directories, open 4 terminal windows, bla bla...  How do that with one script, without having to divide anything?  I mean two things: first how do I from a bash script, fire a process to the background ? (just add &amp; to the end?) Second: how do I stop sending tasks to the background after sending the fourth tasks and put the script to wait until the tasks end? I mean, just sending a new task to the background as one tasks end, keeping always 4 tasks in parallel? if I do not do that the loop will fire zillions of tasks to the background and the CPU will clog. Why does "stigmata" [often] have penult stress? I have been studying the pronunciation of Greek-derived words in English, and I've found an odd anomaly. There are (at least) two possible pronunciation patterns for plural word-forms that end in -&#8288;mata (which correspond to singular word-forms that end in -&#8288;ma).   Antepenult stress (expected)  It appears that it is always possible to place the stress on the antepenult (third-to-last) syllable, such as:    /ˈlɛmə/, /ˈlɛmətə/  /ˈskiːmə/, /ˈskiːmətə/  /ˌtɛrəˈtoʊmə/, /ˌtɛrəˈtoʊmətə/~/ˌtɛrəˈtɒmətə/  /ˈstɪɡmə/, /ˈstɪɡmətə/   This is what would be expected from  (I believe most or all of these words came through Latin before entering English), since the penultimate "a" in the original Greek words is short.  Maybe Latin vowel quality and stress rules are not very relevant; certainly, few English speakers know about them nowadays. And even with antepenult stress, some of these pronunciations do not seem to follow all of the traditional rules for pronouncing Latin-derived terms in English. I was reminded by some comments in this  that  in antepenult stressed syllables, we would expect tense ("long") vowels to be shortened due to  (TSL), yielding pronunciations like /ˌtɛrəˈtɒmətə/ (which I just noticed is in fact listed in the Oxford English dictionary) and ?/ˈskɛmətə/ (which is not). (Compare to genus~genera /dʒiːnəs/~/dʒɛnərə/, and perhaps opus~opera /oʊpəs/~/ɒpərə/). However, there are other Latinate plural forms that typically don't have trisyllabic laxing (matrices, also I think helices), or where both the lax- and tense-voweled pronunciations coexist (codices, apices), so I guess the apparent lack of it in schemata should not be surprising. (There are even some exceptions to TSL in singular nouns like obesity.)  Penult stress (unexpected)  The other pronunciation seems to exist only for a couple of words, in which the penultimate "a" is commonly stressed and broadened: stigma ~ stigmáta  (listed by both the Merriam-Webster dictionary and the ), and also sometimes schéma ~ schemáta /skiːˈmɑːtə/ (listed only by the ). (Neither the Merriam-Webster dictionary nor the Oxford Learner's Dictionaries list *"lemmáta").  I'm wondering why this pronunciation exists. It's an irregular plural either way, and putting the stress on the penultimate syllable creates a stress change between the singular and the plural forms.  (It's true that all of these words are rare, and some people might pronounce some of their plurals differently. The pronunciations I give here are simply the ones listed in dictionaries.)  The plural form "stigmata" is probably most common in religious or theological contexts (where it refers to the wounds of Christ), so at first I wondered if the penultimate stress was supposed to be closer to the original Greek pronunciation, but according to , the stress is on the antepenult in Greek as well.  So, what's up with this? Did the stress perhaps change in Latin over time, is this a tradition of Greek accentuation that I'm not familiar with, is this a simple matter of ignorance of the original position of the stress that has now become entrenched with time and usage, or is this somehow explainable by established English stress patterns? (For example, do English speakers have some natural preference for a penultimate stress on polysyllabic words?)  If nobody knows of a reason, I suppose I can just put it down to people encountering the word mainly in text, not knowing which syllable to stress, and choosing the penult because it sounds better to them.  (I asked this question a while back on , but nobody knew of any reason.) What are tag synonyms? How can tag synonyms be distinguished from "real" tags? How are new tag synonyms created? Who can create tag synonyms? How can I delete/reverse/undo bad tag synonyms? What are merged tags? My table doesn't fit; what are my options? I'm working on this problem already, the domain and co-domain are the set of Rational Numbers. we see that setting $x = 1$ and $y = n$, we obtain $f(n + 1) = f(n) + 1$  But I'm trying to prove that $f(n) = n + 1$ for all $n$, the case when $n = 1, 2$ is obviously true, how do I approach this via induction? Write to FIFO only if it exists How to apply a texture to only one side of a plane How can you have an image as a texture (in this case on cloth) that is only applied to one side of a plane?  I would like the reverse side to be a solid color.  Please see below image where the cloth has the image texture on both sides. Proof of the formula $1+x+x^2+x^3+ \cdots +x^n =\frac{x^{n+1}-1}{x-1}$ Possible Duplicate:          Proof to the formula  $$1+x+x^2+x^3+\cdots+x^n = \frac{x^{n+1}-1}{x-1}.$$ I'm using biblatex for my references.  Normally, if I use \cite{source1, source2, source3}, I get a citation like  [3, 45, 98]   If I now want to give a page number for one of them, it looks confusing imho, as I should get (did not try it out up to now, honestly)   [3, 45, 78, p. 23f, 98]   So imho it would make sense to change one of the separator from a comma to e. g. a semicolon like:  [3; 45; 78, p. 23f; 98]   Question 1: Does that make sense, or are there other conventions for citing sources with and without page numbers together?  (Up to now I collected the citations without page number in one cite command and added singular \cite[][p. xy]{} commands for those with page numbers., so I'd get:   [3, 45, 98][78, p. 23f]   )  the \cites[]{}[]{}[]{} could also do that, but it also uses the same separators for entries and postnotes.  Question 2: How could I change the separator globally for those number-citations from comma to semicolon in biblatex? Firefox Web Console Disabled? Make a substitution to express the integrand as a rational function and then evaluate the integral  $$\int {\frac{2}{x\sqrt{x+1}}}\, dx$$  What is the substitution that I have to make? How to populate UIList with all material slot in scene? 2.8 I want to center a div vertically with CSS. I don't want tables or JavaScript, but only pure CSS. 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