Delete element in associative array
How do I unset an element in an array in javascript?
It is well known that compactness implies pseudocompactness; this follows from . I know that the converse does not hold, but what is a counterexample?  (A  is a topological space $S = \langle X,{\mathfrak I}\rangle$ such that every continuous function $f:S\to\Bbb R$ has bounded range.) Proof relation between Levi-Civita symbol and Kronecker deltas in Group Theory In order to prove the following identity: $$\sum_{k}\epsilon_{ijk}\epsilon_{lmk}=\delta_{il}\delta_{jm}-\delta_{im}\delta_{jl}$$ Instead of checking this by brute force, Landau writes thr product of Levi-Civita symbols as: $$\epsilon_{ijk}\epsilon_{lmn}=\det\left|    \begin{array}{cccc}       \delta_{il}   &amp; \delta_{im}  &amp; \delta_{in}   \\       \delta_{jl}   &amp; \delta_{jm}  &amp; \delta_{jn}   \\       \delta_{kl}   &amp; \delta_{km}  &amp; \delta_{kn}       \end{array} \right| $$  The proof that the equalty holds is quite straightforward if you consider what values the indices can take. But I've been told that there's a much more profound and elegant demonstration based on the representation of the symmetric group.  Does anybody know this approach based on group theory? Using Fermats prime numbers to prove that there is infinitely many prime numbers After the performance problems we have run into with  we've decided to make a change, we're moving the network on to .  Here's where to get started:   What works:   All search operators should be in Many changes below from the old search behavior   What's different:   The new search is AND, adding a search term will narrow your results, not expand them. The look of search results is now more unified with the following differences between Q&amp;A:   "Q:" or "A:" prefix Answer counts and tags will be present in questions. The answer count will be highlighted in green if it's accepted. (We may index other things later, that's why the results are more generic/google-y now.)  It's faster, about 5-10x faster for almost all searches on large sites like Stack&nbsp;Overflow Quoted phrases are exact matches except for case-sensitivity, for example,  or . If not in a quoted phrase, words will now be stemmed () Snippets for context will now be more relevant Excludes are now explicitly supported (like -term and -"my phrase") We don't roll up to the question anymore, if you searched for something that matched an answer, we'll show you the answer directly in search results The search per minute limit is effectively gone, it'll block a bot, but no one else should hit it... We'll be monitoring performance though infavorites:mine is back, with infavorites:12345 (any user id) added   What needs work:   What you tell us is broken... Do your worst.   Testing, not yet final:   New range support, here are some examples:   answers:1..1 (exactly one answer) answers:10..20 (10 to 20 answers) created:2008..2009 (created between Jan 1st, 2008 and Dec 31, 2009) created:2010-04..2010-05 (created between April 1st, 2010 and May 31st, 2010) created:2011-01-05..2011-01-06 (to be clear: it goes to end-of-day) This range syntax applies to a new advanced operator: lastactive: and the other numerical ranges, views:, and score:  Additionally, the above syntax is a bit more flexible if you forget it exactly (e.g. score:20-30) in an effort to be intuitive as possible, give it a try - tell us what you think.    I'll try and improve the search as much as possible before it becomes default... At the very least we want it equivalent in relevance and functionality before the switch, but ideally much better. We won't switch until then.  Please give it a try, tell us what you think here, and we'll continually improve it over the holidays as time allows. Bear in mind you may get a search offline page during this test if a change we're making for results necessitates a reindex, and even that should only last about two minutes here on Meta&nbsp;Stack&nbsp;Overflow.  Give it your worst, compare results to the old search, tell us what's better and what's not. We look forward to the feedback.  Update The new search is now the default across the network - we'll be monitoring things over the next few days and would appreciate reports of any crazy behavior you see here. I'm trying to find the birth certificate of my wife's great grandmother who was probably born in Durban, South Africa in 1884. I'm currently unable to find any online resources for this.  If such a thing does not exist online, is there any other method of retrieving a copy or at least just the details? How to match all occurrences of a regex Is there a quick way to find every match of a regular expression in Ruby? I've looked through the Regex object in the Ruby STL and searched on Google to no avail. This is similar to , but I believe it's a bit different*.  Sites like GMail support a preference that pushes all traffic through the SSL edition of the site rather than the plain-text protocol.   For sites that don't offer such preferences (or ones that may, but I have been unable to find, like facebook), is there a way using only the browser (perhaps with a plugin or addon) to always try SSL first, and fall-back to plain-text iff SSL fails?  Is that solution available on Windows, Mac OS X, and Linux? Just one?     * The previous question was looking for external applications that would accomplish this goal. When should I use the new keyword in C++? Will some parents be offended when being asked, "Is it male or female?" If I ask the parent about a baby's gender, will it be impolite or not appropriate to say, "Is it male or female?"  Is there any subtle difference, in terms of politeness, among   "Is it a boy or girl?" "Is it he or she?" "is it male or female?" Redirect all requests to subdirectory except a few ip addresses [Probability]need help to understand the following expression get value part of specific word in AIX want to search string and need part of string  file.txt:  CREATE MULTISET TABLE $$ENV$$_TEMP_ESM.EMPASGMTAMPTMPRTRSE, NO FALLBACK ,      NO BEFORE JOURNAL,      NO AFTER JOURNAL,      CHECKSUM = DEFAULT,      DEFAULT MERGEBLOCKADSRATIO   while using below sed command getting extra value  Output:   bash-4.3$ sed -n 's/.*$$ENV$$_//p' file.txt  **TEMP_ESM.EMPASGMTAMPTMPRTRSE** ,NO FALLBACK ,   I need only TEMP_ESM.EMPASGMTAMPTMPRTRSE ubi-partman failed with exit code 10 - ubuntu 18.04 I'm trying to install Ubuntu 18.04 on my laptop. After choosing the partitionn i have the following error message: grub-efi-amd64-signed package failed to install into / target/.    Then I tried to install via "try ubuntu" and i get:  ubi-partman failed with exit code 10     What should I do? Choosing equipment options at character creation So if I'm correct, when you chose your starter gear and wealth you can either choose to roll some dice depending on your class and buy everything from that or you can choose the starter gear from your class and add the background items (including some gold). Here are my 2 questions:   If I choose the gear from my class, do I have to take all the equipment from only one of the (a) or (b) choices, or can I freely mix-and-match choices from the two sets? Can you spend the extra gold you get from your background on extra equipment (e.g. some soap and some fishing equipment) or do you have to start with that gold in its pouch?   The reason I ask is that I have recently created a level 1 wood elf druid and I mixed-and-matched the gear from the class, so that I chose a shortbow as a "(b) simple weapon" for the first point and a "(a) Scimitar" at the second point. My DM wasn't so happy about this, as he can't understand why I'm mixing (a) and (b).  He also wasn't so happy with me spending my 10gp from my outlander background. I decided that my druid wouldn't lay so much worth in 10gp compared to a bunch of stuff I got for that (e.g. some soap and some fishing equipment and some other useful things) and he seems to think that I'm supposed to just start with the gold instead. Evaluate $\lim \limits_{n\rightarrow\infty}\sin^2(\pi\sqrt{n^2 + n})$ I'm struggling to find the limit at infinity of : $$\lim \limits_{n\rightarrow\infty}\sin^2(\pi\sqrt{n^2 + n}), n\in\Bbb N$$ I know it is $1$ but I don't understand why this is wrong :  $\sin^2(\pi\sqrt{n^2 + n}) = \sin^2(\pi*n\sqrt{1 + \frac{1}{n}})$.  So $\lim \limits_{n\rightarrow\infty}\sin^2(\pi\sqrt{n^2 + n}) = \lim \limits_{n\rightarrow\infty}\sin^2(\pi*n\sqrt{1 + \frac{1}{n}}) =  \lim \limits_{n\rightarrow\infty} \sin^2(\pi*n) = 0$.  Thanks. Many To Many Relationships I am working on a conceptual model for a database. I have the following entities:  Student (id, name, date of birth, department)  Subject (id, name)   This is a many-to-many relationship, one student may be enrolled in many courses, each course has many students. From what I understand, as I should break this many-to-many relationship by introducing a new into a entity, say 'registered' which allows a one-to-one relationship or one-to-many relationship?  Is this correct design decision? Given $f(x) = x + |x|$ for what values of $x$ is $f$ differentiable The Problem  Accessing my site over https (the only protocol allowed) I get the content, but none of the CSS, images etc.  Drupal is creating pages in response to https requests that include http links to these resources, but it should be using https.  What I've done  I have copied a site to a dev server. The site loads and basically works fine - I can log in etc. It's just that all the links drupal generates are http. The site I've copied it from also runs over https. The site does not exist on http (it would just get a Forbidden error). I've drush cc all.  So Apache's working - I can access the site. .htaccess is working (clean urls work, for example).  I'm using SNI to access the site because the server has other vhosts too, but I'm only accessing the site using the latest Firefox (and as it's a dev site and I'm the only dev, nobody else will use it).  I've done this dozens of times and am quite stumped! Why does Drupal not notice that the request came over https?  The fix  Turns out that .htaccess has this to say:   /* Base URL (optional).                                                          If Drupal is generating incorrect URLs on your site, which could             be in HTML headers (links to CSS and JS files) or visible links on pages     (such as in menus), uncomment the Base URL statement below (remove the       leading hash sign) and fill in the absolute URL to your Drupal installation.    Sure enough, putting $base_url = 'https://example.com'; fixed it.  But why is this necessary? todonotes: How to make multiple listoftodos? In this MWE, I made two commands to highlight parts of the text as a reviewer comment, while the comments are colored uniquely to indicate the author whose comment is typeset.  If I want to make two listoftodos, each has the comments entries of one author, how can it be done?  \documentclass{article} \usepackage{hyperref,lipsum}  \usepackage[textwidth=2.5cm,colorinlistoftodos]{todonotes} \setlength{\marginparwidth}{2.5cm}  \newcommand\stR[2]{% 1st reviewer comment     \todo[%     author=1st Reviewer,noline,caption={1st Reviewer #1 Comment},color=blue!20%     ]%     {#1 Comment}{\color{blue}{\bfseries#2}}}  \newcommand\ndR[2]{% 2nd reviewer comment     \todo[%     author=2nd Reviewer,noline,caption={2nd Reviewer #1 Comment},color=red!50!white%     ]%     {#1 Comment}{\color{red}{\bfseries#2}}}  \begin{document} \listoftodos[Reviewers Comments] \section{Section} Text \stR{2nd}{2nd comment of the 1st reviewer} another text\vspace{\baselineskip} \lipsum[1]\vspace{\baselineskip} Some text \ndR{1st}{1st comment of the 2nd reviewer} continue text \end{document} If a run the watch command containing an alias, it will not expand the alias. I have tried both with single quote and double quotes, in fact given the following alias:  # alias ll alias ll='ls -l --color=tty'   The following command will fail  # watch ll sh: ll: command not found   Shouldn't command line expansion work in this case?