When I enter the command: $ ls -la some_directory  It gives the output: drwx------. 5 user1 user1 1418 Mar 7 11:17 some_directory  What does the dot behind drwx------ signify? What does the 5 before user1 signify?
The ls -al command shows the following output;  -rwxrw-r--    10    root   root 2048    Jan 13 07:11 afile.exe   What are all the fields in the preceding display?
We let a>0 and b>0 and  we have $\sum_{n=0}^{\infty}b^n-a^n$. We have to find all values a,b>0 where $\sum_{n=0}^{\infty}b^n-a^n$ is convergent. I think I can use that $$\sum_{n=0}^{\infty} b_n &lt; \infty , \sum_{n=0}^{\infty} a_n &lt; \infty \implies \sum_{n=0}^{\infty} (b_n-a_n) &lt; \infty. $$. And I think $\sum_{n=0}^{\infty}b^n$ and $\sum_{n=0}^{\infty}a^n$ is convergent if a&lt;1 and b&lt;1? It will make sense. But how can I show it? How fast a (relatively) small black hole will consume the Earth? This question appeared quite a time ago and was inspired, of course, by all the fuss around "LHC will destroy the Earth".   Consider a small black hole, that is somehow got inside the Earth. Under "small" I mean small enough to not to destroy Earth instantaneously, but large enough to not to evaporate due to the . I need this because I want the black hole to "consume" the Earth. I think reasonable values for the mass would be $10^{15} - 10^{20}$ kilograms.   Also let us suppose that the black hole is at rest relative to the Earth.  The question is: How can one estimate the speed at which the matter would be consumed by the black hole in this circumstances? Changing Date format and appending to original file I have file like this called a.txt:  [2016-03-30T04:51:51.599-04:00]!ER_DEV!Port_Conflict!/u05/app/ [2016-01-20T04:30:21.885-04:00]!ER_DEV!Port_Conflict!/u05/app/   I need to modify it so it looks like:    2016-03-30 04:51:51!ER_DEV!Port_Conflict!/u05/app/   2016-01-20 04:30:21!ER_DEV!Port_Conflict!/u05/app/   i already wrote a command to change [2016-03-30T04:51:51.599-04:00] to 2016-03-30 04:51:51 .but how to append the query output to original file.    awk -F'!' '{print $1}' a.txt | awk -F '[T.]' '{print $1 " " $2}' | awk '{gsub(/\[/,"")}1' The Order of Modification in English Nouns, Preceding or Succeeding? As I don't know the exact linguistic terms, what I mean my "preceding" and "succeeding" in modifying nouns is as follows.  Preceding : delicious food, long way, kind person, et cetera Succeeding : faculty of science, land of despair, a book that changed my mind, et cetera  English seems to accept both ways of modification.  Sometimes, either way will not make a difference. department of science == science department a burning book == a book burning  At other times, changing the order will still make sense but be somewhat awkward or bizarre. Kentucky Fried Chicken ?= Chicken Fried in Kentucky free as in free speech ?= as-in-free-speech free  When writing English, I tend to use more the preceding modification style because my native language Korean is quite strictly precedingly modifying. "빠른 판단을 바탕으로 한 재치있는 응수" directly translates to "a quick-decision-based clever response" rather than "a clever response based on a quick decision"  French as well as other Latin-originated languages seems to be succeedingly modifying. Académie Française, Poulet Frit du Kentucky  while German and Dutch more often use preceding modification.  Well, this mixture in English allows rich style with various ways of expression, but it does often make a non-native English speaker be a little confused. Is there any subtle but general difference between these 2 ways? Or is it just simply case-by-case. Any guidance will help. Why is $\mathbb{Z}[\sqrt{-n}], n\ge 3$ not a UFD? I'm considering the ring $\mathbb{Z}[\sqrt{-n}]$, where $n\ge 3$ and square free. I want to see why it's not a UFD.   I defined a norm for the ring by $|a+b\sqrt{-n}|=a^2+nb^2$. Using this I was able to show that $2$, $\sqrt{-n}$ and $1+\sqrt{-n}$ are all irreducible. Is there someway to conclude that $\mathbb{Z}[\sqrt{-n}]$ is not a UFD based on this? Thanks. The problem from Burton: show that the equation $n^2 + (n+1)^2 = m^3$ has no solution in the positive integers.  So far, I can see that gcd($n$,$n+1$)$=1$ and $m \equiv_4 1$ and $m=a^2 + b^2$ for some integers a,b. I'm guessing I need to reach a contradiction.  At this point, I am stuck. Any hints? Highlight a word with jQuery I basically need to highlight a particular word in a block of text. For example, pretend I wanted to highlight the word &quot;dolor&quot; in this text: &lt;p&gt;     Lorem ipsum dolor sit amet, consectetuer adipiscing elit. &lt;/p&gt; &lt;p&gt;     Quisque bibendum sem ut lacus. Integer dolor ullamcorper libero.     Aliquam rhoncus eros at augue. Suspendisse vitae mauris. &lt;/p&gt;  How do I convert the above to something like this: &lt;p&gt;     Lorem ipsum &lt;span class=&quot;myClass&quot;&gt;dolor&lt;/span&gt; sit amet, consectetuer adipiscing elit. &lt;/p&gt; &lt;p&gt;     Quisque bibendum sem ut lacus. Integer &lt;span class=&quot;myClass&quot;&gt;dolor&lt;/span&gt; ullamcorper     libero. Aliquam rhoncus eros at augue. Suspendisse vitae mauris. &lt;/p&gt;  Is this possible with jQuery? Edit: As  , this is quite possible without jQuery - but I was hoping there might be a special method of jQuery which would let you do selectors on the text itself. I'm already using jQuery heavily on this site, so keeping everything wrapped up in jQuery would make things perhaps a bit more tidy. I am trying to modify output in my twig file. In D7, I was able modify data in my array with this  check_markup($tweet-&gt;text, 'full_html');   and I see that this function still exists in D8. However, I'm not sure how I would use this in a filter in twig. This is what I have so far:  {% for tweet in params.tweets %} &lt;div class="tweet-wrapper"&gt; &lt;div class="tweet-profile-image"&gt;     &lt;img src='{{ tweet.user.profile_image_url }}'/&gt; &lt;/div&gt; &lt;div class='tweet-text'&gt;     &lt;!--check_markup($tweet-&gt;text, 'full_html');--&gt;     {{ tweet.text }} &lt;/div&gt;   &lt;/div&gt; {% endfor %}   I actually tried to do this before I sent it to the template as well, but it didn't change anything:   foreach($tweets as $tweet) {   $tweet-&gt;text = check_markup($tweet-&gt;text, 'full_html');   $cleanTweets[] = $tweet; } dpm($tweets); $params = array('tweets' =&gt; $cleanTweets); $tweet_template = array('#theme' =&gt; 'twitter_pull_tweet_listing', '#params' =&gt; $params); return $tweet_template;   What I'm trying to do here is make drupal create links for web links in the twitter tweet text. This worked fine for me in D7. Is there a safe way to determine how powerful an opponent is? Elementary proof for $\lim\limits_{n \to\infty}\frac{n!e^n}{n^n} = +\infty$ As seen in  question, the series $\sum\limits_{n=1}^{\infty} \dfrac{n!e^n}{n^n}$ diverges. (One way to see this is by noting that the terms of the sum are greater than $1$ and, therefore, don't converge to zero.)  However, more is true: not only are the terms greater than $1$, they blow up to $+\infty$! To see this, one can apply Stirling's approximation and get $\dfrac{n!e^n}{n^n} \sim \sqrt{2\pi n}$.  My question is: is there an elementary proof for $\lim_{n \to\infty}\dfrac{n!e^n}{n^n} = +\infty$?  The reason I'm asking this is that I'm taking a Calculus course and I was assigned the exercise of proving the divergence of the series above and I would feel more satisfied if I could prove that its terms go to $+\infty$ (as opposed to merely proving the terms are greater than $1$.) Obviously, things like Stirling's approximation are outside the scope of the course, so I can't really use them.  (To be clear, you can use anything one learns in $4$ semesters of standard Calculus courses. I hope this restriction is not too obscure.) I'm currently taking Quantum Mechanics in school and I came across a table displaying the following in the given order:   $E_n (\text{energy levels}), g_n (\text{eigen functions})$   $n \ l, [m]$  $E_1, 1$   $1s, [0]$  $E_2, 4$   $2s, [0]$ $2p, [-1,0,1]$  $E_3, 9$   $3s, [0]$ $3p, [-1,0,1]$ $3d, [-2,-1,0,1,2]$    Now, as I understand $n$ defines the size of the orbital, $l$ the shape and $m$ the orientation.  My question is, how does the atoms shell model fit into this if one can have two electrons per orbital? Are $1s$ the same as the orbital $2s$, but just renamed for the sake of higher energy levels? Or do two similarly looking orbits exist for different energy levels? For example two "layers" of spherical electron clouds for an atom with $4$ electrons.  I just can't see how $2$, $8$, $18$ becomes $2$, $8$, $8$ as we were taught in Physics at high school? Am I missing something? Does this polynomial evaluate to prime number whenever $x$ is a natural number? Even though I have the latest Adobe Flash player 11.2 for Linux in Firefox -   - a particular online flash game still requests that I update to the latest flash player.  I've tried this online game on my laptop (Windows 8 with Flash Player 11.8) and it has no problems.  Is there a way to trick Ubuntu or this game into thinking Flash Player 11.8 is "installed"? What is a Superblock, Inode, Dentry and a File? From the article  by M. Tim Jones, I read that Linux views all the file systems from the perspective of a common set of objects and these objects are superblock, inode, dentry and file. Even though the rest of the paragraph explains the above, I was not that comfortable with that explanation. Could somebody explain to me these terms? This should be a very easy question but it might just be that I'm confusing myself. So we have the definition of a function $f$ on $S$ being continuous at $x_0$:     For any $\epsilon$>0, there exists $\delta&gt;0$ such that: whenever $|x-x_0|&lt;\delta$, we have $|f(x)-f(x_0)|&lt;\epsilon$   And I assume the negation is     There exists $\epsilon$>0 such that for all $\delta&gt;0$, $|x-x_0|&lt;\delta$ yet $|f(x)-f(x_0)|\ge \epsilon$.   Now I want to show that the function $f(x)=\sin(\frac{1}{x})$ together with $f(0)=0$ cannot be made into a continuous function at $x=0$. So I need to show that there exists $\epsilon&gt;0$ such that for all $\delta&gt;0$, $|x|&lt;\delta$ yet $|f(x)|\ge\epsilon$.  Let $\epsilon = \frac{1}{2}$. Then no matter what $\delta$ we choose, let $|x|&lt;\frac{1}{2}$. It is certainly possible that $|f(x)|\ge \frac{1}{2}$, because, well, $\frac{1}{x}$ can really take on arbitrarily large value as $x$ is small.  Now, what confuses me is that, as $x$ gets small, $f(x)$ can certainly be greater than $\frac{1}{2}$ for infinitely many times, but it will be less than that infinitely many times, too. But I suppose it doesn't really matter. So I think there's something wrong with my negation but I couldn't figure out where.  Update: The correct version can be found . Watch for Lemma 4.6 How to search the internet for terms with special characters As I learnt from this , Google has no ability to search for special characters. Let's say I want to search for ss!. Are there any other search engines that can achieve this? Please do not propose any programming code search engines since this is a general search. Is any aspect of the supernatural testable? What level of proof is possible for the supernatural? Algorithm to detect overlapping periods How to understand the memory usage and load average in linux server I am using a linux server which has 128GB of memory and 24 cores. I use top to see how much it is used. Its output is pasted at the end of the post. Here are two questions:  (1) I see that each of the running processes occupies a very small percentage of memory (%MEM no more than 0.2%, and most just 0.0%), but how the total memory is almost used as in the fourth line of output ("Mem:  130766620k total, 130161072k used,   605548k free,   919300k buffers")? The sum of used percentage of memory over all processes seems unlikely to achieve almost 100%, doesn't it?  (2) how to understand the load average on the first line ("load average: 14.04, 14.02, 14.00")?   Thanks and regards!  Edit:  Thanks!  I also really like to hear some rough numbers based on used percentage of memory to determine if a server is heavily loaded, since I once became the one who cramed the server without understanding the current load.  Is swap regarded as almost the same as memory? For example, when memory and swap are almost of same size, if the memory is almost running out but the swap is still largely free, may I just view it as if the used percentage of memory + swap is still not high and run other new processes?  How would you consider together CPU or memory (or memory + swap) usage? Do you become worried if either of them reaches too high or both?  Output of top：  $ top    top - 12:45:33 up 19 days, 23:11, 18 users,  load average: 14.04, 14.02, 14.00 Tasks: 484 total,  12 running, 472 sleeping,   0 stopped,   0 zombie Cpu(s): 36.7%us, 19.7%sy,  0.0%ni, 43.6%id,  0.0%wa,  0.0%hi,  0.0%si,  0.0%st Mem:  130766620k total, 130161072k used,   605548k free,   919300k buffers Swap: 63111312k total,   500556k used, 62610756k free, 124437752k cached    PID USER      PR  NI  VIRT  RES  SHR S %CPU %MEM    TIME+  COMMAND  6529 sanchez   18  -2 1075m 219m  13m S  100  0.2  13760:23 MATLAB 13210 timothy   18  -2 48336  37m 1216 R  100  0.0   3:56.75 absurdity 13888 timothy   18  -2 48336  37m 1204 R  100  0.0   2:04.89 absurdity 14542 timothy   18  -2 48336  37m 1196 R  100  0.0   1:08.34 absurdity 14544 timothy   18  -2  2888 2076  400 R  100  0.0   1:06.14 gatherData  6183 sanchez   18  -2 1133m 195m  13m S  100  0.2  13676:04 MATLAB  6795 sanchez   18  -2 1079m 210m  13m S  100  0.2  13734:26 MATLAB 10178 timothy   18  -2 48336  37m 1204 R  100  0.0  11:33.93 absurdity  12438 timothy   18  -2 48336  37m 1216 R  100  0.0   5:38.17 absurdity 13661 timothy   18  -2 48336  37m 1216 R  100  0.0   2:44.13 absurdity 14098 timothy   18  -2 48336  37m 1204 R  100  0.0   1:58.31 absurdity 14335 timothy   18  -2 48336  37m 1196 R  100  0.0   1:08.93 absurdity 14765 timothy   18  -2 48336  37m 1196 R   99  0.0   0:32.57 absurdity 13445 timothy   18  -2 48336  37m 1216 R   99  0.0   3:01.37 absurdity 28990 root      20   0     0    0    0 S    2  0.0  65:50.21 pdflush 12141 tim       18  -2 19380 1660 1024 R    1  0.0   0:04.04 top  1240 root      15  -5     0    0    0 S    0  0.0  16:07.11 kjournald  9019 root      20   0  296m 4460 2616 S    0  0.0  82:19.51 kdm_greet     1 root      20   0  4028  728  592 S    0  0.0   0:03.11 init     2 root      15  -5     0    0    0 S    0  0.0   0:00.00 kthreadd     3 root      RT  -5     0    0    0 S    0  0.0   0:01.01 migration/0     4 root      15  -5     0    0    0 S    0  0.0   0:08.13 ksoftirqd/0     5 root      RT  -5     0    0    0 S    0  0.0   0:00.00 watchdog/0     6 root      RT  -5     0    0    0 S    0  0.0  17:27.31 migration/1     7 root      15  -5     0    0    0 S    0  0.0   0:01.21 ksoftirqd/1     8 root      RT  -5     0    0    0 S    0  0.0   0:00.00 watchdog/1     9 root      RT  -5     0    0    0 S    0  0.0  10:02.56 migration/2    10 root      15  -5     0    0    0 S    0  0.0   0:00.34 ksoftirqd/2    11 root      RT  -5     0    0    0 S    0  0.0   0:00.00 watchdog/2    12 root      RT  -5     0    0    0 S    0  0.0   4:29.53 migration/3    13 root      15  -5     0    0    0 S    0  0.0   0:00.34 ksoftirqd/3 Properties vs Methods Quick question: When do you decide to use properties (in C#) and when do you decide to use methods?  We are busy having this debate and have found some areas where it is debatable whether we should use a property or a method. One example is this:  public void SetLabel(string text) {     Label.Text = text; }   In the example, Label is a control on a ASPX page. Is there a principle that can govern the decision (in this case) whether to make this a method or a property.  I'll accept the answer that is most general and comprehensive, but that also touches on the example that I have given.