What elements affects the key pairs generated by ssh-keygen?
Why I can't connect to VPS after changing OS from CentOS to Ubuntu?
Why use a dedicated light meter instead of the one built into the camera? Let $a&gt;b&gt;0$ and let $n \in N$ satisfy $n \geq 2$.  Prove that $$a^{1/n}-b^{1/n}&lt;(a-b)^{1/n}.$$  If we let $a=x$ and $b=x-1$, then we need to show that $f(x):=x^{1/n}-(x-1)^{1/n}$ is decreasing for $1\leq x$ (which means that $f'(x)\leq 0$ and $f$ is differentiable), and evaluate $f$ at $1$ and $a/b$. The sum of an uncountable number of positive numbers Claim: If $(x_\alpha)_{\alpha\in A}$ is a collection of real numbers $x_\alpha\in [0,\infty]$ such that $\sum_{\alpha\in A}x_\alpha&lt;\infty$, then $x_\alpha=0$ for all but at most countably many $\alpha\in A$ ($A$ need not be countable).  Proof: Let $\sum_{\alpha\in A}x_\alpha=M&lt;\infty$. Consider $S_n=\{\alpha\in A \mid x_\alpha&gt;1/n\}$.  Then $M\geq\sum_{\alpha\in S_n}x_\alpha&gt;\sum_{\alpha\in S_n}1/n=\frac{N}{n}$, where $N\in\mathbb{N}\cup\{\infty\}$ is the number of elements in $S_n$.  Thus $S_n$ has at most $Mn$ elements.   Hence $\{\alpha\in A \mid x_\alpha&gt;0\}=\bigcup_{n\in\mathbb{N}}S_n$ is countable as the countable union of finite sets. $\square$  First, is my proof correct? Second, are there more concise/elegant proofs? I'm working from the URL I found here:    My ssh client is Ubuntu 64 bit 11.10 desktop and my server is Centos 6.2 64 bit. I have followed the directions. I still get a password prompt on ssh.  I'm not sure what to do next. What is the tolerable magnetic field (in Tesla) for a hard disk? I was wondering what would be the safest magnetic field for a hard drive so that the data inside it is safe and not wiped off?  For example I have a 2.1 home theatre system and when I take my android phone near it to check the magnetic field range it gives me a reading of 1000 micro Tesla. Would that be considered safe for a nearby hard disk? A positive integer is divisible by $3$ iff 3 divides the sum of its digits I am having trouble proving the two following questions:    If $p|N$, $q|N$ and gcd(p,q)=1, then prove that $pq|N$ If $x$ is non zero positive integer number, then prove that $3|x$ if and only if 3 divides the sum of all digits of $x$.   For both questions I tried to use theorems of discrete mathematics, but I could not find the way to solve them. Reverse (parse the output) of Arrays.toString(int[]) Is there in the JDK or Jakarta Commons (or anywhere else) a method that can parse the output of Arrays.toString, at least for integer arrays?  int[] i = fromString(Arrays.toString(new int[] { 1, 2, 3} ); The story is basically told from an alien's point of view. Essentially they observed us from far off, deemed us as violent and a danger to the universe, and set course (asteroid or something) to kill us. They kept observing and saw all the art and beauty we created and realized we were actually not so bad, but by then they couldn't stop it. So it was sort of also an apology letter to Earth in the end.  First read it like a year ago online and I can't find any trace of it anymore, nor can I recall the site it was on. Anyone know what short story this is? How to define servlet filter order of execution using annotations in WAR I'm an elected diamond moderator on one site, and a user of several others. I think it would be extremely helpful for our flagging process if users had the option to enter freeform text explaining their flag on types of flags other than the "in need of moderator attention" flag.  An example of when this is relevant: Sometimes posts have had rude/abusive flags, but the rude/abusive part might be difficult to notice, or it might be a single word or sentence buried somewhere in the middle of the post. Users have to choose between "flag it as rude with no explanation" or "flag it as misc and explain what's going on". Often they'll pick the first because of course it seems like what they should do (e.g. they know the system has special handling attached to rude/abusive flags) but it means they can't explain what's going on to us, so we have to reach out directly in private to find out.  Sometimes it also helps to be able to explain why a comment is no longer needed, because past experience tells me the "no longer needed" flag on its own might be declined on a particular site -- so I pick the custom reason instead of "no longer needed" just so I can provide explanation.  I'd prefer users be able to understand they can pick the appropriate reason and be able to attach any explanation they deem necessary to further direct moderators to the issue. If not for all kinds of flags, then at least for spam or rude/abusive flags. Does it make sense to use a date variable in a regression? I'm not used to using variables in the date format in R. I'm just wondering if it is possible to add a date variable as an explanatory variable in a linear regression model. If it's possible, how can we interpret the coefficient? Is it the effect of one day on the outcome variable?   See my  with an example what I'm trying to do. Make window always on top? Some applications do not have the functionality like Task Manager's &quot;Always on top&quot; feature.  Is there a way around this? Exact relationship between electric field and intensity I often see $I(t)\propto |E(t)|^2$. What is the exact form ? Which constants are missing to make this an equality and why are they so often omitted ? How can I pass arguments to a batch file? I am a physics Master's student.  I have good grades, with CGPA above 9(/10)(However, all courses in my university are graded on a curve so the actual marks are significantly lower than 90%). This has been my marks throughout my undergraduate and graduate courses and I was happy because this was above average. Also, my summer projects in UG were usually computational and any difficulty I had in theoretical aspects I attributed it to my inexperience in advanced Physics.   However, recently I have started to work on pure theoretical project and while reading for the project I realized that I consistently miss some details from each topic. I understand the general idea, can re-derive most of the equations(with some effort) however when I discuss things with my professor or when I read further topics I realize that I have missed certain key-details. This is exactly similar to the case of me missing a few key questions in my exams and getting that 9 grade point instead of 10(or at-least I think so). I was not worried about this before but now I realize that there is some flaw in the way I study (but I do not know what).   Since I want to apply for Physics PhD I realized that I will need to have solid concepts and it would be best to correct my mistakes but I do not know how or even what could be the reason for my imperfect understanding.  Any direct suggestion would help or even certain general guidelines on what I can do.    Things I've tried recently -   1) I've started to written down almost everything I read. This is slightly laborious but is certainly helping. It also helps me to gloss over the things I read previously when I come back the next day.  2) I completely avoid smartphone when I'm library/study room so that I won't get distracted. Not sure if it helps me solve the above problem but certainly helps me study better in general.  3) I've tried to read the topics from several sources. The books I am reading is somewhat like a collection of research papers and hence does not have a exercises. So I though reading from various sources might help get better ideas but it's not really helping because most other sources are too high level as an introductory text. But this will probably help me in cases where it's practical to do this.  4) Somewhat similar to point (1)- I am trying reread, whenever I can, what I've done until that point. But not sure how much this will help me in filling the gaps. How to log out user from web site using BASIC authentication? Is it possible to log out user from a web site if he is using basic authentication?  Killing session is not enough, since, once user is authenticated, each request contains login info, so user is automatically logged in next time he/she access the site using the same credentials.  The only solution so far is to close browser, but that's not acceptable from the usability standpoint. disable comments if array exists This is the code which is registering the function for rewrite_endpoints():   function wpa121567_rewrite_endpoints(){  add_rewrite_endpoint( 'comments', EP_PERMALINK );  add_rewrite_endpoint( 'stats', EP_PERMALINK );  }  add_action( 'init', 'wpa121567_rewrite_endpoints' );   NOTE  I don't know if this matters but I will write it.   I have single-CPT.php which is calling  /inc/post-format/single-CPT.php like this:      &lt;?php while ( have_posts() ) : the_post(); ?&gt;  &lt;?php   get_template_part( 'inc/post-format/single-debate');      ...   This is the code which is checking if array key exists, which is  inside my /inc/post-format/single-cpt.php:   ?php if( array_key_exists( 'comments', $wp_query-&gt;query_vars ) ){  the_field('comments_section');   } elseif( array_key_exists( 'stats', $wp_query-&gt;query_vars ) ) {   the_field('stats_section');   } else { // the request is for the main post  }   ?&gt;   This is my comments.php :       &lt;div id="comments" class="comments-area"&gt; &lt;?php // If CPT and not logged in, display a message: if ( 'debate' == get_post_type() &amp;&amp; ! is_user_logged_in() ) { echo '&lt;p class="must-log-in" style="padding-left:20px; font-size:20px;"&gt;You must be logged in to post a comment.' . '&lt;/p&gt;';  echo do_shortcode("[upme_login]");   } ?&gt;     &lt;?php if ( have_comments() ) : ?&gt;         &lt;h3 class="comments-title"&gt;              &lt;?php                 printf( _n('%d comment', '%d comments', get_comments_number(), 'outbox' ),                     number_format_i18n( get_comments_number() ) );             ?&gt;         &lt;/h3&gt;             &lt;ol class="commentlist"&gt;              &lt;?php                 wp_list_comments( array( 'callback' =&gt; 'outbox_comment' ) );             ?&gt;         &lt;/ol&gt;&lt;!-- .commentlist --&gt;          &lt;?php if ( get_comment_pages_count() &gt; 1 &amp;&amp; get_option( 'page_comments' ) ) : // are there comments to navigate through? If so, show navigation ?&gt;         &lt;nav role="navigation" id="comment-nav-below" class="site-navigation comment-navigation clearfix"&gt;             &lt;div class="nav-previous"&gt;&lt;i class="icon-left-open-1"&gt;&lt;/i&gt;&amp;nbsp;&lt;?php echo get_previous_comments_link( __( 'Older Comments', 'outbox' ) ); ?&gt;&lt;/div&gt;             &lt;div class="nav-next"&gt;&lt;?php echo get_next_comments_link( __( 'Newer Comments', 'outbox' ) ); ?&gt;&amp;nbsp;&lt;i class="icon-right-open-1"&gt;&lt;/i&gt;&lt;/div&gt;         &lt;/nav&gt;&lt;!-- #comment-nav-below .site-navigation .comment-navigation --&gt;         &lt;?php endif; ?&gt;      &lt;?php endif; // have_comments() ?&gt;      &lt;?php         // If comments are closed and there are comments, let's leave a little note, shall we?         if ( ! comments_open() &amp;&amp; '0' != get_comments_number() &amp;&amp; post_type_supports( get_post_type(), 'comments' ) ) :     ?&gt;         &lt;p class="nocomments"&gt;&lt;?php _e( 'Comments are closed.', 'outbox' ); ?&gt;&lt;/p&gt;     &lt;?php endif; ?&gt;     &lt;?php  // Don't output the comment form if CPT and user isn't logged in if ( 'debate' != get_post_type() || is_user_logged_in() ) {  comment_form(); }  ?&gt;  &lt;/div&gt;&lt;!-- #comments .comments-area --&gt; &lt;?php } ?&gt;    This is how the comments template is included  inside my single-CPT.php :  if ( comments_open()  )  comments_template( '', true );   I want to disable comments if if( array_key_exists( 'comments', $wp_query-&gt;query_vars ) ){  How can I do this? Fitting an infinite collection of balls in an infinite dimensional unit ball Given an infinite dimensional normed linear space, how would one show that it is possible to fit an infinite collection of non-overlapping balls of radius $\frac{1}{4}$ in the unit ball?  I guess one can immediately reduce the problem to a normed linear space of countably infinite dimensions. The solution seems clear if the concept of orthogonality exists, but not every normed linear space has an inner product so it's not possible to apply something like Gram-Schmidt to produce an orthogonal basis. Is there any way around this, or there another approach that can be used? Connecting GSM SIM900A module with Ardunio I have bought an SIM900A Mini V4 GSM module. Here is the module,   I want to configure with arduino to send and receive SMS.   Do I have to connect TXD of this module--Tx of Arduino &amp; RXD of this module--Rx of Arduino or other way around?  There is no datasheet or documents on this new module.  When I search about RXD &amp; TXD, I found this in      TxD means "Data to be transmitted over the comms link" - which will clearly be an input to the modem;    Similarly, RxD means "Data that has been received from the comms link" - which will clearly be an output from the modem.    But I couldn't send or receive SMS using this configurations.  As I am new to this, It would be very helpful if anyone help on this.  Thank you in advance. "Startup Applications" not working