How to use \min in equation
Getting arguments underneath \min in an align environment
NS list does not match list from parent zone I'm attempting to figure out an error message that I got from dnsstuff.com when examining my DNS records.  The error reads as follows.     NS list does not match list from parent zone. This should be addressed because queries for this domain may require an extra lookup (and more overhead) because there is no direct relationship between the NS records at the parent and the NS records at the authoritative servers. This can cause delays. The mismatched NS list is:      nameserver ns1.domain.co. | xxx.xx.xxx.xxx is missing NS2.domain.co. | yy.yyy.yy.yyy   There are a couple questions I have regarding this.   What is the difference between a parent and authoritative zone?  In other forum posts I've seen, the seem to be used interchangeably (although that could be my misperception). What does it mean for the NS list not to match the list from the parent zone?  What is "the list from the parent zone" to which they refer? How might you recommend that I resolve this?   In case this affects any answers, I'm running Virtualmin on Ubuntu 12.04.  Any help is appreciated.  Many thanks in advance! Is there an MD5 Fixed Point where md5(x) == x? Is there a fixed point in the MD5 transformation, i.e. does there exist x such that md5(x) == x? I have seen some examples about using "in" with time expressions. They give some examples as shown below:     I will leave for vacation in a month. (Exactly one month from now I   will go on vacation.)      We’ll be there in an hour.  (Exactly one hour will go by and then we   will arrive.)   But these comments confused me. Then I looked the usage of "in" up in a dictionary and it says about usage of "in" with time expressions :"before or at the end of a particular period". I think the comments and the definition in the dictionary contradict each other?    I have examples of mine:     1- Dinner will be ready in ten minutes. (Maybe dinner will be   ready at the 5th minute? or 8th. Does it strictly mean dinner will be   ready at the end of the ten minutes?)      2- My letter arrived in two days. ( Does that mean it took   exactly two days to arrive? or Could it be just one day because he/she   doesnt remember the exact time?)      3- Imagine you are on the first day of a month and your friend says:   I will be going outside the country in this month. (Does that mean he/she could go tomorrow or ten days later or at the end of the   month?)      4- He can run a mile in 5 minutes. ( Does that mean he has to   spent entire 5 minutes to run a mile? Could it be 4 or 4.5 minutes?) LaTeX to plain text for e.g. generation of statistics I would like to convert a large LaTeX project (i.e. spanning multiple files) into plain text. The purpose is generation of statistics, so representing mathematics is not an issue. In fact, all mathematics is ideally ignored.  I have found  but could not get it to run. It seems unfinished, but is exactly what I am looking for otherwise. $\sum (-1)^n/n$ fails the p-series test, but passes the alternating series test? I installed Windows on my computer, followed by an installation of Ubuntu. However, now I'm unable to boot into my Windows install.  What can I do to fix this? Windows 98 on a modern computer? Install Alongside Windows or Something Else - Which should I use? I have old notebook with BIOS (not EFI) installed with Windows 8 RTM, want to install Ubuntu 12.10 by booting to a LiveCD.   Doing some research, I found method either to choose Something Else or Install Alongside... Which method should I use? Stance on repost question instead of editing to invalidate answers? Does somebody has an example where the left $R$-modules $R^m$ and $R^n$ are isomorphic for all positive integers $m$, and $n$? What is the correct pronunciation of the word "solder"? I have been listening to a podcast where the host pronounces the word solder as "sodder" or "sod-der", even "saw-der". Same thing happened when the lecturer of one of my EE classes pronounced the word solder. As for me I pronounce the word solder as "sole-der" with a distinct L and a longish O. The optical density of a medium is quantified by its refractive index $n$. Does it have any correlation with the mass/number density of the medium? In other words is an optically denser medium must have a greater mass density compared to an optically rarer medium? root folder access via gui I'm new to linux and the terminal. As I learn how to use the terminal to navigate through directories, I like to use the gui file explorer to mirror my terminal navigation. The icons and file extension info in the gui file explorer help me figure out what everything is. However, I can't access the root folder via the gui, I can only access it via the terminal. Is there a way to enable access to the root folder outside of the terminal? How to automatically generate a stacktrace when my program crashes How to remove images from showing in a post with the_content()? Trying to learn more about creating my own themes and not using any plugins I wanted an ability to display all the images in a post excluding the thumbnail in my single-foobar.php file and I can do that with:  &lt;?php if ( have_posts() ) : while ( have_posts() ) : the_post();      $thumb_ID = get_post_thumbnail_id( $post-&gt;ID );  $args = array(    'post_type' =&gt; 'attachment',    'numberposts' =&gt; -1,    'post_status' =&gt; null,    'post_parent' =&gt; $post-&gt;ID,    'exclude' =&gt; $thumb_ID   );  $attachments = get_posts( $args );  if ( $attachments ) {     foreach ( $attachments as $attachment ) {        echo '&lt;div class="portproject"&gt;';        $image_res = wp_get_attachment_image( $attachment-&gt;ID, ' img-responsive' );        echo $image_res;        echo '&lt;/div&gt;';       }  }  else { ?&gt;     &lt;span&gt; No pictures loaded at this time&lt;/span&gt;  &lt;?php } endwhile; endif; ?&gt;   However, when I apply my static HTML and then try to call get_the_content() with:  &lt;?php  $content = get_the_content(); $content = preg_replace("/&lt;img[^&gt;]+\&gt;/i", "(image) ", $content);           $content = apply_filters('the_content', $content); $content = str_replace(']]&gt;', ']]&gt;', $content); echo $content; ?&gt;   it removes the images but leaves a (image) in the post with spaces then displays the remaining text. I did find a similar  but it suggests using get_the_content() but that strips all the styling from the post.  So my question is how can I strip images from the_content()?  I did find "" from my searches but that still uses the get_the_content() approach. Flag post that is already in low quality review queue - any effect? Let's say I see an answer that should not have been one and I flag it as Not An Answer (NAA). On this site I have plenty of reputation and am able to use the Low Quality (LQ) review queue and cast delete recommendation votes.  Of course raising such a flag on a still virgin post brings it to the LQ review queue, but what happens if I flag a post on the main site that is already in the respective review queue?  Is my flag simply useless in that case? I doubt it would be the same as casting a delete (recommendation) vote from the queue. And when I somehow manage to find that specific post in the review queue later, it's locked down for me, because I have already cast a flag. So was that flag without any effect?  Based on how I currently guess the system works, I proposed two alternative solutions to improve the system in my feature request . They were first part of this question, but I decided to split the question from the feature requests. Why don't metals bond when touched together? It is my understanding that metals are a crystal lattice of ions, held together by delocalized electrons, which move freely through the lattice (and conduct electricity, heat, etc.).   If two pieces of the same metal are touched together, why don't they bond?   It seems to me the delocalized electrons would move from one metal to the other, and extend the bond, holding the two pieces together. If the electrons don't move freely from one piece to the other, why would this not happen when a current is applied (through the two pieces)? Prove $\int\cos^n x \ dx = \frac{1}n \cos^{n-1}x \sin x + \frac{n-1}{n}\int\cos^{n-2} x \ dx$ I am trying to prove  $$\int\cos^n x \ dx = \frac{1}n \cos^{n-1}x \sin x + \frac{n-1}{n}\int\cos^{n-2} x \ dx$$  This problem is a classic, but I seem to be missing one step or the understanding of two steps which I will outline below.   $$I_n := \int\cos^n x \ dx = \int\cos^{n-1} x \cos x \ dx \tag{1}$$  First question: why rewrite the original instead of immediately integrating by parts of $\int \cos^n x \ dx$?  Integrate by parts with $$u = \cos^{n-1} x, dv = \cos x \ dx \implies du = (n-1)\cos^{n-2} x \cdot -\sin x, v = \sin x$$  which leads to  $$I_n = \sin x \ \cos^{n-1} x +\int\sin^2 x (n-1) \ \cos^{n-2} x \ dx \tag{2}$$  Since $(n-1)$ is a constant, we can throw it out front of the integral:  $$I_n = \sin x \ \cos^{n-1} x +(n-1)\int\sin^2 x \ \cos^{n-2} x \ dx\tag{3}$$  I can transform the integral a bit because $\sin^2 x + cos^2 x = 1 \implies \sin^2 x = 1-\cos^2 x$  $$I_n = \sin x \ \cos^{n-1} x + (n-1)\int(1-\cos^2 x) \ \cos^{n-2} x \ dx \tag{4}$$  According to Wikipedia as noted , this simplifies to:  $$I_n = \sin x \ \cos^{n-1} x + (n-1) \int \cos^{n-2} x \ dx - (n-1)\int(\cos^n x) \ dx \tag{5}$$  Question 2: How did they simplify the integral of $\int(1-\cos^2 x) \ dx$ to $\int(\cos^n x) \ dx$?  Assuming knowledge of equation 5, I see how to rewrite it as  $$I_n = \sin x \ \cos^{n-1} x + (n-1) I_{n-2} x  - (n-1) I_{n} \tag{6}$$  and solve for $I_n$. I had tried exploiting the fact that  $$\cos^2 x = \frac{1}{2} \cos(2x) + \frac{1}{2} $$  and trying to deal with $\int 1 \ dx - \int \frac{1}{2} \cos (2x) + \frac{1}{2} \ dx$  which left me with $\frac{x}{2} - \frac{1}{4} \sin(2x)$ after integrating those pieces. Putting it all together I have:  $$I_n = \sin x \ \cos^{n-1} x + (n-1) I_{n-2} x \left(-(n-1) (\frac{x}{2} - \frac{1}{4} \sin 2x) \right) \tag{7}$$  but I'm unsure how to write the last few terms as an expression of $I_{something}$ to get it to match the usual reduction formula of   $$\int\cos^n x \ dx = \frac{1}n \cos^{n-1}x \sin x + \frac{n-1}{n}\int\cos^{n-2} x \ dx$$ Number theory lemma - $x^2 \equiv 1 \pmod p$ implies $x\equiv\pm 1\pmod p$ How to show that the spherical metric satisfies the triangle inequality? For $x,y\in \mathbb R^n$ define  $$d(x,y)={\|x-y\| \over \sqrt{1+\|x\|^2} \sqrt{1+\|y\|^2}}$$ Here $\|x\|$ is the euclidean norm of a vector. How to prove that $d$ (the spherical metric) is indeed a metric?     Progress so far:    $d(x,y)\ge 0$ is obvious. $d(x,y) =0 \iff \|x-y\|=0 \iff x=y$, so the positivity holds. $d(x,y) = d(y,x)$ is clear from the formula, so symmetry holds.    But I am having difficulties with the triangle inequality. Writing it out in coordinates leads to a complicated inequality with square roots all over the place in denominators. Is there a better way?