CSS child elements "margin-top" property affects parent element
Margin on child element moves parent element
$A,B,C$ are three $n\times n$ matrices such that $A$ has $n$ distinct eigenvalues, $AB=BA$, and $AC=CA$.   We need to show $BC=CB$.  Let $A$ be diagonalizable with eigenvectors say, $v_1,\dots,v_n$, so there exists $P$ such that $PAP^{-1}=D$. What more I can say from the information? Please help. In Assa Auerbach's book (Ref. 1), he gave an argument saying that in the normal process of path integral, we lose information about ordering of operators by ignoring the discontinuous path.   What did he want to say? I don't think there is any problem related to the ordering of operators.  References:   Assa Auerbach, Interacting Electrons and Quantum Magnetism, p.102, just below eq. (10.6). pdflatex, \includegraphics, and multi-page PDF files I have a PDF file with multiple figures; each figure is a separate page in the PDF file.  I am using pdflatex, and I would like to use \includegraphics or equivalent to include some of the figures.  Of course I could use an external tool to split the PDF file into multiple one-page PDF files. Then I could use \includegraphics as usual. However, I would have a much simpler workflow if I could avoid this extra step. Hence the question:  How can I include, e.g., page 3 of foo.pdf as a figure?  I am aware that there is a Latex package called pdfpages, but it seems to be designed for something else: with pdfpages, each page in the input file will produce a full page in the final document, not just a box. Is it possible to get back your deleted Terraria character? Why can't Transporter technology be used as a weapon? Seems like this is the most powerful weapon of all: transport your enemy into a bulkhead, planet, etc. Transport your enemy's ship inside a planet, etc.  Is there some technical reason that it can not be used this way? I work in D8, I create a custom module first_module. By modules create a url and display all nodes by *.html.twig file.  Write code in controller.php  public function contentthree() {    $connection = Database::getConnection();    $query = $connection-&gt;select('node', 'n');   $query-&gt;fields('n', ['nid', 'type']);    $groups = $query-&gt;execute()-&gt;fetchAll();    foreach ($groups as $group) {     $events[] = [$group-&gt;nid, $group-&gt;type];   }    return [     '#theme'  =&gt; 'first_module_display',     '#events' =&gt; $events,   ]; }   In *.module  function first_module_theme($existing, $type, $theme, $path) {    return [     'first_module_display' =&gt; [       'variables' =&gt; ['events' =&gt; NULL],       'template'  =&gt; 'first-module-list',     ],   ]; }  function _get_node_details() {    $output = 'Welcome D8';    $output .= 'Node Details';    return $output; }   and create templates first-module-list.html.twig and display data  {%for key, data in events %}  {%for key1, data1 in data %}     {{ data1 }}  {% endfor %}  {% endfor %}   work fine and showing data correct. But, my question is how to call function _get_node_details() and how to render node details in first-module-list.html.twig files? Table with actions per row What is the sum of the power series: $\sum_{k=2}^\infty\frac{x^k}{k(k-1)}$? What is the function represented by the power series $$ \sum_{k=2}^\infty\frac{x^k}{k(k-1)}\quad? $$  It looks like $\dfrac1{1-x}$ but I don't know. Is the function $\mbox{tr}(XAX')$ convex? Is the function $\mbox{tr}(XAX')$ convex, where $A$ is a positive semidefinite (PSD) matrix? I know that for a general $A$, the above trace function is not convex. But for a PSD $A$, is the function convex? Eclipse menus are cut off or don't show I'm using Ubuntu 13.10 (with JDK 1.7.0_45).  I've downloaded and uncompressed Eclipse Kepler for Java EE Developers.  The software menus are messed up. I didn't notice similar problems in other software.  When I click any menu in Eclipse, the drop-down seems to be "cut". Sometimes the drop-down shows, but the options are invisible.  I tried Eclipse Indigo, but the same problem occurs. Do you have to take the second leg of a domestic flight? I'm wondering how it is correct to structure sentence and what punctuation should be used. In particular, is the next sentence correct:     I was wondering if there's any progress on the issue.    Or should I put a question mark in the end of it. Also, can it be restructured to:     I was wondering: is there any progress on the issue? Does Ubuntu come with a preinstalled or automatic firewall? If not, do I need one?   I've read some articles about the advantages of Linux over other operating systems about security (no need to have antivirus, ...) but would like to be sure. How do I install an older version of an app on an iPhone? Another homework problem from my Group Theory class.  Let $a,b$ be elements of a group, $G$.  Let $\operatorname{ord}(a)=m$ and $\operatorname{ord}(b)=n$. Let $a$ and $b$ commute. Prove: If $m$ and $n$ are relatively prime, then the $\operatorname{ord}(ab)=mn$.  So I am having trouble starting off on this problem.  Here is what I believe I know:  $a^m=e$ and $b^n=e$ [as defined by the order of the elements] which leads $a^m=b^n$  $\operatorname{ord}(ab)=mn=\operatorname{ord}(ba)=nm$ as defined by commuting.  $\gcd(m,n)=1$ as defined by $m,n$ being relatively prime.    I don't know how to start this proof. Do I want to to go the route of $a^mb^n=e$?  Then $(ab)^{mn}=e$?   Any tips to start this would be greatly appreciated!!! Why do some questions in question lists have a yellow background? On SO, when I'm scrolling through "questions" some have a yellow background.  Is this intuitive to everyone but me?  What is the yellow background trying to tell me about this particular question? Simple past or present perfect? Which is preferable, simple past or present perfect, in situations like this one: I had a conversation with my friend and we planned to do something; shortly afterwards I call him back to announce the accomplishments. My biggest doubt about simple past is that perfect aspect is used to indicate past action (accomplishment) with current relevance, at the same time I'm not sure if I'm allowed to use present perfect, because there's a gap between accomplishing and the current moment, which is a characteristic of simple past. Amy: What day is it today?    Tom: It's Monday. Hmm... I like Monday.   Amy: What do you have today?   Tom: We have math, science and art.What about you?   Amy: We have English and P.E. What do you have tomorrow?    Tom: We have art and P.E.tomorrow.    Amy: Oh, great.      I can understand that "What about you" means "What do you have today?"  But I wonder whether "What about you" is an elliptical sentence. If it is, what is the full sentence? If it isn't, how to parse this structure? Proof that for $a,b,c\in \mathbb{R}$, hold that $\left |\sqrt {a^2+b^2}-\sqrt {a^2+c^2} \right |\leq \left |b-c \right |$. Proof that for $a,b,c\in \mathbb{R}$, hold that $\left |\sqrt {a^2+b^2}-\sqrt {a^2+c^2}  \right |\leq \left |b-c  \right |$. Give me a clue, I don't have any idea to work with that inequality. 20GB of Temporary Files, Only 50MB in Temp Folder I recently discovered that the Settings app is showing around 20GB of space used by temporary files. But when I go to remove them I can only remove about 28MB. When I open the temp folder by using Run and then %temp% it only shows around 40-50MB of files right after boot. How can I remove these 20GB of invisible files? I only have a 240GB SSD so space is quite scarce. Here are a few photos:    I run Windows 10 Home Activated. I have tried Disk Cleanup but this removed only around 30MB of files.  UPDATE: After turning on hidden items I found a folder name WINDOWS-BT, after doing some research it turned out to be a folder for the previous windows version. I deleted it using TakeOwnerShip pro and this removed around 12GB of temporary files, but 8GB still remain. I am currently downloading TreeSize free to find out where the other 8GB is.  UPDATE 2: Hi, I downloaded TreeSizeFree and I didn't really find anything there.   The biggest folder is 87GB of Program Files which mainly consists of my GTA V install. The Program Files (x86) folder was mainly made up of my Steam games (CS:GO, Besiege, etc). The 5.5GB [3 Files] location was noted as being my pagefile.    The Windows folder shows up as 25GB when in Settings it is only 18GB, this could explain where the other 8GB are coming from. What are some things I should look for in there?  FINAL UPDATE: After deleting the Windows-BT folder it reappeared a few hours later. I decided to check from system updates and surely enough one was downloaded and pending to be installed. After installing the update the Windows-BT folder disappeared on it's own and a new folder taking up 20GB called Windows.old was created. I then followed this  to remove the .old folder and I had all my disk space back! NOTE: Disk Cleanup wasn't able to find the Windows.old folder, this is why I had to delete it from the settings app.