From  I used the following codes to add an empty INTENTIONALLY LEFT BLANK page if a section ended in an odd number of pages, as well as if the total document would end in an odd number of pages (because for some reason it doesn't add the blankpage to the last section)  \newcommand*{\blankpage}{% %\setlength{\topskip}{0pt}%    % \setlength{\parskip}{0pt}% \vspace*{\fill} { \centering INTENTIONALLY LEFT BLANK.\par} \vspace{\fill}}  \makeatletter  \renewcommand*{\cleardoublepage}{\clearpage\if@twoside \ifodd\c@page\else \blankpage \newpage \if@twocolumn\hbox{}\newpage\fi\fi\fi} \makeatother  \AtEndDocument{%   \ifthenelse{\isodd{\pageref{LastPage}}}{\null\blankpage}{}}   Now here's my own question: the code made by the famous @DavidCarlisle seems to hint that if a two column setup is used, it would still place the "INTENT...BLANK" part right in the middle of the page. And it did! And then suddenly, it stopped doing it and started placing it on the left side of the page which I would guess to be centered in the left column. So how can I overrule the two columns and still have the sentence placed in the middle? The last page seems to be doing it right even though the \end{multicols} is after that last section.
I have a scrbook document with an openright option, i.e. every once in a while a blank left page appears in the document. Not that I really want to do this, but how could I include the infamous "This page has been intentionally left blank" in those blank pages cleanly, i.e. without too many hacks?  Bonus points for including a different famous quote on each blank page instead of the dull default ;)
This is an attempt to gather together the various questions about time that have been asked on this site and provide a single set of hopefully authoritative answers. Specifically we attempt to address issues such as:   What do physicists mean by time? How does time flow? Why is there an arrow of time? Why an R-module is an R/I-module precisely when it is annihilated by I? Let $I$ be an ideal of $R$ and let $M$ be an $R$-module. Prove that the formula $(r + I) \cdot m = r \cdot m$ for $r + I \in R/I$, and $m \in M$ makes $M$ into an $R/I$-module if and only if $i \cdot m = 0$ for all $i \in I, m \in M$.   I don't quite understand why we must have $i \cdot m = 0$ instead of $I \cdot m \in M$. This is for proving the only if part. How to call a function in a Twig file What does the term saturating nonlinearities mean? I was reading the paper  and in section 3 were they explain the architecture of their Convolutional Neural Network they explain how they preferred using:     non-saturating nonlinearity $f(x) = max(0, x). $   because it was faster to train. In that paper they seem to refer to saturating nonlinearities as the more traditional functions used in CNNs, the sigmoid and the hyperbolic tangent functions (i.e. $f(x) = tanh(x)$ and $f(x) = \frac{1}{1 + e^{-x}} = (1 + e^{-x})^{-1}$ as saturating).   Why do they refer to these functions as "saturating" or "non-saturating"? In what sense are these function "saturating" or "non-saturating"? What do those terms mean in the context of convolutional neural networks? Are they used in other areas of machine learning (and statistics)? Windows 10 high memory usage (unknown reason) How to use regex in String.contains() method in Java Quite a few of the questions given on this site mention a photon in vacuum having a rest frame such as it having a zero mass in its rest frame. I find this contradictory since photons must travel at the speed of light in all frames according to special relativity.  Does a photon in vacuum have a rest frame? How to use stars and bars for solving number of integral solutions to an equality? How to use the  method?  Say I want to find number of combinations I can get with $x_1+x_2+x_3+x_4=22$,  where $x_i\in\mathbb{N}$.  Is this the correct time to apply the method?  This is being repurposed in an effort to cut down on duplicates, see here:     and here: Note: The legacy Skype for Linux application (v4.*) is now discontinued and was removed from Canonical’s partner repositories, so this question and its answers are obsolete. Please refer to  of our .    I am receiving the following message while I am trying to install Skype:  nidhin@ubuntu:~$ sudo apt-get update nidhin@ubuntu:~$ sudo apt-get install skype Reading package lists... Done Building dependency tree        Reading state information... Done Some packages could not be installed. This may mean that you have requested an impossible situation or if you are using the unstable distribution that some required packages have not yet been created or been moved out of Incoming. The following information may help to resolve the situation:  The following packages have unmet dependencies:  skype : Depends: skype-bin but it is not installable E: Unable to correct problems, you have held broken packages   How can I fix this? I have a WinForms app that I am trying to make full screen (somewhat like what VS does in full screen mode).  Currently I am setting FormBorderStyle to None and WindowState to Maximized which gives me a little more space, but it doesn't cover over the taskbar if it is visible.  What do I need to do to use that space as well?  For bonus points, is there something I can do to make my MenuStrip autohide to give up that space as well? Android app intermittently shows blank body in questions and answers (multiple sites) Note: the bug has returned in version 1.0.89 in a somewhat different form. See:      This possible bug report is similar to the bug in  that was deemed not-reproducible.  I can reproduce something similar with more recent app &amp; Android versions.   App Version: 1.0.34 (original report; is still present in 1.0.38, 1.0.42, 1.0.58) Android Version: 4.4 (up to 4.4.4) Device: Motorola Droid Maxx   In the examples below, you can see some blank answer bodies.  These are on different sites, and represent answers with both edited and non-edited text. In the first example, I clicked on the top answer tab to get to the answers, and in the second example I clicked on the bottom "View n Answers" button. (Trying to be a good little tester!)  Because I've seen this blank-answer-body intermittently over the past couple weeks (before the May 7 update), my process to test was just to go to the first site I frequent and then systematically click through the question list until I found a question with answers in which at least one answer was blank.  For all three sites shown below, it was within the first 5 or 7 questions sorted by newest.  Please note that I have seen many questions with several answers, none of which were blank. It is truly intermittent.  Example blank answer body at Workplace.SE:    Example blank answer body at Programmers.SE:    Example blank answer body at UX.SE:    And now here's the kicker, which makes me think this is some sort of content-loading latency issue rather than a rendering issue:  I returned to the left-side menu, selected the User Experience site, picked the same question as above, and then clicked the top answer tab to view answers again, and lo and behold the text is there:    I then went back to the other questions with blank answers, shown above, and the answer bodies were no longer blank.  I am happy to go through more tests/paths and do screenshots if it is helpful.  The same bug also appears in question bodies. I am using Selenium 2/WebDriver for automation. I have a table and am trying to select a row in it. When the test runs, I can see the row become highlighted as if it is clicked, but then immediately I get the "org.openqa.selenium.StaleElementReferenceException: Element is no longer attached to the DOM" error and the test fails.  The code is the following:  @Test public void rowSelection() throws Exception {     SeleniumHelper helper = new SeleniumHelper();     action = new SeleniumActionHelper(driver);      helper.login();      String testUrl = navigateToUrl("option/listOptions.xhtml");     driver.get(testUrl);      WebElement table = findElementById("tableSection:dataTableWrapped_data");     List&lt;WebElement&gt; allRows = table.findElements(By.tagName("tr"));     for (WebElement row : allRows)         {             List&lt;WebElement&gt; cells = row.findElements(By.tagName("td"));             for (WebElement cell : cells)             {                 WebElement listName = cell.findElement(By.xpath("./* [text()='body_build']"));                 listName.click();             }         } }   I have put a Thread.sleep(2000) in front and after the listName.click() action, but neither has helped. Any help would be greatly appreciated. Have men and women in the Wizarding World always had relatively equal rights? There are racial struggles and examples of racism, (Muggle-borns, centaurs, hous-elves, goblins, etc.) but are there any examples in the Wizarding World of sexism?  Have witches and wizards always had equal rights? What is an adjective referring to “someone who puts people down”? I was just thinking about someone I went to school with who had a penchant for putting people down, and I was trying to think of a word that describes this, but couldn’t find it. It would be a synonym of caustic, abrasive, discouraging, and undermining, but these all have slightly different connotations (to wear away", cause discouragement or to make fall). I want an adjective that has the connotation of a hammer hitting you on the head. The word does not necessarily need to describe someone who does this on purpose, out of evil intent. Is there such a word?    The word should give you a mental picture of someone barraging you with negative comments, but it not necessarily affecting you. Think of someone who so often has something negative to “contribute” that many can just either ignore it or roll their eyes at it, and that is the extent of its effect. I keep getting the mental picture of the word buffet as in, how waves buffet the shore. A constant hitting, without the hitting necessarily being devastating in its destruction. Given that $a,b,c$ are distinct positive real numbers, prove that $(a + b +c)\big( \frac1{a}+ \frac1{b} + \frac1{c}\big)&gt;9$   This is how I tried doing it:  Let $p= a + b + c,$ and $q=\frac1{a}+ \frac1{b} + \frac1{c}$.  Using AM>GM for $p, q$, I get:  $$\frac{p+q}{2} &gt; {(pq)}^{1/2}$$ $$\sqrt{(a + b +c)\bigg(\frac1{a}+ \frac1{b} + \frac1{c}\bigg)} &lt; \frac{\big(a+\frac1{a} + b+\frac1{b} + c+\frac1{c}\big)}2$$ And for any $x\in \mathbb{R}, \space \space x+\frac1{x}≥2.$ Thus,   $$(a + b +c)\bigg(\frac1{a}+ \frac1{b} + \frac1{c}\bigg)&lt;9, $$ which is the opposite of what had to be proven. What did I do wrong? Displaying and/or searching across thousands of contacts? The Need  Our application has a chat feature that allows our users to chat with other users within their database.   However, we're adding a feature that allows clients to share data between multiple databases as an "Enterprise" configuration, and we've been asked to update the design of the chat feature to allow users to chat with other users within any of those databases.   We've looked at the numbers of possible users in these scenarios, and the number of chat users in these shared database environments can be as many as 5,000.   Users need to be able find people they need to chat with out of these thousands of contacts. However, up til now, we've had a list of contacts the users can browse. Since that is a user expectation, we were hoping to still maintain a browse-able list of contacts. We have ruled out trying to display a list of 5,000 contacts, as this doesn't seem to be anywhere close to useful or usable.   We've come up with three approaches to solve the problem:  Option One  Show a list of contacts from the local database that user's can browse. Have a second tab that allows users to search the "Full Directory", returning results from multiple databases.     Pros:   Allows us to show a browse-able list of relevant contacts  Clearly indicates to users that another source of chat contacts are available   Cons:   Search would be limited to the current tab, meaning users would have to be in the right tab to return the right result Adds a possible source of user confusion: whats the difference between "contacts" and the "full directory"? Adds another tab to what should be a simple chat list     Option Two  Show a list of contacts from the user's local database, but if they search for a contact, include results from other databases as well.     Pros:   Maintains a list of contacts the user can browse Avoids adding adding another tab One search field searches all sources   Cons:   Searching a finite contact list and returning results that weren't in the contact list may defy user's mental model of how the search will work. Not clear that another source of contacts exist. May need to add explanatory text that says "Search to see contacts from the full directory".      Option Three  Add a dropdown that allows a user to select a what to search in: the local database, or the full directory.     Pros:    No additional tab required Indicates to users that another source of chat contacts are available, though not as clearly as option 1   Cons:    Search still isn't universal: the right search category must be selected to return the right result Users may not notice the dropdown or understand intuitively what its function is. May require explanatory text in search results, reminding the user they can expand the search to the full directory     Thoughts?  Right now I'm leaning towards option two, but is there another option I'm not considering here? Is there another alternative worth considering?   Thanks! Prove that if a function's average is nondecreasing then the function is nondecreasing. Let $\omega:\mathbb{R}_+\to\mathbb{R}_+$ such that $\omega(0) = 0$ and $\xi(s) = \frac{1}{s}\int\limits_{0}^s \omega(t)dt$ is nondecreasing, i.e., $\forall s,s': s\leq s'$, $\xi(s)\leq \xi(s')$. Show that $\omega(t)$ is nondecreasing a.e., i.e. find a function $w(t)$ such that $w$ is nondecreasing and $\omega = w$ a.e.  I was able to show the reverse implication easily, that if $\omega$ is nondecreasing then $\xi$ is nondecreasing. This way seems more difficult. Why does $PSL(2,\mathbb C)\cong PGL(2,\mathbb C)$ but $PSL(2,\mathbb R) \not\cong PGL(2,\mathbb R)$? Why does $PSL(2,\mathbb C)\cong PGL(2,\mathbb C)$ but $PSL(2,\mathbb R) \not\cong PGL(2,\mathbb R)$? Mapping half-plane to unit disk? Say you have the half-plane $\{z\in\mathbb{C}:\Re(z)&gt;0\}$. Is there a rigorous explanation why the transformation $w=\dfrac{z-1}{z+1}$ maps the half plane onto $|w|&lt;1$? Accepted answer appearing below top voted