In the following MWE, what is responsible for the large space before the align environment? How can I remove it (it doesn't appear if I change to \[ \] and remove amsmath) ?  \documentclass{article}  \usepackage[english]{babel} \usepackage{amsmath,amssymb} \usepackage{lipsum}  \begin{document} \setlength{\parskip}{0pt} \setlength{\abovedisplayskip}{0pt} \setlength{\belowdisplayskip}{0pt} \setlength{\abovedisplayshortskip}{0pt} \setlength{\belowdisplayshortskip}{0pt}  \lipsum*[2]  \lipsum*[2]  \begin{align*}1, 2, 3\end{align*}  \lipsum*[2]  \lipsum*[2] \end{document}   I have read  (but it doesn't cover the case in which there's a \par before \align and  (but it attributes the space to \parskip, which seems wrong: setting \parskip to 0 pt doesn't remove the space). I also read  and , but they just say that one shouldn't leave a \par before an \align.  I'm curious to know what actually causes this blank space, even with all seemingly relevant lengths set to zero.   Edit for Reopen   is related, but it doesn't address the why: it says that leaving a blank line in the source causes the space but it doesn't say who is adding this space (and it's clearly an amsmath-specific this: the regular displaymath doesn't do that).
What is the typographic reasoning here? Does it make the text look less crowded?
In "Knots and Primes: An Introduction to Arithmetic Topology", the author uses the following proposition   Let $h: Y \to X$ be a covering. For any path $\gamma : [0,1] \to X$ and any $y \in h^{-1}(x) (x = \gamma(0))$, there exists a unique lift $\hat{\gamma} : [0,1] \to Y$ of $\gamma$ with $\hat{\gamma}(0) = y$. Furthermore, for any homotopy $\gamma_t (t \in [0,1])$ of $\gamma$ with $\gamma_t = \gamma(0)$ and $\gamma_t(1) = \gamma(1)$, there exists a unique lift of $\hat{\gamma_t}$ such that $\hat{\gamma_t}$ is the homotopy of $\hat{\gamma}$ with $\hat{\gamma_t}(0) = \hat{\gamma}(0)$ and $\hat{\gamma_t}(1) = \hat{\gamma}(1)$.  The author then follows with; "In the following, we assume that any covering space is connected. By the preceding proposition, the cardinality of the fiber $h^{-1}(x)$ is independent of $x \in X$."   I am not sure why this results is true. This is my attempt at explaining it to myself. Take two different $x_1, x_2$ and their fibers $h^{-1}(x_1), h^{-1}(x_2)$ such that $y_1 \in h^{-1}(x_1)$ and $y_2 \in h^{-1}(x_2)$. Take two paths $\gamma_1, \gamma_2$ such that $\gamma_1(0) = x_1$ and $\gamma_2(0) = x_2$. Then we get two lifts $\hat{\gamma_1}, \hat{\gamma_2}$ with $\hat{\gamma_1}(0) = y_1$ and $\hat{\gamma_2}(0) = y_2$. Now, since our covering space is connected we can continuously deform $\hat{\gamma_1}$ into $\hat{\gamma_2}$ and conclude that every elements in $h^{-1}(x_1)$ is also in $h^{-1}(x_2)$ and vice versa. I feel that this is wrong but cannot figure out the right way to see this. Any help would be appreciated. I'm not able to get access to $wpdb How to call child component controller function/helper from Parent Component Controller I have requirement to call a child controller function from parent controller whenever the event occurs in parent side.  for e.g  ABC is parent component and DCE is child component, this child component has Span of Text tag and X symbol. when I click on x it is clearing the value using child controller. ABC parent component has Form element and child component is one one of in form.  My requirement is to clear the this child component value when parent component button is clicked.  here is the below sample code of what am trying because i cannot post actual code here  ParentComponent.cmp     &lt;aura:registerEvent name="clrValues" type="c:ClearValues"/&gt;     &lt;div&gt;          &lt;c:ChildComponent textValue="test"/&gt;          &lt;ui:button label="Save"/&gt;          &lt;ui:button label="Clear" press="{!c.clear}"/&gt;           &lt;/div&gt;  &lt;/aura:component&gt;   ParentController.js  ({     clear : function(component, event, helper) {         var evtFire = component.getEvent("clrValues");          evtFire.fire();     } })   ClearValues.evt  &lt;aura:event type="APPLICATION" description="Event template" /&gt;   ChildComponent.cmp  &lt;aura:component &gt;     &lt;aura:handler name="setValues" event="c:ClearValues" action="{!c.clear}"/&gt;     &lt;aura:attribute name="textValue" type="String" default="test"/&gt;     &lt;div &gt;     &lt;ui:inputText label="Expense Name" value="{!v.textValue}" aura:id="input1"/&gt;     &lt;/div&gt;  &lt;/aura:component&gt;   ChildController.js  ({     clear : function(component, event, helper) {         helper.clearValues(component,event);     } }) If the universe is 3D, how is space-time like a "fabric"? Export Windows 7 search results to a text file What is the most "pythonic" way to iterate over a list in chunks? I have a Python script which takes as input a list of integers, which I need to work with four integers at a time.  Unfortunately, I don't have control of the input, or I'd have it passed in as a list of four-element tuples.  Currently, I'm iterating over it this way: for i in range(0, len(ints), 4):     # dummy op for example code     foo += ints[i] * ints[i + 1] + ints[i + 2] * ints[i + 3]  It looks a lot like &quot;C-think&quot;, though, which makes me suspect there's a more pythonic way of dealing with this situation.  The list is discarded after iterating, so it needn't be preserved.  Perhaps something like this would be better? while ints:     foo += ints[0] * ints[1] + ints[2] * ints[3]     ints[0:4] = []  Still doesn't quite &quot;feel&quot; right, though.  :-/ Related question: Why can't two series-connected diodes act as a BJT? Mysql Select some random rows and plus one specific row sqlplus doesn't work in Crontab /oracle/GR1/121/bin/sqlplus / as sysdba &lt;&lt;EOF &gt;&gt; $LOGFILE whenever sqlerror exit sql.sqlcode; set echo on; set serveroutput on; STARTUP; EXIT EOF   Already tried it with the path, but it hasn't worked. Do we have different set of badges in different SE sites. eg. I don't see any 'Pundit' badge in badges popup in Hinduism SE.  Also, if the above is true, then can we include the left badges in a SE site at a later stage. Is "do something by date X" inclusive? Possible Duplicate:          For example, if John says:      Return it to me by March 24th.    Does it mean that I need to return it to him before 23:59 p.m. March 24th, or before 23:59&nbsp;p.m. March&nbsp;23rd? Can a single sentence be used to distinguish between isomorphic classes of finite structures? The answer seems to be yes, judging from the following exercise I found in the book Mathematical Logic by H.D. Ebbinghaus, J. Flum, and W. Thomas:     Let $S$ be a finite symbol set and let $\mathfrak{U}$ be a finite $S$-structure. Show that there is an $S$-sentence $\varphi _{\mathfrak{U}}$ the models of which are precisely the $S$-structures isomorphic to $\mathfrak{U}$.   I think I have an idea of how to solve this exercise, but I seem to be unable to materialize it. Thanks. How to make generated classes contain Javadoc from XML Schema documentation I posted a question and a couple of respondents asked for the source code. I could only post portions of the code.  If attachments were allowed I could have uploaded a .zip file with the whole application.  Will this be a feature in SO? Determinant of an $n\times n$ complex matrix as an $2n\times 2n$ real determinant If $A$ is an $n\times n$ complex matrix. Is it possible to write $\vert \det A\vert^2$ as a $2n\times 2n$ matrix with blocks containing the real and imaginary parts of $A$?  I remember seeing such a formula, but can not remember where. Any details, (and possibly references) for such a result would be greatly appreciated. So I am on my college network which requires me to sign in to the browser before I start using the internet. I do so succesfully but on a clean install of Ubuntu, when I try to do sudo apt update, I get the following output:  $ sudo apt update Get:1 http://in.archive.ubuntu.com/ubuntu xenial InRelease [2,847 B] Err:1 http://in.archive.ubuntu.com/ubuntu xenial InRelease                     Clearsigned file isn't valid, got 'NOSPLIT' (does the network require authentication?) Get:2 http://security.ubuntu.com/ubuntu xenial-security InRelease [2,854 B]     Err:2 http://security.ubuntu.com/ubuntu xenial-security InRelease              ... Get:3 http://in.archive.ubuntu.com/ubuntu xenial-updates InRelease [2,855 B]    Err:3 http://in.archive.ubuntu.com/ubuntu xenial-updates InRelease ... Get:4 http://in.archive.ubuntu.com/ubuntu xenial-backports InRelease [2,857 B] Err:4 http://in.archive.ubuntu.com/ubuntu xenial-backports InRelease Clearsigned file isn't valid, got 'NOSPLIT' (does the network require authentication?) Fetched 11.4 kB in 0s (18.3 kB/s) Reading package lists... Done E: Failed to fetch http://in.archive.ubuntu.com/ubuntu/dists/xenial/InRelease  Clearsigned file isn't valid, got 'NOSPLIT' (does the network require authentication?) ... E: Some index files failed to download. They have been ignored, or old ones used instead.   But when I do wget http://in.archive.ubuntu.com/ubuntu/dists/xenial/InRelease, I get this output success:  2017-04-01 05:34:57  http://in.archive.ubuntu.com/ubuntu/dists/xenial/InRelease Resolving in.archive.ubuntu.com (in.archive.ubuntu.com)... 91.189.88.162, 91.189.88.149, 91.189.88.152, ... Connecting to in.archive.ubuntu.com (in.archive.ubuntu.com)|91.189.88.162|:80... connected. HTTP request sent, awaiting response... 200 OK Length: 246846 (241K) Saving to: ‘InRelease.3’  InRelease.3         100%[===================&gt;] 241.06K   110KB/s    in 2.2s      2017-04-01 05:35:00 (110 KB/s) - ‘InRelease.3’ saved [246846/246846]   Clearly I have internet access from my browser and on wget but when I do sudo apt (or apt-get) update I get this error.  PS: This question is not similar to other threads as their solutions do not seem to work on mine        As I have found out, this problem is happening only to me, not others on the college network. Despite setting up the network according to instructions, this still happens. Any more help would be appreciated  EDIT: So as it turns out, 50% of us in the college are facing this issue, while 50% aren't despite having no issues with the hardware and sudo apt update before the last week. Thanks to @David Foerster for helping me throughout all this time.  As it stands, the issue has been raised to our college's networking department :) Matching a space in regex I need to match a space character in a PHP regular expression. Anyone got any ideas?  I mean like "gavin schulz", the space in between the two words. I am using a regular expression to make sure that I only allow letters, number and a space. But I'm not sure how to find the space. This is what I have right now:  $newtag = preg_replace("/[^a-zA-Z0-9s|]/", "", $tag); When is the sum of divisors a perfect square? For $n=3$, $\sigma(n)=4$, a perfect square. Calculating further was not yielding positive results.  I was wondering is there a way to find all such an $n$, like some algorithm?  We know that if $n=p_1^{k_1}p_2^{k_2}\dots p_r^{k_r}$ then $\sigma(n)=\frac {p_1^{k_1+1}-1}{p_1-1} \frac{p_2^{k_2+1}-1}{p_2-1}\dots \frac {p_r^{k_r+1}-1}{p_r-1}$. So we have to find $n$ such that $\sigma(n)=\frac {p_1^{k_1+1}-1}{p_1-1} \frac{p_2^{k_2+1}-1}{p_2-1}\dots \frac {p_r^{k_r+1}-1}{p_r-1}=t^2$ for some integer $t$. If each $\frac{p_i^{k_i+1}-1}{p_i-1}$ is a square we will get some such numbers (not all though), but let us consider $\frac{p_i^{k_i+1}-1}{p_i-1}=m^2$.   Working a example, If I take $p_i=17 $ , (or any prime such that $p_i-1$ is a perfect square), then if I can find a $k_i$ such that ${p_i^{k_i+1}-1}=16.m^2$ I will get an $n$, so now when can this happen, is something I have to try out.   But out of curiosity I am asking has this been worked out before. Problem looks broad to me, Is there a solution to this problem? Are nested transactions allowed in MySQL? What is $\sum_{n=1}^{\infty} \frac{n}{2^{\sqrt{n}}}$?