When I try to upvote a question, it says that "votes from users with less than 15 reputation are recorded, but do not change the publicly displayed score." How are they recorded? Do they actually do anything?
Users below 15 reputation can't effectively vote. It says:     Votes cast by those with less than 15 reputation are recorded, but do not change the publicly displayed post score   Does it mean that they will take effect after I reach 15 reputation or because they were cast before, they're recorded but ignored?
Do opposite categories always exist? The abstract environment changes the \linewidth for the whole document In the article class, it seems that using the abstract environment has an effect to the rest of the document. More precisely, it seems that it redefines the \linewidth, which equals \textwidth without abstract, is smaller with the abstract. My feeling is that \linewidth is redefined for the abstract environment, but the value is not reseted at the end of the abstract.  Here is a minimal example:  \documentclass{article} \begin{document} \abstract{This is an abstract. This is an abstract.}\bigskip  This is text. This is text. This is text. This is text. This is text. This is text.\\  \rule{\textwidth}{3em} \rule{\linewidth}{3em} \end{document}   The output is not the same if you comment the \abstract line or not.  Do you have the same problem as I do when you compile (if not, I will upload some PDF files to show)? Is this a (known) bug in LaTeX2e? How can we circumvent the problem?  Note: I compile with the pdflatex command, and I use pdfTeX, Version 3.1415926-1.40.10 (TeX Live 2009/Debian). Does a correlation matrix of two variables always have the same eigenvectors? My "credit limit" is now a "credit access line". Does it matter? Does construction of a Lightsaber require use of the Force? It's true that Lightsaber construction is a mandatory skill for a trained Force user, but I am not sure about it in reverse.  @DVK has commented on  that:     Grievous wasn't a Jedi (or a Force Sensitive) at all. He couldn't construct one.   I always thought that a Lightsaber was a normal piece of technology which even non-Force users could construct, and you only need Force sensitivity to master  Lightsaber skills. But, I could be wrong.  Does construction of a Lightsaber require use of the Force? If yes, what role does the Force play in the construction of a Lightsaber? I'm studying the Darboux definition of integrability, which I completely explained . There's an exercise that asks me to prove that the Darboux Integrability is equivalent to Riemann Integrability, but this Riemann integral is defined as the following:  It first defines a 'pointed' partition (I don't know how to say it in ensligh) by the following: a 'pointed' partition $[a,b]$ is a pair $P^*=(E,ξ)$, where $P=\{t_0, t_1, \cdots, t_n\}$ is a partition of $[a,b]$ and $ξ = (ξ_1, \cdots, ξ_n)$ is a list of $n$ chosen numbers such that $t_{i-1}\le ξ_i\le t_i$ for each $i=1,\cdots ,n$.  Now, the Riemann Integral is defined as:  $$\sum(f,P^*) = \sum_{i=1}^n f(ξ_i)(t_i-t_{i-1})$$  (I didn't understand the notation for the left hand side of the equation, by the way)  Finally, I'm asked to prove the following: given $f,g:[a,b]\to \mathbb{R}$ integrable functions, for the entire partition $P=\{t_0, \cdots, t_n\}$ of $[a,b]$ let $P^* = (P,ξ)$ and $P^{\#} = (P, η)$ be pointed partitions of $P$, then:  $$\lim_{|P|\to 0}\sum f(ξ_i)g(η_i)(t_i-t_{i-1}) = \int_a^b f(x)g(x) \ dx$$  I guess here I need to prove that the Riemann Integral of the product of two functions if the darboux integral of $f(x)g(x)$, but it seems too obvious, I just need to verify that $f,g$ are integrable, then their product is too, isn't it? I'm pretty sure this should be a hard question. Is there another interpretation that I'm missing? How do I get the last column text to be at the bottom of the row?  That is I want the XXX to be aligned with the line containing the arrow. I tried playing around with \multirow{3}{-3ex}{XXX}, but obviously I don't understand \multirow. Code: \documentclass{article} \usepackage{tabularx} \usepackage{booktabs} \usepackage{multirow}  \begin{document}     \begin{tabularx}{\linewidth}[t]{l X p{1.3cm}}         &amp; Header &amp; Title \\\cmidrule(lr){2-2}\cmidrule(lr){3-3}         a. &amp; Some text text text text text text text text text text text text text text              text text text text text text text text text text              Want XXX on this line $\rightarrow$%          &amp; XXX\\     \end{tabularx} \end{document} How old is SpongeBob? How old is SpongeBob? I don't mean how old is the series, I mean what is SpongeBob's age if he were a real person. I ask because his age seems to be ambiguous in the show.   He has a full-time job He has his own house He is always referred to as a kid (especially in the movie) He acts childish and immature In one episode, he was pretending to be an adult/grown-up How can I verify a Google authentication API access token? How can I verify a Google authentication access token?  I need to somehow query Google and ask: Is [given access token] valid for the [example@example.com] Google account?  Short version: It's clear how an access token supplied through the  can be used to then request data from a range of Google services. It is not clear how to check if a given access token is valid for a given Google account. I'd like to know how.  Long version: I'm developing an API that uses token-based authentication. A token will be returned upon provision of a valid username+password or upon provision of a third-party token from any one of N verifiable services.  One of the third-party services will be Google, allowing a user to authenticate against my service using their Google account. This will later be extended to include Yahoo accounts, trusted OpenID providers and so on.  Schematic example of Google-based access:    The 'API' entity is under my full control. The 'public interface' entity is any web- or desktop-based app. Some public interfaces are under my control, others will not be and others still I may never even know about.  Therefore I cannot trust the token supplied to the API in step 3. This will be supplied along with the corresponding Google account email address.  I need to somehow query Google and ask: Is this access token valid for example@example.com?  In this case, example@example.com is the Google account unique identifier - the email address someone uses to log in to their Google account. This cannot be assumed to be a Gmail address - someone can have a Google account without having a Gmail account.  The Google documentation clearly states how, with an access token, data can be retrieved from a number of Google services. Nothing seems to state how you can check if a given access token is valid in the first place.  Update The token is valid for N Google services. I can't try a token against a Google service as means of verifying it as I won't know which subset of all Google's services a given user actually uses.  Furthermore, I'll never be using the Google authentication access token to access any Google services, merely as a means of verifying a supposed Google user actually is who they say they are. If there is another way of doing this I'm happy to try. How to generate/view PDF using Lightning Components? I need to view/generate PDF in Lightning component. How can I achieve that?  Do I have to user VF page with "renderAs" attribute inside Lightning Component? Or is there any other way to achieve this? Breaking an equation cluster that does not fit on the rest of page across two pages Java: Detect duplicates in ArrayList? How to Recover truncate table in MySQL? I am getting the "wrong input table name" when use TRUNCATE as following:  TRUNCATE `stats`   The table should bans.  How to recover stats table?  I am using CentOS 6, and MySQL-Server. What's with the Japanese SO's stats? something like wye-delta and delta-wye connection.  we can originally know wye-delta connection is step-down transformer and second side voltage phase is being to -30 degree. And also delta-wye connection is step-up transformer and second side voltage phase is being to +30 degree.  But the other side, we also can make wye-delta connection is step-up transformer if it get turn ratio like 1:2. So in this case maybe will be become +30 degree in second side voltage.   apply this principle in scott connection, how can work it?   case1) turn ration 1:2 - step up second side voltage's angle +90 degree?  case2) turn ration 2:1 - step down second side voltage's angle -90 degree?  if you have any information or homepage link, can you leave it for me?  thank you so much. When is the graph of the divisor relation on $[n]$ planar? A recently-deleted question asked to show that if $G(n)$ is the graph on $[n]=\{1,\dots,n\}$ where $x$ and $y$ are adjacent if $x|y$ or $y|x$, then $G(n)$ is planar.  This is false if $n\geq150$, for the subgraph induced by $\{2,3,5,90,120,150\}$ is isomorphic to $K_{3,3}$.  My question is, what is the largest value of $n$ such that $G(n)$ is planar?  Of course, various software packages would make short work of this, but I'd be interested in a verbal argument, if someone can give one. Computing dominant area in polygon using ArcGIS Desktop? Communicating with all potential clients as a multi niche photographer This may be seen as a bit off topic, but I'm hoping it's a question that some photographers can associalte with and clear up for me.  I'm an amateur wanting to get more serious in the new year, and aiming to build up a portfolio of work that I will showcase on my own website, which will hopefully build up a client base.  I figured that a good way to get started would be to create a few 365 style projects that I can publish on my site and on social media. However, my interests vary a great deal, and therefore my photography will more than likely range from nature and local events, to more NSFW style topics.  My problem is, how to successfully communicate with people who will be interested in certain aspects of my work, without losing touch with those interested in others.  In theory, I'd like to set up a single social media presence, preferably Twitter, where I can freely post anything I want, and connect with anyone I want. Essentailly pointing people in the direction of whatever content they will be interested in. Problem is, social media sites like Twitter publicise ALL of your posts to ALL of your followers, so people who are following for nature/local photography will possibly unfollow me for my NSFW content. At the same time, some SFW followers may be potential clients in other areas, and vice versa.  So as a multi niche photographer, how can you engage with all potential clients, and showcase all portfolio peices ( in my case all 365 project shots ) via a single or limited number of social networks? How are you doing it? Did Dolores Umbridge Have Any Association with Voldemort (or Death Eaters) before His Return? I noticed that Dolores Umbridge was born during the first Wizarding War, so it's very likely she wasn't a Death Eater then (but she is pretty evil -- who knows?).  After that Voldemort was not around in a way that could affect many people, and most wouldn't know he was planning to rise again.  During that time, and up through Voldemort's return (in Goblet of Fire), did Umbridge have any connection with the Death Eaters or with Voldemort?  Was she doing what she did on her own, or was it because of an association with Voldemort or his allies? How to Delete Elements from List1 appearing in List2?