Allow apostrophes when posting data to MySQL using Ajax and Javascript
How can I prevent SQL injection in PHP?
$$\lim\limits_{n\to\infty} \int_{0}^{1} f(x^n)dx = f(0)$$  when f is continuous on $[0,1]$  I know it can be proved using bounded convergence theorem but,  I wanna know proof using only basic properties of riemann integral and fundamental theorem of calculus and MVT for integrals ...   Thank you. What is $\int_0^1\frac{x^7-1}{\log(x)}\mathrm dx$? /A problem from the 2012 MIT Integration Bee is $$ \int_0^1\frac{x^7-1}{\log(x)}\mathrm dx $$ The answer is $\log(8)$. Wolfram Alpha gives an indefinite form in terms of the logarithmic integral function, but times out doing the computation. Is there a way to do it by hand? If, one fine day, someone found a contradiction in ZFC (or even ZF), what implications would such an event have for mathematicians? Is there currently any backup axiomatic system on par with ZFC that would enable mathematicians to continue pursuing mathematics, should the unthinkable occur? I am trying to mimic the interesting proof from  to give a generating set of the ideal correspond to the $d$-uple embedding: We fix the notation $\Delta = \big\{ (\nu_0, \dots, \nu_n) \in {\mathbb{N}}^{n+1}_0 ~:~ \nu_0 + \dots + \nu_n = d \big\}$. The polynomial map is $\theta : k[y_\nu : \nu \in \Delta] \rightarrow k[x_0, \dotsc, x_n]$ given by $$ \theta ( y_\nu ) := x^{\nu_0}_0 \cdots x^{\nu_n}_n $$ and we know that ${\mathrm{ker}}~\theta$ is the ideal of the $d$-uple embedding, i.e., $\rho_d({\mathbb{P}}^n) = Z({\mathrm{ker}}~\theta)$ (cf. Exercise I.2.12 Hartshorne). Now let $W \leq k[y_\nu : \nu \in \Delta]$ denote the ideal $$ W := \Big\langle y_{\tau_1} y_{\tau_2} - y_{\tau^{\prime}_1} y_{\tau^{\prime}_2} ~:~ \tau_1, \tau_2, \tau^{\prime}_1, \tau^{\prime}_2 \in \Delta, \tau_1 + \tau_2 = \tau^{\prime}_1 + \tau^{\prime}_2 \Big\rangle $$ Clearly, $W \subseteq {\mathrm{ker}}~\theta$. Using the lemma in the above link, we need to produce a $k$-subspace $T \subseteq k[y_\nu : \nu \in \Delta]$ with the conditions $$ T + W = k[y_\nu : \nu \in \Delta], \hspace{.2in} \theta \lvert_{T} = {\mathrm{injective}} $$ After a few thoughts it seems reasonable to think of the following subspace as a candidate for $T$: First define the equivalence relation on $\Delta \times \Delta$ given by $(\tau_1, \tau_2) \sim (\tau^{\prime}_1, \tau^{\prime}_2)$ if $\tau_1 + \tau_2 = \tau^{\prime}_1 + \tau^{\prime}_2$. Let $\Omega \subseteq \Delta \times \Delta$ be a subset with a unique representative from each class of $\sim$. Now let $T$ be the $k$-span of the monomials $y^{\alpha_1}_{\tau_1} \dotsc y^{\alpha_r}_{\tau_r}$ (with the distinct elements $\tau_1, \dotsc, \tau_r \in \Delta$ and $\alpha_1, \dotsc, \alpha_r \geq 1$) such that $(\tau_i, \tau_j) \in \Omega$ for each $i \neq j$. Clearly, $\theta$ is injective if restricted to $T$. I got lost in the step : Each monomial $M$ of $k[y_\nu : \nu \in \Delta]$ satisfy $M \equiv b$ mod $W$ for some $b \in T$. Did I do anything wrong? What does an unprocessed RAW file look like? Renewing an unused B1/B2 US visa I have a valid 5 years B1/B2 visa that was issued about 4 years ago.  I never used it as I intended to travel to work in a specific project that was cancelled.  Now, There is a similar project scheduled next year. So, I have to renew the visa as it will expire before the project's start date.  Can I renew the visa although it wasn't used (I never traveled to US) ? What will result in better page ranking in search results: Page views or time spent on page? Evaluating logistic regression and interpretation of Hosmer-Lemeshow Goodness of Fit What does "period" mean when someone says "Sth... Period"? I often hear US citizens say something like this:     &lt;Some phrases>. Period.   What does period mean when it appears in a sentence by itself in this type of situation? I searched all over this site and the web for a good and simple example of autocomplete using jQuery and ASP.NET. I wanted to expose the data used by autocomplete with a webservice (and will probably do that next). In the meantime, I got this working, but it seems a little hacky...  In my page I have a text box:  &lt;input id="txtSearch" type="text" /&gt;   I am using jQuery autocomplete, set up per their example:  &lt;link rel="stylesheet" href="js/jquery.autocomplete.css" type="text/css" /&gt; &lt;script type="text/javascript" src="js/jquery.bgiframe.js"&gt;&lt;/script&gt; &lt;script type="text/javascript" src="js/jquery.dimensions.pack.js"&gt;&lt;/script&gt; &lt;script type="text/javascript" src="js/jquery.autocomplete.js"&gt;&lt;/script&gt;   Here is where it starts to get hacky... I call a page instead of a webservice:    &lt;script type="text/javascript"&gt;     $(document).ready(function(){         $("#txtSearch").autocomplete('autocompletetagdata.aspx');     });         &lt;/script&gt;   In the page I stripped out ALL of the html and just have this (otherwise, various HTML bits show up in the autocomplete dropdown):  &lt;%@ Page Language="C#" AutoEventWireup="true" CodeFile="autocompletetagdata.aspx.cs" Inherits="autocompletetagdata" %&gt;   And in my autocompletetagdata.aspx, I am using SubSonic to query, format and return data from the database (one data item per line):  protected void Page_Load(object sender, EventArgs e) {     // Note the query strings passed by jquery autocomplete:     //QueryString: {q=a&amp;limit=150&amp;timestamp=1227198175320}      LookupTagCollection tags = Select.AllColumnsFrom&lt;LookupTag&gt;()         .Top(Request.QueryString["limit"])         .Where(LookupTag.Columns.TagDescription).Like(Request.QueryString["q"] + "%")         .OrderAsc(LookupTag.Columns.TagDescription)         .ExecuteAsCollection&lt;LookupTagCollection&gt;();      StringBuilder sb = new StringBuilder();      foreach (LookupTag tag in tags)     {         sb.Append(tag.TagDescription).Append("\n");     }      Response.Write(sb.ToString()); }   If you don't do a LIKE query, then it returns everything that contains a match for the character(s) you type -- e.g., typing "a" will include "Ask" and "Answer" as well as "March" and "Mega." I just wanted it to do a starts with match.  Anyway, it works and it's pretty easy to set up, but is there a better way? I have searched, but not found anything on this. I am looking for a functionality in bash, using a terminal.  Way back when, I had a user on a debian system, and a friend set me up with a convenient history search feature (I believe I used tcsh then), where I would type the beginning of a previous command, hit up-arrow, and it would do a search, based on the partial string.  E.g. if my history is:  ./script.pl ./script.pl arg1 cat output cat output | grep yada   And I type ., and press up-arrow, it would show me: ./script.pl arg1. Press it again and it would show ./script.pl, etc.  Very much like it would perform a grep on .bash_history. Is there a way to get this functionality? What are the rules for China's visa-free transit programs? User's suspension period has expired, but they're still suspended? I came across a user with a notification that states:     This account is temporarily suspended network-wide. The suspension period ends on Dec 2 '18 at 2:35.   Screencap for posterity:    Unless this user is  (in which case the full year should be shown, or at least a tooltip), it seems like they should have been unbanned 4 months ago. In The Last Jedi:     The Resistance fleet is tracked through hyperspace by the First Order after they make their jump away from their old base.   As soon as the FO ships appear, the Resistance immediately come to the (correct) conclusion as to the tech that was used.  Why would they assume the use of this tech, that they have never encountered before, as opposed to the more common technique of     tracking a ship through the use of a homing beacon. Definition of "pepper" in hash functions I know many master's students who get an opportunity to talk to their potential PhD advisors well before applying. In most cases this opportunity is available by the professors with whom they worked for their master's. Moreover, there are many others who establish a contact with professors by mailing them and enquiring about PhD vacancies.   My questions are:   How important is knowing an advisor prior to applying for PhD?  Does an email interaction play a vital role when the department makes its admit decisions? If email contact is important, can a student send out mails to 2-3 professors (working in the same area) in case one of them does not bother to reply? To sum up, is applying of any use (especially in top universities) when you have no contacts and only your credentials to bank on? I no longer need an answer to a question; what should I do to the question? How do I get a list of obsolete packages? I'm trying to figure out a way to get a list of the packages that are no longer available in the repositories that I have enabled. This workstation has been through quite a few versions of Ubuntu and has had many 3rd party repositories added and removed. I'd like to get a list of software that I have from these removed repositories, so I can clean it up or add back the appropriate repositories. When can I make opportunity attacks? What provokes an opportunity attack?  In 3.X moving out of a threatened square, standing up from prone, casting a spell (unless cast defensively), or making a ranged attack provoked, while in 4e moving out of a threatened square or making a ranged/area attack provoked. Send Gmail calendar invite from alternate email