Are these conditions enough to recognize an extension method in an expression tree?
Reflection to Identify Extension Methods
I wanted to find a counter example to show that the completeness of the inner product space is necessary in . Please give an example of a bounded linear functional $T$ on an incomplete inner product space $X$ which do not have any inner product representation i.e. there does not exist any $z$ in $X$ s.t. $T(x)= \langle ,z\rangle$ for all $x$ in $X$. Convergence of $\int\limits_1^{\infty}x^\alpha\sin(x^\beta)dx$ I need to show that $$ \int\limits_1^{\infty}x^\alpha\sin(x^\beta)dx $$ converges if and only if $\alpha + 1 &lt; \beta$. I used substitution and integration to get $$ \lim\limits_{t\to\infty}\int\limits_1^tx^\alpha\sin(x^\beta)dx \overset{u = x^\beta}{\underset{du = \beta x^{\beta-1}}{=} }\lim\limits_{t\to\infty}\left(\frac{1}{\beta}\int\limits_1^{t^\beta}u^{\frac{\alpha + 1 - \beta}{\beta}}\sin{u}du\right) $$ If $\alpha + 1 -\beta &lt; 0$, then we have a product if a function with bounded anti-derivative and a differentiable decreasing function which tend to 0, and from Dirichlet's criterion, the integral converges.   For the converse, I used integration by parts $$  = \frac{1}{\beta}\lim\limits_{t\to\infty}\left(\left.-u^{\frac{\alpha + 1-\beta}{\beta}}\cos{u}\right|_1^{t^\beta} + \frac{\alpha+1-\beta}{\beta}\int\limits_1^{t^\beta}u^{\frac{\alpha + 1-2\beta}{\beta}}\cos{u}du\right) $$ For $\alpha + 1 -\beta\geq 0$, I get that the first term indeed diverges, but this is not enough to show total divergence. How can one show it? An example where the output of the k-medoid algorithm is different than the output of the k-means algorithm Which word to use when we ask for help?  Some conditions:     We know that the person asked is able to do it. We don't know if the person asked is able to do it. Why do shell script comparisons often use x$VAR = xyes? I see this often in the build scripts of projects that use autotools (autoconf, automake).  When somebody wants to check the value of a shell variable, they frequently use this idiom:  if test "x$SHELL_VAR" = "xyes"; then ...   What is the advantage to this over simply checking the value like this:  if test $SHELL_VAR = "yes"; then ...   I figure there must be some reason that I see this so often, but I can't figure out what it is. \@seccntformat only for section I would like to add a dot between the number of the section and section name. I used   \makeatletter \renewcommand*{\@seccntformat}[1]{% \csname the#1\endcsname .} \makeatother   The problem is that, obviously, it put a dot also among subsection number and subsection name which I do not want. Is it possible to add the dot only between section number and section using low level instructions i.e. without any additional package? Transpose some columns to rows using pivot with SQL Are there any non-decreasing securities on the stock market? Are there any securities traded on the stock market (i.e. ETPs) that never decrease in value?    As an aside (in case anyone mentions bonds):  I'm aware there's ETFs for AAA-rated government bonds, but even these dip significantly.  For example, the  has dipped by 9% in a 85-day period before (21/08/2016 to 13/11/2016). How to install all possible media codecs from console?  Is there a way to load and save them for some cases without Internet connection?  Thanks in Advance! Install Windows 7 with Bootcamp on OS X Yosemite with USB Key I have an iMac (bought in 2011) and I recently upgraded it with Yosemite. I am trying to install Windows 7 on it via Bootcamp.  However, its optical drive does not work, so I chose the USB key solution using the trick of modifying the file info.plist of Bootcamp (type 'usb bootcamp youtube' in google to see a video of this trick).  So I follow the process religiously and end up with the classic and famous boring screen 'No bootable device -- insert boot disk and press any key'.  So I tried to use Unetbootin (  ) to make my USB Key bootable, and tried to boot on it through the screen that appears when you maintain the Option key (Alt button) while starting the mac. Result: I never managed to have my Unetbootin-formatted USB key appear on this screen :(  I read some stuff about reFit (  ) and GParted, but I just don't know how to use them...  If someone managed to install Windows 7 on his/her iMac with Yosemite using a USB Key, please help me understand why I can't see the USB as a boot option. How can I add a PPA from a previous release? LAN not working on 17.04 Actually yesterday I've upgraded from Ubuntu 16.04 to 17.04 and I got a problem that, if connect LAN cable it does not showing anything and  remains disconnected. But i can connect with WiFi. I don't know what's the problem. Actually its showing "device not managed" under the "Ethernet Network" and both were disabled. I've searched for the solution, but did not found yet. Sobolev space $H^s(\mathbb{R}^n)$ is an algebra with $2s>n$ The entire  site is blank right now.  The header and footer are shown, but no questions. Let $$G_\beta(w) = e^{\beta w^2}$$  Now I get the process of applying a fourier transform (or inverse) to get a new  gaussian:  $$G_\beta(x) = G_\beta(0) e^{\frac{-x^2}{4\beta}}$$  but in doing the derivation the constant $G_\beta(0)$ never arose. I know how to calculate the constant, but where did it come from in the derivation?  edit: Fourier form used: $$\int_{-\infty}^{\infty} f(w) e^{-iwx} dw$$ Android popup window dismissal I am looking for an option to require a passcode to power off my iPhone. That way, if the phone is lost, the person who finds it cannot simply turn it off, rendering Find My iPhone useless. Is there a way to accomplish this? Passing list to viewparams variables in GeoServer SQL views? Here is a DOM-based XSS flaw reported by SalesForce Security Review team in our code:   RootComponent  &lt;aura:component extensible="true" abstract="true" access="global"                 description="Root template component"&gt;     &lt;!-- ... lot of other code ... --&gt;     &lt;aura:attribute name="label"                     type="String"                     access="global"                     description="Label of the form input element" /&gt;     &lt;!-- ... lot of other code ... --&gt;  &lt;/aura:component&gt;   SubComponent  &lt;aura:component access="global" extends="c:RootComponent"                  description="Child extension of RootComponent"&gt;     &lt;!-- ... lot of other code ... --&gt;     &lt;label&gt;{!v.label}&lt;/label&gt;     &lt;!-- ... lot of other code --&gt;  &lt;/aura:component&gt;   According to SFDC, "any app can extend SubComponent component and pass in  as a label and trigger a DOM-based XSS attack." The solution would be to "sanitize" label global attribute to avoid such attack. What is meant by sanitization of global attribute?  I tried to reproduce the so-called security flaw , but as label attribute is of type "String" , when we send it HTML, it is displayed as a string, not as interpreted HTML ... so I don't see where the security flaw could be :/  &lt;aura:application &gt;     &lt;aura:handler name="init" value="{!this}" action="{!c.doInit}" /&gt;      &lt;c:SubComponent aura:id="TestXSS" label="DOM-based XSS attacks" /&gt;  &lt;/aura:application &gt;   JS Controller  ({     doInit: function(component, event, helper) {         var XssAttack = '&lt;img src=x onerror=alert(1) /&gt;';        component.find('TestXSS').set('v.label',XssAttack);     } })   Output    We have global attributes everywhere. Our components are packaged and meant to be extended by client implementation. Do we actually need to sanitize them? How can I remove the qed symbols from all lemma proofs? the following code will only make the qed not appear in the second proof. However, it it possible to make the qed symbol never appear at the end of the proofs without having to specify it locally every time?  \documentclass{article} \usepackage{amsthm} \begin{document} \begin{proof} This has the QED symbol. \end{proof} \begin{proof}\renewcommand{\qedsymbol}{} This hasn't. \end{proof} \begin{proof} And this has it again. \end{proof} \end{document}