In fact, I don't know how to write this expression on LaTeX:     And thanks in advance.
What LaTeX markup would one have to write to produce a result similar to the image below?    Please excuse my Paint-and-mouse drawing skills. :-)
What is the easiest way to strip a desktop edition to a server edition? We have installed Ubuntu desktop edition on our development server. Now that we have it in a data center we would like to strip it down to a server edition.  Is there an easy way of doing so rather than just going in and uninstalling packages by hand? In a custom lightning component where one is using the recordEditForm tag, how can one validate fields that are filled by the user?  For example, in a quick action to create a Case record, we can have the following line inside the recordEditForm:  &lt;lightning:inputField aura:id="caseAccount" fieldName="AccountId"/&gt;   How can one enable or disable a button if certain fields are assigned by the user? Like if the account is specified, then a button on the component is enabled for the user.  Making the field required is not an option. Situation: when a user self-marks their post as a duplicate, it shows as closed by "community" rather than the original poster.  Problems: this is not clear at all to most users of SE what has happened. It looks like the question was "mod closed" as a duplicate against the asker's wishes.    Suggestion: instead of the community user "closing" the post, have the final close user be the asker (or make it "Community &amp; Asker"). This will help clear up confusion and streamline the process for understanding what happens. What exactly goes into a transformer's VA rating? At a fundamental level it seems that there has to be a limit to what the VA rating can represent.  For example if I draw 2 Amps-RMS from the secondary of a 30VA rated transformer at 15 Vrms this makes sense as the maximum Complex Power I can draw. Still, at a power factor of 1 my maximum current in the transformer would be sqrt(2) * 2 Amps.   But what if my power factor is abysmally low (ie in a DC rectifier) due to harmonic distortion and while I still draw 2A-RMS I have brief current spikes of 15 Amps? Surely the transformer's magnetics couldn't handle these spikes as I'd expect the core would saturate.  My question is what is the practical limit for VA ratings of transformers? Would brief current spikes that reduce to only 2A-RMS in this case be fine? Obviously the secondary/primary copper losses play a part in the rating but how do the magnetics factor in?  I ask this because I am designing a simple bench power supply using a 125VA transformer with a 24Vrms secondary and am trying to figure out how much power I can draw before the current spikes into the inductor are too much for the transformer. I also don't want to have to resort to active PFC as I don't want to risk messing up any HVAC PCB design.  Thank you How do I split a string so I can access item x? Using SQL Server, how do I split a string so I can access item x?  Take a string "Hello John Smith". How can I split the string by space and access the item at index 1 which should return "John"? I've got the new Canon Pixma MG 3150 and so far, I can't seem to find a driver anywhere. I do have the CD for both Windows and Mac, but this doesn't help me, as I have Ubuntu 11.10. I'd prefer to have it running on the wifi.  I'm really new to this, so I need for you to explain this to me as basically as possible. I'm trying to make a logo that will be on the header of a website. What I'd like to achieve, and the reason I'm using Blender, is the projected shadows on the background looking perfectly real (as opposed to doing a drop-shadow in Photoshop).  The only thing is, the background has to be transparent because the website might use different background colors / gradients that make it impossible to match with the exported 3D background.  I made this dummy file (not the real logo... duh!):    If I use the file as is, the grey borders of the image will be impossible to match with the website's background color.  Here what I want:    So obviously, I tried masking the plane, which made the shadows disappear. I tried having a plane set to glass, which didn't work either.  And I looked around for a similar question, but didn't find one.   I am not trying to render , or a . I've seen  which has a very difficult solution to this problem, and  that is very similar but in Blender Internal.  is similar too but has never been solved. I'm only a beginner at Compositor, and I'm trying to learn more any chance I get, so any solution in Compositor is welcome if detailed enough. Although if there's a simpler or faster way, it's welcome too!  .blend file: I have this table but check constraint is throwing me an error:     Column CHECK constraint for column 'MedicamentRegulated' references another column, table 'Medicaments'.   I've seen this as allowed in SQL Server but I don't know why it doesn't work :/  CREATE TABLE Medicaments ( MedicamentID INT NOT NULL IDENTITY(1,1) PRIMARY KEY, Name VARCHAR(50), DateValidity DATE, MedicamentRegulated BIT CHECK((MedicamentRegulated = 1 AND DateValidity IS NOT NULL)    OR MedicamentRegulated = 0) ) Back in Europe I have a N64 console. As I am currently living in Japan, I find myself tempted to buy some old N64 games in Japanese. However, the articles about the N64's region locking usually assume Japanese games on an American console...  My question thus is: Can you play a Japanese N64 Game on a European console? User suggested great corrective edit to my answer, but the edit was rejected. What can I do to approve it? A nice user suggested  to . The edit, though very good and desirable, was rejected. I do not understand the reasons, and I did not find a way to contact those people who rejected it. What can I do to re-approve the edit? echo "#!" fails -- "event not found" Find $\lim\limits_{x \to \infty} \frac{x}{(\log{x})^n}$ Find $\displaystyle \lim_{x \to \infty} \dfrac{x}{(\log{x})^n}$.   My book says that $\displaystyle \lim_{x \to \infty} \dfrac{(\log{x})^n}{x} = \lim_{y \to \infty} \dfrac{y^n}{e^y} = 0$, but I don't see how that is true. Photoshop CS6 Resize Rectangle with Rounded Corners This question is about Photoshop CS6. Hopefully the feature was added in this version. Before posting I looked up Google and  and  but didn't find an answer for CS6.  So the question is: Is there a feature within CS6 or a script that allows to resize a vector element with rounded corners without using the Direct Selection Tool (white arrow tool) and not changing the border radius? What would be great would be something like simply using the transform tool or something like a grid resize tool. If $p$ is congruent to $2 \pmod 3$, how can I prove that all $a$, $1 \le a \le p-1$ are cubic residues $\mod p$? If $p$ is congruent to $2 \pmod 3$, how can I prove that all $a$, $1 \le a \le p-1$ are cubic residues $\mod p$?  Here's what I've done:  $1^3$ congruent to $1 \pmod p$ thus, 1 is a cubic residue, Also $(p-1)^3=(p-1) \pmod p$ implies  $$(p-1)^3 - (p-1) = (p-1)[(p-1)^2 -1] = (p-1)(p^2 -2p) = p(p-1)(p-2) $$ implies $$p|(p-1)^3 -(p-1)$$ Thus  $p-1$ is a cubic residue $\mod p$. Now I don't know how to show for $1\lt a \lt p-1$ are all cubic residues when $p$ is congruent to $2\pmod 3$. Proving the universal mapping property for polynomial rings Wrongly set chmod / 777. Problems? I was trying to run chmod -R 777 ./ but ended up typing chmod -R 777 / and set 777 on my entire machine. What can go wrong? How can I fix it? Suppose $\sqrt6 = \frac pq$ where $p$ and $q$ have no common factors.  $$6 = \frac {p^2}{q^2}$$  $$6p^2 = q^2$$  So $q^2$ and therefore $q$ is divisible by $6$.   $$p^2 = \frac {q^2}{6}$$  So $p^2$ and therefore $p$ is divisible by $6$.   S0, $p$ and $q$ have a common factor $6$. Contradiction.  Therefore $\sqrt6$ is irrational.  Does the proof work? When I try to save a new file in TextEdit, I always get a popup saying I can't save with ".txt" at the end of the file name.  I want to save a plaintext file, but TextEdit insists on saving as .rtf instead. It also lists .doc, .odt, .html, and some others.  How can I save a TextEdit document as plain text? Can i install ubuntu on meizu mx4 android edition like ubuntu edition with iso recovery in this page "  " Showing that $f_0 (x_1, \ldots, x_m) \mathrm tr A =\displaystyle{ \sum_{i=1}^n} f_0(x_1, \ldots, Ax_i,\ldots, x_m)$ Question:  Consider $f: (-\epsilon, \epsilon) \to \mathbb R^{m^2}$ a differentiable path of matrices $m \times m$ such that $f(0) = I_m$ and the function $g: I \to \mathbb R$ is defined by $$g(t) = \det f(t)$$  Show that $g'(0) = \mathrm{tr} \,a $ (trace of the matrix $a$), where $a = f'(0)$.   Attempt:  First we use that $\det f(t) = \det (f_1(t), \ldots, f_m(t)) $, where $f_i$ is the $i$-th row of the matrix $f(t)$ $m \times m$. Considering the operator $': \mathbb R^m \to \mathbb R^m$, $f(t) \mapsto f'(t)$  With this in mind $$\begin{align}g'(t) = \det'f(t) &amp;= \sum_{i=1}^{m} \det (f_1(t),\ldots,f'_i(t),\ldots, f_m(t)) \\&amp;\underbrace{=}_{(*)}\det(f_1(t), \ldots, f_m(t))\, \mathrm tr f'(t) \end{align}$$  For $t = 0$ we have   $$\begin{align}g'(0) &amp;=\det(e_1, \ldots, e_m) \,\mathrm tr f'(0) \\&amp;= 1 \dot\, \mathrm tr \,a \\&amp; = \mathrm tr \, a\end{align}$$  I'm trying to come up with a proof using the fact that $\det$ is a $m$-linear form.   In order to prove $(*)$ I need the following equality, which according to this  holds.   If $A: V \to V$ is a linear operator and $f_0$ is a alternated $m$-linear form, such that $f_0 (e_1, \ldots, e_m) = 1$ then   $$f_0 (x_1, \ldots, x_m) \mathrm tr A = \sum_{i=1}^m f_0(x_1, \ldots, Ax_i,\ldots, x_m) $$  Could someone give a proof to this?