I want to draw the following diagram:
I'd like to create a picture like the one with TikZ:    I've already created the electrical part using circuitikz. I'd like to add the part on the right (the motor's shaft with arrows), but don't know how to start, actually. Is there a way to draw 3D shapes, maybe? Or should I draw circles and rotate them?  \documentclass{article} \usepackage{tikz} \usetikzlibrary{intersections} \usepackage{circuitikz} \usepackage{siunitx}  \begin{document}  \begin{figure} \centering \begin{circuitikz} \draw (0,0) to [V, v=$v(t)$, *-*] (0,2)      to [R, l=$R_d$] (2,2)     to [L, l=$L_d$] (4,2)     to [V, v&lt;=$e(t)$] (4,0) to [generic] (4,2) -- (4,0) -- (0,0); \end{circuitikz} \end{figure}  \end{document}   What I have now:   What I'm still missing:
Infinite distinct factorizations into irreducibles for an element Consider the factorization into irreducibles of $6$ in $\mathbb{Z}[\sqrt{-5}]$. We have $6=2 \times 3$ and  $6=(1+\sqrt{-5}) \times (1-\sqrt{-5})$, i.e. $2$ distinct factorizations. And,  $$6^2=3 \times 3\times2\times2$$ $$=(1+\sqrt{-5}) \times (1-\sqrt{-5}) \times (1+\sqrt{-5}) \times (1-\sqrt{-5})$$ $$=(1+\sqrt{-5}) \times (1-\sqrt{-5})\times3\times2.$$ More generally, $6^n$ will have $n+1$ distinct factorizations into irreducibles in $\mathbb{Z}[\sqrt{-5}]$ by a simple combinatorial argument. But, can we construct a ring in which there exists an element that has an infinite number of distinct factorizations into irreducibles? To make life harder, can we construct an extension of $\mathbb{Z}$ in which this happens? I have been thinking about this for a while and have managed to find no foothold.. Any help is appreciated. What's the parameters atribute in apex:canvasApp used for? I'm experimenting with the  feature, and embedding it in a Visualforce page, from where I hoped I would have some control over the canvas.  Now, the apex:canvasApp has a property called  and it's description says that they're parameters passed to the canvas app.    When I don't use the parameters attribute the canvas page draws normally, and using firebug I can see the call to the ip address of the canvas app. But for it to be useful to me I need to pass some parameters to the canvas page and when I do use the parameters attribute the canvas simply does not show, and in firebug it does not show any call to the ip of the canvas.  How are these parameters passed or how can one catch them? Using firebug, in the call to the ip of the canvas app, I can't see any of the parameters that I'm trying to pass.  Here's the simple code I'm experimenting with:  &lt;apex:page &gt; &lt;apex:canvasApp applicationName="Test Canvas" height="400px" width="750px" parameters="{vst_cli: '1293'}" /&gt; &lt;/apex:page&gt;   Inside the parameters attribute I've tried some different things: "{vst_cli: '1293'}" "{vst_cli: 1293}" "{'vst_cli': '1293'}" All of which had the same effect.  Any help or pointers will be welcome.  Thanks in advance. What is the purpose of a serial number? I have got this problem on limits  $$ \lim_{x \rightarrow 0}\left(\frac{\sin(x)}{x}\right)^\frac{1}{x^2}$$ What I am doing here is that taking log and then applying L-Hospital's Rule $$y= \lim_{x \rightarrow 0}\left(\frac{\sin(x)}{x}\right)^\frac{1}{x^2} $$ then $$\ln(y)=\lim_{x \rightarrow 0} \frac{1}{x^2}\ln\left(\frac{\sin(x)}{x}\right)$$ now it becomes $\frac{0}{0}$ type , but problem is how to take derivative here? when differentiating $\ln\left(\frac{\sin(x)}{x}\right)$ it will become $\frac{x}{\sin(x)}$ then we'll have to differentiate one more time like we do in case of $f(f(x))$ ? $\sin(x)$ and $x$ will be separately differentiated or together ? Does the universe have a center? How do I resize my partition in Ubuntu? I had Windows 8 installed on my system, which I screwed up, and now I run Ubuntu 12.04. While installing, Ubuntu used all the 461 GB of HDD space (one partition).   Now I want to make a new partition of maybe 100 GB or so, in order to install Windows 7 alongside Ubuntu (with a dual-boot). But I can't even get a partition done. I can't change the partition in GParted either - the option is disabled. Why Does the Transaction Log Keep Growing or Run Out of Space? This one seems to be a common question in most forums and all over the web, it is asked here in many formats that typically sound like this:  In SQL Server -  What are some reasons the transaction log grows so large? Why is my log file so big? What are some ways to prevent this problem from occurring? What do I do when I get myself on track with the underlying cause and want to put my transaction log file to a healthy size? using $$ in a post causes strange number series to appear What happens when a creature with "Whenever a creature dies" dies simultaneously with multiple other creatures? has the following ability:     Whenever a creature you control with a +1/+1 counter on it dies, return that card to the battlefield under your control at the beginning of the next end step.   I had a number of creatures on the battlefield, including Marchesa herself, with one or more +1/+1 counters on them when  was played, destroying each creature on the board.  When Marchesa and several other creatures would be killed simultaneously,   Does Marchesa's ability trigger for herself? Does Marchesa's ability trigger for the other creatures under my control with +1/+1 counters?   In attempting to resolve the issue, we tried to look things up, leading to , which cites Rule 603.6d as proving that Marchesa's ability should trigger both for herself and for each other creature with +1/+1 counters.  Unfortunately, none of us could actually understand Rule 603.6d, aside from this example:     Two creatures are on the battlefield along with an artifact that has the ability Whenever a creature dies, you gain 1 life. Someone plays a spell that destroys all artifacts, creatures, and enchantments. The artifacts ability triggers twice, even though the artifact goes to its owners graveyard at the same time as the creatures.   The example certainly seems analogous to me, but without understanding the actual rule, rather than just the example, we weren't too sure.  A complete answer has to not only answer the question, but back up that answer with citation and explanation of the official rules on the matter. I'm stuck with this integral  $\int\frac {\cos^4x}{\sin^3x} dx$    which I rewrote as  $\int \csc^3x \cos^4xdx$  then after using the half angle formula twice for $\cos^4x$ I got this  $\frac 14\int \csc^3x (1+\cos(2x))(1+\cos(2x))dx$   then after solving those products I got these integrals  $\frac 14 \{\int \csc^3xdx+2\int \csc^3x \cos(2x)dx + \int \csc^3x \cos^2(2x)dx\}$  I do know how to solve the $\int \csc^3xdx$ one but I'm totally lost on the other ones, any tips/help/advice would be highly appreciated! thanks in advance guys! Improving your own suggested edit makes you leave the First Posts review queue When reviewing the First Posts (and Late Answers) review queue, after you suggest an edit, you're back in the review queue and the I'm Done button is activated. So far, so good, but when I realize I want to edit something else as well (I often forget the tags), I can click the 'edit' link again. When I'm done improving my suggested edit, I'm suddenly outside the review queue.    This does not happen if you have enough reputation (2k) to edit posts straight away; then you always stay in the review queue. I read on  that Ubuntu will no longer use the familiar file size units we all know by now (kB, MB, GB, TB) and switch to a different IEC standard (KiB, MiB, GiB, TiB). If this is true, I would like to know what's the reasoning behind this change, and the impact (if any) this change has, especially with multiplatform applications or applications run with Wine. In a semiconductor memory chip, each bit of binary data is stored in a tiny circuit called a memory cell consisting of one to several transistors. Volatile type.   Suppose an application stored its data in a particular segment on the computers RAM.  How would the CPU know what data to extract and how would it sort through the other data to get to it. If everything in its core level is 0 or 1 its hard to distinguish what purpose 'x' memory has. GTA V Online Character Transfer PS3 to PS4 The spell Armor of Agathys states:      You gain 5 temporary hit points for the duration. If a creature hits you with a melee attack while you have these hit points, the creature takes 5 cold damage.   Now, assume my buddy uses Inspiring Leader to give me 10 temporary hit points — does the effect end? I'm working with jQuery and looking to see if there is an easy way to determine if the element has a specific CSS class associated with it.  I have the id of the element, and the CSS class that I'm looking for.  I just need to be able to, in an if statement, do a comparison based on the existence of that class on the element. Convergence of sequence of real numbers and (sub)subsequence Let $(x_n)_{n\in \mathbb{N}}$ be a sequence of real numbers. A well known result is:     The sequence $(x_n)_{n\in \mathbb{N}}$ converges to $a\in \mathbb{R}$ if and only if every subsequence $(x_{n_k})_{k\in \mathbb{N}}$ converges to $a\in \mathbb{R}$.   Now, I'm working on an exercise which essentialy asks to prove the following:     The sequence $(x_n)_{n\in \mathbb{N}}$ converges to $a\in \mathbb{R}$ if and only if for every subsequence $(x_{n_k})_{k\in \mathbb{N}}$ there is a (sub)subsequence $(x_{n_{k_j}})_{j\in \mathbb{N}}$ which converges to $a$.   Now, one direction is trivial. If in fact $(x_n)_{n\in \mathbb{N}}$ converges to $a$, then by the result I've mentioned, every subsequence of $(x_{n})_{n\in \mathbb{N}}$ converges to $a$. Let then $(x_{n_k})_{k\in \mathbb{N}}$ be an arbitrary subsequence. In that case, we know that it is a subsequence of itself, and hence we've found a (sub)subsequence which converges to $a$.  The other way around seems quite complicated for me. The reason is as follows: I must assume that every subsequence $(x_{n_k})_{k\in \mathbb{N}}$ has a (sub)subsequence which converges to $a$ and the proof that the original one converges to $a$.  My problem is exactly that "a". If it had all (sub)subsequences converging to $a$, then by the result i've mentionted, the subsequence $(x_{n_k})_{k\in \mathbb{N}}$ would converge to $a$. In that case, we would have every subsequence converging to $a$ and the result would follow.  My idea to prove the claim was then:  First remember that a subsequence is the restriction of the original one $x: \mathbb{N}\to \mathbb{R}$ to an infinite subset $\mathbb{N}'\subset \mathbb{N}$. In that case a (sub)subsequence is the restriction of $\tilde{x} = x|\mathbb{N}'$ to an infinite subset $\mathbb{N}''\subset \mathbb{N}$. But since $\tilde{x}$ is the restriction of $x$ to $\mathbb{N}'$ and since $\mathbb{N}''\subset \mathbb{N}'$, the restriction of $\tilde{x}$ to $\mathbb{N}''$ is itself the restriction of $x$ to $\mathbb{N}''$.  In other words, every (sub)subsequence can be viewed as a subsequence of the original one. Considering this, by hypothesis every subsequence has a (sub)subsequence which converges to $a$. But by this argument, this means that we can replace every subsequence with a convergent one. And then we can use the result I stated.  Is my idea correct? Is this really the way to prove the claim? My only doubt is that I need every subsequence converging to $a$ to use the result. In this case I can't see how I can argue that this implies every subsequence converges to $a$.  How can I finish this proof? Old movie about a group of friends with magical weapons fighting monsters I am wondering how to recreate some kinds of effects (you can easily do in Photoshop) in Blender.  I want to create the gradient textures like ones pictured below, should I render objects and blur them in compositor? Or can I achieve it using only material nodes? Where does pp (PAR) unpack add (-a) files?