fill polygon with image / crop image by polygon I would like to have an arbitrary polygon filled with an image (jpg, png, pdf, ...) for it to be included in a beamer frame.  I was thinking this may be possible using tikz, but I couldn't figure it out.  Thanks in advance!
Crop jpeg into circular tikz node \documentclass[demo]{article} \usepackage{graphicx} \usepackage{tikz} \begin{document} \begin{tikzpicture} \node[circle,draw,inner sep=2cm]{\includegraphics{myimage.jpg}}; \end{tikzpicture} \end{document}   How do I modify the above code so that the included image is adapted to the circle shape and cropped of the exceeding parts?  I want to specify a shape (a circle) and then include an image respecting the given dimension and cropped.
Bounds for $n$-th prime In  I have found that the bounds for $n$-th prime is given by, $$n(\ln n+\ln \ln n)&gt;p_n&gt;n(\ln n+\ln \ln n-1)$$ for all $n\ge6$. Are there even stronger bounds for the $n$-th prime?   If possible (of course if the answer is affirmative) in the answer (or comment) please give the link of the paper in which it first appears. What's the difference between declaring a variable "id" and "NSObject *"? In Objective-C, what's the difference between declaring a variable id versus declaring it NSObject *? Windows service stops automatically From      Every linear function on a finite-dimensional space is continuous.   I was wondering what the domain and codomain of such linear function are?   Are they any two topological vector spaces (not necessarily the same), as along as the domain is finite-dimensional? Can the codomain be a different normed space (and may not be finite-dimensional)?  I asked this because I saw elsewhere the same statement except the domain is a finite-dimensional normed space, and am also not sure if the codomain can be a different normed space (and may not be finite-dimensional).  Thanks and regards! I added addresses of python 2.7, and Anaconda 4.1.1(Python 3.5) to PATH variable in Windows 10, whenever I run "python" from cmd, program which was added earlier is executed.How can I access both of them depending on my choice without altering name of either Slope layer with false results in QGIS? After the DEM creation, I wanted to create slope layer.   However, the result has not satisfied me. I don't think the slope map is correct. Have you ever encountered false calculated terrain map?  This is the DEM:    And this is the slope layer. Google results for sponsee have scattered definitions in unreliable sources, so it does not appear that is a real word. I'm looking for something similar, a single word.  The specific context is a social group membership application where new members must be sponsored (as in definition 2, here - "one who assumes responsibility for some other person or thing") by existing members. I am looking for a single word to describe the target of such a sponsorship. I am about to sponsor a fraternity, but I would like to have a more general word for what I'm sponsoring. Next time, the fraternity could well be a study club, or something else.  Therefore, what is the sponsored party also called? E.g. if I sponsor somebody, that person is my __? I would like to know difference between user and service account.  I know that e.g. Jenkins installed to ubuntu is not a user, .    What is use of service account? When we need them? How can I create service account? How to remove chromium-browser settings from Ubuntu 14.04? I have already gone through   and I'm really not getting why the solutions given there are not working for me.  What I'm doing is:   sudo apt-get purge chromium-browser   rm -rf ~/.config/chromium     Then reinstalling by running the following command:   sudo apt-get install chromium-browser    This must remove the settings of chromium-browser and do a fresh installation. The browser is uninstalling, but after being installed it is containing the previous settings, moreover it's not signing me out of even Gmail! It is discouraged to simply catch System.Exception. Instead, only the &quot;known&quot; exceptions should be caught. Now, this sometimes leads to unnecessary repetitive code, for example: try {     WebId = new Guid(queryString[&quot;web&quot;]); } catch (FormatException) {     WebId = Guid.Empty; } catch (OverflowException) {     WebId = Guid.Empty; }  I wonder: Is there a way to catch both exceptions and only call the WebId = Guid.Empty call once? The given example is rather simple, as it's only a . But imagine code where you modify an object multiple times, and if one of the manipulations fails expectedly, you want to &quot;reset&quot; the object. However, if there is an unexpected exception, I still want to throw that higher. Find All Solutions to System of Congruence $$ \begin{cases} x\equiv 2 \pmod{3}\\ x\equiv 1 \pmod{4}\\ x\equiv 3 \pmod{5} \end{cases} $$  $ n_1=3\\ n_2=4\\ n_3=5\\ N=n_1 * n_2 * n_3 =60\\ m_1 = 60/3 = 20\\ m_2 = 60/4 = 15\\ m_3 = 60/5 = 12\\ gcd(20,3)=1=-20*1+3*7\\ gcd(15,4)=1=-15*1+4*4\\ gcd(12,5)=1=12*3-5*7\\ x=-20*2-15*1+12*3\equiv -19 \equiv 41 \pmod{60}\\ $  The above is what I've tried so far. Can someone tell me where I'm going wrong? It's my first time doing this and looking at the explanation and examples for the Chinese Remainder Theorem makes my head want to explode. Limited options in a certain area? Ok so i am a bit of a noob in blender, so I need help with this.  I am trying to texture something, but there is no texture button where there should be, because the blender edge window cuts it off here's a picture If $X_n \stackrel{d}{\to} X$ and $c_n \to c$, then $c_n \cdot X_n \stackrel{d}{\to} c \cdot X$ Let $X_n$, $X$ random variables on a probability space $(\Omega,\mathcal{A},\mathbb{P})$ and $(c_n)_n \subseteq \mathbb{R}$, $c \in \mathbb{R}$ such that $c_n \to c$ and $X_n \stackrel{d}{\to} X$. Then $c_n \cdot X_n \stackrel{d}{\to} c \cdot X$.   Here is my proof: By Lévy's continuity theorem it suffices to show that $$\forall \xi: \quad \hat{\mu}_n(c_n \cdot \xi) \to \hat{\mu}(c \cdot \xi) \qquad (n \to \infty)$$  where $\hat{\mu}_n$ (resp. $\hat{\mu}$) denotes the characteristic function of $X_n$ (resp. $X$). Using the tightness of the distributions one can show that $\{\hat{\mu}_n; n \in \mathbb{N}\}$ is uniformly equicontinuous. We have $$|\hat{\mu}_n(c_n \cdot \xi) - \hat{\mu}(c \cdot \xi)| \leq |\hat{\mu}_n(c_n \cdot \xi)- \hat{\mu}_n(c \cdot \xi)| + |\hat{\mu}_n(c \cdot \xi)- \hat{\mu}(c \cdot \xi)|$$ The first addend converges to zero as $n \to \infty$ by the uniform equicontinuity and the second one converges to zero since $X_n \stackrel{d}{\to} X$.  I was wondering whether there is an easier proof - my own proof seems rather like overkill to me. Thanks! How do I start a process from C#? How can I apply Newton's sums to solve this problem? With arrays, why is it the case that a[5] == 5[a]? As Joel points out in , in  (aka: K &amp; R), there is mention of this property of arrays in C: a[5] == 5[a]  Joel says that it's because of pointer arithmetic but I still don't understand. Why does a[5] == 5[a]? Strange behaviour of macros C/C++ Which one is correct to say: "It's me" or "It's I"? What techniques have been used to repeat geometry or other detail to the infinite horizon? When I composed my     I would have liked to have the camera pitch up enough to show the horizon, except I didn't have enough geometry to extend the cobblestone street and the sidewalk all the way to infinity (mostly because that would require infinite stuff).  Even in that shot it is clear that I need to widen the "sidewalk" to cover up the "sky"box.    Contrast with     where the ray tracer can use the procedurally replicated geometry.   is a failed attempt at faking out the horizon, even with low detail.  It fails because lighting's interaction with the geometry gives it away.  Some techniques that prevent you from having to deal with infinity include   put the scene in a box (usually a room) put the scene in a canyon (which is just a box without a top so you can see the relatively featureless sky) route the road into a tunnel, or around a corner and hide the horizon with other geometry (which is really just a variant on the canyon). have no detail on the ground at all (flat color or gradient)   Those are all dodging the question of interest to me:  What techniques have people used in blender to fake various kinds of detail repeating into the distance (instead of just obstructing the view of infinity)? How can I repair a ceiling fan that hums, but doesn't turn?