I am trying to make it so that there are "beams" coming out of the top of an object. Here is a crappying drawing:  I have made this so far:
(a.k.a. "god rays" and many other names) can be created in Blender Internal by checking the Halo checkbox in the lamp properties box.  How can I create a similar effect using Cycles?
Somewhere on Stack Exchange I saw the equation     $$\gcd(2^m-1,2^n-1)=2^{\gcd(m,n)}-1.$$   I had never seen this before, so I started trying to prove it. Without success...  Can anyone explain me (so actually prove) why this equation is true?  And can we say the same when replacing the '$2$' by any integer number '$a$'? Maven plugin executing another plugin I'm trying to create a new plugin to package my latest project.  I'm trying to have this plugin depend on the maven-dependency-plugin to copy all my projects dependencies.  I've added this dependency to my plugin's pom, but I can't get it to execute.  I have this annotation in my plugins main Mojo:  @execute goal="org.apache.maven.plugins:maven-dependency-plugin:copy"   I've tried a few other names for the goal, like dependency:copy and just copy but they all end with a message saying that the required goal was not found in my plugin.  What am I doing wrong?  Secondary to this is where to I provide configuration info for the dependency plugin? Volume form on $(n-1)$-sphere $S^{n-1}$ Let $\omega$ the (n-1) form on $\mathbb{R}^n$ $$\omega=\sum_{j=1}^{n}(-1)^{j-1}x_{j}dx_{1}\wedge\cdots\wedge \hat{dx_{j}}\wedge\cdots dx_{n}$$ Show that the restriction of $\omega$ to $S^{n-1}$ in precisely the volume for this sphere.  What I did was: $\omega$ never vanish on the sphere, because, defining $\sigma\in \Omega^{n-1}(S)$ for $$\sigma_{p}(v_{1},...,v_{n-1})=det(p,v_{1},...,v_{n-1})$$ and $i:S^{n-1}\rightarrow \mathbb{R}^{n}$ the inclusion function, then $\omega=i^{\ast}(\sigma)$ then $\omega\not=0$ and therfore is a volume form.   How proof that $\omega$ is the volume form?   The first thing that comes to mind is show that $\int_{S^{n-1}}\omega=Vol(S^{n-1})$ but I have serious problems with the definition, I think that is to much.   How see that $\omega$ is invariant on $\mathbb{R}^{n}$ under action of $O(n)$ Why is my mesh inversed when Imported to Unity? So I modeled this sword and all the parts were separate meshes. I used a mirror modifier when I was modeling and then I applied the modifier when I was done to make the parts into solid meshes. Put a UV map on everything and it all looked good in Blender.  Then I put it into Unity and I got what you see in the picture. Part of the sword is inversed. Oddly, the inversed part actually maintains the proper silhouette. It maintains the correct shape, but then is shaded like the front half is missing.  Does anyone have an idea of what's going on and how to fix it?  Thanks, James I read this book series in middle school. I believe that it would be classified as young adult fiction/fantasy. A girl has magical powers, and with her growing powers comes runes/tattoos in her arms. This is shown on every book cover. I know that one cover is blue. This one shows the girl in a black tank top and black pants. One is a yellow cover, with her in a dress (I think).  The girl has a friend/mentor, who she develops feelings for. The girl is the key to stopping a war between multiple factions/people. Each side is trying to use her to their advantage. I think the series was written in the early 2000s. Find the minimal polynomial for $\sqrt[3]{2} + \sqrt[3]{4}$ over $\mathbb{Q}$  I havent covered galois theory, this is an exercise from the chapter algebraic extensions in gallian.  I can see that $\sqrt[3]{2} + \sqrt[3]{4}$ $\in \mathbb{Q}(2^{1/3})$, after this I am clueless.  Need hints will finish the proof. Extracting Z data from point layer using ArcGIS Desktop? I have created a point layer with ~150 points. I have a DEM beneath it, which is where I have taken the X and Y values from.   Does anybody know how I can retrieve the Z values, without using the info button?  I am using ArcGIS Desktop 10. I have licences for the spatial analyst etc tools. As I understand these two statements:   An electromagnetic field gives particles charge A photon is a quantum of electromagnetic field   It must mean that a photon carries charge. But I guess it isn't true. Why not? Retrieving minimum width that contains specified fraction of all values I'd like to find the min/max boundaries of a sliding window of minimum size that contains a certain fraction of the total number of elements in an array or collection of numbers.   Example: taking integers to make it easier to explain, say the proportion of elements that we're looking for is 50% on this array:  [1,1,2,3,3,3,3,3,3,4,5,6,7,8,9,10]  The mystery function would return something like ( 2, 4 ), meaning that the minimum value is 2 and the max value is 4 (let's assume it's inclusive and note that these are VALUES, not indices). That little window contains 8 of the 16 values and it's only 2 units wide, the narrowest such window that contains half the number of values.  Note: the quartiles are [1,1,2,3], [3,3,3,3], [3,4,5,6], [7,8,9,10] so they are NOT what I'm looking for.  I can code it...may take some time to get it nice. Hopefully somebody has run across it before. Does it have a name?  Is there an existing method that somebody knows about?  I am interested in Python implementations.   UPDATE:  Thanks to Glen_b who gave the names 'short-half' and 'shortest interval' I was able to come up with this: What counts as "observation" in Schrödinger's Cat, and why are superpositions possible? So if I understood correctly, Schrödinger's Cat is a thought experiment that puts a cat inside a box, and there's a mechanism that kills the cat with 50% probability based on a quantum process. The argument is that the cat now must be in a superposition of dead and alive.  This makes sense at first, but the state of the cat inside the box will affect the outside world in an observable way, right? For example if the cat dies, it might meow loudly which would be audible. If it didn't meow, it would produce a thud on the ground when it dies. And even if the ground was very solid, the redistribution of mass inside the box will affects its gravity field which means the whole universe theoretically immediately observe's the cat's death.  So extending this argument to all superpositions, the different states would cause different effects on the rest of the universe, usually a slight change in the gravity field is the minimum. This gravity perturbation would propagate throughout the universe, and even all the experimenters go to sleep with thick, thick earplugs, somebody or something in the universe is going to inadvertently observe the event and the superposition immediately collapses. Thus superpositions cannot exist beyond an extremely short amount of time.  What's wrong with my reasoning? What my thought was that the bijection was a piecewise function:  $f(x) = 1/n+1$ if $x = 1/n$ for some $n \in \Bbb N$ and $x=1/n$ if $x \neq1/n$ for some $n \in \Bbb N$.  However, the textbook says this is incorrect. I don't actually see why. Was it a matter of brackets or the open variable $(0,1]$, which is what I tend to think. How to support different screen size in android how to redirect output to multiple log files I have a residence permit (permesso di soggiorno) for Italy. I am currently in the Netherlands for an exchange. My permit expired on the 30th of November and I applied for a new one but I will get the card in January. I have the documents supporting that I have applied for the renewal of the permit. In the middle I want to travel to Italy for Christmas and come back to the Netherlands.    Would this be a problem? Cycles Emit Light from area on Texture So I have a giant object that is completely uv unwrapped. I would like to make areas of the object with a specific area of texture emit light.   The problem is that this object (and it is only one object) only has one material. I would like the lava to emit light, but I cannot move it to a separate material without breaking something.  I'd like to find a method where I can select a part of the texture and tell blender that whatever has that part of the texture emits light.  Is this possible?  Thanks. When ever I need to kill a background process I do ps -e | grep &lt;process_name&gt;  Which prints something like this 1766 ? 00:00:13 conky , Then I use the process ID to kill it like so kill 1766 .   Is there any way I can simplify this ? Make it quicker ? reduce the amount of typing ? Getting a black screen when installing or Live booting Ubuntu (any version) in my laptop I have an ACER Aspire laptop. Model number is E5-573G-56RG. I bought it only 15 days back. There is no DVD drive in it. I have tried various versions of Ubuntu- 14.04.2, 14.04.3, 15.10, 12.04.5. Tried disabling secure boot, fast startup. I current have Windows 10 Home and Windows 10 PRO (not-activated) installed with GPT partition in UEFI bios. I actually want only the Home edition and Ubuntu 14.04.3 (preferably because of LTS) or 15.10. In case more information is required, kindly ask me..  I tried installing through Wubi, when booting if I choose Ubuntu it automatically restarts and goes into Windows 10 Home! (I didn't have Windows 10 PRO at that time)  NONE OF THE SOLUTIONS I REFERRED HELPED ME.  I have spent 5 days (literally at least 20 hours reading all of them and trying out all kinds of editing in the grub command line, like removing quiet splash, adding and replacing with nomodeset, no splash, acpi_osi=off, acpi_osi=Linux, acpi_backlight=vendor,  acpi_backlight=legacy, noveau.modeset=0, i915.i915_enable_rc6=1 and such things! But I was not able to succeed installing which is why I doubt if there is some more thing to be done or know exactly what has to be done. Are $x \cdot 0 = 0$, $x \cdot 1 = x$, and $-(-x) = x$ axioms? Context: Rings.     Are $x \cdot 0 = 0$ and $x \cdot 1 = x$ and $-(-x) = x$ axioms?   Arguably three questions in one, but since they all are properties of the multiplication, I'll try my luck... I drew a parallelepiped that is spanned by three vectors, and we know the volume is given by the absolute value of the determinant of the matrix - with the three vectors arranged in rows (or columns, since $detA = detA^T$).  How can I draw the tetrahedron from this parallelepiped to convince myself it is indeed 1/6th of the volume, i.e., 1/6 * |detA|?  Thanks, What is the best way to parse html in C#? I'm looking for a library/method to parse an html file with more html specific features than generic xml parsing libraries.