How to generate spherical gradient volume
How to make a good glow effect around a sun?
Ocean modifier and foam data export? It is there any way to export the foam data generated from ocean modifier to use it in other render engine, like LuxRender? The manual says that the foam data is stored as vertex color data, but there isn't a way to access the vertexColor data. I know that can be accessed from Cycles from attribute's node. LuxRender supports vertex color and I tried to bake the texture to vertexColor and an image but only get a plain black texture. The no. of all possible matrices of order $3\times 3$ with each entry $0$ and $1$ and $ -1$. I got quite some trouble trying to prove this.  $$\sum_{k=m}^{n}(-1)^k\binom{n}{k}\binom{k}{m}=0, n&gt;m\geq 0$$  I tried using $$\binom{n}{m}\binom{m}{k}=\binom{n}{k}\binom{n-k}{m-k}$$ and then changing the summation boundaries as $k=0, n=n-m$, but that took me nowhere... I would really appreciate help. Thank you. Not getting any reading from FTDI UMFT201XB USB-to-I2C module I got the  in order to interface with an I2C peripheral through a USB port on my Windows 7 computer.  The VCP drivers seem to install correctly, and a COM port is assigned to the module, and can be opened by a terminal emulator. However, I cannot seem to get any signal in or out of the module. That is, I see no activity when I send data through the port, or receive any data when I connect an I2C device to it (this was debugged using a scope). I have also verified that the RESET isn't on.  I found very little helpful information out there on how to get this module to work, so if anyone has experience with it, or with similar FTDI modules, my question is: what are the steps that I need to take in order to get the module to communicate? Inverse Green's Function identity in derivation of Hedin's equations I'm trying to work through a derivation of Hedin's Equations in Effect of Interaction on One-Electron States by Hedin and Lundqvist (1969) and I've come across an identity that is given without much explanation that I'd like to understand.   We start with an equation of motion with single particle Green's functions G:   $\left[ i\frac{\partial}{\partial t_1} - h(1) - \phi(1) - V_H(1)\right] G(1,2) - i\int v(1^{+},3) \frac{\delta G(1,2)}{\delta \phi(3)} d3 = \delta(1,2)$  where $1=(x_1,t_1)$, $h$ is the one-electron kinetic energy and ion interaction, $\phi$ is a small perturbing field that is set to zero at the end, $V_H$ is the Hartree potential, and $v$ is the Coulomb interaction.  They then insert the identity  $\frac{\delta G(1,2)}{\delta\phi(3)} = -\int G(1,4) \frac{\delta G^{-1}(4,5)}{\delta\phi(3)} G(5,2) d(4,5)$  which is then used to define the self energy  $\Sigma(1,2) =  -i \int v(1^+,3) G(1,4)\frac{\delta G^{-1}(4,2)}{\delta\phi(3)} d(3,4)$.  I know this identity is related to the definition of the inverse Green's function  $ \int G(1,3) G^{-1}(3,2) d(3) = \delta(1,2)$  but I can't figure out how to get from this definition to the identity that is inserted into the equation of motion. Any ideas?  Thank you! How to get IOS "tossing feature" in Wolfram IOS Player to work in Mathematica I noticed that I got some initial traffic problems at the point where the initial highway is connected to my city. At the beginning I simply elongated both roads that came from that highway, but this doesn't seem to scale.  What I wanted to do now is to create a single six-lane highway from these two four-lane roads. I'd be open to continue to use two roads in parallel here, but I didn't manage to add any way of crossing between the lanes when I tried that idea.  So, how do I merge two one-way roads into a single two-way road? Or, if my idea is really bad, what is a good way to connect the initial highway access to my fledgling city?  Here's a screenshot of the roads I want to connect, if my description wasn't entirely clear: Outlining in Blender? I am currently working on converting my logo vectored as a SVG to a 3D model using the 2.72 version. I ran into a problem with my logo because it contains a black stroke and an orange stroke (see both images below), but currently all I have is the interior color of each shape. I was wondering whether or not there was a simple way to add in these strokes, and how exactly to go about creating the strokes. Thank you in advance community! $\sum_{1}^{n}\left ( a_{i}b_{i} \right )\geq \prod_{1}^{n}\left ( a_{i}^{b_{i}} \right )$ Let $a,b,c,x,y,z&gt;0$ and $x+ y+ z= 1$. Show that $$ax+ by+ cz\geq  a^{x}.b^{y}.c^{z}$$ I have found the generalization of this inequality: For 2 sets of numbers $\left \{ a_{i} \right \}, \left \{ b_{i} \right \}&gt; 0$ and $\sum_{1}^{n}b_{i}= 1$, we have: $$\sum_{1}^{n}\left ( a_{i}b_{i} \right )\geq  \prod_{1}^{n}\left ( a_{i}^{b_{i}} \right )$$ First solution Simply compare the logs: as the natural logarithm is a concave function, one has $$\ln\bigl(a^x b^y c^z)=x\ln a+y\ln b+z\ln c\le \ln(ax+by+cz)$$ for all non-negative $x,y,z$ such that $x+y+z=1$. How about another solution? I really hope to see that. Thanks! Add new alias to Gmail without SMTP (forwarding-only address) I used to be able to go to Accounts and Import → Add another email address you own and add an email account that's only a forwarding address. That is, it's not a mailbox and I don't have SMTP access to it.  Gmail would send me a confirmation email to that address, I'd confirm it's mine, and done. Now it only gives me the option to add SMTP credentials.  Did they stop supporting the previous method? Is there any other way I can get that option back? WPF Binding to variable / DependencyProperty rstrip not removing newline char what am I doing wrong? Probability of an even number of sixes We throw a fair die $n$ times, show that the probability that there are an even number of sixes is $\frac{1}{2}[1+(\frac{2}{3})^n]$. For the purpose of this question, 0 is even.   I tried doing this problem with induction, but I have problem with induction so I was wondering if my solution was correct:   The base case: For $n=0$, our formula gives us $\frac{1}{2}[1+(\frac{2}{3})^0] =1$. This is true, because if we throw the die zero times, we always get zero sixes.  Suppose it's true for $n=k$. Then the odds of an even number of sixes is $\frac{1}{2}[1+(\frac{2}{3})^n]$, and thus the odds of an odd number of sixes is $1 - \frac{1}{2}[1+(\frac{2}{3})^n]$.    For $n=k+1$, there are two ways the number of sixes are even:  a. The number of sixes for $n=k$ was even, and we do not throw a six for $n=k+1$: $ \frac{5}{6} \cdot  \frac{1}{2}[1+(\frac{2}{3})^n]$  b. The number of sixes for $n=k$ was odd, and we throw a six for $n=k+1$: $\frac{1}{6}(1 - \frac{1}{2}[1+(\frac{2}{3})^n])$  So the probability $p$ for an even number of sixes at $n=k+1$ is $ \frac{5}{6} \cdot  \frac{1}{2}[1+(\frac{2}{3})^n] + \frac{1}{6}(1 - \frac{1}{2}[1+(\frac{2}{3})^n])$  I have two questions   How do I get from $ \frac{5}{6} \cdot  \frac{1}{2}[1+(\frac{2}{3})^n] + \frac{1}{6}(1 - \frac{1}{2}[1+(\frac{2}{3})^n])$ to $\frac{1}{2}[1+(\frac{2}{3})^n]$? I seem to have done something wrong, I can't get the algebra correct, I get $p = \frac{1}{3}[1+(\frac{2}{3})^n] + \dfrac{1}{6}$ Other than that, is my use of induction correct? Is it rigorous enough to prove the formula? This is a  about DNS (Domain Name Service).   If my understanding of the DNS system is correct, the .com registry holds a table that maps domains (www.example.com) to DNS servers.   What is the advantage? Why not map directly to an IP address? If the only record that needs to change when I am configuring a DNS server to point to a different IP address, is located at the DNS server, why isn't the process instant? If the only reason for the delay are DNS caches, is it possible to bypass them, so I can see what is happening in real time? C++ performance of accessing member variables versus local variables Is it more efficient for a class to access member variables or local variables? For example, suppose you have a (callback) method whose sole responsibility is to receive data, perform calculations on it, then pass it off to other classes. Performance-wise, would it make more sense to have a list of member variables that the method populates as it receives data? Or just declare local variables each time the callback method is called?  Assume this method would be called hundreds of times a second...  In case I'm not being clear, here's some quick examples:  // use local variables class thisClass {     public:         void callback( msg&amp; msg )         {             int varA;             double varB;             std::string varC;             varA = msg.getInt();             varB = msg.getDouble();             varC = msg.getString();              // do a bunch of calculations          }  };  // use member variables class thisClass {     public:         void callback( msg&amp; msg )         {              m_varA = msg.getInt();              m_varB = msg.getDouble();              m_varC = msg.getString();               // do a bunch of calculations         }      private:         int m_varA;         double m_varB;         std::string m_varC;  }; Training involved to ride 175 miles (281 km) in a day I want to be able to ride 175 miles (281 km) in a day (to do the ). I used to be able to do about 60 miles (96.5 km), only once hitting 80 miles (128 km), but I'm out of shape now. Wondering how I can systematically train to get to 175 miles at an average of 15 mph (24 km/h) Are there guides out there to help with this?  What's some advice?  [update] The  will happen each year, so my intention isn't to ride this year, rather what do I need to do to ride it in some future year? text-overflow: ellipsis in table-cell without width What does an unprocessed RAW file look like? Run an exe from C# code MySQL strip non-numeric characters to compare