How i can make glass material with increasing amount of sampling
Black artifacts when looking through many transparent objects?
Secretary problem - why is the optimal solution optimal? I have read about this problem:    But I want to see how it is proven that the "optimal" solution is indeed optimal. I understand how to prove that if the optimal solution is of the form "wait for $t$ candidates and then choose the next best one" then $t=n/e$ is optimal; but why is the best strategy of that form in the first place?  A complete proof is not required - a reference to a good text discussing this is good as well. Can a Spring form command be a Map? How to run a LaunchAgent that runs a script which causes failures because of System Integrity Protection After upgrading to Mojave, my rsync based backup script run via a launch agent in ~/Library/LaunchAgents, could no longer read some directories in ~/Library. How to model the curly cable part of the phone Hello. I am a beginner in Blender. I started modeling this phone and when I got to the curly cable part it was a real challenge. Could someone guide me on this. I am trying to model a violin belly and I am intrigued, how is it possible to make faces with soft / rounded edges?    The edges I do are totally straight (see the blue amoeba).  Also, do you have some idea on how to avoid the edge loops getting too "compressed" in the middle of the model (see the red amoeba) ?    I know the Subdivision surface modifier, but I want curved edges after applying the modifier... like in this picture :  Any help will be very appreciated. Thank you in advance!  Marcos  2nd part  In fact, I've tryied to model using nurbs and bezier curves, but I wasn't able to find any tool similar to loft that works with curves, then I was forced to convert it in meshes, the results were not terrific and I've started to move the vertices manually, a real pain... Unlike a guitar, each edge loop is on a diferente elevation on z axis and I have to keep the original dimensions, So I have to be extremely careful when using the subdivision suface modifier. I've already modeled this think on three different CAD softwares, but the meshes are far from good... I want to improve the edge loops, but it will be a long path... Thank you again. horizontal alignment of dot over hat over bold greek letter! For some strange reason, this:   \hat{\dot{\bm{\phi}}}   prints the dot and the hat slightly off the left of the phi letter. Any ideas if this can be fixed? thanks. Using bm package for bold symbols. Make an exam format with a logo How do I ensure a piece of code runs only once? How to force a table into page width? How can I get rid of ants in an environmently friendly way? Formula across objects So, I thought I had a good understanding of this, but just ran a test (in response to a conversation where I disagreed with someone) and found that my understanding is flawed...  In as much detail as possible what exactly happens when I execute a file in my shell? What I mean is, if I type: ./somefile some arguments into my shell and press return (and somefile exists in the cwd, and I have read+execute permissions on somefile) then what happens under the hood?  I thought the answer was:   The shell make a syscall to exec, passing the path to somefile The kernel examines somefile and looks at  of the file to determine if it is a format the processor can handle If the magic number indicates that the file is in a format the processor can execute, then   a new process is created (with an entry in the process table) somefile is read/mapped to memory. A stack is created and execution jumps to the entry point of the code of somefile, with ARGV initialized to an array of the parameters (a char**, ["some","arguments"])  If the magic number is a  then exec() spawns a new process as above, but the executable used is the interpreter referenced by the shebang (e.g. /bin/bash or /bin/perl) and somefile is passed to STDIN If the file doesn't have a valid magic number, then an error like "invalid file (bad magic number): Exec format error" occurs   However someone told me that if the file is plain text, then the shell tries to execute the commands (as if I had typed bash somefile). I didn't believe this, but I just tried it, and it was correct. So I clearly have some misconceptions about what actually happens here, and would like to understand the mechanics.  What exactly happens when I execute a file in my shell? (in as much detail is reasonable...) Evaluating $\frac{1}{2\pi}\int_{0}^{2\pi}\frac{1}{1-2t\cos\theta +t^2}d\theta$ I need solve this integral, and I tried various methods of solving and did not get it. The integral is:   $$\frac{1}{2\pi}\int_{0}^{2\pi}\frac{1}{1-2t\cos\theta +t^2}d\theta,$$  where $t$ is a positive integer. Outline radius? How to get width of the video and scale another video to that width using ffmpeg? I'm using ffmpeg to stack two videos vertically. They might be different size so I need to scale them to same size. I have found following commands.  First one works for different sizes (but won't scale to proper size):  ffmpeg -i input1 -i input2 -filter_complex '[0:v]pad=iw:ih*2[int];[int][1:v]overlay=0:H/2[vid]' -map [vid] -c:v libx264 -crf 23 -preset veryfast output   Second one works if videos have same width and same pixel format:  ffmpeg -i input1 -i input2 -filter_complex vstack output   How to get width of first input inside complex filter argument so second input could be scaled to same width? What would be the command to do so? I would prefer vstack filter since it should be faster than combination of pad and overlay. How is the value of $\pi$ ( Pi ) actually calculated? When I was a child I was taught $\pi$ (Circumference/Diameter) is an irrational number  and can be approximated to $22/7$ but $= 3.(142857)(\ldots)$.      But where does this value comes from?  In short How do I derive $\pi$? $\epsilon$ undefined using Minion Pro with pdftex I'm using MiKTeX 2.9 and have recently installed the Minion Pro fonts for use with pdftex. I followed the instructions available on  to install them.  Everything works as expected, but in place of the Greek letter epsilon I get a box with a cross (see below), and the following warning:    I found the issue was reported , but I still can't fix it. xelatex works fine, but I'd like to to stick to pdftex so I can use microtype.  \documentclass{article}  \usepackage[T1]{fontenc} \usepackage{MinionPro}  \begin{document}  Text here. $\epsilon$  \end{document}       UPDATE: a set of instructions for the installation of the up-to-date FontPro scripts with MiKTeX can be found . Is there a "smallest" divergent sum? We are using .Net to make web service calls the Salesforce API. Is there a way to know for sure that the calls are using TLS 1.2? Are there any API logs or records of the protocol is use in Salesforce we can review to be confident the change is working? Moments of the truncated normal distribution (univariate) away from the mean