Weird dots in my mesh so I'm making a drink scene, but it looks like there are very weird dots around, near the glass. It seems I need to do something to get rid of the white dots.
How to reduce fireflies in Cycles? I often use Cycles' built in Glass BSDF shader to achieve realistic refraction effects, but in many cases, it seems that Cycles' glass caustics creates an unfortunately large number of fireflies (pixels that are abnormally bright relative to their surroundings). In some models of mine, even when I render for 3000 or more samples/pixel, my final image is still covered in fireflies. While I can improve this in many cases by increasing the total amount of light available in the scene, this loses a lot of the potency of the refractive effects I'm looking for, especially in scenes with low light levels.  So my question is, how can I reduce the amount of fireflies while using Cycles' caustics without sacrificing the quality of the refractive effects?  Note: I am aware that Cycles' caustics will perform much better once Cycles has full support for bidirectional path-tracing, but it looks unlikely that that will become , unfortunately.
In my ~/.bashrc file reside two definitions:   commandA, which is an alias to a longer path commandB, which is an alias to a Bash script   I want to process the same file with these two commands, so I wrote the following Bash script:    #!/bin/bash  for file in "$@"     do     commandA $file     commandB $file done   Even after logging out of my session and logging back in, Bash prompts me with command not found errors for both commands when I run this script.  What am I doing wrong? Does "the same number of people" behave as singular or plural? This is a problem from Introduction to Representation Theory by Etingof et al. I have no idea how to approach it. My friend wrote a program that uses Gaussian elimination to find a basis, which starts with x, y, [x, y], [y, [x, y]], ... but freezes once it gets to elements with 9 or more occurrences of x, y.  I expect that there is some way to characterize the nonzero elements of this Lie algebra (i.e., elements that are "immune" to being shown to be zero through repeated application of the Jacobi identity) which could be turned into a way to enumerate them. I don't see what it is, though.  It's also totally unclear to me how to show that some set we know spans the Lie algebra (proven using some criterion as described in the previous paragraph) is actually linearly independent, unless we find a faithful representation... but I have no idea how to find a faithful representation for an infinite-dimensional Lie algebra.  Hints would be greatly appreciated.  Edit: After looking at the partial output, we can form the "straightforward" conjecture that:   If $n \geq 4$ is even, then there is one basis element of grade $n$, namely $\mathrm{ad}([x, y])^{(n-4)/2}[y, [y, [y, x]]]$. If $n \geq 5$ is odd, then there are two basis elements of grade $n$, namely $[x, z]$ and $[y, z]$ where $z$ is the single basis element of grade $n-1$.   I also have a different conjecture, which is mutually exclusive with the above: that if we flatten out all nonzero elements into the form ${\rm ad}(e_1) {\rm ad}(e_2) \ldots {\rm ad}(e_{n-1}) e_n$ using the Jacobi identity, then in the sequences $e_1, \ldots, e_{n-1}, e_n$ and $e_1, \ldots, e_n, e_{n-1}$, any span containing two x's must contain at least two y's and any span containing five y's must contain at least two x's, otherwise we can use the Jacobi identity to rearrange the element somehow to show that it vanishes. If this is true, then the long-range behaviour must be:   For $n \geq 8$ there is exactly one basis element of grade $n$, namely $[... [y, [x, [y, [y, [x, y]]]]] ...]$ (the pattern $y x y$ repeats).   I still don't see an approach to proving that none of the elements in this sequence actually vanishes, though.  Edit 2: Here is the hint given by Etingof in an email:     No, there are no published solutions, since these problems are used as   a homework for classes. This is indeed a nontrivial problem.      This is the positive part of the affine Kac-Moody algebra of type   A_2^2, which is the twisted loop algebra for sl(2). So what you need   to do is to relate this Lie algebra to loops into sl(2). I see from   your post that you are on the right track. When I create a folder or copy files, after the operation finishes I have to manually refresh the Explorer window (F5). For example, when I create a folder, I don't see the "New Folder" until I hit F5.  Does anyone have any idea how to fix this? Find a closed formula for $\sum_{n=1}^\infty nx^{n-1}$  I am trying to use the derivative of generalized binomial theorem, $\frac{d}{dx}[(x+1)^r=\sum_{n=0}^\infty \binom{r}{n}x^n] =r(x+1)^{r-1}=\sum_{n=1}^\infty \binom{r}{n}nx^{n-1}$  However, I am not sure how to "get rid" of the binomial term. How to send array with CURL? Should I `urlencode` it? When is the sum of divisors a perfect square? For $n=3$, $\sigma(n)=4$, a perfect square. Calculating further was not yielding positive results.  I was wondering is there a way to find all such an $n$, like some algorithm?  We know that if $n=p_1^{k_1}p_2^{k_2}\dots p_r^{k_r}$ then $\sigma(n)=\frac {p_1^{k_1+1}-1}{p_1-1} \frac{p_2^{k_2+1}-1}{p_2-1}\dots \frac {p_r^{k_r+1}-1}{p_r-1}$. So we have to find $n$ such that $\sigma(n)=\frac {p_1^{k_1+1}-1}{p_1-1} \frac{p_2^{k_2+1}-1}{p_2-1}\dots \frac {p_r^{k_r+1}-1}{p_r-1}=t^2$ for some integer $t$. If each $\frac{p_i^{k_i+1}-1}{p_i-1}$ is a square we will get some such numbers (not all though), but let us consider $\frac{p_i^{k_i+1}-1}{p_i-1}=m^2$.   Working a example, If I take $p_i=17 $ , (or any prime such that $p_i-1$ is a perfect square), then if I can find a $k_i$ such that ${p_i^{k_i+1}-1}=16.m^2$ I will get an $n$, so now when can this happen, is something I have to try out.   But out of curiosity I am asking has this been worked out before. Problem looks broad to me, Is there a solution to this problem? Overfull hbox using biblatex Practical Uses for the "Curiously Recurring Template Pattern" What are some practical uses for the ""?  The "" example commonly shown just isn't a convincing example to me. how to display the actual network traffic (wireless) in a terminal?  Additionally: Is it possible to add this info to the chart of top? Born's Rule, What is the Reason? It is usually said that existence of discrete spacetime violates Lorentz symmetry. What quantity is used to quantify such violation? I mean could someone points a reference for a derivation that shows such analysis.  My other question is: if Lorentz symmetry is violated, does that imply space-time is discrete? or not necessarily?) Installing a 16-bit Windows 95 game on 64-bit Windows 7 Home Premium I know that the Naruto movies are outside the timeline in the sense that they don't affect whatever happens after them. However, they must fall somewhere in the Naruto timeline — based on who are in the movies and how the characters look like, etc. For example, if Sasuke isn't in the movie, it should take place after he left. For each of the movies, approximately what timeframe (between episodes/arcs) are they set?  The movies:   Ninja Clash in the Land of Snow Legend of the Stone of Gelel Guardians of the Crescent Moon Kingdom Naruto Shippuden the Movie Bonds The Will of Fire The Lost Tower Blood Prison Road to Ninja The Last - Naruto the Movie Boruto: Naruto The Movie Calculating polygon area within polygons in QGIS? I am new to QGIS - I want to estimate the area of the reef under a polygon grid. My shapefiles are already in meters, however I am having a hard time calculating the area under the grid layer. Attached are the photos. I want to calculate the total area of the bold black polygons (reefs) under each grid square (image 2). How much reef is inside each square, for example, grid1: 25 sq.km, grid 1 sq.km, etc. Each reef polygon has its corresponding area in the layer attribute table.    ADDITIONAL PHOTO: RED IS THE REEF  THE ATTRIBUTES OF THE REEF LAYER Homework - set theory infinite union A question from my homework I'm having trouble understanding. We are given:  $A(1) = \{\varnothing\}$, $A(n+1) = A(n)\cup (A(n)\times A(n))$  $A=A(1)\cup A(2)\cup A(3)\cup \cdots \cup A(n)\cup A(n+1) \cup \cdots$ to infinity  The questions are:  1) show that $A\times A \subseteq A$  2) Is $A \times A = A$?  Thank you for your help.  I've tried writing $A(2)$ but it gets really complicated and I'm having trouble understanding what the sets are. Let alone solve the question. What happens to Bucky's arm at the end of Infinity War? Bucky (Winter Soldier) has a metal arm (possibly made from vibranium?) but it's an attachment to his body as far as I understand. Why, when Thanos destroys half of the universe at the end of Infinity War, does his metallic arm also disappear with him? Shouldn't it be left behind as his gun did? Dirac delta function as a limit of sinc function If $[G' : G'']\leq p^2$, then $G'$ is abelian. How do I create RAW TCP/IP packets in C++? I'm a beginning C++ programmer / network admin, but I figure I can learn how to do this if someone points me in the right direction. Most of the tutorials are demonstrated using old code that no longer works for some reason.   Since I'm on Linux, all I need is an explanation on how to write raw Berkeley sockets. Can someone give me a quick run down?