I can only see reflections in shader viewport , why can't I get them to render? I have specular refractions on in the render engine (evee) &amp; material. But still get this grey image when I view render or animaton
Blender 2.8 contains a number of HDRi's in it by default for the LookDev. I'd like to know how to use them in final renders (EEVEE or Cycles), because quite frankly they appear fantastic.
Intuitive explanation for density of transformed variable? Suppose $X$ is a random variable with pdf $f_X(x)$. Then the random variable $Y=X^2$ has the pdf   $$f_Y(y)=\begin{cases}\frac{1}{2\sqrt{y}}\left(f_X(\sqrt{y})+f_X(-\sqrt{y})\right) &amp; y \ge 0 \\ 0 &amp; y \lt 0\end{cases}$$   I understand the calculus behind this. But I'm trying to think of a way to explain it to someone who doesn't know calculus. In particular, I'm trying to explain why the factor $\frac{1}{\sqrt{y}}$ appears out front. I'll take a stab at it:  Suppose $X$ has a Gaussian distribution. Almost all the weight of its pdf is between the values, say, $-3$ and $3.$ But that maps to 0 to 9 for $Y$. So, the heavy weight in the pdf for $X$ has been extended across a wider range of values in the transformation to $Y$. Thus, for $f_Y(y)$ to be a true pdf the extra heavy weight must be downweighted by the multiplicative factor $\frac{1}{\sqrt{y}}$  How does that sound?  If anyone can provide a better explanation of their own or link to one in a document or textbook I'd greatly appreciate it. I find this variable transformation example in several intro mathematical probability/stats books. But I never find an intuitive explanation with it :( Attributing contributions to academic work that occur in Stack Exchange Proof of for-all / there-exists "negation"? Hide the term id on autocomplete widget How can I mitigate edge halo when darkening skies in post-processing? Add 'Page' above page numbers in Table of Contents I am using my school's latex . Unfortunately, since this package was last updated, we are now required to add the word 'Page' above the topmost page number on each page of the Table of Contents. This cls file includes the following bit of code, which puts 'Page' at the top of the first page, but not any subsequent pages (see attached)  \newcommand\chapteruaf{ \if@arabic\relax\else\if@chapterone\setcounter{page}{1}\else\relax\fi\fi \@chapteronefalse                     \if@openright\cleardoublepage\else\clearpage\fi                     \thispagestyle{myheadings}%                                                                                                    \global\@topnum\z@                     \@afterindentfalse                     \secdef\@chapter\@schapteruaf} \def\@schapteruaf#1{\if@twocolumn                    \@topnewpage[\@makeschapterheaduaf{#1}]%                                                                                     \else                    \@makeschapterheaduaf{#1}%                                                                                                     \@afterheading                  \fi} \def\@makeschapterheaduaf#1{%                                                                                                    {\parindent \z@ \centering     \reset@font     \normalsize \bfseries  #1\par                                                                                                  \vspace{-18.3pt}\hspace{143mm} Page                                                                                            \nobreak   }}   First page of the TOC:   second page of the TOC:   Any thoughts here? I have played with this a bit, and can't get it to work. Thanks. Get number of frames in scene from the command line? I'd like to know if there is a command-line option (or combination, or a way!) to get the number of frames that are included in a specified blender scene; for example I'd like to use is like this:  $ blender &lt;option&gt; file.blend $ Number of frames in blender scene: xxxx What's the name of this flat illustration style? I want to buy some stock photos like the ones below. What is this design called?  I don't even know how to start searching... Finding the Transform matrix from 4 projected points (with Javascript) The book Theory of Functions of a Real Variable by I. P. Natanson, proves that a denumerable or finite union of pairwise disjoint sets of cardinality $c$ has cardinality $c$.  The proofs given in the book are fairly easy, using the axiom of choice. But then it is left as an exercise a generalization of the above theorems for not necessarily pairwise disjoint sets.  I have searched all over the web, but all the proofs found so far are for pairwise disjoint sets.  The proof given in the book relies on the fact that each set $A_k$ can be matched with a set like $[a_{k-1},a_k)$, with $a_k$ point of a partition of $[0,1]$, such that $\bigcup_{k=1}^{\infty\lor n}A_k=[0,1)$. So it is easy to guess the bijective function, but I can't generalize this proof.  Any help is highly appreciated. Thanks and regards. How Many Genius Mixes Are There in iTunes? Getting a domain name off of the blacklist I have a friend who purchased a domain name recently that he found out (after buying it) is apparently blocked by many corporate firewalls or proxies b/c it's been tagged as porn by the blacklist db they're using.    Are there any common agencies he can appeal to in order to get the domain name off the black lists?  It's not just one corporation, either, he's looking at marketing a subscription-based service to a certain industry, so any contacting a particular firewall/proxy admin and have them manually update the blacklist won't scale well.  Thanks in advance. Paul Is there another saying/idiom similar to crocodile tears? Getting a vector into a function that expects a vector Properties of $\liminf$ and $\limsup$ of sum of sequences: $\limsup s_n + \liminf t_n \leq \limsup (s_n + t_n) \leq \limsup s_n + \limsup t_n$ Let $\{s_n\}$ and $\{t_n\}$ be sequences.  I've noticed this inequality in a few analysis textbooks that I have come across, so I've started to think this can't be a typo:  $\limsup\limits_{n \rightarrow \infty} s_n + \liminf\limits_{n \rightarrow \infty} t_n \leq \limsup\limits_{n \rightarrow \infty} (s_n + t_n) \leq \limsup\limits_{n \rightarrow \infty} s_n + \limsup\limits_{n \rightarrow \infty} t_n$.  I understand the right two-thirds of the equation, and can prove it.  I'm stuck on the far-left third.  I don't understand how that is true. Would you please explain the difference between these two sentences?     Spain ceded (or gave) Puerto Rico to the United States. Since then, Puerto Rico has been a U.S. territory.      Spain ceded(or gave) Puerto Rico to the United States. Since then, Puerto Rico was a U.S. territory.   I am stuck between 'has been' and 'was' in the above sentences. Problem:  If $\gcd(a, b) = 1$ and If $ab = x^2$ ,prove that $a$, $b$ must also be perfect squares; where $a$,$b$,$x$ are in the set of natural numbers  I've come to the conclusion that $a \ne b$ and $a \ne x$ and $b \ne x$ but I guess that won't really help me.. I understand that if the $\gcd$ between two numbers if $1$ then they obviously have no common divisors but where do I go from this point?  Any tips at tackling this would be great. It looks quite easy though I'm still trying to get my hand around these proofs! Any pointers in the right direction would be great.  Thank you in advance, Run a web server from any directory How do I compute the normalisation of $A=k[X,Y]/(Y^3 - X^5)$? I'm trying to solve exercise 4.7 in Reid's UCA:  "Find the normalisation of $A=k[X,Y]/(Y^3 - X^5)$."  I can easily show $A$ is not normal: let $x$ and $y$ denote the images of $X$ and $Y$ in $A$. Thus $y^3 = x^5$. So there exists $t=y/x\in\operatorname{Frac} (A)$ which is a root of the monic polynomial $T^3 - x^2 \in A[T]$. But since $t\notin A$, $A$ is not normal.  However, I don't know how to compute the normalisation of $A$; I have not seen dimension theory developed, so  to a similar question doesn't really help me. Similarly I cannot try and apply something like  to a related question, because in this case the map $k[X,Y]\rightarrow k[t]$ sending $X\mapsto t^3, Y\mapsto t^5$ is injective so the image isn't isomorphic to $A$  UCA never really gives a good explanation on how to actually compute normalisations, so I'd be grateful if anyone could walk me through it. Is 2h 45m enough for a layover in Newark Liberty International transferring from an international to a domestic flight (Terminal B → Terminal C)?