A Way to Create Blender Materials in Text or Script? (Included: Script to Retexture SFM Models in Blender!)
Control Cycles/Eevee material nodes and material properties using python?
Prove $\sup(f+g) \le \sup f + \sup g$ Suppose $D$ is a nonempty bounded subset of reals. Let $f:D \to \mathbb R$ and $g:D \to \mathbb R$. Define $(f+g)(x)=f(x)+g(x)$. Prove $\sup(f+g)(D) \le \sup f(D) + \sup g(D)$ (also prove that $\sup (f+g)$ exists).   I understand why this is the case, just not how to prove it. Left side is pretty much $\sup  (f(x)+g(x))$ and right side is $\sup (f(x) + g(y))$ for $x,\,y \in D$. Basically $f+g$ has to use the same variable and $f(D)+g(D)$ use different ones. But I don't know how to go about proving this.     The second part of the question is to find a specific example where strict inequality holds.    Let $D=\{a,b\}$ and $f: a \to 1,\, b\to 0, \,g: a \to 0,\, b\to 1$. $\sup f(D) = 1,\, \sup g(D) = 1,\, \sup f(D) + \sup g(D) = 2.$ $\sup (f+g)(D) = 1$ (if we choose a, $f+g = 1+0,\, b,\, f+g=0+1$). Prove that $\liminf x_n = -\limsup (-x_n)$ How can we prove that $\liminf x_n = -\limsup (-x_n)$?  The definitions we are using are $\limsup x_n = \lim\limits_{n\to\infty} \sup\{x_k; k\ge n\}$ $\liminf x_n = \lim\limits_{n\to\infty} \inf\{x_k; k\ge n\}$ Every natural number $n$ can be written as $n=s-t$ with $\omega(s)=\omega(t)$ Can we prove the following statement ?  Let $\omega(m)$ denote the number of all distinct prime factors of a positive integer $m$. Prove that every  natural  number $n$ can  be  written  as $n=s-t$, where $s$ and $t$ are positive integers with $\omega(s)=\omega(t)$, in other words, as the difference of two positive integers with the same number of distinct prime factors.   If $n=1$ , we can choose $\ s=3\ $ and $\ t=2$.  If $n$ is even , we can choose $\ s=2n\ $ and $\ t=n$. Example of non-isomorphic structures which are elementarily equivalent I just started learning model theory on my own, and I was wondering if there are any interesting examples of two structures of a language L which are not isomorphic, but are elementarily equivalent (this means that any L-sentence satisfied by one of them is satisfied by the second).  I am using the notaion of David Marker's book "Model theory: an introduction". Someone flagged my question as already answered, but it's not Can a finite group act freely (as homeomorphisms) on $\mathbb R^n$ I am asking if whether or not a finite group acts freely (as homeomorphisms) on $\mathbb R^n$.  To answer in the negative, it suffices to show: for any homeomorphism $f$ such that $f^d=\text{id}_{\mathbb R^n}$, then $f$ has a fixed point.  I am looking for a complete self-contained answer. Which function (s) is(are) the k-th derivative of itself? As I attempted to solve for a function that is the $k$-th derivative of itself where $k$ is some natural number, and generalise the result, I realised it gets very hard to prove anything. For $k= 1$, apart from trivial corner cases, it's the exponential function with any constant multiplied.  For $k=2$, along with the exponential function and it's reciprocal, it works for their sum along with any mixture by constants multiplied...  For any $k$, I guessed it should be of the form $e^{x w}$ where w is the $k$-th root of unity. And we can add all these $k$ terms for each root with constants multiplied.  While it is easy to verify it's satisfying the condition, it is beyond my scope to prove this is the only family of functions that satisfy it.  I am hoping for some interesting math at work here, and want to know if this is an already established fact. Also, how do I prove anything here? What causes "java.lang.IllegalStateException: Neither BindingResult nor plain target object for bean name 'command' available as request attribute"? Finite Series - reciprocals of sines Find the sum of the finite series $$\sum _{k=1}^{k=89} \frac{1}{\sin(k^{\circ})\sin((k+1)^{\circ})}$$ This problem was asked in a test in my school. The answer seems to be $\dfrac{\cos1^{\circ}}{\sin^21^{\circ}}$ but I do not know how. I have tried reducing it using sum to product formulae and found out the actual value and it agrees well. Haven't been successful in telescoping it. Connect Talend to Salesforce using OAuth JWT Flow I followed the steps exactly mentioned here  for connecting Talend to salesforce.  I have done the configuration in Talend and added the test(sandbox) URL in the advanced setting. I am facing an error while trying to establish the Oauth connection (JWT) between Talend ETL tool and salesforce: {'error':'invalid_grant','error_description':'invalid assertion'} Here is the screenshot of the configuration and error message:   Please help to resolve this issue. How do you create a simple, custom rule using the jQuery Validate plugin (using ) that doesn't use a regex?  For example, what function would create a rule that validates only if at least one of a group of checkboxes is checked? How to calculate a heading on the earths surface? Given an initial position and a subsequent position, each given by latitude and longitude in the WGS-84 system.  How do you determine the heading in degrees clockwise from true north of movement? Can the ship's captain really perform your wedding when in international waters? On , Mark Mayo posted a comment that any marriage has to be on dry land or close to it.  But I'm sure all of us have heard of ships' captains marrying couples at sea.  From the movie Casablanca:     Say, why don't we get married in Marseilles?   ...   Well, let's see. What about the engineer? Why can't he marry us on the train?   ...   Well, why not? The captain on a ship can. It doesn't seem fair that...    So is this fiction after all? If not how does it fit with Mark's comment? What special rules and such should we know?  If I'm travelling at sea with a significant other and wish to tie the knot, can we do so with any captain on any ship on any sea? Must it be international waters? When you discard cards at the beginning of the game, where do they go? The appearance is that they get shuffled back into the deck. However, after discarding key cards and not receiving them the whole game, I am now wondering if they get put in the bottom of the deck. Where do they go after being discarded? Links being changed to cppreference.com Someone just edited a link in one of my answers to point to a 'better reference'.    I've no problem with links being changed in general, but this smells like part of a concerted attempt to redirect traffic.   Is this kind of activity acceptable on SO? We have two PHP5 objects and would like to merge the content of one into the second. There are no notion of subclasses between them so the solutions described in the following topic cannot apply.    //We have this: $objectA-&gt;a; $objectA-&gt;b; $objectB-&gt;c; $objectB-&gt;d;  //We want the easiest way to get: $objectC-&gt;a; $objectC-&gt;b; $objectC-&gt;c; $objectC-&gt;d;   Remarks:   These are objects, not classes. The objects contain quite a lot of fields so a foreach would be quite slow. So far we consider transforming objects A and B into arrays then merging them using array_merge() before re-transforming into an object but we can't say we are proud if this. Omission of 'for' with various quantified time intervals: influence of verb Automatically determine tags while writing a question Can we modify "Ask question" to automatically suggests tags based on your question content.   So instead that user needs to type "team-foundation-server" or "TFS" or "TeamFoundationServer" he will see list of tags auto-populated with ajax which he (or she) can then select and it will be associated with the question. So basically only thing we need is code which will cross-match question content with list of known tags while user is typing and display results in some nice ajax-enabled list/cloud/whatever UI control. This should be separate control for tags suggestions so user still has option to use standard tag list input to type-in tags.  In this case, instead of three (or more) tag variations we would have only one tag for Team-Foundation-Server. Proving the series $\sum_{n=0}^{\infty}\sin(e\pi n!)$ converges The product of $n$ consecutive integers is divisible by $n$ factorial How can we prove that the product of $n$ consecutive integers is divisible by $n$ factorial?     Note: In this  and the comments here the OP has clarified that he seeks a proof that "does not use the properties of binomial coefficients". Please post answers in said newer thread so that this incorrectly-posed question may be closed as a duplicate.