Proof of functional completeness and adequate of logical operators
proof of functional completeness of logical operators
How to disable phone number linking in Mobile Safari? How to do volumetric lighting for a forest scene? I have scene that looks like this:   And I want to add volumetric lighting to it so that light forms a rays of light when it go through the trees like on this example that I found in youtube:   But the problem is that all of these tutorials show how to make this lighting coming from windows, but when I try to replicate it in my forest scene it looks like big ugly fog with cubical shape. Also the light is coming from the back of the camera (as you can see) and there are some spots that needs this special lighting (like places where light goes through trees) and some that don't (like big bright are on the bottom left corner) so I can't just add a giant cube to all of the scene. What is a word for a person who uses resources to the maximum? Is there a word (or words) for a person who uses all resources to the maximum; for example, a person who keeps on using pencils even if they are very small? Option clash for package xcolor How can I have a pointer to the next struct in the definition of this struct:  typedef struct A {   int a;   int b;   A*  next; } A;   this is how I first wrote it but it does not work. Make browser window blink in task Bar How do I make a user's browser blink/flash/highlight in the task bar using JavaScript? For example, if I make an AJAX request every 10 seconds to see if the user has any new messages on the server, I want the user to know it right away, even if he is using another application at the time.  Edit: These users do want to be distracted when a new message arrives. How to sandbox applications? I want to run small untrusted programs, but restrict them from accessing any files outside of their folder, network access, and everything else that they don't really need. What is the simplest way to achieve this? Writing my first script so I'm sure this is a basic question, but can someone please explain to me why I can:  cd ~ cd bin cd ~/bin cd 'bin'   But not  cd '~' cd '~/bin'   I need to cd to a directory path with a space in one of the directory names, so I need the quotes (it's Windows Program Files under wine). I can get around it with two cd commands, but why can't I put ~ in quotes?  If I type cd '~' (or cd "~") I get:  bash: cd: ~: No such file or directory shorter proof of generalized mediant inequality? P-adic expansion construction Plot an elliptic curve in Latex How to sort a list of objects based on an attribute of the objects? I've got a list of Python objects that I'd like to sort by an attribute of the objects themselves.  The list looks like:  &gt;&gt;&gt; ut [&lt;Tag: 128&gt;, &lt;Tag: 2008&gt;, &lt;Tag: &lt;&gt;, &lt;Tag: actionscript&gt;, &lt;Tag: addresses&gt;,  &lt;Tag: aes&gt;, &lt;Tag: ajax&gt; ...]   Each object has a count:  &gt;&gt;&gt; ut[1].count 1L   I need to sort the list by number of counts descending.  I've seen several methods for this, but I'm looking for best practice in Python. "At" vs. "in" before verb In a document I found the following sentence:     listeners are more accurate at understanding speech spoken in their own accent...   Would it be an error to use "in" instead of "at"?  Actually in this case "at" sounds better than "in", but in general before verb is "at" always used? How to evaluate the integral $\int_0^{\pi}\frac{a^n\sin^2x+b^n\cos^2x}{a^{2n}\sin^2x+b^{2n}\cos^2x}dx$? Evaluate the integral $$\int_0^{\pi}\frac{a^n\sin^2x+b^n\cos^2x}{a^{2n}\sin^2x+b^{2n}\cos^2x}dx.$$   I have no idea.   $$\int_0^{\pi}\dfrac{a^n\sin^2x+b^n\cos^2x}{a^{2n}\sin^2x+b^{2n}\cos^2x}dx=\int_0^{\pi/2}\dfrac{a^n\sin^2x+b^n\cos^2x}{a^{2n}\sin^2x+b^{2n}\cos^2x}dx=\int_0^{\pi/2}\dfrac{a^n\tan^2x+b^n}{a^{2n}\tan^2x+b^{2n}}dx$$  I try the substitution $\tan{x}=t$, but it doesn’t work. If $f:\mathbb{R}\rightarrow \mathbb{R}$ is differentiable and $\lim_{x\to \infty } f^\prime(x)=0$ show that $\lim _{x\to \infty } (f(x+1)-f(x))=0$. "Always on top" option missing for Firefox/Chrome in 18.04 Prove without using graphing calculators that $f: \mathbb R\to \mathbb R,\,f(x)=x+\sin x$ is both one-to-one, onto (bijective) function. Prove that the function $f:\mathbb R\to \mathbb R$ defined by $f(x)=x+\sin x$ for $x\in \mathbb R$ is a bijective function.    The codomain of the $f(x)=x+\sin x$ is $\mathbb R$ and the range is also $\mathbb R$. So this function is an onto function. But I am confused in proving this function is one-to-one. I know about its graph and I know that if a function passes the  horizontal line test (i.e horizontal lines should not cut the function at more than one point), then it is a one-to-one function. The graph of this function looks like the graph of $y=x$ with sinusoids going along the $y=x$ line. If I use  a graphing calculator at hand, then I can tell that it is a one-to-one function and $f(x)=\frac{x}{2}+\sin x$ or $\frac{x}{3}+\sin x$ functions are not, but in the examination I need to prove this function is one-to-one theoritically, without graphing calculators. I tried the method which we generally use to prove a function is one-to-one but no success. Let $f(x_1)=f(x_2)$ and we have to prove that $x_1=x_2$ in order fot the function  to be one-to-one. Let $x_1+\sin x_1=x_2+\sin x_2$ But I am stuck here and could not proceed further. What are SPF records, and how do I configure them? I am looking for a book about "advanced" classical mechanics. By advanced I mean a book considering directly Lagrangian and Hamiltonian formulation, and also providing a firm basis in the geometrical consideration related to these to formalism (like tangent bundle, cotangent bundle, 1-form, 2-form, etc.).  I have , but I would like to go into more details about the [symplectic] geometrical and mathematical foundations of classical mechanics.  Additional note: A chapter about relativistic Hamiltonian dynamics would be a good thing. The extension of smooth function