While using Intel GPU, Ubuntu 16.04 freezes on shutdown
Ubuntu MATE freeze on logout/shutdown/reboot when running on Intel graphics card
terminator: permission denied for sudo Evaluate: $\lim_{n\to\infty}\left({2\sqrt n}-\sum_{k=1}^n\frac1{\sqrt k}\right)$ Change logo url link I'm trying to change the logo url of the site to "mywebsite.com/side2", but it is not working, can anyone tell me where is the error in the code below?  add_filter( 'login_headerurl', 'custom_loginlogo_url' ); function custom_loginlogo_url($url) {  return home_url( 'side2' ); } Is $\frac{1}{\sqrt{2}}$ a fraction or not? I listened to this on audiobook and it was great.  The premise was a human ends up travelling to an alien planet. The aliens have a perimeter to their 'base' that is under constant attack from the planet's animals. It is revealed towards the end that there is some sort of signal being transmitted that is making all the animals and plant life attack a certain point on the planet (where the aliens are).   Other major plot points I remember: The human traveller falls in love with an alien. The aliens have a sort of virtual training environment that simulates life outside the perimeter, where plants attack you etc. There is a secondary alien group that the human ends up with, and although they are rivals to other group, they have a trade set up.   Any help much appreciated! Thanks. How many seconds count until bomb detonates in Counter Strike? In Counter-Strike, is there any count (in seconds/minutes) until the bomb explode when it's first set-up? And can the timing be modified? (Re?)Install Ubuntu on a Dell laptop that had Ubuntu preinstalled Can I install pantheon terminal in Ubuntu 14.04 or newer? Is it possible to install Pantheon terminal from elementary OS on my Ubuntu 14.04 or newer LTS releases? If yes, how can I? Every Function in a Finite Field is a Polynomial Function From a bank of past master's exams I am going through:     Let $F$ be a finite field. Show that any function from $F$ to $F$ is a polynomial function.   I know that finite fields are fields of $p$ elements for $p$ prime [EDIT: It's actually $p^n$ for $p$ prime; see comment below]. Since I have $p$ choices for the $p$ elements to map to, then I have $p^p$ distinct functions. I think every function can be written in the form $f(x) = a_{p-1}x^{p-1} + \dots + a_0x^0$. For then given the values $f(0), f(1), \ldots f(p-1)$, I can solve for the coefficents by the linear system of equations  $$ a_0 + \sum_{i=1}^{p-1} n^i a_i = f(n).$$  This then gives me a $p-1 \times p-1$ square matrix over the field $\mathbb{F}_p$:  $$\left( \begin{array}{ccccc} 1&amp; 0 &amp; 0 &amp; \ldots &amp; 0 \\ 1&amp; 1 &amp; 1 &amp; \dots &amp; 1 \\ 1&amp; 2 &amp; 4 &amp; \dots &amp; 2^{p-1} \\ \vdots &amp; \vdots &amp; \vdots &amp; &amp; \vdots \\ 1 &amp; p-1 &amp; (p-1)^2 &amp; \dots &amp; (p-1)^{p-1} \end{array} \right) \left( \begin{array}{c} a_0 \\ a_1 \\ a_2 \\ \vdots \\ a_{p-1} \end{array}\right)  = \left( \begin{array}{c} f(0) \\ f(1) \\ f(2) \\ \vdots \\ f(p-1) \end{array} \right)$$  If I can show this matrix is invertible, then I can always find the $a_i$. But I am a bit stumped on how to show this (partially because I don't think I've ever done linear algebra in a vector space over a finite field). It does not seem easy to show linear independence, or nonzero determinant, or full row rank.    Alternatively (I just thought of this), can I show this is true by arguing that the map between the two sets (the set of polynomials of degree $p-1$; and the set of functions $F \to F$) is injective, and that it must be a bijection because the sets have the same cardinality $p^p$? Mathematical notation around the world Set of continuity points of a real function I have a question about subsets $$ A \subseteq \mathbb R $$ for which there exists a function $$f : \mathbb R \to \mathbb R$$ such that the set of continuity points of $f$ is $A$. Can I characterize this kind of sets? In a topological,measurable or in some way? For example, does there exist a function continuous on $\mathbb Q$ and discontinuous on the irrationals? Why are Icon Overlays (from 3rdParty-Apps) not showing up in the Win8 Explorer? So, I have about 7 actions users may need in my app, and I have to use text instead of icons because it is a customer requirement.  I can add only 3 actions to my toolbar on iPhone 6. On Android you have the hamburger menu (see image), but I have never seen it in iOS.       So, what is the appropriate concept in iOS to add many actions into a menu? Why does HTML require that multiple spaces show up as a single space in the browser? I have long recognized that any set of whitespace in an HTML file will only be displayed as a single space.  For instance, this:  &lt;p&gt;Hello.        Hello. Hello. Hello.                       Hello.&lt;/p&gt;   displays as:  Hello.        Hello. Hello. Hello.                       Hello.  This is perfectly fine, as if you need multiple spaces of pre-formatted text you can just use the &lt;pre&gt; tag.  But what is the reason?  More precisely, why is this in the specification for HTML? How am I to "[u]se induction to show that $n$ straight lines in the plane divide the plane into $\frac{n^2+n+2}{2}$ regions"? It is assumed here that no two lines are parallel and that no three lines have a common point. Further, this is not a non-Euclidean problem, but I wouldn't mind a discussion on the non-Euclidean nature of the problem.  I was thinking it might be easier to show using the unit sphere.    A GOOD REFERENCE I FOUND THAT WILL BE USEFUL TO ANYONE COMING ACROSS THIS PROBLEM IS Concrete Mathematics, Graham, Knuth, Patashnik pp. 4–8. Show that any set in a metric space can be written as the intersection of open sets Are more megapixels good?  Are more megapixels bad?  Do more megapixels increase detail? Do they make my images sharper? On the other side, is there a point that is too much? Do megapixels cause increased noise and other problems? How does print and viewing size come into it?  Widespread Internet-forum wisdom used to be that 6 megapixels was the sweet spot — below that just wasn't enough, but above that, there wasn't much benefit. File sizes got larger, but detail was lost to noise and other problems. The arguments are that cramming too many pixels into a small sensor makes each pixel too small to provide any real benefit, and that higher-megapixel sensors outresolve cheap lenses anyway. (Substitute something like 12 instead of 6 if we're discussing APS-C DSLRs, or 24 for full-frame.)  By 2011,  was in the range of 12-18 megapixels. In 2016 most were are in the 16-24 megapixel range. Certainly none are at 6 anymore; even smartphones come with 8 megapixel cameras. Does this offer any real improvement over that old "sweet spot"? Has technology improved to the point where the "wisdom" needs to be updated, or are we all suffering for marketing? Or have we gone past the sweet spot in some ways, but it's okay because of previously-un-argued points. (For example: more noise, sure, but more detail as well.)  Within the 16-24 megapixel common-today range, for the same sensor size, is there any actual benefit to the higher end? How do megapixels directly affect image quality with today's technology? What are the benefits and when do they apply? What are the drawbacks, and when do they apply? How should I adjust my technique (and expectations) based on my camera's megapixel count? Windows 10 sees much more monitors than I have Why is it a bad practice to lock the object we are going to change? I feel that I might have a complete misunderstanding here. If DNA has two strands, how does the machinery of RNA transcription determine which one to transcribe?