Is it correct that if Ubuntu is installed inside Windows using Windows installer then it works slower?
I know that Wubi is slower in disk IO, but I can't find anything about it online other than vague statements such as "slightly slower disk seeks".  Has anyone done any benchmarks to quantify the speed difference?
Removing spaces between "words" in math mode Launch shell scripts from anywhere Is it possible to run my scripts located in ~/scripts from anywhere?  Say i want to run ./scriptname regardless of my current working directory. What is the argument selector tracking a defined score (not [score_min=])? What if I want to make a command like this:  execute @e[score_A=10] ~ ~ ~ summon Creeper   So that the entity must have a score of 10 (not less, not more)?  Does it even exist that or a [score_A_max=] argument?  I know about scoreboard players test, but i guess it is not the case to use it. Integrating $\int \sin^n{x} \ dx$ I am working on trying to solve this problem:     Prove: $\int \sin^n{x} \ dx = -\frac{1}{n} \cos{x} \cdot \sin^{n - 1}{x} + \frac{n - 1}{n} \int \sin^{n - 2}{x} \ dx$   Here are the steps that I follow in the example that I am reading:     $u = \sin^{n - 1}{x}$      $du = (n - 1) \cdot \sin^{n - 2}{x} \cdot \cos{x} \ dx$      $v = -\cos{x}$      $dv = \sin{x} \ dx$            $\int \sin^n{x} \ dx =  \sin^{n - 1}{x} \cdot \sin{x} \ dx$      $\int \sin^n{x} \ dx = \underbrace{\sin^{n - 1}{x}}_{u} \cdot \underbrace{-\cos{x}}_{v} - \int \underbrace{-\cos{x}}_{v} \cdot \underbrace{(n - 1) \cdot \sin^{n - 2}{x} \cdot \cos{x} \ dx}_{du}$      $\int \sin^n{x} \ dx = -\cos{x} \cdot \sin^{n - 1}{x} + (n - 1)\int \sin^{n - 2}{x} \cdot \cos^{2}{x} \ dx$      $\int \sin^n{x} \ dx = -\cos{x} \cdot \sin^{n - 1}{x} + (n - 1)\int \sin^{n - 2}{x} \cdot \left(1 - \sin^{2}{x}\right) \ dx$   Here is where I get lost. How did we go from $\int \sin^{n - 2}{x} \cdot \left(1 - \sin^{2}{x}\right) \ dx$ to $\int \sin^{n - 2}{x} \ dx - (n - 1) \int \sin^{n}{x} \ dx$? Even more specifically, where did $\sin^{n}{x}$ come from?     $\int \sin^n{x} \ dx = -\cos{x} \cdot \sin^{n - 1}{x} + (n - 1)\int \sin^{n - 2}{x} \ dx - (n - 1) \int \sin^{n}{x} \ dx$   I get this part.     $n\int \sin^n{x} \ dx = -\cos{x} \cdot \sin^{n - 1}{x} + (n - 1)\int \sin^{n - 2}{x} \ dx$      $\int \sin^n{x} \ dx = -\frac{1}{n} \cos{x} \cdot x \ \sin^{n - 1}{x} + \frac{n - 1}{n} \int \sin^{n - 2}{x} \ dx$   Could someone please explain what I am missing?  Thank you for your time. Constants and compiler optimization in C++ I've read all the advice on const-correctness in C++ and that it is important (in part) because it helps the compiler to optimize your code. What I've never seen is a good explanation on how the compiler uses this information to optimize the code, not even the good books go on explaining what happens behind the curtains.    For example, how does the compiler optimize a method that is declared const vs one that isn't but should be. What happens when you introduce mutable variables? Do they affect these optimizations of const methods? How To Make A Solid Object Drop To The Ground Like It Was Liquid Do I need a visa to visit the UK with my EU partner? I am not from EU. I have Spanish partner and we live in Spain and, because of our official relationship, I have a Spanish family resident permit. We are going to travel to the UK together for tourism. I am confused whether I need an EEA family permit or not.  I will not live there and I'm going to travel with my partner. I was told that I don't need a visa, that showing our civil union document will be sufficent. Is this correct, or do I need a visa to enter the UK?    Thank you so much for your answer. Let me give you more detail.  I hold Turkish citizenship.  My resident card exactly says that Residence Card of a Family Member of a Union Citizen " tarjeta de familiar de la union.   my case is like For example, a non-EEA spouse of a German national living in Germany will usually hold a residence permit issued under German domestic law. Therefore, a United Kingdom EEA family permit is required for travel and entry to the UK , therefore I should consider that I need to EEA Family Permit even if for touristic trip with my partner. I have looked everywhere for lava or obsidian in 0.7.1. I've looked all the way from top to bottom and all around, in about a 100 block diameter, but I can't find any. Where can I get some? I want to work with unsigned 8-bit variables in C++.  Either unsigned char or uint8_t do the trick as far as the arithmetic is concerned (which is expected, since AFAIK uint8_t is just an alias for unsigned char, or so the debugger presents it.  The problem is that if I print out the variables using ostream in C++ it treats it as char.  If I have:  unsigned char a = 0; unsigned char b = 0xff; cout &lt;&lt; "a is " &lt;&lt; hex &lt;&lt; a &lt;&lt;"; b is " &lt;&lt; hex &lt;&lt; b &lt;&lt; endl;   then the output is:  a is ^@; b is 377   instead of   a is 0; b is ff   I tried using uint8_t, but as I mentioned before, that's typedef'ed to unsigned char, so it does the same.  How can I print my variables correctly?  Edit: I do this in many places throughout my code.  Is there any way I can do this without casting to int each time I want to print? What are the advantages/disadvantages of the new encryption feature in ubuntu 13.10 I'm in the middle of installing 13.10 and the Ubuntu page I was following on how to install from a USB stick says nothing about these two choices (on the Installation type screen):     1) Encrypt the new Ubuntu installation for security (you will choose a security key in the next step).      2) Use LVM with the new Ubuntu installation (this will set up Logical Volume Management. It allows taking snapshots and easier partition resizing)   I'm a writer using the computer for mostly writing ebooks but I also do all the things most people do: buy stuff online, online banking etc. I want my information to be safe but I don't want to overburden my system with security stuff either. And I've read a lot of the similarly themed questions here on the forum but they've all been about stuff more technical than I'm concerned about.   Can somebody please just tell me in real layman's terms about the implications of these two choices? Thank you. Simple UV Mesh Unwrapping Scale issue I'm having problems using the UV mapping in blender 2.67. Specifically, I am trying to unwrap a really simple mesh, but the UV map is still giving me a net where some of the boxes are completely out of proportion to the others, which causes the texture to stretch horribly. Here is a picture to illustrate:    The mesh only has those three faces you can see in the picture, and the single seam on the front corner. It's a trivially simple mesh, so I really don't understand why the two side faces are being stretched in the UV map to be the same size as the top face. I've tried clicking the average islands scale button as suggested by some of the answers to other questions but that has no effect. It's frustrating because it seems so simple.  Hopefully someone can show me the presumably simple mistake I am making!  Edit: Just to make this clearer, I have already added a seam as the first answer suggests i do. Hopefully this picture will make that clearer, the yellow arrow is pointing to the edge i seamed. The mesh is only three faces so should only need this single seam. The image shows the mesh from infront and behind/underneath so it should make more sense.    Double Edit: One more picture for clarity on the seam issue. The mesh is unfolding correctly, it is just the scale of the unfolded map that is incorrect (in relation to one another) Cardinality of a set A is strictly less than the cardinality of the power set of A jQuery selector regular expressions The category Set has the property that any morphism f can be decomposed into an epimorphism $e$ and a monomorphism $m$ with $f$ = $m\circ e$. (The intermediary set object is the image of $f$.)  Is there a name for this construction?  Is there a name for this property of categories?  In Set, the intermediary object is unique up to isomorphism. Is this the case for all categories with the property? Order discrete x scale by frequency/value Why don't we read ''k'' here?  Know → /nəʊ/   Knotty → /ˈnɒt.i/   Knockout → /ˈnɒk.aʊt/ Can I travel to Dublin, Republic of Ireland with UK Tier 2/Schengen visas with Indian Passport This is a pretty well known quote from the Star Wars movies. But isn't it a bit paradoxical?   It in itself is an absolute, and it was said by a Jedi (Obi-Wan if I recall correctly?). If this holds true, then is he leaning towards the Sith himself? If it isn't true, then both Jedi and Sith can deal in absolutes and the statement is pointless.  Surely it should be phased along the lines of "Jedi's should avoid dealing in absolutes" or something similar? QR factorization of complex matrix If you have two complex numbers $a,b$ how can you find the QR factorization of   $ M = \begin{bmatrix}        aI_n\\          bI_n \end{bmatrix} $,  I can't seem to be able to do it. I tried an earlier trick, but I now know it's not necessary true for complex numbers. Is there anyway to do this?  I think if I use a Givens algorithm I should be able to reduce it to a QR factorization. Multiplicative inverse questions This is my first time posting on Math exchange. I have been self-teaching myself Mathematics and recently started learning some Algebra. I was posed the following questions, in which I would like to answer before I proceed, but having some trouble finding proper solutions. So the format will be question, and my answer.      What name do we give an element $a \in \mathbb{Z}_n$ that has a multiplicative inverse?   A modular multiplicative inverse of an integer $a$ is an integer $x$ such that $ax \cong 1 (\mod m)$. This means that the remainder after dividing $ax$ by integer $m$ is equal to $1$.      Give an example, for some $n \in \mathbb{N}$, of an element of $\mathbb{Z}_n$, that does not have a multiplicative inverse?   This question is throwing me off because - does the $n$ we speak of matter for both $n \in \mathbb{N}$ and $\mathbb{Z}_n$ ot solely $n$? My guess here would be $0$ because we cannot have an inverse of $0$.      Prove that multiplicative inverse are unique; an element $a \in \mathbb{Z}_n$ cannot have two multiplicative inverses.    Suppose that an element $a\in\mathbb{Z}_n$ has an inverse $a'$. Next, suppose that $a^*$ is also an inverse of $a$. Then, $a'$ is a solution to $a \cdot_n x=1$, and similarly $a^*$ has a solution to $a \cdot_n x=1$.   Lemma: Suppose $a'$ is multiplicative inverse of $a$ in $\mathbb{Z}_n$, then for any $b \in \mathbb{Z}_n$ the equation $a \cdot_n x=b$ has a unique solution, such that $x = a' \cdot_n b$.   By Lemma, equation $a \cdot_n x = 1$ has a unique solution, namely $x=a'=a^*$. Therefore, an element $a\in \mathbb{Z}_n$ cannot have two multiplicative inverses.    Thank you for the help. I would love any constructive feedback for these. If you can help me elaborate on some ideas, that would be really helpful also.  Thank you very much!