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Is it possible that galaxies' redshift is caused by something else than the expansion of space? I was thinking that maybe photons loss energy naturally when they travel great distances.  Or maybe the mass of all matter is increasing over time and therefore photons emitted in the past are necessarily less energetic.  Or is the expansion of space backed up by so much other evidences that trying to find another explanation is completely foolish? Uniform convergence of $f_n(z)=nz^n$ in the set $|z|<\frac{1}{2}$ Origins of the nose-bleed in anime/manga In a similar spirit to my , I wonder who was the first artist to feature a nose-bleed when thinking, shall we say, "provocative thoughts"?  Did it become popularized in anime/manga because of the popularity of the artist's work or because it is a common belief in japanese folklore? How do I fix a boolean/bisected surface edge? I am trying to slice up my models using the Boolean modifier.  After applying the modifier on my smooth mesh, I get the expected result, a flat dissection to separate my mesh into two.  The problem lies in how I can resolve the visual "jaggered" edge that separates my (smooth) mesh exterior from the flat dissection face.    Is it possible to achieve a smooth-to-flat variation without this artifact?   I tried to alter a mixture of the two but end up with artifacts, or unwanted blocky flat mesh faces around the dissection edge of my mesh. $\mathbb{Z}[X]/(X^2-1)$ is not isomorphic with $\mathbb{Z}\times \mathbb{Z}$ I have to show that the ring $\mathbb{Z}[X]/(X^2-1)$ is not isomorphic with $\mathbb{Z}\times \mathbb{Z}$.    I know that $(\mathbb{Z}\times\mathbb{Z})^*=\{(\pm1,\pm1)\}$, so I thought I should be looking for elements which have inverses in $\mathbb{Z}[X]/(X^2-1)$ and hopefully find more or less than 4. But I didnt succeed, so I need hints. Thanks. how to remove the double quotes in a csv I have a CSV file like  a.csv "1,2,3,4,9" "1,2,3,6,24" "1,2,6,8,28" "1,2,4,6,30"   I want something like   b.csv 1,2,3,4,9 1,2,3,6,24 1,2,6,8,28 1,2,4,6,30   I tried awk '{split($0,a,"\""); But did not help.Any help is appreciated. Trigger an event with Prototype Does anybody know of a method to trigger an event in Prototype, as you can with jQuery's trigger function?  I have bound an event listener using the observe method, but I would also like to be able to fire the event programatically.  Thanks in advance Some areas of the mesh are dark (Shadow artefacts) I've been modeling a hermit crab and I don't know why but some areas of the mesh are really dark on some spots, like the legs and the claws.   I hope you can help me fix it. Computation of a limit involving factorial $\lim_{n \to \infty} \sqrt[n+1] {(n+1)!} - \sqrt[n] {(n)!} = \frac{1}{e}$ Proof of the formula $1+x+x^2+x^3+ \cdots +x^n =\frac{x^{n+1}-1}{x-1}$ I'm stuck at this algebra problem, it seems to me that's what's provided doesn't even at all.  Provided:  $$a+b+c=0$$  Find the value of:  $$\frac{a^2}{2a^2+bc}+\frac{b^2}{2b^2+ac}+\frac{c^2}{2c^2+ab}$$  Like I'm not sure where to start, and the provided clue doesn't even make sense.  There's no way I can think of to factor this big polynomial into a form like $a\times p+b\times q+c\times r=s$ where $p,q,r,s\in\mathbb{Z}$.  Thanks! Prove that all cyclic groups of the same order are isomorphic I want to prove that 2 cyclic groups of the same order are always isomorph. So, let $G,H$ be cyclic groups with $|G| = |H|$. Then: I suspect the isomorphism would be the one that maps a generator g to a generator h. Thus, consider this function:  $f: G \rightarrow H$ defined by $f(g^k) = h^k$. I already showed that this mapping is surjective and a homomorphism, but I get stuck at the injectivity part. Can someone give a hint (my attempts: I tried to deduce whether the kernel is $e_G$ and I also used the definition of injectivity but I got stuck in both approaches)? Is every dense subspace of a separable space separable? In the current era of cricket, we see batsmen using switch hits to play a ball. That is, while playing a ball they change their batting side (left to right handed and vice versa) just before the ball comes to them.  My question is, can a bowler bowl a switch ball? Meaning, can a left hand bowler bowl right handed to a batsman? If it is not permitted, then is it not unfair to the bowlers that batsmen can change their batting style but not the bowlers? Or are there are any rules against a switch hit? I have a ASUS R500A notebook.Original OS is Windows 7 64bit.Few days ago I tried to Install Windows 8.1 64 bit version.But it failed &amp; error message is,     windows cannot be installed on this disk. The selected disk is of the GPT partition style.   My Steps: First i Deleted C: Partition ( Already installed windows 7 ). Then i Formatted that partition. Tried to install Windows 8.1 64bit.  In this hard disk i have another several partitions with Important data.  How do i Install Windows 8.1 without loosing Data from the Other partitions ? The program ed, a minimal text editor, cannot be exited by sending it an interrupt through using Ctrl-C, instead printing the error message "?" to the console.  Why doesn't ed just exit when it receives the interrupt?  Surely there's no reason why a cryptic error message is more useful here than just exiting.  This behavior leads many new users into the following sort of interaction:   $ ed hello ? help ? exit ? quit ? ^C ? ^C ? ? ? ^D $ su # rm -f /bin/ed    Such a tragic waste—easily avoidable if ed simply agreed to be interrupted.  Another stubborn program exhibiting similar behavior is less which also doesn't appear to have much reason to ignore C-c.  Why don't these programs just take a hint? Using indefinite articles before adjectives: "Let's have a good breakfast" Let's have breakfast    Let's have a good breakfast      I've learned that indefinite articles aren't used before uncountable nouns, so why is a used before the adjective "good" here?    Is there an exception to the rules or is it wrong? Is it true that the order of $ab$ is always equal to the order of $ba$? How do I prove that if $a$, $b$ are elements of group, then $o(ab) = o(ba)$?   For some reason I end up doing the proof for abelian(ness?), i.e., I assume that the order of $ab$ is $2$ and do the steps that lead me to conclude that $ab=ba$, so the orders must be the same. Is that the right way to do it? Who did that to the priest's dog? In John Michael McDonagh's wonderful philosophical black comedy , a good priest receives a death threat during a confessional giving him a week to sort out his affairs.   During the course of the week there are a lot of encounters between the priest and his parishioners, many acting as red herrings to distract the audience form the identity of the potential killer. Several threatening acts also take place: the church is burned and the priest's dog is killed.   But in the final encounter between the priest and the mystery antagonist (I'm not saying who to avoid spoilers) the antagonist admits burning the church but claims not to have killed the priest's dog.  Are they lying? Or is there a good reason that someone else might have killed the dog? The following code snippet (correctly) gives a warning in C and an error in C++ (using gcc &amp; g++ respectively, tested with versions 3.4.5 and 4.2.1; MSVC does not seem to care):  char **a; const char** b = a;   I can understand and accept this. The C++ solution to this problem is to change b to be a const char * const *, which disallows reassignment of the pointers and prevents you from circumventing const-correctness ().  char **a; const char* const* b = a;   However, in pure C, the corrected version (using const char * const *) still gives a warning, and I don't understand why. Is there a way to get around this without using a cast?  To clarify: 1) Why does this generate a warning in C?  It should be entirely const-safe, and the C++ compiler seems to recognize it as such. 2) What is the correct way to go about accepting this char** as a parameter while saying (and having the compiler enforce) that I will not be modifying the characters it points to? For example, if I wanted to write a function:  void f(const char* const* in) {   // Only reads the data from in, does not write to it }   And I wanted to invoke it on a char**, what would be the correct type for the parameter?