Fusion of quarks release 8 times more energy than hydrogen fusion, so I was wondering if quark star exists and before quark degeneracy pressure kicks in wouldn't these tightly packed sea of quarks start fusing and eventually becoming a miniature neutron star?  I think in normal scenario due to the short range of strong force and quark/neutron cannot be found alone in nature compare to the condition of quark star where quarks should easily fused with each other and outshines almost everything in the night sky.
A quark star is a hypothetical type of compact exotic star composed of quark matter. These are ultra-dense phases of degenerate matter theorized to form inside particularly massive[citation needed] neutron stars. -Wikipedia   If you add enough mass to a neutron star it forms a black hole but how much mass is needed to form a quark star? When do neutrons and protons start to break down into a mush of quarks and gluons?
What does the "@" symbol do in SQL? I was browsing through the questions and noticed this:  SELECT prodid, issue FROM Sales  WHERE custid = @custid  AND datesold = SELECT MAX(datesold)               FROM Sales s               WHERE s.prodid = Sales.prodid                   AND s.issue = Sales.issue                   AND s.custid = @custid   I was wondering what the "@" does in front of custID?  Is it just a way of referencing the custID from the table being selected? Is the "the ... the ..." construction governed by some grammatical rule? Is "reserved" an adjective or verb in this example? I need an answer about this sentence please:     We had a reserved seat.   Reserved in this sentence is a verb. I read that in a morphology book.  My question is: how does this become a verb?  I thought it was an adjective. Is there a constraint that restricts my generic method to numeric types? Can anyone tell me if there is a way with generics to limit a generic type argument T to only:   Int16 Int32 Int64 UInt16 UInt32 UInt64   I'm aware of the where keyword, but can't find an interface for only these types,  Something like:  static bool IntegerFunction&lt;T&gt;(T value) where T : INumeric I have the following code:  if ($_POST['submit'] == "Next") {     foreach($_POST['info'] as $key =&gt; $value) {         echo $value;     } }   How do I get the foreach function to start from the 2nd key in the array? Output of getent group Absolute Value Symbols What is the "best LaTeX practices" for writing absolute value symbols?  Are there any packages which provide good methods?  Some options include |x| and \mid x \mid, but I'm not sure which is best... Multiplication in Permutation Groups Written in Cyclic Notation I didn't find any good explanation how to perform multiplication on permutation group written in cyclic notation. For example, if $$   a=(1\,3\,5\,2),\quad b=(2\,5\,6),\quad c=(1\,6\,3\,4), $$  then why does $ab=(1\,3\,5\,6)$ and $ac=(1\,6\,5\,2)(3\,4)$? Im trying to understand the solution about this, and all the other solutions are.. a bit weird for me and dont answer all my questions!  Reference :   Im using the answer there as reference, but my understanding is a bit different!     Find the error in the following proof that all horses are the same   color. CLAIM: In any set of h horses, all horses are the same color.      PROOF: By induction on h.      Basis: For h = 1. In any set containing just one horse, all horses   clearly are the same color. Induction step: For k > I assume that the   claim is true for h = k and prove that it is true for h = k + 1. Take   any set H of k + 1 horses. We show that all the horses in this set are   the same color. Remove one horse from this set to obtain the set H1   with just k horses. By the induction hypothesis, all the horses in H,   are the same color. Now replace the removed horse and remove a   different one to obtain the set H2 . By the same argument, all the   horses in H2 are the same color. Therefore all the horses in H must be   the same color, and the proof is complete.   Here's what i have come up with :  Suppose a set of 1 horse. $H_a = { horse_{1} }$  Obviously, all the horses in set $H_a$ are the same, since theres just 1 horse.  So using that as the Basis of the induction we can proceed and try to prove its true for $N$ horses.  -- I dont fully understand the part below   As an example : set $H_0$ :   $H_0 = { horse_{1}, horse_{2}, horse_{3}... horse_{n} }$  In my understanding, its because, I can make a subset  formed by 1 horse :  $K_1  = {horse_{1}}$ $K_2  = {horse_{2}}$ ...  I don't get it. I clearly know that this proof is a lie.  And for me, its because you cant claim theres a relation on a set with size $&gt;= 2$ , since :  $H_1 = { horse_{1}, horse_{2}}$  Theres nothing that says $horse_{1}$ equals $horse_{2}$. The basis was for one horse. But that alone is not a proof.  So what should I do ? Comaximal ideals in a commutative ring Let $R$ be a commutative ring and $I_1, \dots, I_n$ pairwise comaximal ideals in $R$, i.e., $I_i + I_j = R$ for $i \neq j$. Why are the ideals $I_1^{n_1}, ... , I_r^{n_r}$ (for any $n_1,...,n_r \in\mathbb N$) also comaximal? What exactly are DLL files, and how do they work? How exactly do DLL files work? There seems to be an awful lot of them, but I don't know what they are or how they work.  So, what's the deal with them? When I type dpkg -l | grep xserver-xorg, I get list of installed packages and their versions:  ii  xserver-xorg               1:7.7+3~deb7u1 ii  xserver-xorg-core          2:1.12.4-6 ii  xserver-xorg-input-evdev   1:2.7.0-1+b1 ii  xserver-xorg-input-kbd     1:1.6.1-1+b1 ii  xserver-xorg-input-mouse   1:1.7.2-3 ii  xserver-xorg-video-radeon  1:6.14.4-8   I am wondering what the number  infront of the colon means, ie the number 2 in 2:1.12.4-6 Proof that $ p $ | ${ p^n \choose k } $ for any prime $p$ and $ k < p^n$ I know how to prove the fact that $ p$ | ${ p \choose k } $ (when writing it as a fraction, $p$ cannot be divided by any of the $1\times2\times...\times k$ or $1\times2\times...\times(p-k)$ because $p$ is prime).  When I try to apply the same rationale for $ p$ | ${ p^n \choose k } $ I get stumped because $p^n$ is in fact divisible by one of the $k! = 1\times2\times...\times k$, where $0 &lt; k &lt; p^n$.  If we take the example of $2^3$ and $k = 7$, we can easily see that $k! = 1 \times 2 \times ... \times 6 \times 7$, and $2$ clearly divides $2^3$.  How else can I approach this? How could it be that the entropy of gas is not infinite?  If we use the formula $S=k\ln(\Omega)$ we get infinity because there are an infinite number of possible situations (because there are infinite possibilities of position and momentum for each molecule). How to run find -exec? When we measure the speed of a moving element we do it with the help of a reference frame. Now if we need to measure the speed of time, is it possible? Does time actually have a speed? errors upgrading from 14.04 to 16.04 about Unknown Multi-Arch type for compiz, libkf5akonadisearch-bin packages I'm trying to upgrade my 14.04 machine to 16.04 using do-release-upgrade. After downloading the package lists for wily, I see the following errors:  Unknown Multi-Arch type 'no' for package 'compiz-core' Unknown Multi-Arch type 'no' for package 'compiz-gnome' Ignoring Provides line with DepCompareOp for package python-cffi-backend-api-max Ignoring Provides line with DepCompareOp for package python-cffi-backend-api-min Ignoring Provides line with DepCompareOp for package python3-cffi-backend-api-max Ignoring Provides line with DepCompareOp for package python3-cffi-backend-api-min Unknown Multi-Arch type 'no' for package 'libkf5akonadisearch-bin' Ignoring Provides line with DepCompareOp for package php-psr-http-message-implementation Ignoring Provides line with DepCompareOp for package php-psr-log-implementation Ignoring Provides line with DepCompareOp for package php-math-biginteger Unknown Multi-Arch type 'no' for package 'compiz-core' Unknown Multi-Arch type 'no' for package 'compiz-gnome' Ignoring Provides line with DepCompareOp for package python-cffi-backend-api-max Ignoring Provides line with DepCompareOp for package python-cffi-backend-api-min Ignoring Provides line with DepCompareOp for package python3-cffi-backend-api-max Ignoring Provides line with DepCompareOp for package python3-cffi-backend-api-min Unknown Multi-Arch type 'no' for package 'libkf5akonadisearch-bin' Unknown Multi-Arch type 'no' for package 'compiz-core' Unknown Multi-Arch type 'no' for package 'compiz-gnome' Unknown Multi-Arch type 'no' for package 'compiz-core' Unknown Multi-Arch type 'no' for package 'compiz-gnome' You may want to run apt-get update to correct these problems   It then proceeds to abort the installation. The suggested run of apt-get update doesn't seem to do anything. Googling for the above error messages yielded others having similar problems when upgrading to other, previous releases, although I've not come across any apparent fixes. It's suggested that an apt upgrade could fix the problem, but I don't see a way to easily do that (it's up to date with the latest trusty package).  What should I do in order to upgrade directly to 16.04? Applications of complex numbers to solve non-complex problems Recently I asked a question regarding the diophantine equation $x^2+y^2=z^n$ for $x, y, z, n \in \mathbb{N}$, which to my surprise was answered with the help complex numbers. I find it fascinating that for a question which only concerns integers, and whose answers can only be integers, such an elegant solution comes from the seemingly unrelated complex numbers - looking only at the question and solution one would never suspect that complex numbers were lurking behind the curtain!  Can anyone give some more examples where a problem which seems to deal entirely with real numbers can be solved using complex numbers behind the scenes? One other example which springs to mind for me is solving a homogeneous second order differential equation whose coefficients form a quadratic with complex roots, which in some cases gives real solutions for real coefficients but requires complex arithmetic to calculate.  (If anyone is interested, the original question I asked can be found here: )  EDIT:  I just wanted to thank everyone for all the great answers! I'm working my way through all of them, although some are beyond me for now! I have an alias that I would like to use both as a regular user and as root, via sudo. Specifically, it is this:  alias rm=trash   This works fine as a normal user, and it works fine when I use sudo -i to get a root shell prompt, but if I use sudo rm, the alias does not apply. So where do I need to put my alias so that it works in one-off sudo commands? $a+1,a-1$ invertible for nilpotent element Given a ring $R$ (with unity), prove that if $a \in R$ is nilpotent, then $a+1,a-1$ are both invertible.   Suppose $a^n=0$. Then $1=1-a^n=(1-a)(1+a+\ldots+a^{n-1})$, so $1-a$ is invertible.  If $n$ is odd we can use $1+a^n=(1+a)(1-a+\ldots+a^{n-1})$.  But what if $n$ is even?