I am trying to understand the Georgi chapter of tensor methods in $SU(3)$ representations, and I don't know how to resolve the tensor product of 2 matrices in a 2 heavy quark + 2 light antiquark system. Namely:  Let the tetraquark system be:           $QQ\bar q\bar{q}$  So, those $Q$ heavy quarks interact and can be understood in the $3\bigotimes 3$ representations for $SU(3)$, and $\bar q\bar q$ can be understood as the $\bar 3\bigotimes\bar 3=3\bigoplus\bar 6$ representations for $SU(3)$.  The interaction diagram for the $Q$ heavy quarks is shown in the following scheme, which is an analogy to the Feynman Diagram where a gluon is understood to be exchanged between upper and lower arrows:  $i'\xrightarrow{(T_{a})^{i'}_{i}}i ,  {}^iQ$  $j'\xrightarrow{(T_{a})^{j'}_{j}}j ,  {}^jQ$  So, as usuall we consider the elements of $3$ representation as $u^i$, and therefore the elements of $\bar 3$ representation as $v_{j}$.  I must understand how does the following expression transform:  $(T_{a})^{i'}_{i}(T_{a})^{j'}_{j}\cdot(1/2)\cdot (w^iv^j+w^jv^i)=\Xi\cdot(1/2)\cdot(w^{i'}v^{j'}+w^{j'}v^{i'})$  In other words, how can one give the correct value of $\Xi$?  Note1: $T_a$ is understood to be the $a-ith$ generator of the associated Lie Algebra, which come from the definition of the Gell-Mann Matrices.  $(T_{a})^{i}_{j}\propto(\lambda)_{ij}$, in matrix notation.  Note2: I understand the Young Tableaux and they are not intended to be used here, so please don't try to explain this situation through the tables.   Also requesting information about how to understand the tensor products in these cases, since I have been checking many sources but the definitions seem not clear enough.
I am trying to understand the Georgi chapter of tensor methods in $SU(3)$ representations, and I don't know how to resolve the tensor product of 2 matrices in a 2 heavy quark + 2 light antiquark system. Namely:  Let the tetraquark system be:           $QQ\bar q\bar{q}$  So, those $Q$ heavy quarks interact and can be understood in the $3\bigotimes 3$ representations for $SU(3)$, and $\bar q\bar q$ can be understood as the $\bar 3\bigotimes\bar 3=3\bigoplus\bar 6$ representations for $SU(3)$.  The interaction diagram for the $Q$ heavy quarks is shown in the following scheme, which is an analogy to the Feynman Diagram where a gluon is understood to be exchanged between upper and lower arrows:  $i'\xrightarrow{(T_{a})^{i'}_{i}}i ,  {}^iQ$  $j'\xrightarrow{(T_{a})^{j'}_{j}}j ,  {}^jQ$  So, as usuall we consider the elements of $3$ representation as $u^i$, and therefore the elements of $\bar 3$ representation as $v_{j}$.  I must understand how does the following expression transform:  $(T_{a})^{i'}_{i}(T_{a})^{j'}_{j}\cdot(1/2)\cdot (w^iv^j+w^jv^i)=\Xi\cdot(1/2)\cdot(w^{i'}v^{j'}+w^{j'}v^{i'})$  In other words, how can one give the correct value of $\Xi$?  Note1: $T_a$ is understood to be the $a-ith$ generator of the associated Lie Algebra, which come from the definition of the Gell-Mann Matrices.  $(T_{a})^{i}_{j}\propto(\lambda)_{ij}$, in matrix notation.  Note2: I understand the Young Tableaux and they are not intended to be used here, so please don't try to explain this situation through the tables.   Note3: I assume this is a purely solvable mathematical problem and doesn't need a deep insight into the physical concepts...  Also requesting information about how to understand the tensor products in these cases, since I have been checking many sources but the definitions seem not clear enough.
SF Story about human adapting to alien environment This is a story that was read on BBC radio about thirty years ago, and this is about as right as I can remember it: The human pilot of a spacecraft is doing some reconnaissance on an alien planet. He crashes but survives. For some reason, no one will know where to look for him. He sees something in the distance that looks like a building of some sort. When he gets there, it seems to be a home. Very much like a human home. There's furniture, but it's strange and uncomfortable . There's food, but it's inedible. There's a faucet but what comes out of it seems more like acid. Everything looks as though it should be right, but it's not. He leaves the house, wanders and after a few days is desperate for water. But there isn't any water anywhere. He's close to death, crawling on the ground and then something happens. There are cracks in the soil and there appears to be water bubbling up from perhaps some underground stream. The water revives him. He goes back to the house and tries the food again. It's delicious and he eats enough to gain back his strength. Then he decides to try the water again. It's pure and wonderful. He takes a shower and the last line of the story is how refreshing the water is on his skin and something about him lifting his tail. List creation/manipulation Clipping a figure to content How to list only JPEG files from root below using the command line? So I came across this exercise: Show that if $Y$ is path-connected then the set of homotopy classes $[I,Y]$ of maps of $I=[0,1]$ into Y has a single point.   But I am confused here. If $Y=S^1$ then not all loops are homotopic! I mean, isn't true that $\pi_1(Y)\subset [I,Y]$? Or maybe I don't understand the set $[I,Y]$ well! Biblatex: Don't show n.d. when no year is given Semigroup analogue to the classification of finite simple groups? Is there a semigroup analogue to the classification of finite simple groups?  If so what are some of the major results?  --Edit, reference links--- Why does an error appear every time I try to open the Ubuntu Software Center? There is a glitch on the Ubuntu Software Center and whenever I open it an error appears and it keeps loading and never opens.  Why does this happen?  I have installed Ubuntu 13.04 on a disk and partitioned it.  Please help me and ask for excess information if you need it.  If you know of any duplicates please show me them!!  I get the following error in a terminal  SystemError: E:Type '&lt;!DOCTYPE' is not known on line 1 in source list /etc/apt/sources.list.d/medibuntu.list   The /etc/apt/sources.list.d/medibuntu.list file contains a HTML document. I recently read the .  This book had the idea of the time you live as something that can be used to pay for things. When you run out of "money" you die.  I was wondering is this the original source for this idea? Or does anyone know of an earlier book with the same idea? Is it wrong to place the  tag after the  tag? Is trace invariant under cyclic permutation with rectangular matrices? I'm working with trace of matrices. Trace is defined for square matrix and there are some useful rule, i.e. $\text{tr}(AB) = \text{tr}(BA)$, with $A$ and $B$ square, and more in general trace is invariant under cyclic permutation. I was wondering if the formula $\text{tr}(AB) = \text{tr}(BA)$ holds even if $A$ and $B$ are rectangular, namely $A$ is $n$-by-$m$ and $B$ is $m$-by-$n$. I figured out that if one completes the involved matrices to be square by adding zero entries in the right places, then the formula still works... but I want to be sure about this! If I have a shapefile or geodatabase featureclass that has fields that I want to permanently reorder, is there a tool, script, or utility that will help me quickly accomplish this task? Generally I know you have to create a new field, then populate it with the old values, then delete the old field.  I am hoping there is something already created out there that will help with this. Assuming you don't have FME or another ETL tool available, what is the next best suggestion? This is NOT a view level change (ie- drag/drop the fields in order), but rather write out to a new shapefile or featureclass. Why not use a WAMP stack? This is a  about  the use of a *AMPP's stack.    I recently had a talk with some experienced people and they suggested to me not to use a WAMP stack, and instead install apache, mysql and php separately.  I don't understand why they have suggested this, though, so can anyone tell me?  Is there a particular disadvantage of WAMP, or a particular advantage to installing all of them separately?  Since a WAMP stack itself is composed of apache, mysql and php, then what's the difference between using the WAMP stack and installing them all separately? What's the difference between  and ,  and ? Time dependent Schrödinger equation with time independent potential and separation of variables suppose we have a potential that's independent of time $V(x,t) = V(x)$ so in Schrödinger equation we get: $$i\hbar \frac{\partial \Psi (x,t)}{\partial t}=-\frac{\hbar^2}{2m}\frac{\partial^2 \Psi (x,t)}{\partial x^2}+V(x)\Psi(x,t)$$ since the LHS involves a variation of $\Psi$ with $x$ and the LHS involves a variation of $\Psi$ with $t$ can we say that a basis for the solutions will be with the form $\Psi(x,t)=\psi(x)T(t)$? Non-pejorative synonym of "notoriety" I'm trying to say:       He probably gained some __________ [good notoriety] from this picture.   I was thinking publicity, but that connotes some kind of negative to me as well (like the stuff you see in gossip magazines at the checkout line).  I want a word as powerfully positive as notoriety is powerfully negative. When defining a method on a class in Python, it looks something like this:  class MyClass(object):     def __init__(self, x, y):         self.x = x         self.y = y   But in some other languages, such as C#, you have a reference to the object that the method is bound to with the "this" keyword without declaring it as an argument in the method prototype.    Was this an intentional language design decision in Python or are there some implementation details that require the passing of "self" as an argument? Existence of a Riemannian metric inducing a given distance. Let $M$ be a smooth, finite-dimensional manifold. Suppose $M$ is also a metric space, with a given distance function $d: M \times M \rightarrow \mathbb{R}_{+}$, which is compatible with the original (manifold) topology on $M$.  Question: is there a Riemannian metric $g$ on $M$ such that the distance $$d_g(p, q) = \inf_{\gamma \in \Omega(p, q)} L_g(\gamma)$$ coincides with $d$?  I believe that this setting is very standard, but for the sake of completeness: $L_g$ denotes the Riemannian length of the curve $\gamma$, and $\Omega(p, q)$ the set of all piecewise smooth curves $\gamma : [a, b] \rightarrow M$ s.t. $\gamma(a) = p$ and $\gamma(b) = q$. Thanks in advance. Many other solutions of the Cauchy's Functional Equation By reading the  on the Wiki,  it is said that      On the other hand, if no further conditions are imposed on f, then (assuming the axiom of choice) there are infinitely many other functions that satisfy the equation. This was proved in 1905 by Georg Hamel using Hamel bases. Such functions are sometimes called Hamel functions.   Could anyone give a more explicit explanation of these many other solutions?   Besides the trivial solution of the form $f(x)=C x$, where $C$ is a constant, and the solution above constructed by the Hamel Basis, are there any more solutions existing? Why is variance squared? The mean absolute deviation is:   $$\dfrac{\sum_{i=1}^{n}|x_i-\bar x|}{n}$$   The variance is: $$\dfrac{\sum_{i=1}^{n}(x_i-\bar x)^2}{n-1}$$   So the mean deviation and the variance are measuring the same thing, yet variance requires squaring the difference. Why? Squaring always gives a non-negative value, but the absolute value is also a non-negative value. Why isn't it $|x_i-\bar x|^2$, then? Squaring just enlarges, why do we need to do this?  A similar question is , but mine is a little different. Thanks.