I'm new in general relativity and I readed these two definitions of stress–energy tensor.  In this wikipedia  we have:  The stress–energy tensor is defined as the tensor $T_{αβ}$ of order two that gives the flux of the $α$th component of the momentum vector across a surface with constant $x^β$ coordinate.   In the same page in &quot;Hilbert stress–energy tensor&quot; paragraph we have:  $${\displaystyle T_{\mu \nu }={\frac {-2}{\sqrt {-g}}}{\frac {\delta ({\mathcal {L}}_{\mathrm {matter} }{\sqrt {-g}})}{\delta g^{\mu \nu }}}=-2{\frac {\delta {\mathcal {L}}_{\mathrm {matter} }}{\delta g^{\mu \nu }}}+g_{\mu \nu }{\mathcal {L}}_{\mathrm {matter} }.}$$    Is the first definition equals to the second? If it is so, I would like to see a proof. If it isn't so, why two different stress-energy tensors?
What is the correspondence between the conserved canonical energy-momentum tensor, which is $$ T^{\mu\nu}_{can} := \sum_{i=1}^N\frac{\delta\mathcal{L}_{Matter}}{\delta(\partial_\mu f_i)}\partial^\nu f_i - \eta^{\mu\nu}\mathcal{L}$$ (the four conserved Noether currents corresponding to four possible spacetime translations)  where $\{f_i\}_{i=1}^N$ are the $N$ matter fields in the theory, and we assume $f_i\mapsto\alpha^\nu\partial_\nu f_i$ for translations,  and stress-energy tensor from the Einstein-Hilbert action, which is: $$ T_{\mu\nu}\equiv-\frac{2}{\sqrt{-g}}\frac{\delta\mathcal{L}_{Matter}}{\delta g^{\mu\nu}} $$   In particular, how do you get that the two are equal (are they?) for Minkowski space, for which there is no variation in the metric?
Difference between "@id/" and "@+id/" in Android Should it be obvious that independent quantum states are composed by taking the tensor product? I have run into an issue with WPF and Commands that are bound to a Button inside the DataTemplate of an ItemsControl. The scenario is quite straight forward. The ItemsControl is bound to a list of objects, and I want to be able to remove each object in the list by clicking a Button. The Button executes a Command, and the Command takes care of the deletion. The CommandParameter is bound to the Object I want to delete. That way I know what the user clicked. A user should only be able to delete their "own" objects - so I need to do some checks in the "CanExecute" call of the Command to verify that the user has the right permissions.  The problem is that the parameter passed to CanExecute is NULL the first time it's called - so I can't run the logic to enable/disable the command. However, if I make it allways enabled, and then click the button to execute the command, the CommandParameter is passed in correctly. So that means that the binding against the CommandParameter is working.  The XAML for the ItemsControl and the DataTemplate looks like this:  &lt;ItemsControl      x:Name="commentsList"     ItemsSource="{Binding Path=SharedDataItemPM.Comments}"     Width="Auto" Height="Auto"&gt;     &lt;ItemsControl.ItemTemplate&gt;         &lt;DataTemplate&gt;             &lt;StackPanel Orientation="Horizontal"&gt;                 &lt;Button                                                  Content="Delete"                     FontSize="10"                     Command="{Binding Path=DataContext.DeleteCommentCommand, ElementName=commentsList}"                      CommandParameter="{Binding}" /&gt;             &lt;/StackPanel&gt;                                 &lt;/DataTemplate&gt;     &lt;/ItemsControl.ItemTemplate&gt; &lt;/ItemsControl&gt;   So as you can see I have a list of Comments objects. I want the CommandParameter of the DeleteCommentCommand to be bound to the Command object.  So I guess my question is: have anyone experienced this problem before? CanExecute gets called on my Command, but the parameter is always NULL the first time - why is that?  Update: I was able to narrow the problem down a little. I added an empty Debug ValueConverter so that I could output a message when the CommandParameter is data bound. Turns out the problem is that the CanExecute method is executed before the CommandParameter is bound to the button. I have tried to set the CommandParameter before the Command (like suggested) - but it still doesn't work. Any tips on how to control it.  Update2: Is there any way to detect when the binding is "done", so that I can force re-evaluation of the command? Also - is it a problem that I have multiple Buttons (one for each item in the ItemsControl) that bind to the same instance of a Command-object?  Update3: I have uploaded a reproduction of the bug to my SkyDrive: When is it best to write "can't" versus writing "cannot"? Are they interchangeable in every situation? How should the "and/or" text of a card be interpreted? How should the "and/or" text of a card be interpreted? For example on a card like  the text reads:     Nahiri's Wrath deals damage equal to the total converted mana cost of the discarded cards to each of up to X target creatures and/or planeswalkers.   For the remainder of this question, let's fix X at 2 to keep things simple.  Should the "and/or" be interpreted such that the effect is applied to a combination of targets the player chooses. That is to say for Nahiri's Wrath the player could perform one of the following options:   Nahiri's Wrath deals damage to each of two target creatures. Nahiri's Wrath deals damage to each of two target planeswalkers. Nahiri's Wrath deals damage to each of one target creature and one target planeswalker.   Or should the card's effect be expanded and applied to both sides of the "and/or". With this interpretation the player would have to the following two options when playing Nahiri's Wrath:   Nahiri's Wrath deals damage to each of X target creatures and Nahiri's Wrath deals damage to each of X target planeswalkers Nahiri's Wrath deals damage to each of X target creatures or Nahiri's Wrath deals damage to each of X target planeswalkers   The confusion stems from  (which was formerly formerly worded using the same phrasing) where some commenters have said things like:     So this lets you do a total of 12 damage? 3 each to 2 target creatures AND 3 each to 2 target players, one of which could be a planeswalker? That's how the "and/or" works, right? You can choose. Otherwise it would just be "or"... Finding Zero Divisors and Units of Rings $\mathbb{Z}_n \times \mathbb{Z}_m$ How do I exactly find the zero divisors and units of a ring in the form of $\mathbb{Z}_n \times \mathbb{Z}_m$? For instance, how does one calculate zero divisors and units of $\mathbb{Z}_6 \times \mathbb{Z}_2$? I understand that a zero divisor is a non-zero element of $R$ such that $rs = 0$ for some other non-zero element $s$ in $R$. But I don't really quite understand how to apply that to a ring of the form $\mathbb{Z}_n \times \mathbb{Z}_m$. Also, the units of $\mathbb{Z}_6 \times \mathbb{Z}_2$ would be elements that send some element $s$ in $\mathbb{Z}_n \times \mathbb{Z}_m$ to the multiplicative identity, right? (which would be 1)? How do I apply these concepts to "product" rings? Thank you. override parent theme configuration in child functions.php Does existence of $\gcd$ implies PID? Cleaning unwanted overlapping duplicate meshes I have a model with hundreds of mesh objects. Unfortunately I clicked shift+D to duplicate many and did not notice. Later after working a while, I was rendering, and noticed there are double meshes overlapping each other.   How can I find all duplicate meshes and delete them. I could do it manually,  just clicking,  but it would take a long time and if I miss something i will not notice.   Is there any option,  or can anybody suggest to me,  how can I find all duplicate mesh and delete them.  Model with all double (duplicate) mesh  Final Result Is there a word that contains all the vowels? "Jealousy" contains most of the vowels but lacks 'i'. Is there a word in the English language that contains every vowel (and preferably 'y')? How to get correct scale values? The scale of my map is wrong, no matter what coordinate system I use in my project. The map and all objects show the correct coordinates but the scale of the map shows nonsense and the measurement tool gives wrong dimension.   The map should be like 1:10000 but qgis shows 1:1. Anyone an idea? Proving the summation formula using induction: $\sum_{k=1}^n \frac{1}{k(k+1)} = 1-\frac{1}{n+1}$ I am trying to prove the summation formula using induction:  $$\sum_{k=1}^n \frac{1}{k(k+1)} = 1-\frac{1}{n+1}$$  So far I have...  Base case:   Let n=1 and test   $\frac{1}{k(k+1)} = 1-\frac{1}{n+1}$  $\frac{1}{1(1+1)} = 1-\frac{1}{1+1}$    $\frac{1}{2} = \frac{1}{2}$   True for n=1   Induction Hypothesis:   Assume the statement is true for the n-th case   $\sum_{k=1}^n  \frac{1}{k(k+1)} = 1-\frac{1}{n+1}$  Inductive Step:   Prove, using the Inductive Hypothesis as a premise, that   $$\sum_{k=1}^{n+1}  \frac{1}{k(k+1)} = \sum_{k=1}^{n}  \frac{1}{k(k+1)} + \frac{1}{(n+1)(n+2)} = 1-\frac1{n+1} + \frac{1}{(n+1)(n+2)} = \frac{(n+1)(n+2)}{(n+1)(n+2)}+\frac{-2-n}{(n+1)(n+2)}+\frac{1}{(n+1)(n+2)} = \frac{(n+1)(n+2)-2-n+1)}{(n+1)(n+2)} = \frac{(n+1)(n+2)-n-1}{(n+1)(n+2)} = \frac{n^2+2n+1}{(n+1)(n+2)} = \frac{(n+1)(n+1)}{(n+1)(n+2)} = \frac{n+1}{n+2}$$  To prove $$ 1-\frac{1}{n+2} = \frac{n+1}{n+2} $$ Multiply both sides by $n+2$ to get an equivalent expression. $$ (1-\frac{1}{n+2}) * (n+2) = (\frac{n+1}{n+2}) * (n+2)  $$ $$ n+1=n+2−1 $$  Does this all make sense? How can this be improved upon? CDN - Content Delivery Networks. How do they work and why would I want to use one? What exactly is a Content Delivery Network (CDN), how does it work, and why would I want to use one for my web site?  Which are the well-known CDNs out there? 'This post has been deleted' appears above the flag bar What is the need of acceleration? As we can usually predict the various forces that a body might be undergoing based on its position and its velocity.Hence what is the need of acceleration? This question is essentially the same as one of my , except the only difference is that I am using "only" to change the text at the same location (i.e., ). In other words, I am destroying my earlier text as I go, and not adding new ones underneath the previous ones.   Since the text for the first "only" is shorter than the second "only", therefore the image will shift location. I would like for the image to remain at its location.   Here is an example     it may not be obvious but the second image is higher up than the first.  The code is here, can someone find a solution?  \documentclass{beamer}  \usepackage{graphicx}  \title[Title]{Presentation} \author{Sandro Botticelli} \institute{Italy} \date{1484}  \begin{document}   \begin{frame} \begin{figure} \includegraphics[scale = 0.8]{Venus}     \caption{Nascita di Venere} \end{figure}  \only&lt;1&gt;{In the centre the newly-born goddess Venus stands nude in a giant scallop shell. Its size is purely imaginary, and is also found in classical depictions of the subject. }    \only&lt;2&gt;{Alternative identifications for the two secondary female figures involve those also found in the Primavera; the nymph held by Zephyr may be Chloris, a flower nymph he married in some versions of her story, and the figure on land may be Flora. Flora is generally the Roman equivalent of the Greek Chloris; in the Primavera Chloris is transformed into the figure of Flora next to her, following Ovid's Fasti, but it is hard to see that such a transformation is envisaged here.} \end{frame}   \end{document} Why can't this be done with Master Theorem Apparently recurrences like this cannot be solved with the Master Theorem:  $T(n) = 2T\left(\frac{n}{2}\right) + \frac{n}{\log(n)}$  Because $n^{\log_b(a)} = n^1$ is not a polynomial multiple of $f(n) = \frac{n}{\log(n)}$ since $\frac{n}{\frac{n}{\log(n)}} = \log(n)$, which is less than $n^\epsilon$ for any positive $\epsilon$.  But when is this really even an issue?   For example why wouldn't the time complexity be $n \log n$ using case 2 of the Master Theorem? Unrolling the recursion:  $$T(n) = n\sum_{k=1}^{\log_2(n)} \frac{1}{\log_2(2^k)}$$  $$T(n) = n\sum_{k=1}^{\log_2(n)} \frac{1}{k}$$  Doesn't this suggest $\Theta(n \log n)$ even though it supposedly cannot be done with Master Theorem? Do you need to submit an itinerary to get a Russian visa? And do you have to stick to it? Some publications capitalize He, Him, etc., when referring to a god.    What is this practice called? 'Proper noun' is rather generic. Way to list "Contact Us" email address on web site, yet reduce likelihood of spam? What's a good way to list a "Contact Us" email address on a web site, while reducing the likelihood it will get spammed?  Is putting the email address in an image the best technique, or are there others?