What does the spectrum of the adjacency matrix of a graph tell you?
Motivation for spectral graph theory.
Why can't I use Stack Exchange if I'm under 13 years old, or if I'm under 16 years old and from the EU? I was just reading the , and noticed something:  You must be at least 13 years old to access or use the Network or Services, including without limitation to complete a Stack Overflow account registration. By accessing or using the Services or the Network in any manner, you represent and warrant that you are at least 13 years of age. If you are under 13 years old, you may not, under any circumstances or for any reason, access or use the Services or Network in any manner, and may not provide any personal information to or on the Services or Network (including, for example, a name, address, telephone number or email address). If you are located within the European Union, you must be at least 16 years old to access or use the Network or Services, including without limitation to complete a Stack Overflow Account Registration.  I signed up for Stack Overflow when I was around 11 or 12 and I did provide my email address. Are you saying that my use of Stack Overflow was not legal? I'm 16 now (so I'm in the clear), but that just seems a little harsh. Is that possibly related to the age limit for accepting a binding contract/agreement (although I thought that was 18 in the U.S.)? Is there a way for users under the age of 13, or for users from the European Union who are under the age of 16, to use the site legally? Is there a catch-all place on the Stack Exchange network where one can post any question that does not obviously belong to the Stack Exchange sites? Is there a catch-all place somewhere on the Stack Exchange sites where one can post a (any) question that does not obviously belong to any of the Stack Exchange sites?  Sometimes I have questions but I don't want to ask them on other sites (no need for names). I prefer to post it on the Stack Exchange network for various reasons.  If there isn't, are there plans for one? I imagine that if such a site exists, questions on that site can also be moved to other more specific sites when they exists, and it's not to be used to post questions which obviously belong to a specific Stack Exchange site. Show that $\partial_\nu T^{\mu\nu} = - j_\nu F^{\mu\nu}$ In a theoretical physics homework problem, I have to show the following: $$\partial_\nu T^{\mu\nu} = - j_\nu F^{\mu\nu}$$  Where $T$ is the Energy-Momentum-Tensor, $j$ the generalized current and $F$ the Field-Tensor. We use the $g$ for the metric tensor, I think in English the $\eta$ is more common.  I know the following relationships:   Current and magnetic potential with Lorenz gauge condition: $$\mathop\Box A^\mu = \mu_0 j^\mu$$ Energy-Momentum-Tensor: $$T^{\mu\nu} = \frac1{\mu_0} g^{\mu\alpha} F_{\alpha\beta} F^{\beta\nu} + \frac1{4\mu_0} g^{\mu\nu} F_{\kappa\lambda} F^{\kappa\lambda}$$ Field-Tensor: $$F^{\mu\nu} = 2 \partial^{[\mu} A^{\nu]} = \partial^{\mu} A^{\nu} - \partial^{\nu} A^{\mu}$$ d'Alembert operator: $$\mathop\Box = \partial_\mu \partial^\mu$$ Bianchi identity: $$\partial^{[\mu} F^{\nu\alpha]} = 0$$   So far I have set all the definitions into the formula I have to show, but I only end up a lot of terms from antisymmetrisation and product rule. I also drew all what I have in , but I still cannot see how to tackle this problem.  Could somebody please give me a hint into the right direction? I wrote a DLL in .NET and I want to access it in VBScript. I don't want to add it to the assembly directory.   Is there a way to point too the DLL and create an instance of it? If a product of relatively prime integers is an $n$th power, then each is an $n$th power A sine integral $\int_0^{\infty} \left(\frac{\sin x }{x }\right)^n\,\mathrm{d}x$ The following question comes from   post $$\int_0^{\infty} \left(\frac{\sin x }{x }\right)^n\,\mathrm{d}x$$ but now I'd be curious to know how to deal with it by methods of complex analysis. Some suggestions, hints? Thanks!!!  Sis. Can you stay in Turkey for over 90 days within the 180 day visa period but split over different visits? The Turkish e-visa is valid for a period of 180 days and allows you to stay for a maximum of 90 days. Am I allowed to stay for say 50 days, then another 50 days, over two different visits within the 180 day period?  I'm looking at the e-visa website  and it doesn't seem to be too clear on this. replace often used Tex-Literals ($ and $$) for math regions into \( or \) and \[ or \] Is there an editor or IDE (or a script) for substituting the TeX-Commands $ and $$ for opening and closing math regions into the corresponding LaTeX-Commands \(,\) and \[,\]? I'm sure there is a tool - and I'm searching for. I think, this will result in better readable code. A simple search and replace wont do that - but with regular expressions, that should not be problem. I simply do not want to invent the wheel a second time. Ubuntu 18 - how to ungroup apps in dock? I want to make Ubuntu dock like Windows taskbar  Ubuntu:    Windows:    (as you see Windows has three Explorer icons and Ubuntu has only one Files icon  Is it possible to uncombine/ungroup apps in Ubuntu? What is the problem that gets worse after you try to solve it? Example sentence - This problem is a _____ which gets complicated every time you try to solve it.   Is there such a word that represents a problem which will become worse if/when one tries to solve it?  Note - After seeing the comments and answers I'd like to add that this is not a can of worms or Pandora's box because it doesn't create a new problem but just worsens.   Example: Magic leaves protecting a fruit by enclosing it. Every time a leaf is touched, all the leaves close together further, that is more tight than before. Can "mustn't" be used for conclusions? I heard this sentence in an American film a while ago as I was watching it on DVD (the part after but is verbatim):  "I'm doing my best but I mustn't be doing it right."  This is something I occasionally hear in American films: phrases like "he mustn't have done it" or "she mustn't be studying now", where a logical conclusion is expressed. So far I've thought that the normal thing to say is "he can't have done it" or "she can't be studying now".  My question is: Can mustn't be used to express a logical conclusion when the speaker is certain that something didn't happen or isn't happening, at least in informal speech? Is this an American usage? (I've never heard this usage in British English, but this doesn't mean it doesn't exist.) Is there a change going on in the usage of the particular modal verb?  Note: All the references I've checked don't even mention this use of mustn't. Google books aren't of help either.   EDIT: I should clarify that I'm asking this question because if I wanted to express that I'm certain I'm not doing something right (as in the sentence quoted from the film) I'd say "I'm doing my best but I can't be doing it right". I would think that the use of mustn't/must not wouldn't be standard usage (although the meaning is perfectly clear to me; I never mistook it for an injuction). Can the notion of vector space or algebra over a field be meaningfully extended to fractional dimensions, so that for example $\mathbb{R}^{-2/3}$ makes sense? Has this been explored somewhere?  I know that super vector spaces can be thought of as one way of generalizing vector spaces to negative integer dimensions. Is there a similar concept for dimensions that are rational numbers? I'm not talking about Hausdorff dimension, because it doesn't allow for negative rationals, and I'm rather looking for extensions from a more algebraic point of view (dimension as the trace of the identity map), without recurring to a given metric. Do you recommend using semicolons after every statement in JavaScript? In many situations, JavaScript parsers will insert semicolons for you if you leave them out. My question is, do you leave them out?  If you're unfamiliar with the rules, there's a description of semicolon insertion on the . Here's the key point:     If the first through the nth tokens of a JavaScript program form are grammatically valid but the first through the n+1st tokens are not and there is a line break between the nth tokens and the n+1st tokens, then the parser tries to parse the program again after inserting a virtual semicolon token between the nth and the n+1st tokens.   That description may be incomplete, because it doesn't explain @Dreas's example. Anybody have a link to the complete rules, or see why the example gets a semicolon? (I tried it in JScript.NET.)   is related, but only talks about a specific scenario. Meaning of 'const' last in a function declaration of a class? How precise is the frequency of the AC electricity network? If I make a digital clock which first detects the AC frequency roughly (whether it is 50, 60, 100Hz, etc), then uses it as its clock pulse source, how precise would it be? Would it work world wide precisely?  For instance, in USA, what is the mean and standard deviation of the 60Hz AC frequency? Virtualbox Server/Client topology I have a layout similar to this:  &lt;div id="..."&gt;&lt;img src="..."&gt;&lt;/div&gt;   and would like to use a jQuery selector to select the child img inside the div on click.  To get the div, I've got this selector:  $(this)   How can I get the child img using a selector? Is it possible to detect 32 bit vs 64 bit in a bash script? I am writing a bash script to deal with some installations in an automated way... I have the possibility of getting one such program in 32 or 64 bit binary... is it possible to detect the machine architecture from bash so I can select the correct binary?  This will be for Ubuntu machines. What's the most efficient way to select the last n rows in a table without changing the table's structure? What's the most efficient way to select the last n number of rows in a table using mySQL? The table contains millions of rows, and at any given time I don't know how large the table is (it is constantly growing). The table does have a column that is automatically incremented and used as a unique identifier for each row. Taylor Expansion $\log(\frac{1+z}{1-z})$ Taylor Expansion of $\log(\frac{1+z}{1-z})$ around $z=0$  But $\log(1+z)=\sum_{n=1}^{\infty}(-1)^{n+1}\frac{z^n}{n}$  How can I continue from here?