I want to write a C# method that can accept any number.  Something like:  public static T Sum(T a, T b) where T : number {  // (not real code)     return a + b; }   But I don't see a "number" base class in C#, as exists in most other languages I've used.  The numeric value types are IComparable, IFormattable, IConvertible, IComparable, and IEquatable, but nothing that seems to have any arithmetic capabilities.  They're all structs, with no apparent common superclass, apart from object.  (Forgive me if I'm screwing up the meaning here, since I'm not too familiar with C# structs and precisely all the ways they are like or unlike classes.)  Am I missing something, or is it not possible to write a method in C# that does "a + b" without declaring exactly what a and b are in the context of the "+"?
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 installed the VMware bundle on my Ubuntu 11.04 successfully but when I open it it gives me this window     and I don't know the path to this C headers. Embed data in a C++ program (complex measures) $d\nu=d\lambda +f\,dm \Rightarrow d|\nu|=d|\lambda| +|f|\,dm$ and $f\in L^1(\nu)\Rightarrow f\in L^1(|\nu|)$ Two simple exercises on complex measures I don't know how to solve, from Folland's Real Analysis. I find it difficult to manipulate the definitions in computations. For context, if $\nu$ is a complex measure on $(X,\mathcal{M})$ then $|\nu|$ is defined as $d|\nu|=|g|\,d\mu$ where positive measure $\mu$ and $g\in L^1(\mu)$ are such that $\nu \ll \mu$ and $\nu = g\,d\mu$ (and in the textbook it's shown that this definition does not depend on the choice of $\mu$).     1) Let $\nu$ be a reguar complex Borel measure on $\mathbb{R}^n$, $m$ denote   Lebesgue measure, and   let $d\nu = d\lambda + f\,dm$ be its Lebesgue-Radon-Nikodym   representation. Then ("it is easily verified")   $d|\nu|=d|\lambda|+|f|\,dm$.      2) If $f\in L^1(\nu)$ then $f\in L^1(|\nu|)$. I was able to prove the   reverse implication, but not this one.   The definition of $|\nu|$ in the case of real signed measures (as $|\nu|=\nu^+ + \nu^-$) makes sense to me but I can't see intuitively into the definion of $|\nu|$ for complex measures as given in the textbook. Do you have any advice on this?  Thank you! What is the difference between .profile and .bash_profile and why don't I have a .profile file on my system? So I'm pretty new to Linux and recently installed Fedora 19 on my netbook. I want to have a deeper understanding of Linux and the CLI so I'm now reading .  In exercise 3 the author gives the following commands:   ls -al cat .profile   I try to follow these instructions but to no avail. There is no .profile file in my user name directory as I can see from ls -al. From what I've learned the .bash_profile and .profile file are practically the same. The only difference I concluded from my research is that .bash_profile gets checked first.   What I don't understand is why are there multiple files for the same function in Linux, why is the Author using .profile and not .bash_profile (if I understand correctly .profile won't be read when the system finds .bash_profile first) and how comes that I don't have the .profile file on my system? I have an account on Stack Exchange but when I try to login to  I do not see the option Login with Stack Exchange.       Why is this option now not available? What is currently the best way to get a favicon to display in all browsers that currently support it?  Please include:   Which image formats are supported by which browsers. Which lines are needed in what places for the various browsers. Use of "though" versus "however" Consider the sentence      E-books are on the rise, but they haven't suppressed paper books though.    This usage seems to be quite common, but when I learned English  I was taught to use "however" where I now read "though". My questions on this use of "though" are:     Is this a new trend? Is it restricted to American English? Is "though"  considered more colloquial than "however" ?    And on a syntactic level: Do you put a comma before "though"? Difference between $:=$ and $=$ I am sorry if this is quite elementary question. But I always think, that why we use $:=$ at some places, instead of $=$. Is there any fundamental difference between these two? Before reading Terry Tao's blog (4 months ago), I had never seen a symbol like this (:=). Why aren't logarithms defined for negative $x$? Given a logarithm is true, if and only if, $y = \log_b{x}$ and $b^y = x$ (and $x$ and $b$ are positive, and $b$ is not equal to $1$), are true, why aren't logarithms defined for negative numbers?  Why can't $b$ be negative? Take $(-2)^3 = -8$ for example. Turning that into a logarithm, we get $3 = \log_{(-2)}{(-8)}$ which is an invalid equation as $b$ and $x$ are not positive! Why is this? What is the best prepaid SIM card for data in France? I'm going to travel to Paris in two weeks for 5 days. I'd like to buy a prepaid SIM card for my phone, no calls or SMS needed - only data is sufficient. I've looked through French mobile operators and found nothing really acceptable. For example, in Finland I bought SIM card for €5 with 3GB of data.   So, the question is - what is the best SIM card for me, assuming that 1GB is enough (considering the prices) and that I am actually will be able to use it (I've read that some operators turn on mobile data only after 5 days which is unacceptable for me considering that I'll be there for 5 days only)? Why is $(0, 0)$ not a minimum of $f(x, y) = (y-3x^2)(y-x^2)$? There is an exercise in my lists about those functions: $$f(x, y) = (y-3x^2)(y-x^2) = 3 x^4-4 x^2 y+y^2$$  $$g(t) = f(vt) = f(at, bt); a, b \in \mathbf{R}$$  It asks me to prove that $t = 0$ is a local minimum of $g$ for all $a, b \in \mathbf{R}$  I did it easily: $$g(t) = 3 a^4 t^4-4 a^2 t^2 b t+b^2 t^2$$ $$g&#39;(t) = 2 b^2 t-12 a^2 b t^2+12 a^4 t^3$$ $$g&#39;&#39;(t) = 2 b^2-24 a^2 b t+36 a^4 t^2$$  It is a critical point: $$g&#39;(0) = 0; \forall a, b$$  Its increasing for all a, b: $$g&#39;&#39;(0) = 2b^2 &gt; 0; \forall b \ne 0$$ and $$b = 0 \implies g(t) = 3 a^4 t^4$$ which has only one minimum, at $0$, and no maximum  However, it also asks me to prove that $(0, 0)$ is not a local minimum of $f$.  How can this be possible? I mean, if $(0, 0)$ is a minimum over every straight line that passes through it, then, in this point, $f$ should be increasing in all directions, no? I am trying to solve an integral in $k$-space where I want to calculate the ratio of the average energy of an arbitrary electronic band ($E(k)=k^n)$ to the square of average group velocity of electrons($v_g   = k^{n-1})$ approximately in the form of this expression given by $$L=\frac{\frac{\sum_{\mathbf{k}}k^{n}}{\sum_{\mathbf{k}}1}}{\left(\frac{\sum_{\mathbf{k}}k^{n-1}}{\sum_{\mathbf{k}}1}\right)^2}\;.$$  Now, I want to do this for $d$-dimensions, so I convert this sum to integral.  $$L=\frac{\dfrac{\int_{0}^{k_f}k^{n} d^d k}{\int_{0}^{k_f}1d^d k}}{\left(\dfrac{\int_{0}^{k_f}k^{n-1}d^d k}{\int_{0}^{k_f}1d^d k}\right)^2}$$ where $d^dk  = \dfrac{d \pi^{d/2}}{\Gamma(\frac{d}{2}+1)}k^{d-1}dk$ is the volume element in $d$-dimensional space.  I want to get a simple expression for $L$ and how it depends with $k_f,n$ and $d$. any physical insight into this integral could also be helpful. What's the difference between passing by reference vs. passing by value? What is the difference between    a parameter passed by reference a parameter passed by value?   Could you give me some examples, please? Why put a resistor in series with signal line? A lot of times in circuits I see a resistor placed in series in a signal line and sometimes even in series with an MCU's VDD line. Is the intention of this to smooth out noise in the line? How is this different from using a small cap, like a .1µF to do the same thing? Calculating MEAN and STANDARD DEVIATION confussed [] ** calculate the mean and standard deviation of each investment, assume that both returns come from independent samples, are both normally distributed and that the (true but unknown) variances are the same,, Can someone could check my  calculations for  mean and standard deviation? I did calculations but not sure what to do with negative values of distances(If if am correct Investment A MEAN= 78.6875 when it comes to calculating standard deviation i have to power difference by 2 ?  ** What are the minimum root filesystem applications that are required to fully boot linux? $\operatorname{rank}(T^3) + \operatorname{rank}(T) \geq 2\operatorname{rank}(T^2)$ for finite-dimensional $V$ Consider a finite-dimensional vector space $V$ over the field $\mathbb{F}$ with a linear operator $T.$ Prove that we have $\operatorname{rank}(T^3) + \operatorname{rank}(T) \geq 2 \operatorname{rank}(T^2).$   First, let us assume that $\dim_{\mathbb{F}}(V) = n.$ Our immediate observations include that $T^3(V) \subseteq T^2(V) \subseteq T(V)$ so that $\operatorname{rank}(T^3) \leq \operatorname{rank}(T^2) \leq \operatorname{rank}(T)$ and $\operatorname{rank}(T^3) \geq \operatorname{rank}(T) + \operatorname{rank}(T^2) - n$ by Sylvester's Rank Inequality. Can we do some manipulations with what we have to get the desired inequality, or do we require something else? How do you determine what technology a website is built on? Quite often I come across a nice looking or functional website, and wonder what technology was used to create it. What techniques are available to figure out what a particular website was built with?  Few frameworks seem to include any kind of generator meta tag like web editors do. Are there any tell-tale signs of particular languages and/or frameworks?    Summary of answers  Site URLs may betray the framework and/or programming language but cannot be relied upon (e.g. file extensions such as .asp). HTTP response headers, cookies, stylesheets and source comments may also give clues.  Some nice tools for querying site details (no doubt there are many more):          Firefox addons:    - CMS, frameworks/libraries, e-commerce, message boards etc.  - IP, country and webserver details  - Javascript libraries in use   Chrome Extensions:        Bookmarklets:    - shows Javascript framework in use Question. Let $M = \left\{ \begin{bmatrix} a &amp; b \\ -b &amp; a \end{bmatrix} \,\middle\vert\,  a, b \in \mathbb R \right\}$.  Show that $(M,+)$ and $(\mathbb C,+)$ are isomorphic.  Show that $(M^{*},*)$ and $(\mathbb C^{*},*)$ are isomorphic.    (Here, $M^{*}$ is defined as excluding the zero-element) I understand that there exists an isomorphism $\phi:M \rightarrow\mathbb C$ defined by $\begin{bmatrix} \alpha &amp; \beta \\ -\beta &amp; \alpha \end{bmatrix}\mapsto \alpha+i\beta$, ie. I can show that $\phi(M_{1}+M_{2}) = \phi(M_{1})+\phi(M_{2})$ and $\phi(M_{1}*M_{2}) = \phi(M_{1})*\phi(M_{2})$. However, I'm unsure how to go about the two subquestions seperately. What were Luke's lessons? Luke tells Rey that      there are three lessons he will teach her as he trains her as a Jedi   What are the lessons?