Functions Definition and 1000 Threads

Hello! (Wave) I want to show the following two propositions: The domain of a recursive function is recursively enumerable. The range of a recursive function is recursively enumerable. I have thought the following in order to prove the first proposition. Suppose that we have a recursive...

What exactly does class of time correlation functions measure of particle in quantum mechanics? In particular, I would love to know the answer in the context of Kubo-transform time correlation function.

Homework Statement [/B] Theorem attached. I know the theorem holds for a discrete subgroup of ##C## more generally, ##C## the complex plane, and that the set of periods of a non-constant meromorphic function are a discrete subset. I have a question on part of the proof (showing the second...

$\tiny{242.7x.27}$ $\textsf{Find the slowest growing and the fastest growing functions ${{x}\to{\infty}}$}$ \begin{align*}\displaystyle y&=4x^{10} \\ y&=e^x \\ y&=e^{x-4} \\ y&=xe^x \\ \end{align*} $\textit{I'm clueless... take the limit??}$

Homework Statement ONLY QUESTION 2[/B] Homework EquationsThe Attempt at a Solution Not sure what's going on here. I think the issue is in my own flawed understanding of the notation used in sets generally. So the question states: f : R \rightarrow R such that f(x) = x^{2} My...

Hello Forum, Let's say we have a complete set of functions ##u_{i} (x)## that can be used to represent anyone dimensional function ##f(x)##. We then find another and different set ##v_{i} (x)## that can do the same thing, i.e. represent any function ##f(x)## via a linear superposition. I...

I have a set of variables that are always inputs for several functions that I made. Does MatLab have a kind of function that stores these variables into a single matrix (or similar) so that I just need to call this matrix for each function rather than calling them one-by-one as inputs into the...

Assume f and g are two continuous functions in (a, b). If at the start of the segment I've shown f>g by taking the lim where x ---> a+ and the f ' > g ' for every x in (a,b ) can i say that f >g for all x in (a,b )? is there a theorem for that? that looks intuitively right.

Surface S and 3D space E both satisfy divergence theorem conditions. Function f is scalar with continuous partials. I must prove Double integral of f DS in normal direction = triple integral gradient f times dV Surface S is not defined by a picture nor with an equation. Help me. I don't...

Homework Statement Sketch the graphs of the following functions and show all asymptotes with a dotted line y = (2x - 6)/ (x2-5x+4) i) Equation of any vertical asymptote(s) ii) State any restrictions or non-permissible value(s) iii) Determine coordinates of any intercept(s) iv) Describe the...

Homework Statement I have a question related to taking the logs of transfer functions, getting the individual Bode plots of each subsequent factor, and adding those plots graphically. I'm working from Fundamentals of Electric Circuits, 5th edt. Let me start with the following screen capture...

I've written it out and it seems impossible. I get -50(sin^2(alpha)) = 86.63 cos(alpha) sin(alpha) - 6.54. Where would I go from there?

So I have to show 2sin^2(x) and -cos(2x) have the same antiderative. Here's how I approached this. 2sin^2(x) = 1-cos2x ==> u = 2x intergral of that is (u - sinu)/2 + c = x - (sinx)/2 + c -cos2x ==> u = 2x intregal of that is (-sinu)/2 + c= -(sin2x)/2 + c Have I calculated/approached this...

Homework Statement Happy new year all. I was wondering if you can use matrices to translate and transform a function? So for example if I were to take the function $$f(x)=x^2+4x$$ and I want to the translate and transform the equation to $$2f(x+4)$$. Can this be done by matrices. I know how...

Do higher dimensional branes, like the super membrane (which is a 2D brane) or the NS5/M5 brane, have wave functions? I know that they become unstable once they are quantized, but does that mean that they do not have wave functions? You will never here about any thing regarding an M2 wave...

I have been working on this for several days but getting nowhere. Any help would be great. \begin{align} &\int_0^x dy\,y^2 \cos(y^2) C^2 \!\!\left(\!\frac{\sqrt{2}\,y}{\sqrt\pi}\!\right) \end{align} In reality only the first one is causing me troubles, however I have pasted the entire...

Hello everybody, I'm currently helping a friend on an assignment of his, but we are both stumbled on this exercise, I'm posting it here We define a function ##f## which goes from ##\mathbb{R}## to ##\mathbb{R}## such that its argument maps as $$ x \mapsto...

Heres an example. Let G(s) be the moving average of all previous values of f(s). G(s) and F(s) intersect at multiple points. Is it possible to prove that the intersections happen periodically?

I have a couple homework questions, and I'm getting caught up in boundary applications. For the first one, I have y'' - 4y' + 3y = f(x) and I need to find the Green's function. I also have the boundary conditions y(x)=y'(0)=0. Is this possible? Wouldn't y(x)=0 be of the form of a solution...

Homework Statement For the FM modulation, the amplitudes of the side bands can be predicted from v(t)=ΣAJn(I)sin(ωt) Where is a sideband frequency and Jn(I) is the Bessel function of the first kind and the nth order evaluated at the modulation index .Given the table of Bessel functions...

Hello folks, 1.- In geometry we study for example the conic sections, their exentricity and properties. I was wondering what part of the mathematical science studies the different properties of complex valued distributions. One example are the spherical armonics. I guess mathematicians have...

Hi guys, Here is a wacky question for you: Suppose you have a simple recursive function f(x)=x. Given the fact that a function f(x)=y can be rewritten as a set of ordered pairs (x, y) with x from the domain of f and y from the range of f, it would seem that the function f(x)=x can be written...

I just did a problem for a final that required us to use a green's function to solve a diff eq. y'' +y/4 = sin(2x) I went through and solved it and got a really nasty looking thing, but I checked it in wolfram and it works out. Now, my question is this: After I got the solution from my greens...

Homework Statement I'm trying hard to understand as my professor hasn't taught(nor does my textbook) on how this works. It is known that $$\lim_{x \to 0}\frac{f(x)}{x} = -\frac12$$ Solve $$\lim_{x \to 1}\frac{f(x^3-1)}{x-1}.$$ Homework EquationsThe Attempt at a Solution OK.. so I do this...

For example, I am following the below proof: Although the above derivation involves a projection on the position basis, it appears one can generalize this result by using any complete basis. So despite it not being explicitly mentioned here, are all wave functions with any continuum basis...

Is there a difference between the linear independence of ##\{x,e^x\}## and ##\{ex,e^x\}##? It can be shown that both only have the trivial solution when represented as a linear combination equal to zero. However, the definition of linear independence is: "Two functions are linearly independent...

Homework Statement I need to draw this function: however I don't get how? I have the solution but I don't understand how do I get that from the given function. Someone please try to explain? Thanks

Homework Statement I'm searching for the integral that gives arcosu Homework Equations as we know : ∫u'/[1-u^2]^0.5 dx = arcsinu derivative of arccosu = -u'/[1-u^2]^0.5 + C derivative of arcsinu= u'/[1-u^2]^0.5 The Attempt at a Solution when I type the -u'/[1-u^2]^0.5 on the online integral...

Hey! :o Let $\text{Val} = \{0, 1\}^8$, $\text{Adr} = \{0, 1\}^{32}$ and $\text{Mem} = \text{Val}^{\text{Adr}}$. The addition modulo $2^8$ of two numbers in binary system of length $8$, is given by the mapping: $$\text{add}_{\text{Val}} : \text{Val}\times \text{Val}\rightarrow \text{Val} \\...

Reading through David Tong lecture notes on QFT.On pages 76, he gives a proof on correlation functions . See below link: [QFT notes by Tong][1] [1]: http://www.damtp.cam.ac.uk/user/tong/qft/qft.pdfI am following the proof steps to obtain equation (3.95). But several intermediate steps of the...

Hi folks, When you have a differential equation and the unknown function is complex, like in the Schrodinger equation, What methods should you use to solve it? I mean, there is a theory of complex functions, Laurent series, Cauchy integrals and so on, I guess if it would be possible to...

Homework Statement Can someone check my work? Homework EquationsThe Attempt at a Solution 1. ##\frac{1}{s+2}+\frac{1}{s^2+1}## 2. ##\frac{2}{s}+\frac{3}{s+4}## 3. ##\frac{s*sin(-2)+cos(-2)}{s^2+1}## 4. ##\frac{1}{(s+1)^2}## 5. Don't really know how to do this one...

Hey! :o Could you give me an example of a strong concave function $f:[0,3]\rightarrow \mathbb{R}$ that is not continuous? (Wondering) We have that $f''(x)<0$. Since the function has not to be continuous, the derivatives are neither continuous, are they? (Wondering) Is maybe the...

Hello! (Wave) We consider the following Cauchy problem $u_t=u_{xx} \text{ in } (0,T) \times \mathbb{R} \\ u(0,x)=\phi(x) \text{ where } \phi(x)=-\phi(-x), x \in \mathbb{R} $ I want to show that $ u(t,0)=0, \forall t \geq 0 $. We have the following theorem: Let $\phi \in...

Homework Statement In electron proton scattering, ##\int_0^{1} F^p_2(x)dx = 0.18## For the neutron in electron deuteron scattering, ##\int_0^1F^n_2(x)dx = 0.12## Therefore determine the ratio ##\frac{\int_0^1xu^p_v(x)dx}{\int_0^1xd^p_v(x)dx}##. Homework EquationsThe Attempt at a Solution...

Green functions are defined in mathematics as solutions of inhomogeneous differential equations with a dirac delta as the right hand side and are used for solving such equations with a generic right hand side. But in QFT, n-point correlation functions are also called Green functions. Why is...

Consider the following time-ordered correlation function: $$\langle 0 | T \{ \phi(x_{1}) \phi(x_{2}) \phi(x) \partial^{\mu}\phi(x) \partial_{\mu}\phi(x) \phi(y) \partial^{\nu}\phi(y) \partial_{\nu}\phi(y) \} | 0 \rangle.$$ The derivatives can be taken out the correlation function to give...

I thought I understood the concept of a correlation function, but I having some doubts. What exactly does a correlation function quantify and furthermore, what is a correlation length. As far as I understand, a correlation between two variables ##X## and ##Y## quantifies how much the two...

If ##t## is a function of ##r##, then we may in theory find ##r## as a function of ##t##, as claimed in the last paragraph of the attachment below. My issue is this is only true if ##t## is a 1-1 function of ##r##. Otherwise, suppose ##t=r^2##. Then ##r=\pm\sqrt{t}##, which isn't a function. I...

In my calculus textbook, it shows that a function's solution can be approximated using an approximated function tangent to the original function based on an approximated solution, where the equation to find the approximated is L(x) = f(X0) + f'(X0)*(X-X0), where when rearranged, gives x = Xo -...

Homework Statement Evaluate the following line integrals in the complex plane by direct integration. Homework Equations Z= x+i y = Cos(θ) +i Sin(θ) = e^i*θ The Attempt at a Solution I'm not sure how to evaluated this by hand. I tried using Z= x+i y = Cos(θ) +i Sin(θ), and evaluating the...

Homework Statement Derive the transfer function for both circuits \frac{V_{out}}{V_{in}} sketch Bode plots for each circuit (amplitude and phase) Homework Equations Z_c=\frac{1}{j{\omega}C}~and~{\omega}_C=\frac{1}{RC} The Attempt at a Solution We can treat this as a potential divider using the...

Are there differential equations that, for some reason, don't have a Green function? Are there conditions for a DE to satisfy so that it can have a Green function? Thanks

In functional analysis functions ##f## and ##g## are orthogonal on the interval ##[a,b]## if \int^b_a f(x)g(x)dx=0 But what if we have functions of two variables ##f(x,y)## and ##g(x,y)## that are orthogonal on the interval ##[a,b]##. Is there some definitions \int^b_a f(x,z)g(z,y)dz=0?

Hello! (Wave) I have a question about the proof of the maximum principle for subharmonic functions. The maximum principle is the following: The subharmonic in $\Omega$ function $v$ does not achieve its maximum at the inner points of $\Omega$ if it is not constant. Proof: We suppose that at...

sin\theta 3/5

Suppose u(x,y) and v(x,y) are harmonic on G and c is an element of R. Prove u(x,y) + cv(x,y) is also harmonic. I tried using the Laplace Equation of Uxx+Uyy=0 I have: du/dx=Ux d^2u/dx^2=Uxx du/dy=Uy d^2u/dy^2=Uyy dv/dx=cVx d^2v/dx^2=cVxx dv/dy=cVy d^2v/dy^2=cVyy I'm not really sure how to...

Mentor note: moved to homework section y = sin(x) y = cos(x) y = tan(x) y = csc(x) y = sec(x) y = cot(x) (a) 0 (b) 4 (c) 6 (d) 2 I thought it was (c) because i graphed all the trig functions and they passed the vertical line test but the answer sheet is saying (d) 2

Homework Statement If ##r_1, r_2, r_3## are distinct real numbers, show that ##e^{r_1t}, e^{r_2t}, e^{r_3t}## are linearly independent. Homework EquationsThe Attempt at a Solution By book starts off by assuming that the functions are linearly dependent, towards contradiction. So ##c_1e^{r_1t}...

Given the theory $$\mathcal{L}=\frac{1}{2}(\partial_{\mu}\phi)^{2}-\frac{1}{2}m_{\phi}^{2}\phi^{2}+\partial_{\mu}\chi^{*}\partial^{\mu}\chi-m_{\chi}^{2}\chi^{*}\chi+\mathcal{L}_{\text{int}},\qquad \mathcal{L}_{\text{int}}=-g\phi\chi^{*}\chi,$$ the time-correlation function ##\langle \Omega |...