Functions Definition and 1000 Threads

It is know that let ##M## a compact symplectic manifold with ##G=T^{d_{T}}## a torus of dimension ##d_{T}## acting on ##M## in Hamiltonian fashion with Moment map ##\Phi:M\rightarrow \mathfrak{t}^{*}##, then ##\Phi^{\xi}=\langle \Phi(m),\xi\rangle## is a Morse function in each of its component...

Consider the map ##\phi (t,s) \mapsto (f(t,s),g(t,s))##, a point belonging to the envelope of this map satisfy the condition ##J_{\phi}(t,s)=0##. What is the role of the Jacobian in maps like these and why points in the envelope have to satisfy ##J_{\phi}(t,s)=0##?

hey so if you are taking a floor function of a fraction >1, is there any way to predict anything about it's factorization? what about when the numerator is a factorial and the denominator is made up of factors that divide said factorial but to larger exponents then those that divide the...

I was not sure where to post this here or in calculus, but seeing as the underlying basic principle of my question is regarding parity of functions I am posting it here, but feel free to move if needed. Basically I am getting ready for a (intro to) QM exam and I still struggle with some basic...

What's $1. ~ \displaystyle \arccos(\cos\frac{4\pi}{3})?$ Is this correct? The range is $[0, \pi]$ so I need to write $\cos\frac{4\pi}{3}$ as $\cos{t}$ where $t$ is in $[0, \pi]$ $\cos(\frac{4\pi}{3}) = \cos(2\pi-\frac{3\pi}{3}) = \cos(\frac{2\pi}{3}) $ so the answer is $\frac{2\pi}{3}$

Hello, I am searching for some kind of transform if it is possible, similar to a Fourier transform, but for an arbitrary function. Sort of an inverse convolution but with a kernel that varies in each point. Or, like I say in the title of this topic a sort of continuous equivalent of fitting a...

Hello Forum, I am trying to get clear on the return statement when defining functions in C. A function is a group of statements that together perform a certain task. A function usually receives some input arguments which it uses to produce some output arguments. In C, we must specify what type...

if we draw a line parallel to the x- axis and passes through a point in the image and the graph intersects at one point is this a one to one function ?

when i was reading a supplementary notes doc from open course ware fro MIT on single variable calculus there was a description about a graphical representation of a single valued function as " if each line parallel to the y- axis and which passes through a point in the domain intersects the...

when i was reading a supplementary notes doc from open course ware fro MIT on single variable calculus there was a description about a graphical representation of a single valued function as " if each line parallel to the y- axis and which passes through a point in the domain intersects the...

Hello people ! Hope you are fine! I tried to find the inner product that u can see below, between two different radial functions. I was expecting to find zero but i found something nonzero. You can see my two questions below in the photo.

I want to show that $$\int_0^{\infty} \frac{ds}{s-q^2} \frac{s^{-1-\epsilon}}{s-t \frac{z}{1-z}} = \Gamma(1-\epsilon) \Gamma(\epsilon) \frac{1}{t \frac{z}{1-z} - q^2} \left((-t)^{-1-\epsilon} \left(\frac{z}{1-z}\right)^{-1-\epsilon} -(-q^2)^{-1-\epsilon}\right) $$ I have many ideas on how to...

Here is a simple question : let f(g(x)) = h(x)*g(x). I want to calculate df/dx. If I use the product rule, I get g(x)h'(x) + h(x)g'x). Now if I use the composition/chain rule, I get df/dx = df/dg * dg/dx = h(x) * g'(x) which is different. I guess my df/dg = h is wrong, but I can't see what...

I figured it out... how do I remove this question?

The following text considers the possible wave functions when the potential is symmetric about ##x=0##. Why must even functions have an even number of nodes? ##y=sin^2x## is even but always have an odd number of nodes in any interval centred about ##x=0##. The part preceding the above text:

I have trouble reconciling orthogonality condition for Wannier functions using both continuous and discrete k-space. I am using the definition of Wannier function and Bloch function as provided by Wikipedia (https://en.wikipedia.org/wiki/Wannier_function). Wannier function: Bloch function: I...

Homework Statement I did not manage to get the final form of the equation. My prefactor in the final form always remain quadratic, whereas the solution shows that it is linear, Homework Equations w refers to wannier function, which relates to the Bloch function ##\mathbf{R}## is this case...

1. Given the function ##xy+cos y+6xy^2=0## , it follows that ## dy/dx=-y/x-siny+12xy##2. My problem is how do we integrate this derivative ## dy/dx=-y/x-siny+12xy## to get back the original function3.## ∫dy/dx dx=y ##

In case of the Green's functions for the Laplace equation, we know that they're all symmetric under the exchange of primed and un-primed variables. But is it generally true for the Green's functions of all differential equations? Thanks

Homework Statement I have run into a number of problems while working through problems regarding Bessel and Modified Bessel Functions. At one point I run into i^{m}e^{\frac{im\pi}{2}} and it needs to equal (-1)^m but I'm not sure how it does. This came up while trying to solve an identity for...

What's the type of wave functions? Is it just: function from a point in spacetime to Z; takes a location and returns an amplitude in discrete units? (bonus question: according to your favorite theory, what is the type of points in spacetime (that is, topology of spacetime)? is it like r^n for...

Hey! :o I am looking at the following: I haven't really understood the proof... Why do we consider the differential equation $y'=P(x)y$ ? (Wondering) Why does the sentence: "If $(3)_{\mathfrak{p}}$ has a solution in $\overline{K}_{\mathfrak{p}}(x)$, then $(3)_{\mathfrak{p}}$...

Consider two functions f, g that take on values at t=0, t=1, t=2. Then the total error between them is: total error = mod(f(0)-g(0)) + mod(f(1)-g(1)) + mod(f(2)-g(2)) where mod is short for module. This seems reasonable enough. Now, consider the two functions to be continuous on [0,2]. What...

Homework Statement [/B] Taken straight out of Szabo and Ostlund's "Quantum Chemistry" problem 2.1: Given a set of K orthonormal spatial functions, \{\psi_{i}^{\alpha}(\mathbf{r})\}, and another set of K orthonormal functions, \{\psi_{i}^{\beta}(\mathbf{r})\}, such that the first set is not...

Homework Statement If M[X(t)] = k (2 + 3e^t)^4 , what is the value of k Homework Equations M[X(t)] = integral ( e^tx * f(x) )dx if X is continuous The Attempt at a Solution I tried differentiating both sides to find f(x), but since it is a definite integral from negative infinity to infinity...

Hello everyone! I have a question about angular integration in arbitrary d dimensions. The interest comes from the need to use dimensional regularization. Suppose I start with a 2-dimensional integral and then I have to move to d=2-\epsilon dimension to regularize my integral. Now, suppose...

Hello, Im currently in a Calc II class with unfortunately a bad professor (score of 2 on RateMyProfessor), so I often have to resort to outside sources to learn. Our class is currently on Sequences and Series which has been fine up until we hit the topic of relating Power Series and Functions...

Homework Statement There's no reason to give you the problem from scratch. I just want to show that 5 trigonometric functions are linearly independent to prove what the problem wants. These 5 functions are sin2xcos2x. sin2x, cos2x, sin2x and cos2x. Homework Equations...

Homework Statement Sorry for the pictures, I'd normally write out the problem but it is mostly diagrams. Question and work attached. I am looking for help with part (a) right now, the transfer function I obtain is shown at the end of my work. Homework Equations Knowledge of Laplace transforms...

Homework Statement Supposethat X1and X2 are .random variables and that each of them has the uniform distribution on the interval [0, 1]. Find the p.d.f. of Y =X1+X2. Homework Equations Find cdf of Y and then the pdf The Attempt at a Solution the joint pdf would be f(x1,x2)= 1...

If the moment generating function for the random variable X is M[X(t)] = 1/(1+t), what is the third moment of X about the point x = 2? The general formula only states how to find moments about x = 0. Thanks!

Homework Statement If ##f(2x-1)= 6x + 15## and ##g(3x+1)=\frac{2x-1}{3x-5}##, then what is ##f^{-1}\circ g^{-1}(3)## ? a) -2 b) -3 c) -4 d) -5 e) -6 The Attempt at a Solution I think the f inverse and g inverse is ##f^{-1}(6x+15)= 2x-1## ##g^{-1}(\frac{2x-1}{3x-5})=3x+1## and,##f^{-1}\circ...

Hi! I was wondering how I could find the equations for the bottom two functions. I understand that the amplitude is not constant like that in the circular sine function--could someone please help me out? Thanks!

Homework Statement Given a Uniform Distribution (0,1) and Z = X/Y Find F(z) and f(z) Homework EquationsThe Attempt at a Solution So I'm just trying to make sure i have the range correct on this one... I'm honestly lost from beginning to end with it. R(z) = {0,∞} because as y is very small, Z...

Homework Statement Prove that there do not exist functions ##f## and ##g## with the following property: $$(\forall x)(\forall y)(f(x+y) = g(x) - y)$$ Homework Equations NA The Attempt at a Solution Here is some information I have found out about ##f## and ##g## if we suppose they exist: ##f(x...

Hi, I was just wondering how would you go about finding a harmonic function in complex analysis when given certain conditions such as I am z > 0 and is 1 when x > 0 and 0 when x < 0. Do you draw a diagram? Do you solve the laplace equation? How would you go about doing this? What if there...

How do you memorize the even and odd function?

I'm realizing now how much I need to know the exact values of various trigonometric functions, as shown in various trig tables. Memorizing is pretty arduous, and I'd prefer to understand it, so how can I learn all of these?

Hi all Just to start with I should highlight my general ineptitude with programming, so I apologize if my question is totally basic. I have a program written (by someone else) in fortran 77. Contained within it is a call to a function which acts on a number of variables. My curiosity is about...

Hi, I know that when you take this limit it is equal to e^-wo, but I was just wondering how you got there when taking the limit? lim w-->wo ((exp(w)-exp(wo))/(w-wo))^-1 = 1/e^wo w and wo are both two points within the same plane.

How do you know when to use exponentials and trig functions when solving for the wave function in a finite square well? I know you can do both, but is there some way to tell before hand which method will make the problem easier? Does it have something to do with parity?

As I understand it a Green's function ##G(x,y)## for a translationally invariant differential equation satisfies $$G(x+a,y+a)=G(x,y)\qquad\Rightarrow\qquad G(x,y)=G(x-y)$$ (where ##a## is an arbitrary constant shift.) My question is, given such a translationally invariant system, how does one...

Homework Statement Homework Equations n/a The Attempt at a Solution ##y'=f(x.y)## is a function of two variables. ##y=y(x)## is a function of only one variable. How can they be related? Clearly ##y(x) = f(x) \neq f(x,y)## Thanks

Homework Statement Hi i have an assignment that is asking me to convert 3 temperatures in fahrenheit to celcius and vice versa. I am very new to programming only 2 weeks in(and i learn by playing with the program) so I do not know all of the terminology / principles. I am not allowed to use...

Homework Statement First, I'd like to say that this question is from an Introductory Linear Algebra course so my knowledge of vector space and subspace is limited. Now onto the question. Q: Which of the following are subspaces of F(-∞,∞)? (a) All functions f in F(-∞,∞) for which f(0) = 0...

Hello! (Wave) I want to find all the continuous functions $f: [0,1] \to \mathbb{R}$ for which it holds that:$$\int_0^1 f(t) \phi''(t) dt=0, \forall \phi \in C_0^{\infty}(0,1)$$ If we knew that $f$ was twice differentiable, we could say that $\int_0^1 f(t) \phi''(t) dt= \int_0^1 f''(t) \phi(t)...

We know that in the space of functions, its possible to find a complete set so that you can write for an arbitrary function f, ## f(x)=\sum_n a_n \phi_n(x) ## and use the orthonormality relations between ## \phi##s to find the coefficients. But is it possible to find a set of functions ##...

Is it correct to say that if a relation between a few numbers is represented on a graph and it comes out to be a curve than it can be written in the form of an equation?

What are different ways of ensuring efficiency in a recursive function in C++? i.e. Prevent calling your recursive function when not necessary.

Homework Statement differentiate ∫ e^(-x*t^4)dt from -x to x with respect to x.[/B]Homework Equations erf(x) = (2/sqrt(π)) ∫e^(-t^2)dt from 0 to x. Leibniz rule. I know that ∫t^2e^(-t^2)dt from 0 to x = (√π/4)*erf(x) - (1/2)*x*e^(-x^2)[/B]The Attempt at a Solution By using Leibniz rule...