Function Definition and 1000 Threads

Dear all. I'm learning about the discrete Fourier transform. ##I(\nu) \equiv \int_{-\infty}^{\infty} i(t) e^{2 \pi \nu i t} d t=\frac{N}{T} \sum_{\ell=-\infty}^{\infty} \delta\left(\nu-\ell \frac{N}{T}\right)## this ##i(t)## is comb function ##i(t)=\sum_{k=-\infty}^{\infty}...

a) At which intervals are f strictly increasing and at what intervals are f strictly decreasing. Should I just find the derivative of both of the functions? If so, I get that the function is increasing at the intervals (−∞,0) and (0,∞). Is this right, or can I just say that the function is...

Ok. So if i sketch the curve I can see that this pound has a shape of a square. Ann and KFC has the same distance from the pond. I'm able to calculate the time for Ann to walk around the pond, and if she walks in a straight line from where she stands to KFC. If she walks around it will take...

I got acceleration by dividing force by m then replaced a by dv/dt and then integrated it to get velocity as a fxn of time and hence got kinetic energy but problem is my ans does not match with any option can someone please compare their ans

I am trying to figure out if the use of the Zeta function allows renormalization to be bypassed. I have formed a preliminary view but would like to hear what others think: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.570.4579&rep=rep1&type=pdf Thanks Bill

How do I find the probabilty density function of a variable y being y=ab, knowing the probabilty density functions of both a and b? I know how to use the method to calculate it for a/b - which gives 1/pi*(a²/b²+1) - using variable substitution and the jacobian matrix and determinant, but which...

The strategy here would probably be to find a differential equation that ##f## satisfies, but differentiating with respect to ##x## using Leibniz rule yields ##f'=\int_x^{2x} (-te^{-t^2x}) \ dt + \frac{2e^{-4x^3}-e^{-x^3}}{x}## Continuing to differentiate will yield the integral term again...

I found that <x> of p(x) = 1/π(x2 + 1) is 0. But its <x^2> diverges. I don't know if there are other ways of interpreting it besides saying that the variance is infinity. I usually don't see variance being infinity, so I'm not sure if my answer is correct. So, can variance be infinity? And does...

Given that the wave function represented in momentum space is a Fourier transform of the wave function in configuration space, is the conjugate of the wave function in p-space is the conjugate of the whole transformation integral?

Can you say whether I understood these things correctly? to get condition on wavefunction ##\Psi## for a system that consists of 2 electrons(without taking spin into account) and helium nuclei I can solve schrödinger equation: ##i*\frac{\partial \Psi}{\partial...

Hi PF! The following is a simple ODE I'm solving via DSolve. However, the solution, which I call uEven, does not work as a typical function. Note the last two lines are different. Does anyone know how to fix this, so that I can differentiate and integrate the output of this ODE without...

Hello everyone. I am trying to do a 2D Shannon interpolation, but I cannot use a sinc because later on this expression goes in an optimization software that doesn't recognize it. I have defined my own version of sinc as: sincC = Piecewise[{(Sin[Pi* #]/(Pi*(#))), # >= 1}, {1 - (#^2)/6 +...

In axioms containg S one invariably finds: Sx = Sy -----> x = y The converse, which characterizes S as a function: x = y ------> Sx = Sy Is never shown. Neither is it shown as an Axiom of FOL or formal Theory of Arithmetic. From the basic axioms and rules of FOL, how does one go about...

If the question was $$ \int_{∞}^{∞}dxf(x)δ((x - x_1)) = ? $$ The answer would be ##f(x_1)## So the delta function has two roots, I searched the web and some books but I am not sure what approach should I use here. I guess there's sometihng happens when ##x_1 = -x_2##. So I am not sure what...

Hey guys, got another question for you to look at and hopefully help me out on. For each of the following functions, prove that f is one to one on E and find a formula for the inverse function f-1. (a) f(x)=x2+3x-6 and E=[-3/2,infinity). (b) f(x)=((x)/(x2+1)) and E=[-1,1]. Please help me...

Hello! I am reading Data Reduction and Error Analysis by Bevington, 3rd Edition and in Chapter 8.1, Variation of ##\chi^2## Near a Minimum he states that for enough data the likelihood function becomes a Gaussian function of each parameter, with the mean being the value that minimizes the...

Summary: Please see the attached problem and solution The answer is 1/5. I have tried various solutions and cannot get 1/5. What is my error? [Moderator's note: Moved from a technical forum and thus no template.]

I understand that you need to integrate f(x), and the negative of that is U(x). But the last part of the problem says "Clearly state any assumptions you make." And the answer is just the antiderivative of that f(x) without any constant from integrationHow does that make sense

Consider a continuous charge distribution in volume ##V'##. Draw a closed surface ##S## inside the volume ##V'##. ___________________________________________________________________________ Consider the following multiple integral: ##\displaystyle B= \iint_S \Biggl( \iiint_{V'}...

Summary: I am studying inverse functions and want to see a plot of an inverse function. I hope this is an OK post here. Lets say I have a function y = x^3 + x. This function has n inverse sine the derivitave is always positive and is a one on one function. I can easily graph this function...

I have taken a look but most books and Online stuff just menctions the First order Taylor for 3 variables or the 2nd order Taylor series for just 2 variables. Could you please tell me which is the general expression for 2nd order Taylor series in 3 or more variables? Because I have not found...

I have to integrate this expression so I started to solve the delta part from the fact that when n=0 it results equals to 1. And the graph is continuous in segments I thought as the sumation of integers $$ \int_{-(n+1/2)π}^{(n+1/2)π} δ(sin(x)) \, dx $$ From the fact that actually $$ δ(sin(x))=...

I tried to find the derivative of the function V(P)= k/P which I found to be: V'(P) = kP-1 V'(P) = (1)(-1)(P)-1-1 = -1/(P2) And then I substituted in 1.30 into the derivative to obtain -0.5917 L/atm. And I am kind of confused how to actually find the derivative of this. I thought I was on...

Born's postulate suggests if a particle is described a wave function ψ(r,t) the probability of finding the particle at a certain point is ψ*ψ. How does this work and why?

NOTE: Was not sure where to post this as it is a math question, but a part of my "Theoretical Physics" course. I have no idea where to start this and am probably doing this mathematically incorrect. given the function f(z) = cos(z+1/z) there should exist a singular point at z=0 as at z = 0...

Interpolating a straight line with a trigonometric function. In Matlab I ended up with this expression. fplot(@(x)(.0000001*cos(x*2*pi)+10), [0 1]) Would anyone like to discuss what this could be used in?

In Landau-Lifsits's book about non relativistic QM it is said that if I have a particle described by a plane wave ##\phi = e^{ikz}## (I think he choses the ##z## direction for simplicity) the wave function after the scattering event is (far from the scattering event) $$\psi \approx e^{ikz} +...

I use the equation ##\psi \left ( x, t \right ) = e^{-iEt/\hbar} \psi \left ( x,0 \right )## to calculate ##\psi \left ( x , t \right)##, and the result is ##\psi \left ( x , t \right) = \frac 1 {\sqrt {2 \pi \hbar}} exp \left [ \frac {ip_0 x} {\hbar} - \frac {i p^2 t} {2m \hbar} \right...

I'd like to design a ducted fan capable of generating 800 N of thrust. Though I can do fairly high level math, I just really don't even know where to start in calculating (or at least relatively accurately estimating the thrust generated by a propeller, particularly a ducted one (as I understand...

Why we can't use radical to solve an equations with power greater than 4?

If one approaches the origin from where ##x_2=0##, the terms ##x^2_1x_2+x^2_2x_3## in the denominator equal ##0##. Substituting ##|\textbf{x}|^2## for ##t## yields the expression ##\frac{e^t-1}{t}##, which has limit 1 as ##\textbf{x}\to\textbf{0}## and thus ##t\to0##. So the limit should be 1 if...

Hello everybody! I am working on a code in which I need to study the dependence of ##<p_T>## vs ##p_L## (the average transverse momentum and the longitudinal momentum of a particle). I am looking for references, papers, books, etc. concerning this topic, but I have not been so lucky. My...

f(x)=2xand g(x)=2^x Find the composite function of fg(x) fg(x) =f(g(x)) =f(2^x) =2(2^x) I don’t understand how this in turn equals to 2^(x+1) [Moderator's note: Moved from a technical forum and thus no template.]

I am currently doing some task on a website called Codility (link and bottom of post). The task basically ask for me to create an algorithm to shift an array to the left K times (Full details below). Which seem to work for a non function but I still seem to be shifting it wrong as the output is...

Homework Statement: Solve for x. Homework Equations: sin(3x)= -1/2 sin(3x) = -1/2 3x = sin-1(-1/2) 3x = -π/6 x = -π/18 x = -π/18 + 2π/3 = 11π/18 11π/18 + 2π/3 = 23π/18 11π/18 + (2π(4))/3 = 35π/18 The solutions I obtained were 23π/18 and 35π/18. Are these correct? I'm not entirely sure...

Dear All, Here is my question. The marketing department estimates that if the selling price of the new product is set 40 dollar per unit, sales will be 400 units per week. If the selling price is 20dollar per unit, sales will be 800 units per week. The production dept estimates that variable...

Recently I have come into Special Relativity and specifically Lorentz transformation. Let's assume two frames A and B moving relative with speed ##v##. The position of a particle moving with respect to B is given by ##x′=f(t′)=3t′##. What is the function of position ##x=f(t)## of the particle...

Hi, I understand how any function could be decomposed into even and odd parts assuming the function isn't a purely even or odd to start with. It's just like saying that any vector in x-y plane could be decomposed into its x- and y-component assuming it doesn't lie parallel to x- or y-axis...

Homework Statement: I do know how to solve the resistance network problem in two dimensions. However, in this problem they want it in 3 dimensions and higher and I don't know how to do that Homework Equations: - In the picture you can see the solution to the two dimensional version

I am currently working my way through some w3schools python exercise on tuples and lists etc and one question was to write a program to converted a tuple to a string. Now originally I used the str() function on the tuple and printed the result. I then used the string in a for loop for a...

Heavier bosons like ##W## or ##H## require high energy accelerator to be detected. Yet these bosons fulfill their function in the ambient energy of the universe. Why is it that their detection takes high energy environment but their function is possible in lower ambient energy?

$\textsf{6.2.15 Find the domain of each function.}$ (a) $f(x)=\dfrac{1-e^{x^2}}{1-e^{1-x^2}}$ set the denominator to zero and solve $1-e^{1-x^2}=0$ then $x=1,-1$ from testing the domain is $(-1,1)$(b) $f(x)=\dfrac{1+x}{e^{ \cos x}}$ set $e^{\cos x}=0$...

If we have a function ##f(x+\Delta x)## where ##\Delta x << x##, is it valid to approximate this as: $$f(x + \Delta x) \approx f(x) + f'(x)\Delta x$$ even if ##\Delta x## is not necessarily small? If not, what is the valid expansion to first order?

Basically, I wanted to create a Numpy array with linearly spaced integers between 0 and 3, the increment being 0.01. Yes, I know Numpy offers a linspace function. I used it like this: x = np.linspace(0, 3, num=300) (where np is numpy), and got this: I know that the numbers cannot be exact...

I have a PDE that I want to solve for a stream function ψ(j,l) by discretizing it on a 2D annulus grid in cylindrical coordinates, then solving with guas-seidel methods (or maybe a different method, not the point): (1/s)⋅(∂/∂s)[(s/ρ)(∂ψ/∂s)] + (1/s2)⋅(∂/∂Φ)[(1/ρ)(∂ψ/∂Φ)] Where s and Φ are...

In a simple circuit with battery connected to a resistor or a combination of resistors where is the electric field directed . What do we mean when we say battery creates a potential difference between two points in a conductor? And by the statement that battery moves positive charge from low...

Hi, I was trying to numerically integrate the following inverse Fourier transform integral,, using the code below. The plot is also shown below. The plot looks good which means the result is good as well. By the way, I was getting a warning which I quote below the code. % file name...

Why can't the general state, in the presence of coupling, take the form $$\psi_-(r)\chi_++\psi_+(r)\chi_-$$ where ##\psi_+(r)## and ##\psi_-(r)## are respectively the symmetric and anti-symmetric part of the wave function, and ##\chi_+## and ##\chi_-## are respectively the spinors representing...

Let $f(x)=(2x+1)^3$ and let g be the inverse of $f$. Given that $f(0)=1$, what is the value of $g'(1)?$$(A)\, \dfrac{2}{27} \quad (B)\, \dfrac{1}{54} \quad (C)\, \dfrac{1}{27} \quad (D)\, \dfrac{1}{6} \quad (E)\, 6$ok not sure what the best steps on this would be but assume we first find...

This thread is to look at the notion of wave function collapse and relativity of simultaneity. The other thread I started on QFT has helped to clarify a lot, so hopefully this one can do the same. I may have this all wrong, but I will outline my question and hopefully someone can point out...