Variables Definition and 1000 Threads

How does lemma 18.2.2 imply the definition?

I'm currently working (slowly) through Goldstein (et al), 3rd Edition, and a remark in the section on Action-angle Varibles for Completely Separable Systems (10.7) is giving me pause. We're told that the orbit equations for all ##(q_i, p_i)## pairs in phase space describe libration or periodic...

Homework Statement I am trying to minimize the function ##f(a) = (1+4a^2)^3 \left( \frac{1}{4a^2} \right)^2##. Here we are given that ##a>0## Homework Equations Definition of a minimum of a function The Attempt at a Solution Now the derivative here will be ugly and equating it to zero and...

robphy submitted a new PF Insights post Relativity Variables: Velocity, Doppler-Bondi k, and Rapidity Continue reading the Original PF Insights Post.

Homework Statement Homework Equations N/A The Attempt at a Solution I solved part a. I got an answer of 140. For part b, however, I am stuck. I came up with a set of points for D in the xy plane [(0,3)(0,6)(4,5)(4,8)] giving me a rhombus. How do i integrate this? I tried to split up the...

Homework Statement Homework Equations this is the entire syllabus of the test from which i got this question. Kindly mention if this question is out of syllabus[/B] The Attempt at a Solution I don't have the idea to approach this question. In normal limits, i know that graphically it is...

Hi all, I am developing a very simple computer game to randomly move a point to on a bound region and check how many steps it takes to have the point landing to a certain place. To make it simple, I assume it is a 1D problem, the point could start on origin or any location on positive x axis...

A paradigm shift for me occurred when, I now realize, that position and momentum are random variables in QM. As such, it does not make any sense to say things like "take the derivative of the position with respect time". Instead QM has the position and momentum operators which operate on the...

Find the critical points and test for relative extrema. List the critical points for which the Second Partials Test fails. Given: f (x, y) = (x - 1)^2 (y + 4)^2 I found the partial derivative for x and y to be the following: f_x = 2 (x - 1)(y + y)^2 f_y = 2 (y + 4)(x - 1)^2 I solved for x...

Homework Statement Determine the spherical harmonics and the eigenvalues of \vec{\hat{L}}^2 by solving the eigenvalue equation \vec{\hat{L}}^2 |\lambda, m \rangle in position space, [\frac{1}{sin \theta} \frac{\partial}{\partial \theta} ( sin \theta \frac{\partial}{\partial \theta} ) +...

Homework Statement Consider a charge ##q##, with mass ##m##, moving in the ##x-y## plane under the influence of a uniform magnetic field ##\vec{B}=B\hat{z}##. Show that the Hamiltonian $$ H = \frac{(\vec{p}-q\vec{A})^2}{2m}$$ with $$\vec{A} = \frac{1}{2}(\vec{B}\times\vec{r})$$ reduces to $$...

Hi All, $$\int{\exp((x_2-x_1)^2+k_1x_1+k_2x_2)dx_1dx_2}$$ I can perform the integration of the integral above easily by changing the variable $$u=x_2+x_1\\ v=x_2-x_1$$ Of course first computing the Jacobian, and integrating over ##u## and ##v## I am wondering how you perform the change of...

Q: Suppose ##u(x,t)## satisfies the heat equation for ##0<x<a## with the usual initial condition ##u(x,0)=f(x)##, and the temperature given to be a non-zero constant C on the surfaces ##x=0## and ##x=a##. We have BCs ##u(0,t) = u(a,t) = C.## Our standard method for finding u doesn't work here...

My physics book is showing an example of why it matters "what variable you hold fixed" when taking the partial derivative. So it asks to show that ##(\frac{\partial{w}}{\partial{x}})_{y} \neq (\frac{\partial{w}}{\partial{x}})_z## where ##w=xy## and ##x=yz## and the subscripts are what variable...

Hi all, I have the following ode code, and I want to know how I could output the variable "k_mb" within my main script so that I can plot it to see if it's actually active when the solver is integrating. odescript function zdot = odenesttest(t,z) global r_p r_g I_p I_g m_p m_g V k_mb A_or_B =...

When I hear that mass of a particle has managed to hop through a solid barrier ..it tells me that the mass was a variable and not physical at the time.

COULOMBS LAW F= K Q1 Q2 / R2 How would I solve for Q1 and Q2?

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...

We start with: d2y/dx2 And we want to consider x as function of y instead of y as function of x. I understand this equality: dy/dx = 1/ (dx/dy) But for the second order this equality is provided: d2y/dx2 =- d2x/dy2 / (dx/dy)3 Does anybody understand where is it coming from? The cubic...

Homework Statement Hi guys, I'm struggling to figure out how the solution in the picture that I posted was able to get rid of their mg factors and then come up with a factor of k for x_1 in their eigenvalue equation. You can see that in the second equation of motion there is no k*x_1 but it...

Hi all, I have logistically- regressed 3 different numerical variables ,v1,v2,v3 separately against the same variable w . All variables have the same type of S-curve (meaning, in this case, that probabilities increase as vi ; i=1,2,3 increases ). Is there a way of somehow joining the three...

Homework Statement Transform the equation: x2 * d2y/dx2 + 2 * x * dy/dx + (a2/x2)*y = 0 Using: x=1/t Homework Equations The differential of a function of several variables, and the common rules of differentiation. https://en.wikipedia.org/wiki/Derivative The Attempt at a Solution As...

Homework Statement For the given function z to demonstrate the equality: [/B]As you see I show the solution provided by the book, but I have some questions on this. I don't understand how the partial derivative of z respect to x or y has been calculated. Do you think this is correct? I...

Homework Statement I have ##\int dx \int dy \delta (x^{2}+y^{2}-E) ## [1] I have only seen expressions integrating over ##\delta## where the ##x## or the ##y## appear seperately as well as in the delta function and so you can just replace e.g ##y^2 = - x^{2} +E## then integrate over ##\int...

Homework Statement Problem statement is attached... Homework Equations my attempt at solution is also attached... The Attempt at a Solution One of my assumptions was to treat the inlet concentration as a disturbance variable, and inlet flow rate as a manipulated variable...However, as I try...

Hello, Here is the question: I can not figure out how we are to apply chain rule to the second order derivative. May somebody clarify that?

i All, I have a Jupyter Python Notebook with data like below: \ I want to create an SFrame with 2 columns and 11 rows.Each row has two entries: One containing the name of each word and the other entry containing the total count of the word. The words are part of a list called 'Selected...

hello there Im trying to do a derivation of tsiolkovsky's rocket equation, but i got stuck at the step when i have to use separation of variables (marked with red in the pic), i used maple to solve it, so i could get on with it, but i want to understand what is happening to solve this, so can...

There's this problem that I've been trying to solve. I know the solution for it now but my initial attempt at a solution was wrong and I can't seem to figure out the mistake with my reasoning. I'd appreciate some help with figuring this one out. 1. Homework Statement I have a set of random...

I need help to convert 2 variables A,B into 1 representative variable C, which is used to filter A,B: Below is an example with C=A+B, which makes Set 2 the highest value: Set 1: A=65, B=75, C=140; Set 2: A=50, B=100, C=150; Set 3: A=54, B=90, C=144; Set 4: A=72, B=72, C=144; Set 5: A=71, B=73...

In quantum mechanics, position ##\textbf{r}## and momentum ##\textbf{p}## are conjugate variables given their relationship via the Fourier transform. In transforming via the Legendre transform between Lagrangian and Hamiltonian mechanics, where ##f^*(\textbf{x}^*)=\sup[\langle \textbf{x}...

Let ##f(x,y,z)=x^2e^{-x-xy-xz}##, if ##x,y,z>0## and ##f(x,y,z)=0## otherwise. Are the continuous random variables ##x,y,z## independent or not? Intuitively they are not independent. I calculated the marginal density functions: ##f_x(x)=\iint_{\Omega} f(x,y,z) dydz=e^{-x}##...

I was overlooking page 47 of "The Physics of the Manhattan Project" 2.2 Critical Mass: Diffusion Theory, and author Bruce Cameron Reed reported that: Can anyone explain how Bruce Cameron Reed got from (2.18) to (2.19) I tried plugging ## N(r,t) = N(r) N(t) ## into (2.18) to get (2.19), but it...

For ##2\rightarrow 2## scattering with equal masses in the centre-of-mass frame, are all the four three-momenta equal to each other, or is it that the incoming three-momenta and the outgoing three-momenta sum to 0 separately?

In ##2-2## scattering, the Mandelstam variables ##s##, ##t## and ##u## encode the energy, momentum, and angles of particles in a scattering process in a Lorentz-invariant fashion. ##s=(p_{1}+p_{2})^{2}=(p_{3}+p_{4})^{2}## ##t=(p_{1}-p_{3})^{2}=(p_{2}-p_{4})^{2}##...

My instructor asked us to create a binary search tree in python that supports variables. i.e. the tree will have variables inside, and the user can get the values for those variables by looking for the name of that variable. I don't really know how to implement this. What I have so far: class...

Hey,for following code the 3rd loops i need to have 2 variables m and q .Could anyone help? for t=1:maxiterations toterror=0; for j=1:numfeature totslope=0; for i=1:m&&q=1:numfeature z=0; for jj=1:numfeature...

Hello, I can't figure out why the counter is not working, I have tried moving it before the cout line and after. I should only get two outputs but as of now, I get four. Here is what I have so far: #include <iostream> #include <string> using namespace std; int main() { int userInput1...

This sounds like a common application, but I didn't find a discussion of it. Simple case: I have 30 experimental values, and I have the full covariance matrix for the measurements (they are correlated). I am now interested in the sum of the first 5 measured values, the sum of the following 5...

The question I'm stuck on is: P = NKBT/(V-Nb) - aN2/(V2) -----> (1) Re-arrange variables in the Van Der Waals equation of state, Eq. (1), so that V always appears in the equation as V/(3Nb) and P appears as 27b2P/a. Then T should appear in the combination 27b kBT/(8a). Call these...

In a hydrogen atom, the wave function is written as R(r).Θ(θ).Φ(φ). But how is it separable when the electron is interacting with the nucleus?

Homework Statement [/B] I just got this formula from class : Q=mc(T2-T1) and got task to make 2 more formulas from this oneHomework Equations How do I make these formulas : T1=? and T2=? The Attempt at a Solution T2=Q:mc-T1 T1=-T1 T1=Q:mc+T2 Thanks for help

In the Bell type experiment is the hidden variable just a function of the state or a function of the state and the detector?

Homework Statement Let's say you have a number from [-2,4], with X(ζ) = -ζ + 4[/B] Find (a) P([-2,4]) and (b) P({X≤2}) Homework Equations {X = x} = {ζ ∈ S: X(ζ) =x } The Attempt at a Solution It looks like my sample space, S = [-2,4]. (a) For P([-2,4]) {-2 ≤ X ≤ 4} = {ζ ∈ S: -2 ≤ X(ζ) ≤...

Homework Statement I posted the entire question, but I am only conserned with part B. There was a circuit drawing on there but it is irrelevant for this part of the problem. One can solve it without knowing the circuit drawing. Homework Equations The application for Kirchoff's Voltage Law...

In General Relativity, the subscripts of G and T are u-ish and v. How do we say them?

Jesse Roe and Sal Khan talk about why we use letters in algebra Watch the next lesson: https://www.khanacademy.org/math/algebra/introduction-to-algebra/varia...

Our focus here is understanding that a variable is just a symbol that can represent different values in an expression. We got this. Just watch. Watch the nex...

Homework Statement I have this linear application: ##f : \mathbb {R}^4 \rightarrow \mathbb {R}^4## ##f((x, y, z, t)) = (-2x - y + t, 2x + y - t, -4x - 2y + 2t, 0)## and then I have this vector which I have to find the counter-image of it: ##\vec v = (-k, h - 2, k, h^2 - 4)## With ##h## and...

With the change of variables-method for a many-to-one transformation function Y = t(X), what's the logic behind summing the different densities for the roots of x = t^-1(y)? Probabilities should be ok to add, but densities? Also, is there no way to extend this method for many-to-many...