Variables Definition and 1000 Threads

Within a cylinder with length ##\tau \in [0,2\pi]##, radius ##\rho \in [0,1]## and angular range ##\phi \in [0,2\pi]##, we have the following equation for the dynamics of a variable ##K##: $$\left( - \frac{1}{\cosh^{2} \rho}\frac{\partial^{2}}{\partial\tau^{2}} + (\tanh\rho +...

Homework Statement Solve the system of equations: { (1/2)x-y=3 and x=6+2y Homework Equations NA The Attempt at a Solution The solution is 3=3, which is an identity, which means that there is an infinite amount of solutions to the system. Here's where my question lies (asked my teacher but...

Homework Statement Given ##f_{X,Y}(x,y)=2e^{-x}e^{-y}\ ;\ 0<x<y\ ;\ y>0##, The following theorem given in my book (Larsen and Marx) doesn't appear to hold. Homework Equations Definition ##X## and ##Y## are independent if for every interval ##A## and ##B##, ##P(X\in A \land Y\in B) = P(X\in...

Homework Statement Homework Equations If i solve the wave equation using separation of variable and laplace tranform. Will i get the same answer ? The Attempt at a Solution

Suppose that f is analytic on the disc $\vert{z}\vert<1$ and satisfies $\vert{f(z)}\vert\le{M}$ if $\vert{z}\vert<1$. If $f(\alpha)=0$ for some $\alpha, \vert{\alpha}\vert<1$. Show that, $$\vert{f(z)}\vert\le{M\vert{\frac{z-\alpha}{1-\overline{\alpha}z}}\vert}$$ What I have: Let...

I'd like this issue clarified I understand that a full nonpertubative quantization of a yang mills gauge theory in 4D is unavailable. is Dirac quantization of classical theory of gravity e.g GR rewritten Ashtekar Variables Variables or some variation of the idea, a viable approach to a...

Suppose the polynomial p has all its zeros in the closed half-plane $Re w\le0$, and any zeros that lie on the imaginary axis are of order one. $$p(z)=det(zI-A),$$ where I is the n x n identity matrix. Show that any solution of the system $$\dot{x}=Ax+b$$ remains bounded as $t\to{\infty}$...

Hi! So it's new for me to do physics lab that way and my teacher is asking us to define the independant, dependant and controlled variables of every lab we're doing. I'm not quite sure what they refer to... For example, in a moment of inertia lab (see picture), I am asked this question. The...

Homework Statement I know that k*u^3=F And I have data of when you change Z , so for example if Z is 3, then u is 5 and F is 3. And i need to get the function with only Z and F without u, how do I do it?The Attempt at a Solution I made a function through excel with Z and F but because U also...

We define the Legendre polynomial $P_n$ by $$P_n (z)=\frac{1}{2^nn!}\frac{d^n}{dz^n}(z^2-1)^n$$ Let $\omega$ be a smooth simple closed curve around z. Show that $$P_n (z)=\frac{1}{2i\pi}\frac{1}{2^n}\int_\omega\frac{(w^2-1)^n}{(w-z)^{n+1}}dw$$ What I have: We know $(w^2-1)^n$ is analytic on...

Studying for my complex analysis final. I think this should be a simple question but wanted some clarification. "Extend the formula $$\frac{1}{2i\pi} \int_\omega \frac{h'(z)}{h(z)}\, dz = \sum_{j=1}^N n_j - \sum_{k=1}^M m_k$$ to prove the following. Let $g$ be analytic on a domain...

Homework Statement I have a strip of foil with an area of 10 square cm and a mass of .561392 grams. The length of the foil is 5 cm and the width is 2 cm. The foil is hanging from a pivot point at the very top. The foil rotates 17 degrees backwards from where it started. The foil is in a sealed...

I'm trying to fit a model curve to some data by performing a chi square minimisation wrt three parameters a,b and NN. The trouble I am having is that the variables with which I want to minimise the chi square with respect to appear in an integral. I attach the code I am working with...

Homework Statement I am trying to solve the given wave equation using separation of variables, u_{tt} - 4u_{xx} = 4 for 0 < x < 2 and t > 0 (BC) u(0,t) = 0 , u(2,t) = -2, for t>0 (IC) u(x,0)=x-x^2 , u_t(x,0)=0 for 0\leq x \leq2 Homework Equations We are told we will need to use, x =...

If it is true that the different QM interpretations all make the same experimental predictions, because they all use the same underlying math of QM. That's why they are called "interpretations" instead of "different theories" then it is a fool's errand to keep searching for interpretations to...

Hey! :o Let $D$ be the space in the first quadrant of the $xy$-plane that is defined by the inequality $x^{\frac{3}{2}}+y^{\frac{3}{2}} \leq \alpha^{\frac{3}{2}}$ with $\alpha>0$. I want to transform $\iint_D f(x,y) dx dy$ to an integral on the triangle $E$ of the $uv$-plane that is defined by...

I'd like to start off by saying I'm just a 52 yo interested layman with no back ground in physics so apologize up front for my ignorance! I understand the basic principle behind Bell's Inequality and how it disproves that when measuring the different spin states of a particle, the particle...

Homework Statement Boundary conditions are i) V=0 when y=0 ii) V=0 when y=a iii) V=V0(y) when x=0 iv) V=0 when x app infinity. I understand and follow this problem (separating vars and eliminated constants) until the potential is found to be V(x,y) = Ce^(-kx)*sin(ky) Condition ii...

I am working with multiple regression with two independent variables, and interaction between them. the expression is: y = b1x1 + b2x2 and b3x1x2 The question is: does one center both independent variables at the same time, when checking for the significance of the effect of the independent...

Hi, I am dealing with an equality of the form: f(x)=g(y,z) and I need to compute ##dx##. Is the following relation correct? dx={(\frac{\partial f}{\partial x})}^{-1}( \frac{\partial g}{\partial y}dy + \frac{\partial g}{\partial z}dz ) Thank you in advance.

If a quadratic equation of two variables represents a conic section (planar intersection of a cone), then does a quadratic equation of three variables represent the complete cone? @fresh_42 @FactChecker @WWGD

Homework Statement Homework EquationsThe Attempt at a Solution The probability that ##X_1 ## is between ## X_1 ## and ## X_1 + dX_1 ## and ##X_2 ## is between ## X_2 ## and ## X_2 + dX_2 ## and so on till the nth variable is dP(##X_1, X_2, ..., X_n) = p ( X_1) p( x_2) p(X_3)...p(X_n) dX_1...

Suppose $f$ is a polynomial in $n$ variables, of degree $ \le n − 1$, ($n = 2, 3, 4 ...$ ).Prove the identity: \[\sum (-1)^{\epsilon_1+\epsilon_2+\epsilon_3+ ...+\epsilon_n}f(\epsilon_1,\epsilon_2,\epsilon_3,...,\epsilon_n) = 0\;\;\;\;\; (1)\] where $\epsilon_i$ is either $0$ or $1$, and the...

Homework Statement An experiment was conducted to determine the relationship between metre-stick projection from a table (L) on the vertical depression of the free end (y). Using the collected data, graphs had to be plotted until a linear relation was found, and the equation of the line had to...

Urs and Mitchel aren't fans of polymer quantization used in LQG to quantize Ashketer variables, they regard it as unphysical and unconnected to the rest of physics. LQG based on "polymer quantization" and "generalized connection" is a dead end. fair enough. is there a procedure to...

Hello, I haven't found any program that can be used to perform separation of variables on difficult PDEs. Is there such a method somewhere?

Homework Statement A car starts from rest at a stop sign. It accelerates at 4.3 m/s2 for 6.0 s , coasts for 2.5 s , and then slows down at a rate of 2.5 m/s2 for the next stop sign. How far are the stops signs apart. x0=0m v0=0m/s t0=0s I put 0 because it says a car stars from rest. Not sure if...

Homework Statement w is a function of three variables x, y, and z. Prove that \frac{\partial w}{\partial x}_{y,z} = \frac{1}{\frac{\partial x}{\partial w}}_{y,z} Homework EquationsThe Attempt at a Solution w=w(x,y,z) dx = \frac{\partial w}{\partial x}_{y,z}dx +\frac{\partial w}{\partial...

Hi. I was wondering if it is possible to apply separation of variables for a function of space and time obeying a non homogeneous differential equation. In particular, the heat equation: ##\displaystyle \frac{\partial \Phi(\mathbf{r},t)}{\partial t}-\nabla \cdot \left [ \kappa(\mathbf{r})...

Homework Statement The problem that I am having stems from a problem given in the following way:[/B] "a)Show that for a gas, the mean free path ##\lambda## between collisions is related to the mean distance between nearest neighbors ##r## by the approximate relation ##\lambda \approx...

In our study, we measured the seasonal abundance of selected genes from two sites. We want to make a comparison between the seasonal trends between the genes (i.e. which genes had similar trends and which didn't). What would be the best statistical analysis for this purpose? Thanks!

Hi there. I am willing to plot a function of three space variables plus time, let's say ##\phi(x,y,z,t)##. The idea is to plot the 3D function for each time, i.e. evolving in time. As I have three independent variables, corresponding to the three Cartesian coordinates, the function is actually a...

I'm not sure if this belongs in the Basic area or here. I have a dataset with variables that I think it makes sense to make them into dummy variables (some are categories, some are ordinal). I've been asked to do bivariate tests and regression. I don't understand how I can do bivariate...

Hi All, I need to do some work on Factor Analysis on Non-Continuous variables. I have searched the web, but found nothing of much substance. I would appreciate references on helpful sources on it. Thanks.

Hi. I wanted to learn more on this topic, but it seems all the available resources in the internet points to using R, SPSS, MINITAB or EXCEL. Is there an established numerical method for such cases? I am aware of the Levenberg-Marquardt, Gauss-Newton and such methods for nonlinear regression on...

Evaluate ∫∫∫ over E, where E is the solid enclosed by the ellipsoid x^2/a^2 + y^2/b^2 + z^2/c^2 = 1. Use the transformation x = au, y = bv, z = cw. I decided to replace x with au, y with bv and z with cw in the ellipsoid. After simplifying, I got u^2 + v^2 + w^2 = 1. What is the next step...

Let S S = double integrals S S x^2 dA; where R is the region bounded by the ellipse 9x^2 + 4y^2 = 36. The given transformation is x = 2u, y = 3v I decided to change the given ellipse to a circle centered at the origin. 9x^2 + 4y^2 = 36 I divided across by 36. x^2/4 + y^2/9 = 1 I replaced...

I've solving some separation of variables exercises, and I have a doubt when it comes to the Laplacian $$ u_{xx} +u_{yy} =0 $$ I usually have a rectangle as boundary conditions, so I use the principe of superposition and arrive to $$ \dfrac{X''(x)}{X(x)} = - \dfrac{Y''(y)}{Y(y)} = - \lambda $$...

I'm working through a proof in my differential equations book, but I think I'm hung up on a basic calculus derivative. If we have a function ##f(x,y)## and we substitute ##v=\frac{y}{x}## , rearrange to get ##y=vx##, and then take the derivative, supposedly by the product rule we get...

Homework Statement Hi, I am looking at this question: With this (part of ) solution: Homework EquationsThe Attempt at a Solution I follow up to the last line- I do not understand here how we have simply taken the ##1/t^{\alpha m + \alpha}## outside of the derivative...

Homework Statement I want to generate two random variables, one is normally distributed N ~N(10, 25) and the other one, E, is exponentially distributed with mean 1. I was not given a particular correlation coefficient.Homework Equations normal cdf, exponential cdf, inverse transform method...

I'm working through the problems in Mary Boas's Mathematical Methods text. Here's how she began solving one problem... "We take differentials of the equation 1/i + 1/o = 1/f (f=constant) to get -di/i2 - do/o2 = 0." So on the left side the first term was differentiated with respect to i and...

So I've been reading David Bohm's original paper on the alternative interpretation of quantum mechanics in terms of hidden variables, just out of interest. In the 4th section he presents a complex function ψ in terms of R and S, and then (using the time dependent schrodinger equation, TISE)...

Given a convolution: \begin{equation} \begin{split} g(x) * h(x) &\doteq \int_{-\infty}^{\infty} g(z) h(x-z) dz \end{split} \end{equation} Do ##z## and ##x## have to be independent? For example, can one set ##x=z+y## such that: \begin{equation} \begin{split} \int_{-\infty}^{\infty} g(z)...

Homework Statement In a 2-body scattering event, A + B → C + D, it is convenient to introduce the Mandelstam variables, s ≡ −(PA + PB)2 , t ≡ −(PA − PC) 2 , u ≡ −(PA − PD) 2 , where PA,...,D are the 4-momenta of the particles A, . . . , D respectively, (· · ·) 2 = (· · ·) · (· · ·) denotes a...

Hello! (Wave) I want to check if the method of separation of variables can be used for the replacement of the following given partial differential equations from a pair of ordinary differential equations. If so, I want to find the equations.- $[p(x) u_x]_x-r(x) u_{tt}=0$ - $u_{xx}+(x+y)...

Homework Statement [/B] What is directly given in the problem: Converging lens with f=1.43m Hi = 2m Homework Equations Hi/Ho = di/do M = Hi/Ho = di/do 1/f = 1/do + 1/di The Attempt at a Solution Ho = 2m * 20 = 40m Not sure how I can get do from this. All of the equations seem to need di.

Hello. How do I solve this equation without killing the k(y) term: I managed to derive an analytical solution for this one. I intend to run the numerical solution via Runge-Kutta but I can't stop myself from killing the k(y) term. I'm starting to think I'm doing something wrong... It goes...

Homework Statement [/B] https://www.physicsforums.com/attachments/screen-shot-2017-04-15-at-12-28-52-pm-png.194886/?temp_hash=4939cc24bd25e6adfbe75458bec6d011 Homework Equations [/B] P(X∈A,Y∈B)=P(X∈A)×P(Y∈B) The Attempt at a Solution If X and Y are independent then: P(X∈A,Y∈B)=P(X∈A)×P(Y∈B)...

Would hidden variables still be consistent with QM if we abandon the concept of locality? For example, entangle particles could be connected via Einstein-Rosen bridges and any measurement would cause this bridge to collapse.