Condition Definition and 637 Threads

As homework, I shall show that the retarded scalar potential satisfîes the Lorentz gauge condition as well as the inhomogenous wave equation. We saw in class how to do it. But I was thinking about this, and it seems to me that it's redundant to prove both of those things. For, if the scalar...

Hello! I have some data points generated from an unknown distribution (say a 1D Gaussian for example) and I want to build a neural network able to approximate the underlaying distribution i.e. for any given ##x## as input to the neural network, I want the output to be as close as possible to...

I came across this basic limits question Ltx->0[(ln(1+X)-sin(X)+X2/2]/[Xtan(X)Sin(X)] The part before '/'(the one separated by ][ is numerator and the one after that is denominator The problem is if I substitute standard limits : (Ltx->0tan(X)/x=1 Ltx->0sin(X)/X=1 Ltx->0ln(1+X)/X=1) The...

Hi, I'd like to be clarified regarding the general natural/Neumann boundary condition for a PDE. 1. The natural boundary condition is generally defined as: (1) and can be expressed as, according to this resource: (2) But apparently, according to...

Hi everyone, I'm working through the boundary conditions and I could not figure out what to do with the last boundary condition (when z=L) I know that the values for K are: How so? 1. Homework Statement A hollow right angle cylinder of radius a and length l. The sides and bottom are...

Hi, I am taching myself Python 3.7.2. I think I get how 'While True' statements work, but I am having trouble making sense of this. The program runs, but I would like to understand well what is the condition being tested. (From 'Automate the Boring Stuff with Python) We have a dictionary of...

Homework Statement x(dy/dx) = 3y +x4cos(x), y(2pi)=0 Homework Equations N/A The Attempt at a Solution I've tried a couple different ways to make this separable, but you always carry over a 1/dx or 1/dy term and I can never fully separate this. I've also tried to do a Bernoulli differential...

Hi, initially I am aware of the fact that when slater condition holds, then dual optimum equals primal optimum in convex optimization. But if slater condition does not hold then dual gap exist. When we have nonlinear nonconvex optimization we apply convexification of constraints including...

I am trying to determine an outer boundary condition for the following PDE at ##r=r_m##: $$ \frac{\sigma_I}{r} \frac{\partial}{\partial r} \left(r \frac{\partial z(r,t)}{\partial r} \right)=\rho_D gz(r,t)-p(r,t)-4 \mu_T \frac{\partial^2z(r,t)}{\partial r^2} \frac{\partial z(r,t)}{\partial t} $$...

I wonder these equations can satisfy the Lorenz condition?? I mean.. how above equations can satisfy the divergence A + 1/c^2 dϕ/dt =0.

If all matter was at maximum density, would not the temperature have been extremely cold of the sum of all matter? temperature affects density I think.

A=[ 8147 6324 9575 9572 9058 0975 9649 4854 1270 2785 1576 8003 9134 5469 9706 1419]; D=diag([T^(-3)*L^2 T^(-3)*L^2 T^(-1)*L T^0*L^0]); I have matrix A whose first two columns are of the units T^3/L^2, third columns unit is T/L, and the last...

Hey! :o Let $\gamma\in \mathbb{R}$ and $A=\begin{pmatrix}1 & \gamma \\ 0 & 1\end{pmatrix}$. I want to calculate the condition numbers $\text{cond}_1(A) , \text{cond}_2(A) ,\text{cond}_{\infty}(A) $. The determinant of the matrix $A$ is equal to $\det (A)=1\neq 0$, so the matrix $A$ is...

I think only happens when gravity is zero. But as gravity of Earth won't be zero , we need to be somewhere between Earth and Moon so the g of moon and Earth cancel each other out . At this point we will have true weightlessness. Is this correct and enough?

Hi! I have a question related to boundary condition in a one dimensional beam subject to compression and traction efforts. In my class notes I have the following: If we consider a 1D beam of length L which is fixed at x=0 and subject to an effort F at x=0 we have the following boundary...

Hello, If I have a homgeneous linear differential equation like this one (or any other eq): $$y''(x)-y'(x)=0$$ And they give me these Dirichlet boundary conditions: $$y(0)=y(1)=0$$ Can I transform them into a mixed boundary conditions?: $$y(0)=y'(1)=0$$ I tried solving the equation, derivating...

https://en.m.wikipedia.org/wiki/Coma Can Surgery be done for a patient who is in Coma? If no, What is the medical reason ? Thanks & Regards, Prashant S Akerkar

Homework Statement [/B] An object of m-mass is to be thrown from xy-plane with an initial velocity ##\mathbf v_0 = v_0\mathbf e_z \, (v_0 > 0)## to a force field ##\mathbf F = -F_0 e^{-z/h}\mathbf e_z\,## , where ##F_0, h > 0## are constants. By what condition does the object return to...

i have keithley currnet source that i control with matlab, inside a loop, if i force stop the loop the device continue to output the last current. my question is can i add if condition that turn of the current source? for example if force stop fprintf(device, ':OUTP OFF') end

Homework Statement Verify ## f(z)= z^3-5iz+√7## satisfies cauchy riemann equations.Homework EquationsThe Attempt at a Solution seeking alternative method ## f(z)= (x^3+5y-3xy^2+√7)+ (3x^2y-y^3-5x)i## ##∂u/∂x = 3x^2-3y^2 = ∂v/∂y## ##∂v/∂x=6xy-5= -∂u/dy## hence satisfies.

Homework Statement [/B] Look at this graph.Is Instantaneous Acceleration=Average Acceleration here? Please explain your solution. What should be done to check whether Average Acceleration=Instantaneous Acceleration? Homework Equations Average Acceleration motion equations The Attempt at a...

In case of equation \alpha y''(x)+\beta y'(x)+\gamma y(x)=0 where ##\alpha>0##, ##\beta>0##, ##\gamma>0##, characteristic equation is \alpha r^2+\beta r+\gamma=0 and characteristic roots are r_{1,2}=\frac{-\beta \pm \sqrt{\beta^2-4\alpha \gamma}}{2 \alpha} If ## \beta^2<4\alpha \gamma## system...

Just got back from a conference where one of the invited speakers presented his work on using the Immersed Boundary method with Adaptive Mesh (to model cardiovascular flow): https://cims.nyu.edu/~griffith/ This summer, I have an undergrad modeling pulsatile flow in an elastic tube using the...

How to get overdamping condition of equation m\ddot{x}+\dot{x}+kx=0, Taking ##x=\mbox{e}^{\lambda t}##, we got \lambda_{1/2}=\frac{-1 \pm \sqrt{1-4mk}}{2m}. Is it possible from this ##\lambda## values to got overdamped condition? I found that if we have equation m \ddot{x}+\gamma \dot{x}=f(x)...

Hi, as I see Lipschitz condition is written as: |f(x)-f(x')| <= M*|x-x'| and minimum M is called Lipschitz constant. I would like to ask how the minimum M is found out? For instance for many convergence theorem include Lipschitz condition and no say something about value of M but how M is...

<Moderator's note: Moved from a technical forum and thus no template. Effort in post #3.> What is the condition of tangency of a line y=mx+c on parabola with vertex(h,k) ,say for parabola (y-k)2=4a(x-h)? I could only find the condition of tangency on standard form of parabola, in the internet...

Hello! (Wave) I want to solve the equation $u_t+u^2u_x=0$ with $u(x,0)=2+x$. I have tried the following: The characteristic curves for $u_t+u^2 u_x=0$ are the solutions of the ode $\frac{dx}{dt}=u^2$. We have that $\frac{d}{dt}u(x(t),t)=0$, implying that $u(x(t),t)=c$. The characteristic...

A 4-cyilinder engine with a staggering 432,000 miles on it is actually in surprising good condition.

Homework Statement >There are three vector $$ \vec a ,\vec b, \vec c$$ in three-dimensional real vector space, and the inner product between them $$\vec a . \vec a=\vec b.\vec b=\vec a.\vec c=1, \vec a.\vec b=0, \vec c.\vec c=4 $$ When setting $$x = \vec b.\vec c$$ , (dot here means dot...

Homework Statement I am confused on how it's using the surrounding temperature minus the surface temperature as its the other way around in the Newton's law of cooling, Doing that would change the sign of convection right? I don't see the reason to do that, since if left side is hotter, then...

Homework Statement [/B]Homework Equations shear bending diagram The Attempt at a Solution May I ask for supports like these, if shear force V= 0 or not when x=L? From the shear diagram, it is a shape increase from -0.5P to 0 there. As the shear go back to zero is owing to the reaction force...

Consider a place where General Relativity is the appropriate theory, but suppose we consider just a tiny volume, so to speak, of space-time.. which is to say we are observing a phenomenum for a very short amount of time and the "laboratory" is also very small in space. Under these circumstances...

Homework Statement a)Helium enters a closed system as a flow of compressed gas at a temperature of 14 K and at pressure p (enthalpy conserved). A fraction α emerges as liquid and the rest as gas at 14 K, both at atmospheric pressure p0. Find an expression for α in terms of the enthalpy H(p) of...

Hello, I read article how to check battery condition appropriately (e.g. car battery). (Link: https://www.allaboutcircuits.com/textbook/direct-current/chpt-11/battery-ratings/ ) It's written that: in order to get better results, one must check under load. I'm not EE - I study physics and...

Homework Statement |x-2| < a is a necessary condition for x^2 -3x -10 < 10 . What is the range value of a? |x-2| < a is a sufficient condition for x^2 -3x -10 < 10. What is the range value of a?[/B] The options are a>= 4 a>=3 0<a<=2 0<a<=3 0<a<=5 The Attempt at a Solution Range of x for x^2...

I want a way to map natural numbers to possible values of set A. It would also be helpful if you could tell me how many possible values are for set A(it depends of k). All that is known about set A is: Non of set A elements is subset to another element of A, but all elements of set A are proper...

The question: Show that the Lorentz condition ∂µAµ =0 is expressed as d∗ A =0. Where A is the four-potential and * is the Hodge star, d is the exterior differentiation. In four-dimensional space, we know that the Hodge star of one-forms are the followings. 3. My attempt Since the four...

Homework Statement Homework Equations For lag compensator pole is dominating For lead compensator zero is dominating The Attempt at a Solution So for lag compensator: P1 is closer to origin than Z1, so mod of P1 < mod of Z1 So P1 > Z1 (since the poles and zeroes are negative) And for lead...

I want to make a wire grid surface that transmits no light. For that I wanted to use quarter-circular arc wires. My question is what dimensions would I need to apply to the wires, would an arc with radius = wavelength of incident light be sufficient (since then it is the size of a wavelength in...

Hey, I'm trying to adapt the Bragg condition for the David-Germer experiment, so I can then use their experimental results to show that the measured wavelength is compatible to the wavelength theorized by De Broglie. However I'm having issue with the calculation, any help would be much...

Hello Guys, We haven't yet covered on how to solve 2nd order equation in class however we have this assignment given to us. Any tips would be appreciated for these 2 little problems. 1. Homework Statement We have this initial Equation: d2y/dt2−7dy/dt+ky=0, and we need to find the values of k...

Homework Statement Homework Equations I think both A and C are right answers. The Attempt at a Solution 1 condition is pu Z(leakage) must be same on respective KVA rating for load sharing. Now: Zpu = Z(actual)/Z(base) ----equation 1 For Zpu of both transformers to be same, the right side...

Homework Statement I have an infinitely long cylinder of a dielectric material, surrounded by another dielectric material and coated with graphene which has surface conductivity \sigma, implying it has a superficial current. The sheet of graphene is very thin, and the dielectrics are asumed to...

Hey! :o I want to prove the following relations of condition number: $\operatorname{cond}(\alpha A)=\operatorname{cond}(A)$. The matrixnorm is submultiplicativ. $\operatorname{cond}_2(U)=1$ if $U$ is an orthogonal matrix. $\operatorname{cond}_2(UA)=\operatorname{cond}_2(A)$, $U$ is...

Hi PF! Denote the velocity of a fluid ##\vec u## and define a potential ##\vec u = -\nabla \phi##. Let ##\hat n ## be an outward-oriented surface normal to a solid boundary. I would express no penetration at the boundary as $$ u \cdot \hat n = 0 \implies \nabla \phi \cdot \hat n = 0.$$ However...

Hi, I was wondering what is the physical meaning of these integrals: \begin{equation} \int_{-\infty}^{\infty} \psi \psi^* dx = 0 \end{equation}\begin{equation} \int_{-\infty}^{\infty} \psi x \psi^* dx = 0 \end{equation} \begin{equation} \int_{-\infty}^{\infty} \psi p \psi^* dx = NA...

Homework Statement I am having an issue, not with the maths but with the boundary conditions for this question. A bar 10 cm long with insulated sides, is initially at ##100 ^\circ##. Starting at ##t=0## Find the temperature distribution in the bar at time t. The heat flow equation is...

Hi, I am trying to solve an ODE, however, the initial conditions are not known. From PDE examples, which are quite different, I see that some examples have initial conditions given by functions, and not by constants, i.e:: y(0) = x^2 I may have not modeled the problem correctly yet, however, I...

Hi PF! Given a fluid/fluid interface ##F(t,x,y,z) = 0## the kinematic boundary condition states ##DF/Dt = 0##. Given ##y=F## the text states ##v = \partial_tF+u\partial_xF+w\partial_zF##. How is this possible? I thought ##DF/Dt = 0 = \partial_tF+u\partial_xF+v\partial_yF+w\partial_zF## and...

Homework Statement I'm trying to keep the post brief and will post more info if needed. But I am trying to understand how the value of two "A" constants were found. This is from Griffiths Electrodynamics. In this part of the problem, I am given a boundary condition that is a function of theta...