Condition Definition and 587 Threads

55% of the US rivers in "poor" condition A couple months old, but very troubling. How far do we let it slide? http://yosemite.epa.gov/opa/admpress.nsf/0/26A31559BB37A7D285257B3A00589DDF

Hi there! in a recent lecture on fock space, i was given the brillouin condition for two-particle operators:- <\Phi_{0}|a^{†}_{a}a_{r}h|\Phi_{0}> = \frac{1}{2}\sum\sum<\Phi_{0}|a^{†}_{a}a_{r}a^{†}_{\lambda}a^{†}_{\mu}a_{\lambda'}a_{\mu'}|\Phi_{0}><\lambda\mu|g|\mu'\lambda'> =...

Hello! Let a plane wave propagate towards the -y direction. It is normally incident upon the plane (x,z) (whose normal unit vector is the y-direction unit vector, \mathbf{\hat{u}}_y): the plane represents the interface between the free space (in y > 0) and a general lossy medium (in y < 0). We...

Homework Statement hey, i have a heat equation question which asks to solve for u(x,t) given that u(0,t)=Q_0 + ΔQsin(ωt).Homework Equations d_xx u = k d_t u u(0,t)=Q_0 + ΔQsin(ωt) The Attempt at a Solution so you can solve the equation pretty easily with separation of variables, i.e...

what is physical meaning of Lorentz gauge condition in classical electrodynamics??

could you give an example where the Lipschitz condition fails,like when there is a periodic forcing function? I'm thinking the Lipschitz condition would fail for a non-autonomous differential system because period-2 orbits exist for 2D non-autonomous continuous dynamical systems,which means the...

if I have a functional with a Lagrangian L(t,x(t),y(t),x'(t),y'(t)), meaning two functions x and y of one parameter t. And want to solve the minimization problem $$ \int_0^t L dt $$ . Then I get necessary conditions to find extrema by getting the two Euler Lagrange equation $$ \frac{\partial...

Homework Statement Massless and inextensible string is wrapped around the periphery of a homogeneous cylinder of radius R = 0.5 m and mass m = 2 kg. The string is pulled straight away from the upper part of the periphery of the cylinder, without relative slipping. The cylinder moves on a...

I seem to have a couple of contradictory statements of what a countable set is defined to be: In my textbook I have: 'Let E be a set. E is said to be countable if and only if there exists a 1-1 function which takes ##\mathbb{N}## onto E.' This implies to me that that there has to exist a...

What does it mean when we say that two functions are orthogonal (the physical meaning, not the mathematical one)? I tried to search for the physical meaning and from what I read, it means that the two states are mutually exclusive. Can anyone elaborate more on this? Why do we impose...

Dear experts, I really wonder how to extract the equation of stats w=\frac P \rho from the Friedmann equations and how one can see that dark energy needs to have w<-\frac13 and why does w<-1 violate the null energy condition. Thanks in advance, madster

Here is the question: Here is a link to the question: No idea how to solve this 2nd order IVP. Please help? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Hi, I am trying to solve a Poisson equation \nabla^2 \phi = f in \Omega, with Dirichlet boundary condition \phi = 0 on \partial \Omega. My problem is that I am trying to understand the condition under which a solution exists. All the text I consulted says that the problem is solvable. However...

Hey there guys! So we know that in linearized GR we work with small perturbations \gamma _{ab} of the background flat minkowski metric. In deriving the linearized field equations the quantity \bar{\gamma _{ab}} = \gamma _{ab} - \frac{1}{2}\eta _{ab}\gamma is usually defined, where \gamma =...

Homework Statement Find a solution of the IVP \frac{dy}{dt} = t(1-y2)\frac{1}{2} and y(0)=0 (*) other than y(t) = 1. Does this violate the uniqueness part of the Existence/Uniqueness Theorem. Explain. Homework Equations Initial Value Problem \frac{dy}{dt}=f(t,y) y(t0)=y0 has a...

Hello all, I would like to express the following as an equation, but don't know the nomenclature. 'The point at which a condition is true 95% of the time' ie. I have a function, f(x) which returns some value in the presence of random and uncharicterizable noise. I run this 1000 times. I...

Homework Statement What should be the condition for a compound to be meso? Homework Equations The Attempt at a Solution I know that it should possesses a plane of symmetry. But what if it contains a point of symmetry or alternate axis of symmetry instead of plane. Will the...

We used to apply periodic boundary condition to simulate an infinite system. What will happen if the interactions between atoms do not drop to zero even when they are infinitely far away? Is the periodic boundary still valid? How can I prove the periodic boundary condition is valid or not? thanks.

Hi I was reading Anderson's Modern Compressible Flow and two of his equations were confusing. I attached the relevant pages on this post. He defined two conditions or state the sonic and stagnation state used to define flows. The sonic state was defined as an adiabatic transition of the...

Hello all, I am new to this forum but am glad I found it, I have a quick question about condition numbers and order of operations. Given a symmetric positive-definitive matrix with a initial condition number α, is it possible to improve that condition number with a different access...

Hi. I'm trying to determine the CFL condition for the fourth-order leapfrog scheme. I'm finding 2 as what's published, which does not match what I'm getting. Does anyone know where I can find a von Neumann (or Fourier) stability analysis of the leapfrog (2,4) scheme (so I can compare my work)...

I am trying to understand the derivation of Snell's law using Maxwell's equation and got stuck. My textbook says that "the E field that is tangent to the interface must be continuous" in order to consider refraction of light. If it were static E field I understand this is true because in...

Homework Statement I am trying to solve this PDE with variable boundary condition, and I want to use combination method. But I have problem with the second boundary condition, which is not transformed to the new variable. Can you please give me some advise? Homework Equations (∂^2 T)/(∂x^2...

I am confused by the concept of stability and condition. As I understand it, condition is defined by how much the output changes when the input changes. But why is it linked to the problem and not the algorithm? What if I have two algorithms that calculate the same thing but in a completely...

Hi, Homework Statement What would be the/a condition on vectors in K so that V=W, where V is a vector space which K={v1,v2,v3,v4} spans, and W is a subspace of V defined thus: W=Sp{v1+v2,v2+v3,v3+v4,v4+v1} Homework Equations The Attempt at a Solution I believe V would be equal...

Homework Statement Hopefully no one will mind me posting this as an image. But here it is in tex: Using separation of variables, find the function u(x,t), defined for 0\leq x\leq 4\pi and t\geq 0, which satisfies the following conditions: \frac{\partial^2 u}{\partial...

hello, This is my first post (attempt 2) Question. What is the probability of a theory being correct or valid if it was made under the following circumstances? Conditions: Very little knowledge of science, just a curious mind. Not looking at knowledge that is known and came...

I am toying around with connecting a 236PC 15GW pressure sensor to my arduino board. I am supplying nearly 10 volts to the Sensor and can get +- .1V readings from some simple tests. How do I condition these two lines that give +- .1V to range from 0-5 Volts for the Arduino analog pins.

I'm having trouble finding out how to set up Neumann (or, rather, "Robin") boundary conditions for a diffusion-type PDE. More specifically, I have a scalar function f(\boldsymbol{x}, t) where \boldsymbol{x} is n-dimensional vector space with some boundary region defined by A(\boldsymbol{x})=0...

One of the boundary conditions for a homogeneous uniform waveguide is \frac{\partial H_z}{\partial n}=0. What does this mean physically?

given a compact, orientable, n-dim. Riemann manifold, what is a sufficient condition for globally vanishing curvature i.e. global flatness? I can get necessary conditions from the generalized Gauss-Bonnet theorem, but not sufficient ones thanks in advance

Homework Statement The condition that x^4+ax^3+bx^2+cx+d is a perfect square, is Homework Equations The Attempt at a Solution If the above polynomial will be a perfect square then it can be represented as (x-\alpha)^2(x-\beta)^2 where α and β are the roots of it.This means that two...

Let n be a positive integer and a be a positive divisor of n. Is there any general formula to find the number of positive divisors b of n such that (a,b)=1 ?.

BOUNDARY CONDITION PROBLEM I have came up with matrix for numerical solution for a problem where chemical is introduced to channel domain, concentration equation: δc/δt=D*((δ^2c)/(δx^2))-kc assuming boundary conditions for c(x,t) as : c(0,t)=1, c(a,t)=0. Where a is channel's length...

Homework Statement BOUNDARY CONDITION PROBLEM I have came up with matrix for numerical solution for a problem where chemical is introduced to channel domain, concentration equation: δc/δt=D*((δ^2c)/(δx^2))-kc assuming boundary conditions for c(x,t) as : c(0,t)=1, c(a,t)=0. Where a is...

Homework Statement Let there be two discrete random variables: X \in \lbrace 1,2,3,4,5,6,7,8,9,10 \rbrace \quad \text{where } P[X] \text{ is uniformly distributed over the sample space of } X \text{.} B = \left\lbrace \begin{array}{cl} 1 & \text{if} \quad X>4 \\ 0 &...

How to arrive at Lorenz gauge condition? http://en.wikipedia.org/wiki/Lorenz_gauge_condition I know it's used to simplify the 2 partial differential equations of the potentials, but why can we put such a restriction on the potentials? Doesn't that restriction restrict the possible electrical...

Homework Statement Do all the preimages on X need to have a (and of course I know only one but) image in Y for the f:x->y to be injective? IS THE FOLLOWING FUNCTION INJECTIVE SINCE ONE ELEMENT OF FIRST DOES NOT HAVE ANY IMAGE Homework Equations The Attempt at a Solution Thank You.

Homework Statement Consider the transformation from the variables (q,p) to (Q,P) by virtue of q = q(Q,P), p = p(Q,P) and H(q,p,t) = H(Q,P,t). Show that the equations of motion for Q,P are: \partialH/\partialQ = -JDdP/dt \partialH/\partialP = JDdQ/dt where JD is the Jacobian determinant...

Homework Statement By trial and error, find a solution of the diffusion equation du/dt = d^2u / dx^2 with the initial condition u(x, 0) = x^2. Homework Equations The Attempt at a Solution Given the initial condition, I tried finding a solution at the steady state (du/dt=0)...

Hello people. I'm actually a humanities scholar but who has retained his interest in maths from high school. Well curiously, in relation to one of my projects I'm investigating the properties of third order Beziers. Given the two nodes and control points of a third order Bezier, I needed to...

I am looking for shear modulus (G) for Nitronic 50 or XM-19 High strength hot rolled condition UNS - S20910 and ASTM A276-10 it is surprising for me that material standards like ASME or ASTM does not provide shear modulus data..? even checked "http://www.keytometals.com" and...

Hi, I am looking at a problem where I have two electrically conducting fluids where charge accrues on the interface, I know that one of the equations that I have to use comes straight from the usual boundary conditions for the normal component of the electric field, the other one apparent comes...

Homework Statement A one-dimensional wave function associated with a localized particle can be written as \varphi (x) = \begin{cases} 1- \frac{x^2}{8}, & \text{if } 0<x<4, \\ C_1 - \frac{C_2}{x^2}, & \text{if} \,x \geq 4. \end{cases} Determine C_1 and C_2 for which this wave...

in electromagnetics , considering boundary conditions of dielectric and perfect conductor , inside conductor E = 0. So, there should not be any time varying magnetic field. But in many books i have seen that inside conductor normal component of B is 0 because there is no time varying magnetic...

Hey Guys, WOW, so I am really into a physics forum! :D Well, a brief introduction first so you can understand my case: I am student who just finished high school who wanted to get into medicine school but didn't get enough grades to it (we have it by percentages and I was .75% lower than...

I've been looking over the quantum gravity papers that were posted on another thread, and I've got a question about Berman's calculations I'm not seeing a cosmological constant in that paper, and the identities look to me as if they won't work if you add "dark energy". Is that the case?

Good afternoon, I am a PhD student in motions of damaged ships. I am trying to find a solution of Laplace equation inside a box with a set of boundary conditions such that: ∇2\phi=0 \phix=1 when x=-A and x=A \phiy=0 when y=-B and y=B \phiz=0 when z=Ztop and z=Zbot I have tried...

I have been looking at an example of a initial value condition problem in my notes and don't really understand where the solution came from. Here is the question: Let z(x,y)= 2x+ g(xy) and add the initial value conditon, z= x on the line y=1. Find the general solution of the initial value...

Here's an interesting question--I've asked some faculty members around here and "off the top of their head" none of them knows the answer. My gut says "yes", but my gut sucks at math. So here's the statement: Suppose we have a function f:\mathbb{R}^2\to\mathbb{R}, with the property that for...