Condition Definition and 637 Threads

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...

We have all seen Ohms law, J=σE. This approximations makes sense in simple electric fields in which the charges are accelerated in parallel. However as I will demonstrate, this implies a few conditions on the charge density (ρ) associated with the current density (J). Now, from the continuity...

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...

...is that second partial derivatives are equal - how to prove it?

xy''+y'=-x y(1)=0, y(0) bounded (so the natural log, 1/x etc. terms drop out) homogeneous, cauchy euler: y=a+bx variation of parameters, and using the conditions gives y=1-x, I think (i tried this previously and I think this is what I got, I didnt write it down). Very different from what I...

I am simulating a series-parallel tank circuit in MATLAB. This means parallel resonance (inductor and capacitor in parallel) with an added capacitor in series. I would assume the resonance condition is w^2LC = 1 and the impedance is 1/(1/(z_L+z_R)+1/z_C1) + z_C2 with C1 being the parallel...

Consider the following: On a circle of radius 1, two points are marked: P1 and P2. Two lines are drawn from the center of the circle: one from the center to P1, the other from the center to P2. The angle between these two lines is \theta. One more line is drawn: from P1 directly...

hi can anyone teach me how to put Mur's ABC in my fortran code for 1d fdtd maxwell's equation as below !1d fdtd Simulation in free space subroutine fd1d01(f0,miu,delta,S,E0) implicit none double precision :: f0 !frequency double precision...

I have a problem how to select the boundary condition when i answer this deflection of beam. for example: the boundary condition is [x=o,y=0],[x=l,y=0],[x=o,dy/dx=o] and [x=L,dy/dx=0] given that EIdy/dx= Ax+wx^2/2 EIy= Ax^2/2+wx^3/6 anybody can tell me how to select this?

Homework Statement For a constant k, consider the function f(x) = x2 + kx + k2 - 2k - 4 Find the range of k for which f(x) = 0 has one solution between 0 and 1 and the other solution between 1 and 2Homework Equations quadratic formula discriminantThe Attempt at a Solution x2 + kx + k2 - 2k - 4...

Well i know that an inflection point is where the curve changes its concavity. But i don't really understand the conditions for it. It says that second derivative should be zero(but that's not sufficient). I understand this. Second derivative being zero is not sufficient, example is y =x^4...

Homework Statement Let a and b be real numbers a. The condition “a + b = 0” is ...for the condition “a = 0 and b = 0” b. The condition “a + b > 0” is ...for the condition “a > 0 and b > 0” c. The condition ab = 0 is .... for the condition a = b = 0 d. The proposition “ a + b > 2 and ab >...

A relation R on a set S is transitive: (x, y) and (y, x) ==> (x, z), for all pairs in R So if I cannot find (y, z) for (x, y) in R, does this mean the relation is considered transitive since the condition still holds true because False ==> False/True evaluates to True? Thanks.

I am trying to understand Ritz method, but i have troubles wtih determining the boundary conditions. After weak formulation of a differential equation how do we determine natural and essential b.c.? What are boundary terms, secondary variables, primary variables, natural and essential...

hey, i'm having trouble with this question, x y' - y = x2cosx the solution is y= xc + xsinx and we are asked to solve the equation in the following two cases, 1, y(0)=0 and 2, y(0) = 1 but applying these conditions to the general solution gives no information, in...

This is how Wikipedia summarizes the Poincaré Recurrence Theorem: This is wrong, isn't it? Don't you need to ensure the phase space is bounded, and isn't conservation of energy an insufficient justification for that? Like, imagine throwing two baseballs away from each other into infinite...

Homework Statement If two bodies one light and other heavy have equal kinetic energies, which one has a greater momentum. Homework Equations The Attempt at a Solution the way i am solving this problem is , i am assigning any arbitrary values to both masses and velocity of anyone...

so i have been studying chaotic system in class, and i just want to know if we change the initial conditions of a chaotic system can it become non-chaotic? I think yes because, chaotic system is sensitive to initial condition hence it would have an effect on the chaotic behavior. I'm I...

Homework Statement A Lagrangian for a particular physical system can be written as, L^{\prime }=\frac{m}{2}(a\dot{x}^{2}+2b\dot{x}\dot{y}+c\dot{y}^{2})-\frac{K% }{2}(ax^{2}+2bxy+cy^{2}) where a and b are arbitrary constants but subject to the condition that b2 -ac≠0.What are the...

what if Jacobi Method's condition did not meet? Homework Statement solve by Jacobi Method upto four decimal places 8x+y-z= 8 2x+y+9z= 12 x-8y+12z = 35 Homework Equations The Attempt at a Solution since the condition of convergence of jacobi method is |A1| > |B1|+|C1|...

Homework Statement Solve: dy/dy = y^3 given the initial condition y(0)=0 The Attempt at a Solution \int \frac{dy}{y^3} = \int dt \frac{-1}{2y^2} = t + c y^2 = \frac{-1}{2(t+c)} y = ± \sqrt{ \frac{1}{2(-t-c)}} This equation isn't going to support the initial condition, so can someone tell me...

Have you got a huge crush on someone before? You sure did, but have you got this feeling so strong that you thought she/he just had to be the one, and you'll never going to have the same feeling toward others ever again? I personally had this feeling for several times, and since it's...

Say i have the following function: f(x)= {-45 , x<0.5 45 , x≥0.5} where x\in R is a real variable in [0,1]. What would the condition number k(x) be for all values of x?

Hi, I am a student specializing in material, now i would like to stimulate secondary water of a Pressurized water reactor, could anybody tell me the water property entering the Steam Generator? Thanks!

Hello Everyone :) I have been facing a little difficulty when encountering such kind of problems . i have also written down my line of thinking and approach which i take to solve them. So, please try to give me the correct line of thinking while solving such problems: 1. If A is invertible...

Hi All, I was reading this paper the other day and I've been trying to find the numerical techniques its mentions but have been thus far unsuccessful. The authors simply state that is well know and straightforward, and they believe this so much that they don't even include a reference. Ok...

I have the following ODE system \begin{cases} x' = v \\ v' = v - \frac{v^3}{3} - x \\ x(0) = x_0 \\ v(0) = 0 \end{cases} I am asked to find x_0>0 such that the solution (x(t),v(t)) is periodic. Also, I need to find the period T of such solution. I don't know how to solve the...

Can the Kutta Joukowski condition be derived from the Navier Stokes equations in the limit of vanishing viskosity? Is there some literature on this point?

Consider a polynomial of the following type: A_n w^n + A_{n-1} w^{n-1}k + A_{n-2} w^{n-2} k^2 + ... + A_1 k^n =0 What are the general conditions on {A_i} in order for the roots w(k) to be EITHER real OR functions with even imaginary parts, Im[w[k]]=Im[w[-k]]? I would be interested in...

Hi guys, I'm solving a Poisson Equation with Mixed Boundary condition. But I have trouBle with that mixed BC in MATLAB. Anyone can help to fix? Thanks a lot! dT^2/dx^2+dT/dy^2=-Q(x,y)/k Rectangular domain (HxL), BC: Top: T(x,H)=Th, Left: dT/dx=0, Bottom: dT/dy=q, Right: dT/dx+B(T-Tinf)=0...

Hi, I've encountered a problem in deciding the condition in order for the equality to hold. Here is the problem: If $x\sqrt {1-y^2} + y \sqrt {1-x^2}=1$, prove that $x^2+y^2=1$ By using the Cauchy-Schwarz inequality, it's fairly easy to prove that $x\sqrt {1-y^2} + y \sqrt {1-x^2}\leq1$ Next...

$$ A_{\lambda}= \begin{pmatrix} -\mu\lambda k^2 - k^2 - s & i\tau k & i\tau k - i\beta k^3\\ i\lambda k & \lambda + Dk^2 & -\alpha k^2\\ i\lambda k & 0 & \lambda \end{pmatrix} $$ where $\lambda = \lambda(k^2)$ (this is confusing) is the growth rate and k is the wave number, and tau, mu, D...

Here I have my PDE: http://desmond.imageshack.us/Himg718/scaled.php?server=718&filename=pde.png&res=medium I have found the solution by using the method of characteristics two times, one for x<0 and the other for x>0. I have: U(x,y) = o for x<0 and U(x,y) = Uo(x-1)/(1+Uo*y) for x>0...