Condition Definition and 587 Threads

Hi All , what I am trying to do is, after getting so many solution I just want to print only the intger solution: For[n = 0, n ≤ 10, n++ Do[Print[{n, (n - Sqrt[Sqrt[ 2]Sqrt[3n^2 - 9n + 8] + 3n - 4])/2, OTHER SOLUTION, (n - Sqrt[-Sqrt[2]...

http://www.math.northwestern.edu/~clark/285/2006-07/handouts/lin-constraint.pdf It's actually proof of finding sign definiteness of quadratic form with linear constraints with sign of submatrices of bordered hessian. The proof is from page 2~page 3. I have 2 questions: 1. From about...

Hi, Can anybody tell me the difference between a Cauchy Boundary condition and a combined Dirichlet/Neumann Boundary Condition for PDEs? The reason why I'm asking is because Cauchy boundary conditions can be used to solve Open Hyperbolic PDEs, whereas Dirichlet/Neumann can only be used to...

What is the condition for the continuous time signal x(t) to be periodic if it is the linear combination of n periodic signals. where x(t) = a_{1}x_{1}(t)+a_{2}x_{2}(t)+a_{3}x_{3}(t)+......a_{n}x_{n}(t) where x_{i}(t) is periodic with fundamental period T_{i} \forall i, where i \in...

Faraday's law has an integral and a differential version: curl \mathbf{E} = - \frac{\partial \mathbf{B}}{\partial t} \mbox{ and } \oint_{C} \mathbf{E} \cdot d \mathbf{l}=- \frac{d}{dt} \int_{S} \mathbf{B} \cdot d \mathbf{S} When I use the differential version I always have a constant of...

What condition defines a principal stress? thx

Hi I am studying magnetic vector potential from Griffiths book. The eq 5.76 in his book gives the boundary condition for the magnetic vector potential. \frac{\partial \vec{A_2} }{\partial n}- \frac{\partial \vec{A_1} }{\partial n}=-\mu_o \vec{K} where n is the vector perpendicular to the...

Can someone state clearly a sufficient condition for a 4-tuple of quantities to be a four vector? For instance I saw the naive definition of speed four vector is not but I couldn't really understand when a 4-tuple is or is NOT a four vector.

Is it necessary for the channel walls to move for the applicability of Navier's slip condition at the boundary. i.e., Is it possible that the channels walls are fixed, but we can apply the Navier's slip condition at both the channel walls.

Homework Statement State the condition for the equation px^2 + qx + r = 0 to have: a)two different real roots b)two equal real roots c)no real rootsHomework Equations b^2-4ac maybe?The Attempt at a Solution I missed a class due to ailments and now have to catch up on missed work. I can't find...

Hi Guys, I have some data on a small electric motor being run continuously for a year. The problem is I only have the Headings and numbers and no units or information on what devices were used to measure the data. The variables measured were Time, Speed, Temperature, Power, Powerfactor...

This is an example shown in "Introduction to Electrodynamics" by Griffiths. Page 226 example 5.8. Given a sheet of current K on the xy-plane where current traveling in +ve x direction. Find the magnetic field. I am confused on the way the book justify the z direction of B is zero. The...

i can't see how they got X and Y expressions V_x is the derivative of X(t) by t 'A' and phi are needed to be found but when i don't know how to innpur the initial condition to find A_x and A_y because when we integrate x' expression bot sides i get x(t)-x(0)=[A_x*cos(wt+phi)]/w -...

PDE--initial condition Homework Statement Solve the equation u_x+2xy^2u_y=0 with u(x,0)=\phi (x). Strauss PDE 2nd ed., chapter 1.5, exercise 6. Homework Equations The question is under "Well-Posed Problems" section, so this might be about existence, uniqueness, or stability. The...

Euler's method? Describe how to modify Euler's method to deal with the initial condition of y(5)=3 instead of y(0)=3. Use this on the equation y'=1+t using a time step of 0.1 and initial condition of y(5)=3 and find y(5.4) . ?? Now find the exact solution of this equation using calculus...

What is the condition required for a particle to move relativistically?

Hey, For a problem I am working on I need to know if the energy-momentum tensor of the Reissner- Nordstrom metric obeys the weak energy condition. Since I need the result for the following calculations, I just want to be sure that it is correct. Does anyone of you know the correct answer and...

what is the sufficient condition on a quadilateral to be a trapezium ?

QUESTION: Solve the separable differential equation dy/dx = sqrt(4y+64), Initial Condition: y(4)=9, and find the particular solution satisfying the initial condition. MY ATTEMPT: (dy/dx)^2 = 4y+64 ((dy/dx)^2)-4y = 64 ,/' (((dy/dx)^2)-4y) dx = ,/' 64 dx Is this the right method...

2.2.2 3u_x+4u_y-2u=1\Rightarrow \omega_{\xi}+k\omega=\varphi(\xi,\eta) u(x,y)=u(\xi\cos{\alpha}-\eta\sin{\alpha},\xi\sin{\alpha}+\eta\cos{\alpha})=\omega(\xi,\eta) u_x=\omega_{\xi}\cos{\alpha}-\omega_{\eta}\sin{\alpha} u_y=\omega_{\xi}\sin{\alpha}+\omega_{\eta}\cos{\alpha}...

Please teach me this: Are there any regulating limit on spin of particle?.E.g why spin of electron is 1/2 but not 3/2,spin of photon is 1 but not 2 e.t.c Thank you very much in advance.

Hi there, I am working on a problem in Fluid dynamics. I've written a code in MATLAB which finds the shape of the free surface of the liquid based on Newton Relaxation. The code is fairly robust and produces good results which agree with current papers on the same problem. Unfortunately...

I'm playing with the PDE toolbox in Matlab and solving Laplace's equation, ∇2V = 0, for various electrostatic geometries. I say 'playing' because I started in the wrong end (or right end, depending on how you look at it) by simple trial and error until the solutions looked like something...

I've been trying to work through the heat equation given in this Sous Vide cooking primer: http://amath.colorado.edu/~baldwind/sous-vide.html It gives a modified version of the heat equation with a shape parameter for simplification. The equations are shown below...

1) Consider that one way light speed is anisotropic. 2) Use the Einstein method to synchronize all the watches by the watch located at (x,y,z)=(0,0,0). Now, all the watches are synchronized by the watch at (0,0,0) but they are not necessarily synchronized with each-other (Consider watches...

Homework Statement Given the Lagrangian density L=-{1 \over 2}[\partial_\alpha\phi_\beta(x)][\partial^\alpha\phi^\beta(x)]+{1\over 2}[\partial_\alpha\phi^\alpha(x)][\partial_\beta\phi^\beta(x)]+{\mu^2\over 2}\phi_\alpha(x)\phi^\alpha(x) for the real vector field \phi^\alpha(x) with field...

Homework Statement http://img189.imageshack.us/img189/9859/mathlm.th.jpg (Click the thumbnail)Homework Equations When taking the laplace transform of derivatives L{f^n(t)=(s^n)*F(s) - s^(n-1)*f(0)...}; the step function u(t-a) The Attempt at a Solution we have never done a step function...

My understanding of: \int_S \nabla X \vec{H} \cdot d\vec{S} = \int_C \vec{H} \cdot d \vec{l} = I Means the current I creates the magnetic field in the form of \nabla X \vec{H} instead of magnetic field creates the current I. But in the boundary condition, it claims the tangential...

Hi All, When computing the commutator \left[x,p_{y}\right], I eventually arrived (as expected) at \hbar^{2}\left(\frac{\partial}{\partial y}\left(\frac{\partial f}{\partial x}\right) - \frac{\partial}{\partial x}\left(\frac{\partial f}{\partial y}\right)\right) and I realized that, as correct...

'Condition' is a function which determines whether an element of some type a satisfies some property, and returns True if only if it does. A polymorphic data type 'Condition a' is defined: data Condition a = Con (a -> Bool) Define a function minSol::Ord a => Condition a -> [a] -> Maybe a...

i think jordan wigner transform, when applied to open boundary system, can simplify a spin 1/2 system to a free fermion system but there is a difficulty in the case of periodic boundary condition in this case, we have to deal with terms like S_N^+S_1^-=(-)^{\sum_{k=1}^{N-1}n_k}...

Homework Statement This is what my professor wrote on the board. Suppose the condition is as follows y(0) = y(L) = 0 link to img http://www.izhuk.com/painter/image2.php?id=1286387629-69-86-215-102&md5=c054d375567134a9faa133b47fe690b2 This is the fundamental harmonic - with nodes appear at x...

Homework Statement I need to prove the equation attached. I also have to describe why the integrals vanish. Homework Equations The Attempt at a Solution I am not sure how to begin. Our teacher told us this equation is known as the orthogonality condition for sines. I also know...

Homework Statement \psi(x,t) = \psi_1 e^{-i E_1 t/2} + \psi_2 e^{-iE_2 t/2} under what conditions is the probability density time independent? Homework Equations |\Psi(x,t)|^2 = \psi(x,t)* \psi(x,t) The Attempt at a Solution i found a statement in pg 71 of prof Richard...

Homework Statement i know that "A is necessary for B" means "B implies A". but i confused with the word "A is necessary of B" somebody help

Let's consider a second order differential equation f(x,\dot x,\ddot x,t)=0 and let's suppose that f satisfies all the conditions of the Cauchy Theorem, i.e. f is such that the equation above with the initial conditions x(t_0)=x_0\qquad\dot x(t_0)=v_0 has an unique solution in a...

This question comes from Theorem 16.3 of Bartle's "The Elements of Integration and Lebesgue Measure", in page 163. The condition E\subseteq A is indeed needed in the proof of necessary condition, but I did not find its usage anywhere in the proof of sufficient condition, for example...

Are you satisfied with your current weight and level of fitness? If so, what do you do to maintain it? If not, why do you think you have fallen from it (assuming you were once there)?

Homework Statement For a plane stress condition (stress z-axis = 0 ), prove the following relations if strain x-axis and strain y-axis are determined by experiments. σ_x=(∈_x+v∈_y/1-v^2)E & σ_y=(∈_y+v∈_x/1-v^2)E where: σ_x = stress in x-axis σ_y = stress in y-axis ∈_x = strain...

Homework Statement Ok so this may get a little drawn out here because my book only gives me one example and I guess I can't decipher its meaning. So here is the example they give: For \;\; \lim_{x \to 2} x^{2} = 4 Find a \;\; \delta > 0 \;\; such that whenever 0 < |x-2|< \delta, \;\;\...

Dear all, why is it needed in the diff manifold definition that the base set M is topologically Hausdorf ? Since M is locally homeomorphic with Rn as metric space is Hausdorf, shouldn't this condition be automatically satisfied? Thanks. Goldbeetle

What's the condition for f(x,y) to be differentiable in its domain? I googled for it but couln't find... Thanks in advance.

hello, I would like to know if following reactions are possible/correct and under what condition: 2NaOH+K->KOH+NaOH and HCN+K->KCN+H Theoretically it should be possible but I'm not sure,Please help me understand Thanks

It's obvious that if Maxwell equations are fulfilled by some E(x,y,z,t) and B(x,y,z,t), they are also fullfiled by E(x,y,z,t)+ E_0 and B(x,y,z,t)+B_0, where E_0 and B_0 are constants. This freedom has physical significance as it changes the Lorentz force which act on a charge. It...

Homework Statement stand with one arm and the side of one foot pressed against a wall. can u raise the other leg side ways?if not then why not? Homework Equations The Attempt at a Solution i tried myself but couldnot raise.i m not getting the reason.

Hi, it is possible to solve the following problem, I mean give at least some conditions on f(x,t)? \int_0^{\infty}e^{-x}[f(x,t)+g(t)] xdx=g(t)

Homework Statement consider two conditions x2-3x-10 < 0 and |x-2| < A on a real number x, where A is positive real number (i) find the range of values of A such that |x-2| < A is a necessary condition for x2-3x-10 < 0 (ii) find the range of values of A such that |x-2| < A is a sufficient...

I am working on a project that involves the hydraulic design of a potable water transmission line (diameter 500mm), that conveys water from the source location of elevation 1500m to the end point at an elevation of 950m. The hydraulic design requires several PRVs along the path (around 230Km...

Let's consider two media with magnetic permeability \mu_1, \mu_2 . What's the condition for magnetostatic vector potential \vec{A} on the boundary. Is it true that its tangent component should be continuous. Thanks for replay.

Question regarding GR and the "cylinder condition" Im reading that in Kaluza-Klein theory, the derivatives (of the metric g_{\mu\nu} with respect to the 5th dimension, X^4 , were chosen to be zero, to explain why we do not "feel", or detect, the existence of X^4 i.e. the Cylinder Condition...