Condition Definition and 587 Threads

1. 1D heat conduction problem: Two rods, the first of length a , the second of length L-a with respective cross sectional areas A_1 , A_2 and heat conductivities k_1 , k_2 , are joined at one end. There are some boundary conditions on the other ends of the rods, but my question is only...

Homework Statement f is integrable on the circle and satisfies the Lipschitz condition (Holder condition with a=1). Show that the series converges absolutely (and thus uniformly). i literally spent about 20 hours on this problem today but i just could not figure it out. i have a feeling...

Homework Statement If x_{1} x_{2} \cdots x_{n}=1 (1) show that x_{1}+x_{2}+\cdots+x_{n} \geq n (2)The Attempt at a Solution I attempted as follows. I started with x_{1} + \frac{1}{x_{1}} \geq 2 , which is an inequality I already know how to prove. Then using Eq.(1) I get x_{1} +...

Homework Statement A problem with odd harmonics only. Show that the solution of the heat equation du/dt=c2*(d2u)/(dx2), subject to boundary conditions u(0,t)=0 and ux(L,t)=0, and the initial condition u(x,0)=f(x) , is u(x,t)= \sum Bnsin[(\pi/2L)(2n+1)x]e-((c*\pi/2L)*(2n+1))^2 where n...

Urgent: Boundary Condition querries. Homework Statement Question given: A dielectric interface is described by 4y+3z=12. The side including the origin is free space and its electric flux density, D=ax+3ay+2az (micro) C/m2. On the other side, (Epsilon)r2 = 2. Find D2. Homework Equations...

In simple kinematic problems, the initial velocity can be zero or some nonzero value. A friend asked me: what makes it zero in some cases and nonzero in some others. Take a rocket in take off. It has acceleration moving upward, from the beginning, but its v_0=0. Instead, if I apply...

Hi, I've been learning about the calculus of variations this term, and we just covered the transversality condition for an optimization problem with the right end point free, as well as the first necessary condition on the augmented Lagrangian for a problem with integral constraints. I'm...

Hi Is it true that derivative of a function is possible only if it is continuous!

This question asks to solve the initial value problem and determine the interval in which it is defined. y'=2x/(1+2y) , y(2)=0 and after solving, we get the equation y= -0.5 + \sqrt{x^{2} - 15/4}(discarded the negative squareroot since governed by initial condition). Therefore, the...

Suppose I have a 2nd order differential equation a_1y''(x)+a_2y'(x)+a_3y(x)+a_4=0 and two conditions y(0), y'(0). Then is there any theorem which gives us the condition under which the solution y(x) will be bounded? Note that x-range is entire real line. This is a general version of the...

Hi, I am trying to learn some numerical algebra. Now I don't understand the following. I'm finding the solution to the Linear Least Squares problem min||A\lambda-y||_{2}, which turns out to be (1,1). I did this by doing a QR factorization using Givens rotations. with: A= \[...

The big bang is defined as the theory that the universe has expanded from a primordial hot and dense initial condition. Was it hot? I would suspect that the initial condition was in fact cold due to the lack of space and therefore movement. The heat happen directly after the bang. Does this seem...

Is it a condition or a genetic defect problem ?

I've done searching on the topic, and I really don't know where else to turn, so here it goes. I hope somebody can point me in the right direction. I've been working on using a shooting method to solve the steady-state spherically symmetric fluid equations for an accreting plasma. Basically, it...

Homework Statement An apple weighs 1.11 N. When you hang it from the end of a long spring of force constant 1.53 N/m and negligible mass, it bounces up and down in SHM. If you stop the bouncing and let the apple swing from side to side through a small angle, the frequency of this simple...

Hi, I am new to FORTRAN and am trying to work with a system of ODE's. Does someone know of a routine like DVERK for solving initial condition problems for FORTRAN 90? In MATLAB I would simply use ODE45. I just need something similar. Thank you!

Homework Statement Using the condition of vector equilibrium, prove that \sum^{2n-1}_{k=0} cos ((k*pi)/n) Where n is an integer. Homework Equations I know that if n equal vectors are at an angle (2*pi)/n Their resultant is zero. The Attempt at a Solution Please first explain...

Homework Statement what is/are for a body to move in a straight line? Homework Equations The Attempt at a Solution

[SOLVED] Separable Equation with Condition? Homework Statement Solve. http://www.mcp-server.com/~lush/shillmud/int3.71.JPG Homework Equations The Attempt at a Solution I'm not sure how to separate this. Also, since the directions consist of only one word, I'm not sure if y(2)=2 is...

Hi, I have a question that asks me to explain how you could know if the initial conditions lead to a periodic solution of an ODE but I have no clue right now. I'd appreciate any help. Thanks edit: The question is a bit obscure because I am not sure if they are asking in general of for the...

2. Write a MATLAB® function to calculate the condition number of a symmetric square matrix of any size by means of Eigenvalues: § The power method should be used to calculate the Eigenvalues. § The script (function) should give an error message if the matrix is not...

I am wondering what were the conditions before the big bang

Homework Statement My book uses the following equation to derive the diffraction condition for electromagnetic waves scattering in a crystal lattice: F= \int dV n(\mathbf{r}) \exp \left[i\Delta\mathbf{k}\cdot \mathbf{r} \right] F is the scattering amplitude and n is the electron density. I...

The question : Consider a thin spherical shell of radius R with a uniform charge density sigma. If a very small piece of this surface were removed, leaving a small hole, what would the electric field be at a point just above/below the hole? Relevent info : the field due to the patch of...

suppose that the potential of a harmonic oscilltor is changed slowly i mean, the frequency of the harmonic oscilltor \omega is varying slowly my question is, under what conditions, the particle initially in the ground state follow the potential adiabatically? what conditions \omega(t)...

I've been working on this proof, and I just can't get it backwards or forwards, so I must be going about it wrong or missing something. I'm on a re-do for the homework, because my first attempt was completely wrong, so here I go with the second. Any guidance would be appreciated. Homework...

Is there a known medical/psychological condition or experience that results in a reversal of the flow of time (e.g., from the effect to the cause)?

If not, then what are the conditions for us to construct a periodic boundary condition(PBC)? If so, then please help me construct a PBC for the lattice shape in the attachments. I want to ask that what lattice site m's left neighbor is and what lattice site i's down neighbor is.From the...

Let u_n be a sequence of positive real number. If \sum_{n=1}^{\infty}u_n^{2} finite + (condition??) then \sum_{n=1}^{\infty}u_n finite. I want to find the condition.Please help me.

I am confused on the definition of the "no-slip" boundary condition because of two seemingly contradicting definitions. Definition 1: The no-slip condition for viscous fluid states that at a solid boundary, the fluid will have zero velocity relative to the boundary. Definition 2: The fluid...

Hello Looking for basic boundary-value problems with von Neumann conditions, more specific the applied ones to heat transfer or the wave equation. Could anyone recommend some good book that explains in an easy way the von Neumann conditions or has some solved problems related to the von...

I'm working through a proof of the orthormality condition for a complete set of states and am struggling with one element of it: Consider the eigenstates of the Hamiltonian in the following way: 1: \int\Psi^{*}_{m}H\Psi_{n}dV = E_{n}\int\Psi^{*}_{m}H\Psi_{n}dV and 2...

a.) Apply Normalization condition for the n=3 Ѱ-solution to find constant B. b.) Find <x> c.) Find <p> d.) Calculate probability that particle of mass m is located between 0 and a/2. Given: Ѱn(subscript)(x) = Bcos(n*pi/a)x Solution to ∞ square well from -a/2 to a/2 (Width "a"...

Homework Statement If a+b+c = 0, show that (2a-b)^3 + (2b-c)^3 + (2c-a)^3 = 3(2a-b)(2b-c)(2c-a)[/tex] Homework Equations None that I really need to state. The Attempt at a Solution Well I've just messed around with it, grinding through the algebra, and nothing seems to work. I...

what kind of sensors do EEs use for condition monitoring in the electro- elements of an electromechanical system? with a view to the subsystems inside a space probe.

hi in my engineering design class I've been set a short (1000 word) project on the ulysses space probe or more specifically system condition monitoring and maintenance for the mission. the trouble is, i don't really understand what that involves. can anyone enlighten me or direct me to some...

Homework Statement Suppose that |\alpha> and |\beta> are eigenkets(eigenfunctions) of a hermitian operator A. Under what condition can we conclude that |\alpha> + |\beta> is also an eigenket of A? Homework Equations It's quite basic, I don't think any addtional equations are needed except...

Does anybody know how to put BC at the center of a circle.

Prove that the monotone sequence condition is equivalent to the least upper bound theory. I can't seem to get around how to prove that the two are equivalent. (it seems trivial).

I can't understand the condition for inflation that Liddle presents in his book, Cosmological Inflation and Large-Scale Structure A.Liddle, Pg 51: \frac{d}{dt} \frac{H^{-1}}{a} <0 Because \frac{H^{-1}}{a} is the comoving Hubble length, the condition for inflation is that the comoving Hubble...

On this site http://www.geocities.com/physics_world/mass_paper.pdf It states that the 3 force can be written as... F = M1 x A1 + M2 x A2 Where 1 is the longitudinal component of acceleration and 2 is the transverse component of acceleration. It appears that if there is no...

As we know the spontaneous fission of an odd nucleus to an 2 odd nuclei happens with high probability when (Z^2)/A is greater than or equals 45 The conclusion of this is attached in pdf file with the post using the liquid drop nucleus model to explain the problem The question is here now...

Homework Statement Compute the condition number of the following matrix: | 1 1 | | E -E | where E<<l [SIZE="1"]infinity norm. Homework Equations l [SIZE="1"]infinity norm: ||x||[SIZE="1"]infinity = max |x[SIZE="1"]i| where i goes from 1 to n. Condition number: K(A) =...

what is the physical significance of othogonality condition? or what is meant when we say that two eigen states are orthogonal?

I just finished writing a little recursive function in C++ and when my stopping condition is reached, I need it to do nothing. So the if statement looks funny: if (the condition is met) { //do nothing } else { call yourself with smaller arguments } It works fine, but I feel uneasy...

When we say condition of a vector field F being conservative is curl F=0,does it mean that F=F(r)?.I know normally it does not look so.Please,then site an example where F is not a function of r,but still curl F=0.

What are the condition of agency in the individual and the State? Can someone tell me what the question is asking? I can't quite get what agency means... and condition of agency... any insight will be greatly appreciated.

I am asked to solve this DE with the initial condition of y(1) = 1. (x+y)^2dx + (2xy + x^2-1)dy = 0 So, after working the problem out, I came to this as an answer: F(x,y)=\frac{1}{3}x^3 + x^2y + xy^2-y My question is what do I do with the initial condition. I assume that I am just...

I'm wondering if I have some sort of medical condition, if there's any term for this... or if it's just something that's fairly common... I haven't really talked to anyone about it, just wondering if anyone knew anything about this. When I was about 9 or 10, every month or so, my mind would...

A friend gave me this problem; it's been years since I've taken probability, and I'm really rusty. I'm curious how to solve it. Suppose you have a normal pdf with mean mu and stdev sigma that represents the distribution of test scores. What's the probability that two randomly selected...