Condition Definition and 587 Threads

...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...

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.

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...

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...

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, 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...

Hi, I am solving the diffusion equation using explicit finite difference to model the diffusion of an analyte through a membrane. I am interested in the concentration of the analyte on the other side vs time elapsed. On one side of the membrane is an initial concentration, which I am...

Consider a bearing joint together with a long pipe (with radius a) by using shrink-fitting. The grip between the pipe and the inner ring of the bearing give rise to the surface pressure p at the interface. If a moment M now is applied to the pipe, what will the slip condition between the two...

Can a body be in equilibrium if only one force acts on it? I think it can't, if the force is non-zero. Thoughts?

A function f is both integrable and infinitely differentiable, i.e. f\in L_1(\mathbb{R}) \cap C^{\infty}(\mathbb{R}). Is it correct to say that this implies that the derivatives of f are also in L_1(\mathbb{R})? My reasoning: we have I<\infty, where I=\int_{-\infty}^{\infty} f(x) dx = [x...

Homework Statement A spherical billiard ball radius a and mass M is sitting on a flat surface. The coefficient of friction between the ball and table is u. The moment of inertia for the billiard ball is 2Ma^2/5. The ball is given a sharp horizontal hit at the centre and it starts moving with...

I've been asking myself this question that is not entirely clear to me: the Bragg condition used to describe the constructive interference of waves on a crystal is based on the assumption of reflection. However, x-rays diffract on a crystal rather than reflect, so theoretically there is always...

I'm trying to solve a third-order nonlinear ordinary differential equation. I couldn't get the answer even using Mathematica. The equation is: u'''(t) + u/2 u''(t) = 0 with conditions u(0)=0, u'(0)=0, u(10)=1. I need to get both analytic solution and numerical solution. For the...

I would like to check my reasoning for this problem to make sure I understand what an orthogonal matrix is. Homework Statement Determine if the matrix is orthogonal. If orthogonal, find the inverse. \begin{pmatrix} -1 & 2 & 2\\ 2 & -1 & 2\\ 2 & 2 & -1 \end{pmatrix} Homework...

Anyone know how to solve this one? Homework Statement Determine weights w1 and w2 that cause the tension T in the horizontal cable to be 100 N. Here's the diagram: http://tinypic.com/m/f56cyb/2Homework Equations All I know is the component method but. . .I'm not sure how to apply it here...

I am solving the heat equation in a non comercial C++ finite elements code with explicit euler stepping, and adaptive meshes (coarse in the boundaries and finer in the center). I am aware the CFL condition for the heat equation depends on dt/h**2 for the 1D, 2D, 3D case. When I solve the...

Homework Statement m=6kg r=0.18m Fapp=33N I'm struggling to understand how to answer this question and correlate the linear force applied to rotation without being given the coefficient of friction causing the rotational motion. The question states that a solid sphere of 6kg is...

Hello all: I would very much appreciate advice on setting up a problem. Apologies in advance... This is probably a silly question--I'm more of a chemist than an engineer/math person! I have written a code for calculating changes in concentration/mass within a domain over time, as new...

Homework Statement Consider the PDE xu_x + y u_y = 4 u, -\infty < x < \infty, -\infty < y < \infty. Find an explicit solution that satisfies u = 1 on the ellipse 4x^2 + y^2 = 1. Homework Equations The Attempt at a Solution The characteristic curves are x(t,s) = f_1(s) e^t...

Homework Statement Consider a cyclist turning around a circular track with radius r and speed v as shown in attached fig. Let W be the weight of the system (cyclist + bicycle) (W = mg) N = normal force by ground on the system f = static friction by ground on the system θ = angle of...

I'm asked to determine if for the solution y=c_{1}e^{x}cos(x)+c_{2}e^{x}sin(x) for: y"-2y'+2y=0 whether a member of the family can be found that satisfies the boundary conditions: y(0)=1, y'(\pi)=0 Not quite sure what to do here. The examples in my book give boundary conditions for the same...

Either through gamma decay into electron-positron pairs or straight old beta emission?

Is there a term to describe something like a boundary condition but which can be applied within the domain, not just on the boundaries? For example in a heat transfer problem you might specify a constant rate of heat generation in some region. Is that still called a boundary condition...

Usually positive Ljapunov exponent is said to be a condition for chaos, and the strange atractor is so. Are there any theorem which shows that the two condition is equivalent? They are necessary and sufficent conditions?

The necessary and sufficient condition for homomorphisim f of a group G into a group G' with kernel K to be isomorphism of G into G' is that k={e} ... THOUGH I AM ABLE TO PROVE THAT f IS ONE-ONE AND f IS HOMOMORPHISM (in converse part) BUT CAN'T GET ANY IDEA TO PROVE THAT f IS ONTO. PLEASE...

theorem states that for y'' + p(x)y' + q(x)y = r(x); if y1 & y2 are random numbers such that y(m) = y1 and y'(m) = y2 then we can find a unique solution y for above differential equation... in y'' - y'/x = 0; both y = x^2 and y = 0 and y = k x^2 satisfy above with .. y(0) = 0; and...

The question is x^2dy/dx + y^2=0 , y(1)=3 I re-arrange the equation to get -1/y^2dy=1/x^2dx Seperated them, then I integrate both sides to get 1/y=-1/x + c Now I don't get how they got the answer y=3x/(4x-3), as when I try use the condition I get a different answer, could anyone help? I...

Hello, I want to calculate the conditioning of a matrix, therefore I use the cond() commando in Matlab. A problem with a low condition number is said to be well-conditioned, while a problem with a high condition number is said to be ill-conditioned. If I calculate the condition number of...

Lets us say I have a cube and I apply to a face of the cube a heat flux of 100 watt/m^2. Lets us say i divide the face of the cube into say 10 elements (area of each face of the element is 1 m^2). What will be the flux on each element , will it also be 100 watt/m^2? Sorry for a...

Hi, I was reading Lemon's Perfect Form and it talked about "natural boundary conditions". But I don't understand exactly how one determines them. It seems to me that one imposes some random condition then deduce stuff from it...?! Advanced thanks for any enlightenment!

see this image https://docs.google.com/leaf?id=0B5ZURGN4IHlTZWIxN2Q5NzEtNzQxZC00NTFkLWFkNDAtMTZmMDU5ZGIwOGQx&hl=en_GB&authkey=CL3RqN4O" something about question:=> a block M1 placed over M2 Nd M2 placed on the earth.A constant force F is applied in upward direction. You have to tell about...