# Search results

1. ### Calculate attenuation constant of an aperture

Homework Statement The shielding efficiency of an aperture depends on e−αd, where α is the frequency-dependent attenuation constant of the aperture and d is the thickness of the material (or the cutoff waveguide) at frequencies below cutoff. where ωc=2πfc. Calculate α for an air-vent...
2. ### Estimating loss-limited transmission distance

Homework Statement A high-speed optical data communication system is composed of a transmitter, an unamplified transmission fiber link, and a receiver. The optical transmitter generates a 10-Gb/s non-return-to-zero (NRZ) signal using a 1550-nm laser diode (linewidth=2 MHz) followed by a...
3. ### Solving voltage divider involving capacitors

Homework Statement Given ZV1 = ZV2 = 100Ω, ZCCV = ZCV = 2000/j = -2000j, and VV/VC = 0.04789. I'm trying to get the given VV/VC result. Homework Equations I know that 1/ZV = 1/ZV1 + 1/ZV2 + 1/ZCV VV = ZV / (ZV + ZCCV) * VC The Attempt at a Solution 1/ZV = 1/ZV1 + 1/ZV2 + 1/ZCV = 1/100 +...
4. ### Cable-to-cable crosstalk (Capacitative Coupling)

Homework Statement Compute the cable-to-cable crosstalk due to capacitive coupling in a harness between two cable pairs having an average separation distance of 3 mm and a 10 m in a cable tray. The cable diameters are 1 mm and both cables are operating at a 100 ohm impedance level. Assume h = 5...
5. ### Deriving relationship between LVDT and mass spring damper

Homework Statement [/B] I have this system below. It is the schematic of a linear accelerometer moving horizontally, where m is the total mass of the slide, b denotes the viscous damping, and k represents the spring constant. The relative position between the moving mass and the case is...
6. ### Derive a third order accurate scheme

Homework Statement Hi all, I need help with deriving a third order accurate scheme for the inhomogeneous equation u_t + a u_x = f based on the approach used to derive the Lax-Wendroff scheme, that is, replacing the time derivatives of u by space derivatives of u. The Attempt at a...
7. ### Accuracy of finding eigenvalues of defective matrix

Homework Statement Hi all, I need help with determining the accuracy of finding eigenvalues of defective matrix. The question asks: When a matrix has a defective eigenvalue, the condition number for computing its eigenvalues is infinity. Does this mean that these eigenvalues cannot be...
8. ### Determining critical points

Homework Statement Consider the plane dynamic system \dot{x} = P(x,y), \dot{y} = Q(x,y) with the condition that O(0,0) is a critical point. Suppose P(-x,y) = -P(x,y) and Q(-x,y) = Q(x,y). Is the critical point (0,0) a center? Why? The Attempt at a Solution I know that for (0,0) to be a...
9. ### MATLAB Matlab: Solving linear system with QR/Householder

Homework Statement Hi all, I'm trying to implement the QR method for solving the linear system Ax = b. The QR factorization is achieved using Householder method. The Attempt at a Solution The main function is function x = lin_solve(A,b) [R,v] = householder(A); y = Qt_times_b(v,b); x...
10. ### Matrix/Vector differentiation

Homework Statement Hi all, I need help proving the result: Let g(x) = x'Mx, where M is a n-by-n real constant matrix and x' denotes the transpose of vector x. Then the derivative of g(x) = (M + M')x. The Attempt at a Solution I was thinking of using product rule on x'(Mx) to get...
11. ### Maximum interval of the existence

Homework Statement Suppose f(t,x) is a continuous vector valued function on \mathbb{R} \times \mathbb{R}^n. If f is locally Lipschitz with respect to x with the property that \|f(t,x)\| \le C \|x\| for some positive constant C > 0, then prove that the maximum interval of the existence of the...
12. ### Stability of a solution

Homework Statement Let a(t), b(t) and c(t) be continuous functions of t over the interval [0,\infty). Assume (x,y) = (\phi(t), \psi(t)) is a solution of the system \dot{x} = -a^2(t)y + b(t), \dot{y} = a^2(t)x + c(t) Show that this solution is stable. The Attempt at a Solution I...
13. ### Lipschitz ODE problem

Homework Statement Suppose the function f(t,x) is locally Lipschitz on the domain G in R^2, that is, |f(t,x_1)-f(t,x_2)| <= k(t) |x_1 - x_2| for all (t, x_1),(t,x_2) in G. Define I = (a,b) and phi_1(t) and phi_2(t) are 2 continuous functions on I. Assume that, if (t, phi_i(t)) is in G, then the...
14. ### Parallelizing Crank-Nicolson method

Hello all, I'm trying to learn more about parallelizing the Crank-Nicolson method. Can anyone point me to websites on this subject? Thank you. Regards, Rayne
15. ### DNA sequence alignment

Hi all, I'm interested in learning more about DNA sequence alignment and have been reading up on the topic online. I'm more interested in the Smith-Waterman algorithm for local alignment, but I'm quite confused about how the algorithm works. I know the algorithm works on a MxN matrix...
16. ### Polynomial algebra

Hi all, I have trouble understanding polynomial algebra. Let F[x] in Z_3[x] be the set of all polynomials modulo 1+x^2 where Z_3[x] is the set of all polynomials with coefficients in Z_3. Addition and multiplication are defined in the usual way but modulo 1+x^2 and the arithmetic of the...
17. ### Brownian Motion

Hi all, I need help with a question. Let B(t), t>= 0 be a standard Brownian motion and let u, v, w > 0. Calculate E[B(u) B(u+v) B(u+v+w)], using the fact that for a zero mean normal random variable Z, E[Z^3] = 0. I tried to do this question by breaking up the brownian motions, i.e...
18. ### Evaluate a function via fast fourier transform using Matlab

Hi all, I'm new to Matlab, and I'm trying to evaluate a function via fast fourier transform using Matlab, then compare the values at each gridpoint with the exact value. The function is y1 = cos(x)-20*sin(5*x)+6*sin(12*x) on the interval [-pi, pi], using n = 9 gridpoints. I first tried...
19. ### MATLAB Matlab/Fast Fourier Transform

Hi, I am very new to Matlab, and I'm supposed to use the built-in FFT function to do discrete Fourier Transform for f(x) = sin x + 4 cos(5x) + (sin(6x))^2 on the interval [-pi, pi] with a uniform partition for the interval with n = 9. Then I have to (a) Plot the magnitudes of the Fourier...
20. ### Normal Distribution

Hi all, I need help with a problem. The lifetimes of interactive computer chips are normally distributed with mean u = 1.4 * 10^6 hours and sigma = 3 * 10^5 hours. What is the approximate probability that a batch of 100 chips will contain at least 20 whose lifetimes are less than 1.8 *...