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...
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...
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...
Homework Statement
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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...
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...
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...
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...
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...
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...
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...
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...
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...
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
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...
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...
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...
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...
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...
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 *...