Recent content by HasuChObe

I don't know if you have access but http://www.sciencedirect.com/science/article/pii/S0021999108005962 The paper is called: "One- and two-dimensional lattice sums for the three-dimensional Helmholtz equation"

Does anyone know how to prove this identity? I don't quote understand why the associated Legendre function is allowed to have arguments where |x|>1. h_n(kr)P_n^m(\cos\theta)=\frac{(-i)^{n+1}}{\pi}\int_{-\infty}^\infty e^{ikzt}K_m(k\rho\gamma(t))P_n^m(t)\,dt where \gamma(t)=\begin{cases}...

Can you elaborate?

So I'm looking at Schaum's outlines for Tensors and the definition of a Contravariant vector is \bar{T}^i=T^r\frac{\partial\bar{x}^i}{\partial x^r} Where \bar{x}^i and x^r denote components of 2 different coordinates (the superscript does not mean 'to the power of') and T^i and T^r are...

So, assuming that the contour in the complex plane encloses all the poles, does Jordan's lemma basically say that the integral in the complex plane is always zero (provided that you start at one of the real infinities and end at the other)?

Lets say you're doing one of those integrals from -\infty to \infty on the real axis and you chose to do it by contour integration. Let's say your integral is one of those integrals that's resolved by using Jordan's lemma. If you close the contour by making a giant loop such that Jordan's lemma...

I'm not a very mathy person, so I'll just drop my 2 cents. If B has the same eigenvectors as A, then it commutes with A.

Why does performing unitary similarity transforms on a matrix eventually cause it to converge to Schur form?

I must fundamentally misunderstand what the variational method is. According to my textbook, it's used to find the minimum eigen energy of an operator (in particular, the time-independent Schrödinger equation). This appears to be synonymous to finding the eigenvalues of the matrix representation...

One of the boundary conditions for a homogeneous uniform waveguide is \frac{\partial H_z}{\partial n}=0. What does this mean physically?

f: ℝ^n→ℝ\qquad g: ℝ^n→ℝ^m

Hah; Of course I try to calculate field energy with only the E field :/ Good answer. Should be further along now :P Any inputs on the geometry changes from a smaller to larger impedance? I've concluded that the cross section of the dielectric part has to get bigger, but I could be wrong again -.-

Say you had a lossless transmission line that consists of an ideal source, a 50 ohm impedance, a 100 ohm impedance, and a 100 ohm terminator. The material is the same. You send a pulse down the line. When the pulse hits the impedance mismatch, you get a smaller reflection back, and a pulse...

Gain margin is how much gain (in decibels) you can add to the open loop transfer function of a feedback system before it becomes unstable. Essentially, if the transfer function of the open loop is minimum phase, you want the magnitude of the open loop transfer function to be less than 1 (which...

Alright, I figured out what the answer was. But my original question was this. The book states that, given that a system is minimum phase, if the gain margin or phase margin are negative, the system is unstable. My issue was that a minimum phase system is already stable. Turns out, the book was...