I hope this is not overly speculative: I was wondering if seasonal temperature variations over large land masses can cause the ground to expand in such a way as to offset the straight line distance between two landmarks 730 kilometers apart by about 10 meters, or so? I had spoken a while back...
I have two questions that are based on the following example involving the Hermitian operator i[A,B]=iAB-iBA for the case of a plane polarized photon.
The observable (Hermitian Matrix) for the plane polarized photon, which Professor Susskind gave in his quantum mechanics lecture, lecture...
So linearity is the key to the proof? Or does a topological vector space being finite dimensional also play a role when it comes to being able to uniquely determine a linear mapping by how it maps basis elements?
In other words, is the following statement true:
Given a linear mapping L...
Suppose one has a continuous complex valued function f:X->X, where X is some a non-empty compact subset of the complex numbers, and of the form Z_n+1 = f(Z_n; a1, a2,..., am), where a1, a2,..., am, with 0 <=|ai|<=1, for i =1, 2,...,m, are independant complex valued parameters, and n = 1,2,3 ...
Good question: the following ideas may help.
Let g: A -> B be a function from a set A into a set B.
Definitions of one-to-one and onto:
g is one-to-one iff for every a1, a2 contained in A, g(a1) = g(a2) implies that a1 = a2.
g is onto iff for every b contained in B, there...
Hi, I was playing around with Euler's Identity, and I found something (or at least I think I found something) interesting:
It is a well known identity
sin(z) = [exp(iz) - exp(-iz)]/(2*i), where z is any complex number, exp is the complex exponential function, and i is the imaginary...
Hello,
I was wondering if anyone is familiar with using the Inverse Scattering Transform to solve some kinds of non-linear differential equations.
I have been trying to look up examples of solving non-linear differential equations using the inverse scattering transform, but all the...
Probably the easiest way to disprove this theorem, would be to find a counter example.
The interval [0,1] is a topological space that has the Heine-Borrel property.
It follows that every closed and bounded subset of [0,1], is compact.
The interval (0,1) is an open subset of [0,1]...
I had a quick question on a part of a proof in chapter 1 of Functional Analysis, by Professor Rudin.
Theorem 1.10 states
"Suppose K and C are subsets of a topological vector space X. K is compact, and C is closed, and the intersection of K and C is the empty set. Then 0 has a...
Try rewriting the quadratic expression under the square root symbol in vertex form
sqrt[a]*sqrt[(x-h)^2 + k^2)] , as follows:
sqrt[-1]*sqrt[(x-5)^2 - 9], then let u = x - 5, and use the formula from a table of integrals for an integral of the form
sqrt[u^2 - a^2], for a > 0, and then...