Edit:For part i) I think I've got it. The vector γ' is the unit vector in the direction of the curve, and γ'' is the unit vector in the direction of the curvature. Since the magnitude of the curvature is given by ||γ 00||, then the dot product of γ' and γ'' is equal to the magnitude of the...
The answer is as follows: By definition, the 1-norm of a matrix A is given by ||A||1=max||x||1=1||Ax||. Let x be the j-th basis vector, such that ||x||1=1 and x=(0,0,...,1,0,...) where the 1 is at the j-th place. Then ||Ax||=∑|ai,j|=∑[i=1 to n]|ai,j|. Since ||x||1=1, we can conclude that...
I started out by trying to diagonalize the Hamiltonian by finding the eigenvalues and eigenvectors. I found that the eigenvalues are $E_1 = 2, E_2 = -2$ and the corresponding eigenvectors are $|\psi_1 \rangle=\frac{1}{\sqrt2}(|0 \rangle + |1 \rangle)$ and $|\psi_2 \rangle=\frac{1}{\sqrt2}(|0...
If we have f(z) = \sum_{n=0}^{\infty}c_n q^n with q = e^{2{\pi}inz}, then we can use the definition of a Fourier series to calculate the coefficients c_n. We have that c_n = \frac{1}{2{\pi}}\int_0^{2{\pi}}f(z)q^{-n}dz where q^{-n} = e^{-2{\pi}inz}. This integral can be solved using contour...
I'm sorry if this question is too vague or if it's inappropriate but I have been working on this problem for the past few days and I can't figure out how to get from the linear combination to a solution.Thanks in advance for any help.
What kind of analysis would be appropriate for this sample? A two-way ANOVA might be useful for this data set, as it could help determine the effect of both calorie and sodium content on the type of hot dog. It could also help determine if there is an interaction between the two variables...
Thanks. </code>A:A) The range of values of a such that the body moves with oscillations is 0 < a < 4. The range of values of a such that the body moves without oscillations is a ≥ 4. B) The general solution for any a<4 is y(t) = c1e^(-(a/2m)t) + c2te^(-(a/2m)t). To prove that the body slows down...