2
votes
0answers
85 views

A Conjecture related to minimization of product of determinants over permutations

Hi I have the following problem (and a conjecture which holds in Matlab). Given an $N\times N$ matrix $H$, represent it by its $2N\times 2N$ real-valued representation (which I will also denote by ...
2
votes
1answer
65 views

(A)periodicity and (In)dependence on the boundary condition for optimization problem related to ODE

The question is pair to MO117505 and translates some problem on error-correction codes to similar problem about differential operators. (See also If “force” is periodic does it imply “velocity” is ...
3
votes
1answer
242 views

If “force” is periodic does it imply “velocity” is periodic ? (or decoding tail-bited conv. codes)

I'll try to translate certain problem about convolutional codes to more common language of ODE, hope my translation is correct, but welcome to criticize. Consider two given functions periodic ...
1
vote
1answer
464 views

Solutions to Heat Equations with Obstacles!

Consider a closed Riemannian manifold $(M,g)$ and a positive function $\psi: M \to R$. Fix a point $p \in M$, I have been struggling to construct a solution to the heat equation, $\partial_t u = ...
5
votes
1answer
219 views

A Lagrangian problem with a countable family of local extrema ?

Dear MO contributors, let $r > 0, L > 0$. I am interested in maximizing the integral: $$ \int_0^{2\pi} \frac{f(\alpha)^2 f'(\alpha)^2}{\sqrt{f(\alpha)^2 + f'(\alpha)^2}} \ \mathrm{d} \alpha $$ ...
2
votes
0answers
80 views

Minimum time planar paths under a bound on magnitude of acceleration

On a plane, given initial position (x1,y1), initial velocity (u1,v1), final position (x2,y2), and final velocity (u2,v2), compute the solution to x''= cos(z), y''=sin(z) that has these endpoint ...
-1
votes
2answers
594 views

Optimal tax Rate

Assume you have two countries A and B, with a tax rates $T_A$ and $T_B$. The tax is redistributed to each people equally. Hence if you live in A and you make $I$ as income then you will finally ...
0
votes
2answers
353 views

$H^{-1}$ conservative gradient flow and $L^2$ projection

Consider Cahn-Hilliard (see this) equation hich is known as the $H^{-1}$ gradient flow of Cahn-Hilliard energy functional, also it is easy to verify that this equation is mass preserving i.e. measure ...
2
votes
1answer
395 views

Do upper-semicontinuous polyhedral multifunctions have Lipschitz continuous selections?

We are interested in the following question (definitions and references are given below): Main Question: Given an upper-semicontinuous polyhedral multifunction $F:R^n \rightarrow R^m$, is there ...