5 problems

For a given sensitivity parameter $\lambda>0$, determine a function $u\in C^2([0,1])$ satisfying the nonlinear boundary-value problem $u''(x)=\lambda\sinh(\lambda u(x))$ for…

Determine the optimal control strategies and exact minimum expected cost for the two-stage Witsenhausen problem x1 = x0 + u1, x2 = x1 + u2, where x0 N(0, sigma^2), decision maker 1…

For every finite stochastic game with bounded stage payoffs, every epsilon0, and every initial state s0, prove that there are a behavioral-strategy profile sigma and N such that fo…

In the standard ordered-real Blum–Shub–Smale model, machines use finitely many built-in real constants, real-valued registers, exact field operations (+,-,multiplication,division w…

Determine whether every problem decidable in the existential theory of the reals (exists R) can be decided in nondeterministic polynomial time, i.e., decide whether NP = exists R.…