4 problems

Let a ship start at the origin and follow an arbitrary deterministic unit-speed path $\gamma:[0,\infty)\to\mathbb{R}^2$. For every straight line $L\subset\mathbb{R}^2$ with…

For every stochastic transition matrix $M=(m_{ij})_{i,j\in\{1,2\}}$, every $\alpha_1,\alpha_2\in[0,1)$, and every $C_1,C_2>0$, the two-site moving-target search problem has an opti…

Let $v_A(n,d,k)$ denote the value of Alpern's Caching Game with $n$ doors, $d$ treasures, and searcher power $k$. Csóka's conjecture. If $k\geq 1+\frac{2}{d-1}$ and $n\geq dk$, the…

Let $v_A(n,d,k)$ denote the value of Alpern's Caching Game with $n$ doors, $d$ treasures, and searcher power $k$. Csóka's conjecture. If $k$ is an integer and $n\geq dk$, then … Th…