The theory of electron states on the dynamically deformed adsorbed surface of a solid

Dispersion relations for the spectra of surface electron states on a dynamically deformed adsorbed surface of a monocrystal with the Zinc blende structure are received. It is established that the dependences of the band gap width and of the concentration of electrons on the concentration of adatoms ${{N}_{0\text{d}}}$ upon the solid surface are of nonmonotonous character.Comment: 9 pages, 3 figure

A Linear Bound on the K-Rendezvous Time for Primitive Sets of NZ Matrices

A set of nonnegative matrices is called primitive if there exists a product of these matrices that is entrywise positive. Motivated by recent results relating synchronizing automata and primitive sets, we study the length of the shortest product of a primitive set having a column or a row with k positive entries (the k-RT). We prove that this value is at most linear w.r.t. the matrix size n for small k, while the problem is still open for synchronizing automata. We then report numerical results comparing our upper bound on the k-RT with heuristic approximation methods