Vol 74, No 2 (2019)

The problem of the minimal number of multiplication operations sufficient for joint computing three monomials in three variables is considered. For this problem, we propose a simple proof of the upper bound that is asymptotically equal to the lower bound. The known proof of a similar bound contains more than 60 pages.

Explicit formulas for the initial data stabilization algorithm for the stationary solution are obtained by zero approximation method for the semi-implicit difference scheme approximating a system of equations for the dynamics of a one-dimensional viscous barotropic gas. The spectrum of the corresponding linearized system on the stationary solution is studied and theoretical convergence estimates are obtained. Numerical experiments for the nonlinear problem are carried out to confirm the efficiency of the method and to reflect the dependence of the stabilization rate on the parameters of the original problem and the algorithm.

The full diagnostic test for contact circuits in the presence of one-type contact faults (breaking or closure) is considered. We constructively establish that any Boolean function can be realized by a contact circuit permitting a non-trivial full diagnostic test, i.e., a test containing not all input vectors.

The path connectedness of spheres in Gromov-Hausdorff space is studied. It is proved that (1) each sphere centered at the single point space is path connected; (2) for any compact metric space X there exists a number R_X such that each sphere centered at X and whose radius is greater than R_X is path connected.

An absolute L-realizability of predicate formulas is introduced for all countable extensions L of the language of arithmetic. It is proved that the intuitionistic logic is not sound with this semantics.