Motivated by applications in matrix constructions used the inverse eigenvalue problem for graphs, we study a concept of genericity eigenvectors associated with given spectrum and connected graph. This generalizes established notion nowhere-zero eigenbasis. Given any simple graph G on n vertices no multiple eigenvalues, show that family eigenbases symmetric matrices this is generic, strengthenin...

The study of propositional realizability logic was initiated in the 50th of the last century. Unfortunately, no description of the class of realizable propositional formulas is found up to now. Nevertheless some attempts of such a description were made. In 1974 the author proved that every known realizable propositional formula has the property that every one of its closed arithmetical instance...

Intrusive uncertainty quantification methods for hyperbolic problems exhibit spurious oscillations at shocks, which leads to a significant reduction of the overall approximation quality. Furthermore, challenging task is preserve hyperbolicity gPC moment system. An intrusive method guarantees polynomial (IPM) method, performs expansion on entropy variables. The while still being subject oscillat...