In this paper the Cesaro means of a function f with respect to the Vilenkin system in Kaczmarz rearrengement are considered. We prove for integrable functions f the a.e. convergence of this means to f.
Similarities and differences between the force fields of a classical real dipole and a complex dipole are analyzed. The complex dipole is a pair of points equipped with complex conjugate masses and situated in a complex domain. The results of this analysis are used in the problem of motion of a material point in the field of attraction of a triangle uniformly rotating in its plane about its center of mass. It is assumed that a complex dipole is assigned to each vertex of the triangle. The existence and stability of libration points are studied. In particular, it is shown that there exist libration points outside the plane of the triangle.
We consider systems of Boolean functions inducing algebras of Bernoulli distributions, whose universal set has a single limit point. We establish a criterion for an algebra generated by a given set of distributions to have a unique limit point.
We classify complex linear cocycles over ergodic automorphisms with the help of the barycenter method. A conjugating random matrix is built in explicit form.
The problem of realization of Boolean functions by initial Boolean automata with two constant states and n inputs is considered. Initial Boolean automaton with two constant states and n inputs is an initial automaton with output such that in all states output functions are n-ary constant Boolean functions 0 or 1. The maximum cardinality of set of n-ary Boolean functions where n > 1 realized by an initial Boolean automaton with two constant states and n inputs is obtained.
This paper is focused on multichannel queueing system with heterogeneous servers and regenerative input flow in a random environment. The environment can destroy all the system and then system is reconstructed. Ergodicity condition of the system is obtained.
This paper is devoted to $M|GI|1|\infty$ queueing system with unreliable server and customer service times depending on the system state. Condition of ergodicity and generating function are found in the stationary state.