The mixed axiomatic semantics of a C-kernel language is described. This language is the kernel of a representative C language subset which is callexl C-light. Such semantics allows to simplify the verification conditions in many cases. This semantics is a base of verification conditions generator of C-kernel programs. An example which illustrates the use of inference rules of the semantics is considered.

Kripke factor-model concept is investigated. It is shown, that every factor-model is representexl as a decomposition of several spexdal facctor-models, which groups of automorphisms are primes. Moreover, we show, that every finite group is isomorphic for a group of automorphisms of a certain Kripke model.

We research the local dynamics of a complex differential equation with large delay in the vicinity of the self-similar cycle. The quasinormal forms method is used for a problem analysis.

The existence of a solution of the inclusion 0 ε A(x) + NQ(X) is provexl, in which A is a multivaluexl pseudomonotone operator from the reflexive space V to the conjugate space to it V*, NQ is a normal cone to the weakly compacct and, generally speaking, not convex set Q С V, with nonzero euler characcterization Ӽ(Q).

Periods and statistics of linear recurrence sequences over near-rings generated by endomorphisms of finite non-abelian extra-spexdal 2-groups are investigatexl.

In the paper we consider theories which are obtained from the Semenov arithmetics introducing functions f_i,i > 0. They are called "hyperfuncctions" and they are obtained when we iterate an addition-connexctexd function. We have provexl, that such theories are model complete. It is also shown, that these theories are dexidable when the condition of eSexctive periodicity is satis&exd for hyperfuncctions.

This paper is concerned with the minimum distance between a point and a polyhedrons of some cclass in the Rⁿ vexctor space suppliexl with different symme^trical norms. We find all hyperplanes where for all polyhedrons the point of Euclidean norm minimum is also one of the nearest points in any symmetrical norm. It simplifies the choice of criterion in some optimization problems.

In this paper we consider optimal trading processes in economic systems. The analysis is based on accounting for the irreversibility factor using the wealth func¬tion concept.

The dynamics of two weakly coupled close oscillators FitzHugh - Nagumo occuring in the simulation of the electric impulse exchange between nerve cells is considered. The delay in a connecting element between two oscillators is taken into account. Despite of the weakness of interaction, it is shown by local asymptotic methods that the introduction of a delay leads to significant changes in the script of phase reconstructions. The corresponding numerical analysis allows us to demonstrate that the introduction of the appropriate delay let us avoid the situation of the coexistence of a stable synchronous cycle and nonsynchronous oscillations.

The article is devoted to the creation of a data manipulation language for a new object DBMS, which should allow us to describe a simple data query of this model.