In the article it is considered the Nerve Impulse Saltatore Conduction model in which the Impulse Neuron model modification is used for describing Ranvier Interruptions dynamics. The model contains ordinary differential equations and delay differential equations. The system is investigated by the asymptotic step-by-step integration method. All results were obtained analytically.

A new algorithm for the recognition of digits is proposed. The result of computer experiments is described.

In this work nets of active resources (AR-nets) are presented. This is a generalization of Petri nets (ordinary and Super-dual) with a single type of nodes and two types of arcs (consuming and producing). Each node may contain a number of tokens (resources), that can be consumed or produced by "firings" of other tokens (location of consumed/produced resources is defined by corresponding arcs). So, in this model the same token may be considered as a passive resource (produced or consumed by agents) and an active agent (producing or consuming resources) at the same time.
The expressive power of AR-nets and two modified models is studied. It is shown, that AR-nets and AR-nets with simple firing are equivalent to ordinary Petri nets. AR-nets with simultaneous firing are strictly more expressive.

This article presents a synchronous model of the automaton program. A technique of verification of synchronous-automaton programs has been developed. Some properties of the model are checked automatically. There is an ability of verifying user-defined properties. This technique helps to discover errors often made during the design process.

Here the asymptotic approach in scientific creativity for receiving new knowledge is considered, as well as the creation of words as a scientific method for the preparation of the author's abstract of a dissertational work. The paper is devoted to passports of scientific specialities which define problems, borders and the depth of future research. The resonant interaction of the passport of a scientific speciality and a dissertation defines an algorithmic basis in the practical realization of the cognitive decision-making technology.

In this paper some axiomatic generalization (function of open subsets) of the relative Lyusternik - Schnirelmann category is considered. For this function and a given map of the underlying space to a finite polyhedron some lower bounds on the value of this function on the preimage of some point are given.

Theorems of R. Rado and of D. Watson are generalizations for theorems P. Kirchberger and C. Caratheodory. In the paper we will consider some generalizations and refinements for these theorems .

In the article the formal model of proverb semantics is suggested. The proverb statement is considered as a construction of two semantic oppositions and a so called mythological equation. The opposition lexicon forms a sort of semantic network. This model is to be used as the intellectual module kernel in the information system METAPHORA developed to process proverbs at the semantic aspect.

A permutation т is сallеd k + 1-nondecomposible if the following condition holds: if {ai,..., ain} is a set of natural numbers such that 1 <= a1, <...,< a_i <= n and т(a1) < т(a2) < < т(a_i), then i <= к. By f (n, к) denote the number of all not к + 1-nondecomposible permutations.
The following statement was proved in this paper: suppose K(n) = o( 3 /n/ ln n); then f (n, к) = к^2п-о(п) for every к <= K( n) .