Vestnik KRAUNTS. Fiziko-matematicheskie nauki

12-37

Authors: R. F. Shamoyan, V.V. Loseva

We discuss some new problems in several new mixed norm Hardy type spaces in products of bounded pseudoconvex domains with smooth boundary in Cn and then prove some new sharp decomposition theorems for multifunctional Hardy type spaces in the unit ball and then we show also similar results in pseudoconvex and convex domains of finite type extending previously known assertions obtained by first author earlier in Bergman spaces under certain Poisson integral type condition which vanishes in one functional case. Some new (in particular sharp in the unit ball) embeddings for some new mixed norm Hardy spaces in bounded pseudoconvex domains will be also indicated. Some new extensions of Poisson integral in the unit ball and some new assertions concerning them will be indicated and discussed in product domains. Some related multifunctional results are also given.Some new embedding theorems are also provided in some new mixed norm Hardy spaces in unbounded tubular domains over symmetric cones.

47-54

Authors: Е. R. Novikova

A study is conducted on the asymptotic stability of the rest points of the fractional oscillator Van der Pol-Duffing. The fractional van der Pol-Duffing oscillator is an oscillatory system of two differential equations with fractional order derivatives in the sense of Gerasimov-Caputo. The orders of fractional derivatives characterize the properties of the medium (memory effects) in which the oscillatory process takes place and can be the same (commensurate) or different (incommensurable). Using theorems for commensurable and incommensurable systems, the asymptotic stability of the rest points of the fractional van der Pol-Duffing oscillator is investigated with concrete examples. The results of the studies were confirmed by constructing the appropriate waveforms and phase trajectories.

74-94

Authors: I. I. Chekrygin, A. A. Faraonov

This article describes the problem of using parallel computing for the correlation analysis of large amounts of data.

105-116

Authors: G. I. Druzhin, V.M Pukhov, D. V. Sannikov, E. I. Malkin, I. E. Stasiy

In order to study the natural noise electromagnetic radiation at the Institute of Cosmophysical Research and Radio Wave Propagation FEB RAS, a VLF-recorder was developed, created and installed in Kamchatka, in the expedition point «Karymshina». Continuous observations carried out with the help of VLF-registrator allowed to study various geophysical effects associated with the propagation of radio waves, thunderstorm activity, earthquakes, cyclones.

17-27

Authors: A. Ebadian, A. Jabbari

Let A and B be Banach algebras and T: B→A be a continuous homomorphism. We consider left multipliers from A×TB into its the first dual i.e., A*×B* and we show that A×TB is a hyper-Tauberian algebra if and only if A and B are hyper-Tauberian algebras.

46-53

Authors: E. A. Gafurova, M. L. Mikhaylov, Yu.V. Grushko, R. I. Parovik, I. A. Kashutina

The paper proposes a new mathematical model of the dynamics of small enterprises with the participation of foreign investment, which takes into account the memory effect and affects the rate of change in the value of production assets. This memory effect can be considered as a property of the economic environment, for example, the influence on the production of external factors, in which the cost of production assets will depend on its previous values. This non-local effect can be written in terms of a fractional order derivative. In this paper, we will assume that the order of the fractional derivative is a function of time. Therefore, we will solve the initial model equation using numerical methods of the theory of finite difference schemes. Further, in the work, visualization and interpretation of the calculation result was carried out.

63-70

Authors: O. D. Lipko

In this paper, using the qualitative analysis, we studied the stability of the point of rest of the fractional oscillator FitzHugh-Nagumo in commensurate and incommensurable cases. For the corresponding point of rest, using the numerical method of the theory of finite difference schemes, phase trajectories were constructed. It is shown that quiescent points can be both asymptotically stable, which correspond to stable focus, and are asymptotically unstable (unstable focus), and for them the phase trajectories usually go to the limit cycle.

78-93

Authors: M. E. Semenov, T.Yu. Zablotskaya

In the paper, the biological neural network models are analyzed with a purpose to solve the problems of segmentation and pattern recognition when applied to the bio-liquid facies obtained by the cuneiform dehydration method. The peculiarities of the facies’ patterns and the key steps of their digital processing are specified in the frame of the pattern recognition. Feasibility of neural network techniques for the different image data level digital processing is reviewed as well as for image segmentation. The real-life biological neural network architecture concept is described using the mechanisms of the electrical input-output membrane voltage and both induced and endogenic (spontaneous) activities of the neural clusters when spiking. The mechanism of spike initiation is described for metabotropic and ionotropic receptive clusters with the nature of environmental exciting impact specified. Also, the mathematical models of biological neural networks that comprise ot only functional nonlinearities but the hysteretic ones are analyzed and the reasons are given for preference of the mathematical model with delay differential equations is chosen providing its applicability for modeling a single neuron and neural network as well.

100-109

Authors: L. D. Ostrоverhaya, O. K. Zhdanova

In this paper, an effective spiral method is proposed for selecting the roots belonging to a given interval (longer than 2π) when solving trigonometric equations.