Vestnik KRAUNTS. Fiziko-matematicheskie nauki

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.