Vestnik KRAUNTS. Fiziko-matematicheskie nauki

8-19

Authors: R. I. Parovik

In the training course of the theory of differential equations, there exists a section on the investigation of the stability of systems of differential equations. If the system of differential equations consists of differential equations of integer order, then the stability theory of Lyapunov is usually used to study the stability of their rest points. However, in the case when the system of differential equations consists of differential equations of non-integer order, then it is necessary to use other methods of investigating the stability of such systems. Therefore, this article is devoted to the method of investigating the rest points of systems of differential equations of fractional order. In this paper we will investigate the stability of the rest points of the hereditary dynamical systems by the example of some fractal oscillators. Moreover, we will consider two types of hereditary dynamical systems: commensurable and incommensurate, for which the corresponding stability theorems for rest points are valid. Next, examples of applying these stability theorems to a fractal linear oscillator, the Duffing fractal oscillator, are considered. The results of the study of the stability of the rest points of the hereditary dynamical systems were confirmed by constructing phase trajectories for the fractal oscillators under consideration. This article can be useful in the study of a fairly new section in the theory of differential equations-fractional calculus.

28-32

Authors: A. A. Nabokin

This article describes the problem of creating scientific services based on web technologies. The implementation of the software complex of processing of atmospheric phenomena data at different heights is presented. The software package uses the method of elastic light scattering, atmospheric model NRLMSISE-00 and fork of this model, to get a ratio of scattering at heights from 0 to 150 kilometers.

45-52

Authors: M. I. Garapov

In this article, the problem of using distributed computing systems for solving global projects of simulation simulation and mathematical calculations is considered. Also, in the historical example, the use of BOINC distributed computing in practice is considered. The problems of practical implementation of distributed computing projects and ways to solve them are identified. A distributed computing server and a test task to it have been created. Implemented a system of network services and interaction of project users with the database.

71-84

Authors: Y. I. Senkevich, M. I. Gapeev

We present a technology of creation of visual application design environment for hardwaresoftware complexes (VDE HSC) aimed at acoustic and electromagnetic emission signal processing and analysis. The technology includes the operations of block visual design method with auto-negotiation of interblock connection, method of modeling and design tools integration by connection devices of known and self-developed instrumentation means and algorithms of inner-established blocks. The obtained effect from application of the created environment will allow the researches of laboratories to avoid the necessity of obtaining new special knowledge not referring to their experience and to simplify significantly application of functional modules and electronic libraries of universal design environments built in the developed program interface wrapper, on one side, and to create acting experimental units ready for operation when its structural scheme has been drawn, on the other side. The results of the investigations on implementation and extending the capabilities of experiment software environment receive practical approval at the Laboratory of Acoustic Research of the Institute of Cosmophysical Research and Radio Wave Propagation (IKIR FEB RAS).

100-111

Authors: V.V. Kuznetsov

The author in recent years is developing a shock-wave model of the earthquake. The shock wave (SW) at the time of the earthquake is formed when the structural phase transition is realized in the hypocentre region, it comes to the surface of the Earth and is reflected. In this case, a reflected wave of expansion (discharge) appears, directed opposite to the shock wave. The interaction of these waves leads to strong movements: surface ruptures, decompaction of the ground, its vibrational movements, and so on. It is known that earthquakes and volcanic eruptions are «related phenomena». They occur on Earth, as a rule, in the same place (for example, on the coast of the Pacific Ocean). Analyzing the seismic wave pattern under the source of volcanoes, one can see that in most cases the magmatic source does not have roots that go into the mantle to the outer core of the Earth. The question arises, how is an magma chamber isolated from the outside world created, and how does magma preheat it? As you know, there is no sound answer. In this work, a fundamentally new model of the volcano is proposed, according to which the origin of the magma chamber and its regular «feeding»by energy occur due to shock waves exactly the same as those that cause earthquakes. The shock wave, which leads to an earthquake, spreads in an elastic medium and comes to the Earth’s surface with practically no loss of energy and when it leaves the earth’s surface it destroys it. If the hydrocarbon meets in its path an inelastic (eg porous or liquid) medium in which an unloading wave occurs, then the shock wave dissipates with heating of the medium and the formation of a magmatic source. It is obvious that on the surface of the Earth in this case the SW leaves a completely different «trace and this will already be a volcano.

128-144

Authors: T.P. Yakovleva

In the article the control work on the discipline «Theory and technology of development of mathematical representations in children»is presented. It covers: 25 options; methodical recommendations on writing, execution and execution of the test work.