## Bulletin of KRAESC 2014 #2

#### Mathematics

##### FINITE GENERATED SUBGROUPS OF HYPERBOLIC GROUPS

A.P. Goryushkin

It is proved that finite generated subgroups of infinite index of hyperbolic groups which are not quasi Abelian are complemented with a nontrivial free factor.

##### CERTAIN PROPERTIES OF FRACTIONAL INTEGRO-DIFFERENTIATION OPERATOR OF FUNCTIONS IN OTHER FEATURES

A.S. Nishonboev

Prove an important lemma for the operator of fractional integro-differentiation of functions of other functions.

##### ON ONE PROBLE FOR HIGHER-ORDER EQUATION

A.V. Yuldasheva

In this paper not well posed problem for the even-order equation is studied. The stability of the problem is restored by additional conditions and conditions to domain.

##### ABOUT A METHOD OF RESEARCH OF THE NON-LOCAL PROBLEM FOR THE LOADED MIXED TYPE EQUATION IN DOUBLE-CONNECTED DOMAIN

O.Kh. Abdullayev

#### Mathematical modelling

##### MODELING INVERSIONS WITHIN LOW-MODE MODEL OF LARGE-SCALE DYNAMO

G.M. Vodinchar, A.N. Godomskaya, O.V. Sheremetyeva

##### NUMERICAL ANALYSIS SOME OSCILLATION EQUATIONS WITH FRACTIONAL ORDER DERIVATIVES

R.I. Parovik

The paper presents a mathematical model of non-classical dynamic systems. A numerical method of difference schemes, depending on various parameters of the system were found numerical solutions of models. The phase trajectory.

#### Physics

##### LOCATION OF THE SOURCE OF THE GEOMAGNETIC FIELD GENERATION

V.V. Kuznetsov

Using well-known data on the structure of the geomagnetic field it is shown that its generation source is located at the boundary between the Earth inner and outer cores, most likely, in the F-layer.

##### POSSIBLE EFECTS OF THE LIGHTNING CENTERS IN WHISTLER RATES IN KAMCHATKA

G.M. Vodinchar, V.P. Sivokon'1, N.V. Cherneva, B.M. Shevtsov, E.A. Malysh

The paper investigates possible sources of Kamchatka whistlers in March and September 2013. Applying the data from WWLLN and AWDANet worldwide networks, it is shown that statistically significant sources may be located in the global lightning centers.

##### PASSAGE THROUGH X-RAY PROTECTION HAVING THE STRUCTURE OF HOMOGENEOUS FRACTALS

V.A. Churikov

In this paper we generalize the law of Bouguer-Lambert in the case of a homogeneous fractal. With detailed analysis in terms of d-output operator generalized law of Bouguer-Lambert-Beer law, which in particular includes the classical law of optics Bouguer-Lambert-Beer.

#### Information and Computation Technologies

##### COMPARISON OF THE SPARSE APPROXIMATION METHODS BASED ON ITS USE TO GEOACOUSTIC EMISSION SIGNALS

O.O. Lukovenkova

The paper is devoted to the comparative analysis of some sparse approximation methods. The first part of the paper describes general sparse approximation problem and two main approaches solved it. Classification of testing pursuit algorithm is illustrated. Features of the methods application to geoacoustic emission signals are considered in the second part. The sparseness, accuracy and runtime of described pursuit algorithms are compared.

##### THE USE OF PARALLEL PROGRAMMING METHODS FOR TIME-FREQUENCY ANALYSIS OF GEOACOUSTIC EMISSION SIGNALS

A.A. Kim

It has been shown in previous studies that the sparse approximation methods with combined dictionary and refining have been used for this purpose. The main disadvantage of this method is its computational expensive. The realization of parallel matching pursuit algorithm has been considered in this article. It has been shown that using of parallel algorithm speeds up the processing and enables signal analysis in real time.

##### THE TECHNIQUE OF INCREASE THE EFFICIENCY OF LEARNING NEURAL KOHONEN MAPS FOR RECOGNITION OF PERTURBATIONS GEOACOUSTIC EMISSION

A.V. Shadrin

This work is dedicated to technique of training Kohonen maps on the example of geoacoustical signal in the subrange 1500-6000 Hz. Describes the parameters of learning the Kohonen maps to classify anomalies in geoacoustical signal on different types.