271 Works

ЗАДАЧА С УСЛОВИЕМ САМАРСКОГО ДЛЯ УРАВНЕНИЯ ДРОБНОЙ ДИФФУЗИИ В ПОЛУПОЛОСЕ

Ф.М. Лосанова & F.M. Losanova
In this paper, we construct a solution of a nonlocal boundary value problem with the condition Samarskii for a fractional diffusion equation in the half.

НЕОБХОДИМОЕ И ДОСТАТОЧНОЕ УСЛОВИЕ ЕДИНСТВЕННОСТИ РЕШЕНИЯ ЗАДАЧИ ДИРИХЛЕ ДЛЯ НЕЛОКАЛЬНОГО ВОЛНОВОГО УРАВНЕНИЯ

О.Х. Масаева & O.Kh. Masaeva
In this paper we find necessary and sufficient conditions for the uniqueness of the solution of the Dirichlet problem for the wave equation.

О МОДЕЛИ НАГРУЖЕННОГО ГИПЕРБОЛО-ПАРАБОЛИЧЕСКОГО УРАВНЕНИЯ В ЧАСТНЫХ ПРОИЗВОДНЫХ ВТОРОГО ПОРЯДКА

К.У. Хубиев & K.U. Khubiev
We studied a models of loaded equation of mixed hyperbolic-parabolic type with characteristicly and not characteristicly modifying line. For the proposed equation models boundary value problem is considered and solutions is written out.

КРАЕВАЯ ЗАДАЧА ДЛЯ ДИФФЕРЕНЦИАЛЬНОГО УРАВНЕНИЯ С ПРОИЗВОДНЫМИ ДРОБНОГО ПОРЯДКА С РАЗЛИЧНЫМИ НАЧАЛАМИ

Л.М. Энеева & L.M. Eneeva
We study a spectral problem for an ordinary differential equation with composition of fractional order differentiation operators in Riemann-Liouville and Caputo senses with different origins. We prove that for the problem under study there exist infinite sequences of eigenvalues and eigenfunctions. All of the eigenvalues are real and positive, and the eigenfunctions form an orthogonal basis in L2(0,1).

ИНВЕРСИИ В МОДЕЛИ ГЕОДИНАМО, УПРАВЛЯЕМОЙ 6-ЯЧЕЙКОВОЙ КОНВЕКЦИЕЙ

Г.М. Водинчар, Л.К. Фещенко, G.M. Vodinchar & L.K. Feshenko
We describe the large-scale model geodynamo, which based on indirect data of inhomogeneities in the density of the Earth’s core. Convection structure is associated with spherical harmonic Y42, which defines the basic poloidal component of velocity. Coriolis drift of this mode determines the toroidal component of velocity. Thus, 6 convective cells are formed. The model takes into account the feedback effect of the magnetic field on convection.It was ascertained that the model contains stable regimes...

ИНВЕРСИИ МАГНИТНОГО ПОЛЯ В МОДЕЛИ КРУПНОМАСШТАБНОГО ?? -ДИНАМО

Г.М. Водинчар, А.Н. Годомская, О.В. Шереметьева, G.M. Vodinchar & A.N. Godomskaya
In the paper investigates the question of the possibility of a reversal in the framework of low-mode model, ?? -dinamo. The parameters of the MHD system in which the possible reversal of the magnetic field in the relative constancy of the velocity field are defined. There are results of numerical solution of the assumption of various type of ? -effect amplitude dependence from the radius.

ТЕСТ ПЕНЛЕВЕ ДЛЯ ОДНОЙ СИСТЕМЫ МАГНИТНОЙ ГИДРОДИНАМИКИ

Г.М. Водинчар, Д.С. Нощенко, А.С. Пережогин, G.M. Vodinchar, D.S. Noshenko & A.S. Perezhogin
One approximation of magnetohydrodynamics equations, which describe the cosmic object’s magnetic field, is considered. The analytic properties of a nonlinear system are investigated by Painleve? test. Values of the coefficients in a simplified magnetohydrodynamics system are calculated for the necessary condition of Painleve? property.

СОХРАНЕНИЕ ТРЕТЬЕГО АДИАБАТИЧЕСКОГО ИНВАРИАНТА ДВИЖЕНИЯ В ПЛОСКОСТИ ЭКВАТОРА МАГНИТНОГО ПОЛЯ СО СЛАБОЙ АКСИАЛЬНОЙ НЕСИММЕТРИЕЙ

В.В. Богданов, А.В. Кайсин, V.V. Bogdanov & A.V. Kaisin
The question of preservation of the third adiabatic invariant motion of charged particles vII = 0 (equatorial plane) in the flow and the canonical form in magnetic fields having a weak asymmetry. Go to rotating with the angular velocity of the drift coordinate system allows us to reduce the problem to have been solved, namely, the task of saving the third adiabatic invariant in the axially symmetric, but the time-varying magnetic field.

ОЧИСТКА СИГНАЛОВ ГЕОАКУСТИЧЕСКОЙ ЭМИССИИ ОТ ПРИРОДНЫХ И ТЕХНОГЕННЫХ ШУМОВ МЕТОДОМ РАЗРЕЖЕННОЙ АППРОКСИМАЦИИ

О.О. Луковенкова & O.O. Lukovenkova
The approach of geoacoustic emission signals denoising from native and technogenic noises based on sparse approximation method is offered in this paper. The use of this means made it possible to clear geoacoustic emission pulses from technogenic parasitical component.

КОНЕЧНО-РАЗНОСТНЫЕ СХЕМЫ ДЛЯ ФРАКТАЛЬНОГО ОСЦИЛЛЯТОРА С ПЕРЕМЕННЫМИ ДРОБНЫМИ ПОРЯДКАМИ

Р.И. Паровик & R.I. Parovik
The paper deals with the explicit finite difference schemes for the fractional oscillator. The questions of approximation, stability and convergence of these schemes.

РЕШЕНИЯ ЗАДАЧ МАТЕМАТИЧЕСКОЙ ОЛИМПИАДЫ «ВИТУС БЕРИНГ – 2015»

Г.М. Водинчар, О.К. Жданова, Л.Д. Островерхая, Р.И. Паровик, А.С. Пережогин, О.В. Шереметьева, Т.П. Яковлева, G.M. Vodinchar, O.K. Zhdanova, L.D. Ostroverhaya, R.I. Parovik, A.S. Perezhogin, O.V. Sheremet’Eva & T.P. Yakovleva
We consider solutions of Mathematical Olympiad «Vitus Bering – 2015» for high school students. It was held at Kamchatka State University in November 2015.

ОБ УСТОЙЧИВОСТИ КРАЕВОЙ ЗАДАЧИ ДЛЯ УРАВНЕНИЯ ЧЕТНОГО ПОРЯДКА

А.В. Юлдашева & 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.

МАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕ ЗАКОНА ИЗМЕНЕНИЯ ЗАРЯДА ОБЛАЧНЫХ КАПЕЛЬ ВО ФРАКТАЛЬНОЙ СРЕДЕ

Т.С. Кумыков, Р.И. Паровик, T.S. Kumykov & R.I. Parovik
The paper proposed a new mathematical model of the variation of the charge cloud drops in storm clouds. The model takes into account the fractal properties of storm clouds, and the solution was obtained using the apparatus of fractional calculus.

МАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕ НЕЛОКАЛЬНОЙ КОЛЕБАТЕЛЬНОЙ СИСТЕМЫ ДУФФИНГА С ФРАКТАЛЬНЫМ ТРЕНИЕМ

Р.И. Паровик & R.I. Parovik
The paper considers a nonlinear fractal oscillatory Duffing system with friction. The numerical analysis of this system by a finite-difference scheme was carried out. Phase portraits and system solutions were constructed depending on fractional parameters.

НЕ ПОТЕНЦИАЛЬНОЕ ГЕОМАГНИТНОЕ ПОЛЕ, ТОКИ ШМИДТА-БАУЭРА И АТМОСФЕРНЫЙ ЭЛЕКТРИЧЕСКИЙ ТОК

В.В.Кузнецов & V.V. Kuznetsov
According to the developing model, the nonpotential part of the geomagnetic field is due to the vertical current associated with positive charge transfer by water vapour during plant and water surface evaporation in the same direction and with negative rain current in the opposite direction. These two processes are quite irregular both in space and in time, but the total charge transfered upwards to the clouds is almost equal to the charge transfered downwards to...

ГОРНЫЙ УДАР – ПРИЧИНА ВЫБРОСА МЕТАНА В УГОЛЬНОЙ ШАХТЕ?

В.В.Кузнецов & V.V. Kuznetsov
The model, which hit a mountain (technogenic earthquakes) - is presented as a way out of the shock wave at the inner wall of the shaft. This raises the unloading wave, stretching, moving backward (deep wall) direction. Shock wave accompanied by the movement of the medium in the propagation direction of the shock waves at a speed considerably less than that of the wave. The totality of phenomena occurring on the inner surface of the...

ВЫСОКОЧАСТОТНЫЙ АКУСТОЭМИССИОННЫЙ ЭФФЕКТ

Ю.В. Марапулец & Yu.V. Marapulets
Complex monitoring of acoustic emission (AE) in the sound frequency range has been carried out in the Kamchatka peninsular since 1999. In the course of the investigation, the existence of acoustic emission effect in sedimentary rocks was detected. It consists in the increase of geoacoustic radiation intensity in the frequency range from hundreds of hertz to the first tens of kilohertz during the growth of rock mass deformation rate. This effect was stably observed at...

ОСОБЕННОСТИ КАЛИБРОВКИ ДЕТЕКТОРОВ ИОНИЗИРУЮЩИХ ИЗЛУЧЕНИЙ, ИСПОЛЬЗУЕМЫХ ДЛЯ МОНИТОРИНГА ПОЧВЕННОГО РАДОНА

В.С. Яковлева, П.М. Нагорский, V.S. Yakovleva & P.M. Nagorskiy
The results of calibration of ?-, ?- and ?-radiation detectors mounted into borehole at depths of 0.5 and 1 m, which are destined for soil radon monitoring, are represented and analyzed. The radon isotopes radiometer RTM 2200 (SARAD GmbH, Germany) was used for the calibration aim.

РАЗВИТИЕ ТЕХНОЛОГИИ РАДИАЦИОННОГО МОНИТОРИНГА В ГОРОДСКОЙ СРЕДЕ

В.С. Яковлева, П.М. Нагорский, V.S. Yakovleva & P.M. Nagorskiy
The results of monitoring of meteorological and radiation parameters in Tomsk Observatory of Radioactivity and Ionizing Radiation are presented and analyzed in this work. The advantages of new radiation monitoring technology including the investigation of radiation parameters vertical profiles are presented. The verification of existing soil and atmosphere radon isotopes transport models were conducted for urban environment with help of analysis results of radiation monitoring data.

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.

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.

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.

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.

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