Статьи журнала - Математическая физика и компьютерное моделирование

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3D вариант W-модификации метода Годунова для нестационарных течений совершенного газа

3D вариант W-модификации метода Годунова для нестационарных течений совершенного газа

Васильев Евгений Иванович, Демин Александр Сергеевич

Статья научная

Предлагается модификация метода Годунова повышенной точности для трехмерных нестационарных течений совершенного газа. Доказано свойство позитивности предложенной схемы для линейного скалярного уравнения переноса. Проведено тестирование метода на примере задачи о запуске трехмерного профилированного сопла квадратного сечения.

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A question of ahlfors

A question of ahlfors

Krushkal Samuel L.

Статья научная

In 1963, Ahlfors posed in [1] (and repeated in his book [2]) the following question which gave rise to various investigations of quasiconformal extendibility of univalent functions. Question. Let ?? be a conformal map of the disk (or halfplane) onto a domain with quasiconformal boundary (quasicircle). How can this map be characterized? He conjectured that the characterization should be in analytic properties of the logarithmic derivative log ??? = ????/???, and indeed, many results on quasiconformal extensions of holomorphic maps have been established using ????/??? and other invariants (see, e.g., the survey [9] and the references there). This question relates to another still not solved problem in geometric complex analysis: To what extent does the Riemann mapping function ?? of a Jordan domain ?? ? ??C determine the geometric and conformal invariants (characteristics) of complementary domain ??* = ??C ? ??? The purpose of this paper is to provide a qualitative answer to these questions, which discovers how the inner features of biholomorphy determine the admissible bounds for quasiconformal dilatations and determine the Kobayashi distance for the corresponding points in the universal Teichmuller space.

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AB INITIO расчет поверхности потенциальной энергии водородной связи димера воды

AB INITIO расчет поверхности потенциальной энергии водородной связи димера воды

Лебедев Н.Г.

Статья научная

Проведен квантово-химический неэмпирический расчет профиля поверхности потенци- альной энергии водородной связи молекулы димера воды, находящейся в основном и возбуж- денных состояниях, с помощью метода Хартри - Фока с использованием базисных наборов STO-3G, 6-31G*, 6-31++G**. Показано, что во всех выбранных методах ab initio существует минимум потенциала, соответствующий основному состоянию молекулы димера воды. Пока- зано, что для димера в возбужденном состоянии существует два минимума потенциала водо- родной связи, разделенных переходным состоянием.

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Application Mellin transforms to the Black - Scholes equations

Application Mellin transforms to the Black - Scholes equations

Vasileva T.A., Vasileva O.E.

Краткое сообщение

In this paper we will consider the Mellin transform derived on Black - Scholes formulae in year 2003 by Panini, Srivastav and Jodar [6; 7]. The authors use Mellin transforms to derive at first an equation for the price of a European put on a single underlying stock. This case will be extended to the Amercan put option. It is assumed, there are no dividends. Nowadays derivative markets become extremely popular, this popularity even exceeds that of the stock exchange [4; 5; 10]. Option price estimation as the most interesting of the derivatives has many approaches and is multifaceted [2; 3; 8]. Authors would like to thank Professor E.I. Vasilev for the target setting and useful discussions.

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Application of computational methods for creating and selecting polymeric compositions with given properties

Application of computational methods for creating and selecting polymeric compositions with given properties

Derbisher Evgenia Vyacheslavovna, Derbisher Vyacheslav Evgenievich

Статья научная

The article discusses current mathematical methods (probabilistic, regression, correlation, fuzzy, graph, and others) used in the study of the structure and property dependencies of polymer compositions and polymer composite materials. The authors consider the methodology and theoretical aspects of modeling these dependencies, give technological calculations using models. The paper provides examples of the analysis of the particular case of complex chemical and chemical-technological systems, polymer compositions and composite (polymer) materials. The authors show a possible solution to the problems of assessing the quality of composite polymer materials and the rational choice of the composition in homogeneous sets using fuzzy sets.

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C1-аппроксимация решений эллиптических систем кусочно-гладкими отображениями

C1-аппроксимация решений эллиптических систем кусочно-гладкими отображениями

Болучевская А.В.

Статья научная

В работе рассматривается задача кусочно-гладкой аппроксимации отображе- ний, являющихся решением эллиптической системы уравнений, и аппроксимации их дифференциалов по значениям в узлах треугольной сетки. Показано, что при аппроксимации дифференциалов таких отображений дифференциалами прибли- жающих отображений имеет место зависимость погрешности аппроксимации от геометрических характеристик треугольников в сети. Построено отображение, приближающее дифференциал с погрешностью, независящей от степени вырож- денности треугольников. Аналогичные результаты получены для отображений, аппроксимирующих дифференциал решения уравнения Бельтрами.

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Can one observe the bottleneckness of a space by the heat distribution?

Can one observe the bottleneckness of a space by the heat distribution?

Ishiwata Satoshi

Статья научная

In this paper we discuss a bottleneck structure of a non-compact manifold appearing in the behavior of the heat kernel. This is regarded as an inverse problem of heat kernel estimates on manifolds with ends obtained in [10] and [8]. As a result, if a non-parabolic manifold is divided into two domains by a partition and we have suitable heat kernel estimates between different domains, we obtain an upper bound of the capacity growth of δ-skin of the partition. By this estimate of the capacity, we obtain an upper bound of the first non-zero Neumann eigenvalue of Laplace - Beltrami operator on balls. Under the assumption of an isoperimetric inequality, an upper bound of the volume growth of the δ-skin of the partition is also obtained.

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Combining theory and experiment for understanding of ultrafast photoinduced charge-transfer processes

Combining theory and experiment for understanding of ultrafast photoinduced charge-transfer processes

Vauthey Eric

Статья научная

This article gives a brief overview of the long-standing collabora- tion between our experimental spectroscopy group in Geneva and the theoretical group lead by Prof. A.I. Ivanov in Volgograd. This fruitful collaboration resulted in a significant increase of our understanding of the dynamics of several ultrafast charge-transfer processes in the condensed phase.

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Complex rigidity of Teichmu"ller spaces

Complex rigidity of Teichmu"ller spaces

Krushkal Samuel L.

Статья научная

We outline old and new results concerning the well-known problems in the Teichmu¨ ller space theory, i.e., whether these spaces are starlike in the Bers holomorphic embedding and whether any Teichmu¨ ller space of dimension greater than 1 is biholomorhically equivalent to bounded convex domain in a complex Banach space.

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Crystallographic groups for Ho"rmander fields

Crystallographic groups for Ho"rmander fields

Zegarlinski Boguslaw

Статья научная

This is a preview paper on Crystallographic Groups of Ho¨ rmander Fields. We describe an emerging picture in analysis of extended groups. In particular, we introduce and provide examples of Crystallographic Groups associated to a Ho¨ rmander system of fields as well as discuss some related analysis.

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Dynamics of the magnetization of a single-domain deformed soft magnetic ferromagnet

Dynamics of the magnetization of a single-domain deformed soft magnetic ferromagnet

Yermolenko Igor P., Lebedev Nikolay G.

Статья научная

On the basis of the quantum model taking into account the Zeeman energy and the energy of the crystal field, dynamic equations of Landau - Lifshitz - Hilbert type for the magnetization of the deformed single-domain α-Fe crystal are obtained. The domain deformation is taken into account in the framework of a linear approximation. The equations of motion are solved numerically using the Adams - Multon, Rosenbrock, and RADAU5 methods. It is shown that for some values of the model parameters, the dependence of the magnetization on the strength of an external magnetic field has the characteristic form of a hysteresis loop. Qualitative agreement of the model dependence of the coercive force on the applied longitudinal pressure with similar experimental data for various steel grades Durehete 1055, AS1548-7-46OR, X70, 11HN3D is obtained.

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Effect of vibrational transitions on the nonthermal charge transfer probability

Effect of vibrational transitions on the nonthermal charge transfer probability

Mikhailova Elena Alexandrovna, Mikhailova Valentina Alexandrovna

Статья научная

In the framework of the stochastic approach, the effect of transitions between the vibrational sublevels of products on the ultrafast dynamics of “hot” (non-thermal) electron transfer in donor - acceptor complexes dissolved in a polar medium has been investigated. An analytical expression has been obtained for the probability of electron transfer, which takes into account the transition between the vibrational states of products and the mutual influence of sinks. Quantitative estimates of the scale of the mutual influence of sinks on the probability of electron transfer are made.

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L-устойчивость мульти-неявных методов 8-го порядка для жестких систем дифференциальных уравнений

L-устойчивость мульти-неявных методов 8-го порядка для жестких систем дифференциальных уравнений

Васильев Евгений Иванович, Васильева Татьяна Анатольевна, Киселева Мария Николаевна

Статья научная

Проведено исследование свойств устойчивости расширенного двухпараметрического семейства трижды неявных разностных схем со второй производной. Показано, что семейство имеет 8-й порядок точности. Также показано, что среди множества A -устойчивых SISD-схем существует два однопараметрических семейства: семейство Z-устойчивых схем и семейство схем повышенной точности для линейных задач. Проведено тестирование таких разностных схем на линейной и нелинейной задачах с различной степенью жесткости. Представлены зависимости интегральной погрешности численного решения от величины шага интегрирования, на основе которых проведен анализ свойств устойчивости и точности предлагаемых 3ISD-схем.

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Modeling of two-dimensional light bullets propagation in an array of carbon nanotubes taking into account the mechanical tension and magnetic field

Modeling of two-dimensional light bullets propagation in an array of carbon nanotubes taking into account the mechanical tension and magnetic field

Konobeeva Natalia N., Skvortsov Dmitry S.

Статья научная

In this paper, we study the influence of acoustic and magnetic fields on the propagation of the two-dimensional light bullet in an array of carbon nanotubes. The acoustic field is taken into account in the framework of the gauge theory. A magnetic field is applied along the nanotube axis and leads to a change in the electronic spectrum of π-electrons. It is shown that the pulse stably pro-pagates in the medium, taking into account both of these factors. In this case, themagnetic field and tension slow down the pulse, as well as change its amplitude.

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Multichannel nodes with identical time of service

Multichannel nodes with identical time of service

Pavlov Andrey Valerianovich

Статья научная

The author investigates multichannel nodes in series with different service disciplines of service without an interruption of service in every node. Very big decrease of the virtual time of wait in inlying nodes is proved. Exact estimations of time of wait on the inlying nodes are resulted.

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N-решения уравнения минимальных поверхностей

N-решения уравнения минимальных поверхностей

Романова И.А.

Статья научная

Работа посвящена исследованию решений уравнения минимальных поверхно- стей, полученных методом, разработанным в [3].

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Next-generation network monitoring systems - critical requirements and design

Next-generation network monitoring systems - critical requirements and design

Natarov Alexander Maksimovich, Shirokii Alexander Alexandrovich

Статья научная

The article deals with the monitoring systems and their usage in IT-infrastructure. The first generation of monitoring systems grew up from instruments made by software companies for their internal needs. Such systems currently fail to meet the actual business requirements. The number of used by common enterprises business applications and software services grows vigorously. It led to depletion of legacy systems’‘ scaling abilities. Now business asks for new generation monitoring systems, which are flexible, able to process large-scale IT-infrastructures and has low operation costs. This article is devoted to revealing qualitative monitoring systems requirements by evaluation of several companies’‘ business requirements. Those companies have various level of IT infrastructure integration in their business processes. We interviewed more than 50 tech specialists and managers and grouped requirements by IT-infrastructure scale. We formulated critical requirements for new generation monitoring systems using previously collected data and also opened access to best-practices of such systems implementation and usage. We also proposed feasible architecture of next-generation monitoring system.

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On Phragme'n - Lindelo"f principle for non-divergence type elliptic equations and mixed boundary conditions

On Phragme'n - Lindelo"f principle for non-divergence type elliptic equations and mixed boundary conditions

Ibraguimov Akif, Nazarov Alexander I.

Статья научная

The paper is dedicated to qualitative study of the solution of the Zaremba-type problem in Lipschitz domain with respect to the elliptic equation in non-divergent form. Main result is Landis type Growth Lemma in spherical layer for Mixed Boundary Value Problem in the class of “admissible domain”. Based on the Growth Lemma Phragme´n - Lindelo¨ f theorem is proved at junction point of Dirichlet boundary and boundary over which derivative in non-tangential direction is defined.

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On pseudo-slant submanifolds of nearly quasi-sasakian manifolds

On pseudo-slant submanifolds of nearly quasi-sasakian manifolds

Rahman Shamsur, Khan Mohd Sadiq, Horaira Aboo

Статья научная

The geometry of pseudo-slant submanifolds of nearly quasi Sasakian manifold is studied. It is proved that totally umbilical proper-slant submanifold of nearly quasi Sasakian manifold admits totally geodesic if the∈mean curvature vector µ. The integrability conditions of the distributions ofpseudo-slant submanifolds of nearly quasi Sasakian manifold are also obtained.

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