Статьи журнала - Математическая физика и компьютерное моделирование
Все статьи: 565
3D вариант W-модификации метода Годунова для нестационарных течений совершенного газа
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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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
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
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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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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Статья научная
This work is carried out with the purpose developing the fundamental breast cancer early differential diagnosis foundations based on modeling the spatio-temporal temperature distribution using the microwave radiothermometry method and intelligent analysis of the data obtained. The article deals with the machine learning application in the microwave radiothermometry data analysis. The problems associated with the construction of mammary glands temperature fields computer models for patients with various diagnostics classes, are also discussed. With the help of a computer experiment, based on the machine learning algorithms set (logistic regression, naive Bayesian classifier, support vector machine, decision tree, gradient boosting, K-nearest neighbors, etc.) usage, the mammary glands temperature fields computer models set adequacy.
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C1-аппроксимация решений эллиптических систем кусочно-гладкими отображениями
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?
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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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
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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Conformal cyclic phantom energy dominated cosmological scenario from loop quantum cosmology
Статья научная
Phantom energy dominated final stages of the universe is analyzed with the conformal cyclic scenario. Quantum cosmological implementation on conformal cyclic cosmology is attempted in this work. The conformal emergence of the quantum cosmological scenario is discussed. It is shown that the classical universe will not be completely ripped off at phantom dominated final stages. Further extension of evolution through conformal cyclic evolution is predicted. This article is intended to connect loop quantum formalism with conformal cyclic cosmological formalism.
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Crystallographic groups for Ho"rmander fields
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
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
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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Exact solutions of the generalized nonlinear Schrodinger equation
Статья научная
In this work, the generalized nonlinear Schrodinger equation is investigated. Exact solutions are derived by the sine-cosine method. This method is used to obtain the exact solutions for different types of nonlinear partial differential equations. Graphs of obtained solutions are presented. The obtained solutions are found to be important for the explanation of some practical physical problems.
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Статья научная
In this paper, the authors study the influence of a random stress on the parameters of an extremely short optical pulse as it propagates in a nonlinear medium with carbon nanotubes, taking into account the processes of multiphoton absorption and pumping by an external electromagnetic wave. The dependence of the intensity and width of the pulse field on the number of photons, as well as on the amplitude of the pump pulse, is analyzed.
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Features of the electronic structure of excited quadrupolar molecules in non-polar solvents
Статья научная
Interactions of the electronic subsystem of the quadrupolar fluorophore with intramolecular highfrequency antisymmetric vibrations and solvent polarization are responsible for charge transfer symmetry breaking (SB), which is observed after optical excitation of such molecules in polar solvents. It is known that although these two interactions are mathematically described in similar ways, only the interaction of the fluorophore with solvent orientational polarization can create a state with broken symmetry if this interaction is strong enough. Nevertheless, the interaction of a quadrupolar fluorophore with intramolecular highfrequency antisymmetric vibrations in nonpolar solvents leads to a considerable reconstruction of the electronic subsystem. The analysis of the excited state of quadrupolar molecules in nonpolar solvents performed in this study reveals that such molecules can behave like quantum twostate systems, that is, as a quasispin = 1/2, having an electric dipole moment instead of a magnetic one. This feature of excited quadrupolar molecules may be of interest to emerging technologies of molecular electronics.
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L-устойчивость мульти-неявных методов 8-го порядка для жестких систем дифференциальных уравнений
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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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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