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181 results on '"Vinitsky, S. I."'

159. A symbolic-numeric approach for solving the eigenvalue problem for the one-dimensional Schrоdinger Equation

Author

Belyaeva, I. N., Chekanov, N. A., Gusev, A. A., Rostovtsev, V. A., Vinitsky, S. I., Belyaeva, I. N., Chekanov, N. A., Gusev, A. A., Rostovtsev, V. A., and Vinitsky, S. I.

Abstract

A general scheme of a symbolic-numeric approach for solving the eigenvalue problem for the one-dimensional Shrodinger equation is presented. The corresponding algorithm of the developed program EWA using a conventional pseudocode is described too. With the help of this program the energy spectra and the wave functions for some Schrodinger operators such as quartic, sextic, octic anharmonic oscillators including the quartic oscillator with double well are calculated

160. A REDUCE program for the normalization of polynomial Hamiltonians

Author

Ukolov, Yu. A., Chekanov, N. A., Gusev, A. A., Rostovtsev, V. A., Vinitsky, S. I., Ukolov, Yu. A., Chekanov, N. A., Gusev, A. A., Rostovtsev, V. A., and Vinitsky, S. I.

Abstract

The program LINA01 is proposed for the direct and the inverse normalization of Hamiltonian systems and for the calculation of formal integrals of motion of them. The calculations required in LINA01 are made on the basis of Lie canonical transformation method. The program package of LINA01 is written on REDUCE, Belgorod State University

162. A comparison of algorithms for the normalization and quantization of polynomial hamiltonians

Author

Uwano, Y., Gusev, A. A., Chekanov, N. A., Rostovtsev, V. A., Vinitsky, S. I., Uwano, Y., Gusev, A. A., Chekanov, N. A., Rostovtsev, V. A., and Vinitsky, S. I.

Abstract

Algorithms and programs for the normalization of polynomial Hamiltonians of classical mechanics by the Birkhoff-Gustavson and Deprit-Hori, as well as quasi-classical quantization procedures for normal forms, are compared. The algorithms and programs are represented in a universal pseudocode and implemented in the computer algebra systems REDUCE, MAPLE, and MATHEMATICA. Examples that illustrate the operation of these algorithms and programs for polynomial Hamiltonians of atomic systems in external electromagnetic fields are considered

163. A MAPLE symbolic-numeric program for solving the 2D-eigenvalue problem by a self-consistent basis method

Author

Uwano, Y., Belyaeva, I. N., Chekanov, N. A., Gusev, A. A., Rostovtsev, V. A., Ukolov, Yu. A., Vinitsky, S. I., Uwano, Y., Belyaeva, I. N., Chekanov, N. A., Gusev, A. A., Rostovtsev, V. A., Ukolov, Yu. A., and Vinitsky, S. I.

Abstract

The symbolic-numeric program SELFA for solving the the 2D boundary-value problem in self-consistent basis method is presented. The corresponding algorithm of this program using a conventional pseudocode is described too. As example, the energy spectrum and wave functions of E-type for generalized Henon–Heiles Hamiltonian were obtained

164. Symbolic-numeric solution of the two-dimensional Schrodinger equation with double-well potential

Author

Belyaeva, I. N., Chekanov, N. A., Gusev, A. A., Lukianenko, A. N., Rostovtsev, V. A., Vinitsky, S. I., Belyaeva, I. N., Chekanov, N. A., Gusev, A. A., Lukianenko, A. N., Rostovtsev, V. A., and Vinitsky, S. I.

Abstract

In this work the self-consistent basis method for solving the two-dimensional stationary Schrodinger equation is presented. The solution shows a potential energy surface with two local minima and a unique saddle point. We have developed a symbolic-numeric algorithm and Maple program (SELFA) that realizes the computation

180. POTHEA: A program for computing eigenvalues and eigenfunctions and their first derivatives with respect to the parameter of the parametric self-adjoined 2D elliptic partial differential equation.

Author

Gusev, A. A., Chuluunbaatar, O., Vinitsky, S. I., and Abrashkevich, A. G.

Subjects
*EIGENVALUES, *EIGENFUNCTIONS, *DIFFERENTIAL equations, *SCATTERING (Physics), *NUMERICAL calculations, *BOUNDARY value problems
Abstract

A FORTRAN 77 program is presented for calculating with the given accuracy eigenvalues, surface eigenfunctions and their first derivatives with respect to a parameter of the parametric self-adjoined 2D elliptic partial differential equation with the Dirichlet and/or Neumann type boundary conditions on a finite two-dimensional region. The program calculates also potential matrix elements that are integrals of the products of the surface eigenfunctions and/or the first derivatives of the surface eigenfunctions with respect to a parameter. Eigenvalues and matrix elements computed by the POTHEA program can be used for solving the bound state and multi-channel scattering problems for a system of coupled second order ordinary differential equations with the help of the KANTBP program (Chuluunbaatar et al., 2007). Benchmark calculations of eigenvalues and eigenfunctions of the ground and first excited states of a Helium atom in the framework of a coupled-channel hyperspherical adiabatic approach are presented. As a test desk, the program is applied to the calculation of the eigensolutions of a 2D boundary value problem, their first derivatives with respect to a parameter and potential matrix elements used in the benchmark calculations. [ABSTRACT FROM AUTHOR]

Published
2014
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181. Modeling the multifractal dynamics of COVID-19 pandemic.

Author

Tsvetkov VP, Mikheev SA, Tsvetkov IV, Derbov VL, Gusev AA, and Vinitsky SI

Abstract

To describe the COVID-19 pandemic, we propose to use a mathematical model of multifractal dynamics, which is alternative to other models and free of their shortcomings. It is based on the fractal properties of pandemics only and allows describing their time behavior using no hypotheses and assumptions about the structure of the disease process. The model is applied to describe the dynamics of the COVID-19 pandemic from day 1 to day 699 from the beginning of the pandemic. The calculated parameters of the model accurately determine the parameters of the trend and the large jump in daily diseases in this time interval. Within the framework of this model and finite-difference parametric nonlinear equations of the reduced SIR (Susceptible-Infected-Removed) model, the fractal dimensions of various segments of daily incidence in the world and variations in the main reproduction number of COVID-19 were calculated based on the data of COVID-19 world statistics., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2022 Published by Elsevier Ltd.)

Published
2022
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