Balyaev, I. A.
Published in
Solar System Research

Abstract—Finding and studying possible collisions of asteroids approaching the Earth requires a significant amount of computation. This paper describes the R0 program created to calculate the trajectories of a large number of virtual asteroids and the parameters of approaches with the bodies of the Solar System: planets, the Moon, and the Sun. The ...

Kuznetsov, D. F.
Published in
Computational Mathematics and Mathematical Physics

AbstractThis paper is devoted to the comparative analysis of the efficiency of using the Legendre polynomials and trigonometric functions for the numerical solution of Ito stochastic differential equations under the method of approximating multiple Ito and Stratonovich stochastic integrals based on generalized multiple Fourier series. Using the mul...

Kuznetsov, D. F.
Published in
Computational Mathematics and Mathematical Physics

AbstractThis paper is devoted to the development and application of the Fourier method to the numerical solution of Ito stochastic differential equations. Fourier series are widely used in various fields of applied mathematics and physics. However, the method of Fourier series as applied to the numerical solution of stochastic differential equation...

Zwart, Petrus H Perryman, Elliott D
Published in
Acta crystallographica. Section D, Structural biology

Intensity-based likelihood functions in crystallographic applications have the potential to enhance the quality of structures derived from marginal diffraction data. Their usage, however, is complicated by the ability to efficiently compute these target functions. Here, a numerical quadrature is developed that allows the rapid evaluation of intensi...

Zwart, Petrus H Perryman, Elliott D

Intensity-based likelihood functions in crystallographic applications have the potential to enhance the quality of structures derived from marginal diffraction data. Their usage, however, is complicated by the ability to efficiently compute these target functions. Here, a numerical quadrature is developed that allows the rapid evaluation of intensi...

Vashkov’yak, M. A.
Published in
Solar System Research

AbstractThe outer version of the restricted elliptic three-body problem, where a perturbed body of negligible mass is far from two bodies of finite masses (the main and perturbing ones) close to one another and its orbit is located entirely outside the orbit of the perturbing body, is considered. The terms up to the fourth order inclusive in the ra...

Radhia, Bessi

Function approximations arises in many branches of applied mathematics and computer science, in particular in numerical analysis, in finite element theory and more recently in data sciences domain. From most common approximation we cite, polynomial, Chebychev and Fourier series approximations. In this work we establish some approximations of a cont...

Maddalena, Lucia Ragni, Stefania
Published in
Mathematical medicine and biology : a journal of the IMA

In order to model the evolution of a heterogeneous population of cancer stem cells and tumor cells, we analyse a nonlinear system of integro-differential equations. We provide an existence and uniqueness result by exploiting a suitable iterative scheme of functions which converge to the solution of the system. Then, we discretize the model and perf...

Vashkov’yak, M. A.
Published in
Solar System Research

Abstract—The inner (or satellite) version of the restricted elliptic three-body problem is considered. The terms up to the fourth order inclusive in small parameter are retained in the expansion of the perturbing function for the problem. The ratio of the orbital semimajor axes of perturbed and perturbing bodies is such a parameter, while their mea...

Suvorov, Aleksey Gusev, Alexander Ruban, Nikolay Andreev, Mikhail Askarov, Alisher Ufa, Ruslan Razzhivin, Igor Kievets, Anton Bay, Julius
Published in
International Journal of Emerging Electric Power Systems

Currently, the number of distributed generation (DG) objects in the world is growing mainly due to renewable energy sources (RES). However, the integration of a large volume of DG based on RES into existing electric power systems (EPS) is associated with a number of significant problems. For a comprehensive study and solution of these problems, it ...