28 citations · 173 across the 35 of their papers we have counts for
34 papers
Reproducible Research in Network Modeling
Anna M. Ermolayeva, Tatyana R. Velieva, Anna A. Zhivtsova +2
Background: When we model networks, there is a problem of obtaining experimental data to verify other model approaches. And even if there are some experimental data, it is necessar…
Asymptote-based scientific animation
Migran N. Gevorkyan, Anna V. Korolkova, Dmitry S. Kulyabov
This article discusses a universal way to create animation using Asymptote the language for vector graphics. The Asymptote language itself has a built-in library for creating anima…
Implementation of hyperbolic complex numbers in Julia language
Anna V. Korolkova, Migran N. Gevorkyan, Dmitry S. Kulyabov
Background: Hyperbolic complex numbers are used in the description of hyperbolic spaces. One of the well-known examples of such spaces is the Minkowski space, which plays a leading…
Computer algebra in Julia
Dmitry S. Kulyabov, Anna V. Korolkova
Recently, the place of the main programming language for scientific and engineering computations has been little by little taken by Julia. Some users want to work completely within…
Using a template engine as a computer algebra tool
Migran N. Gevorkyan, Anna V. Korolkova, Dmitry S. Kulyabov
In research problems that involve the use of numerical methods for solving systems of ordinary differential equations (ODEs), it is often required to select the most efficient meth…
Numerical integrating of highly oscillating functions: effective stable algorithms in case of linear phase
Leonid A. Sevastianov, Konstantin P. Lovetskiy, Dmitry S. Kulyabov
A practical and simple stable method for calculating Fourier integrals is proposed, effective both at low and at high frequencies. An approach based on the fruitful idea of Levin,…
Practical application of the multi-model approach in the study of complex systems
Anna V. Korolkova, Dmitry S. Kulyabov, Michal Hnatič
Different kinds of models are used to study various natural and technical phenomena. Usually, the researcher is limited to using a certain kind of model approach, not using others…
Approaches to the implementation of generalized complex numbers in the Julia language
Migran N. Gevorkyan, Anna V. Korolkova, Dmitry S. Kulyabov
In problems of mathematical physics, to study the structures of spaces using the Cayley-Klein models in theoretical calculations, the use of generalized complex numbers is required…
Languages for modeling the RED active queue management algorithms: Modelica vs. Julia
Anna Maria Yu. Apreutesey, Anna V. Korolkova, Dmitry S. Kulyabov
This work is devoted to the study of the capabilities of the Modelica and Julia programming languages for the implementation of a continuously discrete paradigm in modeling hybrid…
A modular extension for a computer algebra system
Migran N. Gevorkyan, Anna V. Korolkova, Dmitry S. Kulyabov +1
Computer algebra systems are complex software systems that cover a wide range of scientific and practical problems. However, the absolute coverage cannot be achieved. Often, it is…
A practical approach to testing random number generators in computer algebra systems
Migran N. Gevorkyan, Dmitry S. Kulyabov, Anastasia V. Demidova +1
This paper has a practical aim. For a long time, implementations of pseudorandom number generators in standard libraries of programming languages had poor quality. The situation st…
Constrained Hamiltonian approach to the Maxwell theory
Dmitry S. Kulyabov, Anna V. Korolkova, Migran N. Gevorkyan +1
The most common physical formalisms are the Lagrangian formalism and the Hamiltonian formalism. From the superficial point of view, they are one and the same, but rewritten in othe…
Finslerian representation of the Maxwell equations
Dmitry S. Kulyabov, Anna V. Korolkova, Tatyana R. Velieva +1
When the Maxwell equations are geometrized, the Maxwell Lagrangian is usually reduced to the Yang-Mills Lagrangian. In this case, the effective quadratic metric, usually correspond…
Two formalisms of stochastization of one-step models
Dmitry S. Kulyabov, Anna V. Korolkova, Leonid A. Sevastianov
To construct realistic mathematical models from the first principles, the authors suggest using the stochastization method. In a number of works different approaches to stochastiza…
Numerical analysis of eikonal equation
D. S. Kulyabov, A. V. Korolkova, T. R. Velieva +1
The Maxwell equations have a fairly simple form. However, finding solutions of Maxwell's equations is an extremely difficult task. Therefore, various simplifying approaches are oft…
New Features in the Second Version of the Cadabra Computer Algebra System
D. S. Kulyabov, A. V. Korolkova, L. A. Sevastianov
In certain scientific domains, there is a need for tensor operations. To facilitate tensor computations,computer algebra systems are employed. In our research, we have been using C…
Issues in the software implementation of stochastic numerical Runge-Kutta
Migran N. Gevorkyan, Anastasia V. Demidova, Anna V. Korolkova +1
This paper discusses stochastic numerical methods of Runge-Kutta type with weak and strong convergences for systems of stochastic differential equations in Itô form. At the beginni…
Algorithm for Lens Calculations in the Geometrized Maxwell Theory
D. S. Kulyabov, A. V. Korolkova, L. A. Sevastianov +2
Nowadays the geometric approach in optics is often used to find out media parameters based on propagation paths of the rays because in this case it is a direct problem. However inv…
The Riemannian geometry is not sufficient for the geometrization of the Maxwell's equations
D. S. Kulyabov, A. V. Korolkova, T. R. Velieva
The transformation optics uses geometrized Maxwell's constitutive equations to solve the inverse problem of optics, namely to solve the problem of finding the parameters of the med…
Implementing a Method for Stochastization of One-Step Processes in a Computer Algebra System
D. S. Kulyabov, M. N. Gevorkyan, A. V. Demidova +3
When modeling such phenomena as population dynamics, controllable ows, etc., a problem arises of adapting the existing models to a phenomenon under study. For this purpose, we prop…
Approaches to Stochastic Modeling of Wind Turbines
M. N. Gevorkyan, A. V. Demidova, Robert A. Sobolewski +4
Background. This paper study statistical data gathered from wind turbines located on the territory of the Republic of Poland. The research is aimed to construct the stochastic mode…
The Stochastic Processes Generation in OpenModelica
M. N. Gevorkyan, A. V. Demidova, A. V. Korolkova +2
Background: Component-based modeling language Modelica (OpenModelica is open source implementation) is used for the numerical simulation of complex processes of different nature re…
Stochastic Runge-Kutta Software Package for Stochastic Differential Equations
M. N. Gevorkyan, T. R. Velieva, A. V. Korolkova +2
As a result of the application of a technique of multistep processes stochastic models construction the range of models, implemented as a self-consistent differential equations, wa…
Using Two Types of Computer Algebra Systems to Solve Maxwell Optics Problems
D. S. Kulyabov
To synthesize Maxwell optics systems, the mathematical apparatus of tensor and vector analysis is generally employed. This mathematical apparatus implies executing a great number o…