The Julia programming language is a specialized language for scientific computing. It is relatively new, so most of the libraries for it are in the active development stage. In …
For describing specialized mathematical structures, it is preferable to use a special formalism rather than a general one. However, tradition often prevails in this case. For …
Tensor formalism (and its special case—vector formalism) is a mathematical technique that is widely used in physical and engineering problems. Even though this formalism is fairy …
Calculations of optical devices in the geometrized Maxwell’s theory use well-known formalisms of general theory of relativity and differential geometry. In particular, for such …
The spectral collocation method for solving two-point boundary value problems for second order differential equations is implemented, based on representing the solution as an …
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 …
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 role in the …
The classical pseudospectral collocation method based on the expansion of the solution in a basis of Chebyshev polynomials is considered. A new approach to constructing systems of …
Geometric algebra is based on the works by Grassmann and Clifford. Its main objects of research are polyvectors (p-vectors) and multivectors. Polyvectors, together with the …
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 …
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 …
The history of using machine learning algorithms to analyze statistical models is quite long. The development of computer technology has given these algorithms a new breath. …
In the special theory of relativity (SR) it is usual to highlight so-called paradoxes. One of these paradoxes is the formal appearance of speed values grater then the light speed. …
In this paper, two approaches (combinatorial and operatorial) to the stochastization of the one-step processes are discussed for the closed and open version of the Lotka–Volterra …
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 …
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 …
For the first time, the theoretical model of the spin-electron structure of a singlelayer graphene film was proposed by Wallace. The literature also describes ferromagnetism …
This paper describes the created mathematical model that allows you to explore the dynamics of cavitation bubbles under the influence of a single negative pressure pulse. The time …
This article presents a numerical method to determine the approximate solutions of the Lienard equations. It is assumed that the second-order nonlinear Linard differential …
In this article, we compare the support for SIMD instructions for Julia and Fortran. The comparison is carried out according to the methodology described in work of T. Kalibera, R. …