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Dual quaternion representation of points, lines and planes

Basic elements of the BibTeX file structure

Using NeuralPDE.jl to solve differential equations

Typesetting tables

Implementation of biquaternions in the Asymptote language. Supplements

The dual quaternion algebra and its implementation in Asymptote language

The algebras of dual quaternions and screws are often opposed to geometric algebra. The purpose of this paper is to describe the algebra of dual quaternions and the algebra of …

Using generative artificial intelligence

The use of generative artificial intelligence (GenAI) in scientific publications requires strict guidelines to ensure transparency, credibility, and ethics of research.

Statistical and density-based clustering techniques in the context of anomaly detection in network systems: A comparative analysis

In the modern world, the volume of data stored electronically and transmitted over networks continues to grow rapidly. This trend increases the demand for the development of …

Analytic projective geometry for computer graphics

Abstract structure

We describe the general requirements for the abstract of a scientific article. We recommend to use the structured abstract approach.

Numerical Integration of Highly Oscillatory Functions with and without Stationary Points

This paper proposes an original approach to calculating integrals of rapidly oscillating functions, based on Levin’s algorithm, which reduces the search for an anti-derivative …

Symbolic-numeric approach for the investigation of kinetic models

Our group has been investigating kinetic models for quite a long time. The structure of classical kinetic models is described by rather simple assumptions about the interaction of …

Solving the eikonal equation by the FSM method in Julia language

There are two main approaches to the numerical solution of the eikonal equation: reducing it to a system of ODES (method of characteristics) and constructing specialized methods …

Numerical solution of first-order exact differential equations by the integrating factor method

A numerical algorithm for solving exact differential equations is proposed, based both on the efficient calculation of integrating factors and on a “new” numerical method for …

Journal rubrics

We describe introduced in the journal the rubric system.

IMRAD structure

We describe introduced in the journal the rubric system. We describe the general structure of an IMRAD research publication. The IMRAD structure for a research article is described …

Author's ethics

We describe the system of ethical disclaimers being introduced in the journal.

Application of the Chebyshev collocation method to solve boundary value problems of heat conduction

For one-dimensional inhomogeneous (with respect to the spatial variable) linear parabolic equations, a combined approach is used, dividing the original problem into two …

Methodological derivation of the eikonal equation

Usually, when working with the eikonal equation, reference is made to its derivation in the monograph by Born and Wolf. The derivation of this equation was done rather carelessly. …

Julia language features for processing statistical data

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 …