Nikolay Balonin

Mersenne-Walsh Matrices for Image Processing

This paper presents a modified Paley method for calculation of Mersenne matrices at order values equal to odd prime numbers. Some examples of Mersenne matrix sorting, allowing for calculation of the complete set of functions, are also considered. A comparison of Walsh and Mersenne-Walsh systems of functions in terms of their properties and fields of application is provided. The efficiency of this topic for use in the development of band-pass filters is indicated.

On two predictors of calculable chains of quasi-orthogonal matrices

The general definition of quasi-orthogonal matrices, the definition of low-level matrices, and partial definitions of quasi-orthogonal Mersenne and Euler matrices are considered. New quasi-orthogonal symmetric Seidel matrices that exist on odd orders and three-level Legendre symbols used to calculate elements of these matrices are defined. A method to calculate Euler matrices via Mersenne matrices is given. A relation between asymmetric and symmetric odd-order Mersenne and Seidel matrices is shown to exist. A new, modified Sylvester method for calculating Euler matrices using symmetric circulant Seidel matrices is proposed.

Matrices in Improvement of Systems of Artificial Intelligence and Education of Specialists

This article is devoted to a significant role of matrices in digital signal processing, systems of artificial intelligence and mathematical natural sciences in the whole. The study of the world of matrices is going on intensively all over the world and constantly brings useful and unexpected results. Some of these results are presented in this paper. Special attention is paid to Hadamard matrices and some their modifications and extensions, which are important for developing systems of artificial intelligence and studying the genetic code. Training courses for specialists in many fields of science should be constantly updated with new knowledge about matrices and their practical applications.

“Living Books” and the Advanced Network Technologies for Education in a Technical University

This article presents an analysis of the future of technical books. The process of formation of network technologies that change the very concept of books, -in particular, technical books - is considered. A new image of a modern technical book, containing algorithms executable from pages and linked to described objects, is suggested. An overview of implementation technologies, including the Java-MatLab language developed by the authors of this article and the new FB + format for representation of information, is presented.