This report presents a method of constructing approximate symmetries and invariants in dynamical systems. At first, a similar approach was developed for linear systems (for example, the time-dependent invariants by Leach and Lewis). Beam line systems are considered as an example of such...

This paper develops a decompose procedure for finding the optimal solution of convex and concave Quadratic Programming (QP) problems together with general Non-linear Programming (NLP) problems. The paper also develops a sophisticated computer technique corresponding to the author's algorithm...

Functional Regression has been an active subject of research in the last two decades but still lacks a secure variable selection methodology. Lasso is a well known effective technique for parameters shrinkage and variable selection in regression problems. In this work we generalize the Lasso...

We discuss some non-standard applications of computer algebra in field theories based on the formal theory of differential equations and present a general programming environment for differential equations currently under construction in MuPAD.

The goal of this short paper is to describe one possible use of sketches in computer algebra. We show that sketches are a powerful tool for the description of mathematical structures and for the description of computations.

With the advent of atonal music at the beginning of the 20th Century, composers drastically changed the way they thought about pitches. Octave equivalence became the prominent idea, in which pitches with the same relative placement in different octaves were considered to be functionally...

A suite of computer algebra programs for tensor and spinor calculations in torsion theories of gravitation is presented. Modules for the algebraic classification of curvature tensors in Riemann-Cartan space-times are discussed. The basic theoretical results and an algorithm for the equivalence...

In the neighbourhood of irregular singularities the formal power series solutions of complex analytic ordinary differential equations are generally divergent. The resummation theory developed by J. Ecalle and J.P. Ramis enables us to sum these series by multisummation effective algorithms. In...

Subject: The education in mathematics, its failure and costs, and how to redesign this market. The political economy of mathematics education. Method: We do not require statistics to show that mathematics education fails but can look at the math itself. Criticism on mathematics itself can only...

The paper discusses algorithms for investigation of the stability of mechanical systems: (i) investigation of stability in the first approximation; (ii) Algorithms for constructing Lyapunov functions. A special attention is given to the cases critical in the Lyapunov sense; (iii) algorithms...