This article is a short supplement to our previously published paper, in which we proved that each semialgebraic set can be represented as a projection of a solution set of some system of interval linear equations with dependent coefficients. The new result says that interval occurring can be chosen as narrow as wanted. The new result is proved by a simple linear transformation.

Five equivalence classes had been found for systems of two second-order ordinary differential equations, transformable to linear equations linearizable systems by a change of variables. An “optimal or simplest canonical form” of linear systems had been established to obtain the symmetry structure, namely, with 5-, 6-, 7-, 8-, and 15-dimensional Lie algebras. For those systems that arise from a ...

Every year, people across the United States predict how the field of 65 teams will play in the Division I NCAA Men’s Basketball Tournament by filling out a tournament bracket for the postseason play. This article discusses two popular rating methods that are also used by the Bowl Championship Series, the organization that determines which college football teams are invited to which bowl games. ...

Mathematical norms are important cultural knowledge of mathematical activities. This paper reports an analysis of mathematical norms in ten consecutive lessons taught by an eighth-grade Japanese teacher. The lessons were located in the unit of simultaneous linear equations. The videotapes of the lessons, their transcripts, and the interview data were analyzed qualitatively. Several major mathem...

We construct new binary and ternary self-orthogonal linear codes. In order to do this we use an equivalence between the existence of a self-orthogonal linear code over a prime eld with a prescribed minimum distance and the existence of a solution of a certain system of Diophantine linear equations. To reduce the size of the system of equations we restrict the search for solutions to solutions w...

The work considers solution of various problems for interval linear systems with nonnegative matrices. Relying on shape monotonicity of the solution sets to such interval systems, we develop a new technique for constructing maximal (with respect to inclusion) inner estimates of the solution sets to nonnegative interval linear equations systems. The main result is extended to general AE-solution...

This paper is an expanded version of the 10 lectures I gave as the 2006 London Mathematical Society Invited Lecture Series at the Heriot-Watt University, 31 July 4 August 2006†. My goal was to give the audience an introduction to the algebraic, analytic and algorithmic aspects of the Galois theory of linear differential equations by focusing on some of the main ideas and philosophies and on exa...