Computations with algebraic curves and surfaces are very well suited for being treated with computer algebra. Many aspects of computer algebra need to be combined for successfully solving problems in this area, e.g. computations with algebraic coefficients, solution of algebraic equations and...

Swimming bacteria of the species Bacillus subtilis require and consume oxygen. In static liquid cultures the cells' swimming behaviour leads them to accumulate up oxygen concentration gradients generated by consumption and supply. Since the density of bacterial cells exceeds that of the fluid in...

The motion planning problem consists in deriving some input steering a dynamical system to a fixed point of the state space. This problem appears to be relevant to the study of mechanical system and robotics when the system is nonholonomic.

We review, compare and experiment with two methods for solving systems of polynomial equations. One of the methods is developed by Wu based on Ritt's concept of characteristic sets, and the other is proposed by the author in extending the idea of Seidenberg's elimination theory. We present the...

In this paper certain properties of algorithms used in symbolic manipulation on signal flow graphs are investigated. The rule-based approach and Mason's formula are compared with respect to preservation of minimal rational representation. It is shown by counter example that rule-based method...

After reviewing the arithmetic of linear ordinary differential operators, we describe the current status of the factorisation algorithm, specially with respect to factoring over non-algebraically closed constant fields. We also describe recent results from Singer and Ulmer (1993) that reduce...

This paper describes a generalization of the real closure computation of an ordered field (Rioboo, 1991) enabling to use different techniques to code a single real algebraic number.

The need to have high integrity, structurally bonded adhesive and sealant joints throughout many industries, such as the automotive and aerospace industries, is increasing. To ensure process integrity, strict process control of the automated dispensing cell is essential. Many industries require...

A very important subject for the consolidation of neural networks is the study of their capabilities. In this paper, the relationships between network size, training set size and generalization capabilities are examined. The phenomenon of overtraining in backpropagation networks is discussed and...