Attention is focused in this paper on: (i) definitions of alternate measures of “stress-resultants” and “stress-couples” in a finitely deformed shell (finite mid-plane stretches as well as finite rotations); (ii) mixed variational principles for shells, undergoing large mid-plane stretches and large rotations, in terms of a stress function vector and the rotation tensor. In doing so, both types...

We study the structure of resultants of two homogeneous partially composed polynomials. By two homogeneous partially composed polynomials we mean a pair of polynomials of which one does not have any given composition structure and the other one is obtained by composing a bivariate homogeneous polynomial with two bivariate homogeneous polynomials. The main contributions are two equivalent formul...

In this paper we apply the idea of Dixon resultant to algebraic differential equations and introduce the Dixon differential resultant. We prove that a necessary condition for the existence of a common solution of two algebraic differential equations is that the differential resultant is equal to zero, which actually provides a method of elimination and reduces a system of multi-variate differen...

New Zernike velocity moments have been developed to describe an object, not only by its shape , but also by its motion throughout an image sequence. These are an extended form of the orthogonal Zernike moment set and include velocity information introduced via centralised moments. Initial analysis shows that they perform well when applied to analysing gait sequences resulting in a good recognit...

These notes correspond to one of the introductory courses for the CIMPA Graduate School on Systems of Polynomial Equations to be held in Buenos Aires, Argentina, in July 2003. We present an elementary introduction to univariate residues and resultants, and we outline some of their multivariate generalizations and applications.

New formulas are given for Chow forms, discriminants and resultants arising from (not necessarily normal) toric varieties of codimension 2. The Newton polygon of the discriminant is determined exactly.

Resultants are defined in the sparse (or toric) context in order to exploit the structure of the polynomials as expressed by their Newton polytopes. Since determinantal formulae are not always possible, the most efficient general method for computing resultants is as the ratio of two determinants. This is made possible by Macaulay’s seminal result [15] in the dense homogeneous case, extended by...

We propose a new resultant operator, providing a geometrically and computationally more intrinsic setting for elimination theory. The aane resultant extends the beneets the sparse resultant provides (for algebraic geometry in the algebraic torus) to aane space minus an arbitrary union of coordinate hyperplanes. As an application of the aane resultant, we give an explicit formula for the degree ...