Given a parametrization of a rational plane algebraic curve C, some explicit adjoint pencils on C are described in terms of determinants. Moreover, some generators of the Rees algebra associated to this parametrization are presented. The main ingredient developed in this paper is a detailed study of the elimination ideal of two homogeneous polynomials in two homogeneous variables that form a re...

A new minimal parametrization of multivariable linear system is proposed. The parametrization is defined as a perturbation around the realization of a nominal transfer function. A particular parameter basis is selected which, for the impulse response identification problem, leads to a Hessian matrix of the criterion function which is equal to the identity matrix.

The existence, uniqueness, and parametrization of Lagrangian invariant subspaces for Hamiltonian matrices is studied. Necessary and sufficient conditions and a complete parametrization are given. Some necessary and sufficient conditions for the existence of Hermitian solutions of algebraic Riccati equations follow as simple corollaries.

Current approaches to compute the arc length of a parametric curve rely on table lookup schemes. We present an approximate closed-form solution to the problem of computing an arc length parametrization for any given parametric curve. Our solution outputs a one or two-span Bézier curve which relates the length of the curve to the parametric variable. The main advantage of our approach is that we...

Texture-mapping is a traditional graphics technique that has several applications in computer graphics rendering. It uses surface signals to achieve a variety of rendering effects, including color mapping, bump mapping (where surface normals are the signal), displacement mapping (geometry), and self-shadowing. While these rendering effects can also be computed in vertex shaders, texturemapping ...

For indecomposable representations of a finite group G in characteristic p , the theory of vertices and sources introduced by J.A. Green in 1959 [G1] is a fundamental tool in modular representation theory. The vertex and source of an indecomposable module are (up to conjugation) two invariants of the module and only finitely many modules (up to isomorphism) have the same invariants. Thus a natu...

We present a new method for the rational parametrization of plane algebraic curves. The algorithm exploits the shape of the Newton polygon of the defining implicit equation and is based on methods of toric geometry.

conclusions major vascular injuries in our center occurred in young men, frequently because of stab wounds. popliteal injuries mostly caused by motor vehicle accidents was the second most common arterial injury, followed by combined ulnar and radial injuries. vascular reconstruction in the first hours after trauma may prevent many unnecessary and preventable amputation procedures. results most ...