In this paper we study polynomial maps of vector spaces zi → Ai1i2···is i zi1zi2zi3 · · · zis and their eigenvectors and eigenvalues. The new quantity called complanart is de ned. Complanarts determine complanarity of solution vectors of systems of polynomial equations. Evaluation of complanart is reduced to evaluation of resultants. As in linear case, the pattern of eigenvectors de nes the pha...

We consider interpolation in Lie groups and homogeneous spaces. Based on points on the manifold together with tangent vectors at (some of) these points, we construct Hermite interpolation polynomials. If the points and tangent vectors are produced in the process of integrating an ordinary di erential equation on a Lie group or a homogeneous space, we use the truncated inverse of the di erential...

This work deals with the design of the low{level stages of any di erential{ based optical ow algorithm. The problem is the accurate estimaton of the spatio{temporal derivatives of the moving image, to be used in the solution of the gradient constraint equation. We claim that the \traditional" techniques for the partial derivatives estimation can be improved by i) exploiting all the information ...

We describe some new algorithm and heuristics for computing the polynomial and rational solutions of bounded degree of a class of ordinary di erential equations, which includes generalized Riccati equations. As a consequence, our methods can be used for factoring linear ordinary di erential equations. Since they generate systems of algebraic equations in at most n unknowns, where n is the order...

In this thesis we study numerical methods for simulating mechanical deformations of cell membranes. Such models are given in terms of fourth order partial di erential equations. In order to enable comparisons of the models predictions to experimental results, the equations must be solved on arbitrary cell geometries. A Finite Element Method based on subdivision surfaces, which is capable of dis...

image restoration has been an active research area. dierent formulations are eective in high qualityrecovery. partial dierential equations (pdes) have become an important tool in image processingand analysis. one of the earliest models based on pdes is perona-malik model that is a kindof anisotropic diusion (andi) lter. anisotropic diusion lter has become a valuable tool indierent elds...

For the approximate representation of large data sets over a parameter domain in IR2, many geological and other applications require the construction of surfaces which have minimal energy, i.e., minimal curvature. One way to achieve this is by solving a fourth order elliptic partial di erential equation. Its discretization by a di erence scheme makes it particularly easy to incorporate (appropr...

in this paper, a three dimensional mathematical model for htlv-1infection with intracellular delay and immune activation delay is investigated.by applying the frequency domain approach, we show that time delays candestabilize the ham/tsp equilibrium, leading to hopf bifurcations and sta-ble or unstable periodic oscillations. at the end, numerical simulations areillustrated.

Symbolic Reachability Computation for Families of Linear Vector Fields Gerardo Lafferriere Department of Mathematical Sciences Portland State University, P.O. Box 751, Portland, OR 97207-0751. [email protected] George J. Pappas Department of Electrical Engineering University of Pennsylvania, 200 South 33rd Street, Philadelphia, PA 19104. [email protected] Sergio Yovine VERIMAG Centre Equat...