There are algorithms for finding zeros or fixed points of nonlinear systems of equations that are globally convergent for almost all starting points, i.e., with probability one. The essence of all such algorithms is the construction of an appropriate homotopy map and then tracking some smooth curve in the zero set of this homotopy map. HOMPACK is a mathematical software package implementing glo...

Let K and T be convex open bounded bodies in R . We will discuss in this note C1-diffeomorphic bijections8:K → T with constant determinant of the Jacobian. So, if volK = vol T our maps are measure preserving. There are several such distinguished maps. For example, a Knothe map ([K]) 8:K → T has a triangular Jacobian with a positive diagonal and may be naturally associated with any fixed orthogo...

. AbstrQct-This paper analyzes the stability of a general RLC circuit with ideal thyristors or diodes and periodic sources. Applications include high power thyristor controlled reactor and bridge rectifier circuits. The periodic steady states of the circuit are analyzed using a Poincar6 map and transversal&y conditions are given to guarantee the smoothness of the Pgincar6 map. A simple and exac...

– We review the definition and main properties of the distributional Jacobians, in particular for Sobolev maps u : R → R with values in the (k − 1)dimensional sphere S.

We show that divergence-free jacobian maps, recently considered in [11], [14], are actually shear maps.

A Riemann surface is associated with its Jacobian through the Abel map. Using a plane algebraic curve representation of the Riemann surface, we provide an algorithm for the numerical computation of the Abel map. Since our plane algebraic curves are of arbitrary degree and may have arbitrary singularities, the Abel map of any connected compact Riemann surface may be obtained in this way.

In this paper, a one-dimensional family of stratiications on a hyperelliptic Jacobian is introduced. It generalizes a well-known stratiication, considered in algebraic geometry, in the context of special divisors. The stratiication is shown to be related to a natural stratiication on the Sato Grassmannian, via an extension of Krichever's map. It is also related to the stratiication associated t...

We consider the moduli space SUsC(2,OC) of rank 2 stable vector bundles with trivial determinant on a smooth projective curve C of genus g. We show that the Abel-Jacobi map on the rational Chow group CH1(SU s C(2,OC))hom ⊗ Q of one cycles which are homologous to zero, is an isomorphism onto the bottom weight intermediate Jacobian, which is identified with the Jacobian Jac(C)⊗ Q.