A sufficient condition for global invertibility of Lipschitz mapping

ar X iv : 1 31 1 . 28 15 v 1 [ m at h . FA ] 1 2 N ov 2 01 3 GLOBAL INVERSION OF NONSMOOTH MAPPINGS USING PSEUDO - JACOBIAN MATRICES

We study the global inversion of a continuous nonsmooth mapping f : R → R, which may be non-locally Lipschitz. To this end, we use the notion of pseudo-Jacobian map associated to f , introduced by Jeyakumar and Luc, and we consider a related index of regularity for f . We obtain a characterization of global inversion in terms of its index of regularity. Furthermore, we prove that the Hadamard i...

Weighted Composition Operators Between Extended Lipschitz Algebras on Compact Metric Spaces

‎In this paper, we provide a complete description of weighted composition operators between extended Lipschitz algebras on compact metric spaces. We give necessary and sufficient conditions for the injectivity and the sujectivity of these operators. We also obtain some sufficient conditions and some necessary conditions for a weighted composition operator between these spaces to be compact.

Non-uniqueness in Reverse Time of Hybrid System Trajectories

Under standard Lipschitz conditions, trajectories of systems described by ordinary differential equations are well defined in both forward and reverse time. (The flow map is invertible.) However for hybrid systems, uniqueness of trajectories in forward time does not guarantee flow-map invertibility, allowing non-uniqueness in reverse time. The paper establishes a necessary and sufficient condit...

A Bernstein-Bezier Sufficient Condition for Invertibility of Polynomial Mapping Functions

We propose a sufficient condition for invertibility of a polynomial mapping function defined on a cube or simplex. This condition is applicable to finite element analysis using curved meshes. The sufficient condition is based on an analysis of the Bernstein-Bézier form of the columns of the derivative. 1 Invertibility of polynomial mapping functions In finite element analysis, it is common to s...

Sufficient Conditions for Density in Extended Lipschitz Algebras