Une nouvelle preuve du théorème de point fixe de Handel
M Handel has proved in [Topology 38 (1999) 235--264] a fixed point theorem for an orientation preserving homeomorphism of the open unit disk, that may be extended to the closed disk and that satisfies a linking property of orbits. We give here a new proof of Handel's fixed point theorem, based on Brouwer theory and some plane topology arguments. We will slightly improve the theorem by proving the existence of a simple closed curve of index 1. This index result was known to be true under an additional hypothesis and has been used by different authors (J Franks [NYJM 2 (1996) 1--19, Trans.AMS 348 (1996) 2637--2662] S Matsumoto [Topol. Appl. 104 (2000) 191--214]) to study homeomorphisms of surfaces.
Cycles of links and fixed points for orientation preserving homeomorphisms of the open unit disk
Michael Handel proved in [7] the existence of a fixed point for an orientation preserving homeomorphism of the open unit disk that can be extended to the closed disk, provided that it has points whose orbits form an oriented cycle of links at infinity. More recently, the author generalized Handel’s theorem to a wider class of cycles of links [13]. In this paper we complete this topic describing exactly which are all the cycles of links forcing the existence of a fixed point.
Treatment of sentence production deficits in aphasia: A linguistic-specific approach to wh-interrogative training and generalization
Abstract The present research examines the effects of a linguistic-specific treatment on acquisition and generalization of wh-interrogative structures in two aphasic subjects presenting with deficit patterns consistent with agrammatism. The underlying linguistic representation of sentence structures selected for treatment and generalization was considered based on aspects of Chomsky's (1981) Government Binding (GB) theory, and a linguistic-based, wh-movement treatment strategy was implemented. Using a single-subject multiple-baseline design across behaviours and subjects, the effects of treatment were explored by examining generalization patterns across wh question forms requiring wh-movement (movement of a direct object NP to COMP). Within question form generalization also was evaluated by examining formulation of untrained sentences of varied complexity—with complexity defined in terms of the number of phrasal nodes in the d-structure representation of sentences. Results indicated that for both subjects...