S. Vassiliadis K. Bertels G. G. Pechanek E.E. Dept Dept. Gestion de l'Entreprise DSP Architecture/Development T.U. Delft, Delft Univ. of Namur IBM Corporation The Netherlands 2628 CD 5000 Namur, Belgium RTP, N.C. 27709 USA Abstract In this paper we investigate the possibility of constructing xed point units using feed-forward neural networks. We investigate the possibility of constructing small...

The problem of transition to chaos, i.e. the destruction of invariant circles or KAM (Kolmogorov-Arnold-Moser) curves, in area preserving nontwist maps is studied within the renormalization group framework. Nontwist maps are maps for which the twist condition is violated along a curve known as the shearless curve. In renormalization language this problem is that of nding and studying the xed po...

We unveil new results based on measurement that guarantee the existence of unique xed points which need not be maximal. In addition, we establish that least xed points are always attractors in the topology, and then explore the consequences of these ndings in analysis. In particular, an extension of the Banach xed point theorem on compact metric spaces 3] is obtained.

The relationship between xed point theory and K {theory is explained, both classical Nielsen theory (versus K 0) and 1{parameter xed point theory (versus K 1). In particular, various zeta functions associated with suspension ows are shown to come in a natural way as \traces" of \torsions" of Whitehead and Reidemeister type.

The square root function has a unique positive ¿xed point. This function has the following properties: it is strictly increasing and strictly concave, with sEf ' f, sE@ : @ for @ , and sEK K for K : . It is shown that any function from U to U satisfying these properties has a unique positive ¿xed point.

In this paper we underline the importance of the parametric subregularity property of setvalued mappings, de…ned with respect to …xed sets. We show that this property appears naturally for some very simple mappings which play an important role in the theory of metric regularity. We prove a result concerning the preservation of metric subregularity at generalized compositions. Then we obtain, on...

We present global and local algorithms for evaluating minimal xed points of dependency graphs, a general problem in xed-point computation and model checking. Our algorithms run in linear-time, matching the complexity of the best existing algorithms for similar problems, and are simple to understand. The main novelty of our global algorithm is that it does not use the counter and \reverse list" ...

The breakdown point behavior of M-estimators in linear models with xed designs, arising from planned experiments or qualitative factors, is characterized. Particularly, this behavior at xed designs is quite diierent from that at designs which can be corrupted by outliers|the situation prevailing in the literature. For xed designs, the breakdown points of robust M-estimators (those with bounded ...

Macbeath gave a formula for the number of xed points for each non-identity element of a cyclic group of automorphisms of a compact Riemann surface in terms of the universal covering transformation group of the cyclic group. We observe that this formula generalizes to determine the xed-point set of each non-identity element of a cyclic group of automorphisms acting on a closed non-orientable sur...