A major concept in diierentiable dynamics is the Lyapunov exponents of a given map f. It combines the results of ergodic theory with diierential properties of f. Consider the following two closely related examples which motivate our paper. Let M be a compact surface and f : M ! M a smooth diieomorphism. Let E denote the set of Borel f-invariant ergodic measures on M. Assume that 2 E. Let h() be...

We investigate whether an arbitrary base for a topological space can be partitioned into two bases. We prove that every base for a T3 Lindelöf topology can be partitioned into two bases while there exists a consistent example of a rst countable, 0-dimensional, Hausdor space of size and weight ω1 which admits a base without a partition to two bases.

This paper proposes two Hausdor! distance (HD) matching algorithms, in which robust HD measures are implemented in pyramidal structures. By computer simulations, the matching performance of the conventional HD measures and the proposed robust HD matching algorithms using pyramidal structures is compared, with real images which are degraded by noise and occlusions. 2001 Pattern Recognition Socie...

Let (X; ) be a metric space, let (K(X); e ) denote the space of nonempty compact subsets of X with the Hausdor metric, and let E X. The purpose of this paper is to investigate the relationships between the entropy dimensions of E and of K(E). 1 The de nition and properties of the entropy indices. Given a separable metric space (X; ), let K(X) denote the set of non-empty compact subsets of X . D...

In this paper we propose a new algorithm for the well known elliptic obstacle problem and for parabolic variational inequalities like oneand two-phase Stefan problem and of obstacle type. Our approach enters the category of xed domain methods and solves just linear elliptic or parabolic equations and their discretization at each iteration. We prove stability and convergence properties. The appr...

We consider the following geometric pattern matching problem: Given two sets of points in the plane, P andQ, and some > 0, nd a similarity transformation (translation, rotation and scale) such that h(T (P ); Q) < , where h(:; :) is the directional Hausdor distance with L1 as the underlying metric. Similarity transformations have not been dealt with in the context of the directional Hausdor dist...

We prove that every Sobolev function de ned on a metric space coincides with a Holder continuous function outside a set of small Hausdor content or capacity. Moreover, the Holder continuous function can be chosen so that it approximates the given function in the Sobolev norm. This is a generalization of a result of Mal y [Ma1] to the Sobolev spaces on metric spaces [H1].

We present an algorithm for tracking objects in a video sequence, based on a novel approach for motion detection. We do not estimate the velocity eld. Instead we detect only the direction of motion at edge points and thus isolate sets of points which are moving coherently. We use a Hausdor distance based matching algorithm to match point sets in local neighborhood and thus track objects in a vi...

The purpose of this paper is to give convergence theorems both for closed convex set valued and relative fuzzy valued martingales, and suband supermartingales. These kinds of martingales, suband super-martingales are the extension of classical real valued martingales, suband super-martingales. Here we compare two kinds of convergences, in the Hausdor metric and in the Kuratowski-Mosco sense. We...

Given an in nite sequence t= ( k)k of −1 and +1, we consider the oriented walk de ned by Sn(t) = ∑n k=1 1 2 : : : k . The set of t’s whose behaviors satisfy Sn(t) ∼ bn is considered (b ∈ R and 0¡ 61 being xed) and its Hausdor dimension is calculated. A two-dimensional model is also studied. A three-dimensional model is described, but the problem remains open. c © 2000 Elsevier Science B.V. All ...