This paper de1nes the new concept of completely Hausdor& axiom of an L-topological space by means of L-continuous mappings from an L-topological space to the re1ned Hutton’s unit L-interval by Wang. Some characterizations of the completely Hausdor& axiom, de1ned in this paper, are given, and many nice properties of this kind of completely Hausdor& axiom are proved. For example, it is hereditary...

We consider the problem of measuring the similarity between two nite point sets using the Hausdor distance H(A;B). This distance is small when each point in A is close to some point in B, and each point in B is close to some point in A. The de nition does not require that A and B have the same number of points. More importantly, H(A;B) is a metric. A point set is identical only to itself, the o...

Let (X; ) be a separable metric space and let (K(X); e ) denote the space of non-empty compact subsets of X with the Hausdor metric. The purpose of this paper is to investigate the relationship of the Hausdor dimension of a set E X to that of K(E) K(X).

We study di erentiability of topological conjugacies between expanding piecewise C1+ interval maps. If these conjugacies are not C1 , then they have zero derivative almost everywhere. We obtain the result that in this case the Hausdor dimension of the set of points for which the derivative of the conjugacy does not exist lies strictly between zero and one. Using multifractal analysis and thermo...

This paper presents a video cut detection algorithm using multi-level Hausdor distance histograms (HDH). Hausdor distance is obtained by comparing edge points of successive frames, wherein the edge information is extracted from compressed frames directly. The use of Hausdor distance histogram instead of the comparison of entering/exiting edge pixel counts [9] makes the algorithm more robust to ...

In this note we present two new positive answers to Tingley’s problem in certain subspaces of function algebras. the first result prove that every surjective isometry between unit spheres, S(A) and S(B), uniformly closed algebras A B on locally compact Hausdor? spaces can be extended a real linear from onto B. second part study isometries spheres abelian JB*-triples represented as continuous fu...

We have given several necessary and su cient conditions for statistically self-similar sets and a.s. self-similar sets and have got the Hausdor dimension and exact Hausdor measure function of any a.s. self-similar set in this paper. It is useful in the study of probability properties and fractal properties and structure of statistically recursive sets. c © 2000 Elsevier Science B.V. All rights ...

We investigate approximate decision algorithms for determining whether the mini mumHausdor distance between two points sets or between two sets of nonintersecting line segments is at most An approximate decision algorithm is a standard decision algorithm that answers yes or no except when is in an indecision interval where the algorithm is allowed to answer don t know We present algorithms with...

For two given simple polygons P Q the problem is to determine a rigid motion I of Q giving the best possible match between P and Q i e minimizing the Hausdor distance between P and I Q Faster algorithms as the one for the general problem are obtained for special cases namely that I is restricted to translations or even to translations only in one speci ed direction It turns out that determining...

In this paper and in we study the structure of spaces Y which are pointed Gromov Hausdor limits of sequences f M i pi g of complete connected Riemannian manifolds whose Ricci curvatures have a de nite lower bound say RicMn i n In Sections and sometimes in we also assume a lower volume bound Vol B pi v In this case the sequence is said to be non collapsing If limi Vol B pi then the sequence is s...