In this paper a spatio-temporal analogic CNN algorithm is designed for front-end filtering, segmentation and object recognition. First, a generalized segmentation strategy is presented based on various diffusion models. Both PDE and non-PDE related schemes are discussed and their VLSI complexity is analyzed. In classification (object recognition) a CNN implementation of the autowave metric, a “...

Considering the increasing interest in fuzzy theory and possible applications,the concept of fuzzy metric space concept has been introduced by severalauthors from different perspectives. This paper interprets the theory in termsof metrics evaluated on fuzzy numbers and defines a strong Hausdorff topology.We study interrelationships between this theory and other fuzzy theories suchas intuitionis...

A local cut point is by definition a point that disconnects its sufficiently small neighborhood. We show that there exists an upper bound for the degree of a local cut point in a metric measure space satisfying the generalized Bishop–Gromov inequality. As a corollary, we obtain an upper bound for the number of ends of such a space. We also obtain some obstruction conditions for the existence of...

In [1], A. Branciari defines a Generalised metric space of finite order and establishes Banach contraction principle in it. The object of this paper is to extend this result to Quasi contraction and prove some fixed point results for two weakly compatible self maps satisfying a generalized contractive condition in this space without assuming it to be Hausdorff . Our result generalizes the said ...

In this paper, we reveal a remarkable connection between the Thue-Morse sequence and the Koch snowflake. Using turtle geometry and polygon maps, we realize the Thue-Morse sequence as the limit of polygonal curves in the plane. We then prove that a sequence of such curves converges to the Koch snowflake in the Hausdorff metric. In the final section we consider generalized Thue-Morse sequences an...

Certain generalized Banach's contraction mapping principles on metric spaces are unified and/or extended to Hausdorff uniform spaces. Also given are some relationships between the set of all cluster points of the Picard iterates and the set of all fixed points for the mapping. These are obtained by assuming that the latter set is nonempty and by considering certain "quasi"-contractive condition...

Making an extensive use of small transfinite topological dimension trind, we ascribe to every metric space X an ordinal number (or −1 or Ω) tHD(X), and we call it the transfinite Hausdorff dimension of X. This ordinal number shares many common features with Hausdorff dimension. It is monotone with respect to subspaces, it is invariant under bi-Lipschitz maps (but in general not under homeomorph...

The main purpose of this paper is to prove the intuitionistic fuzzy contraction properties of the Hutchinson-Barnsley operator on the intuitionistic fuzzy hyperspace with respect to the Hausdorff intuitionistic fuzzy metrics. Also we discuss about the relationships between the Hausdorff intuitionistic fuzzy metrics on the intuitionistic fuzzy hyperspaces. Our theorems generalize and extend some...