the eccentricity connectivity index of a molecular graph g is defined as (g) = av(g)deg(a)ε(a), where ε(a) is defined as the length of a maximal path connecting a to othervertices of g and deg(a) is degree of vertex a. here, we compute this topological index forsome infinite classes of dendrimer graphs.

The proposed analysis of the currently available experimental results concerning the neural cell activity in the brain area known as hippocampus suggests a particular mechanism of spatial information and memory processing. Below it is argued that the spatial information available through the analysis of the hippocampal cell activity is predominantly of topological nature. It is pointed out that...

In the spirit of topological entropy we introduce new complexity functions for general dynamical systems (namely groups and semigroups acting on closed manifolds) but with an emphasis on the dynamics induced on underlying simplicial complexes. For expansive systems remarkable properties are observed. Known examples are revisited and new examples are presented.

Let R be a commutative, noetherian, local ring. Topological Q– vector spaces modelled on full subcategories of the derived category of R are constructed in order to study intersection multiplicities.

Let (X, T ) be a topological dynamical system (TDS), and h(T, K) the topological entropy of a subset K of X . (X, T ) is lowerable if for each 0 ≤ h ≤ h(T, X) there is a non-empty compact subset with entropy h; is hereditarily lowerable if each non-empty compact subset is lowerable; is hereditarily uniformly lowerable if for each non-empty compact subset K and each 0 ≤ h ≤ h(T, K) there is a no...

Contents 1. Introduction 1 2. Structure algebra 4 2.1. Definition of a structure algebra 4 2.2. Semisimple structure algebras 7 2.3. Structure algebra of a finite group 11 3. Cuts of stratified surfaces 15 3.1. Stratified surfaces 15 3.2. Cut systems 17 3.3. Basic and simple surfaces 21 3.4. Neighboring complete cut systems 25 4. Two-dimensional topological field theory 29 4.1. Definition of Kl...

in the present paper for a large family of topological semigroups, namely foundation semigroups, for which topological groups and discrete semigroups are elementary examples, it is shown that ?(s) is the dual of a function algebra.

In the present paper for a large family of topological semigroups, namely foundation semigroups, for which topological groups and discrete semigroups are elementary examples, it is shown that ?(S) is the dual of a function algebra.

$L$-fuzzy rough sets are extensions of the classical rough sets by relaxing theequivalence relations to $L$-relations. The topological structures induced by$L$-fuzzy rough sets have opened up the way for applications of topological factsand methods in granular computing. In this paper, we firstly prove thateach arbitrary $L$-relation can generate an Alexandrov $L$-topology.Based on this fact, w...

This essay is based on the fundmental assumption that any physical system of synergetic parts is a thermodynamic system. The universality of thermodynamics is due to the fact that thermodynamic homogeneous properties, such as pressure, temperature and their analogs, do not depend upon size or shape. That is, thermodynamics is a topological (not a geometrical) theory. By use of Cartan’s methods ...