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Let X, X be two locally finite, preordered sets and let R be any indecomposable commu-tative ring. The incidence algebra I(X, R), in a sense, represents X, because of the well-known result that if the rings I(X, R) and I(X ,R) are isomorphic, then X and X are iso-morphic. In this paper, we consider a preordered set X that need not be locally finite but has… (More)

We study a Gaussian matrix function of the adjacency matrix of artificial and real-world networks. We motivate the use of this function on the basis of a dynamical process modeled by the time-dependent Schrödinger equation with a squared Hamiltonian. In particular, we study the Gaussian Estrada index-an index characterizing the importance of eigenvalues… (More)

unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract Considering a frame L, we introduce the notions of stratified L-semi-topological neighborhood group, stratified L-quasi-topological neighborhood group, and stratified L-quasi-bi-topological neighborhood group. In so doing, we look at the… (More)

- M K Chakraborty, T M G Ahsanullah, T M G Ahsanullah, N N Morsi, A F M Khodadad Khan, Fawzi Al-Thukair
- 2008

Fuzzy topologies on fuzzy sets and tolerance topologies, Internat. Some properties of fuzzy neighborhood normed linear spaces, Internat. A characterization of fuzzy neighborhood commutative division rings, Internat.

Let X be any partially ordered set, R any commutative ring, and T = I * (X,R) the weak incidence algebra of X over R. Let Z be a finite nonempty subset of X, L(Z) = {x ∈ X : x z for some z ∈ Z}, and M = Te Z. Various chain conditions on M are investigated. The results so proved are used to construct some classes of right perfect rings that are not left… (More)

We introduce the notion of N-topo nilpotent fuzzy set in a fuzzy neighborhood ring and develop some fundamental results. Here we show that a fuzzy neighborhood ring is locally inversely bounded if and only if for all 0 < α < 1, the α-level topological rings are locally inversely bounded. This leads us to prove a characterization theorem which says that if a… (More)

Ordered sets are used as a computational model for motion planning problems. Every ordered set has a two-directional point representation using subdivisions. These subdivision points correspond to direction changes along the path of motion.

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