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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 graphs and real-world networks. In particular, we study the Gaussian Estrada index—an index characterizing the importance of eigenvalues close to zero. This index accounts for the information contained in the eigenvalues close to zero in the spectra of networks. Here we obtain bounds for this… (More)

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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