the topological indices, defined as the sum of contributions of all pairs of vertices (among which are the wiener, harary, hyper–wiener indices, degree distance, and many others), are expressed in terms of contributions of edges and pairs of edges.

Since Chang [2] introduced fuzzy theory into topology, many authors have discussed various aspects of fuzzy topology. It is well known that weakly induced and induced topological spaces play an important role in L-topological spaces (see book [8]). According to their value ranges, L-topological spaces form different categories. Clearly, the investigation on their relationships is certainly impo...

It is well-known that one signature of the three-dimensional electron topological insulator is the Witten effect: if the system is coupled to a compact electromagnetic gauge field, a monopole in the bulk acquires a half-odd-integer polarization charge. In the present work, we propose a corresponding phenomenon for the topological insulator of bosons in 3d protected by particle number conservati...

Intrinsically gapless symmetry-protected topological phases (igSPT) are systems with SPT edge states properties that could not arise in a gapped system the same symmetry and dimensionality. igSPT from which an anomaly low-energy (infrared) group emerges extended anomaly-free microscopic (ultraviolet) symmetry. We construct general framework for constructing lattice models emergent anomalies cla...

We study chains in an H-closed topological partially ordered space. We give sufficient conditions for a maximal chain L in an H-closed topological partially ordered space such that L contains a maximal (minimal) element. Also we give sufficient conditions for a linearly ordered topological partially ordered space to be H-closed. We prove that any H-closed topological semilattice contains a zero...

Polymers in a melt may be subject to topological constraints, as in the example of unlinked polymer rings. How to do statistical mechanics in the presence of such constraints remains a fundamental open problem. We study the effect of topological constraints on a melt of directed polymers, using simulations of a simple quasi-2D model. We find that fixing the global topology of the melt to be tri...

the present study investigates the effects of different routes of inulin administration as prebiotic on gut microbiota and survival rate of indian white shrimp post-larvae. four hundred and fifty indian white shrimp post-larvae (pl1) were stocked in nine tanks. the tanks were assigned into three treatments: feeding with inulin-treated (110 mg l-1) artemia nauplii (i-t), feeding with inulin-enri...