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.

In this paper, we present new results on Temporal Decomposition (TD) applied to the Line Spectral Frequencies (LSFs) derived for wideband speech. The paper shows that by incorporating a dynamic programming search algorithm into TD, near transparent quantisation of wideband LSFs can be obtained at approximately 1 kbps. We also show that TD performs significantly better than Split Vector Quantisa...

A new notion of Cartan pairs as a substitute of notion of vector fields in the noncommutative geometry is proposed. The correspondence between Cartan pairs and differential calculi is established.

: Optical separate spatial dark and bright soliton pairs in steady-state case in one dimension, for a series circuit consisting of two-photon photorefractive (PR) crystal are investigated. Each crystal can be supported the spatial soliton, and at least one must be photovoltaic. The two solitons are known collectively as separate spatial soliton pairs with dark–dark, bright–dark and bright–brigh...

We establish a relative spannedness for log canonical pairs, which is generalization of the basepoint-freeness varieties with log-terminal singularities by Andreatta--Wiśniewski. Moreover, we quasi-log pairs.