mathematical chemistry is a branch of theoretical chemistry for discussion and prediction of the molecular structure using mathematical methods without necessarily referring to quantum mechanics. in theoretical chemistry, distance-based molecular structure descriptors are used for modeling physical, pharmacologic, biological and other properties of chemical compounds. the wiener polarity index ...

The Wiener-Khintchine theorem dictates that the correlation function of any stationary, stochastic signal y(t) has as its Fourier transform a function that is necessarily both real and non-negative. In this paper, I explore the real-space, geometric consequences of this reciprocal-space non-negativity constraint. I review prior results addressing this issue, and I also introduce a family of new...

Let (G,w) be a network, that is, a graph G = (V (G), E(G)) together with the weight function w : E(G) → R. The Szeged index Sz(G,w) of the network (G,w) is introduced and proved that Sz(G,w) ≥ W (G,w) holds for any connected network where W (G,w) is the Wiener index of (G,w). Moreover, equality holds if and only if (G,w) is a block network in which w is constant on each of its blocks. Analogous...

We construct several infinite families of trees which have a unique branching vertex of degree 4 and whose Wiener index equals the Wiener index of their quadratic line graph. This solves an open problem of Dobrynin and Mel’nikov.

Let G be a graph. Denote by L(G) its i-iterated line graph and denote by W (G) its Wiener index. Dobrynin, Entringer and Gutman stated the following problem: Does there exist a non-trivial tree T and i ≥ 3 such that W (L(T )) = W (T )? In a series of five papers we solve this problem. In a previous paper we proved that W (L(T )) > W (T ) for every tree T that is not homeomorphic to a path, claw...

The application of a particular branch of non-linear system analysis, the functional series expansion or integral method, to the auditory system is reviewed. Both the Volterra and Wiener approach are discussed and an extension of the Wiener method from its traditional white-noise stimulus approach to that of Poisson distributed clicks is presented. This type of analysis has been applied to comp...

The aim of this paper is to use visual speech information to create Wiener filters for audio speech enhancement. Wiener filters require estimates of both clean speech statistics and noisy speech statistics. Noisy speech statistics are obtained from the noisy input audio while obtaining clean speech statistics is more difficult and is a major problem in the creation of Wiener filters for speech ...

Reliability Wiener number is a modification of the original Wiener number in which probabilities are assigned to edges yielding a natural model in which there are some (or all) bonds in the molecule that are not static. Various probabilities naturally allow modelling different types of chemical bonds because chemical bonds are of different types and it is well-known that under certain condition...