A novel unsymmetric square matrix, WPU , is proposed for calculating both Wiener, W , and hyper-Wiener, WW, numbers. This matrix is constructed by using single endpoint characterization of paths. Its relations with Wiener-type numbers are discussed.

A new approach to robust estimation of signals and prediction of time{series is considered. Signal and system parameter deviations are represented as random variables, with known covariances. A robust design is obtained by minimizing the squared estimation error, averaged both with respect to model errors and noise. A polynomial solution, based on averaged spectral factor-izations and averaged ...

The unitary Cayley graph Xn has vertex set Zn = {0, 1,…, n-1} and vertices u and v are adjacent, if gcd(uv, n) = 1. In [A. Ilić, The energy of unitary Cayley graphs, Linear Algebra Appl. 431 (2009) 1881–1889], the energy of unitary Cayley graphs is computed. In this paper the Wiener and hyperWiener index of Xn is computed.

the edge versions of reverse wiener indices were introduced by mahmiani et al. veryrecently. in this paper, we find their relation with ordinary (vertex) wiener index in somegraphs. also, we compute them for trees and tuc4c8(s) naotubes.

A simpliied way of deriving of realizable and explicit Wiener lters is presented. Discrete time problems are discussed, in a polynomial equation framework. Optimal lters, predictors and smoothers are calculated by means of spectral factorizations and linear polynomial equations. A new tool for obtaining these equations, for a given problem structure, is described. It is based on evaluation of o...

The diffraction by impenetrable wedges having arbitrary aperture angle is studied by means of the Wiener-Hopf (W-H) technique. A system of functional equations called generalized Wiener-Hopf equations (GWHE) is obtained. Only for certain values of the aperture angle these equations are recognizable as standard or classical Wiener-Hopf equations (CWHE). However, in all cases, a mapping to a suit...

The Wiener index of a graph is the sum of the distances between all pairs of vertices, it has been one of the main descriptors that correlate a chemical compound’s molecular graph with experimentally gathered data regarding the compound’s characteristics. In [1], the tree that minimizes the Wiener index among trees of given maximal degree is studied. We characterize trees that achieve the maxim...

A new approach to robust estimation of signals and prediction of time{ series is considered. Possible modelling errors are described by sets of systems , parametrized by random variables, with known covariances. A robust design is obtained by minimizing the squared estimation error, averaged both with respect to model errors and noise. A polynomial solution, based on averaged spectral factoriza...

The Wiener polynomial of a graph G is a generating function for the distance distribution dd(G) = (D1,D2, . . . , Dt ), where Di is the number of unordered pairs of distinct vertices at distance i from one another and t is the diameter of G. We use the Wiener polynomial and several related generating functions to obtain generating functions for distance distributions of unweighted and weighted ...