Classical Volterra and Wiener theory of nonlinear systems does not address the problem of noisy measurements in system identification. This issue is treated in the present part of the report. We first show how to incorporate the implicit estimation technique for Volterra and Wiener series described in Part I into the framework of regularised estimation without giving up the orthogonality proper...

Abstract: The Hosoya polynomial of a molecular graph G is defined as ∑ ⊆ = ) ( } , { ) , ( ) , ( G V v u v u d G H λ λ , where d(u,v) is the distance between vertices u and v. The first derivative of H(G,λ) at λ = 1 is equal to the Wiener index of G, defined as ∑ ⊆ = ) ( } , { ) , ( ) ( G V v u v u d G W . The second derivative of ) , ( 2 1 λ λ G H at λ = 1 is equal to the hyper-Wiener index, d...

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 identification algorithm of Wiener-Hammerstein nonlinear model is proposed in the paper. When the nonlinearity in the Wiener-Hammerstein model is approximated by polynomial or spline function, the identification algorithms can be implemented iteratively, and the compensator for the nonlinear distortion is given by using the estimated Wiener-Hammerstein model and its inverse. A numerical sim...

Topological indices are mathematical descriptors for molecular structures. These used to describe physico-chemical properties such as solubility, shape and weight. In this paper, we present distance-based topological Wiener index hyper-Wiener by using Hosoya polynomial inverse graphs associated with finite cyclic group. Also, have found eccentricity based of

The Hosoya polynomial of a graph encompasses many of its metric properties, for instance the Wiener index (alias average distance) and the hyper-Wiener index. An expression is obtained that reduces the computation of the Hosoya polynomial of a graph with cut vertices to the Hosoya polynomial of the so-called primary subgraphs. The main theorem is applied to specific constructions including bouq...

A topological index plays an important role in characterising various physical properties, biological activities, and chemical reactivities of a molecular graph. The Hosoya polynomial is used to evaluate the distance-based indices such as Wiener index, hyper-Wiener Harary Tratch – Stankevitch Zefirov index. In present study, we determine closed form for third type chain hex-derived network dime...

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 ...

We investigate a special case of the maximum quadratic assignment problem where one matrix is a product matrix and the other matrix is the distance matrix of a one-dimensional point set. We show that this special case, which we call the Wiener maximum quadratic assignment problem, is NP-hard in the ordinary sense and solvable in pseudo-polynomial time. Our approach also yields a polynomial time...