A Wiener model is a fairly simple, well known, and often used nonlinear block-oriented black-box model. A possible generalization of the class of Wiener models lies in the parallel Wiener model class. This paper presents a method to estimate the linear time-invariant blocks of such parallel Wiener models from input/output data only. The proposed estimation method combines the knowledge obtained...

The sum of distances between all pairs of vertices W (G) in a connected graph G as a graph invariant was first introduced by Wiener [9] in 1947. He observed a correlation between boiling points of paraffins and this invariant, which has later become known as Wiener index of a graph. Today, the Wiener index is one of the most widely used descriptors in chemical graph theory. Due to its strong co...

ABSTRACT. We discuss relations between uniform minimality, unconditionality and interpolation for families of reproducing kernels in backward shift invariant subspaces. This class of spaces contains as prominent examples the Paley-Wiener spaces for which it is known that uniform minimality does in general neither imply interpolation nor unconditionality. Hence, contrarily to the situation of st...

This paper examines the use of a so-called “generalised Hammerstein–Wiener” model structure that is formed as the concatenation of an arbitrary number of Hammerstein systems. The latter are taken here to be memoryless nonlinearities followed by linear time invariant dynamics. Hammerstein, Wiener, Hammerstein–Wiener and Wiener–Hammerstein models are all special cases of this structure. The param...

This paper examines the use of a so-called “generalised Hammerstein–Wiener” model structure that is formed as the concatenation of an arbitrary number of Hammerstein systems. The latter are taken here to be memoryless non-linearities followed by linear time invariant dynamics. Hammerstein, Wiener, Hammerstein–Wiener and Wiener–Hammerstein models are all special cases of this structure. The para...

In [1], Hamzeh, Iranmanesh Hossein-Zadeh and M. V. Diudea recently introduced the generalized degree distance of graphs. In this paper, we present explicit formulas for this new graph invariant of the Cartesian product, composition, join, disjunction and symmetric difference of graphs and introduce generalized and modified generalized degree distance polynomials of graphs, such that their first...

Let G and H be connected graphs. The tensor product G + H is a graph with vertex set V(G+H) = V (G) X V(H) and edge set E(G + H) ={(a , b)(x , y)| ax ∈ E(G) & by ∈ E(H)}. The graph H is called the strongly triangular if for every vertex u and v there exists a vertex w adjacent to both of them. In this article the tensor product of G + H under some distancebased topological indices are investiga...

For time-invariant degradation models and stationary signals and noise, the classical Fourier domain Wiener filter, which can be implemented in O(N logN) time, gives the minimum mean-square-error estimate of the original undistorted signal. For time-varying degradations and nonstationary processes, however, the optimal linear estimate requires O(N2) time for implementation. We consider filterin...