Let G be a molecular graph. The Wiener index of G is defined as the summation of all distances between vertices of G. In this paper, an exact formula for the Wiener index of a new type of nanostar dendrimer is given.

We systematically develop real Paley–Wiener theory for the Fourier transform on Rd for Schwartz functions, Lp-functions and distributions, in an elementary treatment based on the inversion theorem. As an application, we show how versions of classical Paley–Wiener theorems can be derived from the real ones via an approach which does not involve domain shifting and which may be put to good use fo...

Expansion of a random function in terms of an orthogonal random base was introduced by Cameron and Martin [1] and Wiener [2], Meecham and Siegel [3] and Meecham and Jeng [4] applied this technique to the problem of hydrodynamic turbulence. Recently, Jahedi and Ahmadi [5] used it in their study of nonlinear structures subjected to random loads. The technique is now well known as the Wiener-Hermi...

This work proposes a new approach to the blind inversion of Wiener systems. A Wiener system is composed of a linear time-invariant (LTI) sub-system followed by a memoryless nonlinear function. The goal is to recover the input signal by knowing just the output of the Wiener system, and the straightforward scheme to achieve this is called the Hammerstein system –– apply a memoryless nonlinear map...

Wiener filtering has many applications in the area of imaging science. In image processing, for instance, it is a common way of reducing Gaussian noise. In color science it is often used to estimate reflectances from camera response data on a pixel by pixel basis. Based on a priori assumptions the Wiener filter is the optimal linear filter in the sense of the minimal mean square error to the ac...

The edge versions of reverse Wiener indices were introduced by Mahmiani et al. very recently. In this paper, we find their relation with ordinary (vertex) Wiener index in some graphs. Also, we compute them for trees and TUC4C8(s) naotubes.

The Wiener index of a graph G is equal to the sum of distances between all pairs of vertices of G, It is known that the Wiener index of a molecular graph correlates with certain physical and chemical properties of a molecule. In the mathematical literature, many good algorithms can be found to eompute the distances m a graph, and these can easily be adapted for the caleulation of the Wiener ind...

Wiener model identification and predictive control of a pH neutralisation process is presented. Input-output data from a nonlinear, first principles simulation model of the pH neutralisation process are used for subspace-based identification of a black-box Wiener-type model. The proposed nonlinear subspace identification method has the advantage of delivering a Wiener model in a format which is...

fullerenes are closed−cage carbon molecules formed by 12 pentagonal and n/2 – 10hexagonal faces, where n is the number of carbon atoms. patrick fowler in his lecture inmcc 2009 asked about the wiener index of fullerenes in general. in this paper werespond partially to this question for an infinite class of fullerenes with exactly 10ncarbon atoms. our method is general and can be applied to full...