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.

We develop a completely new and straightforward method for simulating the joint law of the position and running maximum at a fixed time of a general Lévy process with a view to application in insurance and financial mathematics. Although different, our method takes lessons from Carr’s so-called “Canadization” technique as well as Doney’s method of stochastic bounds for Lévy processes; see Carr ...

Let G be a graph with vertex set V(G) and edge set E(G). For any two vertices x and y in V(G), the distance between x and y, denoted by d(x,y), is the length of the shortest path connecting x and y. The degree of a vertex v in G is the number of neighbors of v in G. Numbers reflecting certain structural features of organic molecules that are obtained from the molecular graph are usually called ...

This paper aims to improve the reliability of optimal control using models constructed by machine learning methods. Optimal problems based on such are generally non-convex and difficult solve online. In this paper, we propose a model that combines Hammerstein-Wiener with input convex neural networks, which have recently been proposed in field learning. An important feature is resulting effectiv...

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...

This is a short tutorial on Volterra and Wiener series applications to modelling of nonlinear systems and phenomena, and also a survey of the recent achievements in this area. In particular, we show here how the philosophies standing behind each of the above theories differ from each other. On the other hand, we discuss also mathematical relationships between Volterra and Wiener ker...

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...

This paper develops and illustrates a new maximum-likelihood based method for the identification of Hammerstein–Wiener model structures. A central aspect is that a very general situation is considered wherein multivariable data, non-invertible Hammerstein and Wiener nonlinearities, and coloured stochastic disturbances both before and after the Wiener nonlinearity are all catered for. The method...

An α-Wiener bridge is a one-parameter generalization of the usual Wiener bridge, where the parameter α > 0 represents a mean reversion force to zero. We generalize the notion of α-Wiener bridges to continuous functions α : [0, T ) → R. We show that if the limit limt↑T α(t) exists and is positive, then a general α-Wiener bridge is in fact a bridge in the sense that it converges to 0 at time T wi...