An extended stochastic gradient algorithm is developed to estimate the parameters of Hammerstein–Wiener ARMAX models. The basic idea is to replace the unmeasurable noise terms in the information vector of the pseudo-linear regression identification model with the corresponding noise estimates which are computed by the obtained parameter estimates. The obtained parameter estimates of the identif...

The vertex-edge Wiener polynomials of a simple connected graph are defined based on the distances between vertices and edges of that graph. The first derivative of these polynomials at one are called the vertex-edge Wiener indices. In this paper, we express some basic properties of the first and second vertex-edge Wiener polynomials of simple connected graphs and compare the first and second ve...

the topological indices, defined as the sum of contributions of all pairs of vertices (among which are the wiener, harary, hyper–wiener indices, degree distance, and many others), are expressed in terms of contributions of edges and pairs of edges.

let g be a molecular graph. the wiener index of g is defined as the summation of alldistances between vertices of g. in this paper, an exact formula for the wiener index of a newtype of nanostar dendrimer is given.

The nonrelativistic standard model for a continuous, one-parameter diffusion process in position space is the Wiener process. As is well known, the Gaussian transition probability density function (PDF) of this process is in conflict with special relativity, as it permits particles to propagate faster than the speed of light. A frequently considered alternative is provided by the telegraph equa...

A positive integer n is said to be Wiener graphical, if there exists a graph G with Wiener index n. In this paper, we prove that any positive integer n( 6= 2, 5) is Wiener graphical. For any positive integer p, an interval [a, b] is said to be a p-Wiener interval if for each positive integer n ∈ [a, b] there exists a graph G on p vertices such that W (G) = n. For any positive integer p, an inte...

Previous research [N. Bhandari and D. K. Rollins, Ind. Eng. Chem. Res., 2003, 42, 5583] introduced a methodology for obtaining accurate continuous-time multiple-input, multiple-output (MIMO) models for Wiener processes with nonlinear static and dynamic behavior. This methodology consists of a model-building procedure for estimation of model forms in the Wiener structure and a choice of two algo...

This study proposes a direct parameter estimation approach from observed input–output data of a stochastic singleinput–single-output fractional-order continuous-time Hammerstein–Wiener model by extending a well known iterative simplified refined instrumental variable method. The method is an extension of the simplified refined instrumental variable method developed for the linear fractional-ord...