Abstract This paper is concerned with the distribution properties of the binomial aX + bXα, where X is a gamma random variable. We show in particular that aX + bXα is infinitely divisible for all α ∈ [1, 2] and a, b ∈ R+, and that for α = 2 the second order polynomial aX+bX2 is a generalized gamma convolution whose Thorin density and Wiener-gamma integral representation are computed explicitly....

Topological indices are numbers that applied to a graph and can be used describe specific properties through algebraic structures. Algebraic theory is helpful tool in range of chemistry domains. Because it helps explain how the different symmetries molecules crystals affect their structure dynamics, powerful theoretical approach for forecasting both common uncommon characteristics molecules. A ...

We present a closed form expression for the information matrix associated with the Wiener model identification problem under the assumption that the input signal is a stationary Gaussian process. This expression holds under quite generic assumptions. We allow the linear sub-system to have a rational transfer function of arbitrary order, and the static nonlinearity to be a polynomial of arbitrar...

We present a generalized polynomial chaos method to solve the steady and unsteady heat transfer problems with uncertainty in boundary conditions, diffusivity coefficient and forcing terms. The stochastic inputs and outputs are represented spectrally by employing the orthogonal polynomial functionals from the Askey scheme, as a generalization of the original polynomial chaos idea of Wiener [1]. ...

It is suggested that the differences between the Hammerstein and Wiener models be interpreted and understood in terms of the system eigenvalues. In particular, it is shown that the Wiener representation should be preferred when the system dynamics vary with the operating point. Conversely, when only the system gain varies with the operating point, Hammerstein models generally outperform the Wie...

A number of approaches for discretizing partial differential equations with random data are based on generalized polynomial chaos expansions of random variables. These constitute generalizations of the polynomial chaos expansions introduced by Norbert Wiener to expansions in polynomials orthogonal with respect to non-Gaussian probability measures. We present conditions on such measures which im...

Abstract The n-th order Wiener index of a molecular graph G was put forward by Estrada et al. [New J. Chem. 22 (1998) 819] as ( ) 1 ( , ) n n x W H G x where ( , ) H G x is the Hosoya polynomial. Recently Brückler et al. [Chem. Phys. Lett. 503 (2011) 336] considered a related graph invariant, ( ) 1 1 (1/ !) ( ( , )) / n n n n x W n d x H G x d x . For n=1, both W and W reduce to the ordinary W...

The paper deals with parameter identification of nonlinear dynamic systems using Hammerstein-Wiener models. Multiple application of a decomposition technique provides special expressions for the model description that are linear in parameters. This allows iterative estimation of all model parameters based on the measured input/output data and estimates of internal variables. The proposed algori...