Chemical structures are mathematically modeled using chemical graphs. The graph invariants including algebraic polynomials and topological indices related to the structure of molecules. Hosoya polynomial is a distance based closed form several indices. This article devoted compute two different atomic configurations (C4C8(R) C4C8(S)) C4C8 Carbon Nanosheets. nanosheets most stable, flexible unif...

In this paper, we consider Wiener nonlinear model for solid oxide fuel cell (SOFC). The Wiener model of the SOFC consists of a linear dynamic block and a static output non-linearity followed by the block, in which linear part is approximated by state-space model and the nonlinear part is identified by a polynomial form. To control the SOFC system, we have to consider various view points such as...

We construct arbitrary matrix elements of the quantum evolution operator for a wide class of self-adjoint canonical Hamiltonians, including those which are polynomial in the Heisenberg operators, as the limit of well defined path integrals involving Wiener measure on phase space, as the diffusion constant diverges. A related construction achieves a similar result for an arbitrary spin Hamiltonian.

In this work, a non-iterative identification approach is presented for estimating a single-input single-output Wiener model, comprising an infinite impulse response discrete transfer function followed by static non-linearity. Global orthogonal basis functions and orthogonal Hermite polynomials are used as expansion bases for the linear subsystem and the non-linearity, respectively. A multi-inde...

We present a new method for solving stochastic differential equations based on Galerkin projections and extensions of Wiener’s polynomial chaos. Specifically, we represent the stochastic processes with an optimum trial basis from the Askey family of orthogonal polynomials that reduces the dimensionality of the system and leads to exponential convergence of the error. Several continuous and disc...

Many nonlinear systems can be described by a Wiener-Schetzen model. In this model, the linear dynamics are formulated in terms of orthonormal basis functions (OBFs). The nonlinearity is modeled by a multivariate polynomial. In general, an infinite number of OBFs is needed for an exact representation of the system. This paper considers the approximation of a Wiener system with finite-order infin...