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A switched reluctance motor (SRM) drive system has highly nonlinear uncertainties owing to a convex construction. It is hard for the linear control methods to achieve good performance for the SRM d...

A six-phase copper rotor induction motor (SCRIM) drive system with nonlinear uncertainties is controlled by a backstepping control system using a revamped recurrent Romanovski polynomials neural ne...

Numerical integration is used to approximate an integral over a certain interval. The purpose of the numerical integration is that it is not always possible to evaluate the integral analytically. So, the numerical integration is used. This articles deals with the approximation of the integral based on the Jacobi and the Romanovski polynomials. This is a quadrature for evaluating the integral. Jacobi and Romanovski polynomials are seen as advanced polynomials that are a solution of a certain Sturm-Liouville type differential equations which is described in this paper.

The energy eigenvalues and eigenfunctions of Schrodinger equation for Modified Poschl-Teller potential plus trigonometric Rosen-Morse non-central potential are investigated approximately in terms of finite Romanovski polynomial. The approximation has been made to solve the radial Schrodinger equation. The approximate bound state energy eigenvalues are given in a closed form and corresponding radial and eigenfunctions are obtained in terms of Romanovski polynomials. The polar eigenfunctions are obtained in terms of Romanovski polynomials. The trigonometric Rosen-Morse potential is considered to be perturbation factor to the modified Poschl-Teller potential since it causes the decrease of the length of angular momentum vectors.

A connection between Romanovski polynomials and those polynomials that solve the one-dimensional Schrodinger equation with the trigonometric Rosen-Morse and hyperbolic Scarf potential is established. The map is constructed by reworking the Rodrigues formula in an elementary and natural way. The generating function is summed in closed form from which recursion relations and addition theorems follow. Relations to some classical polynomials are also given.

The energy eigenvalues and eigenfunctions of Schrodinger equation for Hulthen potential plus Eckart potential with the centrifugal term are investigated approximately in terms of finite Romanovski polynomial. The bound state energy eigenvalues are given in a closed form and corresponding eigenfunctions are obtained in terms of Romanovski polynomials.

We briefly review the five possible real polynomial solutions of hypergeometric differential equations. Three of them are the well known classical orthogonal polynomials, but the other two are different with respect to their orthogonality properties. We then focus on the family of polynomials which exhibits a finite orthogonality. This family, to be referred to as the Romanovski polynomials, is required in exact solutions of several physics problems ranging from quantum mechanics and quark physics to random matrix theory. It appears timely to draw attention to it by the present study. Our survey also includes several new observations on the orthogonality properties of the Romanovski polynomials and new developments from their Rodrigues formula., RevTex, 38 pages, 2 figures, review

In this paper, we apply a simple transformation method to construct exactly solvable potentials of Schrodinger equation in any arbitrary dimensional Euclidean space. The normalized wave functions of the constructed potentials are obtained in terms of Romanovski polynomials.