Polynomial Representation of NURBS and Its Application to High Frequency Scattering Prediction

This article presents a method that uses physical optics （PO） techniques to compute the monostatic radar cross section （RCS） of electrically large conducting objects modeled by non-uniform rational B-spline （NURBS） surfaces. At the beginning, a new algorithm to convert recursive B-spline basis function into piecewise polynomials in power form is presented. Then, algorithm computes the polynomial representation of B-spline basis functions and NURBS surface geometric parameters are obtained. The PO integral over NURBS surfaces of an electrically large conducting object is used to predict the object＇s RCS. The NURBS surface is divided into small piecewise polynomial parametric patches by isoparametric curves, and the PO integral expression over the parametric domain of each polynomial parametric patch is reduced to an analytical expression which permits an accurate and effective computation of the PO integral by using a modified Ludwig＇s algorithm. The RCS of the object can be obtained by adding up the PO integral contribution of each polynomial parametric patch. The effectiveness of this method is verified by numerical examples.

On Polynomial Representations of Strange Lie Superalgebras of Q-Type

In this paper, both canonical and noncanonical polynomial representations of Lie super- algebara of Q-type are investigated. It turns out that not all these representations are completely reducible. Moreover, the representation spaces has only two proper submodules when it is completely reducible, and has a unique composition series when it is not completely reducible.

Erdös Type Inequality for Lorentz Polynomials

An elementary, but very useful tool for proving inequalities for polynomials with restricted zeros is the Bernstein or Lorentz representation of polynomials. In the present paper, we give two classes of Lorentz polynomials, for which the Erd?s-type inequality holds.

Solution of Spin and Pseudo-Spin Symmetric Dirac Equation in (1＋1) Space-Time Using Tridiagonal Representation Approach

The aim of this work is to find exact solutions of the Dirac equation in(1+1) space-time beyond the already known class.We consider exact spin(and pseudo-spin) symmetric Dirac equations where the scalar potential is equal to plus(and minus) the vector potential.We also include pseudo-scalar potentials in the interaction.The spinor wavefunction is written as a bounded sum in a complete set of square integrable basis,which is chosen such that the matrix representation of the Dirac wave operator is tridiagonal and symmetric.This makes the matrix wave equation a symmetric three-term recursion relation for the expansion coefficients of the wavefunction.We solve the recursion relation exactly in terms of orthogonal polynomials and obtain the state functions and corresponding relativistic energy spectrum and phase shift.

Computing PUR of Zero-Dimensional Ideals of Breadth at Most One

In this paper,for a zero-dimensional polynomial ideal I,the authors prove that k[x_(1),x_(2),…,x_(n)]/I is cyclic if and only if the breadth of I is 0 or 1.Furthermore,the authors present a new algorithm to compute polynomial univariate representation(PUR)of such an ideal.