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 repr...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.展开更多
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 polyno...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.展开更多
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 （NURB...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.展开更多
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 p...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.展开更多
文摘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.
基金supported by the National Natural Science Foundation of China under Grant No. 11571362
文摘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.
基金National Natural Science Foundation of China (60831001)Innovation Foundation of Beijing University of Aeronautics and Astronautics for PhD Graduates
文摘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.
基金supported by the National Natural Science Foundation of China under Grant No.11671169。
文摘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.
