This paper presents a basis for the space of hyperbolic polynomials Γm=span{1, sht, cht, sh2t, ch2t, …, shmt, chmt} on the interval [0,α] from an extended Tchebyshev system, which is analogous to the Bernstein basi...This paper presents a basis for the space of hyperbolic polynomials Γm=span{1, sht, cht, sh2t, ch2t, …, shmt, chmt} on the interval [0,α] from an extended Tchebyshev system, which is analogous to the Bernstein basis for the space of polynomial used as a kind of well-known tool for free-form curves and surfaces in Computer Aided Geometry Design. Then from this basis, we construct quasi Bézier curves and discuss some of their properties. At last, we give an example and extend the range of the pa- rameter variable t to arbitrary close interval [r, s] (r<s).展开更多
Let be the class of polynomials of degree n and a family of operators that map into itself. For , we investigate the dependence of on the maximum modulus of on for arbitrary real or complex numbers , with , and , and ...Let be the class of polynomials of degree n and a family of operators that map into itself. For , we investigate the dependence of on the maximum modulus of on for arbitrary real or complex numbers , with , and , and present certain sharp operator preserving inequalities between polynomials.展开更多
In this paper a class of new inequalities about Bernstein polynomial is established. With these inequalities, the estimation of heights, the derivative bounds of Bézier curves and rational Bézier curves can ...In this paper a class of new inequalities about Bernstein polynomial is established. With these inequalities, the estimation of heights, the derivative bounds of Bézier curves and rational Bézier curves can be improved greatly.展开更多
For a polynomial p（z） of degree n which has no zeros in ｜z｜ 〈 1, Dewan et al., （K. K. Dewan and Sunil Hans, Generalization of certain well known polynomial inequalities, J. Math. Anal. Appl., 363 （2010）, 38-41...For a polynomial p（z） of degree n which has no zeros in ｜z｜ 〈 1, Dewan et al., （K. K. Dewan and Sunil Hans, Generalization of certain well known polynomial inequalities, J. Math. Anal. Appl., 363 （2010）, 38-41） establishedfor any complex number β with ｜β｜≤ and｜z｜ = 1. In this paper we consider the operator B, which carries a polynomial p（z） into展开更多
基金Project supported by the National Natural Science Foundation of China (No. 60473130) and the National Basic Research Program (973) of China (No. 2004CB318000)
文摘This paper presents a basis for the space of hyperbolic polynomials Γm=span{1, sht, cht, sh2t, ch2t, …, shmt, chmt} on the interval [0,α] from an extended Tchebyshev system, which is analogous to the Bernstein basis for the space of polynomial used as a kind of well-known tool for free-form curves and surfaces in Computer Aided Geometry Design. Then from this basis, we construct quasi Bézier curves and discuss some of their properties. At last, we give an example and extend the range of the pa- rameter variable t to arbitrary close interval [r, s] (r<s).
文摘Let be the class of polynomials of degree n and a family of operators that map into itself. For , we investigate the dependence of on the maximum modulus of on for arbitrary real or complex numbers , with , and , and present certain sharp operator preserving inequalities between polynomials.
基金Supported by the National Natural Science Foundation of China (60303015,60333010).
文摘In this paper a class of new inequalities about Bernstein polynomial is established. With these inequalities, the estimation of heights, the derivative bounds of Bézier curves and rational Bézier curves can be improved greatly.
文摘For a polynomial p（z） of degree n which has no zeros in ｜z｜ 〈 1, Dewan et al., （K. K. Dewan and Sunil Hans, Generalization of certain well known polynomial inequalities, J. Math. Anal. Appl., 363 （2010）, 38-41） establishedfor any complex number β with ｜β｜≤ and｜z｜ = 1. In this paper we consider the operator B, which carries a polynomial p（z） into
基金国家自然科学基金( the National Natural Science Foundation of China under Grant No.60672135)陕西省自然科学基金( the Natural Science Foundation of Shaanxi Province of China under Grant No.2005F44) 。
