关于Bernstein多项式的一类不等式及其应用

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.     

Pythagorean Bézier速端曲线及其等距线

The Pythagorean Bézier hodograph curves are Bézier curves {x(t), y(t)}, whose hodograph (first-order parametric derivative) components satisfy the Phythagorean condition x'2(t) +y'2(t) = σ'(t) for some polynomial σ(t). For nth degree PB curve (n is odd), its offset curve is represented by rational Bézier curve with (2n - 1)th degree and arc length by polynomial. Specially, the properties of cubic PB curve are studied, its geometric features are discussed and its quasi-Hermite interpolating curve and GC1 composite cubic PB curve are also constructed.     

MODIFIABLE QUARTIC AND QUINTIC CURVES WITH SHAPE-PARAMETERS

1　IntroductionBecause of their good properties,the cubic Bézier,B-spline and NURBScurves play animportantrole in CAD,CAGD and modeling systems.When interpolation by the abovecurvesto all ora partofthe control pointsisrequired,itis necessary eitherto find new control pointsby solving a system of linear equations or to insert additional control points. Moreover,thewhole interpolating curve may be affected by moving an individual control point[1～ 6] .By uisng the matrix form ofthe Bernst…     

一类BZIER型的三角多项式曲线

1引言Bézier方法和B样条方法是表示与设计自由曲线曲面造型的主要方法[2][7],然而它不能描述除抛物线以外的圆锥曲线,NURBS方法虽然可以解决上述问题,但其权因子与参数化问题至今仍没有完全解决[2][7].另一方面,在飞机外形设计与数控加工中经常遇到许多由二次曲线弧等表示的形状,此时一些非多项式类型的曲线曲面造型方法显示了强大的威力[1][3][6][8].文献[4][5]给出了B样条形式和带形状参数的Bézier形式的三角多项式曲线,可以     

Strong Approximations of Martingale Vectors and Their Applications in Markov-Chain Adaptive Designs

The strong approximations of a class of R~d-valued martingales are considered.The conditions usedin this paper are easier to check than those used in [3] and [9].As an application,the strong approximation ofa class of non-homogenous Markov chains is established,and the asymptotic properties are established for themulti-treatment Markov chain adaptive designs in clinical trials.     

ON COEFFICIENT POLYNOMIALS OF CUBIC HERMITE-PAD(?) APPROXIMATIONS TO THE EXPONENTIAL FUNCTION

The polynomials related with cubic Hermite-Padéapproximation to the exponentialfunction are investigated which have degrees at most n,m,s respectively.A connectionis given between the coefficients of each of the polynomials and certain hypergeometricfunctions,which leads to a simple expression for a polynomial in a special case.Contourintegral representations of the polynomials are given.By using of the saddle point methodthe exact asymptotics of the polynomials are derived as n,m,s tend to infinity throughcertain ray sequence.Some further uniform asymptotic aspects of the polynomials are alsodiscussed.     

两种Bézier曲面形式的转换及几何连续拼接

本文讨论两种Bézier曲面形式的转换关系和转换条件,并给出矩阵域Bézier曲面片和三角域Bézier曲面片拼接的几何连续条件。     

Portfolio optimization under entropic risk management

framework in the risk uniqueness In this paper, properties of the entropic risk measure are examined rigorously in a general This risk measure is then applied in a dynamic portfolio optimization problem, appearing management constraint. By considering the dual problem, we prove the existence and of the solution and obtain an analytic expression for the solution.     

GAUSSIAN WHITE NOISE CALCULUS OF GENERALIZED EXPANSION

A new framework of Gaussian white noise calculus is established, in line with generalized expansion in [3, 4, 7]. A suitable frame of Fock expansion is presented on Gaussian generalized expansion functionals being introduced here, which provides the integral kernel operator decomposition of the second quantization of Koopman operators for chaotic dynamical systems, in terms of annihilation operators dt and its dual, creation operators t*.     

Lipschitz Properties in Variable Exponent Problems via Relative Rearrangement

The author first studies the Lipschitz properties of the monotone and relative rearrangement mappings in variable exponent Lebesgue spaces completing the result given in [9]. This paper is ended by establishing the Lipschitz properties for quasilinear problems with variable exponent when the right-hand side is in some dual spaces of a suitable Sobolev space associated to variable exponent.     

BOUNDEDNESS IN p-NFDES

1 IntroductionRecently, the papers (cf [1], [2]) have established stabi1ity of p-NFDEsusing Liapunov-Razumikhin functionaJs. However, in order to study the limtset and the existence of periodic solutions of p-NFDEs, we need to know notonly the stability but ajso the boundedness of solutions. In this paper, weshal1 discuss the boundedness properties of P-NFDEs by Liapunov functionals,which improve some boundedness conditions for FDEs in the literature. Someexamples are also worked out t…     

Bohr Inequality for Multiple Op erators

An absolute value equation is established for linear combinations of two operators. When the parameters take special values, the parallelogram law of operator type is given. In addition, the operator equation in literature [3] and its equivalent deformation are obtained. Based on the equivalent deformation of the operator equation and using the properties of conjugate number as well as the operator, an absolute value identity of multiple operators is given by means of mathematical induction. As Corollaries, Bohr inequalities are extended to multiple operators and some related inequalities are reduced to, such as inequalities in [2] and [3].     

低阶C-Bézier曲线的升阶

C- Bézier曲线是在 Bézier曲线基础上作了改进 ,因此具有与 Bézier曲线类似的性质 .本文主要研究的是 C- Bézier曲线从 3阶到 4阶 ,4阶到 5阶 ,5阶到 6阶的升阶转换     

四次保形有理Bézier曲线的构造

本文讨论四次 Bézier曲线的保形性 ,对不保形的四次 Bézier曲线构造了一类四次有理 Bézier曲线的调整方法 ,论述了保形性定理 ,给出了算法和算例     

保凸分段三次Bézier插值样条曲线

本文讨论分段三次 Bézier曲线的保凸插值 ,对给定的凸数据点列在相邻两型值点之间构造两个三次 Bézier曲线子段 ,两段之间 G2连续的 ,所构造的曲线插值所有型值点且是 G1的和保凸的     

五次C-Bézier曲线的生成及其性质

以sint,cost,t3,t2,t,1为基底构造了一组类似于Bernstein多项式的基函数,它们依赖于参数a,用这组基函数表示的自由曲线称为五次C-Bézier曲线,它不仅具有一般五次Bézier曲线所具有的各种几何性质,同时又可以精确地表示一些圆锥曲线,例如圆弧甚至整圆.     

Some Properties of Two Subclasses of Analytic Functions

This paper discusses some properties of two classes Vk[α,β] and Rk[α,β ]. Sharp distortion theorem and radius of convexity and starlikeness are obtained. Hadamard product of functions in the classes are also studied.     

Derived representation type and Gorenstein projective modules of an algebra under crossed product

Let H and its dual H* be finite dimensional semisimple Hopf algebras. In this paper, we firstly prove that the derived representation types of an algebra A and the crossed product algebra A#σH are coincident. This is an improvement of the conclusion about representation type of an algebra in Li and Zhang [Sci China Ser A, 2006, 50: 1-13]. Secondly, we give the relationship between Gorenstein projective modules over A and that over A#σH. Then, using this result, it is proven that A is a finite dimensional CM-finite Gorenstein algebra if and only if so is A#σH.     

NBELC和NWELC寿命分布类

Two new classes of life distributions, namely the class of new better than its equilibrium life in convex ordering (NBBLC), and its dual class, the class of new worse than its equilibrium life in convex ordering (NWELC), are introduced. Their relations to other classes of life distributlons, closure properties under the three reliability operations, and inheritance properties under shock models and Laplace-Stieltjes transforms are discussed.     

Cyclotomic problem, Gauss sums and Legendre curve

In this paper, explicit determination of the cyclotomic numbers of order l and 2l, for odd prime l ≡ 3 (mod 4), over finite field Fq in the index 2 case are obtained, utilizing the explicit formulas on the corresponding Gauss sums. The main results in this paper are related with the number of rational points of certain elliptic curve, called "Legendre curve", and the properties and value distribution of such number are also presented.