广义Ball曲线的性质及其应用

本文讨论了任意次数的广义Ball曲线的性质和它们的应用,如一般的升阶公式,Bézier曲线与广义Ball曲线之间的转换,极限定理,对偶基,广义Ball基函数下的Marsden恒等式,降阶赋值算法,单位分解性质等.     

Ball基函数的对偶基及其应用

1．引言对于平面或空间上给定的n＋1个点vo，yi，…，v。，熟知的n次Bezier曲线定义为称为n次BernsteiN基函数，vo，yi，…；vn为Bezier曲线的控制点．在Ball开发的英国飞机公司Consurf外形设计系统中，他首先给出了三次Ball基函数的定义l‘，‘］．后来，Goodman和Said定义了［0，1］上Zm＋1次Ball基函数［5］一类似于B6zier曲线，称为［0，1］上关于控制点10，yi，…，vZ。＋1的B。11曲线·类似于B6zier曲线，Ball曲线也具有变差缩减、保凸等良好性质［3］，故在几何外形设计中也有着广泛的应用．熟知的B6zier曲线可由deCasteljan…     

用于积分方程解的函数值Padé-型逼近的正交多项式和行列式公式

为了求解第二类Fredholm积分方程, 引入了一个广义线性泛函,从而定义了一种新的函数值Padé-型逼近．借助于积分方程解的幂级数展开式,这种逼近方法可用来构造积分方程的近似解．定义了Padé-型逼近的正交多项式,在此基础上给出了两种形式的实用的分子行列式和分母行列式公式．     

一类广义Ball曲线的改进

Said将Ball基由三阶延伸到奇数阶。本文在任意阶上讨论广义Ball曲线性质及其求值的新一种递归算法。     

带两个形状参数的四次Bézier曲线的扩展

给出了一组含有两个形状参数α,β的四次多项式基函数,是四次Bernstein基函数的扩展,分析了这组基的性质;基于这组基定义了带两个形状参数的多项式曲线,所定义的曲线不仅保留了四次Bézier曲线一些实用的几何特征,而且具有形状的可调性,在控制多边形不变的情况下,改变参数α,β的取值,可以生成不同的逼近控制多边形的曲线;通过分析该曲线与四次Bézier曲线之间的关系,给出了α和β的几何意义,并利用Bézier曲线递归分割算法给出了这种曲线的几何作图法,同时还讨论了曲线间的拼接问题.     

广义概率对偶犹豫模糊语言幂集结算子在多属性决策中的应用

在对偶犹豫模糊语言集、概率对偶犹豫模糊集和广义幂集结算子的基础上,研究了在概率对偶犹豫模糊语言环境下的广义幂集结算子问题。首先,给出了概率对偶犹豫模糊语言集的定义、运算规则、得分函数、精确函数、距离测度、熵。然后,定义了广义概率对偶犹豫模糊语言幂集结算子,并研究其具有的性质。其次,提出了一种决策方法来解决集结数据之间存在相互关系的概率对偶犹豫模糊语言多属性决策问题。最后,结合相关案例验证了该方法的有效性和可行性。     

带两个形状参数的五次Bézier曲线的扩展

给出了一组含有两个形状参数α,β的六次多项式基函数,是五次Bernstein基函数的扩展,分析了这组基的性质;基于这组基定义了带两个形状参数的多项式曲线,所定义的曲线具有五次Bézier曲线的性质,改变参数α,β的取值,曲线具有更灵活的形状可调性,而且能向上或从两侧逼近控制多边形.另外,经典的五次Bézier曲线和有关文献中带一个形状参数的曲线均是该文所定义曲线的特例.实例表明,定义的曲线为曲线/曲面的设计提供了一种有效的方法.     

一个广义的共轭对偶

本文给出了广义的共轭概念,定义了规划问题的广义共轭对偶问题为;得到了强、弱对偶定理及极性条件的一些等价条件。在本文中,X表示一般非空集合,且H对逐点极大运算是封闭的; 定义1 函数f于x_0是H-Ω凸的是指,如f于X上任意点是H-Ω凸的,则称f是X上的H-Ω凸函数。由定义1得:H-Ω凸函数族的逐点极大函数也是H-Ω凸函数;对,则由     

两类新的广义Ball曲线曲面的求值算法及其应用

本文研究两类新的广义Ball曲线曲面的求值算法及其应用.其一是把Bezier曲线曲面的求值转换到这两类曲线曲面的求值,大大加快了计算速度.其二是给出Bezier曲线与这两类广义Ball曲线的统一表示,并利用这种表示给出它们之间相互转换的递归算法.     

均衡约束数学规划问题的一类广义Mond-Weir型对偶理论

针对均衡约束数学规划模型难以满足约束规范及难于求解的问题,基于Mond和Weir提出的标准非线性规划的对偶形式,利用其S稳定性,建立了均衡约束数学规划问题的一类广义Mond-Weir型对偶,从而为求解均衡约束优化问题提供了一种新的方法.在Hanson-Mond广义凸性条件下,利用次线性函数,分别提出了弱对偶性、强对偶性和严格逆对偶性定理,并给出了相应证明.该对偶化方法的推广为研究均衡约束数学规划问题的解提供了理论依据.     

The Dual Functionals for the Generalized Ball Basis of Wang-Said Type and Basis Transformation Formulas

The generalized Ball curves of Wang-Said type with a position parameter L not only unify the Wang-Ball curves and the Said-Ball curves, but also include several useful intermediate curves. This paper presents the dual functionals for the generalized Ball basis of Wang-Said type. The relevant basis transformation formulae are also worked out.     

The weighted dual functions for Wang-Bézier type generalized Ball bases and their applications

By introducing the inner-product matrix of two vector functions and using conversion matrix, explicit formulas for the dual basis functions of Wang-Bézier type generalized Ball bases (WBGB) with respect to the Jacobi weight function are given. The dual basis functions with and without boundary constraints are also considered. As a result, the paper includes the weighted dual basis functions of Bernstein basis, Wang-Ball basis and some intermediate bases. Dual functionals for WBGB and the least square approximation polynomials are also obtained.     

三角域上Said-Bézier型广义Ball基的对偶泛函及其应用

A family of Said-Bézier type generalized Ball(SBGB) bases and surfaces with a parameter H over triangular domain is introducermediate surfaces.To convert different bases and surfaces,the dual functionals of bases are presented.As an application of dual functionals,the subdivision formulas for surfaces are established.     

DUAL FUNCTIONALS OF SAID-BEZIER TYPE GENERALIZED BALL BASES OVER TRIANGLE DOMAIN AND THEIR APPLICATION

A family of Said-Bézier type generalized Ball (SBGB) bases and surfaces with a parameter H over triangular domain is introduced, which unifies Bézier surface and Said-Ball surface and includes several intermediate surfaces. To convert different bases and surfaces, the dual functionals of bases are presented. As an application of dual functionals, the subdivision formulas for surfaces are established.     

Dual Bases for a New Family of Generalized Ball Bases

This paper presents the dual bases for a new family of generalized Ball curves with a position parameter K, which includes the Bezier curve, generalized Said-Ball curve and some intermediate curves. Using the dual bases, the relative Marsden identity, conversion formulas of bases and control points of various curves are obtained.     

On the generalized Ball bases

The Ball basis was introduced for cubic polynomials by Ball, and two different generalizations for higher degree m polynomials have been called the Said–Ball and the Wang–Ball basis, respectively. In this paper, we analyze some shape preserving and stability properties of these bases. We prove that the Wang–Ball basis is strictly monotonicity preserving for all m. However, it is not geometrically convexity preserving and is not totally positive for m>3, in contrast with the Said–Ball basis. We prove that the Said–Ball basis is better conditioned than the Wang–Ball basis and we include a stable conversion between both generalized Ball bases. The Wang–Ball basis has an evaluation algorithm with linear complexity. We perform an error analysis of the evaluation algorithms of both bases and compare them with other algorithms for polynomial evaluation.     

Stable strong Fenchel and Lagrange duality for evenly convex optimization problems

By means of a conjugation scheme based on generalized convex conjugation theory instead of Fenchel conjugation, we build an alternative dual problem, using the perturbational approach, for a general optimization one defined on a separated locally convex topological space. Conditions guaranteeing strong duality for primal problems which are perturbed by continuous linear functionals and their respective dual problems, which is named stable strong duality, are established. In these conditions, the fact that the perturbation function is evenly convex will play a fundamental role. Stable strong duality will also be studied in particular for Fenchel and Lagrange primal–dual problems, obtaining a characterization for Fenchel case.     

Existence theorem in the variational problem for compressible inviscid fluids

Existence of minima of hemibounded functionals with nonconvex integrand is considered. For this purpose the concept of generalized solutions is introduced. The approach is based on the Young's method; the integrand is imbedded in a suitable topological space, and the dual problem is formulated. The results are obtained for the particular Hamilton action functional which arises in the theory of compressible inviscid fluids.     

Generalized Lebesgue integral

A new definition of integral-like functionals exploiting the ideas of the Lebesgue integral construction and extending the idea of pan-integrals is given. Some convergence theorems for sequence of measurable functions are discussed. As a result, a theoretical basis for applications of the generalized Lebesgue integral is provided. Several types of integrals known from the literature are shown to be special cases of generalized Lebesgue integral.     

On the Variational Approach to Systems of Quasilinear Conservation Laws

The paper contains results concerning the development of a new approach to the proof of existence theorems for generalized solutions to systems of quasilinear conservation laws. This approach is based on reducing the search for a generalized solution to analyzing extremal properties of a certain set of functionals and is referred to as a variational approach. The definition of a generalized solution can be naturally reformulated in terms of the existence of critical points for a set of functionals, which is convenient within the approach proposed. The variational representation of generalized solutions, which was earlier known for Hopf-type equations, is generalized to systems of quasilinear conservation laws. The extremal properties of the functionals corresponding to systems of conservation laws are described within the variational approach, and a strategy for proving the existence theorem is outlined. In conclusion, it is shown that the variational approach can be generalized to the two-dimensional case.