多元三角阵列插值多项式

本文研究多元三角阵列的多项式插值问题,多元Newton插值,多元Abel-Goncarov插值以及Kergin插值都是三角阵列插值的特殊情况,本文首先得到了多元三角阵列插值多项式及其余项的具体表达式;在此基础上,证明了插值问题的存在唯一性;给出了三角阵列插值余项的估计式,进而得到一个有关多元复变函数插值级数的收敛性定理。     

高次样条循环插值的收敛阶

样条函数的Hermite-Birkhoff插值是一类相当广泛的插值类型。循环插值是稍加限制的H-B插值。我们首先讨论了奇次插值样条的正则性问题,然后讨论了循环插值的收敛性问题,给出了循环插值样条逼近达到饱和阶的充分条件。     

S_2~1(△_(mn)~((2)))上的整节点插值

[1]中提出一种二元样条的插值方法,后来[2]对此种方法进行了较深入的分析.[2]中区分了二种不同类型的插值点:基本插值点和附加插值点;也给出了两种不同类型的插值:整节点插值和半整节点插值。本文研究空间S_2~1(△_(mn)~((2)))上的整节点插值,讨论插值     

Thiele重心型矩阵值混合有理插值算法

利用Samelson型矩阵广义逆,构造了一种基于Thiele型连分式插值与重心有理插值的相结合的二元矩阵值混合有理插值格式,这种新的混合矩阵值有理插值函数继承了连分式插值和重心插值的优点,它的表达式简单,计算方便,数值稳定性好.该算法满足有理插值问题所给的插值条件,同时给出了误差估计分析.最后用数值算例验证了插值算法的有效性.     

一种基于函数值的二元有理插值函数及其性质

利用带参数的仅以被插函数的函数值作为插值条件的一元有理插值方法,构造了一种分母为双二次的仪基于函数值的二元有理双三次插值函数,插值函数具有简洁的显示表示,插值函数中含有四个参数,当这些参数满足一定条件时,插值曲而在插值区域上C1光滑.由于插值函数中含有参数,这样可以在插值数据不变的情况下通过对参数的选择进行插值曲面的局部修改,最后讨论了插值函数的一些性质.     

非光滑函数的分数阶插值公式

本文基于局部分数阶Taylor展开式构造非光滑函数的分数阶插值公式,证明了插值公式的存在和唯一性,给出了分数阶插值的Lagrange表示形式及其误差余项,讨论了一种混合型的分段分数阶插值和整数阶插值的收敛阶.数值算例验证了对于非光滑函数分数阶插值明显优于通常的多项式插值,并说明在实际计算中采用分段混合分数阶和整数阶插值可以使得插值误差在区间上分布均匀,能够极大地提高插值精度.     

带有中点插值条件的缺插值多项式样条

本文讨论了带有中点插值条件的任意次多项式缺插值样条,给出了存在唯一性定理和插值误差的估计。这种插值对样条次数的奇偶性不加限制,因而可以应用于以往较少涉及的偶次缺插值情形。     

一种新的基于函数值的二元有理插值及其性质

利用带参数的仅以被插函数的函数值作为插值条件的一元有理插值方法,构造了一种分母为双三次的仅基于函数值的二元有理双三次插值函数,插值函数具有简洁的显示表示.插值函数中含有六个参数,当这些参数满足一定条件时,插值曲面在插值区域上C1光滑.由于插值函数中含有参数,这样町以在插值数据不变的情况下通过对参数的选择进行插值曲面的局部修改.最后讨论了插值函数的-些性质.     

分数年龄生存函数的估计

本文主要讨论了生存函数的插值问题,使用了非节点端点的三次样条插值和α-power插值两种方法对生存函数进行了插值,并与传统的三种插值假设：死亡均匀分布假设、常数死亡力假设、Balducci假设做了比较.另外,我们对α-power插值中的α进行了拟合,并通过误差分析表明先对α拟合后再进行α-power插值,其插值的误差将会变得非常小,几乎与样条插值相仿.     

一种广义插值法

本文考虑一种广义插值问题，插值条件为小区间上的积分值，以弥补现有的插值方法在L2空间不再适用的不足，除了多项式插值外，还讨论了两种一次样条插值方法。     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

On a class of self-similar processes with stationary increments in higher order Wiener chaoses

We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

CONTENTS OF VOLUME 30

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Instructions for contributions

正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with     

Journal of Mathematical Research with Applications Guide for Authors

正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.     

Staircase transportation problems with superadditive rewards and cumulative capacities

A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].