Bernstein型算子的拓广及其收敛性

取插值基函数Pnk（x，α），导出推广的Bernstein算子Bn（α）（f，x）和推广的Bernstein－Kantorovich算子Kn（α）（f，x），并证明其收敛性．     

关于Bernstein-Fan算子的导数与连续模

对具有三角形波基函数的 Bernstein- Fan插值算子建立了导数与连续模之间的关系 .     

Further variation diminishing properties of Bernstein polynomials on triangles

A definition is given of the “variation” of a surface which generalizes those considered previously. It is then shown that the variation of a Bernstein polynomial on a triangle is bounded by that of its Bézier net and conditions are derived under which the bound is attained. A bound is also given for the variation of the Bézier net in terms of the variation of the function itself. Finally, it is mentioned how these results lead to variation diminishing properties of certain approximation operators involving polyhedral splines.     

The Lattice of Definability: Origins,Recent Developments,and Further Directions

Doklady Mathematics - This article presents results and open problems related to definability spaces (reducts) and sources of this field since the 19th century. Finiteness conditions and...     

两个算子不等式之间关系的进一步推广(英文)

In this paper,we give out a further extension of the relations between two famous inequalities（B r 2 A p B r 2） r p＋r≥B r and Ap≥（A p 2 B r A p 2） p p＋r,which can yield the result of Yamazaki and Yanagida’s.     

Reconstruction of the Dirac Operator From Nodal Data

Inverse nodal problems consist in constructing operators from the given nodes (zeros) of their eigenfunctions. In this work, we deal with the inverse nodal problem of reconstructing the Dirac operator on a finite interval. We prove that a dense subset of nodal points uniquely determine the parameters of the boundary conditions, the mass of a particle and the potential function of the Dirac system. We also provide a constructive procedure for the solution of the inverse nodal problem.     

Further Developments of Rp and Ap Error Analysis

Extensions are made of a recently developed theory of floating-pointerror analysis to facilitate the construction and computationof strict error bounds of a posteriori type. Inter alia, theseextensions obviate the need for specially-directed roundingprocedures in computer hardware or software, and reduce computationalcost by enabling error bounds to be computed to a low workingprecision. Applications are made to the evaluation of products, quotients,powers, sums and inner products, and also to the processes ofinput and output.     

Reconstruction of the Dirac-Type Integro-Differential Operator From Nodal Data

Abstract

The inverse nodal problem for Dirac type integro-differential operator with the spectral parameter in the boundary conditions is studied. We prove that dense subset of the nodal points determines the coefficients of differential part of operator and gives partial information for integral part of it.     

From Riemann and Kodaira to Modern Developments on Complex Manifolds

We survey the theory of complex manifolds that are related to Riemann surface, Hodge theory, Chern class, Kodaira embedding and Hirzebruch–Riemann–Roch, and some modern development of uniformization theorems, Kähler–Einstein metric and the theory of Donaldson–Uhlenbeck–Yau on Hermitian Yang–Mills connections. We emphasize mathematical ideas related to physics. At the end, we identify possible future research directions and raise some important open questions.     

The limiting semigroup of the Bernstein iterates: degree of convergence

Summary We study the degree of approximation of the iterated Bernstein operators to the members (T(t)) _{t ≧0}, of their limiting semigroup. This yields a full quantitative version of an earlier convergence result by Karlin and Ziegler.     

The combinatorics of Bernstein functions

A construction of Bernstein associates to each cocharacter of a split -adic group an element in the center of the Iwahori-Hecke algebra, which we refer to as a Bernstein function. A recent conjecture of Kottwitz predicts that Bernstein functions play an important role in the theory of bad reduction of a certain class of Shimura varieties (parahoric type). It is therefore of interest to calculate the Bernstein functions explicitly in as many cases as possible, with a view towards testing Kottwitz' conjecture. In this paper we prove a characterization of the Bernstein function associated to a minuscule cocharacter (the case of interest for Shimura varieties). This is used to write down the Bernstein functions explicitly for some minuscule cocharacters of ; one example can be used to verify Kottwitz' conjecture for a special class of Shimura varieties (the ``Drinfeld case'). In addition, we prove some general facts concerning the support of Bernstein functions, and concerning an important set called the ``-admissible' set. These facts are compatible with a conjecture of Kottwitz and Rapoport on the shape of the special fiber of a Shimura variety with parahoric type bad reduction.

     

Analogies and the modeling of composites

On the basis of the solution of a series of problems of the distribution of static and dynamic fields of various physical kinds in the microstructure of composite materials reinforced with dispersed particles or fibers analogies are established between the stress, displacement, temperature, electromagnetic, and other fields subject to certain similarity criteria imposed on the properties of the components.Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Mekhanika Polimerov, No. 6, pp. 1028–1037, November–December, 1969.     

Pascal算子矩阵在组合恒等式中的应用(英文)

定义了四种Pascal算子矩阵,给出了它们的代数性质及它们之间的关系,并且利用二项式型多项式序列、算子及哑运算得到许多组合恒等式.     

Pascal算子矩阵在组合恒等式中的应用

定义了四种Pascal算子矩阵,给出了它们的代数性质及它们之间的关系,并且利用二项式型多项式序列、算子及哑运算得到许多组合恒等式.