Bernstein-Durrmeyer算子线性组合的点态逼近定理

本文利用点态光滑模对Bernstein-Durrmeyer算子的T阶线性组合的逼近进行了研究,统一了已有的关于古典光滑模和Ditzian-Totik模的结果.     

Bernstein-Durrmeyer算子线性组合的点态逼近定理

本文利用点态光滑模Ｂｅｒｎｓｔｅｉｎ－Ｄｕｒｒｍｅｙｅｒ算子的ｒ阶级性组合的逼近进行了研究,统一了已有的关于古典光滑模和Ｄｉｔｚｉａｎ－Ｔｏｔｉｋ 模的结果．     

Ba空间中的多元加权光滑模与Bernstein Durrmeyer算子

该文引进Ba空间多元加权光滑模,推广L^p空间的DitzianTotik模, 证明该模与K泛函的等价性. 作为应用,讨论定义在单纯形上多元Bernstein-Durrmeyer算子与多元加权光滑模之间的关系. 即以多元加权光滑模为尺度, 建立Bernstein-Durrmeyer算子在Ba空间逼近阶的上界与下界估计.     

球面上Peetre K－模和最佳逼近

本文研究了球面上三种ＰｅｅｔｒｅＫ－模与最佳逼近的关系，建立起它们之间的若干强型和弱型不等式．此外，还讨论了Ｋ－模与光滑模的等价性．     

球面上Peetre K－模和最佳逼近

本文研究了球面上三种ＰｅｅｔｒｅＫ－模与最佳逼近的关系，建立起它们之间的若干强型和弱型不等式．此外，还讨论了Ｋ－模与光滑模的等价性．     

关于凸性特征与光滑模的一个关系

给出了Banach空间凸性特征与光滑模的一个关系。     

特征函数与Banach空间的凸性模,光滑模

本文讨论了Banach空间的特征函数[1]与凸性模及光滑模的关系,从而给出了刻划Banach空间的一致凸性、一致光滑性的另一种方法。     

Warschawski定理的推广

从单位圆到以光滑 Jordan曲线为边界的单连通区域的共形映射 ,其边界的光滑性有经典的Kellogg定理及其推广的 Warschawski定理 ,本文以连续模、P次平均模为工具对原结果进行了深入的讨论 ,得到了更为一般的结果 .     

离散三角子模

为了构造离散三角模,引入了离散三角子模的概念,给出了生成离散三角(子)模的方法;然后讨论了光滑离散三角子模的结构.     

Bernstein算子导数与高阶光滑性

借助于r阶光滑模ωφ^r(f,t)φ是一般的步权函数，给出了Bernstein算子导数与函数高阶光滑性之间的等价关系。     

Tannaka duality for proper Lie groupoids

By replacing the category of smooth vector bundles of finite rank over a manifold with the category of what we call smooth Euclidean fields, which is a proper enlargement of the former, and by considering smooth actions of Lie groupoids on smooth Euclidean fields, we are able to prove a Tannaka duality theorem for proper Lie groupoids. The notion of smooth Euclidean field we introduce here is the smooth, finite dimensional analogue of the usual notion of continuous Hilbert field.     

Smooth格和强Smooth格

引入了强smooth格的概念,讨论了smooth格与强smooth格的一些基本性质,证明了强smooth格可用保任意交和Scott闭集之并的映射嵌入到某方体[0,1]X之中.     

Smooth distributions are finitely generated

A subbundle of variable dimension inside the tangent bundle of a smooth manifold is called a smooth distribution if it is the pointwise span of a family of smooth vector fields. We prove that all such distributions are finitely generated, meaning that the family may be taken to be a finite collection. Further, we show that the space of smooth sections of such distributions need not be finitely generated as a module over the smooth functions. Our results are valid in greater generality, where the tangent bundle may be replaced by an arbitrary vector bundle.     

Approximation in Sobolev Spaces by Kernel Expansions

For interpolation of smooth functions by smooth kernels having an expansion into eigenfunctions (e.g., on the circle, the sphere, and the torus), good results including error bounds are known, provided that the smoothness of the function is closely related to that of the kernel. The latter fact is usually quantified by the requirement that the function should lie in the “native” Hilbert space of the kernel, but this assumption rules out the treatment of less smooth functions by smooth kernels. For the approximation of functions from “large” Sobolev spaces W by functions generated by smooth kernels, this paper shows that one gets at least the known order for interpolation with a less smooth kernel that has W as its native space.     

Ultra smooth continua are smooth

In this paper we to define and study a class of metric continua called ultra smooth, which (by the definition) form a subclass of the class of continua being hereditarily unicoherent at some point. The major result is that every ultra smooth continuum is smooth.     

Hochschild Homology of Singular Algebras

One of the main properties of Hochschild homology of the algebra of smooth functions on a smooth manifold is its local character. In this paper, we consider subalgebras of smooth functions which are significant for singular spaces such that simplicial complexes or cones over smooth manifolds. We compute their Hochschild homology and investigate the local character. Our computations show that, in opposition with the smooth case, the (local part of the) Hochschild homology is not always isomorphic to the corresponding de Rham complex of differential forms. The method we use is a slight modification of the localization procedure introduced in by Sullivan.     

Local Smooth Representations of Parametric Semiclosed Polyhedra with Applications to Sensitivity in Piecewise Linear Programs

In this paper, we establish the equivalence between the half-space representation and the vertex representation of a smooth parametric semiclosed polyhedron. By virtue of the smooth representation result, we prove that the solution set of a smooth parametric piecewise linear program can be locally represented as a finite union of parametric semiclosed polyhedra generated by finite smooth functions. As consequences, we prove that the corresponding marginal function is differentiable and the solution map admits a differentiable selection.     

六阶对流Cahn-Hilliard方程解的整体适定性

In this paper,we consider the global well-posedness of smooth solutions for the Cauchy problem of a sixth order convective Cahn-Hilliard equation with small initial data.We first construct a local smooth solution,then by combining some a priori estimates,continuity argument,the local smooth solution is extended step by step to all t>0 provided that the L1 norm of initial data is suitably small and the smooth nonlinear functions f(u)and g(u)satisfy certain local growth conditions at some fixed point■.     

The convergence of a dual algorithm for nonlinear programming

A dual algorithm based on the smooth function proposed by Polyak (1988) is constructed for solving nonlinear programming problems with inequality constraints. It generates a sequence of points converging locally to a Kuhn-Tucker point by solving an unconstrained minimizer of a smooth potential function with a parameter. We study the relationship between eigenvalues of the Hessian of this smooth potential function and the parameter, which is useful for analyzing the effectiveness of the dual algorithm.