多元Kantorovich算子L_p范数下的渐近展开

本文给出了高维单纯形上Kantorovich算子在Lp（1＜P＜∞）范数下的高阶渐近展开公式．     

单纯形上Bernstein多项式凸性定理的逆定理的一个简短证明

本文给出了张景中、常庚哲、杨路所证明的《高维单纯形上Bernstein多项式凸性定理的逆定理》的一个简短证明.     

关于单纯形的一类三角不等式及高维正弦定理的改进

对于 n 维欧氏空间 E~n 中的单纯形,本文的主要结果是:(1)建立了有关二面角的一类三角不等式(注意,这正是历来在单纯形不等式研究中讨论得较少的部分);(2)对 F.Eriksson 在[1]中给出的高维正弦定理,作了一定意义上的改进.     

d维Bernstein算子加Jacobi权的收敛阶

１．引 言 设Ｓ＝Ｓｄ（ｄ＝１,２,…）是 Ｒｄ中的单纯形,即记ｋ＝（ｋ１,ｋ２,……,ｋｄ）∈Ｒｄ,ｋｉ为非负整数, ,则Ｓ上定义的函数ｆ所对应的ｄ维Ｂｅｒｎｓｔｅｉｎ算子定义为其中 Ｐｎ,ｋ（ｘ）＝是 Ｂｅｒｎｓｔｅｉｎ基函数．引进多维Ｊａｃｏｂｉ权函数, 这里 ．定义Ｂｅｒｎｓｔｅｉｎ权函数 表示微分算子． 记 是单位向量,即第ｉ个分量为１,其余ｄ－１个分量为０, ．定义函数ｆ在方向ｅ上的ｒ阶对称差分为Ｃ（Ｓ）中的加权Ｓｏｂｏｌｅｖ空间为其中Ｓ为Ｓ的内部．定义加权Ｋ－泛函及加权光滑模其中 为加权范数． …     

单纯形上Meyer—Konig—Zeller算子及其逼近定理

本文构造单纯形Ｔ＝｛（ｘ，ｙ）：ｘ，ｙ≥０，ｘ＋ｙ≤１｝上的Ｍｅｙｅｒ－Ｋｏｎｉｇ－Ｚｅｌｌｅｒ算子，并且讨论它的逼近性质。     

单纯形上的q-Stancu多项式的最优逼近阶

构造了单纯形上的多元q-Stancu多项式,它是著名的Bernstein多项式和Stancu多项式的推广.建立该类多项式逼近连续函数的上、下界估计,进而给出其对连续函数的最优逼近阶(饱和阶)及其特征刻画.此外,还研究了该类多项式逼近连续函数的饱和类.     

多元Bernstein-Durrmeyer型多项式及其逼近特征

作为Bernstein-Durrmeyer多项式的推广,定义单纯形上的Bernstein-Durrmeyer型多项式.以最佳多项式逼近为度量,给出Bernstein-Durrmeyer型多项式Lp逼近阶的估计,并且以一个逆向不等式的形式建立其Lp逼近的逆定理,从而用最佳多项式逼近刻画该多项式Lp逼近的特征.所获结果包含了多元Bernstein-Durrmeyer多项式的相应结果.     

单纯形上Durrmeyer多项式对连续函数收敛速度的估计

以Ｋ－泛函、光滑模为工具，利用函数分解等方法，研究单纯形上多元Ｄｕｒｒｍｅｙｅｒ多项式逼近连续函数的速度问题，估计了收敛速度，从而完善了Ｂｅｒｅｎｓ，Ｈ　等人的工作．     

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.     

多元指数磨光算子的构造和相关偏微分方程基本解与磨光核的升维解法

本文目的在于回答:δ分布的多元指数磨光函数,即磨光核函数的解析表示问题.从我们给出的多元指数磨光算子的定义出发,将磨光核函数的表示,归结为先求相应偏微分方程的基本解,再对它的广义差分.然后用我们提出的"升维方法",彻底解决了基本解的解析表达问题.从而也就回答了磨光核函数的解析表示.磨光核函数的支集既可以是高维立方体,也可以是高维单纯形.因此,多元指数箱(E-Box)和单纯形(E-Simplex)样条的表示,皆能用我们的统一方法解决.     

某些多元线性正算子的加权逼近

本文首先给出了在Ｌｐ逼近意义下某些线性正算子加Ｊａｃｏｂｉ权逼近时的特征定理，作为应用，我们给出了多元Ｂａｓｋａｋｏｖ型算子、多元Ｓｚａｓｚ－Ｍｉｒａｋｊａｎ型算子和多元Ｂｅｔａ算子加权逼近时的特征刻划．     

Tractability results for the weighted star-discrepancy

The weighted star-discrepancy has been introduced by Sloan and Wo?niakowski to reflect the fact that in multidimensional integration problems some coordinates of a function may be more important than others. It provides upper bounds for the error of multidimensional numerical integration algorithms for functions belonging to weighted function spaces of Sobolev type. In the present paper, we prove several tractability results for the weighted star-discrepancy. In particular, we obtain rather sharp sufficient conditions under which the weighted star-discrepancy is strongly tractable. The proofs are probabilistic, and use empirical process theory.     

Multidimensional Hilbert-type Inequality on the Weighted Orlicz Spaces

In this paper we derive multidimensional Hilbert-type inequality on the weighted Orlicz spaces with considerable attention given to homogeneous kernels of negative degree. As an application, we also deduce Hardy-Hilbert type inequality in one particular case. As a special case, we consider our general method in the case of the weighted Lebesgue spaces.     

The boundedness of multidimensional hardy operators in weighted variable Lebesgue spaces

The main purpose of this paper is to prove a two-weight criterion for the multidimensional Hardy-type operator in weighted Lebesgue spaces with variable exponent. As an application, we prove the boundedness of Riesz potential and fractional maximal operators on the weighted variable Lebesgue space.     

The boundedness of certain sublinear operator in the weighted variable Lebesgue spaces

The main purpose of this paper is to prove the boundedness of the multidimensional Hardy type operator in weighted Lebesgue spaces with a variable exponent. As an application we prove the boundedness of certain sublinear operators on the weighted variable Lebesgue space.     

The Poisson Operator for Orthogonal Polynomials in the Multidimensional Ball

In this paper we define the Poisson operator related to an orthonormal system on the multidimensional ball and we analyze some weighted inequalities for this operator in mixed norm spaces.     

Multidimensional weighted Opial inequalities

In this article we produce Opial-type weighted multidimensional inequalities over balls and arbitrary smooth bounded domains. The inequalities are sharp. The functions under consideration vanish on the boundary.     

On Hardy Inequality in Variable Lebesgue Spaces with Mixed Norm

In this paper a two-weight boundedness of multidimensional Hardy operator and its dual operator acting from one weighted variable Lebesgue spaces with mixed norm into other weighted variable Lebesgue spaces with mixed norm spaces is proved. In particular, a new type two-weight criterion for multidimensional Hardy operator is obtained.     

Weighted perfect codes in Lee metric

In this talk, we will present results about perfect weighted coverings of radius 1 in the Lee metric. Weighted coverings are a very natural generalization of many classes of codes. Perfect weighted coverings are well studied in the Hamming metric, but also in other contexts with different names, such as regular-sets, multiple coverings or [a, b]-dominating sets. In this talk, we present results of existence as well as of non-existence for perfect weighted coverings of radius one on the multidimensional grid graphs.     

多维标度法在亲属关系中的应用

简单地介绍了多维标度方法的原理及理论,并介绍了加权多维标度方法的理论及原理,对亲属关系亲密的程度采用多维标度法进行了分析,展示了15种亲属关系可分为五大类,并由此得到在人们心中亲属的分类情况,根据这些分类来解释一些亲属间的关系,理解人际关系中的一些社会现象,帮助缓和彼此之间的一些矛盾.