使用相关内射性对拟连续模的一个刻划

近二十年，许多环与模工作对拟投射模与拟内射模作了各种推广与研究。连续模与拟连续模就是拟内射模的一种推广，拟连续模要比连续模弱。在[2]，作对连续模与拟连续模做了深入的研究。在这篇章中，利用相关内射性给出了拟连续模的一个刻划。     

关于基本可数生成子模的扩张性

称左R-模M是ecg-扩张模,如果M的任意基本可数生成子模是M的直和因子的基本子模.在研究了ecg-扩张模的基本性质的基础上,本文证明了对于非奇异环R,所有左R-模是ecg-扩张模当且仅当所有左R-模是扩张模.同时我们还用ecg-拟连续模刻画了Noether环和Artin半单环.     

关于Kellogg定理的若干推广

本文以连续模,光滑模为工具,讨论由单位圆至光滑的若当曲线Ｌ所范单连通区的保角映射问题,对于Ｋｅｌｌｏｇｇ定理作了较大幅度的推广,得出了新的结果。     

多元Stancu多项式与连续模

本文研究单纯形上多元Stancu多项式与连续模之间的关系,证明了Stancu多项式具有保持连续模的性质,推广了一元Bernstein多项式的相应结果.同时,利用多元函数的Ditzian-Totik连续模估计Stancu多项式逼近多元连续函数速度的上界和下界,得到一个使得逼近速度为O(n-a)(0相似文献   

S^P空间的概周期函数

本，首先在Ｖ．Ｖ．Ｓｔｅｐａｎｏｖ空间连续模概念，在此空间内讨论概周期函数的Ｆｏｕｒｉｅｒ系数与连续模之间的关系。     

局部Noether模的相对连续性特征

设M是左R-模,本文证明了M是局部Noether的当且仅当σ[M]中的任意M-内射左R-模的直和是S∧2-连续的（S∧2-拟连续的）。     

一类二元函数连续性的等价刻画及在三角模上的应用

关于二元函数的连续,经典数学分析中有熟知的结果,即"如果二元函数连续,则必关于每个单变量连续。反之,则未必"。本文证明对于单调且对称的二元函数而言,其二元连续等价于单变量连续,并重新定义了三角模的连续。     

一类新的左连续三角模族及其伴随蕴涵算子族

给出一种构造带参数的左连续三角模的新方法,由此得到7种新的左连续三角模族及其伴随蕴涵算子族.证明其伴随蕴涵算子均满足正则性.     

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 .     

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 .     

单子理论对拓扑等度连续与均匀连续的刻画及其应用

在扩大模型下,应用单子理论给出了拓扑等度连续和均匀连续的非标准刻画,并应用均匀连续的非标准特征证明了网收敛与均匀连续之间的关系,最后应用拓扑等度连续和均匀连续的非标准特征证明了拓扑等度连续和均匀连续之间的关系.     

Continuity of approximate solution mappings for parametric equilibrium problems

In this paper, we obtain sufficient conditions for Hausdorff continuity and Berge continuity of an approximate solution mapping for a parametric scalar equilibrium problem. By using a scalarization method, we also discuss the Berge lower semicontinuity and Berge continuity of a approximate solution mapping for a parametric vector equilibrium problem.     

集值映射的伪(*)连续与弱(*)连续性

本文引入了集值映射的伪（＊）连续性与弱（＊）连续性概念的定义,研究了伪（＊）连续、（＊）连续及弱（＊）连续的等价关系,最后研究了乘积空间中的集值映射成为伪（＊）连续和弱（＊）连续的充要条件。     

L~p CONTINUITY OF HRMANDER SYMBOL OPERATORS OpS_（0,0） ~m AND NUMERICAL ALGORITHM

If we use Littlewood-Paley decomposition, there is no pseudo-orthogonality for Ho¨rmander symbol operators OpS m 0 , 0 , which is different to the case S m ρ,δ (0 ≤δ < ρ≤ 1). In this paper, we use a special numerical algorithm based on wavelets to study the L p continuity of non infinite smooth operators OpS m 0 , 0 ; in fact, we apply first special wavelets to symbol to get special basic operators, then we regroup all the special basic operators at given scale and prove that such scale operator’s continuity decreases very fast, we sum such scale operators and a symbol operator can be approached by very good compact operators. By correlation of basic operators, we get very exact pseudo-orthogonality and also L 2 → L 2 continuity for scale operators. By considering the influence region of scale operator, we get H 1 (= F 0 , 2 1 ) → L 1 continuity and L ∞→ BMO continuity. By interpolation theorem, we get also L p (= F 0 , 2 p ) → L p continuity for 1 < p < ∞ . Our results are sharp for F 0 , 2 p → L p continuity when 1 ≤ p ≤ 2, that is to say, we find out the exact order of derivations for which the symbols can ensure the resulting operators to be bounded on these spaces.     

Some comments on “optimal control of a class of strongly nonlinear parabolic systems”

In infinite dimensional Banach spaces both weak continuity and continuity are stronger conditions than demicontinuity. In this note we present an improvement of a recent closure theorem [1, Theorem 3.6, p. 197] by using demicontinuity in the place of weak continuity. This makes the result more powerful and widely applicable.     

On the stability of diffusion processes with state-dependent switching

In this paper we consider the stability for diffusion processes with state-dependent switching. We first prove their Feller continuity by the coupling methods. Furthermore, we also prove their strong Feller continuity and their exponential ergodicity under some reasonable conditions. Finally, we append a very brief discussion about the regularity of these processes.     

Fourier coefficients of functions with a given modulus of continuity

In this paper, we study the role of the convexity condition for the modulus of continuity in the problem of finding an upper bound for the Fourier coefficients taken over the class of functions with a given modulus of continuity. Also, we solve the problem of the Fourier coefficients for the Rademacher system.     

具有离散性的连续性模型映射

为了实现在连续性空间中的离散分段问题,采用解决离散性问题的方法虚拟构造连续性集合,将连续性问题映射为分段的离散问题,根据集合中元素的离散特性实现连续性模型的分段求解.通过数据结构的设计与压缩路径的算法证实,模型的映射能够解决实际问题的分段求解.     

两邻接B样条曲面的G1连续条件

本文得到了非均匀重内节点邻接B样条曲面间G1连续的充要条件 ,给出了一类G1连续的充分条件 ;基于对B样条曲线参数连续性的分析 ,本文着重给出了这类充分条件成立的内在约束 ,即对公共边界控制顶点的约束条件 .     

关于概率赋范线性空间上的线性算子的一致收敛

本文引入了概率赋范线性空间上线性算子的一致收敛和可完全刻划这种收敛的算子间的概率距离概念,并利用这些概念获得了算子连续和算子列一致收敛的本质特征,及其连续性和全连续性对于一致收敛极限运算的封闭性.