Hilbert空间中广义算子半群范数连续的特征

研究了Hilbert空间上最终范数连续广义算子半群的特征条件,利用半群的生成元的预解式,给出了Hilbert空间上广义算子半群范数连续的三个特征条件.     

C_0半群在非线性Lipschitz扰动下的范数连续性保持

研究有界线性算子强连续半群在非线性Lipschitz扰动下的正则性质保持问题.具体地,我们证明:如果强连续半群是直接范数连续的,则非线性扰动半群是直接Lipschitz范数连续的.结论推广了线性算子半群的范数连续性质保持,丰富和完善了非线性算子半群的理论.     

广义算子半群的PERRON问题

借助于广义算子半群和广义积分算子半群的关系,讨论广义算子半群的Perron型指数稳定性,研究了广义积分算子半群的渐近行为.     

广义算子半群与广义分布参数系统的适定性

首先,针对广义分布参数系统的求解问题,提出了由Hilbert空间中有界线性算子所引导的广义算子半群和广义积分半群;其次,讨论了广义预解算子的性质、广义算子半群与广义积分半群的性质;最后,研究了广义分布参数系统的适定性问题.     

广义算子半群的遍历及概率逼近定理

首先给出了广义算子半群的Abel-遍历和Cesaro-遍历的定义,对两种遍历的性质进行了刻画,研究了两种遍历的等价条件.其次,利用Pettis积分、算子值数学期望及广义连续修正模等工具给出广义算子半群的概率逼近表达式.     

广义算子半群的扰动定理

算子扰动问题是研究微分方程的一个重要工具,首先结合Hilbert空间中有界算子引导的广义算子半群的定义研究了广义半群的性质;其次重点讨论了广义算子半群的扰动问题,给出了广义算子半群的加法扰动定理成立的条件.     

非线性Lipschitz算子半群的渐近性质及其应用

本文对一类非线性算子半群————Lipschitz算子半群的渐近性质进行研究,刻划了非线性Lipschitz算子半群所具有的基本渐近性质（这些性质与线性算子半群所具有的基本渐近性质相一致）,证明了作为线性算子对数范数的非线性推广,Dahlquist数能用于刻划非线性Lipschitz算子半群的渐近性质.为克服Dahlquist数只对Lips-chitz算子有定义的缺点,本文引入一个全新的特征数:广义 Dahlquist数,并证明广义Dahlquist数比Dahlquist数能更为精确地刻划Lipschitz算子半群的渐近性质.作为应用,得到关于 Hopfield型神经网络全局指数稳定性的一个新结果.     

广义导算子的范数可达性

若B(H)表示希尔伯特空间H中所有有界线性算子之集.本文研究了定义在B(H)上的初等算子和广义导算子的范数可达性,证明了如果定义在B(H)中的初等算子和广义导算子是范数可达的,那么这些算子在B(H)中酉群上的限制也是范数可达的.     

Hille-Yosida算子的非线性Lipschitz扰动

论文研究非自反Banach空间中Hille-Yosida算子的非线性Lipschitz扰动.首先,证明Hille-Yosida算子的非线性Lipschitz扰动诱导的微分方程的温和解构成非线性指数有界Lipschitz半群;其次,证明非线性扰动半群保持原半群的直接范数连续性质.获得的结果是线性算子半群某些结论的非线性推广.     

广义分布半群与退化发展方程的分布解

在Banach空间中引进了由有界线性算子引导的广义分布半群的新概念,并讨论了它的有关性质.在我们的方法中,广义分布半群的生成元可以不是稠定的.此外,还引进了退化发展方程在Laplace变换意义下的分布解,应用广义分布半群给出了退化发展方程分布解的构造性表达式.     

A Generalization of Herrlich's Question on Almost Reflective and Coreflective Subclasses of Top and Unif

H. Herrlich asked in Topology Appl. 49 (1993), 251–264, whether there are nontrivial classes of topological spaces that are almost reflective and almost coreflective at the same time. This question was dealt with (in Huek and Tozzi, Appl. Categ. Structures 4 (1996), 57–68) in a more general setting than almost reflective and almost coreflective classes. The present paper investigates a modified question: when a nontrivial generalized reflective class of topological or uniform spaces is equivalent to a generalized coreflective class of spaces.     

Generalized topology, generized continuity

The paper defines, with the help of generalized topologies and generalized neighbourhood systems, two kinds of generalized continuity, by giving in this way a general form to various concepts discussed in the literature. In particular, generalized continuity admits a characterization furnishing a known charcterization of θ-continuous maps. This revised version was published online in June 2006 with corrections to the Cover Date.     

Banach空间中线性算子的齐性广义逆

本文首先在Banach空间内引进拟线性投影算子的概念,由此给出Banach空 间内线性算子的齐性广义逆的统一定义。齐性广义逆包含线性广义逆、单值度量广义 逆.本文证得齐性广义逆存在的充分必要条件.     

A Review of White Noise Analysis from a Probabilistic Standpoint

The main notions and tools from white noise analysis are set up on the basis of the calculus of Gaussian random variables and the S -transform. A new proof of the formula for the S -transform of Itô integrals is given. Moreover, measurability and the martingale property with respect to the Brownian filtration are characterized in terms of the S-transform. This allows the extension of these notions to random variables and processes, respectively, in the space of Hida distributions.     

Ishikawa iterative process with errors for nonlinear equations of generalized monotone type in Banach spaces

The concept of the operators of generalized monotone type is introduced and iterative approximation methods for a fixed point of such operators by the Ishikawa and Mann iteration schemes {xn} and {yn} with errors is studied. Let X be a real Banach space and T : D ? X → 2^D be a multi‐valued operator of generalized monotone type with fixed points. A new general lemma on the convergence of real sequences is proved and used to show that {xn} converges strongly to a unique fixed point of T in D. This result is applied to the iterative approximation method for solutions of nonlinear equations with generalized strongly accretive operators. Our results generalize many of know results. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

广义n阶Euler-Bernoulli多项式

本文得到了广义n阶Euler数和广义n阶Bernoulli数,广义n阶Euler多项式和广义n阶Bernoulli多项式的关系式。     

广义梯度计算公式的推广

本文用分析中的几何方法推广了D.E.Ward的广义梯度计算公式,给出一个基本计算定理.     

三角函数的推广

利用函数方程定义仿正切函数类,再用仿正切函数定义仿正、余弦函数类,并对这些函数类进行研究.所定义的函数类中的函数具有通常三角函数的性质及运算规律,故而可将其作为三角函数的某种推广.通过实例证实.了通常的正切函数其实是仿正切函数的一种解析延拓.     

On Conjugations for Functions with Values in Extensions of Ordered Groups

We continue our study of generalized conjugations for functions with values in the canonical enlargement of a complete ordered group, started in [10], which encompass various kinds of known conjugations and polarities. We obtain extensions, to this framework, of some results on d.c. duality theory and subdifferentials, and we give some applications to conjugations and subdifferentials for functions with values in .