标准体系的使用期的模型与分析

本文提出了关于标准体系使用期的两个模型。首先定义了标准使用期,然后讨论了模型的合理性。通过模型讨论了标准使用期的性质,给出了数值示例。提出了需进一步研究的问题。     

模糊集的凸的几点性质

引入了T_λ算子,基于此算子,对模糊集的凸和拟凸的一些性质进行了研究,得出了一些结论。对模糊集的凸和拟凸的概念进行了拓展,引入了半凸模糊集,半拟凸模糊集,研究了半凸模糊集和半拟凸模糊集的性质。     

关于图的因子的一些新问题

本文介绍了近年来关于图的因子的一些新结果、新动态和新问题。文中介绍了有关[a,b]—因子及分支-因子的一些定理。讨论了因子覆盖的性质及正交因子分解问题,并提出了一系列可供研究的未解决问题。     

具有某种断面的半群的研究进展

本文综述了几类具有特殊断面的半群的近期研究结果。在介绍逆半群和正则半群的一般结构之后，概述了具有逆断面的正则半群的结构和同余格的研究成果。总结了作为逆断面的推广的可裂断面，纯正断面，正则^*－断面和恰当断面。提出了可以进一步研究的重要的问题。     

扰动的Couette－Poiseuille流的特征值的计算

本文考虑的问题是二维粘性渠流。对0到2000之间的雷诺数,计算了平稳扰动的Couette-Poiseuille流的下游特征值,其特征方程类似于Orr-Sommerfeld方程。所用的方法是谱方法和初值方法(复合矩阵方法).就几种有趣的流量,给出了相应的特征值的计算结果。这些特征值确定了扰动的衰减率。     

格的模糊素理想的度量

本文主要研究了模糊代数中格的模糊素理想的度量。首先给出了模糊素理想的新概念,并利用模糊素理想度讨论了格的模糊子集是模糊素理想的程度。其次,利用格的模糊集的(强)水平集得到了模糊素理想的等价刻画。最后,讨论了任意多个模糊子集的交、直积的模糊素理想度以及格的模糊子集在同态映射下像与原像的模糊素理想度的性质。     

食饵带疾病的捕食模型的全局稳定性

本文研究了一类三维生态传染病模型的正解性和边界性,并分析了系统平衡点的局部稳定性。利用一种新的几何方法,获得了内平衡点的全稳定性,推广了Li和Muldowney[1]提出的这种方法的应用,这种方法避免了寻找Lyapunov的困难。     

具有时滞的高维生态系统的稳定性

本文引用了混合单调流的概念,利用其性质,我们得到了一类时滞生态系统的稳定性判别准则,推广了文[2][3]的结果。     

计算Hamilton矩阵特征值的一个稳定的有效的保结构的算法

提出了一个稳定的有效的保结构的计算Hamilton矩阵特征值和特征不变子空间的算法,该算法是由SR算法改进变形而得到的。在该算法中,提出了两个策略,一个叫做消失稳策略,另一个称为预处理技术。在消失稳策略中,通过求解减比方程和回溯彻底克服了Bunser Gerstner和Mehrmann提出的SR算法的严重失稳和中断现象的发生,两种策略的实施的代价都非常低。数值算例展示了该算法比其它求解Hamilton矩阵特征问题的算法更有效和可靠。     

扩展的Boussinesq系统Lax对的Bcklund变换和递推求解公式的导出

本文研究2+1维的扩展经典Boussinesq系统。首先,研究了系统的Lax对,找出了一个形式十分新颖的带有一个任意函数的Bcklund变换。然后,又导出了Lax对的特征函数的生成公式。最后,利用Bcklund变换和Lax对特征函数生成公式相结合得出了Lax对的递推求解公式。利用此递推公式,求出了一些Lax对的解。     

On the lattice structure of kernel operators

Consider the lattice of bounded linear operators on the space of Borel measures on a Polish space. We prove that the operators which are continuous with respect to the weak topology induced by the bounded measurable functions form a sublattice that is lattice isomorphic to the space of transition kernels. As an application we present a purely analytic proof of Doob's theorem concerning stability of transition semigroups.     

Toeplitz算子在Dirichlet空间上的亚正规性

In this paper,we prove that the necessary and sufficient condition for a Toeplitz operator Tu on the Dirichlet space to be hyponormal is that the symbol u is constant for the case that the projection of u in the Dirichlet space is a polynomial and for the case that u is a class of special symbols,respectively.We also prove that a Toeplitz operator with harmonic polynomial symbol on the harmonic Dirichlet space is hyponormal if and only if its symbol is constant.     

On The Existence Of A Measurable Optimal Coupling Of Probability Kernels

In this paper, an existence theorem for a measurable optimal coupling of probability kernels on a σ-compact complete separable metric measurable space is obtained     

The Reproducing Kernel Thesis for Toeplitz Operators on the Paley-Wiener Space

It is known that for particular classes of operators on certain reproducing kernel Hilbert spaces, key properties of the operators (such as boundedness or compactness) may be determined by the behaviour of the operators on the reproducing kernels. We prove such results for Toeplitz operators on the Paley-Wiener space, a reproducing kernel Hilbert space over . Namely, we show that the norm of such an operator is equivalent to the supremum of the norms of the images of the normalised reproducing kernels of the space. In particular, therefore, the operator is bounded exactly when this supremum is finite. In addition, a counterexample is provided which shows that the operator norm is not equivalent to the supremum of the norms of the images of the real normalised reproducing kernels. We also give a necessary and sufficient condition for compactness of the operators, in terms of their limiting behaviour on the reproducing kernels.     

Spectral decomposition of self-adjoint cyclically compact operators and partial integral equations

We prove a spectral decomposition theorem for self-adjoint cyclically compact operators on Hilbert–Kaplansky module over a ring of bounded measurable functions. We apply this result to partial integral equations on the space with mixed norm of measurable functions. We give a condition of solvability of partial integral equations with self-adjoint kernel.     

A note on regular Dirichlet subspaces

In this short article we shall consider the Dirichlet space associated with the distorted Brownian motion on a one-dimensional closed interval and prove that it admits no proper regular Dirichlet subspaces.

     

Comparison inequalities for heat semigroups and heat kernels on metric measure spaces

We prove a certain inequality for a subsolution of the heat equation associated with a regular Dirichlet form. As a consequence of this inequality, we obtain various interesting comparison inequalities for heat semigroups and heat kernels, which can be used for obtaining pointwise estimates of heat kernels. As an example of application, we present a new method of deducing sub-Gaussian upper bounds of the heat kernel from on-diagonal bounds and tail estimates.     

Existence of the optimal measurable coupling and ergodicity for Markov processes

The existence theorem of the optimal measurable coupling of two probability kernels on a complete separable metric measurable space is proved. Then by this theorem, a general ergodicity theorem for Markov processes is obtained. And as an immediate application to particle systems the uniqueness theorem of the stationary distribution is supplemented, i.e. the uniqueness theorem also implies the existence of the stationary distribution.     

Singular Integrals on Product Homogeneous Groups

We consider singular integral operators with rough kernels on the product space of homogeneous groups. We prove L ^p boundedness of them for ${p \in (1,\infty)}$ under a sharp integrability condition of the kernels.     

Statistical maps: A categorical approach

In probability theory, each random variable f can be viewed as channel through which the probability p of the original probability space is transported to the distribution p _f , a probability measure on the real Borel sets. In the realm of fuzzy probability theory, fuzzy probability measures (equivalently states) are transported via statistical maps (equivalently, fuzzy random variables, operational random variables, Markov kernels, observables). We deal with categorical aspects of the transportation of (fuzzy) probability measures on one measurable space into probability measures on another measurable spaces. A key role is played by D-posets (equivalently effect algebras) of fuzzy sets. Supported by VEGA 1/2002/06.