几乎第二可数空间、几乎第一可数空间和几乎可分空间

本文定义了几乎第二可数空间,几乎第一数可空间和几乎可分空间,它们分别是第二可数空间,第一可数空间和可分空间的一般化,还研究了这三类新空间以及几乎Lindel?f空间的性质,改进了[2]中的几个定理.     

Parametrized Area Integrals on Hardy Spaces and Weak Hardy Spaces

In this paper, the authors prove that if Ω satisfies a class of the integral Dini condition, then the parametrized area integral μΩ,S^ρ is a bounded operator from the Hardy space H1 （R^n） to L1 （R^n） and from the weak Hardy space H^1,∞ （R^n） to L^1,∞ （R^n）, respectively. As corollaries of the above results, it is shown that μΩ,S^ρ is also an operator of weak type These conclusions are substantial improvement and （1, 1） and of type （p,p） for 1 〈 p 〈 2, respectively extension of some known results.     

First Steps Towards an Institution of Algebra Replacement Systems

Algebra replacement systems are introduced as formal models of state dependent and state transforming systems. The first part of an institution of algebra replacement systems is developed, that is, a model theoretic and logical framework that can be used to describe and reason about such systems. The usual operational understanding of a replacement system as a labeled transition system is then considered as one particular model in the model category. Under appropriate conditions such a constructed replacement system is initial.     

Banach空间中一阶积-微分方程的解

利用新的比较原理和半序方法讨论了Banach空间中的混合型一阶积-微分方程的非线性边值问题,并改进了已有的结果.     

自反算子代数的模和交换子以及一阶上同调空间

设L是赋范线性空间上的子空间格,一个子空间是自反AlgL-模的充分必要条件被得到,当L是完全分配子空间格时,自反AlgL-模的二次交换子被描述,进而,本文引入V-生成子稠格,这是一种严格地包含了完全分配格和五角格的格类。当L是可换的V-生成子稠格时,模模交换子C(AlgL;M)和代数AlgLatM都被分解成直和,并且满足条件H~1(AlgL,B(H))=0的一阶上同调空间H~1(AlgL,M)被刻划。     

First and Second Order Convex Sweeping Processes in Reflexive Smooth Banach Spaces

In this paper we establish new characterizations of the normal cone of closed convex sets in reflexive smooth Banach spaces and then we use those results to prove the existence of solutions for first order convex sweeping processes and their variants in reflexive smooth Banach spaces. The case of second order convex sweeping processes is also studied.     

面积积分及其交换子在广义加权Morrey空间上的有界性

研究含有参变量的面积积分及其与BMO函数构成的高阶交换子在广义加权Morrey空间上的估计,利用函数的局部加权估计,证明了面积积分及其高阶交换子在广义加权Morrey空间上是有界算子.这些结果改进和丰富了一些已有的研究结论.     

Banach空间一阶脉冲微分方程的初值问题

利用单调迭代方法,在Ｂａｎａｃｈ空间研究了更为一般脉冲微分方程的初值问题的最小最大拟解的存在性及迭代逼近程序。     

Beyond Besov Spaces,Part 2: Oscillation Spaces

We study several extensions of Besov spaces; these extensions include the oscillation spaces O_p^s,swhich take into account correlations between the positions of large wavelet coefficients through the scales and, more generally, spaces defined through the distributions of suprema of wavelet coefficients on wavelet subtrees. These spaces are independent of the particular wavelet basis chosen. Examples of applications will be taken from image processing and multifractal analysis.     

The Behavior of the First Variation Under the Fourier-Feynman Transform on Abstract Wiener Spaces

We construct the behavior of the first variation under the Fourier-Feynman transform and we show that theWiener integral of the first variation can be nicely behaved under the Fourier-Feynman transform for functionals F(x) = ∫_H exp{i (h, x)~} dμ(h) in the Fresnel class and the Fourier-Feynman transform of the first variation can be perfectly expressed as the limit of Wiener integrals of the first variation on the abstract Wiener space.     

一阶线性隐式微分算子方程的近似解

本文采用投影法讨论了Hilbert空间中一阶线性隐式微分算子方程的Cauchy问题的近似解的收敛性及误差估计.     

Preduals of Campanato Spaces and Sobolev-Campanato Spaces: A General Construction

In this paper we describe two limiting processes for families of Banach spaces closely related to the standard definition of projective and inductive limits. These processes lead again to Banach spaces. Information about linear operators and duality between basic families of spaces is carried over to the corresponding limit spaces. The abstract results are shown to be applicable to Campanato spaces and Sobolev-Campanato spaces. In particular, we obtain the existence and a characterization of predual spaces. Some imbedding relations are investigated in more detail.     

First and Second Order Optimality Conditions Using Approximations for Nonsmooth Vector Optimization in Banach Spaces

We use the first and second order approximations of mappings to establish both necessary and sufficient optimality conditions for unconstrained and constrained nonsmooth vector optimization problems. Ideal solutions, efficient solutions, and weakly efficient solutions are considered. The data of the problems need not even be continuous. Some often imposed compactness assumptions are also relaxed. Examples are provided to compare our results and some known recent results.This work was partially supported by the National Basic Research Program in Natural Sciences of Vietnam.     

On the Classification of Maxwell Spaces Admitting Hyperbolic Helices and First Integrals of Lorentz Equations

We describe 13 nonempty classes of Maxwell spaces that admit groups containing a one-dimensional subgroup of hyperbolic helices. We obtain first integrals of Lorentz equations for three of these classes.__________Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 10, Suzdal Conference-4, 2003.     

Convergence Approach Spaces : Actions

Properties of continuous actions and pseudoquotients are studied in the category of convergence approach spaces. Invariance properties of continuous actions on convergence approach spaces are given. It is shown that the formation of pseudoquotient spaces is idempotent. Function space actions are also investigated.     

QCLkR空间与QCLkS空间

引入了QCLkR空间和QCLkS空间的概念,以局部自反原理为工具证明了QCLkR空间和QCLkS空间的对偶关系.利用切片给出了QCLkR空间和QCLkS空间的特征刻画,并讨论了它们与其它凸性和光滑性的关系,所得结果进一步完善了关于Banach空间凸性与光滑性的研究.     

Affine Spaces within Projective Spaces

We endow the set of complements of a fixed subspace of a projective space with the structure of an affine space, and show that certain lines of such an affine space are affine reguli or cones over affine reguli. Moreover, we apply our concepts to the problem of describing dual spreads. We do not assume that the projective space is finite-dimensional or pappian.     

Hilbert空间中的一类双层规划问题的一阶与二阶最优性条件

本文考虑Hilbert空间中的,上层为有限个不等式约束,下层是一锥约束参数规划的双层规划问题的最优性条件.首先,利用下层问题最优值函数的方向导数的上下界的性质给出一阶最优性条件.之后,在使下层问题的最优值函数是二阶方向可微的条件下,证明了二阶必要性条件.     

局部强紧空间的Hoare空间与Smyth空间

本文主要讨论局部强紧空间的性质,特别是其Hoare空间和Smyth空间的性质,证明了T_0空间为局部强紧空间的当且仅当其Hoare空间为局部强紧空间,局部强紧空间的Smyth空间为C-空间.对于强局部紧空间,我们有类似的结论.