关于逆系统的几个性质

本文将紧空间的逆系统,紧群的逆系统的几个性质推广于局部紧的,σ-紧的拓扑空间或拓扑群的逆系统。还得到由一般拓扑群的正合下序列所构成的逆系统的极限序列为正合的条件,它包含了紧群情形下的已知结果。     

握手问题

在这篇文章中我们提出并解决一个称为握手问题的组合问题。该问题是受马丁·加德纳在[1]中提出的外科医生问题的启发而提出的。     

Existence theorems of systems of variational inclusion problems with applications

In this paper, we study the existence theorems of systems of variational inclusions problems. As consequences of our results, we study existence theorems of systems of generalized vector quasi-equilibrium problems, mathematical program with systems of variational inclusion constraints, bilevel problem with systems of constraints.     

Bicompletion and Samuel Bicompactification

It is proved that the quasi-proximity space induced by the bicompletion of a quasi-uniform T ₀-space X is a subspace of the quasi-proximity space induced by the Samuel bicompactification of X. The result is then used to establish that the locally finite covering quasi-uniformity defined on the category Top ₀ of topological T ₀-spaces and continuous maps is not lower K-true (in the sense of Brümmer). It is also shown that a functorial quasi-uniformity F on Top ₀ is upper K-true if and only if FX is bicomplete whenever X is sober.     

Approximations of Shape Metrics and Application to Shape Warping and Empirical Shape Statistics

This paper proposes a framework for dealing with several problems related to the analysis of shapes. Two related such problems are the definition of the relevant set of shapes and that of defining a metric on it. Following a recent research monograph by Delfour and Zolésio [11], we consider the characteristic functions of the subsets of R² and their distance functions. The L² norm of the difference of characteristic functions, the L and the W^1,2 norms of the difference of distance functions define interesting topologies, in particular the well-known Hausdorff distance. Because of practical considerations arising from the fact that we deal with image shapes defined on finite grids of pixels, we restrict our attention to subsets of ² of positive reach in the sense of Federer [16], with smooth boundaries of bounded curvature. For this particular set of shapes we show that the three previous topologies are equivalent. The next problem we consider is that of warping a shape onto another by infinitesimal gradient descent, minimizing the corresponding distance. Because the distance function involves an inf, it is not differentiable with respect to the shape. We propose a family of smooth approximations of the distance function which are continuous with respect to the Hausdorff topology, and hence with respect to the other two topologies. We compute the corresponding Gâteaux derivatives. They define deformation flows that can be used to warp a shape onto another by solving an initial value problem.We show several examples of this warping and prove properties of our approximations that relate to the existence of local minima. We then use this tool to produce computational definitions of the empirical mean and covariance of a set of shape examples. They yield an analog of the notion of principal modes of variation. We illustrate them on a variety of examples.     

A Lower Bound of <Emphasis Type="Italic">L</Emphasis><Subscript><Emphasis Type="Italic">p</Emphasis></Subscript> Norms in the CLT for Strongly Mixing Random Variables

We derive a lower bound of L _p norms, 1 ⩽ p ⩽ ∞, in the central limit theorem for strongly mixing random variables X ₁,..., X _n with under the boundedness condition ℙ{|X _i | ⩽ M} = 1 with a nonrandom constantM > 0 and condition ∑ _r⩾1 r ²α(r) < ∞, where α(r) are the Rosenblatt strong mixing coefficients. __________ Translated from Lietuvos Matematikos Rinkinys, Vol. 45, No. 4, pp. 587–602, October–December, 2005.     

Existence of solutions for first order singular problems

We develop the lower and upper solutions method for first order initial value problems as well as for first order periodic problems in case the nonlinearity presents singularities. More precisely we prove that if we have a lower solution and an upper solution of these problems, which are not necessarily continuous nor ordered, we have a solution wedged between and .

     

关于广义近似集的注记

本文讨论了逆串行关系下上近似集和下近似集的关系；进一步讨论子集关于子基的内部和闭包的性质，得到了一些有趣的结果．     

断流河道间断输水两岸地下水的运动模型及其解法--以塔里木河下游断流河段生态输水为例

以塔里木河下游断流河段生态输水为背景,根据间断性输水河道充水和停水2个阶段周期性交替重复出现的特征,建立了断流河道间断输水两岸地下水运动的一维非稳定流模型,并通过水位与流量边界条件相互转换的一种方法实现模型的求解,最后应用该模型分析了塔里木河下游断流河段生态输水两岸地下水位恢复状况,其结果比较满意,表明了模型的实用性。