遗传中紧空间与散射分解

本文证明了可数仿紧(中紧、亚紧)空间有类似Junnila的刻画，遗传中紧空间不具有类似Junnila的刻画，并给出了每个散射分解有紧有限的开膨胀的充要条件．     

σ-ortho紧的逆极限性质

主要证明了如下结果：设X=lim{Xσ，πρ^σ，∧}|∧||=λ，并且每个投射πσ：X→Xσ是开满映,若X是λ-仿紧的，并且每个Xσ是σ-ortho紧空间，则X是σ-ortho紧空间。进一步还可得到遗传σ-ortho紧性质的类似结果。     

正规狭义拟仿紧的乘积性质

本文主要证明了如下一些结果：（１）设Ｘ＝Ｌｉｍ并且每个投射πσ是开满映射，如果Ｘ是－仿紧的且每个 Ｘσ是正规狭义拟仿紧的，则 Ｘ是正规狭义拟仿紧的；如果 Ｘ是遗传－仿紧的且每个 Ｘσ是遗传正规狭义拟仿紧的．则 Ｘ是遗传正规狭义拟仿紧的． （２）如果 Ｘ＝是 －仿紧空间，则Ｘ是正规狭义拟仿紧的当且仅当 是正规狭义拟仿紧的．最后，还给出了诸多覆盖性质的可数乘积的一个等价性命题．     

正规可数仿紧空间的逆极限

得到了如下结果:设X是逆系统{Xα,παβ,Λ}的逆极限,|Λ|=λ,假设每个映射πα∶X→Xα是开的且到上的,X是λ-仿紧,每个Xα是正规可数仿紧的,则X是正规可数仿紧的.进一步得到了关于遗传正规且遗传可数仿紧空间的类似结果.     

正规狭义拟仿紧的乘积性质

本文主要证明了如下一些结果(1)设     

亚紧性在选择理论中的一个刻划(英文)

本文利用集值映射的选择理论,对正则空间的亚紧性给予了一种刻划。本文同时推广了选择理论中的两个经典定理。     

关于遗传可遮和遗传σ-亚紧可数乘积的注记

证明了在逆序列的情形下,可遮空间、强可遮空间在假设X是可数仿紧空间的条件下可被其极限空间保持,进一步证明了遗传可遮,遗传强可遮及遗传σ-亚紧性在无需对投射及极限空间X做任何假设的情况下即可被其逆极限空间保持.作为上述两个结果的应用,分别给出了两个相关的可数Tychonoff乘积定理.     

遗传次亚紧空间

本文获得如下结果：（＊）Ｘ是遗传次亚紧空间当且仅当Ｘ的每个散射分解有个开的θ－膨胀序列．然后，利用这个结果推出了遗传次亚紧空间的两组等价刻画．最后，通过一个例子说明遗传仿紧空间不具有类似于（＊）的刻画．     

紧图的两个结果及其应用

双随机矩阵有许多重要的应用, 紧图族可以看作是组合矩阵论中关于双随机矩阵的著名的Birkhoff定理的拓广,具有重要的研究价值． 确定一个图是否紧图是个困难的问题,目前已知的紧图族尚且不多.给出了两个重要结果：任意紧图与任意多个孤立点的不交并是紧图;任意紧图的每一个顶点上各增加一条悬挂边的图是紧图． 利用这两个结果,从已知紧图可构造出无穷多个紧图族．     

集值映射的广义重心选择

给出了广义重心选择的一些结论.对任意r∈R+我们给出了具有紧凸像的映射F的一个选择.并且如果F的像不是凸集我们同样给出了一个选择.     

Maximizing selections from the core of a cooperative game

A core selection is a function which for each cooperative game with non-empty core selects a subset, possibly a single element, of the core. In this paper, we study selections which maximize some function or binary relation on the core. We present an axiomatic characterization of such core selections, as well as a local characterization using duality which can be applied to investigate properties of core selections. We give an application of the local characterization to a question of coalitional monotonicity of core selections.     

Topological classification of continuous selections of five linear functions

Continuous selections of linear functions play an important role in Morse theory for piecewise C ²-functions. In this article, the topological properties of continuous selections of linear functions are investigated in detail. These are then utilized to provide a complete classification of all continuous selections of five linear functions. This is done by showing that the first four Betti numbers of a simplicial complex induced by such a function fully determine that function up to topological equivalence. The number of different topological types of continuous selections of linear functions has been known only in the case of four or less selection functions so far. The main result of this article now states that there are exactly 26 different topological types of continuous selections of five linear functions.     

关于上半连续集值映象的连续选择问题

本文进一步研究了上半连续集值映象的连续选择问题．首先,用一反例指出Ａｕｂｉｎ Ｊ、 Ｐ［１］中一结果不能成立．另外,对上半连续映象的σ－可选择性给出了另一逼近形式的结果．     

Selections and countably-approachable points

The present paper improves a result of Gutev [V. Gutev, Approaching points by continuous selections, J. Math. Soc. Japan (4) (2006) 1203–1210] by characterizing the countably-approachable points in sense of [V. Gutev, Approaching points by continuous selections, J. Math. Soc. Japan (4) (2006) 1203–1210] by a natural extreme-like condition in the spirit of [V. Gutev, T. Nogura, Vietoris continuous selections and disconnectedness-like properties, Proc. Amer. Math. Soc. 129 (2001) 2809–2815; V. Gutev, T. Nogura, Selection pointwise-maximal spaces, Topology Appl. 146–147 (2005) 397–408]. This demonstrates the natural relationship between different extreme-like points with respect to continuous selections for the Vietoris hyperspace of nonempty closed subsets.     

LZ50车轴钢疲劳长裂纹扩展的概率模型

试验研究了随机疲劳长裂纹扩展率概率模型．首先发展了考虑平均应力影响和低应力强度因子范围趋于门槛值现象的扩展率方程．进而提出了同时考虑试验数据分散性规律与样本数量对概率评价影响的概率模型,模型参量由线性回归法结合极大似然统计分析原理测定．LZ50钢的试验数据分析,验证了方法的有效性与实用性．     

Uniform convexity and the splitting problem for selections

We continue to investigate cases when the Repovš–Semenov splitting problem for selections has an affirmative solution for continuous set-valued mappings. We consider the situation in infinite-dimensional uniformly convex Banach spaces. We use the notion of Polyak of uniform convexity and modulus of uniform convexity for arbitrary convex sets (not necessary balls). We study general geometric properties of uniformly convex sets. We also obtain an affirmative solution of the splitting problem for selections of certain set-valued mappings with uniformly convex images.     

A fifth generation numerical modelling system in coastal zone

Nowadays, artificial intelligence (AI) technology is gradually integrated into the numerical modelling system to make the system more intelligent and more user-friendly. The characteristics of the fifth generation numerical modelling are connected with AI applications. The expert system technology as a widely applied AI technology is integrated into our modelling system for coastal water processes with traditional numerical computational tools and the data and graphical pre-processing and post-processing techniques. Five kinds of knowledge bases are built in the system to describe the existing expertise knowledge about model parameters, relations between parameters and physical conditions, various possible selections for parameters and rules of inference. The inference engine is designed to be driven by the confidence of correctness, and the rule base is built with the factor of confidence to link the various relations. The decision tree is designed to drive the inference engine to explore the route of selection procedure of modeling. The decision tree depends on the real problem specifications and can be modified during the dialogue between the system and the user. The forward chaining and backward chaining inference techniques are mixed together in the system to help matching the parameters in the model and the possible selections with sufficiently high confidence. The expert system technology is successfully integrated into the system to provide help for model parameter selection or model selection, and to make the numerical model system more accessible for non-expert users.     

An integral for nonmeasurable correspondences and the shapley-interval

For a nonmeasurable correspondence there may be no measurable selection and this implies the non-existence of the usual integral of the correspondence. We define an extended integral for correspondences via premeasurable selections and study properties of this new integral.     

Supercalm Multifunctions For Convergence Analysis

Calmness of multifunctions is a well-studied concept of generalized continuity in which single-valued selections from the image sets of the multifunction exhibit a restricted type of local Lipschitz continuity where the base point is fixed as one point of comparison. Generalized continuity properties of multifunctions like calmness can be applied to convergence analysis when the multifunction appropriately represents the iterates generated by some algorithm. Since it involves an essentially linear relationship between input and output, calmness gives essentially linear convergence results when it is applied directly to convergence analysis. We introduce a new continuity concept called ‘supercalmness’ where arbitrarily small calmness constants can be obtained near the base point, which leads to essentially superlinear convergence results. We also explore partial supercalmness and use a well-known generalized derivative to characterize both when a multifunction is supercalm and when it is partially supercalm. To illustrate the value of such characterizations, we explore in detail a new example of a general primal sequential quadratic programming method for nonlinear programming and obtain verifiable conditions to ensure convergence at a superlinear rate.     

The Metric Integral of Set-Valued Functions

This paper introduces a new integral of univariate set-valued functions of bounded variation with compact images in \({\mathbb {R}}^d\). The new integral, termed the metric integral, is defined using metric linear combinations of sets and is shown to consist of integrals of all the metric selections of the integrated multifunction. The metric integral is a subset of the Aumann integral, but in contrast to the latter, it is not necessarily convex. For a special class of segment functions equality of the two integrals is shown. Properties of the metric selections and related properties of the metric integral are studied. Several indicative examples are presented.