度量投影的收敛性

讨论了赋范空间中度量投影的收敛性．得到了在局部紧集控制下．Chebyshov凸集序列的度量投影的收敛性与K-M收敛，Wlisman收敛和Kuratowskl收敛都等价．本文的结论完善了M．Tsukada在[1]和[2]的结果．     

多重集非凸分裂可行问题的非精确均值投影算法

在本文中,我们引入了非精确均值投影算法来求解多重集非凸分裂可行问题,其中这些非凸集合为半代数邻近正则集合.通过借助著名的Kurdyka-Lojasiewicz不等式理论,我们建立了算法的收敛性.     

不分明集的oX-级数收敛及oS-序列紧性

本文研究了不分明集的一些级数收敛性,给出了不分明集的oX-级数收敛定义及oS-序列紧致性.证明了一个在论域上逐点收敛的模订级数,将在某种中的拓扑下,也可以是收敛的.如论域X为紧度量空间,且Ai∈F(X)∩ C(X)时,级数依距离d(A,B)=收敛.     

Hilbert空间中的非扩张映象的不动点集的结构及其迭代集合序列逼近

我们研究Hilbert空间H中的闭凸集C上的非扩张映象T的不动点集F(T)的结构和它的集合序列逼近。我们得到 1 不动点集F(T)是闭的和凸的; 2 提供一个集合序列迭代法,使得由这个方法构造的迭代集合序列在某些条件和某种意义下强(弱)收敛于T的一个不动点,并给出收敛速度估计。 前面叙述的这些结果包含了Browder,Petryshyn,Kirk等人的某些结果。     

Banach空间中一类扰动优化问题最优解的特征与存在性

设(X,‖·‖)是Banach空间,x∈X,Z是X的非空子集,J是Z→R的下半连续下有界函数．本文研究扰动优化问题min_(z∈Z)(J(z)+‖x-z‖)(记作(J,x)-inf)的最优解的特征和最优解的存在性等问题．我们引入J－太阳集的概念,同时在Z是J-太阳集的情形下,给出了扰动优化问题(J,x)-inf的最优解的“Kolmogorov”型特征刻画．并借助于集合的若干紧性概念和最优值函数的方向导数研究了扰动优化问题(J,x)-inf的最优解的存在性．     

不分明集的σX—级数收敛及σS—序列紧性

本文研究了不分明集的一些级数收敛性,给出了不分明集的σX－级数收敛定义及σS－序列紧致性。证明了一个在论域上逐点收敛的模订级数,将在某种中的拓扑下,也可以是收敛的。如论域X为紧度量空间,且Ai∈F（X）∩C（X）时,级数∑i=1^∞Ai依距离d(A,B)=supx∈X│A（x）-B（x）│收敛。     

一类随机规划逼近最优值和最优解集的收敛性

本文提出强上图收敛的概念,讨论了逼近随机规划的目标函数序列的强上图收敛性,研究了逼近随机规划最优值和最优解集的收敛性条件,得到了一类随机规划逼近最优值和最优解集的收敛性.     

不分明集的σX-级数收敛及σS-序列紧性(英文)

本文研究了不分明集的一些级数收敛性 ,给出了不分明集的σX-级数收敛定义及σS-序列紧致性 .证明了一个在论域上逐点收敛的模订级数 ,将在某种中的拓扑下 ,也可以是收敛的 .如论域 X为紧度量空间 ,且 Ai ∈ F( X)∩ C( X)时 ,级数∑∞i=1Ai 依距离 d( A,B) =supx∈ X|A( x) -B( x) |收敛     

一种反向集值鞅型序列的收敛性

本文研究了在非空有界闭凸集的上鞅收敛性和有界闭凸集的适应可积集值序列的收敛性.引入了反向集值mil的基础上,得到了收敛性定理及定理证明.     

物元可拓集集合性质研究

在可拓集合概念基础上,提出了向量可拓集和区间可拓集概念,研究了物元可拓集合的交、并、求补等集合运算及其性质.     

度量投影的收敛性（英文）

讨论了赋范空间中度量投影的收敛性．得到了在局部紧集控制下，Chebyshev凸集序列的度量投影的收敛性与K－M收敛，Wijsman收敛和Kuratowski收敛都等价．本文的结论完善了M．Tsukada在[1]和[2]结果．     

Jensen's inequality for random elements in metric spaces and some applications

Jensen's inequality is extended to metric spaces endowed with a convex combination operation. Applications include a dominated convergence theorem for both random elements and random sets, a monotone convergence theorem for random sets, and other results on set-valued expectations in metric spaces and on random probability measures.     

Convergence of Polynomial Level Sets

In this paper we give a characterization of pointwise and uniform convergence of sequences of homogeneous polynomials on a Banach space by means of the convergence of their level sets. Results are obtained both in the real and the complex cases, as well as some generalizations to the nonhomogeneous case and to holomorphic functions in the complex case. Kuratowski convergence of closed sets is used in order to characterize pointwise convergence. We require uniform convergence of the distance function to get uniform convergence of the sequence of polynomials.

     

A sequential iteration algorithm with non-monotoneous behaviour in the method of projections onto convex sets

The method of projections onto convex sets to find a point in the intersection of a finite number of closed convex sets in a Euclidean space, may lead to slow convergence of the constructed sequence when that sequence enters some narrow “corridor” between two or more convex sets. A way to leave such corridor consists in taking a big step at different moments during the iteration, because in that way the monotoneous behaviour that is responsible for the slow convergence may be interrupted. In this paper we present a technique that may introduce interruption of the monotony for a sequential algorithm, but that at the same time guarantees convergence of the constructed sequence to a point in the intersection of the sets. We compare experimentally the behaviour concerning the speed of convergence of the new algorithm with that of an existing monotoneous algorithm.     

Polynomials and limited sets

We prove that scalar-valued polynomials are weakly continuous on limited sets and that, as in the case of linear mappings, every -valued polynomial maps limited sets into relatively compact ones. We also show that a scalar-valued polynomial whose derivative is limited is weakly sequentially continuous.

     

Orders of Indescribable Sets

We extract some properties of Mahlo’s operation and show that some other very natural operations share these properties. The weakly compact sets form a similar hierarchy as the stationary sets. The height of this hierarchy is a large cardinal property connected to saturation properties of the weakly compact ideal.     

Convergence theorems for adapted sequences of random sets

We consider random sets with values in a separable Banach space. We study set-valued amarts, L¹-amarts, uniform amarts and submartingales. For all these classes of random sets, we prove convergence theorems in all main modes of set convergence (weak, Wijsman, Mosco, and Hausdorff). We also prove new convergence theorems for vector-valued subpramarts and pramarts.     

Connectedness and compactness on standard sets

We present a nonstandard characterization of connected compact sets (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stabilization in a 3D eco-epidemiological model: From the complete extinction of a predator population to their self-healing

In this paper, using the localization method of compact invariant sets, we examine the ultimate dynamics of the 3D prey–predator model containing two subpopulations of susceptible and infected predators. Our attention is focused to finding ultimate sizes of interacting populations, and, in addition, we show the existence of a global attracting set. Then, we derive various global conditions of ultimate extinction of at least one of the predators subpopulations and describe conditions under which all types of internal bounded dynamics are ruled out. In particular, we describe convergence conditions to omega-limit sets located (1) in the intersection of the prey-free plane with the infected predators-free plane and (2) in the infected predators-free plane. Based on the dynamical analysis of the 2D infection-free subsystem, we obtain conditions of global attraction to (i) the prey-only disease-free equilibrium point, (ii) the disease-free prey-predator equilibrium point (self-healing of the predator population), and (iii) the omega-limit set containing an equilibrium point or a periodic orbit. Main theoretical results are illustrated by numerical simulation. Tools and techniques developed in this work can be appropriated in the studies within predictive population ecology of more complex eco-epidemiological models.