正则F集空间中的度量拓扑

本文证明了Ｒ＾ｎ上正则Ｆ集收敛拓扑空间是完备的、可分的度量空间，给出了该种度量的具体表达形式。本文还讨论了弱收敛度量拓扑与正则Ｆ集上另外两种度量拓扑－一致收敛拓扑及积分收敛拓扑－之间的关系。     

关于函数空间上三个特殊拓扑满足第一可数公理的条件

本文给出了函数空间上的一致收敛拓扑、紧收敛拓扑及 Cauchy收敛拓扑满足第一可数公理的条件 .     

Fell—拓扑的某些性质

刻画了Fell-拓扑的某些性质以及Fell-拓扑和拓扑收敛的关系。     

子集网交的拓扑收敛性

本文在给出拓扑空间子集网交的拓扑收敛条件基础上，利用子集网的仅同性进一步讨论了拓扑空间子集网交的收敛性，并深入讨论子集网交对紧致Ｈａｕｓｄｏｒｆｆ空间的Ｖｉｅｔｏｒｉｓ超拓扑空间的收敛性。     

集值映射的拓扑收敛

本文通过例子和定理证明:仅在一定条件下,集值映射网的拓扑收敛与其两种常见的收敛(点态收敛及一致收敛)方能比较。     

模糊拓扑空间的m—收敛理论

本文在模糊拓扑空间中引进了模糊网和模糊滤子的ｍ－收敛概念，探讨了模糊网的ｍ－收敛与模糊滤子的ｍ－收敛之间的关系，得到了Ｈａｕｓｄｏｒｆｆ拓扑与模糊网的ｍ－收敛和模糊滤子的ｍ－收敛之间的关系以及刻画Ｈａｕｓｄｏｒｆｆ拓扑几何特征的定理。     

对应模型中微连续类在两种拓扑下的应用

本文研究了微连续子类的性质 ,证明了 :S′( X,Y)在 *一致收敛拓扑下是 Ym X的闭集 ;若 X是 P空间 ,则 S( X,Y)在图拓扑下在 Ym X中是稠密的     

关于“预拓扑与网族的预收敛类”的注

本文研究了预拓扑空间中的收敛问题.利用完备格同构的方法,获得了预拓扑与预收敛类可以相互确定的结果,推广了拓扑与收敛类可以相互确定的结果,同时推广了文献[1]的结果.     

L-层次拓扑空间

在L-拓扑空间中,利用Dα-闭集推广了远域的概念,定义了L-子集的层次收敛,建立了网的层次收敛理论.     

L-fuzzy N-收敛空间

本文给出L-fuzzy N-收敛空间的定义,讨论L-fuzzy N-收敛空间范畴(L-fuzzyN-收敛空间和它们之间的连续映射构成的范畴)的若干范畴的性质,并且证明它的一个子范畴同构与L-fuzzy拓扑空间范畴.     

Some Convergence Properties of Descent Methods

In this paper, we discuss the convergence properties of a class of descent algorithms for minimizing a continuously differentiable function f on R ⁿ without assuming that the sequence { x _k } of iterates is bounded. Under mild conditions, we prove that the limit infimum of is zero and that false convergence does not occur when f is convex. Furthermore, we discuss the convergence rate of { } and { f(x _k )} when { x _k } is unbounded and { f(x _k )} is bounded.     

Hypertopologies on function spaces

The aim of this paper is to continue Naimpally’s seminal papers [16], [17], [18], i.e. we investigate topological properties of spaces which force the coincidence of convergences of functions associated with different hyperspace topologies. For example a metric spaceX is locally compact iff the topological convergence and the convergence induced by the Fell topology coincide onC(X,IR). Moreover, the proximal topology on the space of functions, not necessarily continuous, is studied in great detail.     

Some examples and counterexamples of convergence of σ-algebras and filtrations

We study some properties of the weak convergence of filtrations, in particular, its behavior under elementary set operations. We also derive relations between the convergence of filtrations generated by point processes with a single jump and the convergence of their compensators or distributions of their jump moments. Finally, we apply a lemma on the intersection of σ-algebras to filtrations generated by different discretizations of a single process. Translated from Lietuvos Matematikos Rinkinys, Vol. 40, No. 3, pp. 295–306, July–September, 2000. Translated by V. Mackevičius     

The Wijsman and Attouch-Wets topologies on hyperspaces revisited

In this paper we will prove that, for an arbitrary metric space X and a fairly arbitrary collection Σ of subsets of X, it is possible to endow the hyperspace CL(X) of all nonempty closed subsets of X (to be identified with their distance functionals) with a canonical distance function having the topology of uniform convergence on members of Σ as topological coreflection and the Hausdorff metric as metric coreflection. For particular choices of Σ, we obtain canonical distance functions overlying the Wijsman and Attouch-Wets topologies. Consequently we apply the general theory of spaces endowed with a distance function and compare the results with those obtained for the classical hyperspace topologies. In all cases we are able to prove results which are both stronger and more general than the classical ones.     

Stability of Doob—Meyer Decomposition Under Extended Convergence

In what follows, we consider the relation between Aldous‘s extended convergence and weak convergence of filtrations. We prove that, for a sequence (X^n) of Ft^n )-special semimartingales, with canonical decomposition X^n =M^n A^n, if the extended convergence (X^n,F.^n)→(X,T. ) holds with a quasi-left continuous (Ft)-special semimartingale X = M A, then, under an additional assumption of uniform integrability,we get the convergence in probability under the Skorokhod topology: M^n↑P→M and A^n↑P→ A.     

新Dirichlet级数Σn=0∞aneλns收敛横坐标

本文给出新Dirichlet级数Σ_n=0^∞a_ne^λ_ns的收敛横坐标σ_c、一致收敛横坐标σ_u和绝对收敛横坐标σ_a的定义.通过指数λ_n和系数a_n的关系去估计三个横坐标,并补充证明两类Dirichlet级数Σ_n=0^∞a_ne^λ_ns和Σ_n=0^∞a_ne^-λ_ns的收敛条件是一致的.     

5元素集合上T_0拓扑总数的计算

利用有限偏序集上的几个重要结果并借助于拓扑空间对应的特殊化序与拓扑之间的关系计算得出5元素集合上T0拓扑总数为4231,拓扑总数为6942.     

求解非线性方程组的一种新的全局收敛的Levenberg-Marquardt算法

本文提出了求解非线性方程组的一种新的全局收敛的Levenberg-Marquardt算法,即μk=ακ(θ||F_k|| (1-θ)||J_k~TF_k||),θ∈[0,1],其中ακ利用信赖域技巧来修正.在不必假设雅可比矩阵非奇异的局部误差界条件下,证明了该算法是全局收敛和局部二次收敛的.数值试验表明该算法能有效地求解奇异非线性方程组问题.     

On the topological structure of the Levi-Civita field

Two topologies on the Levi-Civita field R will be studied: the valuation topology induced by the order on the field, and another weaker topology induced by a family of seminorms, which we will call weak topology. We show that each of the two topologies results from a metric on R, that the valuation topology is not a vector topology while the weak topology is, and that R is complete in the valuation topology while it is not in the weak topology. Then the properties of both topologies will be studied in details; in particular, we give simple characterizations of open, closed, and compact sets in both topologies.