On spaces in which the norm convergence coincides with the order convergence

We investigate partially ordered normed vector spaces in which the norm convergence coincides with the order convergence. We consider spaces where the convergences coincide for arbitrary nets and spaces where the convergences coincide only for sequences. We give conditions which characterize such spaces and investigate their properties. In particular, we study the problem of their Dedekind completeness and -completeness.Translated from Matematicheskie Zametki, Vol. 13, No. 2, pp. 259–268, February, 1973.     

关于一道高等数学竞赛试题的探索与拓广

给出了2004年浙江省大学生高等数学竞赛一题得分率较低的压轴题(判断级数sum from n=1 to ∞ 1/n((n!)~α)～(1/n)的敛散性,其中α>0为常数)的五种不同的解法,建立了它的如下的拓广结果:当α>1且正项级数sum from i=1 to ∞ 1/(a_i~α)收敛时,级数sum from n=1 to ∞ 1/((multiply from i=1 to n)ai)α～(1/n)收敛;当0<α≤1,0相似文献   

Cyrtologies of Convergences,I

We study the complete lattice of convergences, that is, of relations between a set and the set of its filters. Various properties of convergences (like isotonicity, antitonicity, being a pseudotopology, a pretopology, an adherence) determine subsets of the lattice of convergences which possess certain particular features called “cyrtological”. The morphisms associated to these sets, said “cyrtomorphisms”, are basic in the study of convergences. A method of generation of GALOIS connections relative to cyrtomorphisms is proposed. Semigroups generated by some cyrtomorphisms are analyzed.     

幂级数在收敛区间端点收敛时的性质

讨论幂级数及其逐项积分、逐项求导后的级数在收敛区间端点收敛时的若干性质,给出它们之间敛散性的关系,并把连续性和逐项可积性推广到幂级数的收敛域上.     

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.     

双随机狄里克莱级数在收敛平面上的增长性

利用独立不同分布的随机变量序列的强大数定律研究了双随机狄里克莱级数的收敛性和增长性,得到了一些新的结果。     

随机狄里克莱级数的收敛性

该文是利用随机变量序列的局部收敛性及强大数定律研究了随机狄里克莱级数的收敛性,得出了它的收敛横坐标的简洁公式．     

“STRAGEDY” OF THE COMMONS

This paper computes open loop and subgame perfect Nash equilibria for an infinite horizon, common property resource model with congestion and stock externalities. The model permits the comparison of the game-theoretic approach and the traditional commons literature, which preceded the widespread recognition of the games, because the underlying assumptions are equivalent. With access to the commons restricted, the subgame perfect equilibrium captures the inefficiency associated with the strategic scramble to capture the resource reserves the open loop does not. Under sole ownership, the two equilibrium concepts coincide with the surplus maximizing extraction policy. In free access, the extraction strategies under both equilibrium concepts coincide with complete rent dissipation.     

集值映射空间的收敛与邻近结构

S.Lubkin[1]对一个集合X定义邻近结构u,并把(X,u)称为空间。邻近结构是介于拓扑结构和一致结构之间的一种结构。本文将以作者在[6]中使用的集合间包含运算为工具,研究集值映射空间的邻近结构,以及刻划集值映射网的各种收敛的各种邻近结构。     

L—Fuzzy集上的Fuzzy值函数的Fuzzy积分的收敛

本文引入了L-Fuzzy集合上的Fuzzy值函数关于Fuzzy值Fuzzy测度的Fuzzy值Fuzzy积分的概念,给出上述概念的几个等价定义,讨论其基本性质,得到一系列积分序列的收敛定理。     

Convergences in JW-algebras and in their enveloping von Neumann algebras

We study properties of different convergences in JW-algebras with a faithful normal state. The relationship between these convergences and similar convergences in enveloping von Neumann algebras is established. Based on this, ergodic theorems are proved.     

Some properties of bornological convergences

We study some basic properties of the so-called bornological convergences in the realm of quasi-uniform spaces. In particular, we revisit the results about when these convergences are topological by means of the use of pretopologies. This yields a presentation of the bornological convergences as a certain kind of hit-and-miss pretopologies. Furthermore, we characterize the precompactness and total boundedness of the natural quasi-uniformities associated to these convergences. We also obtain an extension of the classical result of Künzi and Ryser about the compactness of the topology generated by the Hausdorff quasi-uniformity to this framework.     

Artinian Serial Modules over Commutative (or,Left Noetherian) Rings are at Most One Step Away from Being Noetherian

We introduce and study the concept of dual perfect dimension which is a Krull-like dimension extension of the concept of acc on finitely generated submodules. We observe some basic facts for modules with this dimension, which are similar to the basic properties of modules with Noetherian dimension. For Artinian serial modules, we show that these two dimensions coincide. Consequently, we prove that the Noetherian dimension of non-Noetherian Artinian serial modules over the rings of the title is 1.     

A note on almost sure uniform and complete convergences of a sequence of random variables

The aim of this note is to introduce another way of defining the almost sure uniform convergence, which is necessary when studying some mathematical results on the existence of price bubbles in certain scenarios of trading securities. This mode of convergence of random variables' sequences is intermediate between the uniform and the almost sure ones, and, more specifically, between the uniform and the complete convergences. In this way, this paper presents some mathematical characterizations of both almost sure uniform and complete convergences, and shows that the almost sure uniform convergence is a particular case of complete convergence, when the number of summands in the series defining this mode of convergence is finite. Finally, this paper presents the relation of almost surely uniform convergence with convergence in mean when the random variable limit is integrable. Moreover, almost surely convergence and local boundedness of the sequence of random variables minus its limit are sufficient to derive convergence in mean.     

直接最优化方法的收敛性与不动点

最优化方法中的直接法是仅仅利用目标函数值(或者通过试验结果)的信息,试图去寻求最优解.直接法迭代步骤简单,特别当目标函数的解析表达式十分复杂,甚至写不出来时,那些要求计算目标函数的偏导数的方法(称为解析方法)就无能为力了.然而,多因     

On the equivalence between (quasi-)perfect and sequential equilibria

We prove the generic equivalence between quasi-perfect equilibrium and sequential equilibrium. Combining this result with Blume and Zame (Econometrica 62:783–794, 1994) shows that perfect, quasi-perfect and sequential equilibrium coincide in generic games.     

SOR和AOR迭代收敛的新判别准则

充分条件1和2,对于SOR迭代(0<ω≤1)和AOR迭代(0≤r≤1,0<ω≤1)也是适用的。那么,充分条件3对于SOR迭代和AOR迭代是否适用呢?迄今为止尚没有讨论过。这里我们给予肯定的回答。我们的结论基于如下两个引理。 引理1 如果A的主对角元全不为零,且满足条件(4),则detA≠0。 引理2 对线性方程组(1)的迭代法     

Equilibrium and perfection in discounted supergames

In this paper, we discuss equilibrium and perfect equilibrium in a simplified model of the supergame. We assume that players can observe the mixed moves employed by all players at each previous stage. For this model, we obtain a complete characterization of the set of equilibrium outcomes, and a fairly weak sufficient condition for this set to coincide with the set of perfect equilibrium outcomes.Inter alia, simple proofs of the Folk Theorem and the result that the requirement of perfection does not eliminate any equilibrium outcomes for the undiscounted supergame are presented.     

Bornological Convergences on the Hyperspace of a Uniformizable Space

Bornological convergence is a generalization of the well known Attouch–Wets convergence. Our aim is to compare lower, upper and “two-sided” convergences generated by two compatible uniformities and two arbitrary bornologies. Moreover, the comparison of convergences induced by bounded-proximal topologies is characterized.     

一类紧Fuzzy测度序列的淡收敛

经典测度的弱收敛和淡收敛在经典概率论等随机数学理论中有着很重要的作用。在局部紧Hausdorff空间中首次引入了一类紧Fuzzy 测度序列的淡收敛的概念,得到了它的等价形式及一些性质,推广了相应的经典结果。