二元稳定网络的算法及模型

通过建立JW(Jackson-Wolinsky)规则之下二元稳定网络的等价条件, 给出其完整算法. 引入边支付后, 证明了增连接情形具有边支付的二元稳定网络集合是二元稳定网络集合与具有边支付的二元稳定网络集合的交集. 考察两个特定的网络模型, 系统分析了它们的二元稳定性.     

A diophantine problem concerning cubes

This paper deals with the problem of finding n integers such that their pairwise sums are cubes. We obtain eight integers, expressed in parametric terms, such that all the six pairwise sums of four of these integers are cubes, 9 of the 10 pairwise sums of five of these integers are cubes, 12 pairwise sums of six of these integers are cubes, 15 pairwise sums of seven of these integers are cubes and 18 pairwise sums of all the eight integers are cubes. This leads to infinitely many examples of four positive integers such that all of their six pairwise sums are cubes. Further, for any arbitrary positive integer n, we obtain a set of 2(n+1) integers, in parametric terms, such that 5n+1 of the pairwise sums of these integers are cubes. With a choice of parameters, we can obtain examples with 5n+2 of the pairwise sums being cubes.     

On complete convergence and the strong law of large numbers for pairwise independent random variables

The complete convergence for the maximum partial sums of pairwise independent random variables is obtained. The Kolmogorov strong law of large numbers for pairwise i.i.d. random variables is also obtained. Similar results are established for the moving average processes of pairwise i.i.d. random variables and for pairwise independent random elements taking values in a Banach space.     

两两PQD序列的一个收敛性质

研究了一类广泛的随机变量序列两两PQD列的收敛性质,得到了与PA序列相类似的完全收敛性和强大数定律的结果.     

两两NQD序列与随机Dirichlet级数

本文研究了一类两两NQD序列加权乘积和的Jamison型强稳定性.利用两两NQD序列的一些极限理论,获得了系数的模为两两NQD列的一类随机Difichlet级数的增长性和值分布的一些新的结果,推广和改进了两两独立序列的相关结论.     

关于对半层空间

利用对$g$-函数和半连续函数给出对半层空间的一些刻画, 并讨论了具有半层拓扑的拓扑序$C$-空间的对半层性.     

ALMOST 2-FULLY NORMAL,PAIRWISE PARACOMPACT AND COMPLETE DEVELOPABLE BISPACES

Abstract

Dedicated to Professor Sergio Salbany on the occasion of his 60th birthday.

We introduce and study the notion of an almost 2-fully normal bispace. In particular, we prove that a bispace is quasi-pseudometrizable if and only if it is almost 2-fully normal and pairwise developable. We obtain conditions under which an almost 2-fully normal bispace is subquasi-metrizable and show that the fine quasi-uniformity of any subquasi-metrizable topological space is bicomplete. We prove that every pairwise paracompact bispace (in the sense of Romaguera and Marin, 1988) is almost 2-fully normal and that the finest quasi-uniformity of any 2-Hausdorff pairwise paracompact bispace is bicomplete. We also characterize pairwise paracompactness in terms of a property of σ-Lebesgue type of the finest quasi-uniformity. Finally, we use Salbany's compactification of pairwise Tychonoff bispaces to characterize those bispaces that admit a bicomplete pair development and deduce that an interesting example of R. Fox of a non-quasi-metrizable pairwise stratifiable pairwise developable bispace admits a bicomplete pair development.     

On pairwise sensitivity

We define the concept of pairwise sensitivity with respect to initial conditions for the endomorphisms on Lebesgue metric spaces. The idea is that the orbits of almost every pair of nearby initial points (for the product of the invariant measure) of a pairwise sensitive map may diverge from a positive quantity independent of the initial points. We study the relationships between pairwise sensitivity and weak mixing, pairwise sensitivity and positiveness of metric entropy and we compute the largest sensitivity constant.     

Online regularized learning with pairwise loss functions

Recently, there has been considerable work on analyzing learning algorithms with pairwise loss functions in the batch setting. There is relatively little theoretical work on analyzing their online algorithms, despite of their popularity in practice due to the scalability to big data. In this paper, we consider online learning algorithms with pairwise loss functions based on regularization schemes in reproducing kernel Hilbert spaces. In particular, we establish the convergence of the last iterate of the online algorithm under a very weak assumption on the step sizes and derive satisfactory convergence rates for polynomially decaying step sizes. Our technique uses Rademacher complexities which handle function classes associated with pairwise loss functions. Since pairwise learning involves pairs of examples, which are no longer i.i.d., standard techniques do not directly apply to such pairwise learning algorithms. Hence, our results are a non-trivial extension of those in the setting of univariate loss functions to the pairwise setting.     

一类两两NQD列乘积和的Jamison型强稳定性

研究了一类不同分布两两NQD列的Jamison型加权乘积和的强稳定性,推广了不同分布独立列部分和与同分布NQD列部分和情形相类似的结论.     

两两PQD序列的完全收敛性和强大数定律

给出两两PQD序列部分和的几个不等式,研究了一类广泛的随机变量序列两两PQD列的收敛性质,得到了与PA序列相类似的完全收敛性和强大数定律的结果.     

PAIRWISE ALMOST COMPACT SPACES

ABSTRACT

The purpose of this paper is to investigate pairwise almost compact bitopological spaces. These spaces satisfy a bitopological compactness criterion which is strictly weaker than pairwise C-compactness and is independent of other well-known bitopological compactness notions. Pairwise continuous maps from such spaces to pairwise Hausdorff spaces are pairwise almost closed, the property is invariant under suitably continuous maps, is inherited by regularly closed subspaces and may be characterized in terms of certain covers as well as the adherent convergence of certain open filter bases. Some new natural bitopological separation axioms are introduced and in conjunction with pairwise almost compactness yield interesting results, including a sufficient condition for the bitopological complete separation of disjoint regularly closed sets by semi-continuous functions.     

Packing cycles in complete graphs

We introduce a new technique for packing pairwise edge-disjoint cycles of specified lengths in complete graphs and use it to prove several results. Firstly, we prove the existence of dense packings of the complete graph with pairwise edge-disjoint cycles of arbitrary specified lengths. We then use this result to prove the existence of decompositions of the complete graph of odd order into pairwise edge-disjoint cycles for a large family of lists of specified cycle lengths. Finally, we construct new maximum packings of the complete graph with pairwise edge-disjoint cycles of uniform length.     

两两NQD列的收敛性质

本文首先给出两两 ＮＱＤ列的 Ｋｏｌｍｏｇｏｒｏｖ型不等式，进而讨论两两 ＮＱＤ列的收敛性质，获得了与独立情形一样的Ｂａｕｍ和Ｋａｔｚ完全收敛定理，几乎达到独立惰形著名的Ｍａｒｃｉｎｋｉｅｗｉｃｚ强大数定律、三级数定理等结果．     

偏好的对子态可分性

本文提出了消费者偏好的对子态可分性概念，并用来揭示一般选择集合上偏好的效用函数表示的特征，证明了偏好关系可用效用函数表示的充分必要条件是该偏好具有对子态可分性和可数满足性，还证明了偏好关系具有长直线ｗ１—表示的充分必要条件是该偏好具有对子态可分性．这两个结果，使得对子态可分性成为用直线上的序来表示消费偏好序之本质所在．     

Strong reciprocity and strong consistency in pairwise comparison matrix with fuzzy elements

The decision making problem considered in this paper is to rank n alternatives from the best to the worst, using the information given by the decision maker in the form of an \(n\times n\) pairwise comparison matrix. Here, we deal with pairwise comparison matrices with fuzzy elements. Fuzzy elements of the pairwise comparison matrix are applied whenever the decision maker is not sure about the value of his/her evaluation of the relative importance of elements in question. We investigate pairwise comparison matrices with elements from abelian linearly ordered group (alo-group) over a real interval. The concept of reciprocity and consistency of pairwise comparison matrices with fuzzy elements have been already studied in the literature. Here, we define stronger concepts, namely the strong reciprocity and strong consistency of pairwise comparison matrices with fuzzy intervals as the matrix elements (PCF matrices), derive the necessary and sufficient conditions for strong reciprocity and strong consistency and investigate their properties as well as some consequences to the problem of ranking the alternatives.     

两两独立同分布序列Cesàro强大数定律的收敛速度

设{X,Xn,n≥0}是两两独立同分布的随机变量序列,11．为了证明这一结论而获得到的两两负相关随机变量序列的Cesaro强大数定律收敛速度的结果本身也是有意义的．此结果对于同分布的两两NQD序列也是对的．     

关于不同分布两两NQD列的Jamison型加权乘积和的强稳定性

本文讨论了不同分布两两ＮＱＤ列的Ｊａｍｉｓｏｎ型加权乘积和的强稳定性及乘积和的Ｍａｒｃｉｎｋｉｅｗｉｃｚ型强大数律,推广并改进了Ｅｔｅｍａｄｉ［１］关于不同分布两两独立列部分和的工作及Ｍａｔｕｌａ［２］,王岳宝等［３］关于同分布两两ＮＱＤ列部分和的工作．     

Partitions and sums and products—Two counterexamples

A negative answer is provided to a question of Erdös. Specifically, a two celled partition of N is provided with the property that neither cell includes an infinite set together with all finite products and pairwise sums from that set. Also, a seven celled partition of N is provided with the property that no cell includes an infinite set together with all pairwise products and pairwise sums from that set.     

Complete moment convergence of pairwise NQD random variables

It is known that the dependence structure of pairwise negative quadrant dependent (NQD) random variables is weaker than those of negatively associated random variables and negatively orthant dependent random variables. In this article, we investigate the moving average process which is based on the pairwise NQD random variables. The complete moment convergence and the integrability of the supremum are presented for this moving average process. The results imply complete convergence and the Marcinkiewicz–Zygmund-type strong law of large numbers for pairwise NQD sequences.