关于D.Burke和E.Michael的一个定理

本文借助Ｂｕｒｋｅ－Ｍｉｃｈａｅｌ条件引入两种集族性质，分析了它们与ｃｓ＊网和ωｅｓ＊网的关系，肯定地回答了１９９６年刘川和Ｙ．Ｔａｎａｋａ在Ｔｏｐｌｏｇｙ　Ｐｒｏｃｅｅｄｉｎｇｓ上提出的下述问题：若具有σ点有限Ｋ网的ｋ空间Ｘ不含有闭子空间同胚于Ｓω，那么Ｘ是否是ｇｆ可数空间？     

度量空间的紧覆盖s-像

本文了给出了度量空间和局部可分度量空间紧覆盖ｓ－像的刻画，部分地回答了Ｍｉｃｈａｅｌ－Ｎａｇａｍｉ问题．     

关于无穷级数等式sum from n=1 to ∞( 1/n~2)=π~2/6的证明

无穷级数是数学分析、微积分、高等数学等课程的重要组成部分 ,它在组合数学、近似计算、敛散性判断等领域中起着不可估量的作用 .本文按照初等数学与高等数学相结合的原则 ,收集整理了无穷级数∑∞ｎ =11ｎ2 =π26 的二种证明方法 ,为同学们学习提供一些参考 .证法一　棣莫佛公式法 (ＤｅＭｏｉｖｅｒ)将ＤｅＭｏｉｖｅｒ公式 (ｃｏｓα+ｉｓｉｎα) ｋ =ｃｏｓｋα+ｉｓｉｎｋα按二项式定理展开为ｃ0ｋｃｏｓｋα +ｃ1 ｋｃｏｓｋ- 1 α·ｉｓｉｎα -ｃ2 ｋｃｏｓｋ- 2 α·ｓｉｎ2 α +… +ｃｋｋ(ｉｓｉｎα) ｋ =ｃｏｓｋα+ｉｓｉｎ…     

ERDS-RE''''NYI大数律下自正则的效用

｛Ｘ，Ｘｉ，ｉ≥１｝是ｉ．ｉ．ｄ．ｒ．ｖ′．ｓ．在矩母函数存在的条件下，由古典的Ｅｒｄｏｓ－Ｒéｎｙｉ大数律有ｌｉｍｎ→∞ｍａｘ０≤ｋ≤ｎ∑ｋ＋［ｃｌｏｇｎ］ｉ＝ｋ＋１Ｘｉ［ｃｌｏｇｎ］＝α（ｃ），α（ｃ）为某常数．自正则下ＭｉｋｌóｓＣｓｏｒｇｏ＆ＳｈａｏＱｉｍａｎ（１９９４）在仅要求一阶矩的条件下就得到了：ｌｉｍｎ→∞ｍａｘ０≤ｋ≤ｎ∑ｋ＋［ｃｌｏｇｎ］ｉ＝ｋ＋１Ｘｉ∑ｋ＋［ｃｌｏｇｎ］ｉ＝ｋ＋１（Ｘ２ｉ＋１）＝β（ｃ），β（ｃ）为某常数．众所周知，自正则下人们往往在较弱条件下取得相应结果是因为：分母中的Ｘ能有效抵销分子中Ｘ较大而引起整个分式极限行为的波动．因此，在什么样的条件下，式ｍａｘ０≤ｋ≤ｎ∑ｋ＋［ｃｌｏｇｎ］ｉ＝ｋ＋１Ｘｉ∑ｋ＋［ｃｌｏｇｎ］ｉ＝ｋ＋１Ｘ２ｉ１－β［ｃｌｏｇｎ］β→ｒ（ｃ）成为非常有意思的问题，因为它将依赖于β的大小．本文给出，当０＜β≤１２时，只要Ｅ（Ｘ）≥０，上式就有有限极限．当１２＜β＜１时，则必须在矩母函数存在下，上式才有有限极限．并都求出了其极限表达式．     

非线性横截入射波在边界上的反射

ＭｉｃｈａｅｌＢｅａｌｓ和ＧｒｕｙＭｅｔｉｖｉｅｒ［１］［２］在余法分布空间的框架下研究了多维高阶方程半线性波的反射问题，但文中均要求非线性自由项ｆ不依赖于ｍ－１ｕ（ｍ是方程的阶数）．本文试图去除上述不自然的假定，运用的方法主要是定义了一类所谓三指标余法分布空间，发展了对非光滑系数拟微分算子的切向微局部分析，在两个互补的锥邻域内，分别利用奇性沿次特征线传播的有关定理和能量估计方法并依赖交换子技术来得出我们的结论．     

多目标优化中的简化定理及其应用

１ 引言 设Ｘ是实的Ｂａｎａｃｈ空间,Ｓ 　 Ｘ是闭子集． 考虑下述多目标优化问题：其中ｆｋ,ｋ∈Ｎ≡｛１,…,ｎ｝,ｇｉ,ｉ∈Ｍ≡｛１,…,ｍ｝,ｈｉ,ｊ∈Ｐ≡｛１,…,ｐ｝均是定义在某开集（包含Ｓ）上的局部Ｌｉｐｓｃｈｉｔｚ函数． 集合Ｓ０＝｛ｘ∈Ｓ：ｇｉ（ｘ）≤０,ｉ∈Ｍ,,ｈｉ（ｘ）＝０,ｊ∈Ｐ｝称为（ＶＰ）的可行解集．（ＶＰ）的局部有效解和局部弱有效解的定义见［２］．设φ：Ｘ→Ｒ是局部Ｌｉｐｓｃｈｉｔｚ函数,则　φ（ｘ）称为φ在ｘ处的Ｃｌａｒｋｅ广义梯度［３］． 关于非光滑多目标优化问题（Ｖ…     

On the Solvability of x∈Ax＋λBx in a General Cone with A and B Multivalued k－set－contractive

ＯｎｔｈｅＳｏｌｖａｂｉｌｉｔｙｏｆｘ∈Ａｘ＋λＢｘｉｎａＧｅｎｅｒａｌＣｏｎｅ　ｗｉｔｈＡａｎｄＢＭｕｌｔｉｖａｌｕｅｄ　ｋ－ｓｅｔ－ｃｏｎｔｒａｃｔｉｖｅＺｈａｎｇＱｉｎｇｙｏｎｇ（张庆雍）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，Ｓｉｃ...     

向量值Musielak-Orlicz空间的两种几何性质(英)

设Ｘ是复Ｂａｎｃｈ空间,Ｍ（ｔ,ｕ）是以ｔ为参数的满足某些通常条件的Φ－函数．我们证明了;（ｉ）Ｍｕｓｉｅｌａｋ－Ｏｒｌｉｃｚ空间Ｌ_Ｍ（Ｘ）具有解析ＵＭＤ性质当且仅当Ｘ具有;（ｉｉ） Ｌ_Ｍ（Ｘ）具有解析ＲＮ性质当且仅当Ｘ具有．     

四元数空间形式中全复子流形的内蕴积分等式

本文给出了四元数空间形式中全复子流形的一个性质．即设Ｍ２ｎ是的全复子流形，ρ，‖Ｒｉｅｍ‖２，‖Ｒｉｃｃｉ‖２分别表示Ｍ２ｎ的纯量曲率和黎曼曲率，Ｒｉｃｃｉ曲率的模长平方，则在Ｍ上处处成立．     

A Mathematical Model for Economic Risk

ＡＭａｔｈｅｍａｔｉｃａｌＭｏｄｅｌｆｏｒＥｃｏｎｏｍｉｃＲｉｓｋ￥ＸｕＺｅｇｕｉ（ＨｅｎａｎＩｎｓｔｉｔｕｔｅｏｆＦｉｎａｎｃｅａｎｄＥｃｏｎｏｍｉｃｓ，４５０００２）Ａｂｓｔｒａｃｔ：Ｂａｓｅｄｏｎｔｈｅａｎａｌｙｓｉｓｆｏｒｅｃｏｎｏｍｉｃａｃ...     

A Family of Stochastic Programming Test Problems Based on a Model for Tactical Manpower Planning

Ariyawansa and Felt (2001, 2004) have recently created a test problem collection for testing software for stochastic linear programs. This freely-available, web-based collection was originally created with 35 problem instances from 11 problem families representing a variety of application areas. The collection was created with plans for enriching it with problem instances based on different application areas from the research community. The work of Martel and Al-Nuaimi (1973) on manpower planning under uncertain demand represents an application area suitable for creating new problem instances to be added to the collection. The purpose of this paper is to describe the construction of a new family of stochastic programming test problems based on the work of Martel and Al-Nuaimi (1973). As part of our construction, we review the work of Martel and Al-Nuaimi (1973) leading to an extension of their models for which their solution procedure does not apply. The new test problems are based on this extension. We also present solutions to the test problems obtained using the software package CPA (2002) for stochastic programming developed by Ariyawansa, Felt and Sarich. Mathematics Subject Classifications (2000) 90C15, 90C90, 65K05. K. A. Ariyawansa: The work of this author was supported in part by the U.S. Army Research Office under Grant DAAD 19-00-1-0465.     

Rational functions and value sharing

This note gives a survey on shared value problems for rational functions. In particular a solution to a problem in [A.K. Pizer (1973). A problem on rational functions. Amer. Math. Mon., 80, 552–553.] is given.     

Asymptotic analysis of a certain random differential equation

We prove a limit theorem for the mathematical expectation of the solution of an initial value problem in a Hilbert space. The random differential equations considered here satisfy a strong mixing condition which is weaker than the one imposed in analogue results (Cogburn and Hersh, 1973; Papanicolaou and Varadhan, 1973). Our motivation to develop this analysis comes from a system (Nogueira, preprint) formed by coupling an external source to the Martin-Emch model (Martin and Emch, 1975).     

The existence of a periodic solution in a tide dynamics problem

We examine a quasilinear boundary-value problem describing the dynamics of tidal flow in the sea. For small values of ground friction coefficient and under the fulfillment of a certain condition on the function giving the depth of the sea, we prove the existence of a generalized periodic solution. We construct a difference scheme for the numerical solution of the problem being examined and we prove its stability.Translated from Problemy Matematicheskogo Analiza. No. 4: Integralnye i Differentsial'nye Operatory. Differentsial'nye Uraveniya, pp. 3–9, 1973.     

On a filtration problem through a porous medium

Summary We prove the existence of a unique solution for a free boundary problem relative to the stationary flow between two water reservoirs of different levels separated by a dam of a non-homogeneous porous medium. Entrata in Redazione il 5 maggio 1973.     

On a boundary-value problem solvability condition

We prove a sufficient condition for the solvability of a two-point problem.Translated from Matematicheskie Zametki, Vol. 13, No. 2, pp. 247–250, February, 1973.     

On the Number of Records in an iid Discrete Sequence

The problem of the rate of growth of the number of record values and weak record values in an iid sequence of integer valued random variables is attacked as a perturbation of the case for continuous random variables. Conditions in terms of either the underlying probability mass function or the hazard function of the underlying distribution are given for the rate of growth of the number of records to be log(n) almost surely. The record problem has been considered by Gouet et al.(2001) [Adv. Appl. Prob. 33, 473-864] and by Vervaat(1973) [Stochastic processes Appl. 1, 317-334]. The results for records overlap those found in the former paper. The methods here are more elementary, and the results on weak records are not mentioned there. This paper improves on what may be derived from results in Vervaat. (1973) [Stochastic Processes Appl. 1, 317-334] An erratum to this article can be found at     

A new nonparametric approach to the problem of agreement between two groups of judges

The problem of agreement between two or more groups of judges has receivedconsiderable attention during the past decede, beginning with the papers by Schucany & Frawley (1973) and Hollander & Sethuraman (1978). Twovery different definitions of agreement have emerged in the literature. The first states that two groups of judges agree if they use the same probability distribution to select their rank vectors, while the second defines agreement In terms of correlation coefficients. We utilize the first definition in developing a new approach to solving this agreement problem, relying heavily on computer-generated tables     

Estimation of IBNR claims by credibility theory

We develop a stochastic multiplicative model for the forecasting of IBNR claims. The factor depending on the accident year is credibility adjusted.The title of this note also suits for the papers by Straub (1971) and Kramreiter and Straub (1973). We made stronger assumptions simplifying drastically the numerical calculations and the parameter estimation problem.As showed in the numerical illustrations, the developed method is also applicable in case of scarce irregular data.     

The polynomial reconstruction problem: The first 50 years

The problem of reconstructing the characteristic polynomial of a graph of order at least 3 from the collection of characteristic polynomials of its vertex-deleted subgraphs was posed by Cvetkovi? in 1973 as a spectral counter part to the well-known Ulam's reconstruction conjecture. Over the last 50 years, this problem has received notable attention, many positive results have been obtained, but in the general case the problem is still unresolved. In particular, no counter example is found in literature. In this expository paper we survey classical and some more recent results concerning the polynomial reconstruction problem, discuss some related problems, variations and generalizations.