PN-空间中的集值非线性算子方程解的存在性和唯一性问题

提出了集值映射下的SV-（φ，△）-型概率收缩的概念，并在PN-空间中研究了这类概率收缩的非线性算子方程解的存在性与唯一性问题，推广了张石生等人的结果。     

PN-空间中一类算子方程序列的解及其应用问题

给出并证明了MengerPN-空间中一类具有(Φ,Δ)-型概率收缩序列的非线性集值及单值算子方程序列解的存在性与唯一性定理,推广了张石生等人的结果,并利用这些定理获得了几个不动点定理.     

概率收缩偶与非阿基米德Menger概率赋范空间中非线性方程组的解*

本文在非阿基米德Menger概率赋范空间中引入了概率收缩偶的概念,研究了非阿基米德Menger概率赋范空间中具概率收缩偶的非线性方程组的解的存在性与唯一性.发展和改进了引文[1～5]的相应结果.     

广义概率收缩偶与概率赋范空间中非线性方程的解

在本文中引入了广义概率收缩偶的概念，研究了具广义概率收缩偶的非线性集值和单值算子方程组（族）的解的存在性和唯一性，并讨论了ＰＮ－空间中集值和单值映象对（族）的公共不动点的存在性．本文改进和发展了［１—４，６—９］中的相应结果．     

SST空间中压缩映射的几个不动点定理

本文给出了SST概率度量空间中压缩型映射的几个不动点定理,改进并推广了张石生[2],方锦暄[3]及陈肇姜[4]中的许多重要结果.     

概率度量空间中压缩映象的不动点定理

本文通过引入压缩映象集序列的概念,推广并综合了张石生以及V.M.Sehger和A.T.Bharucha-Reid中某些主要定理的结果。     

关于概率度量空间中扩张型映象的几个不动点定理

近年来,游兆永,张石生等人对概率度量空间中压缩型映象的不动点定理进行了广泛地研究。本文引入并讨论了概率度量空间中扩张型映象不动点的存在性和唯一性问题。     

连续随机算子的不动点定理

一、引言 由于求解随机方程的需要,近年来许多数学工作者研究了随机算子的不动点问题. 王梓坤介绍了以概率1为Bahach压缩的随机算子的不动点原理.Bharucha-Reid指出各类决定性不动点定理的随机化是有意义的并给出了这类结果的若干应用.最近刘作述,张石生推广了[1—3]的某些结果.     

随机针偶与凸体K相交的几何概率问题

本文研究了随机针偶与凸体K相交的几何概率,利用有向直线偶的运动不变密度公式,获得了针偶的运动不变密度公式,从而进一步得到随机针偶与凸体K相交且针偶的交点属于K的几何概率.     

超平面偶与凸体相交的几何概率

本文利用凸体的均质积分理论,得出超平面偶与凸体相交的几何概率.在此基础上推出超平面偶与球体相交的几何概率序列,并证明了此序列与球体的半径无关且收敛.     

强概率收缩对与概率赋范空间中非线性算子方程组的解

在Menger PN空间引入强概率收缩对的概念,并研究了具有强概率收缩对的非线性算子方程组解的存在性和唯一性.这些结果改进和推广了非Archimedean Menger PN空间中相应的结果.     

Optimal Risk-Sharing When Risk Preferences are Uncertain

In many cases, a firm or agency needs a product that only one vendor can supply and for which the final cost is uncertain. An optimal risk-sharing arrangement is sought when the buyer and contractor agree on the probability distribution of cost but the buyer is uncertain of the contractor's risk-preferences. We find that when the buyer and contractor have exponential utilities, the optimal profit arrangement for the higher risk-averse contractor is no longer linear but concave in the costs. The degree of concavity is affected by the probabilistic beliefs on the contractor's risk-preferences. As the more risk-averse contractor becomes more likely, her chosen profit arrangement becomes less concave approaching the ideal, linear arrangement. The less risk-averse contractor is provided a profit arrangement with a certainty equivalent above her reservation price. This is the price the buyer must pay in order to entice a less risk-averse contractor into agreeing to accept a more risky profit arrangement.Another formulation is considered that assumes the buyer and contractor maximize approximations to their certainty equivalents in order to provide a more practical and possibly viable approach to sole-source contracting.     

Statistical issues in measurement

Measurement theories are traditionally couched in algebraic terms, which makes them unsuitable for statistical testing. A probabilistic recasting of these theories is proposed here. It is observed then that an axiom of probabilistic measurement has typically the form of a logical polynomial, the structure of which induces a particular partition of the parameter space, giving rise to a calss of statistical problems for which the null hypothesis is a union of convex polyhedrons. This is a consequence of the fact that a logical polynomial can always be rewritten in normal form, that is, as a disjunction of conjunctions. A likelihood ratio method is worked out in a couple of exemplary cases. One of these examples provides a test of transitivity, a property which lies at the heart of ordinal measurement.     

Error bounds in divided difference expansions. A probabilistic perspective

We give error bounds for the remainder term, as well as sharp upper and lower bounds for the leading term, in divided difference expansions. A main feature of this paper is the use of a probabilistic approach in the spirit of Ignatov and Kaishev [Z.G. Ignatov, V.K. Kaishev, B-splines and linear combinations of uniform order statistics, Math. Res. Cent. TSR, 2817, Univ. of Wisconsin, Madison, 1985; Z.G. Ignatov, V.K. Kaishev, A probabilistic interpretation of multivariate B-splines and some applications, Serdica 15 (1989) 91-99] and Karlin et al. [S. Karlin, C.A. Micchelli, Y. Rinott, Multivariate splines: A probabilistic perspective, J. Multivariate Anal. 20 (1986) 69-90] based on the representation of divided differences as mathematical expectations involving linear combinations of uniform order statistics.     

The method of contractor directions for partial differential equations

A further development of the concept of contractor directions is presented. An application of the method of specialized contractor directions to local existence theorems for general nonlinear equations and to solutions of some partial differential equations is discussed. An implicit function theorem of the type investigated by Nash, Schwartz and Moser follows.     

灰色关联分析在最佳承包商选择中的应用

承包商选择方法是否科学合理直接关系到工程项目的成败.由于承包商选择方的主观性和承包商信息获取的不完备性,若采用传统选择方法,难以取得良好的效果,并最终影响到业主的利益.针对承包商信息的灰色特征,建立了承包商选择的灰色关联度决策模型,选用投标报价、施工方案、施工工期、质量水平和企业信誉作为5个主要评价指标,运用该模型并结合工程实例进行了灰色关联分析,获得了较为可靠的承包商排序,选出了最佳承包商,证明了该方法在最佳承包商选择中的可行性和有效性.旨在为承包商选择方提供一种简单、快捷而有效的评价方法,帮助承包商选择方做出综合和相对客观的评价.     

考虑质量失误的建筑供应链质量控制协调研究

考虑内外部质量损失条件下,研究由分包商和总包商组成的两级建筑供应链中的质量控制博弈问题。根据典型的建设工程施工质量控制流程,建立了建筑供应链的三层质量控制树。基于质量控制树分别建立了集中决策条件下和协调决策条件下的收益函数模型。通过对模型求解结果的对比分析,得出在双方共同原因导致的内部质量损失由双方分摊的情况下,双方共同分担外部质量损失可使供应链质量控制决策达到协调。进一步的分析得出,内外部质量损失比率越大,总包商所承担的内部质量损失比例越大,而分担的外部质量损失比例越小。     

考虑关联性指标的工程投标决策方法

工程项目投标决策对于任何一个承包商来说都是至关重要的.考虑到我国当前工程投标现状中,投标决策索要考虑的指标很多,但建立相互独立的指标体系往往比较困难、指标之间互相影响的特点,结合模糊数大小比较和Choquet积分,给出了考虑关联性指标的工程投标决策方法.最后用数值算例说明了方法的可行性及实用性.     

The Atiyah—Singer theorems: A probabilistic approach. I. The index theorem

The Atiyah-Singer index theorem for classical elliptic complexes is proved by using probabilistic methods. The general idea is to use a probabilistic construction of the heat equation kernel, which permits the direct derivation of the index formulas, without using the theory of invariants of Gilkey. Stochastic calculus on the exterior algebra is then used to find the classical local formula for the index theorem. The Lefschetz fixed point formulas of Atiyah-Singer will be proved in Part II.