敏感性问题“随机变量和”回答模型

孔圣元，孟生旺．敏感性问题“随机变量和”回答模型．数理统计与管理，１９９８，１７（２），３５～３９．本文依据概率论中“随机变量和”的分布理论，对敏感性问题的调查，提出了一个新模型，即“随机变量和”回答模型，实现了敏感性问题的问卷调查。本文给出了模型的最优估计量及其方差的计算公式，讨论了模型参数的合理选择，同时还得出了一个有趣的结果：“随机化回答模型”包含在“随机变量和”回答模型之中。     

项目投资组合的风险度及其最优决策

本文针对项目组合投资问题引入了风险度概念，并建立其风险度模型．在无零风险度项目的情况下，给出了该模型的最优项目组合投资策略并证明该策略为马氏有效．在有零风险度项目的情况下，讨论了该模型的有效前沿的结构、性质和有效性，同时还论证了该模型的有效前沿与威廉·夏普提出的资本资产定价模型的有效前沿相一致的线性关系．最后作为本模型的应用，构造了”保证还本”模型，给出了其最优项目投资组合的策略．     

开发区居民分布模型研究

本文从规划区土地利用状况出发，建立了居民分布的引力模型和概率模型，在规划区就业人口分成就业区就业人口和居住区服务就业人口的基础上，研究了运用模型分布这两种就业人口的方法，并建立分布全部居民的模型，最后给出了模型应用实例．     

股票价格波动的塑性性质及模型探讨

首先基于股票价格和成交量，根据股票的量价规律，分析了股价波动的塑性性质；然后使用计量经济学方法建立描述股价波动的塑性模型，包括股价塑性基本模型、基本模型的一阶自回归模型、幂指数模型及幂指数模型的一阶自回归模型，基于12支样本股对这些模型进行参数估计和检验；最后对4种形式的股价塑性模型进行了总结。由4种模型均能够通过经济学检验和统计学检验可知股价波动具有塑性性质，且幂指数模型描述股价塑性较为科学、合理。     

客户发展关系的Markov链一般模型

根据客户发展关系的Markov链的转移概率矩阵，建立了客户发展关系的一般模型，它包含许多特殊模型。前人研究的一些模型正是该一般模型的特例。一般模型的建立不但刻画了各种客户发展关系，而且为企业对客户发展进行定量分析和管理奠定了基础。     

物元评判模型及其在学习评价中的应用

对物元评判模型进行了分析，将它应用于学生学习评价，定义了新的关联度函数，分析表明模型是一类优良模型，能有效的运用于学生学习评价中。     

灰色组合模型及其应用

本建立了GM(1．1)与线性回归模型的组合模型，改进了单一模型的局限性，并用此模型预测了郑州市粮食总产量，得到了较为满意的结果。     

电力系统中非同期合闸情形下跳闸过电压模型的讨论

本文给出了电力系统中非同期合闸情形下运行过程中跳闸的过电压模型，利用泛函微分方程振动性理论，得到了该类模型解的振动性与稳定性结论；同时，将控制变量引入到模型，得到了使得系统稳定的变结构控制策略     

流通量间断守恒高阶交通流模型及其数值模拟

在非均匀道路条件下，推广了各向异性守恒高阶交通流模型(CHO模型)，获得流通量间断CHO模型，并基于其Riemann不变量性质，运用局部简化方法及δ映射算法，设计了求解流通量间断CHO模型的一阶Godunov、EO(Engquist-Osher)和LF(Lax-Friedrichs)等数值格式.通过数值模拟表明流通量间断CHO模型是合理有效的，它可以描述平衡态和非平衡态交通流，相对于流通量间断LWR(Lighthill-Whitham-Richards)模型，其能更好地刻画实际交通现象.     

随机化交通灯的二维元胞自动机交通模型

元胞自动机交通模型以简单的规则反映交通系统中的多种因素，可以分析各种交通现象，且可在计算机上方便、高效地运作·Ｂｉｈａｍ－Ｍｉｄｄｌｅｔｏｎ－Ｌｅｖｉｎｅ模型（ＢＭＬ模型）实现了二维交通问题的元胞自动机模型的模拟研究·本文对ＢＭＬ模型作了改进，解除了该模型中关于交通灯同步变化的限制·在新模型中，每个路口的交通灯可以自由选定起始工作时间和变化节奏，于是可以更全面、准确地反映交通灯对交通系统性能的影响·本文还对新模型中出现的若干新效应作了解释·     

Best approximation by downward sets with applications

We develop a theory of downward sets for a class of normed ordered spaces. We study best approximation in a normed ordered space X by elements of downward sets, and give necessary and sufficient conditions for any element of best approximation by a closed downward subset of X. We also characterize strictly downward subsets of X, and prove that a downward subset of X is strictly downward if and only if each its boundary point is Chebyshev. The results obtained are used for examination of some Chebyshev pairs （W,x）, where ∈ X and W is a closed downward subset of X     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

The use of phase portraits to visualize and investigate isolated singular points of complex functions

ABSTRACT

Undergraduate students usually study Laurent series in a standard course of Complex Analysis. One of the major applications of Laurent series is the classification of isolated singular points of complex functions. Although students are able to find series representations of functions, they may struggle to understand the meaning of the behaviour of the function near isolated singularities. In this paper, I briefly describe the method of domain colouring to create enhanced phase portraits to visualize and study isolated singularities of complex functions. Ultimately this method for plotting complex functions might help to enhance students' insight, in the spirit of learning by experimentation. By analysing the representations of singularities and the behaviour of the functions near their singularities, students can make conjectures and test them mathematically, which can help to create significant connections between visual representations, algebraic calculations and abstract mathematical concepts.     

Nonexistence in power and gamma density regression, sum of nonnegative terms

When we use the power function α(c x)^b and gamma density αx^be^-cx to fit the data by the least squares method, we have to address the question of existence. The closure of the set of each type of these functions defined on a finite domain is determined. We derive a way to determine the closure of a sum of nonnegative functions if the closures of the summands are available.     

Sur l'existence, l'unicité, la stabilité et les propriétés de grandes déviations des solutions d'équations différentielles stochastiques rétrogrades à horizon aléatoire. Application à des problèmes de perturbations singulières

We study the existence, uniqueness and stability of solutions of backward stochastic differential equations with random terminal time under new assumptions; then we establish a large deviation principle for the solutions of such equations, related to a family of Markov processes, the diffusion coefficient of which tends to zero. Finally we apply these results to the analysis of some singular perturbation problems for a class of nonlinear partial differential equations.     

Schreier rewriting beyond the classical setting Dedicated to our teacher Alfred Lvovich Shmelkin on his 70th birthday

Using actions of free monoids and free associative algebras, we establish some Schreier-type formulas involving ranks of actions and ranks of subactions in free actions or Grassmann-type relations for the ranks of intersections of subactions of free actions. The coset action of the free group is used to establish a generalization of the Schreier formula in the case of subgroups of infinite index. We also study and apply large modules over free associative and free group algebras.     

A quantum spin system with random interactions I

We study a quantum spin glass as a quantum spin system with random interactions and establish the existence of a family of evolution groups {τ_t(ω)}_ω∈/Ω of the spin system. The notion of ergodicity of a measure preserving group of automorphisms of the probability space Ω, is used to prove the almost sure independence of the Arveson spectrum Sp(τ(ω)) of τ_t(ε). As a consequence, for any family of (τ(ω),β) — KMS states {ρ(ω)}, the spectrum of the generator of the group of unitaries which implement τ(ω) in the GNS representation is also almost surely independent of ω.     

Absolute Continuity of Measures in the Class of Markov and Semi-Markov Processes of Diffusion Type

The property of absolute continuity of measures in the class of one-dimensional semi-Markov processes of diffusion type is investigated. The measure of such a process can be composed of two measures. The first one is a distribution of a random track, and the second one is a conditional distribution of a time run along the track. The desired density is represented in the form of product of two corresponding densities.     

Toward eudaimonology: notes on a quantitative framework for the study of happiness

After noting factors (concern for others, ignorance, irrationality) accounting for the divergences between preference and happiness, the question of representing the preference of an individual by a utility function is discussed, taking account of lexicographic ordering, imperfect discrimination and the corresponding concepts of semiorder and sub-semiorder. Methods to improve upon the interpersonal comparability of measures of happiness such as pinning down the dividing line of zero happiness and the use of a just perceivable increment of happiness are discussed. The relation of social welfare to individual welfare (i.e. happiness) is then considered. Some reasonable set of axioms ensuring that social welfare is a separable function of and indeed an unweighted sum of individual welfares are reviewed. Finally, happiness is regarded as a function of objective, institutional and subjective factors; an interdisciplinary approach is needed even for an incomplete analysis.     

Clustering Methods in Microarrays

Summary DCT Given a finite set of points in an Euclidean space the \emph{spanning tree} is a tree of minimal length having the given points as vertices. The length of the tree is the sum of the distances of all connected point pairs of the tree. The clustering tree with a given length of a given finite set of points is the spanning tree of an appropriately chosen other set of points approximating the given set of points with minimal sum of square distances among all spanning trees with the given length. DCM A matrix of real numbers is said to be column monotone orderable if there exists an ordering of columns of the matrix such that all rows of the matrix become monotone after ordering. The {\emph{monotone sum of squares of a matrix}} is the minimum of sum of squares of differences of the elements of the matrix and a column monotone orderable matrix where the minimum is taken on the set of all column monotone orderable matrices. Decomposition clusters of monotone orderings of a matrix is a clustering ofthe rows of the matrix into given number of clusters such that thesum of monotone sum of squares of the matrices formed by the rowsof the same cluster is minimal.DCP A matrix of real numbers is said to be column partitionable if there exists a partition of the columns such that the elements belonging to the same subset of the partition are equal in each row. Given a partition of the columns of a matrix the partition sum of squares of the matrix is the minimum of the sum of square of differences of the elements of the matrix and a column partitionable matrix where the minimum is taken on the set of all column partitionable matrices. Decomposition of the rows of a matrix into clusters of partitions is the minimization of the corresponding partition sum of squares given the number of clusters and the sizes of the subsets of the partitions.