Discrete approximation of integral operators

A method to approximate the eigenvalues of linear operators depending on an unknown distribution is introduced and applied to weighted sums of squared normally distributed random variables. This area of application includes the approximation of the asymptotic null distribution of certain degenerated U- and V-statistics.

     

Fractional-Linear Transformations of Operator Balls; Applications to Dynamical Systems

The operator sets, which are the subject of this paper, have been studied in many papers where, under different restrictions on the generating operators, convexity, compactness in the weak operator topology, and nonemptiness were proved for sets of different classes under study. Then the results obtained were used in these papers to solve several applied problems. Namely, they played the key role in establishing the dichotomy of nonautonomous dynamical systems, with either continuous or discrete time. In the present paper, we generalize and sharpen the already known criteria and obtain several new criteria for convexity, compactness, and nonemptiness of several special operator sets. Then, using the assertions obtained, we construct examples of sets of the form under study which are nonconvex, noncompact in the weak operator topology, as well as empty, and are generated by ＂smooth＂ operators of a special class. The existence problem for such sets remained open until the authors of this paper announced some of its results.     

An experiment with arithmetic precision in linear algebra computations

Several techniques for experimental determination of floating point precision in practical computations are examined, and applied to linear algebra algorithms. These techniques are simple enough to be directly applicable to existing production codes, requiring a very limited amount of software on many machines, and yet they yield interesting information on the numerical precision of a computation. Our choice of linear algebra algorithms includes a direct solver (namely the MA32 program from the Harwell Library) and several variants of preconditioned conjugate gradients (the methods DIAG, INV, MINV and POL of Reference 1). The results may be of interest as method selection criteria, and thus complement Mflop performance data available from several sources.     

一个组合分布模型及其参数估计

本文根据极值分布理论,提出了一个由原始分布和尾分布组成的组合分布模型,研究了组合分布模型中原始分布和尾分布的确定方法,建立了组合分布模型参数估计的加权最优化模型,实例计算说明,组合分布较好地反映了风险变量极值事件的风险。     

有序分组资料的线性趋势检验的确切概率计算

有序分组资料的线性趋势检验主要用于检验几个二项总体反应率的线性趋势；在医学与生物学中最典型的用途是研究剂量和反应的关系． 如果用Ｚ检验来代替通常在本检验中所用的卡方检验，就可容易地导出本检验的确切概率计算方法，和其他２×Ｃ有序列联表有着相同的形式．本文给出了该检验的确切概率计算方法．     

Elliptic integral solutions of spatial elastica of a thin straight rod bent under concentrated terminal forces

In this article, we solve in closed form a system of nonlinear differential equations modelling the elastica in space of a thin, flexible, straight rod, loaded by a constant thrust at its free end. Common linearizations of strength of materials are of course not applicable any way, because we analyze great deformations, even if not so large to go off the linear elasticity range. By passing to cylindrical coordinates ρ, θ, z, we earn a more tractable differential system evaluating ρ as elliptic function of polar anomaly θ and also providing z through elliptic integrals of I and III kind. Deformed rod’s centerline is then completely described under both tensile or compressive load. Finally, the planar case comes out as a degeneracy, where the Bernoulli lemniscatic integral appears.     

无严格互补松驰条件的序列线性方程组新算法

该文通过构造特殊形式的有效集来逼近KKT点处的有效集，给出了一个任意初始点下的序列线性方程组新算法，并证明了该算法在没有严格互补松驰条件的情况下具有全局收敛性和一步超线性收敛性。      

线性加指数效用函数的组合投资研究

应用无差异曲线法较好地解决了在投资决策分析中具有特殊重要地位的线性加指数效用函数的最优组合投资比例的求解问题,并给出实例予以说明.     

截断情况下线性回归模型响应变量均值的经验似然

本文讨论了在带有截断情况的线性回归模型中 ,响应变量均值的估计问题 .将经验似然的方法应用到带有截断情况的回归模型中 ,在估计响应变量的均值时构造了调整的经验似然统计量 ,证明了在一定的条件下 ,该统计量渐近服从 χ2 分布 ,给出了均值的置信区间 ,并与正态下得到的结果进行了比较 ,模拟的结果说明了经验似然的优良性 .