Jordan函数r次方Jrk（n）的均值误差项研究

设ｋ，ｒ分别是自然数和非零整数，Ｊｋ（ｎ）是Ｊｏｒｄａｎ函数．文［３］求出了和式∑ｎ≤ｘＪｒｋ（ｎ）的渐近公式．以Ｅ（ｘ；ｋ，ｒ）表示该公式中的误差项，本文研究了Ｅ（ｘ；ｋ，ｒ）的算术均值和积分均值     

碳原子线的电子传输特性

单分子电子器件的电子传输特性是当前分子电子学领域研究的热点.本文采用第一原理的ab inito法与格林函数方法,对Au电极-碳原子线-Au电极体系的电子结构以及电子传输等特性进行了分析,给出了C5、C10与C15原子线的电导 -电压曲线与伏安曲线.研究结果表明:碳原子线与Au电极之间的"接触"(结合)既有共价键的成分,又有离子键的成分;碳原子线的电导率及伏安特性具有特殊的量子效应和尺寸效应.     

q-Deformed Gelfand-Dickey系列规范变换的行列式表示

Gelfand-Dickey系列是十分重要的可积系统.本文用规范变换来讨论q-Deformed GelfandDickey系列的解,得到了由两种基本规范变换迭代(n+k)次产生的规范变换算子Tn+k的行列式表达,并由此给出规范变换后的τ函数Tq(n+k)的形式.     

有限元超收敛新论

本文从三个方面讨论二阶椭圆问题有限元超收敛．1．一致网格上的新超收敛结果．利用新的“投影型插值”,我们解决了高次三角形元的超收敛问题．2．一般网格的超收敛性．利用局部插值处理和局部磨光处理我们获得了整体超收敛性结果．3．关于当前的两种超收敛技巧．Cornell学派利用一个精致的内估计和网格的点对称性,获得了一个“普遍”的结果,中国学派利用两个基本估计和离散Green函数理论获得了令人满意的结果,两者均很复杂．本文综合了两个学派的方法,简洁地证得上述普遍结果．     

Predictor-Corrector Smoothing Methods for Monotone LCP

In this paper, we analyze the global and local convergence properties of two predictor-corrector smoothing methods, which are based on the framework of the method in [1], for monotone linear complementarity problems (LCPs). The difference between the algorithm in [1] and our algorithms is that the neighborhood of smoothing central path in our paper is different to that in [1]. In addition, the difference between Algorithm 2.1 and the algorithm in [1] exists in the calculation of the predictor step. Comparing with the results in [1],the global and local convergence of the two methods can be obtained under very mild conditions. The global convergence of the two methods do not need the boundness of the inverse of the Jacobian. The superlinear convergence of Algorithm 2.1‘ is obtained under the assumption of nonsingularity of generalized Jacobian of Φ(x,y) at the limit point and Algorithm 2.1 obtains superlinear convergence under the assumption of strict complementarity at the solution. The efficiency of the two methods is tested by numerical experiments.     

Inequalities of Hadamard Type for r-Convex Functions in Carnot Groups

For a Carnot group G,we establish the relationship between extended mean values and r-convexfunctions which is introduced in this paper,which is a class of inequalities of Hadamard type for r-convexfunction on G.     

Explicit Expressions for the Ruin Probabilities of Erlang Risk Processes with Pareto Individual Claim Distributions

In this paper we first consider a risk process in which claim inter-arrival times and the time untilthe first claim have an Erlang (2) distribution.An explicit solution is derived for the probability of ultimateruin,given an initial reserve of u when the claim size follows a Pareto distribution.Follow Ramsay,Laplacetransforms and exponential integrals are used to derive the solution,which involves a single integral of realvalued functions along the positive real line,and the integrand is not of an oscillating kind.Then we showthat the ultimate ruin probability can be expressed as the sum of expected values of functions of two differentGamma random variables.Finally,the results are extended to the Erlang(n) case.Numerical examples aregiven to illustrate the main results.     

The General Solution of Ming Antu＇s Problem

In two centuries ago,Ming Autu discovered the famous Catalan numbers while he tried to expand the function sin(2px) as power series of sin(x) for the case p=1,2,3.Very recently,P.J.Larcombe shows that for any p,sin(2px) can always be expressed as an infinite power series of sin(x) involving precise combinations of Catalan numbers as part of all but the initial p terms and gave all expansions for the case p=4,5.The present paper presents the desired expansion for arbitrary integer p.     

钝体后湍流预混燃烧的PDF模拟

本文采用PDF方法对矩形燃烧室内钝体后的湍流预混火焰进行了数值模拟。脉动速度-频率-标量联合的PDF输运方程用Monte Carlo方法求解,质量、动量和能量的平均值由基于无结构网格的有限体积法求解,压力通过状态方程获得。PDF方程中所需的平均密度、平均速度和压力由有限体积法提供,并将用Monte Carlo方法求出的雷诺应力、化学反应源项和比热比传递给有限体积法。本文对丙烷和空气燃烧的不同简化化学反应机理进行了研究,并与实验结果进行比较,获得满意的结果。     

BERNOULLI CONVOLUTIONS ASSOCIATED WITH CERTAIN NON——PISOT NUMBERS

The Bernoulli convolution Vλ measure is shown to be absolutely continuous with L^2 density for almost all 1/2＜λ＜1, and singular if λ^-1 is a Pisot number. It is an open question whether the Pisot type Bernoulli conuolutions are the only singular ones. In this paper, we construct a family of non-Pisot type Bernoulli convo-lutions Vλ such that their density functions, if they exist, are not L^2. We also construct other Bernolulli convo-lutions whose density functions if they exist, behave rather badly.