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.     

DIMENSIONS FORRANDOM SELF——CONFORMAL SETS

A set is called regular if its Hausdorff dimension and upper box-counting dimension coincide. In this paper, we prove that the random self-con formal set is regular almost surely. Also we determine the dimen-sions for a class of random self-con formal sets.     

非负Ricci曲率开流形的拓扑

我们证明了对于具有非负Rieei曲率,大体积增长且内半径下有界的完备n维Riemann流形,只要存在常数C>0使得 则它微分同胚于欧式空间Rn.我们还证明了在某些pinching条件下具有非负射线曲率的完备n维Riemarm流形微分同胚与Rn,改进了已知的结果.     

THE SPACE—FRACTIONAL TELEGRAPH EQUATION AND THE RELATED FRACTIONAL TELEGRAPH PROCESS

The space-fractional telegraph equation is analyzed and the Fourier transform of its fundamental solution is obtained and discussed.A symmetric process with discontinuous trajectories, whose transition function satisfies the space-fractional telegraph equation, is presented. Its limiting behaviour and the connection with symmetric stable processes is also examined.     

具时滞的奇异(n-1,1)共轭边值问题的多重正解

Abstract. This paper discusses the singular (n-l, 1) conjugate boundary value problem as fol-lows by using a fixed point index theorem in cones     

B2C(1A1)和BC2(2A′)的结构与解析势能函数

采用单双取代的二次组态相互作用方法，分别选用6-311++G(d,p)和6-311G(df,pd)基组，对B₂C和BC₂分子的结构进行了优化，得到这两个分子的基态结构为C_2v和C_s，基态电子状态为¹A₁和²A′，同时还得到了它们的平衡几何结构、离解能、谐振频率和力常数. 关键词： 碳化硼 Murrell-Sorbie函数 谐振频率 势能函数     

激子自旋弛豫对简并量子点发射光子对纠缠度的影响

利用粒子数运动方程和量子回归理论，计算了单个半导体量子点双激子体系脉冲激发下粒子在各能级间辐射跃迁的二阶交叉相关函数以及系统发射光子对的偏振密度矩阵.分析了激子态能级简并量子点体系发射光子对偏振纠缠特性，讨论了纠缠度随激子态间自旋弛豫的变化关系.研究表明，激子自旋弛豫会破坏该系统发射光子对的纠缠度. 关键词： 纠缠光子对 半导体量子点 二阶相关函数     

X射线探测器图像的恢复研究

图像退化是引起X射线探测器图像质量下降的主要原因。图像恢复,可以提高系统的分辨率和对比度灵敏度。通过对射线成像系统图像退化的分析,介绍了反滤波信号恢复方法,并提出了一种近似恢复算法,该算法将反滤波恢复近似为除法运算的恢复。给出了恢复前后的图像及标准差的对比,实验结果表明了该算法的有效性。