C60、C60F60及C60H60“分子滚珠”的压缩特性与电子结构

采用量子分子动力学技术,模拟了C60、C60F60与C60H60分子的压缩过程,计算了这些"分子滚珠"受压变形后的电子结构.根据计算结果,对比、分析了三种分子的压缩力学特性以及压缩变形对其电子结构的影响.研究表明,1)三种分子的抗压缩载荷与能量吸收能力有C60F60＞C60H60＞C60的排序,但抗变形能力相当;2)随着压缩变形的增大,三种分子的化学活性增加,但相同应变下,C60F60和C60H60分子有着比C60更好的化学稳定性.     

The local time of self-intersections of Brownian motions as generalized Brownian functionals

In this Letter, we show that the local time of self-intersections ofd-dimensional Brownian motions is a generalized Brownian functional in the sense of Hida.     

水溶性C60衍生物的电化学合成及光谱分析

通过电化学方法合成一种具有良好水溶性并能在水及空气中长期稳定存在的Ｃ６０衍生物。用电 方法确定了该电解产物带负电荷，红外光谱及近红外光谱的表片，显示该水溶性Ｃ６０衍生物稳定键合的ＯＨ基，所以表现出强亲水性。     

Comparison of electrical parameters of Zn/p-Si and Sn/p-Si Schottky barrier diodes

In this study, current-voltage (I-V) and capacitance-voltage (C-V) characteristics of metal-semiconductor (MS) Zn/p-Si and Sn/p-Si Schottky diodes, with high resistivity silicon structures, are investigated. The parameters of series resistance (R_S), the ideality factor (n) and the barrier height (Φ_b) are determined by performing different plots from the forward bias current-voltage (I-V) and reverse bias capacitance-voltage (C-V) characteristics. Thus, the barrier heights (Φ_b) for the Si Schottky diodes obtained between 0.725 and 1.051 eV, the ideality factor (n) between 1.043 and 1.309, and the series resistance (R_S) between 12.594 and 12.950 kΩ. The energy distribution of interface states density was determined from the forward bias I-V characteristics by taking into account the bias dependence of the effective barrier height. It was concluded that the density of interface states in the considered energy range are in close agreement with each other values obtained for Zn/p-Si and Sn/p-Si Schottky diodes.     

二维R-C60聚合物的核磁共振波谱研究

合成了二维rhombohedral(2D-R)相C60聚合物,对其固体核磁共振(NMR)波谱进行了详细的讨论. 13C固体核磁共振魔角谱(13C MAS NMR )上δ145附近的sp2杂化峰出现展宽并伴有边带,并且在δ72附近出现了一个相对较弱的新的峰.这表明通过[2+2]加环反应在邻近C60分子之间形成了sp3杂化共价键,使得C60分子球笼上出现了五个位置不等价的sp2杂化碳原子,导致位于δ145附近的sp2杂化峰展宽.利用拟合分峰的方法得出了这五个不等价的碳原子的峰的位置,分别位于δ134.6、δ139.6、δ145.1、δ147.9 以及δ149.1,这五个不等价的碳原子数目上的比例关系和核磁共振曲线的积分面积吻合.     

T1uhg杨-泰乐系统：D5d势阱中的各向异性现象

杨-泰乐(Jahn-Teller缩写为JT)系统在其最低的绝热势能面上常常典型地含有一系列相互等同的势阱.在C60分子中，若一个电子占据该分子的三重简并的能量最低电子态，这一具有T1u对称性的电子态将会与具有hg对称性的五重简并振动态发生相互作用，形成所谓的T1uhg JT系统.当考虑电声的非线性相互作用时，该系统的势能面上将出现D5d对称性的势阱并伴随D3d对称性的势垒；反之亦然.本文在幺正平移变换的基础上，引入了标度变换，研究了该JT系统中D5d势阱中的各向异性现象：在电子空间中，非线性项的引入使得 关键词： C60 杨-泰乐效应 各向异性 电声耦合 标度变换     

C60激发三重态被哌嗪猝灭特性研究

本文使用激光诱导瞬态吸收光谱装置,研究了C60激发三重态在乙腈/甲苯混合溶剂中的光物理性质,得到了3C60的激发态寿命、自猝灭速率常数和时间分辩的瞬态吸收光谱.此外,实验中引入了哌嗪作为激发三重态猝灭剂.我们发现哌嗪能有效的猝灭3C60,猝灭速率常数kq接近扩散控制极限.改变混合溶剂的比例,相应的猝灭速率常数值也发生变化,即kq随混合溶剂极性的增加而增加,随溶剂粘度的增加而减小.稳态光解实验反映了反应物向产物转化过程中在紫外-可见波段吸收强度的变化.     

原子、分子和纳米材料中非线性高次谐波的产生:一个潜在的极超快和高能量的新型光源

在原子、分子和纳米材料中的高次谐波为非线性光学开辟了一个崭新的研究领域.其响应时间之短、能量之高,引起了人们的高度重视.目前的研究达到了白热化的程度.还有很多问题没有解决.文章首先简要地介绍了这一个新的领域.然后用一个简单的例子引出有名的辐射截断方程,最后用C60作为一个例子说明如何详细地计算辐射能量谱.     

密度泛函理论计算内掺富勒烯M@C60H60(M=Li、Na)的几何结构和电子性质

采用密度泛函理论中的广义梯度近似(generalized gradient approximation,简称GGA),对M@C_(60)H_(60) (M=Li、Na)几何结构和电子性质进行计算研究.发现M原子的平衡位置处在偏心位置处,并且稳定的存在于一个围绕中心的球体内;掺杂能计算表明:M@C_(60)H_(60)需要在一定的实验条件下才能被合成出来;电子性质分析表明:M原子掺入到C_(60)H_(60)中,对费米能级附近有一定贡献,并产生了1 μB的净磁矩.     

Some connectedness problems in positively curved Finsler manifolds

This paper studies some connectedness problems under the positivity hypothesis of various curvatures (k$k$-Ricci and flag curvature). Our approach uses Morse Theory for general end conditions (see [Ioan Radu Peter, The Morse index theorem where the ends are submanifolds in Finsler geometry, Houston J. Math. 32 (4) (2006) 995–1009]). Some previous results related to the flag curvature were obtained in [Ioan Radu Peter, A connectedness principle in positively curved Finsler manifolds, in: H. Shimada, S. Sabau (Eds.), Advanced Studies in Pure Mathematics, Finsler Geometry, Sapporo 2005-In Memory of Makoto Matsumoto, Mathematical Society of Japan, 2007]. Some results from Riemannian geometry are extended to the Finsler category also. The Finsler setting is much more complicated and the difference between Finsler and Riemann settings will be emphasized during the paper.     

Charged Particles in Monopole Background on Fuzzy Sphere

In this note we study the quantum mechanics of a charged particle on fuzzy sphere and in the presence of magnetic monopoles. We discuss the proper inclusion of the electromagnetic interaction in the Hamiltonian through the covariant form of the momentum operator. We consider two different kinds of monopoles. The first one is associated with projective modules and obtained from the corresponding projector. The second one we obtain by solving directly the noncommutative Maxwell equations over the fuzzy sphere. Among these, are the monopole connections for which the Hamiltonian operator can be diagonalized in an algebraic way.      

Stochastic order and monotonicity in temperature for Gibbs measures

The monotonicity in temperature of the Gibbs mean in Ising-type systems is proved for a class of random variables. In particular, considered are the absolute value of the total magnetization, the cyclomatic number and a percolation variable. The main tool is the stochastic order of the Fortuin-Kasteleyn representation.     

紫外激光和压力共同作用下C60-peapod的聚合相变研究

采用气相扩散方法将C60分子填充到单壁碳纳米管(SWNTs)中,制备出高填充比率的豆荚形纳米材料C60@SWNT,又称为peapod.用金刚石对顶砧(DAC)装置获得高压,在高压下同时利用紫外激光处理样品,通过激光和压力的共同作用研究了C60分子在碳管内的聚合相变.在21.5 Gpa高压下,同时紫外激光(325 nm)照射30 min后,拉曼光谱表明C60分子在碳管内发生了聚合,形成一维链状O相聚合结构,且该相变是不可逆的.紫外激光的引入使样品发生O相聚合所需的压力值低于仅由压力诱导的聚合压力.     

A note on q-weak law of large numbers

q-limit theorems for random variables are arising from non-extensive statistical mechanics. In this note we will prove q-weak law of large numbers using the notions of q-Fourier transform, q-independence, q-weak convergence.     

Local derivative post-processing for the discontinuous Galerkin method

Obtaining accurate approximations for derivatives is important for many scientific applications in such areas as fluid mechanics and chemistry as well as in visualization applications. In this paper we discuss techniques for computing accurate approximations of high-order derivatives for discontinuous Galerkin solutions to hyperbolic equations related to these areas. In previous work, improvement in the accuracy of the numerical solution using discontinuous Galerkin methods was obtained through post-processing by convolution with a suitably defined kernel. This post-processing technique was able to improve the order of accuracy of the approximation to the solution of time-dependent symmetric linear hyperbolic partial differential equations from order k+1$k+1$ to order 2k+1$2k+1$ over a uniform mesh; this was extended to include one-sided post-processing as well as post-processing over non-uniform meshes. In this paper, we address the issue of improving the accuracy of approximations to derivatives of the solution by using the method introduced by Thomée [19]. It consists in simply taking the α$\alpha$th-derivative of the convolution of the solution with a sufficiently smooth kernel. The order of convergence of the approximation is then independent   of the order of the derivative, |α|$|\alpha |$. We also discuss an efficient way of computing the approximation which does not involve differentiation but the application of simple finite differencing. Our results show that the above-mentioned approximations to the α$\alpha$th-derivative of the exact solution of linear, multidimensional symmetric hyperbolic systems obtained by the discontinuous Galerkin method with polynomials of degree k$k$ converge with order 2k+1$2k+1$ regardless of the order |α|$|\alpha |$ of the derivative.     

Some Berwald spaces of non-positive flag curvature

In this paper, by using left invariant Riemannian metrics on some three-dimensional Lie groups, we construct some complete non-Riemannian Berwald spaces of non-positive flag curvature and several families of geodesically complete locally Minkowskian spaces of zero constant flag curvature.     

A three-dimensional Brownian path reflected on a Brownian path is a free Brownian path

Three-dimensional Brownian path reflected on Brownian path is a free Brownian path.Research partially supported by NSF grant DMS 91-00244.     

基于VB的照明专用CAD软件设计

根据点光源和线光源基本模型与光线追迹理论,借助前台开发工具(Visual Basic6.0)和后台开发工具(Microsoft Office Access)开发了一套照明专用CAD软件。该软件既能成功模拟光线追迹,又能借助后台数据库进行光源模型选取、典型结构选取和打印报表等。可满足光学设计人员的需求。     

A generalization of Hamilton’s gradient estimate

In this short note, we obtain a “Φ$\Phi$-gradient estimate” for bounded solutions to the heat equation on compact Riemannian manifolds, which generalizes the well-known Hamilton gradient estimate [R.S. Hamilton, A matrix Harnack estimate for the heat equation, Comm. Anal. Geom. 1 (1993) 113–126]. We derive as applications some useful estimates for the Φ$\Phi$-entropy and the associated heat kernel.     

He原子嵌入富勒烯过程的从头算研究

采用从头算方法,利用密度泛函理论（DFT）模拟不同路径、不同压力条件下He@C60的形成过程。 通过对He嵌入富勒烯的势垒进行研究发现,He原子进入碳笼最可能的路线是：He原子沿曲线路径靠近碳笼,然后沿六边形中心进入碳笼,并最终停留在碳笼中心。并通过模拟不同压力条件下He原子进入碳笼的势垒大小,简要探讨了合成He@C60的最佳条件。并进一步研究了nHe@C60(n=1,2,3)的反应势垒问题。