Convergence in Conformal Field Theory

Convergence and analytic extension are of fundamental importance in the mathematical construction and study of conformal field theory. The author reviews some main convergence results, conjectures and problems in the construction and study of conformal field theories using the representation theory of vertex operator algebras. He also reviews the related analytic extension results, conjectures and problems. He discusses the convergence and analytic extensions of products of intertwining operators (chiral conformal fields) and of q-traces and pseudo-q-traces of products of intertwining operators. He also discusses the convergence results related to the sewing operation and the determinant line bundle and a higher-genus convergence result. He then explains conjectures and problems on the convergence and analytic extensions in orbifold conformal field theory and in the cohomology theory of vertex operator algebras.     

The distribution of the likelihood ratio for mixtures of densities from the one-parameter exponential family

We here consider testing the hypothesis ofhomogeneity against the alternative of a two-component mixture of densities. The paper focuses on the asymptotic null distribution of 2 log _n , where _n is the likelihood ratio statistic. The main result, obtained by simulation, is that its limiting distribution appears pivotal (in the sense of constant percentiles over the unknown parameter), but model specific (differs if the model is changed from Poisson to normal, say), and is not at all well approximated by the conventional ₍₂₎ ² -distribution obtained by counting parameters. In Section 3, the binomial with sample size parameter 2 is considered. Via a simple geometric characterization the case for which the likelihood ratio is 1 can easily be identified and the corresponding probability is found. Closed form expressions for the likelihood ratio _n are possible and the asymptotic distribution of 2 log _n is shown to be the mixture giving equal weights to the one point distribution with all its mass equal to zero and the ²-distribution with 1 degree of freedom. A similar result is reached in Section 4 for the Poisson with a small parameter value (0.1), although the geometric characterization is different. In Section 5 we consider the Poisson case in full generality. There is still a positive asymptotic probability that the likelihood ratio is 1. The upper precentiles of the null distribution of 2 log _n are found by simulation for various populations and shown to be nearly independent of the population parameter, and approximately equal to the (1–2)100 percentiles of ₍₁₎ ² . In Sections 6 and 7, we close with a study of two continuous densities, theexponential and thenormal with known variance. In these models the asymptotic distribution of 2 log _n is pivotal. Selected (1–) 100 percentiles are presented and shown to differ between the two models.     

EFFECTS OF SOURCE PROPERTIES ON CUTOFF FREQUENCY f_(max)

The cutoff frequency f_(max) of radiation from earthquakes is one of the important parameters for studying the source process. By theoretical analysis and numerical experiments on acceleration Fourier spectrum it is suggested that f_(max) mainly depends on the lower values of slip rise time. This result can be used to explain the observational fact that the greater the earthquake magnitude, the smaller the value of f_(max).     

Inclusion of α-phenyl-N-p-methylphenyl Nitrone in β- Cyclodextrin: Formation of 1G : 1H and 1G : 2H Complexes and the Remarkably Fast 1,3-Dipolar Cycloaddition of the 1G : 2H Complex with Olefins in the Solid State

The nitrone is found to be included in the -cyclodextrin cavity in two different stoichiometries viz., 1G : 1H and 1G : 2H – the existence of which is proved by physical methods. The 1G : 2H complex of the nitrone serves as a good potent dipolarophile in the 1,3-dipolar cycloaddition reactions with olefins resulting in rate acceleration and regioselection.     

求解非线性中立型延迟微分方程一类线性多步方法的收敛性

本文致力于带有Lagrang插值的一类线性多步法求解非线性中立型延迟微分方程的误差分析.证明了一个p′阶的线性多步方法配上一个q阶的Lagrang插值导致一个minf[p′,q 1]阶的E-(或EB-)收敛的非线性中立型延迟微分方程数值方法.     

ENERGY ESTIMATES FOR DELAY DIFFUSION-REACTION EQUATIONS

In this paper we consider nonlinear delay diffusion-reaction equations with initial and Dirichlet boundary conditions. The behaviour and the stability of the solution of such initial boundary value problems （IBVPs） are studied using the energy method. Simple numerical methods are considered for the computation of numerical approximations to the solution of the nonlinear IBVPs. Using the discrete energy method we study the stability and convergence of the numerical approximations. Numerical experiments are carried out to illustrate our theoretical results.     

微米光栅加速度计的加工与性能研究

介绍了一种以微米衍射光栅为敏感元件的微机电加速度计敏感头的加工和性能。硅质量块底部加工有铝反射膜,透明玻璃基底上制作有金微米光栅,中间为空气腔,经硅玻璃阳极键合,构成敏感头的核心敏感部件。光源透过透明基底,照射在光栅上,在反射场内会产生一系列衍射级次,且各级次衍射光强与外界加速度之间呈函数关系。完成了微米光栅加速度计敏感头的加工,搭建了实验测试平台,完成了加速度计的灵敏度以及静电驱动性能测试。为未来新型集成式微米光栅加速度计设计和加工提供参考。     

HIRFL-SFC采用平顶波加速的模拟研究

近代物理研究所针对改善兰州重离子加速装置注入器（HIRFL-SFC）引出束流的品质,将主要考虑改进高频系统以提高Dee盒的加速电压、增加一个相位狭缝和采用平顶波加速等。其中采用平顶波加速可以有效地减小扇形聚焦回旋加速器(SFC)引出束流的能散并且提高其自身的传输效率。采用回旋加速器束流模拟程序AGORA对SFC进行模拟计算,并比较有无平顶波加速系统下束流品质的变化。结果表明,采用平顶波加速后,SFC的引出束流能散明显减小,而且在引出偏转板入口处束流的径向尺寸及圈间距满足单圈引出的条件。     

强激光脉冲在部分离化等离子体中的传播特性

采用变分法给出了强激光脉冲在部分离化等离子体中传播的参数演化方程,其中考虑了相对论自聚焦、有质动力激发尾波场以及部分离化非线性极化强度的影响。通过非线性动力学分析的方法,得到了强激光脉冲以恒定焦斑半径传播时的激光、等离子体参数匹配条件。研究表明：在部分离化等离子体中,激光自聚焦随着电离程度的增大而增强;有质动力激发的尾波场进一步增强激光脉冲的自聚焦;相对于等离子体密度而言,激光强度对激光脉冲的自聚焦更有影响。     

实时单发测量的汤姆逊离子谱仪

介绍一种使用闪烁体耦合电子倍增电荷耦合器件（EMCCD）的方式对离子进行记录的汤姆逊能谱仪,可实现对离子能谱的实时单发测量。同时,该谱仪利用倾斜电极板对离子进行偏转,可减少由于离子打在电极板上产生的电磁噪声,能够提高实验结果的信噪比。该谱仪在北京大学4.5 MV静电加速器和26 MV串列加速器上进行了标定实验,测量了闪烁体将离子转化成光子后的探测效率,实验结果也验证了该谱仪的可行性和稳定性。该汤姆逊谱仪将用于北京大学激光加速器CLAPA对离子束流的测量研究。