On Solving Three-Dimensional Electrostatic Field Distribution by Multigrid Method

A highly efficient numerical algorithm using the multigrid method (MGM) is introduced to solve a three-dimensional (3-D)field distribution. Taking advantage of the restriction and prolongation in MGM computation, a more accurate field distribution can be acquired rapidly. According to the MGM algorithm, a 3-D program is accomplished, which can solve the field distributions in electron optical systems for various electrostatic lenses. The 3-D field distribution in an electrostatic concentric spherical model is tested with the MGM algorithm and with an algorithm based on the finite difference method (FDM). Comparing these two results in terms of computational efficiency and computational accuracy, it appears that MGM is superior to FDM, which is now used the most in field computations. This paper shows that the 3-D field computation using MGM greatly improves the computational efficiency of field distributions in electron optical systems and shortens the computational time.     

基于分数阶傅立叶变换的线性调频回波参数估计

本文提出了一种适用于宽带线性调频回波的分数阶傅立叶变换参数估计方法。它通过寻找合适的信号代替发射信号做模版,使得模版信号与接收信号的模糊函数匹配度高,峰值尖锐,失真率低。再利用分数阶傅立叶变换与模糊函数的关系,使用两次分数阶域的峰值搜索代替原有的一次二维搜索降低计算量。仿真实验结果表明,本文提出的方法在精确估计宽带回波的时延和频移的同时降低了计算复杂度。     

关于某些循环矩阵的特征值

本文给出了某些循环矩阵特征值的具体形状和降阶计算方法.     

Computer simulation of moist atmospheric convection with finite elements

A computer simulation is made of cellular convection in a moist atmosphere in an endeavour to obtain a computer model which more closely approximates the observed modes of convection. A finite element Galerkin technique, with Taylor approximation and Crank-Nicolson, is employed and comparisons are made with the author's earlier finite element models of convection in an absolutely unstable atmosphere and with finite difference models. It is found that the inclusion of the moisture effects alters the structure of a cell to that of a narrow ascending region and a wider descending region with the former of larger velocities than the latter, and also alters the preferred mode of convection by increasing the aspect ratio. This more closely resembles that which is observed in the atmosphere.     

On the rapid computation of various polylogarithmic constants

We give algorithms for the computation of the -th digit of certain transcendental numbers in various bases. These algorithms can be easily implemented (multiple precision arithmetic is not needed), require virtually no memory, and feature run times that scale nearly linearly with the order of the digit desired. They make it feasible to compute, for example, the billionth binary digit of or on a modest work station in a few hours run time. We demonstrate this technique by computing the ten billionth hexadecimal digit of , the billionth hexadecimal digits of and , and the ten billionth decimal digit of . These calculations rest on the observation that very special types of identities exist for certain numbers like , , and . These are essentially polylogarithmic ladders in an integer base. A number of these identities that we derive in this work appear to be new, for example the critical identity for :

     

Parameter inference in small world network disease models with approximate Bayesian Computational methods

Small world network models have been effective in capturing the variable behaviour of reported case data of the SARS coronavirus outbreak in Hong Kong during 2003. Simulations of these models have previously been realized using informed “guesses” of the proposed model parameters and tested for consistency with the reported data by surrogate analysis. In this paper we attempt to provide statistically rigorous parameter distributions using Approximate Bayesian Computation sampling methods. We find that such sampling schemes are a useful framework for fitting parameters of stochastic small world network models where simulation of the system is straightforward but expressing a likelihood is cumbersome.     

轮换对称性在微分与重积分计算中的应用

本文介绍轮换对称的定义以及应用条件,并列举若干例子说明了如何利用轮换对称性简化多元函数微分与重积分的计算。     

晴朗无云天空光谱辐射的近似计算模型

 利用大气光学质量和大气气溶胶光学厚度的经验公式,由HITRAN数据库获得大气分子谱线参数,基于辐射传输方程,给出了晴朗无云天空光谱辐射的近似计算模型。根据该近似计算模型对晴朗无云天空光谱辐射亮度进行的计算结果表明：天空光谱辐射亮度曲线上存在明显的O₂和H₂O吸收线;晴朗无云天空辐射的光谱分布偏蓝,天空亮度主要集中在短波段部分;太阳角小的天空光谱亮度出现“红移”现象;由于大气厚度变大,近地平的天空辐射亮度较大。     

What is the basic chromophore of a dye?

Taking the 4,5-diphenyl-substituted 2-dimethylamino-3-azacyclopentadienone (4) as an example its colour has been discussed in relation to different basic chromophores (parent chromophores). The parent chromophore can be defined either as the structure which has nearly the same absorption wavelength as the dye under consideration or as the substructure which is electronically most closely related to the dye. In the case of4 both considerations lead to different results. Based on the correlation diagram between the electronic states involved in the electronic excitation the long-wavelength absorption of4 is better understood in terms of the merocyanine parent chromophore than in terms of a betainic substructure, which should have the same colour as4 and is the parent chromophore according toKlessinger. This conclusion is drawn fromPPP configuration analysis of the wavefunctions of4 relative to different molecular substructures. The molecular geometry predicted by the geometry-optimized MINDO/3 and QCFF/Pi calculations provided additional arguments in favour of the cyclomerocyanine structure of4. In respect to the colour4 belongs to a new series of cyclic-conjugated chromophoric systems.