Rational approximation in the complex plane using a τ-method and computer algebra

Numerous versions of the Lanczos τ-methods have been extensively used to produce polynomial approximations for functions verifying a linear differential equation with polynomial coefficients. In the case of an initial-value problem, an adapted τ-method based on Chebyshev series and the use of symbolic computation lead to a rational approximation of the solution on a region of the complex plane. Numerical examples show that the simplicity of the method does not prevent a high accuracy of results. This revised version was published online in June 2006 with corrections to the Cover Date.     

原子结构参数的改进Xa法计算

六十年代后期,在Hartree－Fock-Slater法的基础上,提出了Xα法［1］．用于原子结构计算的Xα法与HF（Hartree－Fock）法的主要区别在于：用简单的统计平均交换势替代了HF法中计算最为困难的电子交换势,从而在保持较高理论严谨性和计算精确度的同时,大大减少了计算工作量,近年来获得了广泛的应用．我们尝试用经过适当修改的Xα方法,计算原子参数,解决分子结构中的某些问题．用原子参数解决分子问题,历来是化学和物理工作者常用的方法．本工作的意图是引入一个比HF法简单的容易在微机上实现的某种表现原子参数的计算方法,提供…     

高精度半导体激光打标机F-θ镜头设计

为保证半导体激光打标机F-θ镜头的扫描质量,实现系统像高与扫描角的线性变化,需对F-θ镜头给予一定的畸变量,并使其满足等晕条件。分析F-θ镜头工作原理及像差要求,根据1 064 nm半导体激光打标机的光源成像要求选择合适的玻璃材料,合理分配每片透镜的光焦度,以保证等晕成像;根据F-θ镜头线性成像要求,计算系统总畸变量为1.6%,系统总畸变量为系统的实际桶形畸变与相对畸变量之和;在光学系统优化设计时,引入这两项优化参数,优化过程中观察系统成像变化情况。设计结果表明:系统MTF曲线接近衍射极限,F-θ镜头相对畸变小于0.36%,各视场均方根半径均小于艾里斑直径,并且整个系统70%的能量集中在直径为16 μm的圆内,系统总畸变量为1.58%,满足设计指标要求。     

SN方法粒子输运计算程序自动建模关键技术问题研究

在充分调研和分析SN方法粒子输运计算程序自动建模方法的基础上，对建模过程中的模型文件格式识别、属性编辑、空腔处理及自动划分离散网格等关键技术问题进行了研究，并提出了合理可行的解决方法。通过对SNAM程序建模部分功能测试，验证了这些方法的正确性和有效性。This paper presents two approaches to enhance the geometry modeling ability of SN particle transport simulation codes and focus on the key issues that lie in the processing from CAD model to SN code geometry model, e.g. CAD file format support, void modeling, mesh generation and model-editing. SNAM （SN Automatic Modeling system） has been developed as an interface code between commercial CAD software and SN particle transport simmulation codes. The testing results have shown that the algorithm and implementation used in SNAM are efficient and capable of all the necessary processing from CAD model to SN geometry model.     

The population-sample decomposition approach to multivariate estimation methods

In this paper it is argued that all multivariate estimation methods, such as OLS regression, simultaneous linear equations systems and, more widely, what are known as LISREL methods, have merit as geometric approximation methods, even if the observations are not drawn from a multivariate normal parent distribution and consequently cannot be viewed as ML estimators. It is shown that for large samples the asymptotical distribution of any estimator, being a totally differentiable covariance function, may be assessed by the δ method. Finally, we stress that the design of the sample and a priori knowledge about the parent distribution may be incorporated to obtain more specific results. It turns out that some fairly traditional assumptions, such as assuming some variables to be non-random, fixed over repeated samples, or the existence of a parent normal distribution, may have dramatic effects on the assessment of standard deviations and confidence bounds, if such assumptions are not realistic. The method elaborated by us does not make use of such assumptions.     

Dimensional variance inequalities of Brascamp–Lieb type and a local approach to dimensional Prékopaʼs theorem

We give a new approach, inspired by Hörmander?s L²$L^2$-method, to weighted variance inequalities which extend results obtained by Bobkov and Ledoux. It provides in particular a local proof of the dimensional functional forms of the Brunn–Minkowski inequalities. We also present several applications of these variance inequalities, including reverse Hölder inequalities for convex functions, weighted Brascamp–Lieb inequalities and sharp weighted Poincaré inequalities for generalized Cauchy measures.     

假期中顾客以概率θ进人的Geo/G/1(E,SV)排队系统的队长分布

考虑单重休假的Geo/G/1离散时间排队系统,其中在服务员休假期间到达的顾客以概率θ(0<θ≤1)进入系统.通过引入"服务员忙期"和使用全概率分解技术,从任意初始状态出发,研究了队长的瞬态和稳态性质,导出了在任意时刻n瞬态队长分布的z-变换的递推表达式和稳态队长分布的递推表达式,以及稳态队长的随机分解.最后,通过数值实例,讨论了稳态队长分布对系统参数的敏感性,并阐述了获得便于计算的稳态队长分布的表达式在系统容量设计中有重要的价值.     

DFT Study on Some Properties of Polybrominated Phenoxathiin 10-Oxides

With the B3LYP calculation method of density functional theory(DFT)and the 6-31G* basis set,full optimization calculation was made for phenoxathiin10-oxide(PTO)and 135 polybromine phenoxathiin 10-oxides(PBPTOs)with the Gaussian 03 program and molar heat capacity in constant volume(CVθ)value of each molecule in the standard state was obtained.The relation between CVθ and the substitution position and number of bromine atom(NPBS)was studied,and the results indicated good correlation(R2 = 1.000)between CVθ and NPBS of PBPTO compounds.Based on the output file of Gaussian 03 program,molar heat capacity at constant pressure(Cp,m)of PBPTO compounds from 200 to 1,000 K was calculated with the statistical thermodynamics program,and the correlation equation between Cp,m and temperature(T,T-1 and T-2)was obtained with the least-squares method,and the correlation coefficient of the correlation equation(R2)was 1.000.In addition,based on the partition function of each molecule calculated by vibration analysis,the relative rate constant of formation of each molecule was calculated.