Rotationally averaged linear absorption spectra beyond the electric-dipole approximation

ABSTRACT

Based on the recently developed implementation of the full semi-classical field–matter interaction operator, we present a numerically accurate yet efficient scheme to perform rotational averaging of linear absorption spectra beyond the electric-dipole approximation. This allows for a gauge-origin independent determination of UV/vis and X-ray absorption spectra for randomly oriented systems such as multilayers, liquids, and gas phase samples. The approach is illustrated by the determination of spectral intensities of electric-dipole allowed π → π* transitions and electric-dipole forbidden n → π* transitions in the UV–vis region of the spectrum as well as electric-dipole forbidden 1s → 3d transitions in the X-ray region of the spectrum. The employed Lebedev quadrature scheme shows very fast convergence with respect to the number of symmetry-independent quadrature points – in all considered cases, the oscillator strengths for the randomly oriented systems are fully converged with use of only seven quadrature points.     

聚变堆深穿透屏蔽计算方法研究

为了提高具有复杂孔道的聚变堆深穿透屏蔽问题的计算精度,研究了蒙特卡罗法和离散纵标法(MC-S_N)的耦合方法。同时,在权重差分方法的基础上引入具有自适应特性的定向权重和指数定向权重方法,并基于勒让德-切比雪夫求积组和极角细化技术研究了偏倚求积组,有效解决聚变中子穿透能力强、强各向异性散射等屏蔽计算难点。通过与MCNP程序模拟结果的比较分析发现,这些研究方法能有效提高聚变堆深穿透屏蔽计算的精度。     

Computation of Bessel and Airy Functions and of Related Gaussian Quadrature Formulae

Procedures are described for the high-precision calculation of the modified Bessel function K (x), 0 < < 1, and the Airy function Ai(x), for positive arguments x, as pre-requisites for generating Gaussian quadrature rules having these functions as weight function.     

Positivity of the Weights of Interpolatory Quadrature Formulae with Jacobi Abscissae

We consider interpolatory quadrature formulae, relative to the Legendre weight function w(t) = 1 on [–1, 1], having as nodes the zeros of the nth degree Jacobi polynomial P _n ^{(, )} plus the points 1 and –1. We show that in specific domains of and gb the weights of these formulae are almost all positive, exceptions occurring only with the weights corresponding to 1 and –1.     

Numerical Quadratures for Hadamard Hypersingular Integrals

In this paper,we develop Gaussian quadrature formulas for the Hadamard fi- nite part integrals.In our formulas,the classical orthogonal polynomials such as Legendre and Chebyshev polynomials are used to approximate the density function f(x)so that the Gaussian quadrature formulas have degree n-1.The error estimates of the formulas are obtained.It is found from the numerical examples that the convergence rate and the accu- racy of the approximation results are satisfactory.Moreover,the rate and the accuracy can be improved by choosing appropriate weight functions.     

Analysis of convective diffusion problem with first-order chemical reaction by boundary element method

A boundary element method is presented for a steady state convective diffusion problem with a first-order chemical reaction. In the chemical reaction system the usual conservation law for calculation of the diagonal components of the matrix H cannot be satisfied. Thus in the boundary element formulation the emphasis is laid on how to compute these diagonal components. The main aim of this paper is to present the method of numerical quadrature to obtain the principal values, using the splitting technique to treat the singular integration.     

中频采样和数字正交器的原理及工程实现

阐述了中频采样和数字正交器的原理，给出了三种新的中频采样和数字正交的工程实现方法，测试后的性能指标完全能满足现代雷达的实际要求。     

基于信号I、Q通道信号分布的MPSK信号分类

本文针对MPSK信号的识别,通过对MPSK信号I、Q通道信号的分布规律进行分析,寻找到一种在低信噪比下仍然具有较高识别率的分类准则。该分类准则首先根据M≤2和M≥4信号的特点进行粗识别,再根据各类信号在经过I、Q通道后的分布规律最后进行识别。计算机仿真计算了算法的性能。     

An Error Expansion for some Gauss–Turán Quadratures and <Emphasis Type="Italic">L</Emphasis><Superscript>1</Superscript>-Estimates of the Remainder Term

Our aim in this paper is to obtain error expansions in the Gauss–Turán quadrature formula ∫₋₁¹f(t)w(t) dt=∑_ν=1ⁿ∑_i=0^2sA_i,νf⁽ⁱ⁾(τ_ν)+R_n,s(f), in the case when f is an analytic function in some region of the complex plane containing the interval [−1,1] in its interior. Using a representation of the remainder term R_n,s(f) in the form of contour integral over confocal ellipses, we obtain R_n,1(f) for the four Chebyshev weights and R_n,2(f) for the Chebyshev weight of the first kind. Also, we get a few new L¹-estimates of the remainder term, which are stronger than the previous ones. Some numerical results, illustrations and comparisons are also given. AMS subject classification (2000) 41A55, 65D30, 65D32.Received January 2004. Accepted October 2004. Communicated by Lothar Reichel.M. M. Spalević: This work was supported in part by the Serbian Ministry of Science and Environmental Protection (Project: Applied Orthogonal Systems, Constructive Approximation and Numerical Methods, grant number 2002).     

The best quadrature formula based on Hermite information for the class <Emphasis Type="Italic">KW</Emphasis><Superscript>2</Superscript> [<Emphasis Type="Italic">a,b</Emphasis>]

The best quadrature formula has been found in the following sense: for a function whose norm of the second derivative is bounded by a given constant and the best quadrature formula for the approximate evaluation of integration of that function can minimize the worst possible error if the values of the function and its derivative at certain nodes are known. The best interpolation formula used to get the quadrature formula above is also found. Moreover, we compare the best quadrature formula with the open compound corrected trapezoidal formula by theoretical analysis and stochastic experiments.