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).     

A Petrov-Galerkin method with quadrature for elliptic boundary value problems

We propose and analyse a fully discrete Petrov–Galerkinmethod with quadrature, for solving second-order, variable coefficient,elliptic boundary value problems on rectangular domains. Inour scheme, the trial space consists of C² splines of degreer 3, the test space consists of C⁰ splines of degree r –2, and we use composite (r – 1)-point Gauss quadrature.We show existence and uniqueness of the approximate solutionand establish optimal order error bounds in H², H¹ and L² norms.     

A Unified Analysis of Quaternary DS-CDMA Systems with Arbitrary Chip Waveforms and Its Applications

This paper is to present a systematic performance analysis of asynchronous quaternary direct sequence code division multiple access (DS-CDMA) systems using random signature sequences with arbitrary chip waveforms. The simplified improved Gaussian approximation method for bit error rate computation is extended to include arbitrary time-limited (full response or partial response) or band-limited chip waveforms with arbitrary receiver filters. As a time-limited partial response chip waveform modulation format, the well-known power and spectral efficient superposed quadrature amplitude modulation with matched filter or zero-forcing filter is evaluated, and the results show that the optimum zero-forcing filter will yield a performance better than the matched filter counterpart. For band-limited chip waveforms, based on an elementary density function of a second-order polynomial, a class of second-order continuity pulses is proposed for analysis. It is found that all common band-limited pulses are only its special cases. As a member of the class, the widely used frequency domain raised cosine pulse has the worst anti-multiuser-access-interference capability, which has been pointed out in (H. H. Nguyen, Proceedings of IEEE Canadian Conference on Electrical & Computer Engineering, 2002, pp. 1271–1275).     

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.     

Tight Gaussian 4-Designs

A Gaussian t-design is defined as a finite set X in the Euclidean space ℝⁿ satisfying the condition: for any polynomial f(x) in n variables of degree at most t, here α is a constant real number and ω is a positive weight function on X. It is easy to see that if X is a Gaussian 2e-design in ℝⁿ, then . We call X a tight Gaussian 2e-design in ℝⁿ if holds. In this paper we study tight Gaussian 2e-designs in ℝⁿ. In particular, we classify tight Gaussian 4-designs in ℝⁿ with constant weight or with weight . Moreover we classify tight Gaussian 4-designs in ℝⁿ on 2 concentric spheres (with arbitrary weight functions).