A combined Filon/asymptotic quadrature method for highly oscillatory problems

A crossing between the asymptotic expansion of an oscillatory integral and Filon-type methods is obtained by applying a Filon-type method to the error term in the asymptotic expansion, which is in itself an oscillatory integral. The efficiency of the approach is investigated through analysis and numerical experiments, revealing a method which in many cases performs better than the Filon-type method. It is shown that considerable savings in terms of the required number of potentially expensive moments can be expected. The case of multivariate oscillatory integrals is discussed briefly. AMS subject classification (2000)  65D30     

On the problem of crack system with an elliptic hole

The problem of cracks with an elliptic hole in an infinite plane is investigated. By introducing the fictitious loads on the hole edge and using the Muskhelishvili method, the problem is reduced to solving a system of mixed-type integral equations in which some are Fredholm equations but others Cauchy-type singular ones. A numerical method is suggested and can be used for the treatment of other similar equations. The numerical results for some typical examples are given, showing that the method is really effective.     

基于对称螺旋型电感和差分二极管的2.4GHz CMOS正交输出压控振荡器

提出了一种产生2.4GHz正交本地振荡信号的方法.它将LC-VCO和两级环路振荡器两种结构组合起来以实现正交输出的低相位噪声压控振荡器.LC网络是由在片对称螺旋型电感和差分二极管组成的.详细论述了VCO原理及其噪声性能.该电路已经用0.25μm单层多晶、五层金属N阱CMOS数字工艺制作.测量结果表明:它可以提供正交的本地振荡信号,其振荡频率可以在300MHz的范围内调节,当仅对差分输出振荡信号的一端进行测试时,振荡频率为2.41GHz时,去偏移中心为600kHz时的相位噪声为-104.33dBc/Hz.而且,它能在很低的电源电压下工作,功耗也很低,所以,它在集成收发机中将得到广泛的应用.     

Quadrature methods for highly oscillatory linear and nonlinear systems of ordinary differential equations: part I

This work presents methods of efficient numerical approximation for linear and nonlinear systems of highly oscillatory ordinary differential equations. We show how an appropriate choice of quadrature rule improves the accuracy of approximation as the frequency of oscillation grows. We present asymptotic and Filon-type methods to solve highly oscillatory linear systems of ODEs, and WRF method, representing a special combination of Filon-type methods and waveform relaxation methods, for nonlinear systems. Numerical examples support this paper. Dedicated to the memory of Rudolf Khanamiryan. AMS subject classification (2000)  65L05, 34E05, 34C15     

The best quadrature formula based on Hermite information for the class KW~2[a,b]

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

A quadrature finite element Galerkin scheme for a biharmonic problem on a rectangular polygon

A quadrature Galerkin scheme with the Bogner–Fox–Schmit element for a biharmonic problem on a rectangular polygon is analyzed for existence, uniqueness, and convergence of the discrete solution. It is known that a product Gaussian quadrature with at least three‐points is required to guarantee optimal order convergence in Sobolev norms. In this article, optimal order error estimates are proved for a scheme based on the product two‐point Gaussian quadrature by establishing a relation with an underdetermined orthogonal spline collocation scheme. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008     

Numerical treatment of retarded boundary integral equations by sparse panel clustering

Stefan Sauter Institute for Mathematics, University of Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland ^{We consider the wave equation in a boundary integral formulation.The discretization in time is done by using convolution quadraturetechniques and a Galerkin boundary element method for the spatialdiscretization. In a previous paper, we have introduced a sparseapproximation of the system matrix by cut-off, in order to reducethe storage costs. In this paper, we extend this approach byintroducing a panel clustering method to further reduce thesecosts.}     

A 2.4GHz Quadrature Output Frequency Synthesizer

A design and implementation for a 2.4GHz quadrature output frequency synthesizer intended for bluetooth in 0.35μm CMOS technology are presented.A differentially controlled quadrature voltage-controlled oscillator (QVCO) is employed to generate quadrature (I/Q) signals.A second-order loop filter,with a unit gain transconductance amplifier having the performance of a third-order loop filter,is exploited for low cost.The measured spot phase noise is –106.15dBc/Hz@1MHz.Close-in phase noise is less than -70dBc/Hz.The synthesizer consumes 13.5mA under a 3.3V voltage supply.The core size is 1.3mm×0.8mm.     

模拟数字电视信号同缆传输的调试问题

有线数字电视整转过渡期间,模拟、数字电视信号同缆传输将会存在一段时间,如何尽量减少模拟、数字两种电视信号的相互干扰是至关重要的问题,这里包括对机房前端的信号调制、网络传输的技术指标分配、终端接收的信号调节等环节,必须严格执行有关的技术规范。     

基于晶体延迟干涉仪的20-Gb/sNRZ-DQPSK解调实验研究

光差分四相移键控(DQPSK)信号解调技术是相位调制光纤通信系统中的关键技术,本文利用钒酸钇(YVO4)晶体设计制作了2 bit延迟干涉仪(DI)作为DQPSK解调器。相对于传统的基于光纤结构的DI,用晶体材料制作的DI具有温度稳定性高的特点,其作为光DQPSK解调技术中的关键器件,具有广泛的应用前景。实验搭建了20 Gb/s光NRZ-DQPSK背靠背实验系统,并利用自主设计制作的DI成功实现了NRZ-DQPSK信号解调。实验结果与计算机仿真计算结果一致。