The Iyengar inequality,revisited

Detailed analysis shows that the famous Iyengar inequality actually says that the Trapezoidal formula is a central algorithm for approximating integrals over an appropriate interval for the class of functions whose derivatives are bounded by a positive number K in L _∞-sense. The inherent nonlinearity from central algorithms reflects the importance of the Iyengar inequality and thus makes familiar linear methods malfunction when one tries to generalize it. It is shown that the generalization depends on a nonlinear system of equations satisfied by a set of free nodes of a perfect spline. Explicit constructions are obtained in the spirit of the Iyengar inequality for the class of functions whose rth (r≤4) derivatives are bounded by a positive number K in L _∞-sense because a closed solution to the nonlinear system is only available for r≤4. Connections with computational mathematics, especially with best interpolation and best quadrature, are discussed. Numerical experiments are also included. AMS subject classification (2000)  65D30, 41A17     

Natural frequencies of a functionally graded cracked beam using the differential quadrature method

The present work is concerned with the free vibration analysis of an elastically supported cracked beam. The beam is made of a functionally graded material and rested on a Winkler–Pasternak foundation. The line spring model is employed to formulate the problem. The method of differential quadrature is applied to solve it. The obtained results agreed with the previous similar ones. Further, a parametric study is introduced to investigate the effects of the geometric and elastic characteristics of the problem on the values of natural frequencies and mode shape functions.     

A two-dimensional layerwise-differential quadrature static analysis of thick laminated composite circular arches

In this paper, a high accuracy and rapid convergence hybrid approach is developed for two-dimensional static analyses of circular arches with different boundary conditions. The method essentially consists of a layerwise technique in the thickness direction in conjunction with differential quadrature method (DQM) in the axial direction. Hence, the high accuracy and fast convergence of DQM with generality of layerwise formulations for modeling the transverse deformations of arbitrary laminated composite thick arches are combined. This results in superior accuracy with fewer degrees of freedom than conventional finite element method (FEM) or finite difference method (FDM). The convergence behavior of the method is shown and to verify its accuracy, the results are compared with those obtained based on the first order shear deformation Reissner–Naghdi type shell theory and also higher order shear deformation theory. The effects of opening angles, ply angle, boundary conditions, and thickness-to-length ratio on the stress and displacement components are studied.     

非线性抛物型方程有限元法数值积分的有效性

Abstract. The effect of numerical integration in finite element methods applied to a class of nonlinear parabolic equations is considered and some sufficient conditions on the quadrature scheme to ensure that the order of convergence is unaltered in the presence of numerical integration are given. Optimal Lz and H1 estimates for the error and its time derivative are established.     

三共振准相位匹配光学参量振荡器反射抽运场的正交位相压缩

利用全固化单频Nd∶YVO₄激光器抽运由periodically poled lithium niobate(PPLN)准相位匹配晶体组成的光学参量振荡器,通过调节晶体的温度,在信号模与闲置模近简并的情况下,完成了抽运场与两个亚谐波模在腔内同时共振,实现了光学参量振荡器的极低阈值运转(阈值为1.2mW);当抽运功率为阈值抽运功率的2.8倍时,观察到反射抽运光的正交位相压缩,压缩度达1.1dB.数值计算与实验结果一致     

Quantum Statistical Behaviors of Interaction of an Atomic Bose-Einstein Condensate with Laser

We have investigated quantum statistical behaviors of photons and atoms in interaction of an atomic Bose Einstein condensate with quantized laser field. When the quantized laser field is initially prepared in a superposition state which exhibits holes in its photon-number distribution, while the atomic field is initially in a Fock state, it is found that there is energy exchange between photons and atoms. For the input and output states, the photons and atoms may exhibit the sub-Poissonian distribution. The input and output laser fields may exhibit quadrature squeezing, but for the atomic field, only the output state exhibits quadrature squeezing. It is shown that there exists the violation of the Cauchy-Schwartz inequality, which means that the correlation between photons and atoms is nonclassical.``     

A Quadrature Formula Based On Sampling In Meyer Wavelet Subspaces

In this paper we discuss a weighted trapezoidal rule based on sampling in Meyer wavelet subspaces. For a wide class of functions, we obtain convergence and error bounds. Some examples are given to construct sampling functions.     

空时块码与波束形成结合方案及性能分析

Alamouti空时块码与波束形成相结合的方案只使用了两个功率均分的波束,在很多情况下并非最优。该文提出了新的空时块码与波束形成相结合的方案,新方案能够根据信道互相关矩阵的特征值,展开不超过发射端天线数量的波束,在满足空时块码发射天线数量等于波束数量的条件下,与任意码率空时块码结合。该文还利用Gauss-Chebyshev积分对线性调制下新方案的误符号率进行了性能分析,得出了简单的数值计算表达式。新方案由于同时获得了分集增益和波束形成增益,显著提高了系统的性能。     

Molecular integrals by numerical quadrature. I. Radial integration

 This article presents a numerical quadrature intended primarily for evaluating integrals in quantum chemistry programs based on molecular orbital theory, in particular density functional methods. Typically, many integrals must be computed. They are divided up into different classes, on the basis of the required accuracy and spatial extent. Ideally, each batch should be integrated using the minimal set of integration points that at the same time guarantees the required precision. Currently used quadrature schemes are far from optimal in this sense, and we are now developing new algorithms. They are designed to be flexible, such that given the range of functions to be integrated, and the required precision, the integration is performed as economically as possible with error bounds within specification. A standard approach is to partition space into a set of regions, where each region is integrated using a spherically polar grid. This article presents a radial quadrature which allows error control, uniform error distribution and uniform error reduction with increased number of radial grid points. A relative error less than 10⁻¹⁴ for all s-type Gaussian integrands with an exponent range of 14 orders of magnitude is achieved with about 200 grid points. Higher angular l quantum numbers, lower precision or narrower exponent ranges require fewer points. The quadrature also allows controlled pruning of the angular grid in the vicinity of the nuclei. Received: 30 August 2000 / Accepted: 21 December 2000 / Published online: 3 April 2001     

一种无人机载合成孔径雷达宽带波形产生及正交接收的实验研究

对无人机载合成孔径雷达的宽带波形产生及正交接收进行了分析、研究,给出了基于数字直读和模拟正交解调的实验结果,该技术已应用于某超宽带VHF/UHF合成孔径雷达中,取得了较好的效果。