Linearized and rational approximation method for solving non‐linear Burgers' equation

A new numerical method called linearized and rational approximation method is presented to solve non‐linear evolution equations. The utility of the method is demonstrated for the case of differentiation of functions involving steep gradients. The solution of Burgers' equation is presented to illustrate the effectiveness of the technique for the solution of non‐linear evolution equations exhibiting nearly discontinuous solutions. Copyright © 2004 John Wiley & Sons, Ltd.     

An existence result for a quadrature surface free boundary problem

The aim of this paper is to present two different approachs in order to obtain an existence result to the so-called quadrature surface free boundary problem. The first one requires the shape derivative calculus while the second one depends strongly on the compatibility condition of the Neumann problem. A necessary and sufficient condition of existences is given in the radial case.     

A note on generalized averaged Gaussian formulas

We have recently proposed a very simple numerical method for constructing the averaged Gaussian quadrature formulas. These formulas exist in many more cases than the real positive Gauss–Kronrod formulas. In this note we try to answer whether the averaged Gaussian formulas are an adequate alternative to the corresponding Gauss–Kronrod quadrature formulas, to estimate the remainder term of a Gaussian rule.     

A six-dimensional quadrature procedure

An account is given of the use of Gaussian quadrature product formulae in the evaluation of certain six-dimensional, two-centre integrals involving one-electron Green's functions. These integrals occur in a new molecular variational principle recently proposed by Hall, Hyslop and Rees [1] from which an approximate energy may be derived which can be shown to be at least as good as that obtained from the Rayleigh-Ritz principle. Reductions in computing time are realized by removing certain singularities using a subtraction technique and also by using an empirically determined Richardson-type extrapolation formula.This paper was presented during the session on numerical integration methods for molecules of the 1970 Quantum Theory Conference in Nottingham. It has been revised in the light of the interesting discussion which followed.     

一种6~18 GHz宽带高精度有源移相器

设计了一种6 bit 6~18 GHz工作频段的宽带高精度有源移相器。片上集成了输入无源巴伦、逻辑编码器、RC多相滤波器、矢量合成单元、数控单元等。该移相器的设计采用55 nm CMOS工艺实现,芯片尺寸为1.29 mm×0.9 mm,移相器核心尺寸为1.02 mm×0.58 mm。后仿结果表明,在6~18 GHz频率范围内,增益误差RMS值小于1 dB,相位误差RMS值小于0.75°,输入回波损耗、输出回波损耗分别小于-8.5 dB、-8.9 dB,芯片总功耗为20.7 mW。该6 bit移相器的相对带宽为100%,覆盖C、X和Ku波段,适用于雷达探测等领域。     

On the convergence of multipoint Padé-type approximants and quadrature formulas associated with the unit circle

We study the convergence of rational interpolants with prescribed poles on the unit circle to the Herglotz-Riesz transform of a complex measure supported on [–, ]. As a consequence, quadrature formulas arise which integrate exactly certain rational functions. Estimates of the rate of convergence of these quadrature formulas are also included.This research was performed as part of the European project ROLLS under contract CHRX-CT93-0416.     

The zeros of Faber polynomials generated by an -star

It is shown that the zeros of the Faber polynomials generated by a regular -star are located on the -star. This proves a recent conjecture of J. Bartolomeo and M. He. The proof uses the connection between zeros of Faber polynomials and Chebyshev quadrature formulas.

     

Comparison study of several numerical integration schemes used in calculations of density functional theory

Several numerical integration schemes for the evaluation of matrix elements in density functional theory calculations have been studied and compared by computational practice. The best scheme was found to be the combination of the atomic partition function proposed by Becke with the scaled generalized Gauss-Laguerre quadrature formula for radial integration suggested by Yang, which achieve the highest convergence rate to the numerical integration. With the same number of integration points, the accuracy of the calculated results by this scheme is higher by 1 to 2 orders of magnitudes than that by other schemes. The reason for achieving higher accuracy by this scheme has been proposed preliminarily.     

瑞利衰落信道采用组合发射机SC/接收机 MRC的MQAM性能分析

日益增长的无线业务需求要求提高衰落信道上无线通信的频谱利用率.本文研究一种使用组合发射机SC/接收机MRC(SC/MRC)的MQAM方案,推导其在平坦瑞利衰落信道上的误符号率,分析无线信道时变特性对系统性能的影响.数值计算结果表明该组合空间分集方案可以通过调整发射天线和接收天线的数目来获得比传统接收机分集接收更大的分集增益.     

SQM-OTFT: A compact model of organic thin-film transistors based on the symmetric quadrature of the accumulation charge considering both deep and tail states

A physically-based compact model of organic thin-film transistors suitable for CAD simulators is proposed. It is worked out by means of a newly developed and particularly simple form of the charge-sheet model: the symmetric quadrature of the accumulation charge. The model is based on the variable-range hopping and accounts for both deep and tail states. It is simple, symmetric, accurately accounts for the below-threshold, linear, and saturation regimes via a unique formulation. The symmetric quadrature is accurate within 5% in all regions of operation and the resulting current model is suitable both for p- and n-type transistors. The model leads to a significant simplification of the drain current and of the quasi-static expressions of the terminal charges based on the Ward–Dutton partition. Finally, the symmetric quadrature leads to an explicit and analytically tractable solution for the surface potential as a function of position in the device channel that can be extremely useful to implement advanced physical effects.