Extrapolation of Mixed Finite Element Approximations for the Maxwell Eigenvalue Problem

In this paper,a general method to derive asymptotic error expansion formulas for the mixed finite element approximations of the Maxwell eigenvalue problem is established.Abstract lemmas for the error of the eigenvalue approximations are obtained.Based on the asymptotic error expansion formulas,the Richardson extrapolation method is employed to improve the accuracy of the approximations for the eigenvalues of the Maxwell system from θ(h2) to θ(h4) when applying the lowest order Nédé1ec mixed finite element and a nonconforming mixed finite element.To our best knowledge,this is the first superconvergence result of the Maxwell eigenvalue problem by the extrapolation of the mixed finite element approximation.Numerical experiments are provided to demonstrate the theoretical results.     

On the boundedness of rough oscillatory singular integrals on Triebel-Lizorkin spaces

We obtain appropriate sharp bounds on Triebel-Lizorkin spaces for rough oscillatory integrals with polynomial phase. By using these bounds and using an extrapolation argument we obtain some new and previously known results for oscillatory integrals under very weak size conditions on the kernel functions.     

碘分子吸收光谱研究

我们用HRD-1型双光栅单色仪记录了碘分子在可见光区域的吸收光谱。确定了大量的带头,由此得出了碘分子的离解限、离解能、力常数和振动基频。实验结果与理论结果很符合。     

Fredholm积-微分方程Galerkin解的加速收敛分析

本文对一般形式的线性Fredholm积-微分方程推导出迭代Galerkin解及其导数的渐近展式，从而得到了迭代解的外推估计，同时还获得了理想的校正结果．     

On extrapolation of Jagerman and Stetter rules

In this paper quadrature rules introduced by Jagerman [1] and Stetter [2] are considered and asymptotic expansions for the error given. This allows to make use of the Romberg extrapolation process. Such rules can be viewed as generalizations of the well-known mid-point rule. Thus, numerical examples comparing these rules are finally presented.     

Some algorithms for numerical quadrature using the derivatives of the integrand in the integration interval

Some quadrature formulae using the derivatives of the integrand are discussed. As special cases are obtained generalizations of both the ordinary and the modified Romberg algorithms. In all cases the error terms are expressed in terms of Bernoulli polynomials and functions.     

Photoelectric cross-sections of light elements and compounds at low photon energies

Total photon mass attenuation coefficients in C, Al, S, Ti, B₂O₃, LiF, ZnO, Y₂O₃ and H₈O₂C₅ (perspex) are measured on a good geometry set-up using proportional counter, Si(Li) and Ge(Li) detecting systems in the energy region from 6.47 to 52.014 keV employing x-rays and gamma rays from radioactive sources. The deduced photoelectric cross-sections are found to agree with the theoretical values of Storm and Israel, Scofield and semiexperimental values of Veigele wherever available within a few percent. The photo-electric cross-sections in elements, S, Ti and Y at their respectiveK-edges obtained by extrapolation technique agree with the theoretical values of Storm and Israel and Scofield at the respectiveK-edges except in S. In the case of S both the theoretical values atK-edges are found to be underestimations, more in the case of Scofield evaluations.     

The method eliminating nearfield effect for measurement sound absorption coefficient

The numerical simulation is used in this work to study the nearfieldradiation pressure of a piston projector,the smooth effect on the pressure fieldby using a“big”receiver and the influence of the nearfield and in the transitionregion on measurement of sound absorption coefficient.The result indicatesthat the big error would appear when using usual absorption coefficientmeasurement method.According to the reason causing the error,the methodeliminating nearfield effect (MENE) is proposed and some digital results aregiven for a/λ=3,9 and b=0,0.5a,a(a and b are the transducer and re-ceiver radii respectively).The calculation results show that the method not onlywidens measurement range in nearfield,but also gives accurate results.     

基于波叠加法的近场声全息空间分辨率增强方法

提出一种基于波叠加法的近场声全息空间分辨率增强方法. 该方法在波叠加法的基础上,利用全息面声压信号求得布置在全息面附近的虚源面上的简单源源强,再根据求得的简单源源强实现对全息面声压的插值,进而利用插值后的全息面声压数据进行重建. 该方法可以提高近场声全息重建图像的空间分辨率,减少测量工作量,简化测量过程. 通过仿真对影响插值结果的参数进行了分析,给出了合理的选取范围;通过仿真和实验研究验证了该方法的有效性. 关键词： 波叠加法 近场声全息 空间分辨率     

基于多项式外推的Richardson-Lucy算法加速研究

提出一种新的可加速Richardson-Lucy(R-L)图像迭代恢复算法的方法.该方法基于阻尼R-L算法,通过存储阻尼R-L算法的前若干次(n次)迭代运算结果,利用多项式外推法分析这前n次迭代运算结果,并用一个多项式函数近似描述各结果之间的关系.通过该多项式的外推,预测以后的迭代结果,从而减少迭代运算的次数,取得了较好的加速效果.该方法可以实现几乎没有图像失真的复原,并能应用于其他类型的算法.