求解不适定方程的两步定常迭代法

讨论了方程Kx=y两步定常迭代的近似解,推导出滤波函数.通过适当地确定α,β的范围,证明此滤波函数是正则滤波函数,并给出此迭代的收敛阶及停止法则.     

多个额外维存在时的Casimir效应

在Kaluza—Klein理论框架下分析具有多个紧致额外维时两平行导体平板间的Casimir效应．假定所有的额外维具有相同的尺度R，利用Epsteinzeta函数对Casimir能量密度进行正则化，得到Casimir力密度并与实验结果比较，可确定额外维的尺度为R≤10nm．     

A regularization method in the electromagnetic inverse scattering problem

Based on the normalization of measurement data equations of the inverse scattering problem, a new regularization matrix is proposed. It can eliminate the unfavorable effects caused by difference of distances between field-point or source-point and target region, reduce the loss of useful information in regularization procedure, and decrease condition numbers of the ill-posed problems. Inversion for conductivity distribution of two-dimensional axisymmetric inhomogeneous media is carried out by combing this new regularization method with distorted Born iterative method. Simulation results show that compared with the conventional method, the new regularization method is of better stability, quicker convergence, higher accuracy of inversion and higher resolution.     

The lower orders of Dirichlet and random Dirichlet series

the formulas of the lower orders of Dirichlet series are given by means of the exponents and the convex regularized sequences of the logarithms and the convex regularized sequences of the logarithms of the moduli of the coefficients. Corresponding results are obtained for some random Dirichlet series. Yu Jiarong: born in Nov. 1920, Professor, Current research interest is in complex analysis Supported by the National Natural Science Foundation and the Doctoral Programme Foundation of China     

基于积分方程正则化的重力异常超定问题解法

地球重力场的观测信息越来越丰富，求稳重力异常的超定模型将具有实用价值，据此给出了基于第一类Fredholm型积分方程离散型解法求解重力异常的超定模型，建立了地面重力、测高数据、重力梯度和垂线偏差求解重力异常的观测方程，并给出求解病态观测方程的正则化算法。     

广义Arcangeli方法在迭代TИХОНОВ正则化中的应用

应用广义Ａｒｃａｎｇｅｌｉ方法，讨论了迭代正则化方法的正则参数选取，给出逼近解的收敛速度估计．     

一种基于实测模态参数的结构损伤诊断方法

本文提出了一种利用实测结果固有频率与振型诊断结构损伤大小和位置的方法，并提出了一种能抑制测试误差对诊断准确性影响的正则化技术求解质量和刚度损伤诊断方程，以三根模型的损伤诊断实例说明了本方法的有效性。     

带Carleman位移的奇异积分方程的正则化问题

本文在文献[1]、[2]的基础上,在空间H_μ或空间μ中,构造了各种带有Carleman位移和未知函数复共轭值的奇异积分Noether算子的正则化算子,指出了构造等价正则化算子的方法,给出了在一些特殊条件下的等价正则化算子的表达式。     

基于L曲线法的电容层析成像正则化参数优化

电容层析成像（ECT）系统的不适定性问题严重影响重建图像质量，为此必须减小灵敏度矩阵的争件数．以Tjkhonov正则化和后验策略为基础，从灵敏度矩阵广义逆的角度阐述了L曲线法并设置滤波函数，建立极小化泛函及L曲线图，最终确定正则参数．仿真实验表明，L曲线法具有较强的抗噪声性能和较快的收敛速度，明显改善了ECT系统的重构图像质量．