二维逆散射问题探测方法的数值实现

探测方法是最近发展起来的逆散射问题的一种重要的求解方法,其主要思想是由散射波测量数据构造一个带有散射体外面参数点的指示函数,当参数点靠近散射体的边界时,指示函数爆破,由此重建散射体的边界．本文对具有Sound-soft边界的二维散射体给出了探测方法的数值实现．在给出标志函数的构造的基础上,进一步提出了利用模拟数据实现探测法的一个改进的逼近方法．为了更清楚地检验所提出的方法的数值结果,我们直接从Ω边界上的 D-to-N映射来研究探测方法的数值解．     

基于遗传算法重建多个散射体的组合Newton法

本文研究由单个入射声波或电磁波及其远场数据反演多个柔性散射体边界的逆散射问题.通过建立边界到边界总场的非线性算子及其n6chet导数,本文首先给出了基于单层位势的组合Newton法.将组合Newton法转化为泛响优化问题,从而获得了该方法重建单个散射体的收敛性分析.然后,基于遗传算法和正则化参数选取的模型函数方法,给出...     

具有未知阻尼边界的逆散射问题解的惟一性及重构

考虑R3中的散射体D在阻尼边界条件下由散射波的远场形式重建散射体边界的逆散射问题. 证明了该反问题解的惟一性, 并给出了确定边界形状的精确的反演方法．由于边界阻尼是未知的, 这预示着散射波的远场形式含有散射体的比现在已知的更多的信息.     

由近场谱数据确定阻抗散射体的形状

本文考虑由点源波入射，在获取近场散射数据时具有阻抗边界的散射体的重构问题．区别于N．Grinberg利用Herglotz波函数和单层势的途径，我们利用混合互易关系，得到了远场和近场算子的关系，由该关系和奇异值分解，得到了算子的谱，从而将散射体特征化．数值实验表明，能得到良好的重构．     

逆散射问题求解的正则化GAUSS-NEWTON法

本文研究了一类重要的反问题-逆散射问题,它是从远场散射数据识别散射体中的障碍物的形状问题.利用迭代正则化Gauss-Newton法,通过数值模拟比较分析,验证了本文所提出的方法在求解逆散射问题时是可行有效的.     

数学年刊第25卷B辑第1期(2004)目次和提要

逆声波散射问题在多边形区域类中的全局唯一性 程晋 YAMAMOTO,M. 该文在凸多边形的类中考虑了由散射波信息重构散射物体形状的问题。基于在直线上解析一致连续性原理,证明了:在“软”(Sound-Soft)和“硬”(Sound-Hard)边界条件的情况下,一个入射波方向的散射信息可以唯一决定边界;在阻尼边界条件下,两个入射波方向的散射信息可以唯一决定边界。     

海洋波导的可穿透障碍物散射场远场分布的若干性质

研究了海洋波导中可穿透目标时谐声波散射传播远场分布的性质,构造了透射问题解的集合,使得所构造解的集合在边界上的限制在某个Hilbert空间中是稠密的,确定了传播远场分布的集合在某个Hilbert空间中是完备的．这些性质对研究海洋波导中的逆透射问题有重要的应用．     

由半直线上Strum-Liouville方程的散射数据重构位势

本文考虑半直线Strum-Liouville方程的逆散射问题,研究如何重建出位势函数.重建位势时,我们利用矩阵薛定谔算子理论及其散射矩阵的性质,证明了半直线上Strum-Liouville方程可通过散射数据重构位势.     

双连通区域上的电磁波散射问题数值解

对于双连通区域上的电磁波散射问题,通过位势理论将其转化为边界积分方程组问题,然后采用Nystrom法和配置法对其离散求解,针对不同形状的障碍散射体,给出远场模式的数值解.     

分解法在声波反散射问题中的最新进展 献给林群教授80华诞

本文旨在总结分解法在声波反散射问题中的最新进展,其中包括经典的分解法如何应用于可穿透散射体和具有广义阻尼边界条件的复杂散射体情形,以及分解法在处理混合型散射体、近场数据反演和避免内部特征值等情形的修正方法.     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

Qualitative Analysis of Bifurcating Solutions in the Lengyel-Epstein Model

One of the most fundamental problems in theoretical biology is to explain the mechanisms by which patterns and forms are created in the＇living world. In his seminal paper ＂The Chemical Basis of Morphogenesis＂, Turing showed that a system of coupled reaction-diffusion equations can be used to describe patterns and forms in biological systems. However, the first experimental evidence to the Turing patterns was observed by De Kepper and her associates（1990） on the CIMA reaction in an open unstirred reactor, almost 40 years after Turing＇s prediction. Lengyel and Epstein characterized this famous experiment using a system of reaction-diffusion equations. The Lengyel-Epstein model is in the form as follows     

On a class of self-similar processes with stationary increments in higher order Wiener chaoses

We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.     

(0,1 ;0)-INTERPOLATION ON INFINITE INTERVAL (-∞, +∞)

In this paper, we study the explicit representation and convergence of (0, 1; 0)-interpolation on infinite interval, which means to determine a polynomial of degree ≤ 3n - 2 when the function values are prescribed at two set of points namely the zeros of Hn(x) and H′n(x) and the first derivatives at the zeros of H′n(x).     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

CONTENTS OF VOLUME 30

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Instructions for contributions

正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with     

Journal of Mathematical Research with Applications Guide for Authors

正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.     

Staircase transportation problems with superadditive rewards and cumulative capacities

A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].