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.     

声波阻尼系数的反演方法

1引言 声波反散射理论在雷达、声纳及地球物理勘探等领域有着广泛的应用前景,因此反散射理论及计算方法的研究获得了国内外众多专家学者的重视,对其大量研究见[1-5].文[5]中采用单层位势对散射波进行逼近,由给定的散射波的远场模式来反演阻尼系数.     

利用远场模式的不完全数据反演声波阻尼系数

1.引言 对声波反散射理论的研究,已经有大量的研究[1.5].[7]利用散射波的远场模式反演边界条件中的阻尼系数.但是在实际问题中,要在物体的一周测量到远场模式的值是不现实的.因此,利用远场模式的不完全数据来进行反演有明显的物理和实际意义.一些文献将此类问题称为声波反散射理论的“limited aperture problem”.本文利用远场模式的不完全数据,反演边界条件中的声波阻尼系数.     

利用散射波的叠加重建声波散射区域

本文研究了声波散射区域的重建，给上散射波的叠加重建散射区域的一个方法，该方法利用散射波的叠加，将声波障碍反散射这个非一不适定问题分两步处理，第一步求解一个第一类线性积分方程。第二步求解一个非线性最优化问题，我们证明了该方法的收敛性。     

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...     

石油地震勘探波动方程速度反演方法评介

<正> 石油地震勘探中的速度反演问题是一个散射方程的混合初边值问题.它是波动方程散射问题的推广.由地表上点震源的激发给大地一个入射波,由于地层的不均匀性而产生反射波,整个波场是二者的迭加.根据反射波在地表的数据 (即边值条件,亦称附加条件)来确定地层中波传播的速度.由于地层的复杂性,目前主要以波动方程近似描述地震波的传播.入射波可以直接给出,也可以用一个常系数波动方程的定解问题来确定.反射波或全波也由一个波动方程的定解问题确定,方程中包含有需要反演的速度.     

反演声波阻尼系数的另一种方法

提出了一种方法,利用正则化方法和积分方程,由散射波的近场数据反演时间调和声波阻尼系数.给出了该方法收敛性的证明及数值例子,算法与数值例子表明这种方法不仅简单而且很有效.     

一维弹性波方程双参数反演的省去Green函数法

为了提高一维弹性波方程反演的精度,推出了严格省去Green函数的反演方程,并通过选取适当的稳定泛函、合理地运用正则化方法,获得了即可以同时反演介质的密度和弹性参数,也可以同时反演出介质密度和波速的新方法,这可为地震勘探提供较多的岩性参数.经过一系列的数值模拟计算,验证了该方法提高了反演的精度.     

P-反演半群上的强P-同余

本文介绍了P-反演半群S(P)的概念，借助于核与迹刻画了P-反演半群上的强P-同余，并且证明了S(P)上的任一强P-同余可以决定S(P)的一个强P-同余对，反之S(P)的任一强P-同余对，可以决定S(P)上的一个强P-同余.     

一类泛函方程的存在定理的修正

假设X和Y是Banach空间,SX和DY。又设T:S×D→S,g:S×D→R,G:S×D×R→R及f:S→R,其中R是实数域。若把S看作状态空间,D看作决策空间,动态规划问题被化为解下面的泛函方程问题:其中x∈S。 R. Baskaran和P. V. Subrahmanyam在[1]中首先建立一个不动点定理,试图用该不动点定理研究方程(1)的解的存在性与唯一性。他们给出了如下的定理(即[1]中定理3.1):     

Propagation of torsional surface waves in a homogeneous layer of finite thickness over an initially stressed heterogeneous half-space

In the present paper, the dispersion equation which determines the velocity of torsional surface waves in a homogeneous layer of finite thickness over an initially stressed heterogeneous half-space has been obtained. The dispersion equation obtained is in agreement with the classical result of Love wave when the initial stresses and inhomogeneity parameters are neglected. Numerical results analyzing the dispersion equation are discussed and presented graphically. The result shows that the initial stresses have a pronounced influence on the propagation of torsional surface waves. It has also been shown that the effect of density, directional rigidities and non-homogeneity parameter on the propagation of torsional surface waves is prominent.     

Rayleigh waves from a point source on a boundary free of tensions

The solutions of equations of elasticity theory that have a discontinuity only on a boundary free of tensions (Rayleigh waves) are considered. Initial data for the complex intensity of the surface Rayleigh waves are found in two simple media. The first elastic medium fills a half-space with Lamé parameters and density dependent on depth. The second medium is bounded by a curve determined by a natural equation. The parameters of the second medium depend on the arc length along the curve. Bibliography: 12 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 354, 2008, pp. 132–149.     

Scattering of elastic waves by nonaxisymmetric three-dimensional dipping layer

Using a boundary method, we investigated the scattering of elastic plane harmonic SH, SV, P, and Rayleigh waves by three-dimensional nonaxisymmetric dipping layers embedded in an elastic half-space. The valley was subjected to incident Rayleigh wave and oblique incident SH, SV, and P waves. The method utilized spherical wave functions to express the unknown scattered field. These functions satisfy the equation of motion and radiation conditions at infinity but they do not satisfy the stress-free boundary conditions at the surface of the half-space. The boundary and continuity conditions are imposed locally in the least-square-sense at several points on the layer interface and on the surface of the half-space. A comparative study was done to examine the validity and limitations of the two-dimensional approximations (antiplane and plane strain models) of three-dimensional models. It is demonstrated that the two-dimensional approximations may be inadequate to represent actual displacement field for three-dimensional irregularities.     

Shortest Inspection Curves for the Sphere

What is the form of the shortest curve C going outside the unit sphere S in ?³ such that passing along C we can see all points of S from outside? How will the form of C change if we require that C has one (or both) of its endpoints on S? A solution to the latter problem also answers the following question. You are in a half-space at a unit distance from the boundary plane P, but you do not know where P is. What is the shortest space curve C such that going along C you will certainly come to P? Geometric arguments suggest that the required curves should be looked for in certain classes depending on several parameters. A computer-aided analysis yields the best curves in the classes. Some other questions are solved in a similar way. Bibliography: 4 titles.     

Seminégativité des courbes compactes des revêtements non compacts des surfaces projectives complexes

We show that the intersection form of a compact complex curveof any non compact cover ƒ:→ S of a smooth projective complex surface S is seminegative. Ifis not exceptional in , then C ≔ ƒ(C) is a fibre of the Albanese map α: S → B, whose image is a positive genus curve B (after possibly replacing S by a suitable finite cover), provided C is smooth and its normal bundle in S is torsion.These results agree with a question raised by I. Shafarevich in [1].     

Z_2-商的秩为r的超椭圆纤维化曲面的斜率

设Ｓ是一般型的相对极小曲面，ｆ：Ｓ→Ｃ是亏格ｇ的超椭圆纤维化．本文中我们证明了如果 Ｓ的代数基本群的垂直部分的极大挠 ２商为，那么其斜率且等号成立仅当 Ｓ上的超椭圆对合所诱导的二次复盖的分歧除子 Ｒ仅有（ｒ＋１→，＋１）（当ｒ为偶数）型奇点，或（ｒ＋２→ｒ＋２）（当ｒ为奇数）型奇点．     

Two-dimensional problem of a two-temperature generalized thermoelastic half-space subjected to ramp-type heating

In this work, we will consider a half-space filled with an elastic material, which has constant elastic parameters. The governing equations are taken in the context of the theory of two-temperature generalized thermoelasticity. A linear temperature ramping function is used to more realistically model thermal loading of the half-space surface. The medium is assumed initially quiescent. Laplace and Fourier transform techniques are used to obtain the general solution for any set of boundary conditions. The general solution obtained is applied to a specific problem of a half-space subjected to ramp-type heating. The inverse Fourier transforms are obtained analytically while the inverse Laplace transforms are computed numerically using a method based on Fourier expansion techniques. Some comparisons have been shown in figures to estimate the effect of the ramping parameter of heating.     

The Reissner-Sagoci problem for a half-space with a surface constraint

In this paper, the Reissner-Sagoci problem for a half-space with a surface constraint is considered. The problem is reduced to the triple integral equation by use of integral transforms. The triple integral equations are solved for small values of parameters characterizing the geometry of the problem. An expression for the torque required to rotate the disc through a fixed angle is obtained.     

On the brauer group of a designularization of a normal surface 1

If ‰ : ? S → is a desingularization of the norm3 surface S, then it is shown that the induced map H² _et:(S, G_m) → H^2: _et(?, G_m) is surjective. It

follows that if all of the singularities of S are rational, the Brauer group

map B(S) → B(?) is surjective. An example is given to show that this

property fails if the dimension of S ≥ 3.     

不规则界面对扭转表面波在初应力各向异性多孔弹性层中传播的影响

研究了扭转表面波在一个半无限非均匀半空间中的传播,半空间上覆盖着具有初始应力的各向异性多孔弹性层,弹性层的刚度和密度线性地变化,造成了界面的不规则性．半空间中界面的不规则性,用一个矩形形式表示．可以发现,扭转表面波在这样假定的介质中传播,得到了没有不规则性时的扭转表面波的速度方程．还可以发现,对于均匀半空间覆盖的层状介质,扭转表面波的速度与Love波的速度相一致．