利用远场模式反演声波阻尼系数

1．引言声波反散射理论在二十世纪的数学物理领域占有重要的地位,在这方面已有大量的研究工作,而对声波反散射理论的研究,大量的研究才是近十多年的事＞51．由于声波反散射理论在雷达、声纳及地球物理勘探等领域的迫切需要,对反散射理论及计算方法的研究有着广泛的应用前景．本文研究时间调和声波的反散射问题,利用散射波的远场模式（farfieldPattern）反演边界条件中的阻尼系数．考虑在均匀介质中传播的声波,此声波碰到一个无限长的柱体．设柱体的截面DCRZ,母线平行于。轴,设人射波为平面波。如）二exphkx·叫,其中k为波数,a为…     

完全k叉树的粘连度

相对于其他网络抗毁性的描述指标来说,图的粘连度是比较理想,也是比较合理的刻画参数．而完全k叉树作为重要的网络结构被广泛地应用在通信网和嵌入式系统芯片的优化设计方面．本文通过优化组合方法界定了完全k叉树的粘连度和毁裂度．从某种程度刻画了网络的抗毁性,为网络设计提供了一种客观的理论依据．完全k叉树的粘连度为1k＋1（kh＋1-1）,如h是奇数;1k＋1（（kh＋1-1）,如h是偶数．完全k叉树的毁裂度为（2k-1）kh-12,如h是奇数;kh＋22-1k-1,如h是偶数．     

利用远场模式的完全与不完全数据反演声波阻尼区域

提出一种方法,利用远场模式的完全数据与不完全数据反演声波阻尼区域,证明了方法的收敛性,并给出若干数值例子.     

完全3-一致超图K_n~((3))的哈密顿圈分解

基于王建方和李东给出的超图哈密顿圈的定义和Katona-Kierstead给出的超图哈密顿链的定义,近年来,国内外学者对一致超图的哈密顿圈分解的研究有一系列结果.特别是Bailey-Stevens和Meszka-Rosa研究了完全3-一致超图K_n~((3))的哈密顿圈分解,得到了n=6k+1,6k+2(k=1,2,3,4,5)的哈密顿圈分解.本文在吉日木图提出的边划分方法的基础上继续研究,得到了完全3-一致超图K_n~((3))的哈密顿圈分解的算法,由此得到了n=6k+2,6k+4(k=1,2,3,4,5,6,7),n=6k+5(k=1,2,3,4,5,6)时的圈分解.这一结果将Meszka-Rosa关于K_n~((3))的哈密顿圈分解结果从n≤32提高到了n≤46(n≠43).     

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.     

若干完全三部图的色唯一性

用P(G,λ)表示图G的色多项式.若对任意图H,当P(H,λ)=P(G,λ)时都有H和G同构,则称图G是色唯一的.给出了以下结果:m≥2且k≥0时,完全三部图K(m,m,m+k)是色唯一的;m≥2且m+1>k≥0时,完全三部图K(m,m+1,m+k)是色唯一的.     

耦合Schrdinger-KdV方程组Cauchy问题的适定性

本文研究了耦合Schrodinger－KdV方程组的Cauchy问题，此耦合方程组刻化了一维Langmuir和离子声波相互作用的非线性动力学行为．本文建立了此问题在Hk×Hk中的整体适定性理论（k∈Z+）．     

完全二部图的全符号{k}-控制数和全符号{k}-色数

Sheikholeslami把求完全二部图图的全符号{k}-控制数和全符号{k}-色数作为待研究的一个问题,本文用构造的方法彻底解决了这个问题.     

利用散射波远场模第P个傅立叶系数重建声波阻尼系数

阐述了利用声波散射远场模Fourier展开的第P个傅立叶系数（声散射远场模的不完全信息）,重建声阻抗系数的一种非线性最优化方法．并给出了该方法收敛性的证明,其数值例子说明这种方法的有效性和可行性．     

有向图的上广义指数

本文得到了n阶k上本原有向图的第k重上广义指数的最大值,1≤k≤n,完全刻画了第k重上广义指数达到最大值的n阶有向图,讨论了第k重上广义指数可取得的值。     

Identification of objects in an acoustic wave guide inversion II: Robin–Dirichlet conditions

In this paper we investigate the unknown body problem in a wave guide where one boundary has a pressure release condition and the other an impedance condition. The method used in the paper for solving the unknown body inverse problem is the intersection canonical body approximation (ICBA). The ICBA is based on the Rayleigh conjecture, which states that every point on an illuminated body radiates sound from that point as if the point lies on its tangent sphere. The ICBA method requires that an analytical solution be known exterior to a canonical body in the wave guide. We use the sphere of arbitrary centre and radius in the wave guide as our canonical body. We are lead then to analytically computing the exterior solution for a sphere between two parallel plates. We use the ICBA to construct solutions at points ranging over the suspected surface of the unknown object to reconstruct the unknown object using a least‐squares matching of computed, acoustic field against the measured, scattered field. Copyright © 2005 John Wiley & Sons, Ltd.     

Cases,clusters, densities: Modeling the nonlinear dynamics of complex health trajectories

In the health informatics era, modeling longitudinal data remains problematic. The issue is method: health data are highly nonlinear and dynamic, multilevel and multidimensional, comprised of multiple major/minor trends, and causally complex—making curve fitting, modeling, and prediction difficult. The current study is fourth in a series exploring a case‐based density (CBD) approach for modeling complex trajectories, which has the following advantages: it can (1) convert databases into sets of cases (k dimensional row vectors; i.e., rows containing k elements); (2) compute the trajectory (velocity vector) for each case based on (3) a set of bio‐social variables called traces; (4) construct a theoretical map to explain these traces; (5) use vector quantization (i.e., k‐means, topographical neural nets) to longitudinally cluster case trajectories into major/minor trends; (6) employ genetic algorithms and ordinary differential equations to create a microscopic (vector field) model (the inverse problem) of these trajectories; (7) look for complex steady‐state behaviors (e.g., spiraling sources, etc) in the microscopic model; (8) draw from thermodynamics, synergetics and transport theory to translate the vector field (microscopic model) into the linear movement of macroscopic densities; (9) use the macroscopic model to simulate known and novel case‐based scenarios (the forward problem); and (10) construct multiple accounts of the data by linking the theoretical map and k dimensional profile with the macroscopic, microscopic and cluster models. Given the utility of this approach, our purpose here is to organize our method (as applied to recent research) so it can be employed by others. © 2015 Wiley Periodicals, Inc. Complexity 21: 160–180, 2016     

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.     

Data preparation using data quality matrices for classification mining

Data mining aims to find patterns in organizational databases. However, most techniques in mining do not consider knowledge of the quality of the database. In this work, we show how to incorporate into classification mining recent advances in the data quality field that view a database as the product of an imprecise manufacturing process where the flaws/defects are captured in quality matrices. We develop a general purpose method of incorporating data quality matrices into the data mining classification task. Our work differs from existing data preparation techniques since while other approaches detect and fix errors to ensure consistency with the entire data set our work makes use of the apriori knowledge of how the data is produced/manufactured.     

利用近场数据反演声波阻尼系数

１引言声波散射理论在二十世纪的数学物理领域占有重要的地位,在这方面已有大量的研究工作,而对声波反散射理论的大量的研究才是近十多年的事．Ｄ．ＣｏｌｔｏｎａｎｄＲ．Ｋｒｅｓｓ［１－４］等人利用积分方程方法对反散射问题作了很深刻的研究．反散射问题的实质性困难是问题的非线性与强不适定性,对不适定性,Ｔｉｋｈｏｎｏｖ［５］正则化方法是一个有力工具．由于声波反散射理论在雷达、声纳及地球物理勘探等领域的迫切需要,对反散射理论及计算方法的研究有着广泛的应用前景．考虑在均匀介质中传播的声波,此声波碰到障碍Ｄ发生散…     

高波数问题的超收敛性

 本文考虑求解Helmholtz方程的有限元方法的超逼近性质以及基于PPR后处理方法的超收敛性质.我们首先给出了矩形网格上的p-次元在收敛条件k（kh）^2p+1≤C₀下的有限元解和基于Lobatto点的有限元插值之间的超逼近以及重构的有限元梯度和精确解之间的超收敛分析.然后我们给出了四边形网格上的线性有限元方法的分析.这些估计都给出了与波数k和网格尺寸h的依赖关系.同时我们回顾了三角形网格上的线性有限元的超收敛结果.最后我们给出了数值实验并且结合Richardson外推进一步减少了误差.     

Universal Deformation Rings of Modules over Self-injective Cluster-Tilted Algebras Are Trivial

Let k be a fixed algebraically closed field of arbitrary characteristic,let Λ be a finite dimensional self-injective k-algebra,and let V be an indecomposable non-projective left Λ-module with finite dimension over k.We prove that if τΛV is the Auslander-Reiten translation of V,then the versal deformation rings R(Λ,V)and R(Λ,τΛV)(in the sense of F.M.Bleher and the second author)are isomorphic.We use this to prove that if Λ is further a cluster-tilted k-algebra,then R(Λ,V)is universal and isomorphic to k.     

REPRESENTATIONS OF AFFINE HECKEALGE BRAS OF TYPE G2

Let k be a field and q a nonzero element in k such that the square roots of q are in k. We use Hq to denote an affne Hecke algebra over k of type G2 with parameter q. The purpose of this paper is to study representations of Hq by using based rings of two-sided cells of an affne Weyl group W of type G2. We shall give the classification of irreducible representations of Hq. We also remark that a calculation in [11] actually shows that Theorem 2 in [1] needs a modification, a fact is known to Grojnowski and Tanisaki long time ago. In this paper we also show an interesting relation between Hq and an Hecke algebra corresponding to a certain Coxeter group. Apparently the idea in this paper works for all affne Weyl groups, but that is the theme of another paper.