Borg-Levinson定理新证

对于Sturm-Liouville特征值逆问题,Borg-Levinson定理描述了Sturm-Liouville算子的两组谱可唯一确定其势函数.本文利用整函数的Liouville定理,并通过对谱参数趋于无穷时Sturmo-Liouville方程基本解的渐进估计,给出了Borg-Levison定理一个简单的证明.同时还证明了Sturm-Liouville算子的两组谱与其Weyl-Titchmarsh m-函数及谱函数三者之间的等价关系.     

随机内积模上正算子及正交投影算子的性质

得到了随机内积摸上正算子厦正交投影算子的一些性质，这些结果有利于进一步讨论随机内积摸上a．s有界自伴线性算子谱的性质．     

非线性Sturm-Liouville奇异边值问题正解的存在唯一性

本文用正则锥上的非紧减算子不动点定理,讨论了一类非线性Sturm-Liouville奇异边值问题正解的存在性和唯一性。对此问题的讨论,我们构造了一个新的正则锥。这样的方法完全可以应用到其它奇异边值上去,用以讨论正解的存在性。     

一类基于比率的广义Holling-Tanner系统的定性分析

本文在齐次Neumann边界条件下研究了一类捕食-食饵模型正平衡解的稳定性与存在性.首先,我们利用算子谱理论得到了正常数平衡解的一致渐近稳定性,其次,运用最大值原理和Harnack不等式,我们给出了正平衡解的先验估计,再次,利用积分的性质并结合ε-Young不等式和Poincar′e不等式,文中证明了非常数正平衡解的不存在性,最后,利用Leray-Schauder度理论证明了非常数正平衡解的存在性,并且给出了正平衡解存在的充分条件.研究结果表明,当参数满足一定条件时,两物种可以共存.     

附有选择性服务与无等待能力的M/G/1排队系统稳定性分析

研究附有选择性服务与无等待能力的M/G/1排队系统。通过对描述其系统行为的偏微分方程组的规范化,将其转化为Banach空间中抽象的Cauchy问题。然后,利用强连续有界线性算子半群理论,证明了系统的非负稳定解恰是系统算子的0本征值对应的非负本征向量。同时通过研究系统算子的谱特征,证明了系统算子的谱点均位于复平面的左半平面且虚轴上除0外无谱,进而得到系统的渐近稳定性,特别在范数意义下系统的动态解收敛到稳态解。     

谱元法与透射边界的配合使用及其稳定性研究

在无限域波动模拟中引入透射边界条件时,目前多将边界上的透射公式与内域的有限元法结合使用,其计算精度由有限元方法决定,而谱元法因结合有限元和频谱法的优势则比有限元空间域积分具有更高的计算精度。该文基于谱元法非等距网格划分特性,研究了内域的谱元法与边界上的透射公式结合的理论方法,给出了相应的透射公式使用方法,并基于建立的谱元法波动数值模型探讨了透射公式的稳定性问题。研究表明:空间域插值系数需控制在一个合理范围内,空间域插值方法相对于时间域插值方法更为稳定,高频失稳出现可能性相对较小;Gamma算子的使用可提高模拟的精度,采用Gamma算子后对于高阶透射公式仍可出现低频漂移现象,可结合降阶消漂的方式实现稳定精度高的透射边界应用。     

分数导数微分算子描述的粘弹性土层中群桩的水平振动研究

将桩周土体视为粘弹性介质,利用分数导数粘弹性模型描述土体的力学特性,在Novak 平面应变假定的基础上,借助于势函数并考虑土体边界条件求得了分数导数微分算子描述的粘弹性土层水平位移的衰减函数以及分数导数粘弹性土层的刚度和阻尼系数。利用Winkler 动力弹簧-阻尼器模型模拟桩-土之间的动力相互作用,并在此基础上利用初始参数法求解了分数导数粘弹性土层中桩-桩水平动力相互作用和群桩的水平振动问题。以数值算例的形式讨论了分数导数微分算子的阶数和土体的模型参数对分数导数微分算子描述的粘弹性土层水平位移的衰减函数和群桩的水平动力阻抗的影响。研究表明:分数导数微分算子的阶数对土层水平位移的衰减函数的影响与桩间距和荷载方向角有关;分数导数粘弹性土中群桩的动力阻抗可以退化到经典粘弹性和弹性情况;分数导数微分算子的阶数和土体模型参数对群桩水平动力阻抗有较大影响。     

基于多色集合理论的分层印刷工艺规划

目的在多印刷工艺的复杂印刷系统中,研究无冗余计算的计算机辅助印刷工艺规划算法。方法首先,在研究多色集合理论的基础上,按照给出的分层模型构建策略构建出"印刷需求双层模型"和"印刷工艺双层模型"。然后,计算出可用"工序组",并据此构造最小规模的产品围道和围道矩阵。最后,利用分层工艺算子搜算算法计算出可用工序,从多色图中获得待印品的工艺路径。结果建立了一种基于多色集合理论的分层印刷工艺规划理论。结论基于多色集合理论的分层印刷工艺规划可有效地降低工艺算子搜索过程中的冗余计算。     

线弹性问题的locking-free双参数元

文中运用双参数法提出了一个4参数的四边形非协调有限元,讨论了该单元对纯位移边界条件下的均匀介质线弹性方程的逼近问题.证明了在材料几乎不可压时单元对弹性问题的一致最优收敛性,数值试验验证了理论分析结果.并通过构造后处理算子,得到了超收敛结果.所有的分析结果都可以推广到三维情形.     

弹性地基上椭圆薄板自由振动的一个解析解

借助椭圆坐标变换，并利用微分算子分解给出了弹性地基上椭圆薄板的自由振动解．根据马休函数特性，并考虑模态的正交性，针对周边固定和周边滑动固定2种边界条件，求得了弹性地基上椭圆薄板固有频率和相应振型的解析表达式．     

非线性三阶边值问题的多解性

研究了三阶边值问题多个正解的存在性。当函数满足一些增长性条件时，该边值问题至少有三个正解。     

Numerical solution of the variation boundary integral equation for inverse problems

In this paper a procedure to solve the identification inverse problems for two‐dimensional potential fields is presented. The procedure relies on a boundary integral equation (BIE) for the variations of the potential, flux, and geometry. This equation is a linearization of the regular BIE for small changes in the geometry. The aim in the identification inverse problems is to find an unknown part of the boundary of the domain, usually an internal flaw, using experimental measurements as additional information. In this paper this problem is solved without resorting to a minimization of a functional, but by an iterative algorithm which alternately solves the regular BIE and the variation BIE. The variation of the geometry of the flaw is modelled by a virtual strainfield, which allows for greater flexibility in the shape of the assumed flaw. Several numerical examples demonstrate the effectiveness and reliability of the proposed approach. Copyright © 2000 John Wiley & Sons, Ltd.     

Free Boundary Problems in the Steel Industry

This paper considers two novel free boundary problems that emerge from modelling processes basic to steel manufacture. The first process concerns the spray cooling of hot steel sheet during the process of continuous casting. Here, an important practical consideration is the non-monotonicity of the measured heat transfer from the steel as a function of the steel temperature. In order to understand this phenomenon, a two-phase flow model is written down for the heating and vapourisation of the water spray. This model relies on a microscale analysis of droplet vapourisation and, in a steady state, it reduces to a coupled system of nonlinear ordinary differential equations for the spray temperature and water content. This system predicts the conditions for the existence or otherwise of a free boundary separating the two-phase region from a dry vapour layer close to the steel plate.The thickness of this vapour layer is determined by the solution of a generalised Stefan problem. The second process concerns the macroscopic modelling of pig .iron production in blast furnaces. In the simplest scenario, the blast furnace may be roughly divided into a porous solid region overlaying a hot high pressure gaseous zone. The gas reacts with the solid in a thin “intermediate region“ at the base of the solid region and it is in this intermediate region that the pig iron is produced. A free boundary model is proposed for the location of the intermediate region and its stability is investigated.     

压电材料变分原理逆问题的研究——动力学中的逆问题

研究了压电材料耦合动态场中Hamilton 型和Gurtin 型变分原理的逆问题。采用变积方法, 建立了各级变分原理和广义变分原理, 为建立横观各向同性压电材料的动力学有限元分析模型提供了依据。      

A general procedure transferring domain integrals onto boundary integrals in BEM

This paper is concerned with transferring to the boundary the domain type integrals occurring in the boundary integral approach applied to boundary value problems with nonzero body force terms. The framework used encloses many interesting engineering applications, e.g. elastostatics, heat conduction and magnetostatics. Beside this are pseudo plastic strains are incorporated due to interaction phenomena with relevant quantities. The proposed method is based upon the homogenization of the governing differential equation by using a particular solution of the inhomogeneous one. Various methods deriving such particular solutions are considered.     

Comparison of regularization methods for solving the Cauchy problem associated with the Helmholtz equation

In this paper, several boundary element regularization methods, such as iterative, conjugate gradient, Tikhonov regularization and singular value decomposition methods, for solving the Cauchy problem associated to the Helmholtz equation are developed and compared. Regularizing stopping criteria are developed and the convergence, as well as the stability, of the numerical methods proposed are analysed. The Cauchy problem for the Helmholtz equation can be regularized by various methods, such as the general regularization methods presented in this paper, but more accurate results are obtained by classical methods, such as the singular value decomposition and the Tikhonov regularization methods. Copyright © 2004 John Wiley & Sons, Ltd.     

动水压力问题的一种边界元解法

本文将动水压力设定为有限个半平面解答的线性组合,它精确满足域内的方程,然后令解答在N 个边界点满足给定的边界条件求解设定的解答中的待定常数。该方法有简单,避免奇异积分、解设定常数的方程组状态好等优点。文中给出的算例说明了方法的正确性。     

几类边值问题的正解

本文利用存在性定理,考察了二阶常微分方程两点、三点以及m-点边值问题正解的存在性.在较弱的条件下,给出了几类边值问题至少有一个正解存在的充分性条件.所得结果改进和推广了文献中的相应结论.     

三阶奇异边值问题对称正解的最优存在性(英文)

本文利用Leggett-Williams不动点定理,通过构造特殊的锥,得到了三阶奇异边值问题三个对称正解最优存在性的新结果,最后,通过具体的例子说明了我们所得结果的有效性。     

Dual boundary integral equations for exterior problems

A dual integral formulation for the interior problem of the Laplace equation with a smooth boundary is extended to the exterior problem. Two regularized versions are proposed and compared with the interior problem. It is found that an additional free term is present in the second regularized version of the exterior problem. An analytical solution for a benchmark example in ISBE is derived by two methods, conformal mapping and the Poisson integral formula using symbolic software. The potential gradient on the boundary is calculated by using the hypersingular integral equation except on the two singular points where the potential is discontinuous instead of failure in ISBE benchmarks. Based on the matrix relations between the interior and exterior problems, the BEPO2D program for the interior problem can be easily reintegrated. This benchmark example was used to check the validity of the dual integral formulation, and the numerical results match the exact solution well.