The Moment Problem for a Sobolev Inner Product

The concepts of definite and determinate Sobolev moment problem are introduced. The study of these questions is reduced to the definiteness or determinacy, respectively, of a system of classical moment problems by means of a canonical decomposition of the moment matrix associated with a Sobolev inner product in terms of Hankel matrices.     

直观Menger内积空间及其在积分方程中的应用

首先引出和定义了直观的Menger内积空间的概念,然后在完备的直观的Menger内积空间中得出了一个新的不动点定理.作为应用,利用文中所得的结果,研究了线性Volterra积分方程解的存在性和唯一性.     

城市交通投资结构调整与交通需求互动优化模型研究

城市交通投资结构研究有助于了解交通供给能力特征,缓解城市交通拥堵状况.北京市在过去的十几年来大量的交通资金投入到道路建设中,但并没有从根本上扭转日益突出的交通供需矛盾状况.从交通投资与交通需求的关系出发,探讨投资方向和投资力度对交通供需结构的影响.给出交通投资结构阶段统计特征、分析了北京市"七五"至"十五"时期交通投资系统与交通需求、交通供给和社会经济系统关系.应用多目标优化方法,并运用M atlab软件计算不同交通结构情境下的交通投资取向、结构、管理上提出建议.     

The Inner Radius of Univalency of the Rhom busDom ain

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎａｎｄＮａｒｒａｔａｔｉｏｎｏｆｔｈｅＴｈｅｏｒｅｍＩｆｆｕｎｃｔｉｏｎｆｉｓａｎａｌｙｔｉｃｉｎｄｏｍａｉｎＤａｎｄｆ′（ｚ）≠０ａｔｐｏｉｎｔｚ，ｗｅｄｅｆｉｎｅｔｈｅｓｃｈｗａｒｚｉａｎｄｅｒｉｖａｔｉｖｅｏｆｆａｓＳｆ（ｚ）＝（ｆ″（ｚ）ｆ′（ｚ））′－１２（ｆ″（ｚ）ｆ′（ｚ））２．（１．１）　　Ｆｏｒａｌｏｃａｌｌｙｕｎｉｖａｌｅｎｔｈｏｌｏｍｏｒｐｈｉｃｆｕｎｃｔｉｏｎ，ｉｔｓＳｃｈｗａｒｚｉａｎｄｅｒｉｖａｔｉｖｅｉｓｃｌｅａｒ．Ａｔｐｏｌｅｓ，ｔ…     

内积空间中Witt定理的推广

在特征不是2的正交空间中,相关文献给出了Witt定理.华罗庚把它推广到体上的一些内积空间.把域上内积空间中的Witt定理推广到奇异内积空间,并给出相应的证明.     

The Far-Field Equations in Linear Elasticity for Disconnected Rigid Bodies and Cavities

In this paper the far-field equations in linear elasticity for scattering from disjoint rigid bodies and cavities are considered. The direct scattering problem is formulated in differential and integral form. The boundary integral equations are constructed using a combination of single- and double-layer potentials. Using a Fredholm type theory it is proved that these boundary integral equations are uniquely solvable. Assuming that the incident field is produced by a superposition of plane incident waves in all directions of propagation and polarization it is established that the scattered field is also expressed as the superposition of the corresponding scattered fields. A pair of integral equations of the first kind which hold independently of the boundary conditions are constructed for the far-field region. The properties of the Herglotz functions are used to derive solvability conditions for the far-field equations. It is also proved that the far-field operators, in terms of which we can express the far-field equations, are injective and have dense range. An analytical example for spheres illuminates the theoretical results.     

Constant-Sign Solutions for Systems of Fredholm and Volterra Integral Equations: The Singular Case

We consider the system of Fredholm integral equations

单叶性内径研究的新方法

用与Leila Miller-Van Wieren的方法不同的方法对一类六边形H进行了研究,得到了此类六边形H的单叶性内径的计算公式.同时证明了此类六边形H是Nehari圆.     

一阶常系数线性微分方程组的另一种向量解法

讨论一阶常系数线性微分方程组通解问题,给出一种新的向量解法.     

线性流量阀的内孔设计模型

在详细分析线性流量阀工作原理的基础上,应用平面解析几何、微积分等相关概念,给出了不存在呈严格线性的流量阀的数学论证.在设计近似线性流量阀时,首先构造了"线性误差函数"用以刻画"过流面积"与角度之间的线性误差.之后在分析内孔为对称直线、对称1/2次曲线的基础上,设计出内孔为倒"S"形内孔曲线图,通过最小化线性误差函数,得到内孔曲线的最佳参数.最后针对外孔有磨损时,给出了设计方案.     

二维空间中具有积分型非线性Schrodinger方程组的初值问题

具有积分型非线性ｓｃｈｒｏｄｉｎｇｅｒ方程是在研究非线性Ｌａｎｇｍｕｉｒ波时考虑到离子惯性作用而导出的．本文讨论了二维空间中具有积分型非线性ｓｃｈｒｏｄｉｎｇｅｒ方程组的初值问题，用积分估计方法证明了整体解的存在唯一性．     

非线性随机积分和微分方程组的解*

在本文中我们首先对具有随机定义域的连续随机算子组证明了Darbao型不动点定理。应用此定理我们给出了非线性随机Volterra积分方程组和非线性随机微分方程组的Cauchy问题解的存在性准则。这些随机方程组的极值随机解的存在性和随机比较结果也被获得。我们的定理改进和推广Tyaughn,Lakshmikantham,Lakshmikantham-Leela,DeBlast-Myjak和第一作者的相应结果。     

基于软硬件特性可修计算机系统非负弱解存在唯一性

讨论由有软件和硬件构成的串联可修计算机系统,利用可修计算机系统算子生成的Banach空间中的正压缩c0-半群的性质及泛函分析的方法,证明该系统具有唯一非负时间依赖弱解.     

The Facial and Inner Ideal Structure of a Real JBW*–Triple

Let B be a real JBW*–triple with predual B_* and canonical hermitification the JBW*–triple A It is shown that the set 𝒰(B)^∼ consisting of the partially ordered set 𝒰(B) of tripotents in B with a greatest element adjoined forms a sub–complete lattice of the complete lattice 𝒰(A)^∼ of tripotents in A with the same greatest element adjoined. The complete lattice 𝒰(B)^∼ is shown to be order isomorphic to the complete lattice ℱ_n(B_*1 of norm–closed faces of the unit ball B_*1 in B_* and anti–order isomorphic to the complete lattice ℱ_w*(B₁) of weak*–closed faces of the unit ball B₁ in B. Consequently, every proper norm–closed face of B_*1 is norm–exposed (by a tripotent) and has the property that it is also a norm–closed face of the closed unit ball in the predual of the hermitification of B. Furthermore, every weak*–closed face of B₁ is weak*–semi–exposed, and, if non–empty, of the form u + B₀(u)₁ where u is a tripotent in B and B₀(u)₁ is the closed unit ball in the zero Peirce space B₀(u) corresponding to u. A structural projection on B is a real linear projection R on B such that, for all elements a and b in B, {Ra b Ra}_B is equal to R{a Rb a}_B. A subspace J of B is said to be an inner ideal if {J B J}_B is contained in J and J is said to be complemented if B is the direct sum of J and the subspace Ker(J) defined to be the set of elements b in B such that, for all elements a in J, {a b a}_B is equal to zero. It is shown that every weak*–closed inner ideal in B is complemented or, equivalently, the range of a structural projection. The results are applied to JBW–algebras, real W*–algebras and certain real Cartan factors.     

The exact solution of a class of Volterra integral equation with weakly singular kernel

In this paper, the weakly singular Volterra integral equations with an infinite set of solutions are investigated. Among the set of solutions only one particular solution is smooth and all others are singular at the origin. The numerical solutions of this class of equations have been a difficult topic to analyze and have received much previous investigation. The aim of this paper is to present a numerical technique for giving the approximate solution to the only smooth solution based on reproducing kernel theory. Applying weighted integral, we provide a new definition for reproducing kernel space and obtain reproducing kernel function. Using the good properties of reproducing kernel function, the only smooth solution is exactly expressed in the form of series. The n-term approximate solution is obtained by truncating the series. Meanwhile, we prove that the derivative of approximation converges to the derivative of exact solution uniformly. The final numerical examples compared with other methods show that the method is efficient.