Menger PN空间中的固有值与固有元

本文提出了Menger PN空间中固有值和固有元的新概念，研究了M—PN空间中的固有值与固有元的若干问题，得到了几个重要的结论．     

强概率收缩对与概率赋范空间中非线性算子方程组的解

在Menger PN空间引入强概率收缩对的概念,并研究了具有强概率收缩对的非线性算子方程组解的存在性和唯一性.这些结果改进和推广了非Archimedean Menger PN空间中相应的结果.     

Z-P-S空间中一类非线性算子方程解的研究

本文利用Menger PN空间中半闭1-集压缩算子的拓扑度理论研究Z-P-S空间中非线性算子方程Ax=ux解的存在性问题,改进和推广了相关文献中的结果.最后,我们给出主要结果的一个具体应用.     

模糊距离空间中几类非线性压缩不动点定理

在Kaleva-Seikkala型模糊距离空间中建立了Boyd-Wong型和Alber-Guerre Delabriere型非线性压缩不动点定理.这些结果补充了Xiao等人的几个结果.作为应用,获得了通常距离 空间和Menger概率距离空间中的几个非线性不动点定理.     

概率收缩偶与非阿基米德Menger概率赋范空间中非线性方程组的解*

本文在非阿基米德Menger概率赋范空间中引入了概率收缩偶的概念,研究了非阿基米德Menger概率赋范空间中具概率收缩偶的非线性方程组的解的存在性与唯一性.发展和改进了引文[1～5]的相应结果.     

关于M-PN空间中的非线性算子

在Menger概率线性赋范空间中,利用该空间中的Leray-Schauder拓扑度理论,研究非线性算子T,建立了紧连续算子了T有固有值γ和δW上存在对应于γ的固有元的一系列充分条件．同时,也改进和推广了若干个重要结论。     

Menger PM-空间中广义非线性压缩映射的公共不动点定理及其应用

在Menger PM-空间中引入了两个新的广义非线性压缩的概念.在不要求三个映射任何连续性和单调性的情况下,研究了三个映射在广义非线性压缩条件下公共不动点的存在唯一性问题,获得了一些新的结果,推广和改进了最近相关文献中的定理.最后,给出了主要结果的一个例子.     

PM-空间中混合压缩的不动点定理与重合点定理

引进了Menger PM-空间中多值情形下的相容映象和弱相容映象概念，并研究了二者之间的联系．在此基础上，获得了Menger PM-空间中若干新的不动点和重合点定理．最后，给出了这一结果在度量空间中的应用．     

直觉Menger空间中的广义压缩映射原理及其在微分方程中的应用

利用Atanassov的思路,将直觉Menger空间定义为由Menger提出的Menger空间的自然推广.同时也得出一个新广义压缩映射,并运用该压缩映射证明了直觉Menger空间中微分方程解的存在性定理.     

Menger空间对拟距离空间族的嵌入定理及其应用

在本文中,我们引进了Menger空间中拟距离空间族的嵌入概念并研究了它的一些性质.证明了Menger空间中连续映象序列的一个公共不动点定理.这些映象是假设满足广义的压缩条件的.这里采用的证明方法对于Menger空间的映象而言是一种新的思想.     

Nonlinear optical media in photonic crystal waveguides: Intrinsic localized modes and device applications

A review is given of some of the properties of photonic crystal waveguides containing or interacting with nonlinear optical media including discussions of potential device applications. An introduction is given to photonic crystals, photonic crystal waveguide technologies, the properties of Kerr nonlinear dielectric media, the properties of new types of excitations in these systems known as intrinsic localized modes, and optical bistability. Device designs for switches, waveguide couplers, interferometers, transistors, photonic crystal receivers and transmitters, and photonic crystal sensors are reviewed. © 2007 Wiley Periodicals, Inc. Complexity 12: 18–32, 2007     

Intrinsic Geometry of the NLS Equation and Its Auto-Bäcklund Transformation

The nonlinear Schrödinger equation is derived in a general intrinsic geometric setting involving a normal congruence originally investigated by Marris and Passman in 1969 in a hydrodynamical context. Geometric properties of members of the normal congruence are adduced and an intrinsic representation of the auto-Bäcklund transformation is obtained for the nonlinear Schrödinger equation.     

低维混沌时序非线性动力系统的预测方法及其应用研究

主要研究由低维混沌时序所确定的非线性动力系统的预测方法及其应用。在国外学者研究工作的基础上,应用一种非线性混沌模型在相空间内对时序进行重构工作,先通过改进的最小二乘方法来估计模型的参数,满足一定精度后,再采用最优化方法来估计模型的参数,并用所求得的混沌时序模型在其相空间内对时序的未来值进行预测。给出了非常有代表性的实例对文中模型和算法进行验证。结果发现采用该算法能较准确地求得模型的参数,在相空间中对混沌时序进行预测,将传统方法中的外推变成了相空间中的内插,及选取最佳的模型阶数等工作都能增加预测的准确程度,且混沌时序不可能进行长期的预测。     

应用于非惯性系湍流模拟的扩展内禀旋转张量

研究扩展内禀旋转张量在非惯性系湍流模拟中的作用,特别是对代数Reynolds应力湍流模式(如非线性K-ε模式)的重要性．为此,采用几个近年来发展的非线性K-ε湍流模式模拟旋转坐标系下均匀剪切湍流,并且和大涡模拟的结果进行比较．计算结果和分析表明,需要发展更先进的非线性K-ε模式从而更好地描述非惯性系下的复杂湍流．     

Intrinsic nilpotent approximation

This report is a preliminary version of work on an intrinsic approximation process arising in the context of a nonisotropic pertubation theory for certain classes of linear differential and pseudodifferential operatorsP on a manifoldM. A basic issue is that the structure ofP itself determines the minimal information that the initial approximation must contain. This may vary from point to point, and requires corresponding approximate state spaces or phase spaces.This approximation process is most naturally viewed from a seemingly abstract algebraic context, namely the approximation of certain infinite-dimensional filtered Lie algebrasL by (finite-dimensional) graded nilpotent Lie algebrasg _x, org _(x,), wherex M, (x, ) T^* M/0. It requires the notion of weak homomorphism. A distinguishing feature of this approach is the intrinsic nature of the approximation process, in particular the minimality of the approximating Lie algebras. The process is closely linked to localization, associated to an appropriate module structure onL.The analysis of the approximating operators involves the unitary representation theory of the corresponding Lie groups. These representations are for the most part infinite-dimensional, and so involve a kind of quantization. Not all the representations enter. The filtered Lie algebraL leads to an approximate Hamiltonian action ofG _(x,), the group associated tog _(x,), and thus induces (via an adaptation of a construction of Helffer and Nourrigat) an intrinsically defined asymptotic momentmap with image ing _(x,) ^*. The relevant representations are those associated to this image by the Kirillov correspondence.The genesis of this work has been in the context of linear partial differential operators, in particular the question of hypoellipticity. For example, our framework leads to a natural hypoellipticity conjecture enlarging on that of Helffer and Nourrigat. We believe, however, that the approximation process is likely to have broader applicability, particularly in those contexts where the process can be extended to filtrations with anL ⁰term. This yields not simply a graded nilpotent algebra, but a semi-direct sum with a graded nilpotent. As we show, one such context arises in the approximation of nonlinear control systems.This research was conducted at the MIT Laboratory for Information and Decision Systems, with support provided by the Army Research Office (DAAG29-84-K-0005).     

求解2—D波动方程系数反问题的迭代方法及收敛性

本文针对地震勘探中提出一类重要的２－Ｄ波动方程反演问题，通过定义一个新的非线性算子将２－Ｄ波动方程的反演问题归结为一个新的非线性算子方程，详细讨论了非线性算子的性质，给出了求解反问题的迭代方法，并证明了这种迭代方法的收敛性。     

Nonlinear thresholding of multiresolution decompositions adapted to the presence of discontinuities

A new nonlinear representation of multiresolution decompositions and new thresholding adapted to the presence of discontinuities are presented and analyzed. They are based on a nonlinear modification of the multiresolution details coming from an initial (linear or nonlinear) scheme and on a data dependent thresholding. Stability results are derived. Numerical advantages are demonstrated on various numerical experiments.     

ON MONOTONE CONVERGENCE OF NONLINEARMULTISPLITTING RELAXATION METHODS

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Intrinsic theory of projective changes in Finsler geometry

The aim of the present paper is to provide an intrinsic investigation of projective changes in Finsler geometry, following the pullback formalism. Various known local results are generalized and other new intrinsic results are obtained. Nontrivial characterizations of projective changes are given. The fundamental projectively invariant tensors, namely, the projective deviation tensor, the Weyl torsion tensor, the Weyl curvature tensor and the Douglas tensor are investigated. The properties of these tensors and their interrelationships are obtained. Projective connections and projectively flat manifolds are characterized. The present work is entirely intrinsic (free from local coordinates) (arXiv:?0904.?1602 [math.DG]).