具有无限时滞的随机泛函微分方程的解的唯一存在性

本文主要证明了在相空间（B）中具有无限时滞随机泛函微分方程解的唯一存在性.推广了文献[2]中的相空间,并且给出了一些相空间存在的例子.另外,本文建立了一个Banach空间（M）^2t0（（-∞,T],Rd）依范数‖·‖,并在这个空间上讨论了具有无限时滞随机泛函微分方程的解的唯一存在性.     

混沌时序相空间重构的分析和应用研究

在国内外学者工作的基出上,应用Legendere坐标法重构动力系统的相空间,研究了时序时隔τ的取值范围,讨论了时序间隔τ对相空间重构工作的影响,并用所提方法重构了系统的吸引子.算例表明所提方法是有效的.     

高能强子-强子碰撞多粒子末态纵向相空间的研究

对高能强子-强子碰撞多粒子末态高度各向异性的相空间(称为“纵向相空间”)进行了深入的研究。指出,相空间的各向异性除了表现在纵横两个方向上平均动量的大小悬殊之外,也应表现在这两个方向上的动力学起伏各向异性,导致相空间中的粒子分布有自仿射分形性质。给出了一种用实验检验自仿射分形和测量自仿射的特征量——Hurst指数的方法。此外,还讨论了纵向分形和横向动量之间的关联,给出了表征碰撞事件性质(硬、软、超软)的一个新特征量——单事件平均横动量Pt.将所得到的结果和实验作了比较。     

长期预报相空间模式的预报误差估计

§1.预报误差与资料个数、相空间维数和模式阶数的关系 设时间序列的点间隙为ε,模式的阶数为q,相点数为N,资料数为n,相空间维数为d,则:     

基于相空间重构技术的原油价格的时序混沌判据和混沌特征量

通过相空间重构技术,对Brent和WTI原油价格增长率的时间序列分别进行相空间重构,将若干固定时间延迟点上的数据作为新维处理,形成相点,应用Wolf方法得出了最大的Lyapunov指数,从而给出了系统混沌存在的证据;利用关联函数求出了关联维度和Kolmogorov熵,从而给出了对系统的混沌程度的估计和对Brent和WTI原油价格进行有效性预测的时间尺度.     

二维输运方程离散格式的对称性

讨论了二维柱几何非定态中子输运方程离散格式的对称性问题，在几何空间和相空间连续的情况下，证明了时间离散方程的一维球对称性；而在时间和相空间离散的情况下，阐述了格式不具有一维球对称性；对时间和相空间离散情况下的几何空间间断有限元方程，得到了左右对称性。     

量子系统的整体正则对称性

基于相空间路径积分,分别导出了正规和奇异拉氏量系统在增广相空间中整体对称的Ward恒等式,从而可给出Green函数间的关系.在量子水平上建立了正则整体对称和守恒量之间的关系.一般来说,经典理论中对称性所联系的守恒量,在量子理论中不一定再保持.这里给出的形式其显著优点在于勿需作出生成泛函中对正则动量的路径积分.重新讨论了含Hopf项和Chem-Simons项的非线性σ-模型,在量子水平上对“分数自旋”性质给予了说明.     

基于混沌最小二乘支持向量机的时间序列预测研究

为了对这种具有非线性特性的时间序列进行预测,提出一种基于混沌最小二乘支持向量机.算法将时间序列在相空间重构得到嵌入维数和时间延滞作为数据样本的选择依据,结合最小二乘法原理和支持向量机构建了基于混沌最小二乘支持向量机的预测模型.利用此预测模型对栾城站土壤含水量时间序列进行了预测.结果表明,经过相空间重构优化了数据样本的选取,通过模型的评价指标,混沌最小二乘支持向量机的预测模型能精确地预测具有非线性特性的时间序列,具有很好的理论和应用价值.     

太阳风质子各向异性速度分布的产生机制

太阳风高速流中观测到质子速度的各向异性分布, 但是长期没有得到合理解释. 用质子与回旋波共振产生的扩散平台解释了这一观测现象. 研究了色散对回旋共振形成的扩散平台的影响, 发现用冷等离子体的色散关系求出的扩散平台与0.3AU高速流中观测到的质子速度相空间中的密度等值线符合得很好, 对于0.7~1.0 AU高速流中观测到的质子相空间密度等值线则需要考虑热等离子体的色散关系. 还给出了太阳风高速流中质子速度各向异性A与等离子体β 值的关系.     

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。     

On uncertainty bounds and growth estimates for fractional fourier transforms

Gelfand–Shilov spaces are spaces of entire functions defined in terms of a rate of growth in one direction and a concomitant rate of decay in an orthogonal direction. Gelfand and Shilov proved that the Fourier transform is an isomorphism among certain of these spaces. In this article we consider mapping properties of fractional Fourier transforms on Gelfand–Shilov spaces. Just as the Fourier transform corresponds to rotation through a right angle in the phase plane, fractional Fourier transforms correspond to rotations through intermediate angles. Therefore, the aim of fractional Fourier estimates is to set up a correspondence between growth properties in the complex plane versus decay properties in phase space.     

Sampling and interpolation in de Branges spaces with doubling phase

The de Branges spaces of entire functions generalize the classical Paley-Wiener space of square summable bandlimited functions. Specifically, the square norm is computed on the real line with respect to weights given by the values of certain entire functions. For the Paley-Wiener space, this can be chosen to be an exponential function where the phase increases linearly. As our main result, we establish a natural geometric characterization in terms of densities for real sampling and interpolating sequences in the case when the derivative of the phase function merely gives a doubling measure on the real line. Moreover, a consequence of this doubling condition is that the spaces we consider are model spaces generated by a one-component inner function. A novelty of our work is the application to de Branges spaces of techniques developed by Marco, Massaneda and Ortega-Cerdà for Fock spaces satisfying a doubling condition analogous to ours.     

Phase space analysis of semilinear parabolic equations

We present a wave packet analysis of a class of possibly degenerate parabolic equations with variable coefficients. As a consequence, we prove local wellposedness of the corresponding Cauchy problem in spaces of low regularity, namely the modulation spaces, assuming a nonlinearity of analytic type. As another application, we deduce that the corresponding phase space flow decreases the global wave front set. We also consider the action on spaces of analytic functions, provided the coefficients are analytic themselves.     

Maximal regularity in continuous interpolation spaces and quasilinear parabolic equations

In this paper we establish a geometric theory for abstract quasilinear parabolic equations. In particular, we study existence, uniqueness, and continuous dependence of solutions. Moreover, we give conditions for global existence and establish smoothness properties of solutions. The results are based on maximal regularity estimates in continuous interpolation spaces. An important new ingredient is that we are able to show that quasilinear parabolic evolution equations generate a smooth semiflow on the trace spaces associated with maximal regularity, which are the natural phase spaces in this framework. Received August 10, 2000; accepted September 20, 2000.     

On the symplectic structure of instanton moduli spaces

We study the complex symplectic structure of the quiver varieties corresponding to the moduli spaces of SU(2) instantons on both commutative and non-commutative R⁴. We identify global Darboux coordinates and quadratic Hamiltonians on classical phase spaces for which these quiver varieties are natural completions. We also show that the group of non-commutative symplectomorphisms of the corresponding path algebra acts transitively on the moduli spaces of non-commutative instantons. This paper should be viewed as a step towards extending known results for Calogero–Moser spaces to the instanton moduli spaces.     

On Hom-Prealternative Bialgebras

The aim of this paper is to study phase spaces of Hom-alternative algebras. We introduce notions of Hom-prealternative algebra and Hom-prealternative bialgebra. Bimodules and matched pairs of Hom-prealternative algebra are also considered. Furthermore, we show that the notion of phase space of a Hom-alternative algebra is equivalent to the notion of Hom-prealternative bialgebra. The coboundary Hom-prealternative bialgebra and Hom-PA equation are also described.     

Asymptotic expansions for ornstein-uhlenbeck semigroups perturbed by potentials over banach spaces

An asymptotic expansion of Schilder-type integrals with general phase function on abstract Wiener spaces is given and good control on remainders is obtained. For Ornstein –Uhlenbeck semigroups perturbed by potentials on Banach spaces the asymptotic expansion is given in terms of explicitly discussed “classical orbits”, in the case of finitely many non-degenerate maxima of the phase function. A representation of the leading term by a solution of an infinite dimensional Sturm-Liouville problem is also provided     

Integrable Systems on Phase Spaces with a Nonflat Metric

We study the integrability problem for evolution systems on phase spaces with a nonflat metric. We show that if the phase space is a sphere, the Hamiltonian systems are generated by the action of the Hamiltonian operators on the variations of the phase-space geodesics and the integrability problem for the evolution systems reduces to the integrability problem for the equations of motion for the frames on the phase space. We relate the bi-Hamiltonian representation of the evolution systems to the differential-geometric properties of the phase space.     

Banach Space-Valued Ornstein–Uhlenbeck Processes with General Drift Coefficients

We construct Ornstein–Uhlenbeck processes with values in Banach space and with continuous paths. The drift coefficient must only generate a strongly continuous semigroup on the Hilbert space which determines the Brownian motion. We admit arbitrary starting points and consider also invariant measures for the process, generalizing earlier work in many directions. A price for the generality is that sometimes one has to enlarge the phase space but most previously known results are covered.The constructions are based on abstract Wiener space methods, more precisely on images of abstract Wiener spaces under suitable linear transformations of the Cameron–Martin space. The image abstract Wiener measures are then given by stochastic extensions. We present the basic spaces and operators and the most important results on image spaces and stochastic extensions in some detail.     

A Variation-of-Constants Formula for Abstract Functional Differential Equations in the Phase Space

For linear functional differential equations with infinite delay in a Banach space, a variation-of-constants formula is established in the phase space. As an application one applies it to study the admissibility of some spaces of functions whose spectra are contained in a closed subset of the real line.