一般状态空间跳过程的遍历性

该文研究了一般状态空间跳过程的遍历性,得到了与连续时间可数状态空间马氏链类似的结果.     

一般状态空间跳过程的强遍历性

研究了一般状态空间跳过程的强遍历性,利用最小非负解理论及马氏性,得到了强遍历性的几个等价条件,把连续时间可数状态马氏链的相关结果推广到一般状态空间跳过程的情形.     

随机环境中的马氏链状态分类

给出了随机环境中马氏链的特征数和状态的定义,讨论了状态间的传递性,自反性,对称性,是经典马氏链相应结果的一般化.并运用位势方法研究了状态间的关系,它们在极限理论的研究中非常有用.     

股票指数的时间序列模型分析

借助于SA S软件将工程中的K a lm an滤波方法与时间序列的状态空间模型结合对上海A股指数进行了拟合与预测分析,通过对拟合与预测误差的计算可以发现这种模型是可行的;然后还把与滤波结合的状态空间模型的分析结果和常见的时间序列模型如:AR IM A模型、逐步自回归模型以及指数平滑模型的分析结果进行比较,比较的结果说明结合滤波的状态空间模型分析的结果比后三种的结果更加精确.结果为时间序列数据分析提供了一个较好的分析工具.     

带强迫项的二阶泛函微分方程解的振动性和渐近性

该文建立了偏差变元依赖于状态的二阶强迫泛函微分方程解的若干振动和渐近性质 ,所得结果推广和改进了文献中的有关结果     

具有不同耦合强度且带有时滞的振子网络上的同步

本文研究了具有不同耦合强度且带有时滞的振子网络上的同步问题．我们给出了该网络同步状态的稳定性准则，证实了其同步状态的稳定性与网络的拓扑性无关．最后，通过数值模拟验证了我们的理论结果．     

全局最优信息融合估计算法(Ⅱ)

假定局部滤波器的状态估计是相关的条件下，得到了状态向量的全局最优融合估计，作为应用，得到了比文[1]中更为普遍，实用的结果。     

一般状态空间跳过程不变测度的存在性和唯一性

本文利用一般状态空间马氏链关于不变测度的有关结果和跳过程的性质，研究了一般状态空间跳过程不变测度的存在性和唯一性。     

离散时间模糊控制系统的新型状态观测器设计

针对离散时间模糊控制系统的状态估计问题,设计出一种新颖的多时刻依赖型模糊状态观测器.与已有结果不同,所设计的模糊状态观测器设计不仅依赖于当前时刻的模糊隶属函数,还依赖于过去时刻的模糊隶属函数;这些特性为状态估计设计引入更多的自由度,可以得到保守性显著降低的模糊状态观测器.此外,针对衍生出多时刻模糊求和问题,还提出了一种新型松弛变量技术来进一步降低模糊状态估计问题的保守性.特别地,本文所设计的模糊观测器属于可求解的一组线性矩阵不等式,所以具有较好的可实现性.最后,通过一组仿真实验来验证本文结果的优越性.     

树上路径过程的随机路径条件概率的强极限定理

本文研究了树上路径过程随机转移概率和状态序偶出现频率的强极限定理.通过利用若干重要不等式,获得了树上路径过程的随机路径条件概率用不等式表示的几何平均强极限定理以及树上路径过程关于状态序偶出现频率的用不等式表示的强极限定理,所得结果推广了树上马氏链及非齐次马氏链中的结果.     

Bounds on the density of states for Schrödinger operators

We establish bounds on the density of states measure for Schrödinger operators. These are deterministic results that do not require the existence of the density of states measure, or, equivalently, of the integrated density of states. The results are stated in terms of a “density of states outer-measure” that always exists, and provides an upper bound for the density of states measure when it exists. We prove log-Hölder continuity for this density of states outer-measure in one, two, and three dimensions for Schrödinger operators, and in any dimension for discrete Schrödinger operators.     

混合态的不确定关系与压缩效应

在关于混合态的海森堡不确定关系的基础上，研究了纯态和混合态的最小不确定性和压缩效应.虽然最小不确定态必定是纯态，但在某些并非最小不确定态的纯态或混合态中，依然可 以实现力学量不确定度的压缩.还给出了普通统计学的不确定关系，它们不涉及量子相干性却与量子力学的海森堡不确定关系具有相似的数学结构.     

一类特殊非齐次树上马氏链的若干强大数定律

首先给出了一类特殊非齐次树上可数状态马氏链的局部收敛定理,作为推论,得到了此类树上可数状态马氏链关于状态与状态序偶出现频率的若干极限性质,最后得到了这类特殊非齐次树上有限状态马氏链关于状态与状态序偶出现频率的强大数定律.     

Calculation of Berry's phase in squeezed states

A simple method based on generalized coherent states is proposed for calculation of Berry's phase. In this paper we calculate Berry's phase for a translated oscillator in standard coherent states as well as Berry's phase in squeezed states and spin coherent states, i.e., coherent states for the SU(1, 1) and SU(2) groups, respectively.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 169, pp. 51–59, 1988.     

Dynamical systems which realize given random bi-sequences of points on their orbits

A dynamical system consists of a phase space of possible states, together with an evolution rule that determines all future states and all past states given a state at any particular moment. In this paper, we show that for any countable random infinite bi-sequences of states of some phase space, there exists an evolution rule in C⁰-topology which realizes precisely the given sequences of states on their orbits and satisfies some regular conditions on the times to realize the states.     

Asymptotic profiles of positive steady states for a diffusive predator–prey model with predator interference

This paper is concerned with positive steady states for a diffusive predator–prey model with predator interference in a spatially heterogeneous environment. We first establish the necessary and sufficient conditions for the existence of positive steady states. In order to get a better understanding of the structure of positive steady states, we further investigate the asymptotic profiles of positive steady states as some parameter tends to zero or infinity.     

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??In this paper, various concepts of states for Markov chains in random environments are introduced into the research field, and the relationships between these states are discussed. Especially, a partition of the state space is given. Also, the properties of those states are investigated. At last, some examples are given to illustrate the rationality of those states.     

Coherent states for the Hartmann potential

We obtain the coherent states for a particle in the noncentral Hartmann potential by transforming the problem into four isotropic oscillators evolving in a parametric time. We use path integration over the holomorphic coordinates to find the quantum states for these oscillators. The decomposition of the transition amplitudes gives the coherent states and their parametric-time evolution for the particle in the Hartmann potential. We also derive the coherent states in the parabolic coordinates by considering the transition amplitudes between the coherent states and eigenstates in the configuration space. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 155, No. 3, pp. 439–452, June, 2008.     

Scale transformations in phase space and stretched states of a harmonic oscillator

We consider scale transformations (q, p) → (λq, λp) in phase space. They induce transformations of the Husimi functions H(q, p) defined in this space. We consider the Husimi functions for states that are arbitrary superpositions of n-particle states of a harmonic oscillator. We develop a method that allows finding so-called stretched states to which these superpositions transform under such a scale transformation. We study the properties of the stretched states and calculate their density matrices in explicit form. We establish that the density matrix structure can be described using negative binomial distributions. We find expressions for the energy and entropy of stretched states and calculate the means of the number-ofstates operator. We give the form of the Heisenberg and Robertson–Schrödinger uncertainty relations for stretched states.     

Wigner distribution functions for a relativistic linear oscillator

We construct the Wigner representation for a relativistic model of the linear harmonic oscillator governed by a finite-difference equation. We find Wigner functions for the stationary states, the thermodynamic equilibrium states, and the coherent states. We examine their nonrelativistic limits and the high and low temperature limits for the equilibrium states. We compute the mean values of the position and momentum coordinates for these Wigner functions. Translated from Teoreticheskaya i Matematicheskaya Fizika. Vol. 114, No. 3. pp. 410 425, March, 1998.