Classification problems for shifts on modules over a principal ideal domain

In this paper we study symbolic dynamics over alphabets which are modules over a principal ideal domain, considering topological shifts which are also submodules. Our main result is the classification, up to algebraic and topological conjugacy, of the torsion-free, transitive, finite memory shifts.

     

EAPPROXIMATE INERTIAL MANIFOLDS FOR THE SYSTEM OF THE J-J EQUATIONS

ＡＰＰＲＯＸＩＭＡＴＥＩＮＥＲＴＩＡＬＭＡＮＩＦＯＬＤＳＦＯＲＴＨＥＳＹＳＴＥＭＯＦＴＨＥＪ－ＪＥＱＵＡＴＩＯＮＳＡＰＰＲＯＸＩＭＡＴＥＩＮＥＲＴＩＡＬＭＡＮＩＦＯＬＤＳＦＯＲＴＨＥＳＹＳＴＥＭＯＦＴＨＥＪ－ＪＥＱＵＡＴＩＯＮＳ￥ＣａｉＲｉｚｅｎｇ（...     

Asymptotic behavior of non-autonomous Lamé systems with subcritical and critical mixed nonlinearities

This paper deals with the asymptotic behavior of solutions to a class of non-autonomous Lamé systems modeling the physical phenomenon of isotropic elasticity. The main feature of this model is that the nonlinearity can be decomposed into a subcritical part and a critical one. We first show that the system generates a non-autonomous dynamical system, and then prove that the system has a minimal universe pullback attractor. The upper-semicontinuity of these pullback attractors is also established as the perturbation parameter of the external force tends to zero. The quasi-stability ideas developed by Chueshov and Lasiecka (2010, 2008, 2015) are used to prove the pullback asymptotic compactness of the solutions in order to overcome the difficulty caused by the critical growthness of the nonlinearity.     

带有热源项的非线性扩散方程的精确解

讨论了带有热源项的非线性扩散方程.通过一种直接简洁的方法得到了几种精确解.该方法可用于更高阶演化方程的求解问题.     

Renormalization group for Markov chains and application to metastability

In this paper we introduce a new renormalization group method for the study of the long-time behavior of Markov chains with finite state space and with transition probabilities exponentially small in an external parameter. A general approach of metastability problems emerges from this analysis and is discussed in detail in the case of a two-dimensional Ising system at low temperature,     

MANET中基于动态拓扑的多路径自适应流量分配算法

移动自主网络中的大多数多路径路由方案几乎没有考虑流量分配和负载均衡问题。显然,无论路径质量好坏给每条路径分配相同的负荷,会大大降低多路径路由机制的性能,最后会大幅增加网络的通信开销和节点的处理开销。围绕这些问题,提出了一个基于动态拓扑的多路径自适应动态流量分配方案,根据路径质量的权重来动态地给多条路径分配数据流量的比例。大多数情况下仅用局部的信息做路由决定,因此大大减少网络开销。在OPNET模拟平台中实现了这个协议,结果表明,该方案对于MANET网络来说的确是一个可行的方法。     

Raman Theory for a Molecule in a Vibrating Microcavity Oscillating in Fundamental Resonance

We propose a model to describe the energy structure and dynamics of a system of a molecule interacting with infinite photon modes in a vibrating microcavity whose boundary oscillates in the fundamental resonance.By constructing an so(2,1) Lie algebra for the infinite photon modes,we obtain analytical expressions of the energy eigenstates,energy eigenvalues and the system‘s evolution operator for this Raman model under certain conditions.     

单自由度磁浮陀螺寻北仪的控制及分析

提出了一种结构简单的新型磁悬浮寻北仪,建立了电磁轴承约束的单自由度陀螺罗盘的数学模型,讨论了陀螺框架轴在弹性约束下偏离铅垂方向对寻北精度及定向时间的影响。采用动态补偿器使磁浮轴承系统稳定工作,并通过适当选取控制策略,有效地降低了由于框架轴运动而造成的寻北误差,并解决了可能出现的转子轴轨迹发散的问题。仿真结果表明,该磁悬浮寻北仪具有明显优于现有寻北仪的性能,当寻北时间为40 s时,定向误差小于2.3081×10?11 rad。     

一种新的混沌同步及保密通信方式

本文提出一种新的混沌同步及保密通信方式。在发送端，将信息信号与混沌载波的和经取模运算后再嵌入混沌动力系统的迭代之中以实现调制；在接收端，用一个相应的非动力学系统从接收信号中提取混沌载波并进而恢复信息信号。研究表明，该混沌同步方式具有较强的抗干扰能力并且实现容易；该保密通信系统保密性能良好。