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In the first part, for competitive discrete-time dynamical systems on a strongly ordered topological vector space, we prove that any α-or ω-limit set is unordered and lies on some invariant hypersurface with codimension one, which generalizes M.

在第一部分中，对于强序拓扑向量空间上的竞争离散动力系统，我们研究了极限集的序结构和极限集的几何位置，证明了任何α-或ω-极限集是无序的且位于一个完全无序的，余维为1的不变Lipschitz流形上。

The loca l bifurcation characteristic near by codimension two bifurcation point is discus sed,which testifies that the local dynamical behavior of map fmay be known under the condition of cod.

通过分析范式在余维二分岔点附近的局部分岔行为，可以了解映射f在余维二分岔条件下的局部动力学行

In chapter 2, a new concept- property T〓 is introduced, it is proved that nest subalgebras of von Neumann algebras, finite width CSL and atomic CSL subalgebras of von Neumann algebras have property T〓. Some tensor product formulae of nest subalgebras and CSL subalgebras in von Neumann algebras are obtained. Tensor products of W〓-dynamical systems are studied. Finally, the essential commutant of tensor product of operator algebras is discussed.

第二章我们引入了性质T〓这一新概念，并证明了任一vonNeumann中的任何套子代数，有限宽度的可交换格子代数和原子可交换格子代数都具有性质T〓；得到了von Neumann代数中套子代数和可交换格子代数的张量积公式；研究了W*-动力系统的张量积问题；最后讨论了张量积代数的本性换位。

Other semirings arise naturally in such diverse areas of mathematics as combinatorics, functional analysis, topology, graph theory, Euclidean geometry, probability theory, commutative and noncommutative ring theory, optimization theory, discrete event dynamical systems, automata theory, formal language theory and the mathematical modeling of quantum physics and parallel computation systems.

在许多不同的数学领域存在着其它形式的半环，比如组合学，泛函分析，拓扑学，图论，欧式几何，概率论，交换和非交换环，优化论，离散动力系统，自动化理论，形式语言理论，量子物理的数据模型和并行计算系统。

The design of a dynamical compensator to stabilize simultaneously the family of given systems is studied.

研究了多重系统同时稳定和同时强稳定的动态补偿控制器设计问题。

Besides, in the new spectral dynamical framework the calculation amount firstly is decreased to half by properly using the complex conjugate relation of spectral coefficients and the symmetric and anti-symmetric character of spherical function.

另外，新方案中的纬向谱系数计算式，合理利用谱系数的复共轭性质及球函数关于赤道对称或反对称特性，使计算量减半。

In this design, the dimension M of the memory vector field may be not necessarily equal to the dimension N of the network vector field. This may be the usually case in applications. Designing a network with either static or oscillating behavior, after analysing the dynamical. behavior of its four-dimension subspace, we get 2-torus in the subspace. If we vary the ratio of the imagine parts of the complex conjugate eigenvalues, the periodic motion of all kinds of period ratio on 2-torus are obtained.

设计一个既具有静态平衡点又具有动态振荡的网络，其静态平衡点由多余维叉形分叉得到，动态振荡形式由多余维Hopf分叉得到，通过对其中一个具有振荡行为的四维子空间的进一步分析，可以得到网络在四维子空间中的二环面运动，适当调整约当形中共轭复特征根虚部的比值，可以得到各种周期比的二环面上的周期运动。

In chapter three, the problem of the nonlinear dynamical stability of the shallow reticulated conical shell is analyzed.

在第三章中主要研究了扁锥面网壳的非线性动力稳定性问题。

Analysis of dynamical simulation data shows as follows: Wheel tread LMA is able to satisfy the requirements of the 300 km/h~350 km/h high-speed wheel-rail technology, and wheel tread XP55 is able to reach 250 km/h~300 km/h; the main issue of Wheel tread LM is that the larger equivalent conicity may cause the bigger lateral wheel-rail force, and wheel tread S1002 has the severe problem of harmful wheel-rail wear.

动态仿真数据分析表明：LMA型车轮踏面可以满足300 km/h~350 km/h高速轮轨技术要求，而XP55型踏面则可以满足250 km/h~300 km/h速度的要求；LM型踏面的主要问题是等效锥度比较大，从而造成轮轨横向力也比较大，S1002型踏面对轮轨存在比较严重的有害磨耗问题。

In this paper, we review some back ground and recent advances in the field of complex networks, and give the sufficient conditions guaranteeing the local and global synchronization stability of the complex connected dynamical networks with asymmetrical coupling matrix and time delay in coupling by using Lyapunov functional.

在这篇论文中，较全面地介绍了复杂网络研究的背景，发展和现状，着重讨论了动态网络模型的同步性质，应用Lyapunov泛函，考察了带有更一般的不对称连接矩阵以及时滞的复杂动态网络的同步性质，给出了局部和全局同步的充分条件。

Diabetes is a social disease that affects several million people worldwide.

糖尿病是一个社会性疾病，全世界有数百万人罹患此病。

I'll call you on Friday to see if we can reschedule our luncheon meeting at your convenience.

我星期五会给您打电话在您方便的时候我们重新安排我们的午餐约会。