Introduction to wave mechanics : schroedinger ' s equation , wave functions , wave packets , probability amplitudes , stationary states , the heisenberg uncertainty principle , and zero - point energies 介绍波动力学:薛丁格方程式，波方程式，波包，或然率，稳定态，海森堡不确定原理以及零点能量。
The observation results prove that the " fixed point attractor " exists really and it keeps the crustal movement system at " stable steady state " ( dynamic balancing 5tate ) " self - organized stability " 观测结果证明确实存在“不动点吸引子” ，故而能使地壳运动系统长期保持在“稳定态（动平衡态） ” ，即“自组织稳定态” 。
The ground state corresponds to a bent 2a " sno structure . the state - state correlation and the isomerization mechanism are also predicted by searching the transition states and the intrinsic reaction coordinate analysis 基态结构为弯曲的sno ( ~ 2a )结构，通过寻找过渡态和内禀反应坐标分析预测了各稳定态之间的态态相关和异构化机理。
After transient state process ( earthquake , etc ) having occurred , present - day crustal movement ( the changing process with time , the space distribution and the structure of spectrum ) will return to " stable steady state ( dynamic balancing state ) " voluntarily 在地震等暂态过程发生后，现今地壳运动（时变过程、空间分布、频谱结构）仍将自动回归到“稳定态（动平衡态） ” 。
As the reaction time and standing time increase , the percentage of calcium oxalate trihydrate ( cot ) decreases and the percentage of the thermodynamic stable calcium oxalate monohydrate ( com ) increases . the metastable calcium oxalate dihydrate ( cod ) is not observed 随着反应时间和陈化时间的增加，三水草酸钙( cot )直接转化为稳定态的一水草酸钙( com ) ，而没有经过亚稳态的二水草酸钙( cod ) 。
This paper used system dynamics to found the system dynamics model of wuhu city ecosystem . to study the stability of wuhu city eocosystem if it keeps at the development tendency of now or at different productive forces ' parameters . to study the people ' living conditions of the years when the city ecosystem is stability 研究在芜湖市在现状发展情况下和在不同生产力发展参数情况下芜湖市生态系统的稳定性情况，并给出该市的生态系统稳定性达到稳定态之后，该市的人民生活水平状况和在当时生活水平下的承载力情况。
What we do at this aspect are : firstly , we describe the permutation symmetry of the structure of some special networks and the corresponding attractor sets with some geometric graphs in euclidean space , which are called attractors graph and geometrized structure graph of the networks respectively ; the geometrizing conditions are also given ; we study the dynamical behavior of the networks using the geometrized structure graph and attractors graph of the network ; moreover , we propose an approach to construct a big - size network with some small - size network with symmetry by the method of direct - sum , direct - produce and semidirect - produce . we also study the dynamical properties " relation between the big - size network and the small - size networks . all those results will provide some theoretical basis for designing a special large - scale network 本文在这方面所做的工作如下：首次将一些特殊网络的结构和吸引子集的置换对称性用三维欧氏空间中的一些几何图来表示，分别称之为几何结构图和吸引子图；给出了网络对称性的几何化条州即相应的对称性群为可迁群） ：并惜助网络的几何结构图和吸弓吁图分析网络的动力学性质；此外，我们提出了用简单的具有一定对称性的小网络按照群的直和、半直积和直积的方式组合成较大的网络的方法，探讨了这些小网络和所组成的大网络的一些动力学性质的关系，如稳定态的个数、各稳定态的回忆性质等，为较大网络的设计提供一些理论依据。
We also prove the following properties : the stable states of the network in the same sh orbit have a same dynamical behavior , such as the size of attraction basin and the energy ; the relation of the symmetry of two isometric networks h and h ' = g - h is s ' h = g - sh - g ~ } for any isometry g , where sh and s ' h are the symmetry of h and h " respectively ; the isometry will not change the dynamical properties of the stable states set of the corresponding networks ; etc . ) g的对称性s _ h和s _ n的关系为s _ h = g ? s _ h ? g ~ ( - 1 ) ；等距变换不会改变网络稳定态集的动力学性质等一系列的结论。所有这些研究结果表明了hebb学习法则是通过调整网络的连接矩阵，使得其的结构的对称性包含存储样本集的对称性这一存储机理。
Because of " fixed point attractor " , " limit cycle attractor " , " tons attractor " and " strange attractor " dominating the dynamics system , present - day crustal movement presents the various dynamics states such as " stable state ( dynamic balancing state ) " , " period state " , " quasi - period state " , " chaos state " and " edge of chaos " 在”不动点吸引子” 、 “极限环吸引子” 、 “环面吸引子”和“奇异吸引子”的作用下，现今地壳运动呈现出“稳定态（动平衡态） ” 、 “周期态” 、 “拟周期态” 、 “混沌态”和“混沌边缘态”等多种动力学状态。
Hi the aspect of symmetry analyzing to the hopfield model neural network with hebbian learning , we study on the dynamical behavior of the state space under the action of isometric transformation group g = z2 ? n , and prove the invariant property of the energy orientation ? / / " ) of the state space under the action of g . we find that the symmetry relationship of the network is sx - sw = sh when the active function of the neuron is odd , where sx is the symmetry of the patterns set x under hebbian learning rule , sh is the symmetry of the network and sw is the symmetry of the weight matrix w of the network ) s _ n为手段，研究了网络状态空间在群g作用下各点的运动情况，证明了群g作用下的不变性。证明了当神经元的激活函数f为奇函数时， hebb法则下存储样本集x的对称性s _ x 、网络对称性s _ h以及连接矩阵对称性s _ w三者之间满足s _ x = s _ w = s _ h的关系；同时，我们还证明了：网络稳定态集vf同一s _ h轨道中的两个稳定态的动力学行为(能量和吸引域大小)相同；两个等距网络h和h 1 = g ? h ， ( ? ) g (
