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Simulation indicates that the Hamiltonian function contains detailed information of transient energy changing.

仿真表明，系统的哈密顿函数包含了系统暂态中能量变化的详细信息。

Hamilton principle can be used in holonomic system and intrinsical linear nonholnomic system. The formulas of them are unified. Hamiltonian action is stability in intrinsical linear nonholnomic system.

本文将Hamilton原理应用到本质线性非完整系统，首次证明了在本质线性非完整系统中，Hamilton作用量为稳定的作用量；将完整系统和本质线性非完整系统的Hamilton原理从形式和本质上统一起来。

Result we get the Hamiltonian expressed by Hubbard operators of the spin-ladder model.

结果我们得到了用Hubbard算符表示的自旋梯模型的哈密顿量。

One important feature ofHamiltonian systems is that it has energy(its energic function is Hamiltonian func-tion),then,its solutions on 2-dimensional plane are some contour lines,the points onstable manifold emanating from hyperbolic equilibrium point have the same energyas that on unstable manifold,then,one can guess that they form a closed curve,i.e.homoclinic orbits under certain conditions,and the contour lines in the innerpart of homoclinic orbit are periodic orbits.

哈氏系统的一个重要特征是它有能量存在(以Hamiltonian函数作为它的能量)，那么在二维平面上，它的解表现为一些等值线，从双曲平衡点发出的稳定流形和不稳定流形上的点具有相同的能量，那么可以猜测，在一定条件下它们构成一条封闭的曲线，即同宿轨，而且其内部的等值线都是周期轨道。

Structure-preserving algorithm for infinite dimensional Hamiltonian systems also made many results.

无穷维Hamilton系统的保结构算法也有很多成果。

For example,we shall be discussing graphs which contain paths which include every edge or every vertex exactly once,ending up at the initial vertex [7];such graphs will be called Eulerian and Hamiltonian graphs respectively.

例如，我们将讨论这样一些图，图中存在包含所有边或所有顶点一次且仅一次而回到出发顶点的路，我们分别称之为欧拉图和哈密尔顿图。

For Example,we shall be discussing graphs which cintain paths which include every edge or every vertex exactly once,ending upa at the initial vertex;such graphs will be called Eulerian and Hamiltonian graphs respectively.

例如，我们将讨论这样一些图，图中存在包含所有边或所有顶点一次且仅一次而回到出发顶点的路，我们分别称之为欧拉图和哈密尔顿图。

By virtue of the invariant manifolds and conservative property of Hamiltonian system, we construct a"switching algorithm"to compute the periodic solution of equation (4) when the dispersion distribution σ is periodic and piecewise constant function.

4运用不变流形的分析方法和哈氏系统的守恒性质，给出了当色散分布σ为周期的分片常数情形计算方程(4)的周期轨的一个"开关算法"。

The completely diagonalized Hamiltonian matrices of 3d2/3d8 ion configuration in the trigonal symmetry have been established by irreducible representation method. Taken into account the influence of the spin-spin coupling interactions omitted in previous publications, the spectra and the constants of crystal structure and zero-field splitting parameters of CsNiCl3 crystal and CsNiCl3: Mg2+ crystal are calculated and the influence of the doping to the spectra, the constants of crystal structure, zero-field splitting parameters and Jahn-Teller effect are studied. The results show that doping can change the structure of crystal which brings about the changes in the spectra and zero-field splitting parameters as well as Jahn-Teller effect.

应用不可约张量理论构造了三角对称晶场中3d2/3d8态离子的45阶可完全对角化的微扰哈密顿矩阵，在考虑了以前工作中被忽略的自旋-自旋耦合作用的基础上计算了CsNiCl3晶体和CsNiCl3：Mg2+晶体的基态能级、晶体结构、零场分裂参量和Jahn-Teller效应，研究了掺入Mg2+对CsNiCl3晶体的光谱、零场分裂参量及Jahn-Teller效应的影响和自旋单重态对基态能级的贡献，发现掺杂使得晶体结构产生畸变，从而改变晶体光谱的精细结构和零场分裂参量，不改变Jahn-Teller效应的分裂规律但改变分裂的大小。

The complete diagonalized Hamiltonian matrixes of order 120 of 3d~3/3d~7 ions configuration in the trigonal symmetry have been established by irreducible representation method and group theory,taking spin-orbit interaction,spin-spin interaction and spin-other-orbit interaction into account.

应用不可约张量方法和群的理论构造了三角对称晶场中考虑自旋-轨道相互作用，自旋-自旋相互作用和自旋-其它轨道相互作用的3d3/3d7态离子的可完全对角化的120阶微扰哈密顿矩阵。

In the days of sailing vessels the crew were afraid they would be becalmed on the ocean.

在使用帆船的时代，船员们担心他们会因为无风而无法在海洋上航行。

As long as foreign donors pay the PA's salary bill, few expect a new intifada.

只要外国继续为巴权力机构的薪水买单，希望发动新暴动的人便寥寥无几。