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本文研究了辛群胚上的拉格朗日双截面。In this paper, we study the Lagrange bisection at the symplectic groupoids.

研究的是辛三代数的幂零性。The nilpotency about the symplectic ternary algebra is discussed in this paper.

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同时给出了一种辛空间中处理端部条件问题的有效方法。Meanwhile, an effective method for end conditions was given in the symplectic space.

这种辛方法和数值算法为解决其他问题提供了一种可行的思路。The symplectic method and numerical method provide an idea for other researches also.

在辛体系下描述了二维热粘弹性力学问题。Two-dimensional problems of thermo-viscoelasticity in the symplectic system were described.

利用辛本征解空间的完备性，建立一套封闭的求解问题方法。With the aid of the completeness of symplectic eigensolutions, a close method was presented.

给出了一种构造完全随机的正交辛矩阵的数值实现方法。And a numerical algorithm for constructing a random symplectic orthogonal matrix is put forward.

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本文研究了李群的余切丛上的辛群胚结构。In this paper, we study the symplectic groupoids structure on the cotangent bundle of Lie group.

通过谱问题的双非线性化，导出一个新的可积的辛映射。A new integrable symplectic map is derived by means of nonlinearization of the eigenvalue problem.

本文主要以李群、辛流形及群胚等为基本研究对象。In this paper, Lie group, Symplectic manifolds, Groupoids are treated as fundamental research subjects.

然后给出正则变换的摄动保辛方法。The canonical transformation method is proposed for symplectic conservative perturbation approximation.

本文研究了矩映射在泊松G-空间及辛群胚中的应用。In this paper, we study the application of the momentum mapping to a Possion G-space and symplectic groupoids.

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在辛几何空间中直接描述正则方程和对应的边条件。The dual equations and conditions of the corresponding boundary are obtained directly in the symplectic space.

结果表明，此前提出的所有不等价表示式中，只有个别表示式对这些算子是可计算的。The connotation and denotation representations of pseudo-symplectic space about symplectic space are demonstrate.

本文介绍了用辛显式格式计算一类哈密顿方程的理论及实例。The paper introduces the theory and example counting a class of Hamilton equations by symplectic obvions schemes.

建立电磁波导问题的变分原理，构造电磁辛有限元。Based on the variational principle for dual variables, the electro-magnetic symplectic finite element method is derived.

因此，研究保持哈密尔顿系统的辛几何结构特征的数值方法是必然的。Therefore, it is necessary to study numerical methods which preserve the symplectic structure of the Hamiltonian system.

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基于该变分原理，提出一种称之为辛空间有限元-时间子域法的辛算法。Based on this variational principle in phase space, a symplectic space finite element_time subdomain method is presented.

三步量子辛算法进行波包演化被用于研究碘甲烷的光解。Three-step symplectic quantum propagation of wavepacket has been applied to study the photodissociation of methyl iodide.

论述欧氏空间、辛空间、伪辛空间的本质属性及演变过程。The essential property and developmental course of Euclidean space, symplectic space and bogus symplectic space are studied.