代数拓扑；辛几何与拓扑；常微分和偏微分方程。
Algebraic Topology; Symplectic Geometry and Topology; Ordinary and Partial Differential Equations.
辛几何理论是一种求解电磁场波动方程的高频近似法。
Sympleetic Geometrical Theory is a kind of high-frequency asymptotic method of solving electromagnetic wave propagation.
本文主要讨论辛几何中群作用的商的有理上同调的计算方法。
In this paper, we mainly discuss the procedure for computing the rational cohomology of quotients group actions in symplectic geometry.
文中采用辛几何方法得到了二维反射天线上电磁波传播问题的解。
Solution on electromagnetic wave propagation in a two-dimensional reflector antenna by Symplectic Geometrical Theory has been gotten.
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.
从代数动力学算法的观点考察了辛几何算法和龙格-库塔算法的保真问题。
The symplectic geometric algorithm and the Ronge-Kutta algorithm are examined from the viewpoint of the algebraic dynamical algorithm.
利用辛几何的方法推导出了两邻边固支另两邻边简支弹性矩形薄板问题的理论解。
The analytical solutions for an elastic rectangular thin plate with two adjacent boundaries clamped-supported and the others simplified-supported are derived by a symplectic geometry method.
结果再次表明经典力学中的弹性楔佯谬解对应的是哈密顿体系下辛几何的约当型解。
It shows further that solution of the special paradox in classical elasticity is just Jordan canonical form solutions in symplectic space under Hamiltonian system.
因此，研究保持哈密尔顿系统的能量守恒性及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 energy conservation or the symplectic structure of the Hamiltonian system.
在辛几何数学框架下，采用共轭辛正交归一关系给出精确解，并与经典层板理论进行了比较。
The analytical solution for the Angle ply laminated plates is derived by the adjoint orthonormalized symplectic method, and is also compared with the Kirchhoff plate theory.
提出了一种基于辛几何的高频近似的新方法，并用此方法求解了电磁波在一非均匀媒质中的传播问题。
A new symplectic geometrical high frequency approximation method for solving the propagation of electromagnetic wave in an inhomogeneous medium is presented.
通过引入对偶变量，将平面正交各向异性问题导入哈密顿体系，实现从欧几里德几何空间向辛几何空间的转换。
Based on the dual variables, the Hamiltonian system theory is introduced into plane orthotropy elasticity, the transformation from Euclidian space to symplectic space is realized.
二利用辛几何理论求解电磁波在二维凹面体散射中的传播问题，与经典的GO解比较，特别在焦散区得到较理想的场解。
Second, solve electromagnetic wave propagation of two-dimension concave objects by symplectic Geometrical Theory, and get better field solutions in caustic field2)comparing with classical GO method.
从那时开始，人们发现量子群在很多领域都有着深刻的应用，范围遍及理论物理、辛几何、扭结理论与约化代数群的模表示理论等。
Since then they have found numerous and deep applications in areas ranging from theoretical physics, symplectic geometry, knot theory, and modular representations of reductive algebraic groups.
本文利用群胚的有关知识证明了李群在基本群胚上的提升作用有余伴随等变的动量映射这一结论，进而刻划了辛群胚的几何性质。
In this paper, in accordance with the knowledge of Groupoid, we proved that the nature life of Lie Group on a Fundamental Groupoid has a coadjoint equivariant momentum mapping.
本文利用群胚的有关知识证明了李群在基本群胚上的提升作用有余伴随等变的动量映射这一结论，进而刻划了辛群胚的几何性质。
In this paper, in accordance with the knowledge of Groupoid, we proved that the nature life of Lie Group on a Fundamental Groupoid has a coadjoint equivariant momentum mapping.
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