查询词典 symmetries

The two kinds of symmetries in holonomic and non-holonom-ic mechanical systems,i.e.symmetries of differential equations of motion(ab-breviated as SDEM)and symmetries of Noether-type,and interrela-tions among all kinds of symmetries are investigated.The necessary and suffi-cient conditions of SNT to be SDEM are found out.It is pointed out thatSDEM have distinct geometric properties which are equivalent to the geodesiccharacteristic of differential equations of motion and geodesic deviation.

文中研究了完整与非完整力学系统的两类对称性，即运动微分方程的对称性和Noether型对称性，以及各种对称性之间的相互关系，确定了Noether型对称性为运动微分方程对称性的充分必要条件，并指出运动微分方程的对称性具有明确的几何性质，即它等价于运动微分方程的测地性质以及测地偏离性质。

Contents: A Brief Review of Elementary Quantum Chemistry; An Introduction to Electronic Structure Theory; The Born-Oppenheimer Approximation; Time Evolution of Wavefunctions; Angular Momentum Summary; The Unitary Group Form of the Hamiltonian; Introduction to Hartree-Fock Theory; Permutational Symmetries of Integrals; Notes on Excited Electronic States; The Quantum Harmonic Oscillator; Assigning Symmetries of Vibrational Modes; Notes on Elementary Linear Algebra

内容： 初等量子化学的简评；电子结构理论的介绍；天生奥本海默的接近； Wavefunctions的时间演化；角动量摘要； Hamiltonian的单位的组形式；哈特里-Fock 理论的介绍；积分的Permutational对称性；在令人激动的电子国家上注明；这台量谐波振荡器；分配振动的方式的对称性；在初等线性代数上注明

In the fourth chapter,we study theperturbation to the symmetries and adiabatic invariants of Birkhoff system.

第四章研究了Birkhoff系统的对称性摄动与绝热不变量。

On the other hand, equivariant algebraic topology concerns the study of algebraic invariants of space with group actions. It is really a study of symmetries on spaces, and has always occupied a central role in mathematics.

在另一方面，等变代数拓扑关注于带有群作用的拓扑空间代数不变量的研究，其更深刻的本质在于对空间对称性的揭示，因此从来都在数学研究中占有重要的地位。

Therefore, with variations of spatial orientation of the symmetry axis and the surveying line azimuth, patterns of body_wave velocity show variety, and have some symmetries, gradual changes and repetitions.

因此，随着TI对称轴取向的空间变化和测线方位的变化，体波速度图案呈现多样性变化，并具有一定的对称性、渐变和重复性。

Then, have explored the conformer interconversion among all glycine conformers, and discussed some arguments about glycine conformers' symmetries.

研究所有的苷氨酸构象异构体之间相互转换，并且探讨了苷氨酸构象异构体的对称性问题。

Thus, we can determine the degeneracy of modes by simply inspecting mode symmetries.

模式的简并与非简并可以直观地通过考察模式场分布的对称关系而得到。

In the fourth section of this paper, we take into account one of the main features of the problem: namely, the presence of large symmetries in the solution space. In fact, the degree of symmetry grows exponentially with the cardinality of the set of colors.

在本文的第四章节中，研究发现在利用遗传算法解决图的着色问题中存在着一个重要的不足，即在问题解空间中存在着大量的冗余数据。

We present the fundamental theories of Noether symmetries and conserved quantities of mechanco-electrical dynamical systems, including variation principle of the system, Noether symmetry transformation, Noether quasi-symmetry transformation, generalized Noether quasi-symmetry transformation, Killing equations, Noether theorem, the form of conserved quantity. And then the basic theory of Lie symmetry is advanced, including the determining equation, structure equation and the form of conserved quantity.

给出机电动力系统的Noether对称性和守恒量基本理论，包括系统的变分原理、Noether对称性变换、Noether准对称性变换、广义Noether准对称性变换、Killing方程、Noether定理和守恒量的形式；给出机电动力系统Lie对称性的基本理论，包括确定方程、结构方程以及守恒量的形式。

In this paper linear algebra and differential geometry are used to analyze the structure of linear and nonlinear control systems possessing symmetries.

这一方法对于非线性系统的很多方面，如能控性，能观性，分解，解耦及精确线性化。。。

Vishnu entered a dark fourth dimensional dream that did not support his field or continued life.

毗瑟挐进入了一个第四密度的黑暗梦想，那里并不支持他的能量场或继续生命。

Leaders and decision-making persons use it to collect the data, including the information of unit work, handing in fee, oweing fee, prepaying fee,changing and afterpaying and account transfering of joining-insurance employee, and account paying of all kinds of insurances from hospitalization insurance institutions.The collected data is picked up, organized, switched and showed to user.

该子系统主要面向各级领导、决策分析人员；从各个医疗保险经办机构和定点医疗机构采集数据，包括在各个医疗保险经办机构处理的单位办公信息，单位缴费、欠费、预缴费信息，参保职工变更信息，参保职工增减变动信息，参保职工补缴信息，参保职工帐户划拨信息：包括各定点医疗机构处理的各险种帐户支出信息，各险种的统筹金支付信息等；将采集的数据提取，组织和转换，然后展示给用户。