代数形式

In section 1 and section 2, I present a simple overview of the bosonic realization of the SU(1,1) Lie algebra, single-mode SU(1,1) coherent states and their main non-classical properties.

第一部分和第二部分，对SU(1，1)李代数的玻色子算符实现形式，单模SU(1，1)相干态及其主要的非经典特性进行了简单的回顾。

Matrix decomposition meams the summation of dividing matrix into several pieces of matrix or product, it is the important in which solved method of some linear algebras problem, its research is significant.

摘要矩阵分解是将一矩阵分解为若干个矩阵的和或乘积的形式，它是解决某些线性代数问题的重要方法，它的研究具有重大的意义。

The Italians mercifully took the second and third words of this phrase and combined them to form algebra.

意大利仁慈了第二次和第三次的话这句话并结合他们的形式代数。

In this paper,a rational approximation method of the norm of parametric speed is given,which is more effective than the polynomial approximation.

文章根据等距曲线逼近的关键在于对其参数速度模的逼近，提出了对参数速度模有理逼近的2种形式，在此基础上给出了平面Bézier曲线等距曲线的逼近函数和误差估计函数，并导出了保持法矢平移方向的代数方式的等距有理逼近算法。

And resolves many difficult issues for complex multibody systems dynamic analysis, design and simulation in engineering areas. Therefore, it is worth to deeply investigate and perfect the spatial operator algebra.

本篇论文也是以空间算子代数理论为研究对象，对其理论作深入研究，并在Lie群、Lie代数、Riemannian流形理论体系中建立空间伴随算子形式的高效率建模和高效率递推运算动力学模型。

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

The basic idea of the method is as follows: an algebraic theorem is used to avoid computing the composition and multiplication of B-spline basis function by Blossom and Polar form, and to reduce the computation by solving linear equations.

基本思想是：运用代数基本定理避免通常B样条基函数复合所采用的极形式以及非常烦琐复杂的开花运算，把B样条基函数的复合、乘积运算转化为求解线性方程组。

The theory of rings is an important content of Modern Algebra, while the polynomial rings is an important part of the rings. Polynomial ring is similar with power series ring, and it is a subset of the power series.

摘要环论是近世代数中的重要内容，而多项式环的性质又是环论理论中的重要组成部分，多项式环是幂级数环的子环且与幂级数环形式相近。

The problem is reduced to a single unknown equation after algebraic elimination. The input-output equation, which is proved to be a 42th degree polynomial equation, is obtained.

首先根据不同的环路列出矢量方程，然后将方程转化成复数形式，经过代数消元后得到了输入输出方程。

Thisdissertation introduces all kinds of tabular methods for function expression in thisalgebraic system, and discusses all forms and characteristics of tabular in detail, at thesame time; the compression method of truth value table is presented.

本文系统地介绍了该代数系统中各种表格表示方法，并对表格的各种表现形式及相应的性质做了详细的分析，同时给出了真值表规模的压缩方法。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。