定理

Two basic theorems are given by researching Hamilton's two steps linear differential equations of bender equations which provide widespread application methods of normal differential operator correspond to ladder operators,then the solutions of general equations are obtained by taking advantage of the two above theorems: The energy eigenvalue equation of one-dimensional oscillator; the common state of ; the radial equation of a bondage state of hydrogen atom; the radial equation isotropic three-dimensional harmonic oscillator; the infinity deep potential well of ball

本文通过研究束缚态本征方程里的哈密顿算符的二阶线性常微分形式，给出两个基本定理并证明，提供构造二阶线性常微分算符相应的阶梯算符的普遍实用的方法，然后利用这两个定理构造量子力学中常见力学量的阶梯算符，并用以计算其能量本征值和对应本征函数：一维谐振子的能量本征方程；共同本征态；氢原子束缚态径向方程；三维各向同性谐振子的径向方程；无限深球势阱。

II, Polynomial rings on a general field( on contrast of those over a number field): concepts of ring, ideals, field and several special rings as domains, principal ideal domains and unique factorization domains, the unique factorization theory of polynomial rings.

二、一般域上的多项式理论（是数域上多项式理论的推广）：学习环、域和几类特殊结构的环（整环、主理想环，唯一分解环等）的概念，多项式环的唯一分解定理；三、线性代数：讲述一般数域上的向量空间理论（是数域上向量空间理论的继续和推广），模的概念，主理想环上的模的结构及其线性变换的若当标准型等；四、一元多项式的解及域论：学习域扩张及其相关概念，伽罗瓦理论，用伽罗瓦定理判断根式解的存在性。

The famous probabilist Kolmogorov from previous Soviet Union said: Only probability limit theory can reveal the epistemological value of probability.

前苏联著名的概率学家Kolmogorov曾说过："概率论的价值只有通过极限定理才能被揭示，没有极限定理就不可能去理解概率论中的基本概念的真正含义。"

It has deep connections with the theory of projective space and justifies the use of unitary and anti-unitary group representations in physics.

鉴于Wigner定理的重要意义，本文对Wigner定理的提出、论证、在不同背景条件下的推广和发展做了简要的总结。

The computational formula of the gradient matrix in subspace is obtained by applying Taylor series expansions, decomposition theorem of space and projective theorem (The gradient matrixs in different subspace are different).

利用子空间上的泰勒展式、空间分解定理以及投影定理得到了子空间上梯度矩阵的计算公式(不同的子空间，梯度矩阵是不相同的)。

This is the content of Brauer's first main theorem for such projective characters and projective blocks.

这一定理包含了经典Brauer第一主定理为其特例(即当α=1时)。

A theorem of the alternative for the generalized subconvexlike set-valued maps is established using the separation theorem of convex sets in a Banach spaces, the concept of weak Benson proper efficient elements for a vector optimization problem is introduced, and the optimality necessary and sufficient Lagrange conditions for a vector set-valued map constrained optimization problem with the weak Benson proper efficiency is developed, with which the optimality Lagrange conditions for a nonconvex vector top-base constrained optimization of set-valued maps with the Benson proper efficiency are obtained.

刘莹 ，刘三阳，盛宝怀运用凸集分离定理对广义锥次类凸集值映射建立了一种择一性定理。引入向量优化弱Benson真有效元的概念，对带约束的非凸向量集值优化问题建立了在弱Benson真有效意义下有效元应满足Lagrange乘子型的必要及充分条件，并用这一结果建立了多目标主从非凸向量集值优化在弱Benson真有效意义下最优解的Lagrange乘子型充要条件。

By using the model of this interpretation, the reliability theorem and the uniformity theorem are proved of the propositional calculus plus syllogistic system.

本文最主要的工作是建立了三段论的一种解释，并且在这种解释模型中，证明了命题演算+三段论系统的可靠性定理，一致性定理，还从语义角度，对项的周延性等问题发表了一些意见。

This paper proves that it is impossible for all the theorems in classical propositional calculus to be tautologies in the field of fuzzy propositional calculus, then a quasi formal deductive system is established for fuzzy propositional calculus based on a kind of type algebra.

引入了一种代数，称为模糊公式代数。在这种代数上建立了一个准形式演绎系统，证明了相应的可靠性定理与相容性定理，提出了程度化的ModusPonens规则和HypotheticalSylogism规则

The paper, taking Pythagorean Theorem for example, analyzes the function, effect and the practice in the modern teaching.

分析了数学定理演变的原因及其对数学发展的作用，并以数学教材中典型的定理"勾股定理"为例，分析其在历史演化中的作用与影响，以及在现代中学里的教学。

The labia have now been sutured together almost completely.The drains and the Foley catheter come out at the top.

此刻阴唇已经几乎完全的缝在一起了，排除多余淤血体液的管子和Foley导管从顶端冒出来。

To get the business done, I suggest we split the difference in price.

为了做成这笔生意，我建议我们在价格上大家各让一半。