定理

This paper makes the range of integral mid-value point in Rn narrowed from integral region D to the inside of D/D .

将Rn中积分中值定理的中值点取值范围，由积分区域 D上缩小到D的内部D/D上取到。

This result is a higher-dimentional analogue of the Fundamental Theorem of Calculus: it expresses the integral over D of some kind of derivative of P and Q in terms of an integral of P and Q over the boundary of.

格林公式建立了曲线积分和二重积分的关系 O 这是微积分基本定理在高维情形的推广：它将上P、Q某种形式的导数的积分用的边界上 P、 Q 的积分表示出来。

And based on this conclusion, Darboux theorem on open interval is also given.

在此基础上给出有限开区间上的达布定理。

Darboux theorem on open interval is also given.

在此基础上给出有限开区间上的达布定理。

The Darwinist concept of survival through change has never been so true in today's fast changing and diverse consumer markets.

达尔文的生存定理从来没有像现在瞬息万变和多元化的消费市场这样真实。

Two normal forms, best-simple normal form and literal normal form, are presented at first in order to eliminate the complexity of formulas decision. Based on the two normal forms, a deduction proof of decidability theorem in L and a decision algorithm P based on deduction for proportional formulas are given and a decision machine found on P, DMBD, is also designed.

首先提出了消解复杂性的两种范式：最简范式和文字范式，在此基础上给出了L的可判性定理的演绎证明及命题公式的演绎判定算法P，并基于ML语言设计了基于P的演绎判定机DMBD。

Based on the two normal forms, the decidability theorem in L is then proved and a deduction-based decision algorithm P is designed. The time complexity O(n3) of P is much less than the complexity O(2n) of the true value table method and the complexity O(n5) of HAL based on the tactic scheme.

首先定义了消解复杂性的两种范式：最简范式和文字范式，在此基础上采用演绎方法证明了L中的可判定性定理，并设计了命题公式的演绎判定算法P。P的时间复杂度为O(n^3)，远远小于基于真值表法的O(2^n)和基于策略方案HAL的O(n^5)。

The basic decomposition result is that if a vertex cut S of G is a clique, then G is decomposable by S.

基本的可分解定理是：如果图G的一个点割集S是一个团，则G经由S是可分解的。

Chapter 4 is the hedging strategies of optimization in insurance:In virtue of Galtchouk-Kunita-Watanabe Decomposition Theorem to decomposite the natural value prcess V_t~* toupdate the risk expression, then we can get the hedging strategies of optimization with minimal risk.

第四章最优保险对冲策略：利用Galtchouk-Kunita-Watanabe分解定理将本性价值过程V_t进行分解。采用一定的替换技巧可将风险表达式重新表示，从而找到保险公司所能采取的最优对冲策略。

In this paper we introduce some new definitions, they are the generalizations of those concepts in Lie theory, and we discuss initially the elementary properties of operator Lie algebras. Finally, the famous Jordan-Holder theorem and the uniqueness of decomposition theorem of operator Lie algebras are proved.

在这篇文章里，我们将李代数理论中的诸多概念加以推广，并初步地探讨了算子李代数的性质，最后还给出了算子李代数的一个分解定理，其唯一性也得到了证明。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新