| 1. | We spell out the details below .
我们在下面详细证明。 |
| 2. | In this chapter , some theorems are proposed and detailed proofs of these theorems are presented . these proofs will guide our ccga designs for the future
本章提出了一些定理，并给出了这些定理的详细证明，对今后的遗传算法设计具有一定的指导意义。 |
| 3. | This paper based on the definition of measurable mapping and the characters of mapping , gives the detailed identification of judging measurable mapping theorem
摘要根据可测映射的定义以及映射的相关性质，给出了关于判定可测映射的相关定理的详细证明。 |
| 4. | The criterion that is based on nonlinear mode of transformers can better reflect the state of transformers that have been proved by academic analysis and empt emulation
该励磁涌流判据采用了变压器非线性模型，能更好的反映变压器的工作状态，论文用理论分析和数字仿真作了详细证明。 |
| 5. | The unique source of pycnogenol ? , the " pine bark " has a well - established monograph based on macroscopic and microscopic findings defining its pharmacogonistic characteristics , an essential feature of the quality confirmation
碧萝芷?的独特来源? ? “松树树皮” ，具有基于宏观和微观全面研究的专题论述，详细证明了它的医学特性，保证了它的非凡品质。 |
| 6. | Thereafter , the engineer shall , within 28 days after receiving a statement and supporting documents , issue to the employer an interim payment certificate which shall state the amount which the engineer fairly determines to be due , with supporting particulars
此后，在收到承包商的报表和证明文件后28天内，工程师应向雇主签发期中支付证书，列出他认为应支付承包商的金额，并提交详细证明资料。 |
| 7. | In third chapter , we study the relation of the expansion of a space ' s scattered partition and the open refinement of open sets in it . we give the sufficient conditions for a space having the property that its every scattered partition has a open expansion of a given property
第三章详细证明一个空间中的开集族的开加细与空间的散射分解的开膨胀之间的关系，给出了空间的散射分解具有某种性质的开膨胀的充要条件。 |
| 8. | This paper has three parts , introduction gives the origin of the problem , some definitions and some lemmas . in the second chapter , we give the proof of extended lemmas and theorems in details . in the third chapter , we discuss the necessity of moment conditions in the case of i . i . d . r . v .
全文分三个部分，引言介绍了问题的提出，一些定义及引理；第二章详细证明了推广的引理和定理；第三章讨论了独立同分布的情形中矩条件的必要性。 |
| 9. | ( 4 ) this dissertation makes a summery of decision thought of ahp and makes a study on structuring method of the complicated problems . it set up two combination ways of judgment matrixes in group ahp . it also proves its theory
( 4 )在总结ahp决策思想的基础上，提出了一种复杂问题群体结构化方法，合肥工业大学博士论文摘要给出了群体ahp判断矩阵的两种集结算法，并详细证明了这两种集结方法的理论依据；研究了群体ahp判断矩阵的优化集结原理；合作提出了一个基于rooghset的判断矩阵构造方法。 |
| 10. | And about a given property p which satisfies some conditions , we give a condition for the open sets in the tychnoff product of two spaces which have a open refinement having the property p . the last chapter obtains a result about the limit of the inverse system of a normal mesocompact space and a hereditar ily normal and hereditarily mesocompact space
而且给出了，对满足一定条件的某种性质p ，两个空间的乘积中的每个开集族有p性质的开加细的一个充分条件。第四章详细证明了关于正规中紧空间及遗传正规且遗传中紧空间的逆极限的一个结果。 |
