轭

Owing to the key conclusion, this paper lays emphasis on the possible ways of realizing the singular conjugation by single—enveloping method. It is proved that the hyperbolic normal arc surface and the involute helicoid both may conjugate in singular points on the condition of single—envelope.

在奇点共轭理论的工程实现方面，文中明确指出二次包络是获得奇点共轭的有效手段，但并非唯一手段，在满足特定的运动几何条件下，一次包络即可获得奇点共轭。

Chapter 4 establishes the theory of convex fuzzy mappings: The concepts, such as Jensen's inequality, positively homogeneous, infimal convolution, right scalar multiplication and convex hull are introduced. The corresponding theorems are demonstrated by using the parametric representations of fuzzy numbers. In anti-fuzzy number space, the conjugate mapping of convex fuzzy mapping is concerned, and convexities of conjugate set and conjugate mapping of convex fuzzy mapping are proved. The notions of subgradient, subdifferential, differential with respect to convex fuzzy mappings are investigated, which provides the basis of the theory of fuzzy extremum problems.

在第4章中，建立了有关凸模糊映射的理论：建立了关于凸模糊映射的Jensen不等式、模糊正齐次映射、凸模糊映射的下卷积、右数乘和凸包等概念，利用模糊数的参数化表示，给出了相应的定理；在反模糊数空间，对凸模糊映射的共轭也作了探讨，证明了凸模糊映射的共轭集合和共轭映射都是凸的；最后对凸模糊映射的次梯度、次微分和微分等概念进行了研究，为模糊极值理论打下了基础。

To reduce the sensitivity of conjugate initial values, the initial values of control variables are used to replace the initial values of conjugate variables based on the transformation between conjugation variables and control variables.

为了降低共轭变量初值选取的敏感性，引入共轭变量与控制变量之间的变换，用控制变量初值代替了共轭变量初值。

The accurate solution of linear equations could be expressed linearly by the conjugate vector base, and the iterative strategy was used to construct the conjugate vector base groups and the corresponding coefficient. The constructed conjugate vector base groups were proved to be conjugated.

线性方程组的精确解能够由共轭向量基线性表示，利用迭代的方式给出了构造共轭向量基以及对应系数的方法，证明了算法所构造的向量基的共轭性。

Chapter 3, in the above system, gives out the definitions of topological new transitivity, topological transitivity, topological strong transitivity and topological conjugate of a sequence of maps, studies basic properties of the above topological conjugate, and obtains some main results, proves topological new transitivity and topological transitivity are equivalent u-under a compact metric space, a sequence of full maps and interchangeable with each other, and that some conclusions associated with topological conjugate.

第三章，在上述系统中给出了一列映射的拓扑新传递、拓扑传递、拓扑强传递和拓扑共轭的定义；研究了一列映射的拓扑共轭的基本性质，得到了一些主要结果；证明了在底空间是紧致度量空间、一列映射是满映射并且两两可交换的条件下拓扑新传递和拓扑传递是等价的；还证明了几个与拓扑共轭相关的结论。

Chapter 4,based on strong efficiency rather than efficiency or weak effi-ciency,discusses the similar problem to chapter 3.The concepts of strongsupremum and strong infimum for the set in finite-dimensionalEuclidean space are given,s-conjugate functions and s-subdifferentials theory is developed,by means of which,the duality problem ofmulitobjectivre programming for strong efficient solutions or called absoluteoptimal solutions is analysed,and a new duality theory-s-conjugateduality theory is proposed.

第四章，基于强有效性而不是有效性和弱有效性，给出了类似于第三章的结果，提出了有限维欧氏空间中集合的强上、下确界等概念，研究了点集映象的强共轭函数和强次微分问题，建立了点集映象的s-共轭函数及其s-次微分理论，并借助于这一理论，讨论了多目标规划关于绝对最优解或称强有效解的对偶性问题，建立了基于强有效性的s-共轭对偶理论。

By giving the definition of mapping space, some abstract and basic conjugation elements can be impressed by direct geometric graphics. Also, resort to the mapping space, the fundamental theorem of singular conjugation is proved.

本文研究了共轭曲面原理的奇点共轭理论，并在此理论指导下对新型奇点共轭传动——0°渐开线包络蜗杆传动进行了系统的理论分析与实验研究。

Ecause of stronger resonance enhancement to incident pump beam given by the Bragg microcavity, the enhancement effect of the phase conjugation wave produced by Bragg microcavity was more outstanding than that caused by naked third order NLM.

ragg微腔中的三阶NLM产生的相位共轭波相对于该介质裸露时产生的相位共轭波具有明显增强，这主要是Bragg微腔对入射泵浦光产生了较大的共轭增强作用。

The aim of this paper was to measure the ultraviolet absorption value of conjugated linoleic acid and some unconjugated fatty acids as well as to study the influence of conjugated double bond on the ultraviolet absorption of fatty acids.

测定共轭亚油酸及部分非共轭脂肪酸的紫外吸收，研究共轭双键对脂肪酸紫外吸收的影响。

In Chapter 2,we introduce the definition of adding machines,and give sev-eral equivalent conditions on the existence of several kinds of conjugacy and semi-conjugacy relations between adding machines.

第二章介绍了广义符号空间上的加法机器的定义，给出了加法机器之间存在着各种共轭及半共轭关系的多个充要条件，证明了加法机器之间的拓扑半共轭一定是一个群同态与一个平移映射的复合，并研究了此同态的核的构成。

In the United States, chronic alcoholism and hepatitis C are the most common ones.

在美国，慢性酒精中毒，肝炎是最常见的。

If you have any questions, you can contact me anytime.

如果有任何问题，你可以随时联系我。