集合性的

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。

It also pointed out that thesolution set of the equation is inconsistent.

3首次提出了逻辑方程的概念，给出了逻辑方程的解的存在性定理，并详细分析了逻辑方程解的性质，指出对于一般的逻辑方程而言，其解集合是不相容的。

I. on limited time segment, and the ergodicity and stationarity of the C. I. on T, M are studied. After that, a relationship between C. I. and gradient of objective function is revealed and a recurrence formula of C.

为此，我们首先定义了作为全文基础的双随机过程的相关积分，研究了集合平均上的相关积分，有限时间域上的相关积分和T.M区间上的相关积分及其各态历经性问题。

In Luo Zhong-rong"s modern compositions, the pitch organization and the form of it"s structure hold the prominent position and issue significant function in music context, and the researches of these aspects in this dissertation occupied referentially also a more wide space. The first three chapters introduced three kinds of pitch organization used in these compositions: serial set, twelve-tone tonality and pentatonic aggregate.

音高的组织与结构方式在罗忠铬的现代音乐创作中有着十分突出的作用，论文在这方面的研究也相应占据了较大的篇幅，前三章分别介绍了作曲家在这些创作中使用的三种音高组织："序列"、"十二音调式体系"以及"五声性十二音集合"。

Through a new analysis on the essential relationship between Russell's Paradox and Cantor's proof on the uncountability of real number set and the proof on the Cantor's Theorem of , a mysterious error was found:the very same logic contradiction was applied in both Russell and Cantor's work.

分析了罗素悖论与康托的实数集合不可数证明及康托定理证明之间的本质性联系，发现康托在这两个非构造性证明中所依赖的、用对角线法所构造出的矛盾其实就是罗素悖论中所揭示的逻辑矛盾。

Here we clarify that areal-type of a genus is defined by concluding distributions of all species in the genus, therefore specific distribution types are not the same as their generic areal-types except monotypic genera. Similarities of composition of areal-types between compared regional floras do not necessarily represent their floristic similarities because the same generic areal-type can be composed by different genera from different plant families.

根据植物区系学理论，属的分布区是该属内所有物种的分布区的集合，除单种属外，不能直接套用属分布区类型作为该属内各个种的分布区类型；亲缘关系疏远的不同植物属可以有同样的分布区类型，若把不同地区植物区系各地理成分的比例关系的类似性解读成各地区间植物区系的亲缘关系，显然是不适合的。

The original video is spitted into a series of frame groups,for each frame in the group,the points of contour shape are described by MPEG-7,and taking advantage of hash function to calculate the keys between those points in the 1D- DFT transform domain and the watermark signals.

在该算法中，原始视频数据被分割成等帧数的视频组，利用MPEG-7的轮廓编码计算每个视频帧的主要物体轮廓坐标点集合；接着通过傅立叶变换得到该帧轮廓点形状不变量，利用哈希的方法计算水印信号并将这些不变量的有效值作为密钥之一；再对整个视频组的轮廓点进行傅立叶变换，得到其时间轴上的有效不变域，将水印信号嵌入在这个不变域的中频部分以确保了水印的鲁棒性。

The utility function of the integrated model was divided into two stages, choice set and alternative choice. The specification of factor structure was used to capture the individual heterogeneity and marketing positioning of the alternatives in the second stage, and the effects of new modes on choice behavior and market structure were studied by hypothesizing coefficients' specifications in the joint estimation process.

整合性模式的效用函数区分为选择集合及方案选择两阶段，而於方案选择效用函数中以因素结构的指定方式，考量个体偏好的异质性与方案的市场定位，并藉由联合估计过程中的系数假设，分析新运具对於旅运选择行为及市场结构的影响。

The main purpose of this paper is to propose a unsupervised clustering-based method to pre-extract the support vector for training the SVM in light of the theory that the classification facet of SVM is determined by support vector only. By analyzing the limitation existed in current multi-class classification methods, and taking into account comprehensively the separability of the class set of nodes, a hierarchical classification method of SVM binary tree based on tree classifier with optimized overall performance is designed.

针对SVM的分类面仅由支持向量决定的理论，提出一种基于无监督聚类方法来预抽取支持向量，训练向量机；并分析现有多类分类方法所存在的弊端，基于综合考虑节点的类集合可分性，设计一种基于树分类器整体性能最优的SVM二叉树层次分类方法。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。