和向量

At polymorphic gene locus, the variance components of quantitative trait was described as follows:VA=2βp and VG=p′Xp-G2 in which p=column vector of polymorphic allele frequencies,β=row vector of2,X=［a2ij］i×i matrix,aij=genotype value,and G=population mean.

数量性状相对多态座位的加性方差和遗传方差分别为VA=2βp和VG=p′Xp-G2，其中p′和p分别表示多态等位基因频率的行向量和列向量，X表示以基因型值平方为元素的矩阵，β表示以基因均效平方为元素的行向量，G为群体均数。

You need to know what the cross product is and what it means geometrically (a vector perpendicular to the vectors with a length equal to the sine of the angle between them).

你需要知道向量积是什么，以及它的几何意义(一个和两个向量都垂直的向量，长度等于原来两向量的长度乘以两向量的夹角的正弦)。

The main contributions of the second part of this dissertation are focused on the cryptographic properties of logical functions over finite field, with the help of the properties of trace functions, and that of p-polynomials, as well as the permutation theory over finite field: The new definition of Chrestenson linear spectrum is given and the relation between the new Chrestenson linear spectrum and the Chrestenson cyclic spectrum is presented, followed by the inverse formula of logical function over finite field; The distribution for linear structures of the logical functions over finite field is discussed and the complete construction of logical functions taking on all vectors as linear structures is suggested, which leads to the conception of the extended affine functions over finite field, whose cryptographic properties is similar to that of the affine functions over field GF (2) and prime field F〓; The relationship between the degeneration of logical functions and the linear structures, the degeneration of logical functions and the support of Chrestenson spectrum, as well as the relation between the nonlinearity and the linear structures are discussed; Using the relation of the logical functions over finite field and the vector logical functions over its prime field, we reveal the relationship between the perfect nonlinear functions over finite field and the vector generalized Bent functions over its prime field; The existence or not of the perfect nonlinear functions with any variables over any finite fields is offered, and some methods are proposed to construct the perfect nonlinear functions by using the balanced p-polynomials over finite field.

重新定义了有限域上逻辑函数的Chrestenson线性谱，考察了新定义的Chrestenson线性谱和原来的Chrestenson循环谱的关系，并利用一组对偶基给出了有限域上逻辑函数的反演公式；给出了有限域上随机变量联合分布的分解式，并利用随机变量联合分布的分解式对有限域上逻辑函数的密码性质进行了研究；给出了有限域上逻辑函数与相应素域上向量逻辑函数的关系，探讨了它们之间密码性质的联系，如平衡性，相关免疫性，扩散性，线性结构以及非线性度等；讨论了有限域上逻辑函数各类线性结构之间的关系，并给出了任意点都是线性结构的逻辑函数的全部构造，由此引出了有限域上的"泛仿射函数"的概念；考察了有限域上逻辑函数的退化性与线性结构的关系、退化性与Chrestenson谱支集的关系；给出了有限域逻辑函数非线性度的定义，利用有限域上逻辑函数的非线性度与相应素域上向量逻辑函数非线性度的关系，考察了有限域上逻辑函数的非线性度与线性结构的关系；利用有限域上逻辑函数与相应素域上向量逻辑函数的关系，揭示了有限域上的广义Bent函数与相应素域上的广义Bent函数的关系，以及有限域上的完全非线性函数与相应素域上向量广义Bent函数之间的关系；给出了任意有限域上任意n元完全非线性函数存在性与否的完整证明，并利用有限域上平衡的p-多项式的性质给出了有限域上完全非线性函数的一些基本构造方法。

Targeted at maximizing the market surplus, we established both a fixed merchandise combination model and an uncertain merchandise combination auction model. A "queue list" method is put forward to solve the fixed merchandise combination vector's auction model, and discussed the pricing methods of different final prices. Additionally, we discussed the auction contract-matching algorithm of the unit combinations vector.

以市场盈余最大为目标建立常商品组合向量的拍卖模型和不确定商品组合向量的拍卖模型，提出"队列表"法求解常商品组合向量的拍卖模型，讨论不同成交价的定价方法，并对只有两种商品组合的不确定商品组合向量的拍卖进行拍卖合同的匹配分析，讨论了单位商品组合向量的拍卖的合同匹配算法。

The image information storing means provides a vector data storing means which stores vector data of an original drawing, and a vector data projecting means which projects the vector data to four kinds of coordinate systems.

图象信息存储器提供存储原始绘图向量数据的向量数据存储器，和将向量数据投影到四种坐标系中的向量数据投影器。

In this thesis, we study two problems: the existence results of solutions for generalized vector quasi-equilibrium problems and Hlder continuity of solutions to generalized vector equilibrium problems. The detailed contents are listed as following:In Hausdorff topological vector space, we discuss the existence results of solutions for three types of generalized vector quasi-equilibrium problem (GVQEP1,(GVQEP2) and (GVQEP3), for short respectively.

本文主要研究了两类问题：广义向量拟平衡问题解的存在性以及广义向量平衡问题解的Hlder连续性，具体内容如下：在Hausdorff向量拓扑空间中，讨论了三类广义向量拟平衡问题(GVQEP1)，(GVQEP2)和(GVQEP3)解的存在性定理。

Since fast algorithm for multiwavelet decomposition and reconstruction are crucial steps inapplication,discretion form of multiwavelet is obviously necessary.This dissertation makes asuccessful exploration in this aspect,synchronously designs a new pre-filter method for multiwavelet,and gives evaluation regulations of pre-filters for different objects.These research results providereliable guarantee for exploration and study of multiwavelet application.

由于向量小波的分解、重构快速算法在应用中是必不可少的重要环节，故必须给出向量小波的离散化形式，本文在这方面做了成功的探索，同时还设计了一种新的向量小波的预滤波器，并给出了选择适合于不同对象的预滤波评判准则，这些研究成果使向量小波应用潜力和应用前景的拓展有了可靠的保证。

These methods lead to the absence of the assessment subject and results in inevitable systematic error.

本文介绍了支持向量机方法和模糊积分，通过与基于投票方式的集成支持向量机、单一支持向量机和模糊神经网络的方法进行比较，结果表明基于模糊积分的集成支持向量机的分类准确性明显好于其它几种方法。

Briefly covered vector and tensor notation, vector and tensor algebra, wave kinematics, eigenvectors/values, dimensional analysis, and scale analysis.

简要的介绍向量和张量符号，向量和张量代数，波的运动，特徵向量／值，向量分析，以及尺度分析。

This paper generalizes the conclusion of Perfect nonlinear S-boxes by Nyberg(1991), and introduces the conception of inverse regular generalized vector Bent function. It shows that for inverse regular generalized vector Bent function f with even variables, m is no more than half of?. It also shows that when the input dimension n is odd, the regular generalized vector Bent function and the inverse regular generalized vector Bent function do not exist. This may prevent the cryptology designer from seeking the inexistent function.

摘要该文完善并拓展了Nyberg(1991)的关于广义向量Bent函数性质的结论，相应于Nyberg给出的正则广义向量Bent函数，提出了&负则的广义向量Bent函数&的概念：得到有偶数个输入的负则的广义向量Bent函数输出维数也不大于输入维数的一半；证明了奇数个输入的正则和负则的广义向量Bent函数都不存在，这些结果的给出，可使密码设计者避免一味去寻找某类不存在的函数。

We have no common name for a mime of Sophron or Xenarchus and a Socratic Conversation; and we should still be without one even if the imitation in the two instances were in trimeters or elegiacs or some other kind of verse--though it is the way with people to tack on 'poet' to the name of a metre, and talk of elegiac-poets and epic-poets, thinking that they call them poets not by reason of the imitative nature of their work, but indiscriminately by reason of the metre they write in.

索夫农 、森那库斯和苏格拉底式的对话采用的模仿没有一个公共的名称；三音步诗、挽歌体或其他类型的诗的模仿也没有——人们把&诗人&这一名词和格律名称结合到一起，称之为挽歌体诗人或者史诗诗人，他们被称为诗人，似乎只是因为遵守格律写作，而非他们作品的模仿本质。

The relationship between communicative competence and grammar teaching should be that of the ends and the means.

交际能力和语法的关系应该是目标与途径的关系。