查询词典 linear independence

Chapter 4 presents five design criteria of S-boxes of block ciphers, develops a method of constructing large S-box by use of algebraic group operation, proves the balance property of these large S-box, tests the strict avalanche and independence of avalanche variables properties of S-boxes in NEA cipher, analyses the nonlinearity and best linear approximation of the S-box, and finally defines the differential of input/output of S-boxes of this cipher and analyses the distribution of them.

第二部分即第三章，提出了一种新的分组密码类NEA(NEA-4A，NEA-8A，NEA-4B，NEA-8B)，完整地描述了该密码类的加解密过程和密钥协议；证明了NEA-4B和NEA-8B的完全对合性和没有不动点的性质；分析了该密码类的安全特征；具体地介绍了实现该类密码的途径；给出了NEA-4A的计算机C语言程序和样本数据。

Taking into account the orthogonality and linear independence of trigonometric functions, closed-form expressions for scattering coefficients are developed by imposing continuity conditions of pile-soil interfaces and equilibrium conditions of piles.

通过施加问题的连续条件和平衡条件，利用三角函数的正交性以及不同阶三角函数线性无关的性质，得到问题的解。

Generally ,in the traditional text classification system , there is a assuming that the relation between words in article is linear independence and inter-relationship between feature dimensions in the vector space model is orthogonal, however ,in face there are various relationships in the text context , such as synonymy , similarity , conjunction etc.

在传统的文本分类系统。

Another reason is that the degree of linear independence of the variable basis functions composed by sigmoid functions decreases as the hidden nodes increasing, and this lead up to the inferior matrix condition number during learning, which forces the learning step length to decrease and the convergence speed to slow down.

一是因为未知系统复杂时需要较多的隐节点，从而学习的参数过多减慢了学习速度；另一个原因是随着隐节点数增加，由Sigmoid函数构造的可变基函数线性无关程度减弱，从而导致学习过程中矩阵条件数变差，迫使学习步长减小，收敛速度不得不减慢。

In theory we require linear independence among variables used as inputting or outputting of BP net when we model the mineral processing plant with BP net. However it is always definite relativity in inputting variables or outputting variables in modeling of the mineral processing plant, which sets definite obstacle in high quality modeling.

在应用BP网络建立选矿厂数学模型时，理论上要求作为BP网络的输入变量之间或输出变量之间应是线性无关的，而选矿厂数学建模中，输入变量之间或输出变量之间往往存在着一定的相关关系，这对建立高质量的模型设置了一定的障碍。

First, the reason behind the negative data is analyzed and a nonnegative constraint is imposed on the classic PCA. Then a set of nonnegative linear independence weight vectors of principal components is obtained, by which a low dimensional space is constructed. Finally, a nonlinear optimization technique is used to determine the projection vectors of the high-dimensional multi-spectral data in the constructed space.

首先分析主成分分析法产生非光谱数据的原因，据此对经典主成分分析模型增加非负约束；然后求出一组线性无关的非负主成分权向量，用该组向量构造低维空间；最后用非线性优化技术确定高维数据在该低维空间中的投影值，实现了高维空间与低维空间的相互转换。

Then through solving that equation, a set of nonnegative linear independence weight vectors of principal components was obtained, by which a low-dimensional spectral space was spanned.

针对经典主成分分析法进行多光谱图像数据降维会使重构光谱反射比出现负值的问题，提出一种非负主成分分析法，并用该法构造低维光谱空间，实现高维多光谱数据与低维光谱空间的转换。

Chapter2, mainly summarizing the optimality conditions for the nonconvex semidefinite programming, first recalls the concept of transversality condition, proves that transversality condition and linear independence condition are equivalent, and shows that under strict complementarity condition, the transversality condition is a sufficient condition for uniqueness of the Lagrange multipliers.

第2章，主要综述非凸半定规划的最优性条件，首先回顾了横截性条件的概念，证明了横截性条件与线性无关条件是等价的。并且说明了在严格互补松弛条件下，横截性条件是Lagrange乘子矩阵唯一的充要条件。

In statistical analysis of ordinal data, we usually build up linear-by-linear association model and meet a trouble of choice of scores. Graubards et a1 (1987) proposed several methods for score choice in independence test in ordinal 2×κ contingency tables: equally spaced scores, midpoint scores and midrank scores. He also pointed out that the result of independence test may be different for the different choice of scores according to the same association model. Agresti et a1 (1987) treated the score vector in row effects and column effects model for two-way contingency tables as parameters and derived the necessary and sufficient condition of the solution under monotone order restriction by Kuhn- Tucker conditions.

在有序数据的统计分析中，通常要建立线线相关模型，其中得分的选取是一个棘手的问题，Graubard et a1（1987）给出了有序2×κ列联表中独立性检验的几种得分选取方法：等距离得分，中点得分和midrank得分等，同时指出，对于同一个相关模型，独立性的检验会由于得分选取的不同而得到不同的结论，Agresti et al（1987）把二维列联表中的行效应和列效应模型中的得分向量作为参数，在满足递增的序关系情况下，利用Kuhn-Tucker条件给出了解的充要条件。

The author constructed a linear schemes type Region-Project-Join-Normal-Form based on lossless join decomposition, and gave the form of RPJNF through the presentation of equivalence between semantic variable independence and syntax variable independence under finite precision domain. Some other new constraint data dependencies including partitioned multi-region existence dependency and single region existence dependency were also presented. A result of variables set under linear transformation was discussed.

文中给出并证明了多区域存在依赖满足的几条推理规则；提出并证明了线性序约束关系进行模式无损连接分解的充要条件是变量集满足变量独立和多区域存在依赖；设计了一种基于模式无损连接分解的区域投影连接范式；通过证明有限精度域上语义变量独立和语法变量独立的等价性，给出有限精度域上RPJ范式的表达形式。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。