线性

Linear Algebra is mainly a subject which studies the linear structure of finite dimensional linear space and its linear transformation while linear concept is in itself from the old Euclid Geometry. The concept of "Linear Space" is a kind of algebraic abstract. In many fields of modern engineering project and technology, because of the influence of computer and graph showing, the algebraic disposal of geometric questions, the visual disposal of algebraic questions, algebra and geometry are tightly combined.

线性代数主要是研究有限维线性空间及其线性变换这一代数结构的学科，而线性概念究其根源则是来自古老的Euclid几何，线性空间概念是几何空间的一种代数抽象，在现代工程技术的许多领域里，由于计算机及图形显示的强大威力，几何问题的代数化处理，代数问题的可视化处理，把代数与几何更加紧密地结合在一起。

The proof is given that the category of linear fuzzy neighborhood spaces in the sense of Katsaras is isomorphic to that of co-towers of topological vector spaces and the intersection of the category of linear fuzzy neighborhood spaces with the category of type fuzzy topological vector spaces is the extract category of induced fuzzy topological vector spaces.

证明了Katsaras的线性fuzzy邻域空间范畴与分明线性拓扑空间的余塔空间范畴同构，而Katsaras的线性fuzzy邻域空间范畴与型fuzzy拓扑线性空间范畴的交集恰为诱导的fuzzy拓扑线性空间范畴。

Based on the analysis of interactions between different systems in the network, it is proved that, for a class of complicated linear switched system network, an equivalent model of ordinary linear switched system exists and the corresponding model is given.(4) Block simulation model of linear switched system is established in Matlab/Simulink environment and, moreover, a linear switched system simulation tool with the function of model automatic generation is developed. With the aid of this simulation tool, influence caused by switching sets on stability characteristic of linear switched system is investigated.

对线性切换系统网络中各系统之间的交互作用作了分析，在此基础上证明了一类复杂线性切换系统网络可用等价的线性切换系统模型来表示，并得到了该等价模型；（4）在Matlab/Simulink环境下建立了线性切换系统的框图仿真模型，并进一步开发了具备模型自动生成功能的线性切换系统仿真工具。

In the algorithm, the conditional linear state equation is first inserted into the measurement equation, which fuses the linear state process noise and the original measurement noise, whereafter the GHF is used to estimate the nonlinear states. Then the estimated means of the nonlinear states are inserted into the linear state equation and the original measurement equation to estimate the linear states by the KF. Moreover, in order to improve the accuracy of the estimates, the estimated variances of the nonlinear states are fed back to modify the estimations of the linear states using the KF.

算法将模型中的条件线性状态方程代入观测方程，并融合线性状态的过程噪声和观测噪声，由GHF获得非线性状态的估计；再将非线性状态的估计均值代入线性状态方程与观测方程，由KF获得线性状态的估计；获得的非线性状态估计方差还用于修正由KF估计的线性状态，以提高精度。

The characters of linear complexity profile of periodic sequences are investigat- ed. The relation between the continued fraction expansion of rational function and its 1- inear complexity profile is established. The expression of linear complexity profite is gi-~~en and a condition estimating the randomness of a sequence is presented. By the linear complexity profile, the bound of sphere complexity is proposed. A formula to record the number of sequences with given linear complexity profile is presented.

研究了周期序列的线性复杂度曲线特性，在周期序列生成函数的连分式展开式与线性复杂度曲线之间建立联系，给出了周期序列线性复杂度曲线的表达式；给出了判断序列随机性好坏的一个条件；利用线性复杂度曲线特性给出周期序列球体复杂度的一个估计；给出了具有给定线性复杂度曲线的序列个数的一个计数公式。

The early references include -[5], which are based on the linear models or generalized linear models; on the other hand, [6]-[10] are those based on the nonlinear models which are more practical. But they are all restricted in the exponential family of distributions. That will not practice in most of the trials. Although being the most flexible among them, the estimation methods in [1] has many disadvantages for requiring the model to be generalized linear. Based on [1], this paper extended the method to the generalized nonlinear model.

较早的如[1]-[5]，他们都是基于线性或广义线性模型进行分析研究；而基于更为实用的非线性模型的研究则有：[6]-[10]等，他们大多由于模型要求数据属于指数分布族或者模型假定为线性模型，这都限制了模型的实用性，其中以[1]所提的一系列广义线性估计方程实用范围较广，但其模型中要求的广义线性模型还是具有一定的局限性。

This dissertation investigates the construction of pseudo-random sequences (pseudo-random numbers) from elliptic curves and mainly analyzes their cryptographic properties by using exponential sums over rational points along elliptic curves. The main results are as follows:(1) The uniform distribution of the elliptic curve linear congruential generator is discussed and the lower bound of its nonlinear complexity is given.(2) Two large families of binary sequences are constructed from elliptic curves. The well distribution measure and the correlation measure of order k of the resulting sequences are studied. The results indicate that they are "good" binary sequences which give a positive answer to a conjecture proposed by Goubin et al.(3) A kind of binary sequences from an elliptic curve and its twisted curves over a prime field F_p. The length of the sequences is 4p. The "1" and "0" occur almost the same times. The linear complexity is at least one-fourth the period.(4) The exponential sums over rational points along elliptic curves over ring Z_ are estimated and are used to estimate the well distribution measure and the correlation measure of order k of a family of binary sequences from elliptic curves over ring Z_.(5) The correlation of the elliptic curve power number generator is given. It is proved that the sequences produced by the elliptic curve quadratic generator are asymptotically uniformly distributed.(6) The uniform distribution of the elliptic curve subset sum generator is considered.(7) We apply the linear feedback shift register over elliptic curves to produce sequences with long periods. The distribution and the linear complexity of the resulting sequences are also considered.

本文研究利用椭圆曲线构造的伪随机序列，主要利用有限域上椭圆曲线有理点群的指数和估计讨论椭圆曲线序列的密码性质——分布、相关性、线性复杂度等，得到如下主要结果：(1)系统讨论椭圆曲线-线性同余序列的一致分布性质，即该类序列是渐近一致分布的，并给出了它的非线性复杂度下界；(2)讨论两类由椭圆曲线构造的二元序列的"良性"分布与高阶相关性(correlation of order κ)，这两类序列具有"优"的密码性质，也正面回答了Goubin等提出的公开问题；(3)利用椭圆曲线及其挠曲线构造一类二元序列，其周期为4p(其中椭圆曲线定义在有限域F_p上)，0-1分布基本平衡，线性复杂度至少为周期的四分之一；(4)讨论了剩余类环Z_上的椭圆曲线的有理点的分布估计，并用于分析一类由剩余类环Z_上椭圆曲线构造的二元序列的伪随机性；(5)讨论椭圆曲线-幂生成器序列的相关性及椭圆曲线-二次生成器序列的一致分布；(6)讨论椭圆曲线-子集和序列的一致分布；(7)讨论椭圆曲线上的线性反馈移位寄存器序列的分布，线性复杂度等性质。

A new SVM is presented in this paper to solve the approximately linear separable problem of pattern recognition:First,we transform the two convex hulls which are made up of the approximately separable training set to make them separable;Second,we can figure out a separating hyperplane by halving the nearest points method or maximal margin method;Then,we get the approximately linear SVM by solving the dual problem of maximal margin method.

对模式分类中的近似线性可分问题提出了一种新的近似线性支持向量机：先对近似线性分类中的训练集所形成的两类凸壳进行了相似变形，使变形后的凸壳线性可分，再用平分最近点和最大间隔法求出理想的分划超平面，然后再通过求解最大间隔法的对偶问题得到基于相似压缩的近似线性SVM。

The heat generation curves of seven rubber materials used in tires with the changes of temperature have been obtained by using Dynamic Mechanics Analysis technique on NETZSCH DMA242 instrument, knowing that the heat generation of every other rubber materials except inner liner rubber changes lightly alone with the temperature within 10℃～80℃. According to the Fourier law, the heat transfer coefficients of tire rubber are measured by stable method on self-made experiment instrument. The coefficients changes lineally within 20℃～80℃ and the relation formulas λ=λ〓+bt are given out attached with λ〓 and b. The specific heat of tire rubber are measured on Differential Scanning Calorimeter NETZSCH DSC204 and the relations with temperature are linear and the formula is c=c〓+bT, where c〓 and b gained from experiment result data are presented in the paper. The heat convection coefficients on the surface of rolling tire are measured according to the principle of heat-mass transfer analogy principle after simplifying rolling tire into rotating disk with straight movement on wind channel. The relation with rotation speed of disk is linear as h=5. 399+0.0258n and the relation with straight line speed of tire is linear too, h=

论文采用动态力学分析技术，使用NETZSCH DMA 242型实验仪，获得了轮胎用七种胶料的生热率随温度变化曲线，确知除内衬层胶以外，其它各种胶料在一般胎温范围内（10℃～80℃）的生热率随温度变化不大；轮胎胶料的导热系数根据傅立叶定律的基本原理，采用稳态法在自行搭建的实验台上进行测试，结果表明，材料的导热系数在20℃～80℃的温度范围内随温度呈线性变化，论文给出了各种材料导热系数的线性变化的关系式λ=λ〓+bt及其λ〓和b的值；轮胎胶料的比热运用差式扫描量热原理，在NETZSCH DSC204型DSC实验仪上进行测试，结果表明，胶料的比热随温度的变化呈线性变化，其关系可用c=c〓+bT表示，文中给出了根据实验数据拟合的c〓、b的值；对轮胎表面的对流换热系数的测定，本文先将滚动的轮胎简化为有直线运动的旋转圆盘，而后采用萘升华热质比拟技术，在风洞中测量了滚动轮胎表面的对流换热系数，结果表明，圆盘表面对流换热系数与转速呈线性关系，即h=5.399+0.0258n，轮胎表面对流换热系数与其直线运动的速度呈线性关系，即h=

Then gives judging the vector linear relevance by the value of determinant, the order of matrix, the solution to uneven sublinear system of equations, Cramer principle, linear substitution, the theory of matrix and so on in the linear space and Ou Shi space, produces 13 equivalences of the vector linearity relevant under the dissimilar condition, and elaborates the widespread application of the vector linearity relevant through concrete examples.

在线性空间、欧氏空间中给出了运用行列式的值、矩阵的秩、齐次线性方程组的解、Cramer法则、线性变换、矩阵理论等知识来判定向量的线性关系，及不同条件下向量线性相关性的十三个等价命题，并通过具体例题阐述向量线性相关性的广泛应用。

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。