线性的

The content of this course is divided into four chapter, the normed linear space and bounded linear operator on the normed space; the character of finite dimensional linear space; the basic theorems on Banach space.

本课程主要分为四章，赋范线性空间与内积空间；赋范线性空间上的有界线性算子，有限维赋范线性空间的特征。Banach空间中的基本定理：泛函存在定理，一致有原理，开映象，闭图象、逆算子定理。

Under quadratic loss function, the definition of conditional admissible prediction is given and some necessary and sufficient conditions for linear predictions Ly_s of conditional linear predictable variable Qy to be admissible are obtained.

在二次损失函数下，给出了条件可容许预测的定义，在齐次线性预测类和非齐次线性预测类中得到了条件线性可预测变量Qy的线性预测Ly_s是可容许预测的充要条件。

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 effects of the initial field states, different value of decay constant and the initial atomic states on all the entropies are discussed.

结果表明：光场的不同量子统计性质使得系统线性熵、原子线性熵和光场线性熵均发生明显改变。

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。

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。

To similinear hyperbolic system, we use interpolated coefficient FEM and get similar results as the linear one.

对于一阶半线性双曲组，我们对半线性项插值系数有限元方法，得到了和线性问题类似的结论。

Through the use of linear space of the basic nature of the linear mapping, linear transformation, the matrix theory of knowledge, some of the linear transformation of the nature of proof, reasoning and calculation.

本文通过利用线性空间的基本性质、线性映射、线性变换、矩阵理论的知识，对线性变换的一些性质进行证明，推论和计算。

Using the result for non-restricted model, we transform the restricted model to common model, and multi collectivity model to single collectivity model, thus, the necessary and sufficient conditions that nonhomogeneous linear estimators for Sβ are admissible in the class of nonhomogeneous linear estimators are obtained which filled the blank for admissibility for restricted linear model.

对线性等式约束的共同均值线性模型，利用无约束单总体模型的现有结果，通过适当变换，把等式约束模型向无约束转换，并把多总体转换为单总体，在矩阵损失下找到了均值参数β的条件可估函数Sβ的线性估计∑mAiyi+a在非齐次线性估计类中可容许的充要条件，填补了等式约束的共同均值线性模型可容许性方i=1面的空白。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。