线性的

All real simple Malcev algebra,are classified according to whether or not they have a compatible complex structure and simultaneously we give all the invariant bilinear forms by the killing form of the real simple Malcev algebra or the killing form of it s complexification .

研究实单Malcev代数上的不变双线性型，仿照李代数的情形给出实Malcev代数上的容许复结构、实Malcev代数的复化以及Malcev代数上的不变双线性型等概念，并通过对实单Malcev代数上容许复结构的讨论，将实单Malcev代数上的不变双线性型分为两种情形。

A comprehensive research has made in the application of elliptic curve based bilinear mapping in the group signature, security of bilinear mapping is established on the GAP group. Because the DDH problem is easy to solve in GAP, this fact results it is very difficult to design a bilinear mapping based group signature scheme which can satisfy anonymity and the tractability.

对基于椭圆曲线的双线性映射在群签名中的应用进行了深入的研究，由于双线性映射的安全性建立在GAP群上，而在GAP群上的DDH问题是容易求解的，这样导致在基于双线性映射的群签名方案设计中很难同时兼顾群签名的匿名性和可跟踪性。

The first part of this thesis is basic on the generalized Hamming weights of linear codes over rings and arranged as follows: In section one, we first introduced the definition of generalized Hamming weights and weight hierarchy over binary field GF (2) and its extension to nonlinear codes over GF (2) and linear codes over rings.

本文的第一部分就是围绕环上线性码的广义Hamming重量这个课题展开的，主要内容如下：第一节，首先介绍了GF(2)上线性码的广义Hamming重量和重量分级的概念，以及这些概念是如何被推广至非线性码及环上的线性码上的。

We first show some properties of such operators and give an explit description about the image of a linear bounded operator on a linear normed space. Then based on these results, we show the mean ergordic theorem on a C*-bial-gebra and get a sufficient and necessary condition for a linear functional to be Haar measure. Finally we discuss the sufficent conditions for the existence of Haar measure on C*-bialgebras.

本文首先通过考察这样算子的性质和刻画赋范线性空间中连续线性算子的像集的性质，证明了C*－双代数中的一个平均遮历定理，得到了C*－双代数中的线性泛函是 Haar 测度的充分必要条件；利用遍历定理和这个充分必要条件探讨了C*－双代数中 Haar 浏度存在的一些充分条件。

By transforming the nonlinear saturation constraint into the special linear constraint, the problem of solving the feedback controller with saturated actuator is converted to the design of controller with linear constraint. The stochastic stability is ensured by using the intersection of ellipsoid invariant set of different modes existing in the attraction domain of the closed loop system. In this case, solving controllers can be equivalent to a solvability problem of linear matrix inequalities.

通过将非线性饱和约束转化为特殊的线性约束，使具有饱和执行器的控制器求解问题转化为线性约束控制器的求解问题，利用位于闭环系统吸引域内的不同模态下椭圆不变集的交集来保证系统的随机稳定性，此时控制器的求解可等效为线性矩阵不等式的可解性问题。

Ln this paper, a new learning method is presented which is based on analyzing a set of linear separable structures. The most important benefit of this method is all binary neurons belong to one or more types of linear separable structure sets. If those linear separable structure sets have clear logical meaning, the whole knowledge of binary neural networks can be dug out.

该文提出了一种基于线性可分结构系结构分析的学习算法，采用这种方法对布尔空间的样本集合进行学习，得到的二进神经网络隐层神经元都归属于一类或几类线性可分结构系，只要这几类线性可分结构系的逻辑意义是清晰的，就可以分析整个学习结果的知识内涵。

Firstly, we give out a reduction way for quasilinear generalized system A〓=G , and the concept of the index κ geometrically nonsingularity, where A is singular and of smooth kernal space. By using the canonical projection mappings onto the space of ker A , a class singular pointimpasse point only owned by nonlinear generalized system is also studied and we also prove that the regular index κ quasilinear generaized system A〓=G defined on the region W is equivalent with an ODEs 〓 defined on a submanifold W〓 of the W, so we reduce the problem of quasilinear generalized system to the problem of an ODEs.

首先利用投影函数，给出了拟线性广义系统A〓=G的一种归约方法，提出了指数κ几何非奇异的概念，同时对广义系统特有的一类奇点-寂点进行了研究，证明了正则指数κ的拟线性问题A〓=G等价于在其定义域W中某一个子流形W〓上的正常微分方程〓，从而将拟线性广义系统的问题归结为常微分方程问题。

A necessary and sufficient condition for the existence of guaranteed cost control is derived. Furthermore, it is shown that this condition is equivalent to the solvability of a system of linear matrix inequalities, and its solution provides a parameterized representation of guaranteed cost controllers. Based on that, the design of the optimal guaranteed cost controller is formulated as a convex optimization problem, which can be solved by the existing convex optimization techniques.

通过采用线性矩阵不等式的方法，导出了存在保性能控制律的一个充要条件，进而，证明了该条件等价於一组线性矩阵不等式的可解性问题，并用这组线性矩阵不等式的可行解给出了保性能控制律的一个参数化表示。

Variance and correlation of the data was analyzed with SPSS software. It was found that height, width, and thickness are main factors influencing paper angle bead compressive strength; moreover there are linear relations between the height, the width, and the thickness of paper angle bead and the compressive strength, and the error of equation is ±3%.

通过SPSS软件对数据进行方差及相关性分析，确定了纸护角的高度、宽度、厚度是影响纸护角抗压性能的主要因素，并且高度、宽度、厚度值与纸护角抗压强度之间呈线性相关；最后利用SPSS的线性回归分析，得到纸护角的抗压性能与高度、宽度、厚度之间的线性回归方程，对方程进行验证，其误差为±3%。

Based on the pattern of partial double-layer LICS, different analysis models of nonlinear, linear, rigid joint and pin joint were compared, linear property of double-layer region and nonlinear property of single-layer region was disclosed, and then a nonlinear-linear combine method was put forward with a definite object in view.

针对局部双层叉筒网壳的布局特点，本文对局部双层叉筒网壳进行了非线性、线性、刚接、铰接等多种分析方法的比较，揭示了双层区域的线性性质和单层区域的非线性性质，进而有的放矢地提出了&非线性-线性联合&这种适合局部双层网壳分析的合理、准确、高效的方法。

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。