必要条件

The sufficient-necessity condition for the system stability and the distribution of stationary queue length are obtained by means of matrix analysis in the third model.

在本文模型三假设下利用矩阵分析方法得到了系统达到稳态所应满足的充分必要条件。

By using the Lie group theory of differential geometry and Pontryagin's maximum principle, it is pointed out that the mobile CRS robot on surface is controllable, and the necessary conditions and the structure equations of extremal trajectories are proposed.

为了解决曲面上移动CRS机器人的路径规划问题，在曲面上建立了机器人的动态模型，利用微分几何的李群理论和庞特里亚金最大值原理，证明了曲面上CRS机器人是可控的，并给出了机器人的最小时间控制的必要条件和结构方程。

From the matrix theory and the general principle of the iterative convergence of the linear coupled equations, this dissertation firstly proved the sufficient necessary convergent conditions for CMAC batch learning as well as the necessary convergent conditions for CMAC incremental learning, in which no additive conditions were needed. The past researchers'conclusions under the special condition of the positive articulation matrix are generalized and improved.

从矩阵理论和线性方程组迭代收敛的一般性原理出发，首次在不附加特殊条件的情况下，证明了CMAC学习算法在批量和增量两种学习方式下收敛的一般性定理，给出CMAC算法在批量学习方式下收敛的充要条件，以及在增量学习方式下收敛的必要条件，对前人在关联矩阵正定的特殊条件下得出的结论进行了推广和改进。

If deg f = n, then Rfc is an empty set. For all the functions of degree 2, Rf have at least 2n-1 vectors, when Rf is a linear subspace, the relationships between Rf and Lf are discussed . Boolean functions have no nonezero linear structure if and only if there are n linear independence vectors in f, the correlation of the vectors in ?

证明了，若degf=n，则R_f~c为空集，对于所有的二次布尔函数而言，均有R_f~c中的元素个数大于等于2~(n-1)，给出了R_f构成线性子空间时，R_f和L_f之间的关系，还给出布尔函数不含有非零线性结构的充分必要条件是ζ_f中含有n个线性无关的元素。

The main achievements of this dissertation are as follows: Let W be a nonsingular matrix. 1. Problem I and Problem II are considered under the matrix set S is as the following: 1 the set of real W-symmetrizable matrices; 2 the set of real W-symmetrizable nonnegative definite matrices; 3 the set of real W-symmetrizable matrices on the linear manifold.

对于问题I和问题II，本文就S是W可对称化矩阵集合、W可对称非负定化矩阵集合以及线性流形上W可对称化矩阵集合等三种情况进行了研究，分别给出了这三种情况下问题I的解存在的充分必要条件，以及解集合的通式表达式，给出了这三种情况下的最佳逼近解，并提供了相应的数值算法和数值实例。

Chapter four (application of chaos in measurement field): In this chapter firstly the sensitivity of initial values and parameters that chaos can be used in the measurement field has been analyzed quantitatively, on this basis, the necessary conditions of chaotic system that can be used in measurement are concluded and presented; then the mechanism of measurement implemented by subsection linear map chaotic system, the coordinating relationship between chaotic output signal and the values being measured, and the precision of system measurement are further analyzed quantitatively.

第四章（混沌在测量领域中的应用）首先对混沌可用于测量领域的初值敏性和参数敏感性进行了定性分析，在此基础上，归纳并提出了可用于测量的混沌系统应具有的必要条件；定量地分析了分段线性映射混沌系统实现信号测量的基本原理、输出混沌序列与被测量间的数值对应关系及系统的测量精度等问题；并以DSP为核心设计了混沌型电压测量系统；其次提出了混沌参数敏感性用于测量的基本思路，并对此进行了计算机仿真及原理性实验电路设计。

Chapter four (application of chaos in measurement field): In this chapter firstly the sensitivity of initial values and parameters that chaos can be used in the measurement field has been analyzed quantitatively, on this basis, the necessary conditions of chaotic system that can be used in measurement are concluded and presented; then the mechanism of measurement implemented by subsection linear map chaotic system, the coordinating relationship between chaotic output signal and the values being measured , and the precision of system measurement are further analyzed quantitatively . And a chaotic voltage measurement system using DSP is designed. Secondly a basic thought that thesensitivity of chaotic parameters can be used in measurement is presented and simulated. Its theoretical testing circuits are designed.

第四章(混沌在测量领域中的应用)首先对混沌可用于测量领域的初值敏性和参数敏感性进行了定性分析，在此基础上，归纳并提出了可用于测量的混沌系统应具有的必要条件；定量地分析了分段线性映射混沌系统实现信号测量的基本原理、输出混沌序列与被测量间的数值对应关系及系统的测量精度等问题；并以DSP为核心设计了混沌型电压测量系统；其次提出了混沌参数敏感性用于测量的基本思路，并对此进行了计算机仿真及原理性实验电路设计。

In this paper,the new Theorems are presented to prove some sufficient and necessary condition of Ishikawa iterative sequence with error member for Lipschitz hemi-contraction mapping in Hilbert space converging to the fixed point.

本文给出了Hilbert空间上的Lipschitz半压缩映像的具有误差项的Ishikawa迭代序列收敛于不动点的充分必要条件。

A certain given low-temperature is necessary for the transition from vegetation growth to reproduction growth; a relatively high temperature is good for the formation of floral organ and floral stalk. The vernalized plants can finish the development stages of floral organ and floral stalk, no matter long-day or short-day.

其生殖生长过程包括了花器发育和花茎发育两个相对独立的生理过程；一定量的低温（7～8℃，26d）是诱导花器和花茎分化的必要条件，而较高的温度（17℃左右）对花器和花茎的形成均为有利。

However, methods and references for difference equation are relatively less. The new method proposed in this paper transfer the complex boundary value problem into the existence and uniqueness of the solution of the linear equations. For linear case , we obtained the necessary and sufficient conditions for the existence and uniqueness of the solution for the BVP; For the nonlinear case ,we got a series of new sufficient conditions by using contraction mapping theory and cone theory .

而差分方程边值问题的研究方法和文献还很少，文中新的研究差分方程边值问题的方法是将复杂的边值问题求解转化为代数理论中的线性方程组解的存在和存在唯一问题；对线性情形，较容易地获得了边值问题的解存在以及唯一的充分必要条件，而对非线性情形，则通过压缩原理和锥理论等各种不动点定理，获得了一系列新的充分条件。

Recall that, in the Kolmogorov axiomatization, measurable sets are the sets which have a probability or, in other words, the sets corresponding to yes/no questions that have a probabilistic answer.

延期开工的Kolmogorov宣布要衡量所有套职能有限许多坐标限制在于衡量子寅。换句话说，如果是/否的问题回答f可看的价值观念在许多最有限坐标，然后它有一个概率的答案。

The experimental results showed that the algorithm can filter singular points and remain fixity of the target edge.

实验表明：基于模糊理论的图像智能滤波方法比常规图像滤波方法运算量小，它既能去除奇异点，又能保持图像中目标的边缘不变性，具有很好的滤波效果。