查询词典 generalized Boolean algebra

Based on the existing generalized synchronization, a new synchronization the full-state generalized synchronization is proposed for nonidentical chaotic systems. The controller with a unified structure is designed for this new synchronization. This simple and adaptive controller can be applied to a wide range of generalized synchronizations.

在已有的广义同步定义基础上，提出了一种新的概念—-非恒同混沌系统的全状态广义同步，给出了实现全状态广义同步的统一的控制器形式，该控制器适用范围大，结构相对简单，并且是自适应的。

By applying these two tools,we mainly discuss the problems as follows:1 Perturbation identities for the generalized polar decomposition:By applying singular value decomposition, we study the perturbation bounds of the generalized polar decomposition under unitary invariant norms when A is perturbed by addition or multiplication,respectively and give our bounds in identities.2 A class of new unitary invariant metrics: This paper generalized a class of new unitarily invariant metrics and give the upper-bounds and lower-bounds by C-S decomposition.

利用这两个强有力的工具，本文主要讨论了如下问题：1 矩阵广义极分解的扰动等式：利用奇异值分解，本文分别讨论了加法扰动和乘法扰动下矩阵广义极分解在任意酉不变范数下的扰动界，并首次以恒等式的形式给出了酉极因子和半正定因子的扰动界。2 一类新的酉不变度量：本文推广了文[22] 中的结论，定义了一类新的酉不变度量。

Generalized way ; graph analysis ; prime number distribution ; Kronecher function ; Hanavan model ; generalized coordinate ; generalized inertia force ; technical movement.

国家自然科学基金；高等学校博士学科点专项科研基金广义路径；线图分析；素数分布；卷和函数； Kronecher函数； Hanavan模型；广义坐标；广义惯性力；动作技术

Using operator-theoretic-methods, we give some characterizations for a dual generalized frame of a generalized frame in a separable Hilbert space H. We also prove a result concerning two strongly disjiont generalized frames.

本文研究了可分的Hilbert空间H中的广义框架，运用算子理论方法，研究了可分的Hilbert空间H中广义框架的性质，给出了广义框架的对偶广义框架的一些刻画，并且证明了两个广义框架是强非交的一个充分必要条件。

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。

With the idea of smoothing Newton method, we propose a new class of smoothing Newton methods for the nonlinear complementarity problem based on a class of special functions. In this paper, complementarity problem is converted into a series of smoothing nonlinear equations and a modified smoothing Newton algorithm is used to solve the equations. We use Newton direction and Gradient direction together in the algorithm which guarantees that our method is globally convergent. Also using another smoothing function, we reformulate the generalized nonlinear complementarity problems defined on a polyhedral cone as a system of smoothing equations and a smooth unconstrained optimization problem. Theoretical results that relate the stationary points of the merit function to the solution of the generalized nonlinear complementarity problems are presented, we use the modified smoothing Newton algorithm in generalized nonlinear complementarity problems, under mild hypothesis, a global convergence is proved.

本文一方面基于现有的各种光滑Newton法的思想和半光滑理论，利用著名的F-B互补函数的光滑形式，首先将互补问题的求解转化为求解一系列光滑的非线性方程组，然后给出了一种修正的光滑Newton法，该方法不仅放宽对函数F的要求，在Newton方程不可解时引入初始效益函数的最速下降方向，而且光滑因子的选择也比较简单可行，同时在适当的条件下，证明了其算法具有全局收敛性；另一方面，借助另一种F-B光滑函数，将多面体锥上的广义互补问题转化为一种光滑形式，讨论了优化问题的稳定点与广义非线性互补问题的解之间的理论关系，并将这种修正的光滑Newton法用于求解广义非线性互补问题中，在适当的条件下，该算法同样具有全局收敛性。

We divide the existence of generalized solutions into three theorems becauseof the existence of a generalized supersolution we need in the proof.To ob-tain this fact,we discuss three different cases separately.WhenΩhas strictconvexity,it can be proved that the generalized supersolution of (1)(2)is theconvex-monotone hull of 〓in 〓,this is theorem 2.WhenΩdoesn't hasthe strict convexity,in theorem 3 we have to suppose there exists a generalizedsupersolution.

我们的广义解的存在性结果之所以分成三个定理陈述，主要是因为在我们的存在性证明中，一个重要的事实就是广义上解的存在性，而为了得到这个事实，我们分别讨论了三种不同的情况：在定理2中的假设〓具有严格凸性时，我们证明了问题（1）（2）的广义上解就是初边值〓的凸单调包，而在〓没有严格凸性时，我们在定理3中假定了一个广义上解的存在性。

In chapter 4, we discuss further some properties of generalized fuzzy inte-grable functions, and prove that not only generalized fuzzy integrable functions have the weak integral absolute continuity, but also sequences of generalized fuzzy integrable functions have uniform weak and absolute continuity.

进一步讨论了广义模糊可积函数的某些性质，证明了在广义三角模S满足(S-1)的条件下，不仅广义模糊可积函数具有弱积分绝对连续性，而且广义模糊可积函数列具有一致弱绝对连续性。

In this paper, we first introduce the concepts and structures of generalized per-symmetric matrix, generalized centro-symmetric matrix or generalized bisymmetric matrix.

本文介绍了广义广对称矩阵、广义中心对称矩阵以及广义双对称矩阵的概念及结构，研究了这些特殊矩阵集合中，矩阵方程AXB=C及矩阵方程组A_1XB_1=C_1，A_2XB_2=C_2的迭代解法，同时考虑了相应的最佳逼近问题。

For any initial generalized bisymmetric matrix $X_1$, when $AXB=C$ is consistent, we can obtain the generalized bisymmetric solution of the matrix equation AXB=C within finite iterative steps by the iteration method in the absence of roundoff errors; Moreover, the least-norm solution $X^*$ can be obtained by choosing a special kind of initial generalized bisymmetric matrix.

在不考虑机器误差的情况下，当矩阵方程AXB=C相容时，对任意广义双对称X_1，矩阵方程AXB=C的解可以经过有限步迭代得到；特别地，通过选择特殊地初始广义双对称矩阵极小范数解X^*。

I was up all night because I was in pain, she said.

我整夜，因为我在疼痛，她说。

A crow caws /craoks.

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