唯一性定理

On the applications of the uniformly Besicovitch almost periodic functions to differential equations, the main works are as follows:First, the paper proves that the space of the uniformly B2 almost periodic functions, with a special norm, is a Banach space, and then the Fixed Point Methods could be used in this function space.Second, since the space of the uniformly B2 almost periodic functions is per-fect, the paper investigates the existence and uniqueness of uniformly B2 almost periodic solution of a wave equation involving reflection of the argument by the principle of contraction mapping.

关于一致Besicovitch概周期函数在微分方程中的应用，本文主要做了以下工作：第一，证明了一致B~2概周期函数空间在其特定范数下构成Banach空间，从而可以在此函数空间上应用不动点定理；第二，由一致B~2概周期函数空间的完备性，应用压缩映像原理，讨论了一类满足一定初始条件的带反射变量的波方程一致B~2概周期解的存在唯一性。

The purpose of this part is to study the delay differential systems in Banach space using the method of fixed point theorem.

一方面在非时滞的情况下通过构造比较函数，利用Brouwer不动点定理得到非时滞微分方程正周期解的存在唯一性，及周期解全局吸引的充分条件。

A fast algorithm for calculating the inverse and Moore-Penrose inverse of the permutation factor circulant matrix is presented. Then, a fast algorithm for the product of the permutation factor circulant matrix is given. Finally, The least-square solutions of inverse problems and the optimal approximation problems for the permutation factor circulant matrix are discussed.

首先给出了一种求n阶置换因子循环矩阵的逆阵、自反g-逆、群逆、Moore-Penrose逆的快速算法，然后给出了计算两n阶置换因子循环矩阵之乘积阵的一种快速算法，最后给出了其反问题的最小二乘解的存在性定理及它的一般表示，并证明了逼近矩阵的存在唯一性且给出它的具体表达式。

In this paper we introduce some new definitions, they are the generalizations of those concepts in Lie theory, and we discuss initially the elementary properties of operator Lie algebras. Finally, the famous Jordan-Holder theorem and the uniqueness of decomposition theorem of operator Lie algebras are proved.

在这篇文章里，我们将李代数理论中的诸多概念加以推广，并初步地探讨了算子李代数的性质，最后还给出了算子李代数的一个分解定理，其唯一性也得到了证明。

In part III by using capacity theory and extension theorem of Lip-schitz functions we first discuss the uniqueness of weak solution ofnonhomogeneous quasilinear elliptic equations〓in space〓,which is bigger then〓.

第三部分首先用容量理论、Lipschitz函数延拓定理讨论了一类非齐次拟线性椭圆型方程〓在比〓更大的空间〓中弱解的唯一性。

The model in this paper takes the form as belowThe main contents and results in this paper are as follows:In section 1, we state our main analytical results on equilibria of the above system. First, several sufficient conditions for coexistence of the steady-state are given by the standard fixed-point index theory in cone. Second, the global structure of the coexistence solutions and their local stability are established by using bifurcation theory. Third, the multiplicity, uniqueness and stability of positive steady-state solutions to this system are derived by means of perturbation theory of eigenvalues, standard regularity theory, Sobolev embedding theorem and fixed-point index theory.

本文主要有两章内容：第一章研究了该模型正平衡解的性质，可分为三部分：第一部分运用极值原理、上下解方法和锥映射不动点指标理论得到正平衡解存在的充分条件；第二部分利用分歧理论给出了平衡态系统正分歧解的结构，并讨论了局部分歧解的稳定性；第三部分利用特征值扰动理论、标准椭圆正则化理论、Sobolev嵌入定理及指标理论讨论了正平衡解的多重性、唯一性及稳定性，并讨论了参数对解的影响。

Firstly, by constructing the Lyapunov function with a special structure, a prior estimate is obtained. Secondly, with the help of Green\'s function, the original problem is transformed into an equivalent operator equation, and the fixed point theory of contraction mapping in a Banach space guarantees the existence and uniqueness of the global solution.

首先，构造具有特殊结构的Lyapunov函数，得到解的先验估计；其次，借助Green函数将原方程等价变换成算子方程，Banach压缩映射的不动点定理保证了全局解的存在唯一性；最后通过常微分方程的定解，证明了主要结论，即平凡解全局渐近稳定。

The existence and uniqueness of the solutions are proved by Leray-Schauder fixed point theorem.

相应解的存在唯一性由Leray-Schauder不动点定理得以证明。

Using Nevanlinna value distribution theory, the research we studies the uniqueness of meromorphic functions concerning the multipliable value, and proves one theorem, which generalizes and improves previous results.

运用亚纯函数的值分布理论，研究了亚纯函数涉及重值的唯一性问题，证明了一个定理，所得定理改进了先前的一些结果。

Using the asymptotically compact theory of Anselone' and Stepleman' theorem, the existence, the unicity , the convergence and the error estimate with O(h3) of the discrete equations are shown....

并借助Anselone的渐近紧收敛理论和Stepleman定理，证明了离散方程组的解存在性、唯一性、收敛性和精度阶O(h~3)。使用Ostrowski的不动点定理，提供了三阶收敛的迭代法。

However, as the name（read－only memory）implies, CD disks cannot be written onorchanged in any way.

然而，正如其名字所指出的那样，CD盘不能写，也不能用任何方式改变其内容。

Galvanizes steel pallet is mainly export which suits standard packing of European Union, the North America. galvanizes steel pallet is suitable to heavy rack. Pallet surface can design plate type, corrugated and the gap form, satisfies the different requirements.

镀锌钢托盘多用于出口，替代木托盘，免薰蒸，符合欧盟、北美各国对出口货物包装材料的法令要求；喷涂钢托盘适用于重载上货架之用，托盘表面根据需要制作成平板状、波纹状及间隔形式，满足不同的使用要求。