存在性定理

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。

This result can best be viewed as a quantum black hole version of the third law of thermodynamics. As a result of this area spectrum, the spectrum of M is discrete, bounded below, and can be made positive. Prom the physical point of view, the semiboundedness and positivity of the spectrum are very satisfying results: The semi-boundedness of the spectrum implies that one cannot extract an infinite amount of energy from the system, whereas the positivity of the spectrum is in agreement with the well-known positive-energy theorems of general relativity.

同时根据EMDA黑洞动力学，存在与面积谱对应的大于零且有下界的质量离散谱，从物理上来看，质量谱的半有界性意味着不可能从系统吸取无限的能量，而正定性则与广义相对论中的正能定理一致，也就说稳态轴对称EMDA时空的ADM能量总是大于零。

It has been showed that the quantum PCII can be still valid for the general case Jacobi J 1, which is different from quantum Noether theorem. The equivalence between quantum canonical equation and PCII is deflved at the quantum level. The comparisons of these results in quantum level with those in classical theories are discussed in detail. The relationship of canonical transformation with quantum PCII is obtained.

结果表明，当变换的Jacobi行列式不为1时，量子PC积分不变量仍然存在，从而把PC积分不变量推广到了最一般情形；在量子水平上，证明了量子正则方程与该积分不变量之间的等价性；比较了经典与量子PC积分不变量以及PC积分不变量与Noether定理；给出正则变换与量子PC积分不变量间的关系。

Basic concept of Dimension and ∏ theorem and principle of homogeneity on dimensional analysis are introduced in this paper.

主要介绍了量纲的基本概念、量纲分析的∏定理及齐次性原则，用两个实例解释了量纲分析在物理中的应用，最后指出了用量纲分析问题时应注意的问题和存在的不

The first part presents develops of predator-prey systems and gives the model that is investigated in our paper; Chapter 2 presents the results on boundedness of solutions and permanence of system; In chapter 3, we explicitly derive a domain of attraction for the positive equilibrium of system by using Liapunov method; The local stability and the conditions that Hopf bifurcation occurs are obtained in chapter 4; In chapter 5, some explicit fomulae of the direction of Hopf bifurcation and the stability of bifurcating periodic solutions on the center manifold are determined,using normal form and center manifold introduced by Hassard et al; In chapter 6, some numerical simulations are performed to illustrate the analytical results found; Our paper ends with a brief conclusion.

全文共分七章，第1章对捕食-食饵系统的发展背景做了介绍并给出了本文研究的模型；第2章讨论了系统的保持性和解的有界性；第3章研究正平衡点的全局性质，对正平衡点的吸引域进行了精确估计；第4章研究了系统的正平衡点的局部稳定性和Hopf分支存在的条件；第5章利用规范型和中心流形定理得到了一个决定Hopf分支方向、分支周期解的稳定性及其他性质的精确公式；第6章对一个具体模型进行了数值模拟；第7章对全文进行了总结。

The wave-particle duality and uncertainty relation in quantum mechanics are very hard to imagine,but they are very similar to the phenomenon of the society and human in which copy and cloning is possible.If the quantum state has something like gene,it is possible to cloning a quantum state.

量子力学中的波粒二象性、不确定性关系等等难于理解，但是却与人类社会中的许多现象绝妙地类似，从更加微观的角度分析，如果量子态也存在类似基因的成分，可以绕开量子不可克隆定理的证明中假定的情况进行克隆。

In this paper, the nonexistence of the closed orbit which circles the equilibrium is proved by using the Dulac function, then all the orbits of the system are bounded by the Filippov transformation and comparability theorem.

本文利用Dulac函数法，首先判定了不存在绕平衡点的闭轨线，然后利用Filippov变换和比较定理，证明了系统所有轨线的有界性，进而得到了平衡点是全局渐近稳定的。

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。

In section one, we introduce some background of the topic, in section two we review some basic and recent results about the structure and hierarchies of the computably enumerable degrees which are closely related to our topic- the algebraic structure of the plus cupping Turing degrees, in section three, we outline the basic principles of the priority tree argument, one of the main frameworks and tools of theorem proving in computability theory, and in section four, we prove a new result concerning the algebraic structure of the plus cupping Turing degrees that there exist two computably enumerable degrees a, b such that a, b ? PC, and the join a V b of a and b is high.

度结合为0′。本篇论文分为4个部分：第一部分介绍了这个领域的一些背景知识；第二部分主要回顾了前人在研究可计算枚举度的结构和层谱时所取得的一些基本和最新结果，这些结果与我们的主题—加杯图灵度的代数结构密切相关；在第三部分中，我们概要的描述了优先树方法的基本原理，此方法是可计算性理论中定理证明的一个重要框架和工具；第四部分证明了一个加杯图灵度代数结构的新结果：存在两个可计算枚举度a，b，满足a，b∈PC，而且a和b的并a∨b是一个高度。

The Remark about Some Theorems of Real Number s Continuity;2. A class of fixed point theorems on a compact hausdorff topological space;3. This article has introduced some common basic natures of prime numbers,and has discussed other non-common natures and theorems of prime numbers.

主要介绍了量纲的基本概念、量纲分析的∏定理及齐次性原则，用两个实例解释了量纲分析在物理中的应用，最后指出了用量纲分析问题时应注意的问题和存在的不

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。