证明性的

Firstly, we consider SIQR epidemical models with continuous and pulse vaccinations; the reproduction numbers have been obtained for those models; by using Dulac function, we prove the global stabilities of equilibrium of SIQR model with continuous vaccination. In the SIQR epidemical models with pulse vaccinations, we have also discussed the existence of the infection-free periodic solution, the global stabilities of the infection-free periodic solutions, and the effectiveness of pulse vaccination and continuous vaccination policies has been compared for the two models.

文中首先考虑具有连续免疫接种和脉冲免疫接种的SIQR传染病模型，分别获得了它们各自的基本再生数；利用Dulac函数方法证明了具有连续免疫接种的SIQR模型无病平衡点的全局渐近稳定性；在脉冲免疫接种下SIQR传染病模型里，讨论了无病周期解的存在性，证明了该周期解的全局渐近稳定性，并且对连续和脉冲接种下的SIQR传染病模型的接种效率进行了比较。

The purpose of this paper is to investigate the representation problems of strong efficient solutions by generalized saddle point in nearly cone-subconvexlike set-valued vector optimization problems.

1引言近几年，集值映射的广义凸性倍受一些学者的关注，这主要是由于在集值向量优化理论的证明中它能代替凸性要求。

In part V using Lions' second Concentrate Compactness Lemma andvariational method,we prove the existence of minimal positive solutionof a class of quasilinear elliptic obstacle problems〓in space〓.

第五部分使用Lions的集中紧性原理和变分方法，我们证明了一类非齐次拟线性椭圆型方程对应的障碍问题〓在〓中极小正解的存在性。

The model as follows:〓 u =0,∈〓Ω×J u =u〓, x∈Ω chapter 3 is devoted to study the moving grid timediscretization FEM of above model, the optimal energy norm error estimate is obtained.

本文第二章重点研究了上述模型有限元算法的构造及收敛性，克服了ρ同时依赖压力p、浓度c带来的困难，证明了有限元半离散解的整体存在性和最优误差估计。

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。

In 1892, D.Ivanowsky of Russia had first shown that the causal agent of tobacco mosaic disease was filterable, but Beijerinck went much further and provided strong evidence that although the causal agent was filterable, it had amny of the properties of a living organism.

在 1892年，俄国的 D.Ivanowsky 首先证明了烟草花叶病的病原体是具有可滤过性。但是荷兰的Beijerinck研究得更深入，不仅提供了充分的证据证明尽管病原体是可滤过的，但是它却具有了生命体的所有特征。

Under some reasonable hypothetic conditions,the error of inverse wavelet which is caused by non-orthogonality is nearly Gauss distribution.

通过分析非正交性对滤波器的影响，可以证明：逆子波因非正交性产生的误差呈近似的高斯分布。

After taking experiments on PPC, it shows that the performance can be improved more than 50% for comparison of the supper sampling with satisfying image quality and the table size is only about 10% of the Walter Algorithm.

通过手持设备上的实验证明，与传统的过采样方式相比，在不影响图像质量的前提下，性能提高了50％，与Walter的编码滤波器相比，查找表的大小缩减到了原来的10％左右，从而证明了此方案的可行性和高效性。

There are detailed expositions on directness of market administration and indirectness of macro control in law works and textbooks.

在经济法学界及许多教科书中，都有关于市场规制法的直接性特点与宏观调控法的间接性特点的表述，论述和证明得都比较充分。

There is no parameter involved,and the existence of global solutionof the initial value problem of the proposed network,its convergence and stability are strictlyproved by establishing a Lyapunov function.

构造了恰当的Lyapunov函数，证明了初值问题解的整体存在性，网络的稳定性和收敛性。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新