证明性的

In this master thesis, we mainly discuss the adjacent vertex- distinguishing total chromatic numbers of some special graphs and prove that Zhang"s conjecture holds for these graphs. Then we get the adjacent vertex-distinguishing total chromatic numbers of the Halin Graphs. Moreover, we investigate the Generalized Petersen Graphs, prove that some classes of positive integers can"t structure the Generalized Petersen Graphs and get the result that the adjacent vertex-distinguishing total chromatic number is 5. Finally, based on the number and the parity of circles contained by the graph, we get the adjacent vertex-distinguishing total chromatic number of two classes of graphs.

本学位论文首先主要针对几个特殊图类讨论其邻点可区别全色数，验证了其满足图的邻点可区别全色数的猜想；再证明了非轮的Halin图的邻点可区别全色数；接着研究的是广义Petersen图，讨论了不能构成广义Petersen图的几类正整数，并证明了该图的邻点可区别全色数等于5；最后，根据图所含圈的个数及其奇偶性得到了两类图的邻点可区别全色数。

We develop his ideas by finding some algebraic invariants under the adjoint actions of the group in addition to the Killing form and give a rigorous proof of the optimality of the one-parameter systems for the symmetry group of the given equations.

本文系统地研究了1+2维非线性发展方程的对称代数，证明了该方程容许一个七维李点对称群，利用Olver提出的方法，详细地建构了1+2维非线性发展方程的一维最优系统，在此基础上我们发展了他的方法，发现了除Killing型之外的其它六个在群伴随作用下的代数不变量，利用这些不变量证明了该最优系统的最优性。

In chapter four,at first,we investigate classification theory of the positive homogeneous p-Laplacian equation ,the main method is Prufer's transformation,and then we discuss the nontrivial solution for associated nonhomogeneous equation by making use of Leray-Schauder degree.

接着研究了非齐次方程的可解性。在第四章中，我们首先是建立了正齐次p-Laplacian 方程的分类理论，主要利用Prufer 变换。再应用Leray-Schauder 度理论证明非齐次方程的可解性。

We also give some conservation and convergence analysis for the Dirac equation and the Korteweg-de Vries equation.

在第七章中，我们建立了全直线上不带权的Legendre有理谱逼近，并以Dirac方程作为实例，证明了谱格式的守恒性和收敛性。数值结果表明了算法是有效的。

This paper proves the existence of utility function by using Riemannian geometry methods, which build a bridge between Riemannian geometry and economics.

运用黎曼几何的方法证明了效用函数的存在性，引进了广义的边际效用趋势概念，该定义揭示了以效用函数为度量与一般的欧氏度量的偏离，并证明了这个定义是内蕴的。

Based on a method of portioning customers, the paper first formulates the objective function, and provides and proves the low-bound of objective value; and then designs a heuristic algorithm using some known ideas of capacitated concentrator location problem, and verifies the designed algorithm to be asymptotic optimal simultaneously.

基于一种客户分组方法，首先讨论了目标函数的建立、目标值下界的构造和证明，然后借鉴通讯领域中约束集中器选址问题的一些成熟理论设计了求解所研究问题的启发式算法，同时证明了所设计算法的渐进最优性。

And trust region type algorithm with memoryless technology not only satisfies new factorized quasi-Newton equation, but also saves much storage and algebraic operations than the original factorized quasi-Newton methods.we prove it posses the global convergence and the local superlinear convergence under some condition.

本文中利用无记忆技术产生的无记忆型信赖域算法不仅满足新分解牛顿方程，具有其所有的良好性质，而且比一般的分裂拟牛顿法节省存储空间，减少计算量。本文证明了在一定假设条件下该算法具有全局收敛性及局部超线性收敛性。

The products can filter ultraviolet ray automatically , desmut automatically ,especially strong to protect color , regulate the difference in temperature intelligently etc . After becoming membrane , the products become the very cold-resistant ,high-fever-resistant and has a good adaptability ; the paint membrane has such excellent functions as hiding power ,fine adhesive force , be able to bear scrubbing .

PAYTON佩盾漆经国家各级检测机构证明，各项性能均大大高于市场上的普通涂料，是传统涂料的又一次重大科技突破，产品具有自动过滤紫外线、自动除污、特强保色性、智能调节温差；成膜后可耐严寒、高热，地区适应性强；漆膜遮盖力、附着力好、耐洗刷性好等优异性能。

The thesis of self-ownership itself, in Cohen's mind, has apparently irresistible moral appeal, so Cohen does not directly rebut the thesis of self-ownership in later criticism of Nozick's theory of justice in holdings, instead, he takes an indirect strategy, trying to weaken appeal of the thesis and therefore enter into the criticisim of Nozick's theory of justice in acquisition.

首先，柯亨否证了诺齐克为资本主义初始不平等分配所作的论证，证明即使承认自我所有命题所支撑的自我所有原则，也不能由此证明私人占有意义上的资本主义初始分配的正当性。

The new ideas from this paper: using mechanics principle study of soil, create a practical test to prove that it could change the physical mechanics character of base soil completely, reducing distortion, improving strength, and eliminating wet or sinking of base soil by seal extrusion during hole formation process at certain replacement rate; it could strengthen the loessial soil base to high bearing capacity to standard value of 300 to 400kPa through seal extrusion to hole formation technology together with rammed cement soil pile. Some value of the parameters adopted by bearing capacity calculation of the composite base of rammed cement soil pile with seal extrusion to hole formation exceeded the criteria of 'Technical Regulation on Building Ground Treatment'.(JGJ79-2002) This technology meet the design requirements and save investment.

本课题的创新点：1 利用土力学原理进行研究及理论推导，并经实践：证明了在置换率为某一定值的情况下，在成孔过程中通过挤密作用可以从根本上改变地基土的物理力学性质，使地基土的变形减小，强度提高，湿陷性消除；2 挤密成孔工艺与夯实水泥土桩的组合，可使低强度的湿陷性黄土地基变成高强度的复合地基，其承载力特征值可达 300~400kPa；3 挤密成孔法夯实水泥土桩复合地基承载力计算所采用的有关参数取值范围超出了《建筑地基处理技术规范》JGJ79-2002 中的有关规定；4 在节省投资的前提下，解决了地基高承载力、低变形及黄土湿陷性问题，达到了设计要求。

Singer Leona Lewis and former Led Zeppelin guitarist Jimmy Page emerged as the bus transformed into a grass-covered carnival float, and the pair combined for a rendition of "Whole Lotta Love".

歌手leona刘易斯和前率领的飞艇的吉他手吉米页出现巴士转化为基层所涵盖的嘉年华花车，和一双合并为一移交&整个lotta爱&。

This is Kate, and that's Erin.

这是凯特，那个是爱朗。