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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。

First we prove that 0 is an eigenvalue of the operator with geometric multiplicity one,next we prove that all points on the imaginary axis except for zero belong to the resolvent set of the operator,last we prove that 0 is an eigenvalue of the adjoint operator of the operator.

首先证明0是对应于该排队模型的主算子的几何重数为1的特征值，其次证明在虚轴上除了0以外其他所有点都属于该算子的豫解集，然后证明0是该主算子共轭算子的特征值。

First we prove that all points on the imaginary axis except for zero belong to the resolvent set of the operator corresponding to the model, second prove that 0 is an eigenvalue of the operator and its adjoint operator with geometric multiplicity and algebraic multiplicity one,last by using theabove results we obtain that the time-dependent solution of the model str.

首先证明在虚轴上除了0以外其他所有点都属于该算子的豫解集，其次证明0是对应于该系统的主算子及其共轭算子的几何与代数重数为1的特征值，由此推出该系统的时间依赖解当时刻趋向于无穷时强收敛于系统的稳态解。

It consists of the next three aspects: firstly, we study Murthys' open problem whether the augmented matrix is a Q0-matrix for an arbitary square matrix A , provide an affirmable answer to this problem , obtain the augmented matrix of a sufficient matrix is a sufficient matrix and prove the Graves algorithm can be used to solve linear complementarity problem with bisymmetry Po-matrices; Secondly, we study Murthys' conjecture about positive semidefinite matrices and provide some sufficient conditions such that a matrix is a positive semidefinite matrix, we also study Pang's conjecture , obtain two conditions when R0-matrices and Q-matrices are equivelent and some properties about E0 ∩ Q-matrices; Lastly, we give a counterexample to prove Danao's conjecture that if A is a Po-matrix, A ∈ E' A ∈ P1* is false, point out some mistakes of Murthys in [20] , obtain when n = 2 or 3, A ∈ E' A ∈ P1*, i.e.

本文分为三个部分，主要研究了线性互补问题的几个相关的公开问题以及猜想：(1)研究了Murthy等在[2]中提出的公开问题，即对任意的矩阵A，其扩充矩阵是否为Q_0-矩阵，给出了肯定的回答，得到充分矩阵的扩充矩阵是充分矩阵，并讨论了Graves算法，证明了若A是双对称的P_0-矩阵时，LCP可由Graves算法给出；(2)研究了Murthy等在[6]中提出关于半正定矩阵的猜想，给出了半正定矩阵的一些充分条件，并研究了Pang~-猜想，得到了只R_0-矩阵与Q-矩阵的二个等价条件，以及E_0∩Q-矩阵的一些性质；(3)研究了Danao在[25]中提出的Danao猜想，即，若A为P_0-矩阵，则，我们给出了反例证明了此猜想当n≥4时不成立，指出了Murthy等在[20]中的一些错误，得到n=2，3时，即[25]中定理3.2中A∈P_0的条件可以去掉。

In order to prove the reliability, test studies have been primarily carried out in the indoor soil bin. The data of the vehicle driving state parameters under the same or different terrain are analyzed. The process curves are compared by different control schemes. The theoretical model of the optimum driving state is reliable and fuzzy control scheme is feasible. The disturbances and unknown factors of control system are analyzed. Test results prove that the half-tracked air-cushion vehicle can drive steadily under control of the computer. At the same time the sensors used to measure soil mechanics characteristics on line need to be developed. And it is the important problem to be solved in the future study. The necessary regulation and correction are put up. So the studies in this paper provide some instruction for the further research work.

为了验证本文提出的最佳工作状态及最佳垫压理论，并分析控制系统的可靠性和稳定性，本文在半履带式气垫车的模型车上，在室内土槽中进行了初步的实车性能和理论验证试验，考察了在同种和不同土壤条件下气垫车的行驶状态参数的测量数据，比较了采用不同控制方法下的过程曲线，验证了最佳工作状态的理论模型和模糊控制系统方案的可行性与可靠性，从而保证了采用自整定模糊PID控制器能够使半履带式气垫车在稳定行驶最佳工作状态下；同时通过试验研究，分析了系统中各干扰与未知因素，对控制方案进行了相应的调整和修正，为今后进一步的研究工作提供了一定的指导。

In chapter three, we prove that there exist solutions to the Ky Fan variation inequality, as the set-valued mappings are defined on spheres in infinite dimensional Banach spaces or odd dimensional Euclidean spaces, following from these theorems, we obtain some fixed point theorems for set-valued mappings defined on a sphere. When G is an approximate compact convex subset of E, or G is a almost quasi-convex set-valued mapping, we prove that there exist solutions to and type generalized Ky Fan variation inequality, following these theorems, we prove several best approximation theorems and coincidence theorems involving two set-valued mappings and two different spaces. In chapter four, we first present a new Simplicial algorithm for computing the Leray - Schauder fixed points, the algorithm can solve the set-valued nonlinear complementarily problem. We give a condition to guarantee the computation proceeding in a bounded region. We present integer-labeling algorithms for computing fixed points of some set-valued mappings, the best approximation points and solutions to a kind of set-valued variation inequalities.

第四章给出了计算定义在非凸集上的非自映射的Leray-Schauder不动点的算法，而现有的不动点算法都是计算凸集的上半连续集值自映射的不动点；给出了保证计算有界的一个充分条件，我们的条件大大弱于Mdrrill条件，我们的算法也可用来计算Eaves不动点；给出了集值非线性互补问题存在解的一个充分条件，此时可利用Leray-Schauder不动点算法来求解；向量标号算法以往是计算集值映射不动点的唯一有效算法，我们给出用整数标号算法计算一类集值映射的Kakutani 不动点的算法；定义在紧凸集上的连续映射不一定有不动点，但一定有最近点，最近点是不动点概念的推广，我们给出了计算最近点的算法；集值映射变分不等式尚无有效的求解算法，我们给出求解一类集值映射变分不等式的算法。

Finally, in the third section, by constructing some functional which similar to the conservation law of evolution equation and the technical estimates, we prove that in the inviscid limit the solution of generalized derivative Ginzburg—Landau equation converges to the solution of derivative nonlinear Schrodinger equation correspondently in one-dimension; The existence of global smooth solution for a class of generalized derivative Ginzburg—Landau equation are proved in two-dimension, in some special case, we prove that the solution of GGL equation converges to the weak solution of derivative nonlinear Schr〓dinger equation; In general case, by using some integral identities of solution for generalized Ginzburg—Landau equations with inhomogeneous boundary condition and the estimates for the L〓 norm on boundary of normal derivative and H〓 norm of solution, we prove the existence of global weak solution of the inhomogeneous boundary value problem for generalized Ginzburg—Landau equations.

第三部分：在一维情形，我们考虑了一类带导数项的Ginzburg—Landau方程，通过构造一些类似于发展方程守恒律的泛函及巧妙的积分估计，证明了当粘性系数趋于零时，Ginzburg—Landau方程的解逼近相应的带导数项的Schr〓dinger方程的解，并给出了最优收敛速度估计；在二维情形，我们证明了一类带导数项的广义Ginzburg—Landau方程整体光滑解的存在性，以及在某种特殊情形下，GL方程的解趋近于相应的带导数项的Schr〓dinger方程的弱解；在一般情形下，我们讨论了一类Ginzburg—Landau方程的非齐次边值问题，通过几个积分恒等式，同时估计解的H〓模及法向导数在边界上的模，证明了整体弱解的存在性。

In chapter 2, we prove that sn—first countable spaces are preserved by the finite subsequence-covering mappings.By this result, we prove that the finite subsequence-covering, quotient mappings preserve g—metrizable spaces, also prove that the finite subsequence-covering, closed mappings preserve sn—metrizable spaces, g-metrizable spaces, metrizable spaces, point-countable bases.

在第二章中，我们主要证明了有限子序列覆盖映射保持sn-第一可数空间，作为它的应用，又证明了有限子序列覆盖、商映射保持g-第一可数空间，也证明了有限子序列覆盖闭映射保持sn-度量空间，g-度量空间，度量空间，点可数基。

However,To prove Inequality with elementary method,we often create complex computational process. The second ,we will take full advantage of the knowledge of calculus Inquiry Testimony of inequality,and concluded the higher mathematics to prove Inequality several main method and its application conditions.Constructors in the context of the use of the monotone function,Calculus value theorem,function and the most extreme value,integral, it can be a very effective solution to the inequality problem proof. At last,we summed up several convenient and simple way to prove Inequality.It will be play a great role in our problem Solving.

但是用初等方法证明往往会造成复杂的运算过程，本文接着充分利用微积分的知识探究不等式的证明方法，并指出微分学和积分学在不等式的证明的具体应用，那就是在构造函数的背景下运用函数的单调性、微积分中值定理、函数的极值和最值、定积分，那么就可以十分有效地解决不等式中的证明问题，从而归纳出几种方便而又简捷的方法，这样对我们解题将会起到很大的作用。

Main points of this paper are as follows:(1) to explain emphatically and to prove the Jukes-Cantor Model, Kimura Model and the relationships of them;(2) to construct and to prove, using EM algorithm, the theorems of estimating best branches of DNA sequences having censored data for Jukes-Cantor Model under the conditions of rooted tree and unrooted tree respectively;(3) to construct and to prove, using EM algorithm, another three theorems of estimating best parameters of DNA sequences having censored data for Kimura Model under the conditions of rooted tree and unrooted tree.

本论文的重点在于解释和证明Jukes-Cantor模型、Kimura模型及两模型之间的关系；运用EM算法构造并证明Jukes-Cantor模型下含缺损数据的DNA序列构建有根树的最佳分枝长度估计定理；运用EM算法构造并证明Kimura模型下含缺损数据的DNA序列构建有根树的最佳参数估计定理。

Neither the killing of Mr Zarqawi nor any breakthrough on the political front will stop the insurgency and the fratricidal murders in their tracks.

在对危险的南部地区访问时，他斥责什叶派民兵领导人对中央集权的挑衅行为。

In fact,I've got him on the satellite mobile right now.

实际上 我们已接通卫星可视电话了