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When the mind apprehends the essence of a thing (quod quid est; tò tí en enai), the external object is perceived without the particular notes which attach to it in nature, and it is not yet marked with the attribute of generality which reflection will bestow on it.

当铭记apprehends的本质的东西（狱吏嚼1-5 ；德州仪器恩enai ），外部对象被认为没有特别注意到它重视它的性质（中存在singularibus ），这是没有标明属性一般性的反映将赋予它

Two merging methods of Bézier curves are generalized to tensor product Bé zier surfaces, we propose two methods to approximate two pieces of adjacent tensor product Bézier surfaces by a piece of tensor product Bézier surface. We offer the explicit formulas of the merged tensor product Bézier surfaces with all kinds of merging conditions.

同样，Bézier曲线的两种合并方法也被成功的推广到张量积Bézier曲面上，得到把两片相邻张量积Bézier曲面合并成一片张量积Bézier曲面的两种合并方法，并给出在各种合并条件下的合并曲面控制顶点的显示表示式。

The research indicated that,the 36°Bè xylose mother liquor was used as material,9.60% catalyst M-16 was added,and after caramelized 180min at 120℃,a caramel...

研究表明，在36°Be′的木糖母液中，加入9.60%的M-16催化剂，于120℃下焦糖化反应180min，得到色率为2.8万EBC单位，红色指数达6.3以上的焦糖色素。

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。

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。

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。

Objective:To explore the feasibility of laparoscopy in diagnosing and treating of abdominal diseases.

目的：探讨腹腔镜用以诊断腹部外科疾病及选择治疗方案的可行性。

The lifetime of nylon 1010 and nylon 1010/POSS composites decreased with increasing temperature.

热重-红外联用分析表明尼龙1010在氮气气氛下的降解产物主要为小分子的低聚物，POSS并不改变尼龙1010降解产物的组成。