解曲面

Using the substitution-elimination method affine algebraic variety can be resolved to pure d-dimensional subvariety and expressed by an algebraic hypersurface on d+1-dimensional space with a sequence of elimination-polynomial systems. All 0-dimensional solution can be found, too.

利用变换消元法可以把代数簇分解成纯d维的子簇，并把代数簇表示为d+1维子空间上的超曲面形式和一系列的消元多项式组，且能求出全部孤立解，同时给出了算法及其在多项式因式分解中的应用。

In chapter two, under the assumption that the set of decision variables is convex and the objective functions are concave, it is shown that the set of noninferior solutions in valued space of the objective functions turns out to be a strictly decreasing, concave and no chinky block of surface, and it can be constructed recursively.

在第2章凸性假设下非劣解集的构造及其几何性质中，在假设决策变量集为凸集，目标函数向量是凹的情况下，证明了目标函数向量值空间中的非劣解集是一严格单调递减，无缝隙且凹的曲面块，并给出了m维目标函数向量值空间中非劣解集的一种递归构造方式。

Therefore at each time we get the roots of this cubic equation, we can decide if we keep or reject each root according to the continuity of the curved surface, the method is as follows: If , the relative cubic plane curve is just a circle, this circle can be gotten by solving .

因此在每次求得该一元三次方程的解时，我们根据曲面的连续性来判断这些根的取舍，方法如下：在处，所得的平面曲线就是圆截线，该圆截线可以由相截得到，即。

Then, for the first time, a finite element model of the cylindrical shell surface was bring forward and set up.

首次提出和建立了柱体坐标系下的曲面柱壳单元有限元模型，以及在柱坐标系下的边界元法基本方程和柱坐标系下无限域与半无限域基本解。

For the timelike surfaces with constant positive Gaussian curvature (K=1) in R〓, we construct the correspondence between R〓 and sl (2, R), and deduce the fundamental equations for a special choice of the velocity of motion of time-like surfaces in asymptotic coordinates under suitable conditions, meanwhile, we give the B〓cklund transformation and one soliton solution of the evolution equations, then in terms of a gauge transformation we obtain the explict expression of the motion of surfaces.

对于三维Minkowski空间R〓中具有正常高斯曲率（K=1）的类时曲面，取定特定速度，在以渐近线作为坐标曲线的情况下，曲面运动满足两个基本方程，即sinh-Gordon方程和θ随时间演化的方程（其中θ表示两条渐近线之间的夹角），同时给出两个基本方程的B〓cklund变换和单孤子解，并通过规范变换给出相应的正常高斯曲率曲面的显式表达式。

Pentose and hexose hydrolyzed from crop straw with hydroxide and enzyme were determined by HPLC. Based on the analysis of metabolic pathway, the fermentation technology was optimized by orthogonal design and response surface methodology.

采用碱解与酶解方法处理原料秸秆，并利用高效液相检测水解液，结合代谢途径的分析对发酵工艺进行了正交试验与响应曲面优化。

Multiobjective optimization problem has a wide range of applications in the real world. It is different from the single objective optimization. It often involves incommensurable and competing objectives, and the number of its Pareto optimal solutions is usually infinite. Therefore, it is very important to design new algorithms which can find well distributed and close-to-Pareto-optimal solutions.

在现实世界中很多问题都是多目标优化问题，不同于单目标优化，在多目标优化中，各目标之间是互相冲突的，其最优解往往有无穷多个，如何使得到的Pareto最优曲面距离真正的Pareto最优曲面最近、最优解的分布均匀且范围更广是求解多目标优化问题的关键。

Igusa's p-adic zeta function is associated to a polynomial f in several variables over the integers and to a prime p. It is a meromorphic function which encodes for every i the number of solutions M_i of f=0 modulo p^i.

在探究利用辐射型基底函数去解超奇异积分方程的数值解，我们选择了多重二次曲面函数和薄板型云线以及李纳德多项式去估计我们的解。

Taguchi method, technique for order preference by similarity to ideal solution method, principal components analysis, dual response surface method and scatter search are used to optimize the multi-objective simulation models.

有鉴於此，本研究以模拟为工具，并结合田口方法、理想解类似度顺序偏好法、主成份分析法、双反应曲面法、分散式搜寻法等方法为主体来寻求多目标模拟模式最佳解。

Chapter 2 is devoted to study of exact solutions of the nonlinear evolution equations. Using solutions of a Bernoulli equation instead of tanh in tanh-function method we find some more general solutions of the KdV-Burgers-Kuramoto equation , and by using the nonlinear telegraph equation we show that there are many different choices on its balancing number m and the power n of the nonlinear term in Bernoulli equation by which we can recover the previously known solutions and also can derive new square root type solitary wave solutions. Exact solitary wave solutions for a surface wave equation are obtained by means of the homogeneous balance method. We also present an approach for constructing the solitary wave solutions and non-solitary wave solutions of the nonlinear evolution equations by using the homogeneous balance method directly, which is also used to find the steady state solutions, solitary wave solutions and the non-solitary wave solutions of the 2+1 dimensional dispersive long wave equations. The soliton-like solutions of the BLMP equation and the 2+1 dimensional breaking soliton equation are found by use of the symbolic-computation-based Method.

第二章中研究了非线性发展方程的精确解：用双曲正切函数法中的双曲正切函数换为Bernoulli方程的解的方法而给出KdV-Burgers-Kuramoto方程的精确解并用非线性电波方程为例说明了平衡数m和Bernoulli方程中非线性项的次数n有着多种选择的可能，它不但使我们能找到已知解而且也能找出新的根式孤立波解；用齐次平衡法给出一个曲面波方程的精确孤立波解，并提出直接用齐次平衡法寻找非线性发展方程的孤立波解、非孤立波解的方法，作为应用给出2+1维色散长波方程组等的定态解、孤立波解、非孤立波解等；用Symbolic-computation-basedMethod获得BLMP方程和2+1维破裂孤子方程的类孤子解；提出sine-Gordon型方程的直接求解方法，并获得sine-Gordon方程、双sine-Gordon方程、sinh-Gordon方程、MKdV-sine-Gordon方程和Born-Infeld方程等的精确孤立波解。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失