解空间

Let f be a solution of the higher order differential equation, a sufficient condition for f belonging to the weighted Dirichlet space D or to the Bergman space L, respectively, is obtained.

设f是高阶微分方程的解，得到了f分别属于加权Dirichlet空间D和Bergman空间L的一个充分条件，并得到了f是不可容许解的一个充分条件。

The optimization problem was constructed in a prime space,the dual problem was solved in a eigenspace by the kernel skill and the solutions were the same as nonlinear KPLS.

在初始空间中构造优化问题，应用核技术在特征空间中解对偶问题，这种解与非线性的KPLS具有相似性。

Under suitable assumptions, the relationship is established between the unconstrained minimization of the Hestenes-Powell augmented Lagrangian function on the space of problem variables and the solution of the original constrained problem, and a relationship is also presented between the unconstrained minimization of the Hestenes-Powell augmented Lagrangian function on the product space of problem variables and multipliers and the solution of the original constrained problem.

在适当的条件下，我们建立了Hestenes-Powell增广拉格朗日函数在原问题变量空间上的无约束极小与原约束问题的解之间的关系，并且也给出了Hestenes-Powell增广拉格朗日函数在原问题变量和乘子变量的积空间上的无约束极小与原约束问题的解之间的一个关系。

Under the Lipschitz conditions,using Morrey space and Campanatospace methods and filling-hole technique to clear off the difficulty,whicharoused by that monotonic inequalities are no longer true and blow-uptechnique are very difficult to be used again,we obtain that the weaksolutions or the very weak solutions to systems(3)are locally Holdercontinuous.

对方程组（3），我们增加了Lipschitz条件，利用Morrey空间法和Campanato空间法和补洞技巧等来克服非齐次项带来的，单调不等式不再成立和Blow-up技巧难于适用的困难，得出了方程组（3）在一定的条件下的很弱解和弱解是局部〓连续的。

According to the existence results of general equilibrium problems and vector equilibrium problems have been studied more and more. Inspired and motivated by these research results, this paper is devoted to study systematically a class of equilibrium problems, which is unify and extension of a large number of known equilibrium problems and variational inequalities problems. The research is carried on from three aspects.Firstly, in finitely continuous topological spaces, we introduce four new types of the system of generalized vector quasi-equilibrium problems, and we derive some existence results of a solution for the system of generalized vector quasi-equilibrium problems via the maximal element theorems in product finitely continuous topological spaces.Secondly, in complete metric spaces, we provide the Ekeland variational principle to equilibrium problems with set-valued maps. And via the Ekeland variational principle, existence results for vector equilibrium problem with set-valued maps and the system of vector equilibrium problem with set-valued maps.

针对一般的均衡问题和向量均衡问题解的存在性，已有许多研究成果，受这些成果的启发，本文主要从理论上较为系统地研究了一类均衡问题，它统一和推广了许多已有的均衡问题和变分不等式问题，研究分有三个方面；首先，在有限连续拓扑空间中，我们提出了四类广义向量拟均衡系，并借助于有限连续拓扑空间中的极大元定理讨论了这四类均衡系问题的解的存在性问题，然后，在完备度量空间中，我们给出了关于集值均衡问题的Ekeland变分原理，并利用Ekeland变分原理分别讨论了集值向量均衡问题和集值向量均衡系问题的解的存在性。

II, Polynomial rings on a general field( on contrast of those over a number field): concepts of ring, ideals, field and several special rings as domains, principal ideal domains and unique factorization domains, the unique factorization theory of polynomial rings.

二、一般域上的多项式理论（是数域上多项式理论的推广）：学习环、域和几类特殊结构的环（整环、主理想环，唯一分解环等）的概念，多项式环的唯一分解定理；三、线性代数：讲述一般数域上的向量空间理论（是数域上向量空间理论的继续和推广），模的概念，主理想环上的模的结构及其线性变换的若当标准型等；四、一元多项式的解及域论：学习域扩张及其相关概念，伽罗瓦理论，用伽罗瓦定理判断根式解的存在性。

The notion of - resolvent operator of set-valued mappings is introduced.

利用η-预解算子在有限维空间中探讨了集值混合拟类变分不等式问题和广义集值变分包含问题存在唯一解的条件；利用分析的方法在实Hilbert空间中讨论了集值混合拟类变分不等式问题解集的非空性。

In the method of numerical analysis, the spatial part of equation system in strong conservation form is first discretized by conventional central finite-difference approximation and then the system of partial differential equations becomes a system of ordinary difference equations.

本文所建数值方法的基本空间离散格式是中心差分，并用源于Jameson的标量耗散模型抑制数值波动；采用经典四阶龙格—库塔法积分经过空间离散后得到的常微分方程组当残差足够小时的解为稳态解。

This thesis focuses on studying the matrix equa-tion problem systematically, and proposed an abstract algorithm of solving the matrixequation with constraints, and established a strict convergence theory. Using this algo-rithm, we can solve the sets of matrix equation satisfying some constraint conditions,such as symmetric, antisymmetric, centrosymmetric, centroskew symmetric, re?exive,antire?exive, bisymmetric, symmetric and antipersymmetric, symmetric orthogonalsymmetric, symmetric orthogonal antisymmetric, Hermite generalized Hamilton ma-trix;So we can solve the problem with this algorithm, if the set of constrain matrixcan make a subspace in matrix space, and this algorithm also can solve the optimalapproximation and least squares problem. So this abstract algorithm has universal andimportant practical value.

本篇硕士论文系统地研究了此类问题，并找到了求解约束矩阵问题的抽象算法，并建立严格的收敛性理论，利用这一算法可求解约束条件为对称矩阵、反对称矩阵、中心对称矩阵、中心反对称矩阵、自反矩阵、反自反矩阵，对称正交对称矩阵、对称正交反对称矩阵、双中心矩阵、Hermite广义Hamilton矩阵等；可以说只要约束矩阵集合在矩阵空间中构成子空间，都可以考虑用此算法求解，而且这一算法还能把矩阵方程解及其最佳逼近，最小二乘解及其最佳逼近统一处理，因此本文算法有普适性和重要的实用价值。

Abnormity sampling method was adopted and there was 128 sampling points in this field.The statistical laws of soil pH,organic matter,total phosphorus,total nitrogen,alkaline hydrolyzable nitrogen,available potassium and available phosphorus were analyzed, and the results indicated that the variation coefficient of soil nutrients was between 6.3% and 356.1%,pH was 5.3%.Using the geostatistica...

以土壤的pH、有机质、全磷、全氮、碱解氮、速效钾和速效磷含量为研究对象，研究其相应的统计规律，结果表明土壤各养分属性的变异系数在6.3%~35.61%之间，pH为5.3%；采用地统计的半方差函数分析，发现有机质，全氮，碱解氮和速效钾在一定范围内存在空间相关性；采用克立格方法进行最优内插，绘制了养分含量分布图，并对其空间变异进行了初步分析。

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