函数代数

Involves the membership function specifically, the operations research, and so on linear algebra, as well as mathematical model of analytic hierarchy process, matrix representation and so on.

具体涉及隶属函数，运筹学，线性代数等数学知识，以及层次分析法，矩阵计算等数学模型。

Using a method of algebraic transformation such as power series expansion, it is found that, three crop water production functions, the Jensen mold, Rao model and Stewart model, are transformable mutually, and their water sensitive indices are approximately equivalent.

通过幂级数展开等代数变换发现，3种作物水分生产函数Jensen模型、Rao模型和Stewart模型可以近似相互转化，其各自水分敏感指数近似等价。

In the thesis, we study the applications of algebaric approximation in numerical mathematics, especially in the numerical solution of differential equations.

本文着重研究代数函数理论在计算数学领域中的问题和应用。

Then the interpolation representations of fuzzy controllers with Mamdani implication operator, algebra product implication operator, Zadeh implication operator and implication operator are introduced separately.

然后分别获得了基於POFI方法的Mamdani蕴涵算子模糊控制器、代数积蕴涵运算子模糊控制器、Zadeh蕴涵运算子模糊控制器及加乘运算子模糊控制器的插值表示，由此发现这些模糊控制器具有函数逼近的泛性。

Firstly, the three-dimension boundary question and its corresponding variation question concerning the point-source electrical field on a 3-D structure are presented. Secondly, the finite element method is used to solve the variational equation. The study area is divided into many tetrahedral elements. Then, we interpolate with a tri-linear function in each element. So, the variational equation is converted into a linear equation system. Finally, taking into account saving of time, we make use of symmetric successive overrelaxation preconditioned conjugate gradient algorithm to solve large linear system, and obtain the potential value of each node, resulting in the calculation of the apparent resistivity values on the ground surface.

首先给出了三维构造中点源电场的边值问题以及相应的变分问题；然后利用有限单元法求解变分问题，采用四面体单元对研究区域进行剖分，在单元中进行三线性函数插值，将变分方程化为线性代数方程组；最后，考虑到节约计算时间，利用对称超松弛预条件共轭梯度迭代算法求解大型线性方程组，得到了各节点的电位值，进而计算出地表的视电阻率。

Then the stability solution of the variable cross-section compression bar, that is discribed by a partial differential equation with variable coefficient is transformed into solving a set of algebraic equations established in the subspace.

首先以均匀梁的低阶纵向振动模態函数构成求解子空间，然后在此子空间中把变截面压桿稳定由变系数偏微分方程描述的求解问题转化为非线性代数方程组的求解，从而简化了计算过程。

Questions in this content area are based on an understanding of the quadratic formula, rational and radical expressions, absolute value equations and inequalities, sequences and patterns, systems of equations, quadratic inequalities, functions, modeling, matrices, roots of polynomials, and complex numbers.

中等代数（ 15 ％）。这方面的考试内容包括理解二次公式，有理式及根式，绝对值方程和不等式，序列，方程组，二次不等式，函数，建模，矩阵，多项式的根以及复数。

The Riemann- Jacobi inversion is discussed to yield the final expression of explicit solution by means of the Riemann theta function, which is directly related to algebraic geometry.

为了最终生成由θ函数所给出的显式解，我们讨论了Riemann-Jacobi反演，这一过程直接关系到代数几何。

Angular momentum: operators, commutator algebra, eigenvalues and eigenstates, spherical harmonics.

角动量：算符，对易代数，本征值和本征态，球谐函数。

By introducing the nonlinear complementarity problem function, the Karush-Kuhn-Tucker conditions of OPF model are transformed equivalently into a set of semismooth nonlinear algebraic equations. Then the set of semismooth equations can be solved by a semismooth L-M method based on the subdifferential. The method belongs to Newton-type method. It can ensure the positive defmitiveness of the iterative coefficient matrix by using the L-M parameter, which avoids the ill-conditioning of iterative equations. The method, requiring only the approximate solution of a linear system at each iteration, is quite applicable to the large-scale cases.

在利用非线性互补函数将OPF模型的KKT条件转化为半光滑非线性代数方程组后，采用基于次微分的半光滑L-M法求解，该方法属于牛顿法范畴，可通过对L-M参数的调整保证迭代系数矩阵的正定性，克服了系数矩阵的奇异引起的"病态"，且该方法在确定搜索方向时只需求解线性系统的加热器近似解，适用于大规模系统的求解。

The concept of equivalent rotationally rigidity is offered and the formula of rotationally rigidity is obtained.

主要做了如下几个方面的工作：对伸臂位于顶部的单层框架—筒体模型进行分析，提出了等效转动约束的概念和转动约束刚度的表达式。

Male cats normally do not need aftercare with the exception of the night after the anesthetic.

男猫通常不需要善后除了晚上的麻醉。