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Libermann.The early researcheson this kind of manifolds were closely related to Physics and Mechanics.But since1991,S.Kaneyuki published his result on the algebraic condition for the existence ofinvariant〓structures on a coset space,Lie theory has played the most impor-tant role in the study of this kind of manifolds.In particular,dipolarizations in a Liealgebra are closely related to the homogeneous〓manifolds.Dipolarizationsin semisimple Lie algebras and the homogeneous〓manifolds associated withthese dipolarizations have been studied by S.Kaneyuki,Z.X.Hou and S.Q.Deng.Inthe partⅡ of this thesis we study the dipolarizations in some quadratic Lie algebrasand the homogeneous parakahler manifolds associated with these dipolarizations.

Libermann给出的，早期的有关类流形的研究与物理和力学密切相关，自从1991年金行壮二发表了陪集空间上存在不变仿凯勒结构的代数化结果后，李群及李代数理论在这类流形的研究中起着主要作用，特别地，李代数的双极化与这类流形密切相关，半单李代数的双极化的相关几何，金行壮二，候自新和邓少强等人已作了研究，二次李代数是比半单李代数更广且带有非退化不变双线性型的李代数，本文主要研究了二次代数的双极化及相关几何。

This method includes fixed cost in generation and transmission cost optimization function and a quadratic programming model is proposed.

该方法在目标函数中考虑了电网的固定成本，形成了以系统发、输电费用最小为优化条件的二次规划模型。

When the generation cost function is quadratic curve,the new bargaining is compared with the former one.

比较了发电费用曲线为二次曲线时新的定价方式与已有定价方式的关系。

The minimal surface have been extensively employed in many areas such as architecture, material science, aviation, ship manufacture, biology and crystallogeny and so on. In this paper we have some element works on minimal surface from the point view of CAGD It is well-known that there does not exist any other quadratic minimal surface except for the plane.

以肥皂膜问题为物理背景的极小曲面问题或者Plateau问题—寻找以给定空间曲线为边界的面积极小的曲面，从18世纪提出到现在一直是微分几何和偏微分方程理论的重要课题，微分几何领域已经有了极其丰富的极小曲面理论。

Our result is not equivlent to the one in[6],that shows the condition for the cubic curve homoclinic cycle of quadratic system in[6]isnot complete.

我们详细地分析了对应系统的动力性质，一些复杂的分枝曲线的计算借助于计算机的编程来解决。

The pencil of plane quadratic lines is the foundation for studying plane cubic curve and hig-her plane curves.

平面二次线束是研究平面三次代数曲线和高次曲线的基础。

The grain filling process of two wheat cultivars with different spike-types were modeled with Cubic, Quadratic and Logistic equation,in which all the R~2 values were significant, and the difference among the R~2 values was also significant.

结果表明：通过用不同方程对籽粒生长动态进行拟合，Cubic、Quadratic及Logistic方程的R2值均达显著水平，且三种曲线的R2值间差异明显。

A rational cubic interpolating spline based on function values and with quadratic denominators is constructed.

构造了一种基于函数值的分母为二次的C1连续有理三次插值样条。

This paper proposes a robust filter function, called trilateral filter function, to filter the noises in the domains of surface curvature, normal and position at each sample point while the local surface is fitted in a quadratic form. By optimizing the filtering result of curvature tensor, our approach is capable of preserving the feature on the target model.

通过在扫描模型每个采样点处拟合一个二次型曲面，设计了一个鲁棒的滤波函数--三边滤波函数；应用该函数分别对模型表面上每个点的法线、曲率和位置进行滤波；通过对曲率的滤波结果进行优化，可有效地保持三维模型表面上的特征。

Forming principle of cone quadratic curved line is analyzed and result is given.

结果通过空间不同情况下圆锥截交线的坐标变换，获得了圆锥截交线的真实特征。

The dissecting of samples in group2 were difficult. The root of pulmonary artery and ascending aorta failed to be unfolded because fibrous tissue was tough, right and left fibrous trigone were too firm to be solved by hand. Cardiac muscle fibers couldn't be stripped along myofibrillar trajectory since they were prone to break because of their friability.

组2的心脏解剖困难，表现为纤维组织坚韧，游离肺动脉非常困难；徒手无法松解左、右纤维三角，肺动脉和主动脉根部的游离非常困难；心肌纤维坚硬、质脆，解剖时容易断离成碎块，无法沿纤维走行方向剥离。

We have battled against the odds in a province that has become increasingly violent.

我们对在一个争夺日益激烈省的可能性。