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The spacing triangulation was achieved by restricting the angle between two adjacent triangle's normals, which can decrease or increase the data efficiently, varying with the surface's curvatures, added to the optimizing local triangulation, and uniform and smooth triangulation are obtained.

该方法从插值曲面的形状变化来考虑，根据空间离散点曲面的曲率变化有效地剔除或增加离散点，实现了离散点曲面的疏密三角网格划分。

To extract shaft orbit\'s features invariant to rotation, scaling and translation, the unique strengths of Haar orthogonal matrix type are found, the horizontal and vertical coordinates of shaft orbit are fast proceeded by Haar transform, respectively, and the slopes with different resolutions are obtained at different positions by using the corresponding transform coefficients, and then the multi-resolution angles between the adjacent slope straight line are extracted skillfully and used for the hierarchical recognition, the recognition process accords with the principle of human\'s recognizing things by using hierarchy analysis approach.

为提取轴心轨迹平移、旋转、尺度不变性特征，本文挖掘出Haar正交矩阵在图形识别中的独特优点，引入Haar正交矩阵分别对轴心轨迹的横、纵坐标进行快速变换，并利用变换后的对应系数得到轴心轨迹不同位置不同分辨率下的斜率，继而推求出相邻斜率直线之间的多分辨率夹角，所获夹角用于轴心轨迹的分层识别，其识别过程符合人类识别事物层次分析的规律。

The adjacent strong edge chromatic number of join graph of star and path is obtained.

证明了圈Cm与圈C5n的笛卡尔积图的全色数和邻强边色数都为5。

To resolve the algorithm of the chromatic number of a graph,a special method is adopt to remember the coloring process of graph,and the method does different jobs for four given cases during the coloring process.The adjacent strong edge chromatic number of join graph of star and path is obtained.

为了解决图的邻强边染色问题中一个图的色数算法问题，通过特别的方法来记图的染色过程，同时分4种情况讨论了星和路联图的邻强边染色问题，指出在染色过程中给定的4种情况的染色方法各不相同，并通过对图的着色得到了星和路联图的邻强边色数。

The optimal control law obtained is composed of feedforward and feedback optimal terms without time-delay in analytic forms and a compensation term with time-delay in a sequence limit form of adjoint vectors.

得到的最优控制律由解析的无时滞前馈－反馈控制部分和伴随向量序列极限形式的时滞补偿控制部分组成。

And an optimal operation strategy of any kind of products subject to spoilage at any time is obtained on the basis of the proposition of the model of distributed parameter control systems. Moreover, definite economic explanations to spatial adjoint function and control variables are presented.

通过建立可变质产品的最优经营管理的分布参数控制系统模型，得出了零售企业每个瞬间每种可变质产品的最优经营管理策略，并对空间伴随函数和控制变量给出了明确的经济学解释。

A novel direction of arrival and polarization estimation of electromagnetic vector sensors mounted on the airframe is proposed based on biquaternion. The signal processing model for EM-sensor mounted on the airframe is made by biquaternion and then the eigenvalue decomposition of spectral matrix is obtained by means of the EVD of its quaternion adjoint matrix. The memory requirement for data is reduced, and more accurate estimation result is gotten by deducing the stronger orthogonality constraint between the sin- gal and noise subspaces on the field of biquaternion. The performance of the new algorithm is confirmed through numerical examples.

针对机载电磁矢量传感器阵列DOA和极化参数估计问题，提出了一种基于复四元数估计方法，该算法利用四元数建立机载电磁矢量传感器阵列信号处理模型，然后利用四元数联合矩阵的特征分解得到阵列数据相关矩阵的特征分解，一方面使得计算过程中数据的贮存量大大减少，另一方面通过推导得到信号子空间和噪声子空间在四元数域上的正交性从而使DOA和极化参数佑计的精度更高，仿真证实了本算法的有效性。

Then, the relations between the general nonlinear systems and its adjoint system were discussed, from which the sufficient and necessity conditions for exact linearization of general nonlinear control systems were obtained.

近20年来，由于微分几何等数学工具的引入，非线性控制系统的理论取得了长足的进展［1］，其中包括仿射非线性系统的精确线性化［2～4］。

Then, the relations between the general nonlinear systems and its adjoint system were discussed, from which the sufficient and necessity conditions for exact linearization of general nonlinear control systems were obtained. The conclusions include the corresponding results of the affine nonlinear systems.

引入一类相关的仿射非线性系统，通过研究一般非线性系统与其伴随系统的关系，利用伴随系统的精确线性化结论，获得一般非线性系统精确线性化的充要条件，其结果包含了仿射非线性系统的已有结果。

In the second chapter, the problem of the optimal inputting rate control for a class of competitive population dynamics system with age-structure is discussed. By means of characteristic line, Gronwall Lemma, Bellman Lemma, adjoint system and so on, the Lipschitz continuity properties of the system in terms of the control variable is certificated, and the necessary condition of the optimal control is obtained.

第二章讨论了一类具有年龄结构的竞争种群系统最优输入率控制问题，综合应用特征线法，Gronwall引理，Bellman引理，共轭系统等知识，证明了系统解关于控制变量的Lipschitz连续性，给出了控制为最优的必要条件。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。