极小

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。

A sufficient and necessary condition of an isothermal surface being a minimal surface is obtained.

除平面外没有其它二次多项式极小曲面，Enneper曲面是目前微分几何文献中唯一出现的三次参数多项式极小曲面，还没有出现高次多项式极小曲面的例子。

The equivalent definition of the minimal strong component is given, and it discusses the relation between the standard form and the minimal strong component in the paper. Consequently, the theory is proved that the periodicity of a fuzzy matrix is the least common multiple of periodicity of its minimal strong component.

给出了极小强支的等价定义，讨论了模糊矩阵的标准型与极小强支关系，从而得到了模糊矩阵周期是极小强支周期的最小公倍数的定理。

And then, this paper presents an algorithm of computing the left inverse or right inverse for these special rectangle matrices. In thenormal algorithms for solving these problems, we need O(m2n) multiplications ordivisions. The algorithms in this paper only need O + O(n2) multiplications ordivisions. The paper is built as follows.

常规的计算m×n阶不相容线性方程组的极小范数最小二乘解的算法所需计算量为O(m~2n)，而本文根据特殊矩阵的特殊结构，通过两种不同的构造方式给出了两类不同的计算极小范数最小二乘解的快速算法，并给出了求特殊矩阵的左逆及右逆的快速算法，它们的计算量均为O+O(n~2)。

The results showed that there were three minimum values in the second derivative spectrums of normal person, in contrast there were four minimum values in most diabetic second derivative spectrums, the diabetic urine had one minimum value more than normal urine during the range from 550 nm to 570 nm.

发现健康人的二阶导数光谱都有三个极小值，与之形成对比的是绝大多数糖尿病患者的二阶导数光谱却有四个极小值，糖尿病患者的尿样在550 nm～570 nm区间范围内比健康人多出一个极小值。

Considering that the NURBS has become a standard in CAD/CAGD, we shall investigate the approximation to the solutions of the minimal surface equation with the tensor Bezier surface and B-spline surface.

首先我们讨论极小曲面的分片线性的逼近，由于NURBS已经成为形状描述的唯一工业标准，而且极小曲面本身至少应该是二阶光滑的，因此我们讨论了极小曲面方程的Bezier和B样条逼近。

In the studying of image segmentation, six crucial technologies havebeen developed successfully. 1 In one dimension histogram of original DRimage of luggage, there remain maximum-value wave crest havingapproximately stationary position, and the first minimum to the left of thewave crest performs excellently to be used to get rid of background of DRimage. 2 Open operation, one type of math morphology, is the right idea toerase luggage disturbance in DR image and at the same time, can be retaininteresting region appropriately. 3 After open operation, there are only a few minimums on image histogram, one of which can be to segment image furtherand achieves satisfying result. 4 Method of histogram analyzing and that oferosion performs well in the re-segmentation of conglutinative region in DRimage. 5 Method of image distance switch can ensure Luggage CT sectionautomatically obtained to have rich suspicious region information. 6 Todecompose structure element of math morphology is a way to save a great dealrunning time for automatically discerning interesting regions algorithm,apparently improving implementation efficiency.

在对图像可疑区域分割研究中，主要开发成功以下几项关键技术：1发现原始箱包DR图像的一维直方图中，均具有位置相对稳定的最大值波峰，以波峰左边第一个极小值为分割阈值，去除DR图像背景，效果非常好。2运用数学形态学中的开运算能够非常有效地去除箱子的干扰，同时能够比较好地保留可疑区域。3发现开运算后的DR图像直方图只有若干个极小值点的特点，其中用最大值波峰左边的第二个极小值点进一步分割DR图像，能够更有效地提取箱包中的可疑区域。4运用直方图分析法和腐蚀法，对粘连区域实行再分割，效果较好。5运用距离变换法，能确保自动设定的箱包CT截面包含丰富的可疑区域信息。6运用形态学结构元素分解技术，大幅度减少可疑区域的自动判别算法运行时间，提高算法软件执行效率。

In the last of this dissertation, we give necessary and sufficient conditions for the existence of and the expressions of perpositive semidefinite solutions and bipositive semidefinite solutions to some systems of quaternion matrix equations.

给出了某些四元数矩阵方程组有广亚半正定解，双半正定解的充要条件及其表达公式；研究了矩阵方程组的最小二乘解，极小范数的最小二乘解，在某些约束条件下的最小二乘解和极小范数的最小二乘解，给出了其有这些解的充要条件及其表达公式。

E. thickness of the copper wire wall, length of the single conductor wire, height of the solenoid, the exciting current and the current density, the working temperature of the conductor, time of exciting and demagnetizing, the cooling water pressure and flux density, etc..

所建立的数学模型包含3个目标函数（即能耗极小化目标函数、铜耗极小化目标函数和纯铁用量极小化目标函数）、7个设计变量（即铜管规格参数a、b、t，线圈匝数N〓、N〓，铁铠磁通密度B〓和冷却水压p）和8类14个约束条件（即铜管壁厚、单饼导线长度、螺线管高度、激磁电流与电流密度、导体工作温度、激退磁时间，冷却水压和铁铠磁通密度等约束条件）。

There are mainly four innovations in this dissertation. It's the first time that the minimal operator was introduced into martingale theory, and a series of -type inequalities for the minimal operator on martingales and supermartingales are established.

特别地，在证明中新定义了一个算子—几何极小算子，最终利用几何极大算子和极小算子序列的收敛关系以及前面所得的有关极小算子的结果使得本章中有关几何极大算子的结论证明显得简洁明了。

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