微分的

With the advancement of science and technology, some new theories and new ways emerged gradually, some of them merged with specific theoretical tools, this specific theoretical tools include mathematical morphology, fuzzy techniques, neural networks, wavelet and so on. Secondly, in this paper, it described and analyzed the segmentation method based on the edge in the domain of image segmentation in detail. It did experiments on several edge detection operators using MATLAB, it summarized the advantage and the shortcoming of traditional edge detection operators, and the operating environment. On the basis of the experimental analysis, it implemented an edge location more precise, more efficient operating speed edge extraction method——Template Vector. In this method, it optimized differential approximate calculation of first differential operators the paper mentioned. After experimented on this edge extraction method, contracted with the traditional methods, the edge outline is extracted more accurately and more exquisitely, furthermore, it retained the object outline furthest, and achieved more satisfied edge extraction result.

其次，对图像分割领域中常用的基于边缘的分割方法进行了详细的研究与分析，对各种边缘检测算子进行了MATLAB环境下的实验，分析总结了各种传统边缘检测算子的优缺点和适应环境，并针对传统边缘检测算子在处理显微图像时的缺陷，在实验分析的基础上研究并实现了一种边缘定位更加精确、运算速度更加快捷的边缘提取方法——模板向量算法，在该算法中，对文章提到的一阶微分算子中微分的近似计算作进一步优化，经过对该边缘提取方法进行实验，其结果与传统方法相比，轮廓提取更为精确细腻，且最大程度的保留了图像中物体(目标个体或者明显噪声点)的轮廓，得到了比较理想的边缘提取效果。

Family of Swiss mathematicians and scientists, includingJakob or Jacques (1654-1705), an important theorist of ordinary calculus and the calculus of variations.

伯努利：瑞士数学家和科学家家族，包括雅各或雅克（1654-1705年），是关于一般微积分和变分微分的重要理论家。

The main results, obtained in this dissertation, may be summarized as follows:1. In chapter 2, the differential property of the optimal value function with a non-compact set is studied. The expression of its lower-Hadamard directional derivative is obtained.

第2章研究了非紧致集上最优值函数的微分性质，首先给出了最优值函数的Hadamard下方向导数的表达式，其次在最优值函数的有效域为非空凸集的情况下刻画出了次微分的表达式。

The method can beused to solve the integro-differential equation included fractional integral orfractional derivative in a long history and the difficulty of storing all history data isovercome and the error can be controlled.Two numerical examples are presented.

利用该方法可对包含分数积分和微分的积分-微分方程进行较长时间的数值模拟，克服了存储全部历史数据的困难，并能对计算误差进行控制。

Direct difference is sensitive to noisy data, so a threshold limitation is given, which can not only filter the result from noisy data but also pick edge points up according men's desire. On the other hand, artificial intelligence is used for segmentation in reverse engineering. Because the essence of segmentation is clustering similar characteristics and self-organizing feature mapping is one function of neural network, SOFM network is used for segmentation in the thesis, coordinates and normal of data points is took as the characteristics vector.

第二种方法，基于双向角度微分的边点提取法，针对三维正交模型采用基于截面线的方式组织数据，此方法比基于曲率半径方法更简洁，不用进行曲面拟合，大大提高了计算速度；计算过程中由数据点的直接差分逼近微分，但直接差分对数据误差敏感，为此，本文提出了阈值过滤的方法，一方面过滤了数据误差在计算结果中引起的噪音，另一方面可以按照设计意图控制边点的提取；来决定是否提取光滑交接的边点。

Based on structuring a quotient space,consisting of pairs of convex compact sets,this paper discusses the uniqueness of quasidifferential of quasidifferentiable function.

本文在构造凸紧集对商空间的基础上，讨论了拟可微函数拟微分的唯一性，指出拟微分的表示可以不唯一。

By means of the concept of η-subdifferential, this paper employs a new method and constructs resolvent formula of η-subdifferential operators.

本文用一种新颖的方法，借助于η-次微分的概念，构造η-次微分算子的预解式来逼近问题的解。

Systems with hysteresis are nondifferentiable nonlinear systems. So they cannot be studied through control theories and methods used in differentiable nonlinear and linear systems.

具有回滞特性的系统是不可微分的非线性系统，所以不能采用可微分的非线性和线性系统的控制理论和方法来进行研究。

Secondly, the fractional order differentiation of rectangle signal, triangle signal and trapezia signal are carried out, meanwhile the analytical expressions of them are presented in this paper.

给出了一些常用周期信号分数阶微分的解析形式，同时也研究了周期序列的分数阶微分运算的数字实现。

It is also a further improvement to the Newton-PCG algorithms. Moreover, by applying the Newton-PCG method and automatic differentiation, one new inexact method of tangent hyperbolas is proposed.

进一步将自动微分应用于牛顿-PCG型算法，构造了新算法，并从理论上证明了使用自动微分的牛顿-PCG型算法有非常显著的进一步的改进。

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％。