积分曲线

At last,for the double integral which the boundary curve of its domain of integration is denoted by the panameter equation, we will supply a directed method which do not eliminate the parameter.

对积分区域的边界曲线由参数方程表示的二重积分，我们也将给出两种不经消参数而直接计算的方法。

It gives a relationship between a surface integral over an oriented surface and a line integral along a simple closed curve .

它建立了有向曲面上的曲面积分与它的边界曲线积分的关系。

This paper studies the curvilinear integral ∮ L[xn-1yn-1]/[x2n+k2y2n]where L is a sectioned smooth and no multiple points closed curve, n is some natural number, k is some positive number.

本文研究曲线积分x~(n-1y~(n-1)/x~(2n+k~2y~(2n)，其中L是公段光滑无重点的闭曲线，n为某一自然数，k为某一正数。首先利用极坐标变换将曲线积分化简，然后对n、L不同情况给出相应结果

For this purposewe need to develop some new methods and new techniques.For example we studythe properties of the"centroid curve"and the"auxiliary curve",and identify twoplanes in which these two curves are defined respectively;we also use the relationshipbetween the"centroid curve"and its"dual curve".

为此需要发展一些新技巧和新方法，例如研究由Abel积分之比定义的"质心曲线"和"辅助曲线"的几何性质，并把这两条在不同平面上定义的曲线放在同一个坐标系中考虑，或把"质心曲线"与其"对偶曲线"联系起来考虑。

In this article we induce and study the physical background ,definition, quality ,and calculating method of the curve and surface integral of the first kind ,and at the base of these , calculate formula and providence was proposed in the special coordinate transformation.

摘要本文归纳研究了第一型曲线积分与曲面积分的物理背景，定义，性质及计算方法，并在此基础上给出了它们在特殊坐标变换下的计算公式及证明。

Under some conditions,the effective method in the second kind of line integrals and the differential equation is derived by using the improvising differential method of indefinite integral.

给出了在一定的条件下，利用不定积分的凑微分法得到了第2类曲线积分及微分方程的一些较为方便的解法

The maincontents of this thesis include:Firstly,by using inherent relationship between region integral and curve integral,designing the image transform operator,a novel snake model using both boundary andregion information was proposed,which more directly integrated the prior knowledgeincluding region information with the traditional deformable model,so that the abilityabout evolving contour curve was improved.

本论文将以严密的数学理论、可靠的物理原理和实际的应用背景为出发点，研究这一图像处理和分析的基本问题，并相应开展了以下几个方面的工作：首先，本论文利用区域积分与曲线积分之间转化的内在联系，通过设计相应的图像变换算子，提出了一种基于边缘与区域信息的图像可变形轮廓提取模型。

Ifandare continuous functions andis a smooth curve C which runs from a to b asvaries, then the corresponding line integral with respect to coordinate variables or line integral of the second type is expressed as follow

定义 设和是连续函数，是一光滑曲线，从a变到b，则对应的关于坐标的曲线积分或第二类曲线积分为

On each sub-interval, the quartic Bézier curve segment has one freedom degree that is used to adjust the shape of the segment.

zier曲线的形状。自由度由极小化样条曲线和辅助曲线的一阶导矢差的平方的积分确定。

For example, we study the properties of the"centroid curve" and the"auxiliary curve", and identify two planes in which these two curves are defined respectively; we also use the idea of homotopy method to prove a fact that the orbit of a differential system has no triple contact point with the line we considered. Another key technique, which we use several times, is deformation argument.

例如研究由Abel积分之比定义的"质心曲线"和"辅助曲线"的几何性质，并把这两条在不同平面上定义的曲线放在同一坐标系中考虑；利用拓扑中同伦的思想来证明微分系统的轨线不可能与某条直线三重相切；利用几何方法与分析计算相结合证明了某一曲线是正则的；以及连续变动参数的技巧。

Plunder melds and run with this jewel!

掠夺melds和运行与此宝石！

My dream is to be a crazy growing tree and extend at the edge between the city and the forest.

此刻，也许正是在通往天国的路上，我体验着这白色的晕旋。