A discussion on some characterized mapping conclusions similar to Cauchy integral theorem.
讨论具有某种特征映射的类似柯西积分定理的结论。
Based on the stationary condition of energy functional, we set up the integral theorem along the boundary of arbitrary element and get the energy release quantity with the integral theorem.
根据裂纹扩展时能量泛函的驻值条件，建立了任意元素的围道积分定理。
And so that's why you have this line integral that makes perfect sense, but you can't apply Green's theorem to it.
这就是为什么，这个线积分，有着完美的定义，但却不能对它使用格林公式的原因。
Or, if you really don't like that line integral, you could close the path by adding some other line integral to it, and then compute using Green's theorem.
如果不喜欢计算线积分，可以通过增加一条线积分让曲线封闭起来，然后就可以用格林公式来计算了。
To compute things, Green's theorem, let's just compute, well, let us forget, sorry, find the value of a line integral along the closed curve by reducing it to double integral.
用格林公式计算…，只是计算…，让我们忘记…，应该是，算沿闭曲线的线积分值，可以通过二重积分来算。
So, using Green's theorem, the way we'll do it is I will, instead, compute a double integral.
那么，使用格林公式，我们去计算二重积分。
There is a similar thing with the divergence theorem, of course, with flux and double integral of div f, you can apply exactly the same argument.
有一个和散度定理很像的东西，当然，对于通量和div,f的二重积分，都可以使用类似的理论。
Then, yes, we can apply Green's theorem and it will tell us that it's equal to the double integral in here of curl F dA, 0 which will be zero because this is zero.
那就可以使用格林公式了，并且我们知道,它就等于的二重积分，结果为0，因为旋度F等于。
In this paper we obtain several theorem of the definite integral of triangle composite function.
本文给出了计算三角复合函数的定积分的若干方法。
This paper gives a simple proof of the first mid -value theorem of Integral.
本文就积分第一中值定理给出了一个简单的证明。
In deriving the integral equation, the convergence of series is modified by application of the plane Gauss Theorem.
在建立积分方程时，运用平面高斯定理改善了级数的收敛性。
As to the limit question of integral included in sequence terms, the paper summarizes two adequate conditions for integral limit from the theorem and provides some examples.
对于数列通项含有积分的极限问题，文章以定理形式总结概括出两类数列极限存在的充分条件，并附以实例。
This paper gives the control convergent theorem of integral for fuzzy random functions on basis fuzzy functions and fuzzy integral.
在可测模糊随机函数及模糊值函数积分的基础上，研究了模糊值函数的有界控制收敛定理。
In this paper, by estimates of spectral of an integral operator, the authors give a theorem on the existence of solutions for first order differential difference equations with boundary condition.
摘要通过对积分算子谱的估计，作者给出了一阶线性微分差分方程在边值条件下解的存在唯一性定理。
Then the eigenvalue problem of free vibration of annular sector plates is transformed into the eigenvalue problem of integral equation by using superposition theorem.
然后由叠加原理将环扇形板的自由振动问题转化为积分方程特征值问题；
In this paper the theorem in which a curve integral is independent of the integral path on a single connected region is generalized.
本文把在单连通区域上成立的曲线积分与路线无关性定理推广到复连通区域。
The integral expressions for scattered fields including the second-order scattering terms are given based on the reciprocity theorem.
在互易原理的基础上，得到了计入相邻目标二次散射的散射场的积分表达式。
Based on the integral inequality and other quality proved, the paper discusses the conclusion of the mid-value in theorem of integration mean which is got in open interval.
在证明了定积分不等式等性质的基础上，给出并证明了积分中值定理的中值在开区间内取得的结论。
Especially, we give a calculation method for higher order singular integral by equation (3.1) when the wavelet function is unknown. At last, we create a convergence theorem.
特别是当小波函数未知时，借助于方程(3.1)，对高阶奇异积分作数值计算，建立了收敛性定理。
This article explores the four ways for solving integral inequality with the nature of definite integral, mean value theorem of differentials, Schwarz inequality and double integral.
本文利用定积分的性质、微分中值定理、施瓦兹不等式、二重积分等内容，研究了积分不等式的四种证法。
In this article, the author has proved the theorem of "middle point" in the second integral mean value.
给出并证明了关于积分第二中值定理“中间点”的渐近性定理。
Integral that upper limit of integral is variable is a important theory, results of operation is function forma after all. Research this kind of function, get a few theorem.
变上限积分是积分学的一个重要理论，其运算结果仍以函数的形式体现。研究这类函数，得出几个颇有理论意义的定理。
In this paper, a new proving of the mean value theorem of integral on surface is given, with some application in related cases presented.
对曲面积分中值定理，给出了一个新的证明，并举出相关例子加以应用。
In this paper, a theorem which turns double integral into linear integral is given, and its application is discussed.
给出把一类二重积分化为曲线积分的一个定理，讨论定理的一些应用。
Finally, the condition and result of integral mean-value theorem are also improved combined with the Lagrange mean value theorem of differentials.
最后，结合拉格朗日微分中值定理改进了积分中值定理的条件和结论。
Two kinds of generalizations of the first mean value theorem of integral for integrable functions with different properties are established in the paper, the results extend the previous conclusions.
本文建立了两类可积函数的积分第一中值定理的推广形式，推广了已有结论。
In this paper, by estimates of spectral of an integral operator, the authors give a theorem on the existence of solutions for first order differential difference equations with boundary condition.
通过对积分算子谱的估计，作者给出了一阶线性微分差分方程在边值条件下解的存在唯一性定理。
Applying fixed points theorem, we give the sufficient conditions of the existence of positive ergodic solutions for a class of infinite nonlinear integral equations.
利用不动点理论，给出了一类非线性积分方程正的遍历解存在的充分条件。
This paper discusses the asymptotic property of the Mid-point of the mean theorem for first form curvilinear integral.
文章研究了第一型曲线积分中值定理“中间点”的渐近性，获得了一些重要结果，得出它也是定积分中值定理相应结果的推广。
This paper discusses the asymptotic property of the Mid-point of the mean theorem for first form curvilinear integral.
文章研究了第一型曲线积分中值定理“中间点”的渐近性，获得了一些重要结果，得出它也是定积分中值定理相应结果的推广。
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