本文进一步研究了函数项级数的逐项积分定理。
In this paper, the theorems of term-by-term integration have been studied further.
讨论具有某种特征映射的类似柯西积分定理的结论。
A discussion on some characterized mapping conclusions similar to Cauchy 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。
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.
早期的人工智能研究集中在了一些看起来很困难的智力活动上，如高水平国际象棋，或者积分定理的证明。
Early A.I. research concentrated on what seemed to be difficult intellectual tasks, such as playing grandmaster level chess, or proving theorems in integral calculus.
早期的人工智能研究集中在了一些看起来很困难的智力活动上，如高水平国际象棋，或者积分定理的证明。
I. research concentrated on what seemed to be difficult intellectual tasks, such as playing grandmaster level chess, or proving theorems in integral calculus.
为什么定理选择逆时针积分而不是顺时针呢？
Why does the theorem choose counterclockwise over clockwise?
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。
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.
微积分基本定理，不是曲线积分的，告诉我们，如果对函数的导数积分，就会得回原函数。
So, the fundamental theorem of calculus, not for line integrals, tells you if you integrate a derivative, then you get back the function.
这些都是反映了,线积分的微积分基本定理的特例。
So, these are special cases of what's called the fundamental theorem of calculus for line integrals.
讨论局部对称空间中具有平行平均曲率向量的子流形，得到其关于第二基本形式模长平方的积分不等式的相关定理。
This paper discusses submanifolds with parallel mean curvature vector in local symmetric Spaces and obtains integral invariants about the square of modulus-length.
本文就积分第一中值定理给出了一个简单的证明。
This paper gives a simple proof of the first mid -value theorem of Integral.
本文依据积分中值定理给出了适宜于实验计算的积分平均值的近似公式，并举例加以说明。
This paper gives some approximate formulas of the integral average value for experimental calculation on the basis of the integral mean law. Examples are given for explanation.
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。
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.
给出了积分中值定理的一个注记，证明了中值点的存在性与覆盖中值点的区间的存在性是相互对应的。
By increasing the condition of the integral mean value theorem, we prove that the existence of intermediate point and the existence of interval are corresponding to each other.
本文推证了一个积分展开定理。
本文研究了伪黎曼空间型中具有常平均曲率的类空子流形，得到了这类空子流形的一个积分不等式及刚性定理。
This paper discusses the space-like submanifolds with constant mean curvature in a pseudo-Riemannian space form, and obtain an integrate inequality and a rigidity theorem.
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 new proving of the mean value theorem of integral on surface is given, with some application in related cases presented.
本文用随机积分的控制收效定理直接推出了这一结果，从而大大简化了原证明。
In the present note we propose to deduce this result directly from the dominated convergence theorem of stochastic integrals, so our proof is much simpler than the original one.
讨论了第一类曲线积分中值定理“中间点”的渐近性质，得到了更具一般性的新结果。
This paper is devoted to studying the asymptotic behavior of the intermediate point in the mean value theorem for first form curve integrals. A general result is obtained.
给出了拉格朗日微分中值定理和第一积分中值定理中值点的渐进性的更一般性的结果及其简洁证明。
Gives more general results on the gradualness of the median point of Lagranges median theorem and first median theorem for integrals and its succinct proof.
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。
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.
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。
In this paper, a theorem which turns double integral into linear integral is given, and its application is discussed.
给出系统的时间积分等式，并由此等式导出类能量方程、类维里定理、一个积分变分原理和一个微分变分原理。
A power-like equation, a Virial-like theorem, an integral variational principle and a differential variational principle for the system are deduced by using the time-integral identity.
根据引力场的两个定理，导出了引力势的微分和积分形式。
Consequent differential form and integral form of gravitational potential are deduced from the two laws of gravitational field.
主要讨论了第二积分中值定理“中值点”的渐近性和渐近速度。
This paper discusses the asymptotic rate of "mean value point" in second mean value theorem for integrals.
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。
In deriving the integral equation, the convergence of series is modified by application of the plane Gauss Theorem.
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。
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。
In this article, the author has proved the theorem of "middle point" in the second integral mean value.
应用推荐