函数的积分

In order to simplify the numerical computation, Ambrosio and Tortorelli's Γ-convergence approximation is also employed to substitute irregular parts of MS functionals with the auxiliary smooth function.

采用了Ambrosio和Tortorelli提出的Γ-收敛逼近方法，将MS函式对边界积分转化为一类合适的辅助光滑函数的区域积分。

In this paper,a proof is made of the equivalence in three definitions of the integral of bounded function in finite set measure.

关于Lebesgue积分，文献有不同的定义，本文给出了测度有限集上有界函数 Lebesgue积分三种不同定义的等价性的一种证明。

By discussing the position hypothesis of fractional-dimension derivative about general function and the formula form the hypothesis of fractional-dimension derivative about power function, the concrete equation formulas of fractional-dimension derivative, differential and integral are described distinctly further, and the difference between the fractional-dimension derivative and the fractional-order derivative are given too. Subsequently, the concrete forms of measure calculation equations of self-similar fractal obtaining by based on the definition of form in fractional-dimension calculus about general fractal measure are discussed again, and the differences with Hausdorff measure method or the covering method at present are given. By applying the measure calculation equations, the measure of self-similar fractals which include middle-third Cantor set, Koch curve, Sierpinski gasket and orthogonal cross star are calculated and analyzed.

通过讨论一般函数的分维导数的位置假设及幂函数的分维导数的形式假设，进一步明晰了幂函数的分维导数、分维微分及分维积分的具体方程形式，给出分维导数与分数阶导数的区别，随后讨论了基于一般分形测度的分维微积分形式定义导出的自相似分形的测度计算方程具体形式，给出了其与目前 Hausdorff 测度方法的区别，并对包括三分 Cantor 集合、 Koch 曲线、 Sierpinski 垫片及正交十字星形等自相似分形在内的测度进行了计算分析。

Say from the angle of mathematics, This software mainly plays to show the integral calculus of Bernhard Riema , together two heavy integral calculuses of a function.

从数学的角度说，本软件主要将演示黎曼积分、齐次函数的二重积分。

Based on the special matrix operations including Kronecker product, Hadamard product and vectorization, the integration of monomial integrand on simplex domain is expressed in matrix form and a recursive formula for the simplex integration is presented.

基于Kronecker积、Hadamard积和拉直等矩阵特殊运算，将单项式函数在单纯形上的积分表示为矩阵形式，提出了单纯形积分的递推公式。

Based on second-order Laplace equation and boundary condition, obtains the integral equation after Green transformation.

基于二维Laplace方程和边界条件，经过Green转换得到以势函数及势函数法向导数为未知量的积分方程。

Aiming at the engineering application of the two-layer fuzzy integration, we established the concepts of "two-layer measurable function on domain" and "two-layer measurable function for the monotone class".

针对二重模糊积分工程实用化，建立了备域上二重可测函数、单调类上二重可测函数的概念。

Around the finite solution problem of fuzzy differential equation, the fuzzy structure element method is put forward about the calculation of fuzzy analysis, and this method is applied to systematically study many problems such as formulation of fuzzy-valued function, difference of fuzzy-valued function, integration of fuzzy-valued function under the Riemann meaning, and the solution structure of fuzzy differential equation etc..

围绕模糊微分方程定解问题，提出了模糊分析计算的模糊结构元方法，并利用模糊结构元的方法对模糊值函数的表述问题、模糊值函数的微分、黎曼意义下的模糊值函数积分以及模糊微分方程的解的结构等问题，进行了深入系统的研究。

The key matter to raise accuracy of transient stability analysis by TEF method is to properly deal with the critical energy point and the critical disturbed trajactoryIn addition, the reason why the critical energy point docs not coincide with the relevant unstable equilibrium point is given.

时至今日，有必要也更有条件再度审视暂态能量函数的内涵与机制。现行的相对于故障后稳定平衡点的暂态能量函数导致的积分路径的虚构在动力学意义上是费解的。那么暂态能量函数应

In NWFM,to solve self-consistently the set of DFT Kohn-Sham equations,nuclear weight function is employed for numerical solution of multicenter integra-tion,which decomposes the problem of three dimensional integration to a sum ofone-center,atomic-like integrations.

首先介绍如何利用线性组合的原子轨道方法求解密度泛函理论中的K-S方程；接着详细地说明了核权重函数的概念，并列出了两种常用的核权重函数形式，同时阐述了如何利用核权重函数求解包含多中心积分的矩阵元以及复杂的三维泊松方程以获得电子间库仑势的方法；然后给出了求解矩阵元、有效势以及体系总能的具体数值计算公式。

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。