函数的积分

In order to get the principle of cell distribution in buffer, the local rate function is obtained, which can be expressed in detail with the help of DuBoisReymond equation and conditional integral. This gives us the system's rate function.

为了能够分析缓存器中分组信息变化的规律，论文首先给出了主干系统的本地速率函数，利用变量积分的DuBois-Reymond方程，给出了本地速率函数所满足的微分方程，在条件积分的约束下求得本地速率函数表达式，由此求得系统的速率函数。

It is difficult to compute directly the coefficients from the integral formula, since the integral function in the formula of the ideal digital fractional differentiator is a high-order oscillating function.

从理想数字分数微分器系数计算公式的特点考虑，利用变量代换把积分函数中的振荡因子转换成积分上限，避免高阶振荡函数积分计算，给出了计算分数微分器系数的递推公式。

Secondly,the one-step and multistep methods of the precise integration algorithms arederived by means of the integration of functional matrix by parts and interpolation function,and some recursion schemes suitable for precise integration are obtained.

然后，以函数矩阵的分部积分法和插值函数为工具，推导出精细积分的单步法和多步法，给出了多种精细积分的递推格式。

Therefore, it is not every Newton indefinite integral that can carry on Riemann integral, and not every Riemann integral has Newton Indefinite integral.

牛顿所积分的函数都是连续的，可分为牛顿不定积分和牛顿定积分，而黎曼所积分的函数又是有界的。

This article compared the integrand of infinite integral and unbounded function integral by comparing the infinitesimal with the infinity, obtained the corresponding equivalence theorem of criterion of convergence of abnormal integral, and gave out the proof.

将无穷积分及无界函数积分的被积函数运用无穷小和无穷大比较的方法进行比较，得到了相应的反常积分敛散性极限审敛法的等价定理，并给予证明，从而可运用等价定理灵活的判断反常积分的敛散性。

The present method is applied to two-dimensional potential problems and the corresponding discrete equations are derived. Because the shape functions so-obtained possess the Kronecker delta property, the essential boundary conditions can be enforced as the FEM; furthermore, the Heaviside step function is used as the test function, there is no domain integral, and only a regular boundary integral is involved.

因为滑动Kriging插值方法构造的形函数满足Kronecker函数性质，所以本文建立的改进的无网格局部Petrov-Galerkin法可以像有限元法一样直接施加边界条件；由于采用Heaviside分段函数作为局部弱形式的权函数，因此在计算刚度矩阵时只涉及边界积分，而没有区域积分。

In the new method for two-dimensional problems the line integrals onboundary elements are converted into the evaluation of potentialfunctions at the ends of these elements.For three-dimensional cases,thesurface integrals on the usual boundary elements are transformed,through an application of Stokes'theorem,into line integrals on thebounding contours of these elements.

边界轮廓法是刚刚出现的一种新型的边界元法，该方法的核心是利用边界积分方程被积函数散度为零的特性，对二维问题，原积分方程中沿边界单元的线积分被化为单元两端点势函数之差计算，对三维问题，将边界单元上的面积分转变为沿单元轮廓的线积分，它是一种十分简便有效的边界元新技术。

It is found thatthe fractal dimension D=1.25 corresponds to the lowest criticalcoupling constant αc=1.9,D=1.73 corresponds to the highest criticalratio of dielectric constants ηc=0.163,and when D≤1.145 bipolaronscan not exist at any rate.In chap,4,we will propose a novelapproach to the calculation of the exciton ground-state energy for thestrong-coupling case.Different from all previous methods,the wavefunction of the phonon part is assumed to take a form related to thewave function of the relative motion.We obtain the exciton energy bysolving the derived integrodifferential equation rather than select ahydrogen-like form to minimize the energy expectation.

结果发现，分数维的维数D＝1.25对应最小的临界的电-声耦合常数(αo＝1.9)，D＝1.73对应最大的临界的介电常数比(ηc＝0.163)，当分数维的维数D≤1.145时，双极化子无论如何也不可能存在，在第四章中，我们将提出一种新颖的变分方法来计算强耦合的激子-声子系统的基态能，不同于以前所有的方法，我们取声子的波函数与相对运动波函数有关的形式，而不是假定一个固定的关于相对运动坐标r的函数形式，得到相对运动波函数所满足的非线性的微分积分方程，我们数值求解这个微分积分方程得到系统基态能，而不是选择一个类氢原子的波函数变分使得能量的期待值最小。

Since RKPM is a kind of Galerkin meshfree methods, in this thesis, penaltyfunction method is employed to enforce the essential boundary conditions,trapezoidal rule is used for the approximation of displacement field function, Gaussand Hammer quadratures are applied for the numerical integration of systemequation,self-adapting method is applied for confirming the support of the pointinterpolated.

针对 RKPM 是一种伽辽金型的无网格方法，本论文采用罚函数法引入位移边界条件，用梯形积分法则近似位移场函数，对系统方程进行积分时分别使用了 Gauss 积分和 Hammer 积分，采用自适应的方法确定计算点的定义域。

Conditions of integral chain can be closed.

基于函数S粗集和F粗积分，本文研究粗积分的动态特征，定义粗积分链和粗积分环的概念，给出上积分链，下积分链定理，粗积分链定理，以及积分链的存在性定理，讨论了积分链的可闭条件，得到积分环定理，粗积分环定理。

The medicinal plant resources of Gentianaceae in Sichuan Province.

四川省龙胆科药用植物资源。

"Some fortuneteller," scoffed the man, I'm the father of THREE children.

" "一些算命"，嘲笑他，"我的父亲有三个孩子。