被积函数

在用积分方程和矩量法（MM）或快速多极子法（FMM）分析三维矢量散射时，都要对有奇异性的被积函数进行积分。

When three dimensional vector scattering is analyzed by integral equation and the moment method ( MM ) or the fast multipole method ( FMM ), the singular integrand will he done .

证明面力边界积分方程被积函数的散度等于零，应用Stokes公式，对平面线弹性问题，将面力边界积分的求解转化为边界点的位移势函数的点值计算。

Based on testifying the integrand divergence free property of the traction boundary integral equation and Stokes ' theorem , the computation of traction boundary integral equation can be transformed into the evaluation of the displacement potential function on the boundary points .

为了获得被积函数的0（1／r）奇异积分高精度的解，采用坐标转化的方法，消除被积函数中的弱奇异积分。

In order to calculating the weak singular integral , the coordinate transform method is used .

本文给出了一类被积函数为正值的无穷积分收敛的条件下，当X→∞时，f（X）→0的充分条件。

This paper gives an account of the full condition of f ( X )→ 0 when X →∞ underthe condition of infinite integral convergence of a kind of positive-valued inte-grands .

在充分分析被积函数特点的前提下，采用改进的高斯方法直接计算Bessel函数的无穷域积分代替传统的傅立叶&汉克尔变换方法。

Improved Gauss numerical integral method is used to calculate the infinite integration of Bessel function instead of traditional Fourier-Henkel transform method .

在被积函数具有分段连续三阶导数的条件下给出一个新的Simpson不等式，其误差估计是最佳的。

A new Simpson inequality with best estimation of error was given under the condition that the integrand has piecewise continuous third derivative .

剩下的部分是关于标量Green函数与场强值或与它们的一阶导数值乘积的面积分，这样积分方程的被积函数高阶奇异性被降到一阶，有利于计算机的程序实现。

The residual parts are surface integrations whose integrands are the products of the scalar Green 's function and fields or their derivatives . The high order singularity of integrands in the integral equation is reduced to one order , making for program implementation .

本文讨论了Lebesgue积分中被积函数为零函数的条件，并给出了较弱的条件。

In this paper the conditions for a integrand in lebesgue integral to become a zero function are discussed and weaker conditions are given .

下面是第二步，在被积函数中，当然需要把，用u，v来替换，目标是把被积函数化为，只关于u和v的函数。

The second thing to know is x y you need to of course substitute any x and y 's in the integrand to convert them to u 's and v 's so that you have a valid integrand involving only u and v.

并据此基本解得到了圆柱壳受集中法向载荷、集中温度载荷作用下的奇异解，这些积分形式的解的被积函数具有第二种Hankel函数和指数函数乘积的形式，容易获得数值结果。

Numerical results for the singular solutions with integrands expressed in terms of the product of the second Hankel function and the exponential function agree well with FEM results .

在求解过程中，利用成熟的Delaunay三角形剖分技术，采用FEM三节点三角形单元的形函数作为权函数，可以减少域积分中被积函数的阶次，提高了计算效率。

In the implementation , based on the well established Delaunay triangulation , the FEM shape functions of three nodes triangular are taken as test functions , which reduce the order of integrands involved in domain integrals and improves the computational efficiency of the method .

本文分析了Tada等人合编的裂纹应力分析手册中，通过积分集中载荷的Westsrgaard应力函数得到分布载荷的Westergaard应力函数的方法，指出对被积函数必须作谨慎分析。

This paper analyses the method to obtain Westergaard stress function of any distributed load by integrating the Westergaard stress function of concentration load in " The stress Analysis of Cracks Handbook " by Tada and others and shows that the function integrated must be discreetly analysed .

不定积分的被积函数线性组合化及降幂的积分原则

An Indefinite Integral Principle of Making Linear Combination and Reducing Power of Integrand

这种方法在计算劲度矩阵时，被积函数大为简化，因而具有实用意义。

The method remarkably simplifies the integrand for the stiffness matrix , and therefore has practical significance .

收敛无穷限反常积分被积函数在无穷远处的极限

The Limit of the Integrand of Convergent Abnormal Integral in the Infinite Range of Integration at Infinity

实际计算步长的确定由计算精度的需要和被积函数的性质确定。

The calculation step is established by the demanded precision and the quality of the integral function .

被积函数的第一项表示噪声对误差功率的影响。

The first term of the integrand represents the contribution to the error power due to noise .

从被积函数的性态，判别正函数广义积分的敛散性。

From the characteristics of integrated function , broad integral 's convergence and scatter of positive function is discriminated .

矢量的面积分方程因其被积函数具有高阶奇异性，不能直接应用于数值计算。

The vector surface integral equation can 't be applied to numerical computation directly because its integrands possess the high order singularity .

边界型求积公式正是仅仅利用被积函数在区域边界上的数值构造的公式。

The boundary type cubature is quite the type of formulae that only use numerical values on the boundary of the domain .

采用将圆电流磁矢势表达式中一部分展成级数，使被积函数变成可积分的函数。

A part of results on magnetic vector potential of circular loop are expanded , so the integral function is transformed to integrable series .

讨论了被积函数或积分区域可以用二次型来表示的重积分的计算问题，通过引入进非退化线性变换，简化了这类重积分的计算，得出了计算公式。

By introducing the non-degenerate linear transformation , the calculation procedure of this type of multi-integration is simplified and the calculation formula is obtained .

本文论述了无穷积分收敛时，被积函数当自变量趋于无穷大时的极限何时为零的问题。

During the process of infinite integral converging , when does the limit of integrand become zero while the independent variable tends to be infinity .

确定卷积积分的积分限和在相应区间上的被积函数是计算卷积积分的两个难点。

There are two difficult points in convolution integral : how to determine the limit of the integral , and the integrands on the convolution integral .

为了有限元列式的保辛，变分原理被积函数可导向对于对偶变量为对称的形式。

In order to maintain the symplectic conservation conditions of FEM formulation , the integrand in the variational principle is rewritten in symmetrical form for duality variables .

灵活应用凑微分与分部积分法解被积函数为三个因子连乘形式的不定积分。

Flexible apply " gather together differential " and " divide part integral " method to solve the indefinite integral whose integrable function is the three factor multiple formative .

从不定积分的线性运算性质出发，给出了计算不定积分的被积函数线性组合化、降幂的积分原则，并结合实例分析了这一原则在不定积分计算中的指导作用。

Based on the quality of linear operation about indefinite integral , the article puts forward an indefinite integral principle of making linear combination and reducing power of integrand .

积分式中的被积函数包含一噪声强度垂直指向性因子，海洋介质分层条件通过该指向性因子影响噪声场的空间相干。

The integrand includes a multiplying factor of the vertical directivity of the noise intensity , and the layered ocean environment affects the spatial coherences via this directivity factor .

指出三角函数有理式不定积分中一个值得商榷的地方，对计算结果给出一种补充方法，使得不定积分为被积函数在连续的所有区间上的不定积分。

A new view is put forward about the trigonometrical Function Rational Formula Indefinite Integral , which is , how to make the indefinite integral belong to all the continual periods .

对弦向积分的被积函数作多项式分段逼近，可使核函数的表达式成为封闭形式的有限和，导致性态很好的系数矩阵。

A segmented polynomial approximation for the integrand of the chordwise integral is deduced to evaluate the kernal function in a closed form finite-sum manner , resulting a well-behaved coefficient matrix .