查询词典 integral

To simplify the detrusion of the double integral exchange formula,a simple method is derived after using the recevant knowledge of the methed of substitution in definite integral and double integral.

为简化二重积分换元公式的推导，利用定积分的换元法及二重积分的有关知识，提出了一种简便的推导方法。

The traditional virtual boundary integral expression is based on the extension of single layer potential, for the integral formulas related to single layer potential for parabolic problem, the numerical computation of the exponential integral function is unavoidable.

通常的虚边界积分公式是利用单层位势的延拓来建立虚边界元积分方程，但对带时间变量的单层位势，要涉及到指数积分函数的计算。

As a foundation, the definition of elementary integral transformation and the method to factorize an integral matrix with elementary integral transformation is proposed firstly. After that, the problem how to find identification vectors in Modular-S-invariants is solved.

文中首先给出初等整数变换的概念，之后借助初等整数变换对整数矩阵进行分解，并在此基础上给出从加模S-不变量中求取不可达见证向量的方法。

Then, the differential equations are solved by the Fourier expanding and Hankel integral transform method. Integral solutions of soil skeleton displacements and pore pressure as well as the total stresses for poroelastic media are obtained. Furthermore, a systematic study on Lamb's problems in transversely isotropic saturated half-space is performed. Integral solutions for surface radial, vertical and tangentical displacements are obtained both in the case of drained surface and in the case of undrained surface excited by vertical and tangentical harmonic resources respectively. Numerical results show the obvious difference between the model of isotropic saturated poroelastic media and that of transversely isotropic saturated poroelastic media.

其次，基于Biot波动理论，在圆柱坐标系下求解了横观各向同性饱和土的Biot波动方程：通过引入位移函数，在圆柱坐标系下将横观各向同性饱和土的Biot波动方程转化为两个解耦的6阶和2阶控制方程，然后根据方位角的Fourier展开和径向Hankel变换，求解波动方程，得到以土骨架位移和孔隙水压力为基本未知量的积分形式一般解，并用一般解给出了饱和土总应力分量的表达式；再以基本解为基础，系统地研究了横观各向同性饱和半空间体的Lamb问题，考虑表面排水或不排水两种情况后，首次得到横观各向同性饱和半空间体在表面竖向和水平谐振力作用的下径向、竖向和周向位移的解析解。

By integral transformation of basic equations, the stress and displacement expressions with unknown coefficients of elastic and viscoelastic materials were obtained in Laplace domain respectively, and introducing dislocation density functions, the singular integral equations were got according to the boundary conditions and interface connection conditions, further adopting Gauss integration and Gauss-Jacobi integration formula, the problem was reduced to algebraic equations, then it can be solved with the method of collocation dots in Laplace domain. Finally, the time response of dynamic stress intensity factor was calculated with the inverse Laplace integral transformation.

采用积分变换方法，得到Laplace域内弹性和粘弹性材料的应力和位移的含未知系数的表达式；引入位错密度函数，并通过边界条件和界面连接条件，导出反映裂纹尖端奇异性的奇异积分方程组，采用Gauss积分，并运用Gauss-Jacobi求积公式化奇异积分方程组为代数方程组，利用配点法进行求解；最后经过Laplace逆变换，求得动态应力强度因子的时间响应。

The subsection integral is used to get a simple function at first in the numerical calculation, and boundary integral is realized by gauss integral on each panel and line, then the complexity and isstability as a result of the high frequency surge function can be avoided.

数值计算中，首先采用分部积分对被积函数进行简化处理，然后采用高斯积分实现面元和线元上的积分，避免了被积函数为高频振荡函数所带来的数值计算的复杂性和不确定性。

Infinite integral is a type of improper integral in calculi, and it is also a difficult point in integral.

无穷限积分是微积分学中广义积分的一种类型，是积分知识的一个难点内容。

Infinite integral is a type of improper integral in calculi,and it is also a difficult point in integral.

无穷限积分是指函数在无限区间上的积分，例如+∫∞afdx型，它属于广义积分的一种。

Meanwhile, having a good knowledge of the concept of the indefinite integral and selecting and using the indefinite integral method in the right way, is the key to put the indefinite integral calculates into practice.

不少学生对不定积分的计算总是掌握不好，究其原因，一是对不定积分的基本概念不清楚，二是对如何正确使用不定积分方法不清楚。1不定积分在计算中常用的概念1原函数的定义：若F′=f，则称F为f的一个原函数。

"Economic Mathematics" on the function of the limit, derivative and differential, derivative applications, indefinite integral, integral, integral and infinite binary Series and the first order differential equations, and so forth.

经济数学》介绍了函数、极限、导数与微分、导数的应用、不定积分、定积分、二元积分和无穷级数与一阶微分方程等内容。

I am accused of being overreligious," she said in her quiet, frank manner,"but that does not prevent me thinking the children very cruel who obstinately commit such suicide.""

客人们在卡罗利娜·埃凯家里，举止就文雅一些，因为卡罗利娜的母亲治家很严厉。

Designed by French fashion house Herm è s, this elegant uniform was manufactured in our home, Hong Kong, and was the first without a hat.

由著名品牌 Herm è s 设计，这件高贵的制服是香港本土制造，是我们第一套不配帽子的制服。