查询词典 harmonic integrals

Area coordinates and general Duffycoordinates are employed to transform the singular integrals of the Time-Domain Electric Field Integral Equation into non-singular integrals, which can be accurately and efficiently evaluated by dividing the transformed domain of integration into sub-domains.

摘要该文首先利用参数坐标和广义Duffy坐标变换将时域电场积分方程的奇异性积分转换成非奇异性积分，然后根据时间基函数的特点将该积分转换成可以快速精确计算的分区域积分。

The nonsingular integrals are popularly calculated by the Gauss numerical integral, and they are low in precision when the source points approach the element, and the singular integrals are complex.

非奇异积分一般采用数值积分，当配置点接近积分单元时，计算精度较低，奇异积分的计算也很复杂。

A method for integrating infinite integrals that occur in solving the fields of source coil and equivalent coils is presented. Subtraction of asymptotic terms is proposed to speed up the truncation process of an infinite integration interval, which greatly improves the infinite integrals.

给出了一种简单有效的数值积分方法计算激励线圈和等效线圈解析解中遇到的无穷积分，提出了一种加速无穷积分收敛的有效方法，显著提高了磁场及涡流场的计算效率。

A method of integrating infinite integrals which occur in axisymmetrical field in eddy current testing is presented. Subtraction of asymptotic terms is proposed to speed up the truncation process of an infinite integration interval, which greatly improves the integration of infinite integrals.

本文对涡流检测中解析求解轴对称场时遇到的无穷积分给出一种简单有效的数值积分方法，提出一种改进积分收敛性的方法，加速了无穷积分的截断，显著提高了轴对称场的计算效率。

Limits, Continuity, Derivatives, and Integration of Single Variable, Integration Techniques, Applications of Derivatives and Integrals, Infinite Sequences and Series, Multivariable Function and Their Derivative, Multiple Integrals, Integration in Vector Fields.

课程内容：单变数函数之极限、连续、微分、积分，积分技巧，微分与积分的应用，无穷数列与级数，多变数函数之偏微分、可微性，多重积分，极值问题，向量场积分。

The asymptote behavior of intermediate point in the Mean Value Theorem for integrals ;2. Based on numerical integrals , the model parameters are estimated from the differential equation without iterations, the method is very effective in overcoming large amounts of measurement noise in the output.

提出一种简单但鲁棒性强的传感器动态建模方法，该方法基于数值积分思想，能有效克服测量噪声，无需迭代即可直接从微分方程辨识出模型参数，所建模型阶次较低、准确度较高，且较易实现递推算法，为传感器改善动态特性、实现动态补偿提供一种有效方法。

Multiple integrals generalizing the iterated kernels of integral operators are expressed as single integrals in the case of a special representation of the kernel.

下面是我自己翻译的第一段和第二段的部分，翻译不行的话，顺便帮忙修饰下，先谢谢啦上面麻烦大家翻译的这几段都是关于数学方面的的

Numerical integration of ordinary integrals and line integrals.

一般的积分以及线积分的数值积分。

In accord with the characteristics of singular integrals in boundary element method for solving problems of thick plates on two parameter foundation,all formulas for calculating singular integrals are set up by selecting the displacements and stresses which satisfy the governing differential equations in this paper,on the principle of virtual energy.

根据双参数地基上厚板弯曲问题边界单元法中所遇奇异积分的特点，选取满足该问题微分控制方程的位移及内力场，建立了全部奇异积分的计算公式，有效地解决了边界元法在该问题应用中高阶奇异积分的计算问题

In the past, there exists difficulty for calculating nearly singular integrals arising from boundary element analysis of the problems of thin body. However, by now, the difficulty of nearly singular integrals has been resolved by analytical integral algorithm, which has been put into uses in analyzing the conventional structures and thin body structures in the potential problems.

过去边界元法求解薄体结构存在着几乎奇异积分的困难，目前几乎奇异积分问题已得到成功解决，解析积分算法也已成功应用于分析二维位势问题常规结构和薄体结构。

I hope that this success is just the first in a long series.

我希望这只是成功的开始。

Three dimensional stresses on the interface of tire and soil, tire deflection and soil sinkage are measured.

测试轮胎——沙土界面上的三向应力、轮胎变形和沙土沉陷；建立考虑剪切应力对沙土承载特性产生影响的车轮牵引性能预测模型；分析车轮作用下土壤的纵向稳定性。