查询词典 kernel of integral equation

A spectral-domain full-wave model for the coaxial probe is established and the Galerkin's moment method is used to solve the integral equation, with efforts on numerical treatments of the singular infinite integral.

微波电磁参数测量技术作为微波传感的重要分支，在国防、工业、农业、材料科学、生物医学、微波遥感、隐身技术等电磁场和微波工程技术的实践中发挥着重要作用。

A series of theoretical and experimental studies on the microstrip patch antennas with dielectric superstrates is carried out systematically. Firstly, a comprehensive survey of the microstrip antenna technology and its theories are presented. Then, two analysis techniques, named as the spectral domain Green's function method and the spectral domain integral equation method are developed. The SDGF method is a simplified analysis technique, which takes advantage of the spectral domain immittance approach to find the dyadic Green's function for the stratified media, and obtains the complete closed-form formulas for radiation patterns, directivity, efficiency, gain etc. Some interesting calculated results are presented. The SDIE method is capable of determining resonant frequency, radiation characteristics, input impedance etc, for the covered microstrip patch antennas. Comparing with other full-wave analyses it reduced computation and mathematical labour remarkably. The singularities near the pole location of the surface-wave modes and the difficulty of the integral computation over infinite range of oscillating integrands are dealt with actively and documented well. Results predicted by the SDIE method agree extremely well with our experimental results for resonant frequencies of various superstrates. The superstrate effects on impedance and radiation characteristics also have been investigated experimentally so that the gap due to lack of measured data and computed results for multi-layered superstrate has been filled to some degrees and two useful observations have been achieved for weakening the resonant frequency shift and optimizing the microstrip antenna gain. As a meaningful application, the design and analysis of a 4×4 patch array are introduced.

实用微带天线普遍加介质覆盖层来防护热，物理损伤和环境影响，也可能在飞行或严酷气候条件下自然形成覆盖层本论文对带介质覆盖层的微带贴片天线系统地作了一系列理论和实验研究首先，对微带天线技术和理论作了全面的综述然后，发展了两种分析方法，称为谱域格林函数法和谱域积分方程法SDGF法是一种简化的分析技术，它利用谱域导抗法来求得分层媒质的并矢格林函数，并得出方向图、方向性系数、增益等参数的完整的闭式公式，给出了一些令人感兴趣的计算结果SDIE法能确定介质覆盖微带天线的谐振频率、辐射特性和输入阻抗等与其它全波分析方法相比，它明显减小了计算量和数学工作量已有效地处理了表面波模极点附近的奇异性和对振荡的被积函数的无限区间积分计算的困难对于不同覆盖层情况下的谐振频率，由SDIE法所预示的结果与我们的实验结果吻合得很好对于覆盖层对阻抗和辐射特性的影响也已作了实验研究这在某种程度上填补了缺少实验数据和计算结果之间的间隙，并得出了缓解谐振频率偏移和优化天线增益的两点有用的结论作为有意义的应用，介绍了一个4×4元矩形贴片天线阵的设计和分析。

To do that,the integral definition of vector magnetic potential and the Lorentz gauge is used to expand the integral equation of the PEEC model.

为此它以矢量磁位的积分表达式和洛仑兹规范代替了矢量磁位和标量电位的积分表达式，对积分方程进行展开。

Furthermore, by using the corresponding inverse Laplace integral transform and numerical solution of integral equation, the displacement and axial force as well as the shear stress of the pile are obtained.

对变换域内的积分方程采用Schapery逆变换方法得到时域内单桩的近似积分方程。数值求解所得的积分方程可以得到桩的沉降、轴力、剪力和孔压。

Fenton has given particular attention to the treatment of singularities in the governing integral equation involving the symmetric Green's function — a feature apparently not accounted for by Black — and he reduces the relevant line integral equations to forms possessing series which are rapidly convergent.

Fenton 已经把特别的注意给奇异的治疗在那统治包括对称的格林的功能的整体的相等-一个特征显然地不根据黑色解释-而且他让有关的线整体相等变成持有快速趋集于一点的系列的表格。

In this paper, applying an integral expression of linear viscoelastic theory, several integral equation expressions for obtaining shear modulus G from stress relaxation modulus E{t and bulk modulus K are acquired by using inversion of the Laplace Transform.

本文应用线粘弹性理论的一种粘弹性积分变换式，采用拉氏逆变换，导出了由拉伸松弛模量E和体积松弛模量K求解剪切模量G的几种积分方程，并给出了由已知试验数据E和K通过迭代和数值积分求G的数值积分算法。

By applying the H〓lder inequality, the Gronwall inequality, the Doob's inequality and the properties of the Ito stochastic integral to the integral form of the test equation, several important inequalities related to the analytical solution are proved, and the local order of the numerical solutions in mean square sense is obtained accordingly.

通过对试验方程的积分形式使用Holder不等式、Gronwall不等式、Doob不等式和Ito随机积分的性质，得出了试验方程解析解满足的几个重要不等式，进而得出了数值方法在均方意义下的局部误差阶。

And by using the initial conditions as well as the end conditions, the dynamic problem is then transferred to a second kind Volterra integral equation about the function of the axial strain with respect to time which can also be solved successfully by the interpolation method. For piezoelectric and pyroelectric hollow cylinders, by following the solving procedure for elastic hollow cylinder and by using the electric boundary conditions, the dynamic problems are transferred to two Volterra integral equations about two functions of time, one is axial strain and the other is related to electric displacement, which can also be solved efficiently and quickly by employing interpolation method. The elastodynamic solutions of hollow spheres, which are made of elastic, piezoelectric and pyroelectric materials, respectively, for spherically symmetric problems are also obtained.

对于弹性空心圆柱，通过引入一特定函数将非齐次边界条件化为齐次边界条件，然后利用正交展开技术，导出关于时间函数的方程，再结合初始条件和端部边界条件，将原问题转化为关于一个时间函数的第二类Volterra积分方程，运用插值法可给出此积分方程的解；对于压电和热释电空心圆柱，利用求解弹性空心圆柱相似的方法，再结合电学边界条件，原问题转化为关于两个时间函数（轴向应变和与电位移有关的函数）的第二类Volterra积分方程组，同样可用插值法来构造相应的递推公式高效地求解此积分方程组。

The improved variational-perturbation method based on integral equation (variational-integral perturbation method) is applied to solve the quartic anharmonic oscillator in the ground state.

利用基于积分方程的改进的变分微扰方法求解四次方非谐振子基态。

The symbolic expression, which based on integral solution give the equation of asymmetric traveltime, have great significance on focusing capability of Kirchhoff integral method.

基于积分解的象征表达式给出了非对称走时公式，对改善Kirchhoff积分的聚焦性能有重要意义。

These are places without aristocratic baggage; egalitarian places open to talent, self-improving, engaged in learning and innovation through networks that were at once competitive and cooperative.

这些地方没有贵族遗风作祟，而且对于那些有天分的人是开放的平等之地，这些人善于通过那些曾经很具有竞争力与合作精神的关系网进行自我提高以及学习创新。

Christine: You don't want to see me?

你不想见我？