查询词典 kernel of an integral equation

Then the boundary element integral equation of interior and exterior form is deduced in detail, also the form with corner coefficient. The significance for numerical calculation and principle of the singular integral is analyzed, and a non-isoparametric transformation method is presented to calculate weak singular integral and Cauchy integral, the method presented provides us a very simple way to computer the two kinds of singular integral of Helmholtz boundary integral equation, and it is easy to program in computer. After the difficulty of the calculation for multi-frequency of Helmholtz boundary element is explained, a method named SECHIEF (Series Expansion Combined Helmholtz Integral Equation Formulation), which is focused on the computational efficiency, is presented.

对结构声辐射的边界积分方程的内部形式与外部形式进行了详细的推导，给出了角点系数的计算方法与边界积分方程的形式，在此基础上，分析了奇异积分产生的原理及其对数值计算的重要性，提出了一种计算奇异积分的非等参(来源：Ae8a8BC论文网www.abclunwen.com)单元的变换方法，该方法给Helmholtz 声学边界积分方程中的弱奇异积分与Cauchy 奇异积分的计算以及编程提供了极大便利。

In this topic, the dynamic analysis methods for piezoelectric vibrator are studied systematically based on the theoretical model, FEM numerical experimentation and FEM governing equation for given compound-mode vibrator, and some valuable conclusions are obtained. The main work accomplished is summarized as follows: 1.Elaborate the main modeling methods for piezoelectric vibrator and the significance and necessity to study the dynamic characteristics of piezoelectric vibrator which emphasize the urgency of this paper. 2.Take the bending deformation induced by piezoelectric ceramic as example, the energy transfer mechanism of electric energy to mechanical energy are analyzed; the motion and force transfer mechanism are analyzed for the longitudinal-bending vibrator. 3.Based on mode assumption and Hamilton principle, the coupling model of piezoelectric vibrator of linear USM is built; moreover, the equivalent circuit model is obtained and a coupling equation represents the relation between electric parameters and mechanical parameters is derived which provides foundation to match the vibrator and driving circuit. 4.Combine the constitutive equation of piezoelectric ceramic with elastic-dynamical equation, geometric equation in force field and the Maxwell equation in electric field and the corresponding boundary condition equation, the FEM control equation for piezoelectric vibrator of USM to solve dynamic electro-mechanical coupling field is established by employing the principle of virtual displacement. The equation lays the foundation to study the non-linear constitutive equation of piezoelectric ceramic driven by high-power. 5.Define the dynamic indexes of characteristic of vibrator and carry out variable parameters simulation by calculating the model parameters and the electric characteristics of vibrator are simulated according to the equivalent circuit model. By numerical experimentation, the working mode of vibration of vibrator and the shock excitation results of the working frequency band which provides the mode frequency to realize bimodal are analyzed. Detailed calculation of the electro-mechanical coupling field parameters is made by programming the FEM control equation.

本课题从理论模型、有限元数值试验、有限元控制模型等方面以复合振动模式振子为例对超声电机压电振子的动力学特性及其分析方法进行了全面系统地研究，得出了许多有价值的结论，主要概括如下： 1、阐述了目前针对超声电机压电振子的主要建模方法，对压电振子动态特性的研究意义和必要性进行了论述，突出了本文研究内容的迫切性； 2、以压电陶瓷诱发弹性体发生弯曲变形为例，分析了压电陶瓷通过诱发应变来实现机电能量转换的机理；对基于纵弯模式的压电振子的运动及动力传递机理进行了分析； 3、基于模态假定，利用分析动力学的Hamilton原理，建立了面向直线超声电机压电振子的机电耦合动力学模型，并据此建立了压电振子的等效电路模型，导出了电参量与动力学特性参量的耦合方程，为压电振子与驱动电路的匹配提供了依据； 4、从压电陶瓷的本构方程出发，综合力场的弹性动力学方程、几何方程、电场的麦克斯韦方程以及相应的边界条件方程，采用虚位移原理，建立了压电振子动态问题机电耦合场求解的有限元控制方程，为研究其大功率驱动下的非线性本构模型奠定了基础； 5、界定压电振子的动力学特性指标，对压电振子的机电耦合动力学模型参数进行计算及变参数仿真；依据等效电路模型，对压电振子的电学特性进行了仿真分析；通过有限元数值实验，对压电振子工作模态附近的模态振型及工作频率附近的频段进行了激振效果分析，找出了实现模态简并的激振频率；利用有限元控制方程，通过编程计算，对压电振子的力电耦合场参数进行了详细计算，得出了一些有价值的结论。

By usingthe relation between the Bergman kernel and the Riemann mapping and Plemly for-mulae,the second boundary integral equation about the Bergman kernel is obtained,moreover,the integral kernel is a continuous,without any singularity,parametized Neu-mann kernel.We discuss the case of some symmetric property,and get correspondingresults.

主要利用Bergman核与Riemann映照之间的关系，推导出Bergman核满足带有参数化Neumann核的第二类边界积分方程，积分核是连续的没有任何奇性，并讨论了具有某种对称性质的情形。

This paper discusses the Noether theorem of complete singular integral equation which containsboth the convolution kernel and the Cauchy kernel, and comes up with the Noether theoremwhich is similar to the Fredholm integral equation, the convolution equation and the singularintegral equation.

本文讨论了既含卷积核又含Cauchy核的完全奇异积分方程的Noether定理，得到了与Fredholm积分方程、卷积型积分方程、奇异积分方程相类似的Noether定理。

In the computation of aerodynamic forces, the present work is based on the work of Morino et al., but the following aspects are improved:(1) In computing the steady transonic aerodynamic load, the steady transonic nonlinear integral equation is solved by relaxation-iteration method in this thesis, instead of solving the time dependent transonic nonlinear integral equation, so that the computing time is saved greatly;(2) The influence coeifficients represented by volume integral are transformed to surface integral by using the Gaussian Theorem, so the analytical form of these coeifficients can be obtained and this leads to be more convenient to analyse and compile computer program;(3) The shock capturing method is used in every time step in present work, no shock moving term is added in the integral equation, so that it is more convenient and simpler to treat.

在气动力计算方面，本文基于Morino等人的工作，作了如下几方面的改进：（1）在计算定常跨音速流场（作为非定常绕流计算的初场）时，本文采用松驰迭代法直接求解跨音速定常非线性积分方程，而不是采用时间相关法求解非定常非线性积分方程，这样大大节省了计算机时；（2）将以体积分形式出现的影响系数化为面积分，并获得解析公式，这样便于分析和编写程序；（3）对运动的激波，本文通过在每一个时间步长上采用激波捕捉法而得到，而不是在积分方程中附加激波运动项，因而处理起来简单方便得多。

Firstly, Wavelet-Galerkin algorithm for solving the first kind of singular integral equation with the Hilbert kernel is proposed, we use the characteristic of periodic wavelet on L~2([0,1]) and Hilbert kernel to solve and make stiff matrix lower dimensions and become sparser through thresholding,thus the cost of computation is reduced. Because of the singularity of Hilbert kernel we use Tikhonov regularization method to solve the system of stiff equation. At last the convergence and numerical result of approximate solution are given. Secondly, an approach of regularization based on Fourier is presented for sideways heat equation; we give the theory proof and error estimate.

首先，提出了含Hilbert核的第一类奇异积分方程的小波伽辽金(Wavelet-Galerkin)数值算法，该算法中利用了L~2([0，1])上的周期小波和Hilbert核的特点进行处理，使得刚性矩阵维数降低并且通过阈值使得它更加稀疏，减少了计算量；由于Hilbert核的奇异性，通过Tikhonov正则化方法求解所得到的刚性方程组，给出了收敛性和数值结果；其次，对标准的一维逆热传导方程给出了一种基于Fourier正则化方法，给出了理论证明及其误差估计，解决了文献中算法与理论误差估计的不相匹配的现象，该正则化方法不仅保留了测量数据的部分高频成份，且与文献中的算法具有同样的计算量和误差估计。

this article discusses the integral theorem of mean the promoted question, mainly has two aspects: On the one hand in analyzes in the teaching material under the first integral theorem of mean condition, had proven lies between the value spot to have to be possible to obtain in the open-interval, further discusses this knot promotes to the generalized Riemann integral, and further proved the conclusion also establishes to the promoted first integral theorem of mean; Promotes on the one hand in addition the integral theorem of mean to in the curve and the curved surface, and has proven the curvilinear integral theorem of mean and the surface integral theorem of mean.

本文讨论积分中值定理的推广问题，主要有二个方面：一方面在分析教材中第一积分中值定理的条件下，证明了介值点必可在开区间内取得，进一步将这个结论推广到广义Riemann积分，并进一步证明结论对推广的第一积分中值定理也成立；另一方面，将积分中值定理推广到曲线和曲面中，并证明了曲线积分中值定理和曲面积分中值定理。

Indefinite integral concept,, indefinite integral nature of the basic integral formula, the indefinite integral proofs, indefinite integral substitution integration, integration by parts, the indefinite integral rational function integral.

不定积分概念，，不定积分性质，基本积分公式，不定积分证明方法，不定积分换元积分法，分部积分法，不定积分有理函数积分。

This curriculum primary coverage includes: Function and limit, a circular function derivative and differential, theorem of mean and derivative application, indefinite integral, definite integral, definite integral application, space analytic geometry and vector algebra, function of many variables differential method and application, multiple integral, curvilinear integral and surface integral, infinite series, differential equation.

该课程的主要内容有：函数与极限，一元函数的导数与微分，中值定理与导数的应用，不定积分，定积分，定积分的应用，空间解析几何和向量代数，多元函数微分法及其应用，重积分，曲线积分与曲面积分，无穷级数，微分方程。

The differences of providing amino acid to kernel of different winter wheatculfivars.93-52 with high protein content in kernel had highest content of amino acid innutrition organs,indicated 93-52 can provide abundance material for protein synthesis ofkernel,namely the source in full,so the content of amino acid in kernel was highest;Compared Lumai21 with Jinanl7,the amino acid content in leaf of Lumai21 was a littlehigher than Jinan17,but the amino acid content in stem、sheath and spike was obviouslylower than Jinan17,also the amount of amino acid restored in nutrition organs was large,the translocation degree was low to kernel,namely the flow was not fluency,which wasthe main reason of low content of amino acid in kernel.

小麦不同品种向籽粒供应氨基酸水平的差异。籽粒蛋白质含量高的93-52各营养器官中的游离氨基酸含量均最高，说明93-52籽粒蛋白质合成所需底物供应充足，即源足，因而其籽粒游离氨基酸含量最高。鲁麦21和济南17相比，鲁麦21叶片中的游离氨基酸含量虽略高于济南17，但茎鞘和穗中的游离氨基酸含量却明显比济南17低，并且在后期鲁麦21营养器官中游离氨基酸滞留的多，向籽粒中的转移程度低，即流不畅，是造成鲁麦21籽粒游离氨基酸含量低的主要原因之一。

More direct, directer ; most direct, directest

径直的，笔直的

Do you know how to use a chain saw?

你知道如何使用链锯吗？