查询词典 fredholm alternative

In the second part,we have mainly discussed the error es-timates of the numerical methods for solving ill-posed problem,including the error estimate of finite-dimensional regulariza-tion method in Chapter 5,and the error estimate of regulariza-tion-spline method for solving Fredholm integral equation ofthe first kind.

在第二部分，我们主要讨论了不适定问题数值方法的误差估计，包括有限维正则化方法求解不适定问题的误差估计以及用样条正则化方法求解第一类Fredholm积分方程的误差估计，两者均是目前还未有的结果。

By using the Copson method, one of these equations is transformed into a Fredholm integral equation of the second kind to obtain the solution. Furthermore, the intensity factors, the total energy release rate and the mechanical strain energy release rate are obtained and compared with the classical results without considering the electric field gradient effects.

采用了Copson方法，将其中一组对偶积分方程转化为第二类Fredholm 积分方程来进行数值求解，得到了裂纹尖端的强度因子、总能量释放率和机械应变能释放率，并与经典理论中的结果进行了比较。

In this paper the direct boundary integral equation of two-dimensional Laplace equation for Dirichlet problem is considered, which is deduced by Green's formula and the fundamental solution, and is a Fredholm integral equation of the first kind.

本文考虑用Green 公式和基本解推导得出直接边界积分方程来求解二维Laplace 方程的Dirichlet 问题，该直接边界积分方程是第一类Fredholm 积分方程。

The probability generating function of queue length under stability is obtained by supplementing variables,where, p\-0 may be found numerically by solving first kind Fredholm integral equation.

尽管系统队列中仍有顾客在等待。对服务员有休假的排队系统的全面介绍可参看文献[1—3]。

Fourier transforms are used to reduce the problem to the solution of a pair of dual integral equations, which are then reduced to a Fredholm integral equation of second kind by the Copson-Sih method, and anti-plane displacement, electric potential and stress are obtained.

通过Fourier积分变换，将混合边值问题转化为对偶积分方程，并利用Copson-Sih方法将对偶积分方程转化为第二类Fredholm积分方程进行求解，给出了反平面位移、电势及应力分量的解析表达式。

In previous paper1-3, from the results of the electronic computer simulation experiments and the analysis of the corresponding optical properties, we presented a stabilization condition for numerically solving a Fredholm Integral equation of the first kindσ2σ1kBdσ=I in Fabry-Perot interferencespectroscopy.

在以前的论文中，我们从计算机模拟实验及相关的光学现象出发提出了Fabry—Perot干涉光谱技术中的积分方程数值求解的稳定条件。

The inversion of particle size distribution from measured data of light scattering, as a typical inverse problem, has been studied by many reseachers and solved by several numerical methods. Among which, direct Tikhonov regularization method with Morozov discrepancy principle, is often used to overcome the ill-posedness linked with the Fredholm integral equation of the first kind, so the stability of inversion has been heightened. But there has much room for improvement of the inversion accuaracy, especially for the double-peak problems.

由测量得到的散射光强数据来反演颗粒粒径分布是一个典型的反问题，它已为许多的学者所研究，并用多种数值方法来求解，其中带Morozov偏差原理的直接Tikhonov正则化方法经常被采用，以便用来克服与上述反演相联系的第一类Fredholm积分方程的不适定性带来的困难，因而反演的精度得到了提高；然而仍有许多改进的余地，特别是对于所谓"双峰"问题更是如此。

Through establishing the functional of the source pulse which is based on the concept of "usable energy" in the received pulse and then extremizing the functional by means of the calculus of variations, the mathematical models of the optimized source pulse waveforms are shown to be associated with the eigenfunctions of a homogeneous Fredholm linear integral equation of the second kind. An efficient algorithm is developed for numerically solving the integral equation models.

论文研究了基于延迟反射脉冲序列无源标签的UWB RFID系统的基本工作原理并进行了详细的信号描述和分析，通过建立基于接收脉冲"有效能量"概念的源脉冲波形函数的泛函和使用变分计算泛函极值，得到了相关于第二类齐次Fredholm线性积分方程特征函数的源脉冲波形最优解数学公式模型，并开发了一套有效的数值求解算法。

Transversely isotropic ; layered saturated ground ; Biot's motion equation ; elastic circular plate ; Fredholm integral equation

横观各向同性；饱和层状地基； Biot动力方程；弹性圆板； Fredholm积分方程

Then, under the consideration of mixed boundary value condition, a pair of dual integral equations for the rocking vibrations of a disk on saturated grounds are obtained, which can be reduced to a Fredholm integral equation of the second kind and solved by numerical procedures. Consequently, the dynamic compliance coefficient is evaluated and numerical results are presented to portray the influence of poroelastic effects on the dynamic interaction problem.

对于刚性圆板，作者首先采用Hankel变换对波动方程进行求解，得到了该控制方程在Hankel变换域内的通解，然后由混合边值条件建立了饱和地基上刚性基础摇摆振动的对偶积分方程，并将其化为第二类Fredholm积分方程，用数值方法计算了不同频率下基础的动力柔度系数，从而考察孔隙水的存在对基础摇摆振动特性的影响。

The United Kingdom has pledged to provide technical assistance to the peacekeeping effort in Darfur, including airlifting supplies and equipment to assist the African peacekeepers.

英国承诺为达佛的維和努力提供技术帮助，包括提供非洲的維和部队空运补給和裝备。

Results: The level of ET-1mRNA in placental villus was significantly higher in pre-eclamptic women than that in control group.

结果：妊高征组患者胎盘绒毛组织ET-1 mRNA的表达较正常妊娠组明显增高。