查询词典 hilbert problems

The problems dealt with can be readily transformed into Riemann-Hilbert problems by this technique, and general expressions of analytical solutions are given considering the action of pulse loads and unit-step loads located at the origin of the coordinates respectively.

应用该法可以迅速地将所论问题转化为Riemann-Hilbert问题，并给出了坐标原点分别受到脉冲载荷、阶越载荷作用下解析解的一般表达式。

This thesis is divided into six parts. The first chapter is preface, the current status of research in the inverse problems for parabolic partial differential equations is reported; the second chapter is "regularization methods for numerical differentiation and their applications ", in this chapter we investigate many regularization methods from a viewpoint of regularization theory and algorithm, some applications in the inverse problems for parabolic partial differential equations are given; the third chapter is "spectral regularization methods". Based on Fourier analysis, within the framework of regularization theory, we apply the spectral methods to some ill-posed problems. Many numerical experiments are done in order to show the validity of the methods; the fourth chapter is devoted to wavelet dual least squares method and a revised wavelet method; in the fifth chapter,we combine finite difference method with method of lines and apply it to the backward heat conduction problem in time; in the sixth chapter "identification problems for unknown source ", the essence and the degree of two problems related to source identification are pointed out, at the same time, some numerical methods are reported.

本文分为六个部分，第一章前言简要分析了国内外抛物型偏微分方程反问题的研究现状；第二章数值微分的正则化及其应用从正则化理论和算法的角度出发，考察了许多正则化方法，还给出了数值微分在抛物型偏微分方程反问题的一些应用；第三章谱正则化方法是在Fourier分析的基础上，在一般正则化理论的框架下，给出了这种方法在各种不适定问题中的应用，数值实验表明谱方法是有效的；第四章研究了小波对偶最小二乘方法和改进的小波方法；第五章主要研究了有限差分方法结合线方法在时间反向热传导问题中的应用；第六章是未知源识别问题，主要指出了两类未知源问题的不适定程度和不适定本质，同时报告了一些数值方法。

Additionally, a great deal of contradictions and problems in current Chinas socio-economic development, such as, the problems caused by duality structures in urban and rural areas, three main problems in rural area (problems in agriculture, in rural areas and with farmers), problems in industrial structure adjustment, urban planning and infrastructure construction, rational utilization of land resource and ecological environmental protection etc, unexceptionally have close connections to relative lag of urbanization.

更重要的是，当前中国社会经济发展中的诸多矛盾和问题如城乡二元结构与"三农"问题、产业结构调整问题、城市规划与基础设施建设问题、土地资源合理利用和生态环境保护问题等等，无例外的与我国城镇化发展相对滞后有密切的联系。

The ways to deal with other problems in the numerical simulations of injection-molding filling process, such as multicontinued field problems, multigate problems and weldline formation problems, are presented in this thesis, a simplified algorithm is also developed to solve axisymmetrical problems.

一种新的简化的温度场模型用来计算充模过程中熔体前缘附近的温度场，区域内温度场计算时，引入了温度边界层模型，显著简化了计算过程。

The boundary element method for the Riemann-Hilbert boundary value problems for the generalized analytic function uses Cauchy integral formula as the foundation . The singularity of the Cauchy

广义解析函数的Riemann-Hilbert边值问题的边界元方法是以Cauchy公式为基础，Cauchy核具有奇性，这是所面临的困难，可以设法利用Cauchy主值积分来解决，最后给出问题的解。

In this paper,four aspects of the above problems were studied:Firstly, the problem of solving continuous linear operator equation inseparable Hilbert space is studied .

通过把第一类连续不适定算子方程转换为等价的无穷维方程组，然后利用投影法，给出了解存在唯一的充要条件；给出了连续线性不适定算子方程解析解，解决了不适定情况下解的表示问题，由此给出了算子方程的数值求解公式；进一步证明了，在解不唯一情况下，此表达式给出的解为算子方程的最小范数解，同时表示出了连续线性不适定算子方程的解集。

The problems considered can be very facilely translated into Riemann-Hilbert problem by application of the approaches which are resolved by usual Muskhelishvili's methods, and their closed solutions are acquired rather straightforward.

应用该法可以很容易地将所讨论的问题转化为Riemann-Hilbert问题，而后一问题可以用通常的Muskhel-ishvili方法进行求解，并且可以相当简单地得到问题的闭合解。

In the first chapter,the Riemann-Hilbert boundary value problem of non-normal type for biregularfunctions and some boundary value problems of the inhomogeneous secondorder equation

共有三章，在第一章中主要运用文[2]中的理论与方法讨论了平面上双解析函数的非正则型Riemann-Hilbert边值问题及非齐次二阶方程

Then, we investigate iterative methods in Hilbert spaces for solving such problems in the second part.

本文在第二部分讨论了Hilbert空间中均衡问题的近似迭代解。

An improved method using two pairs of Hilbert filters can solve these problems.

基于2对相同Hilbert移相滤波器的改进方法能够解决这些问题。

"I came down to say good-bye to my friends," answered Presley shortly.

"我是来向我的朋友们告别的，"普瑞斯莱直截了当的回答。

She is ostracized. She loses friends, job, family.

她被流放，失去了朋友、工作、家庭。