基于预条件LANCZOS算法快速实现三维地电场正演计算

针对三维地电场正演计算过程中形成的超大规模稀疏线性方程组,采用不完全Cholesky分解方法进行预条件处理,经过条件数改善后形成的新线性方程组的系数矩阵变为一个近似的单位矩阵,再应用Lanczos算法将会提高数值计算的稳定性,加快迭代收敛的速度,通常在迭代次数远小于系数矩阵阶数时就能得到较好精确解的近似值,为下一步的电阻率三维反演计算打下了非常好的基础.     

Generalized Watson transforms I: General theory

This paper introduces two main concepts, called a generalized Watson transform and a generalized skew-Watson transform, which extend the notion of a Watson transform from its classical setting in one variable to higher dimensional and noncommutative situations. Several construction theorems are proved which provide necessary and sufficient conditions for an operator on a Hilbert space to be a generalized Watson transform or a generalized skew-Watson transform. Later papers in this series will treat applications of the theory to infinite-dimensional representation theory and integral operators on higher dimensional spaces.

     

一类不变的Hankel算子

对于Ｌ^a,2（Ｄ）的两类Ｍｏｅｂｉｕｓ不变子空间Ａ_l^a,2（Ｄ）与Ａ_l^-a,2（Ｄ）,定义了对解析的记号函数ｂ（ｚ）的大的和小的Ｈａｎｋｅｌ算子Ｈ_b^ll′与ｈ_b^ll′,研究了它们的有界性、紧性及其Ｓｃｈａｔｔｅｎ－ｖｏｎ Ｎｅｕｍａｎｎ类的Ｓ_P估计．性质。     

EXTENSIONS OF HILBERT MODULES AND HANKEL OPERATORS

1.IntroductionInthepresentpaper,wewillcontinuethestudyofHilbertmodules[1-5].LetHbeaHilbertspaceandAafunctionalgebra.WesaythatHisaHilbertmoduleoverAifthereisamultiplication(a,f)-affromAxHtoH,makingHintoanXmoduleandif,inaddition,theactionisjointlycontinuousinthesup-normonAandtheHilbertspacenormonH.ThecategoryHofallHilbertNmodulesisanaturalsettingfornumerousquestionsinoperatortheory.In[9],DouglasandPaulseninitiatedasystematicstudyofHilbertmodules'theywereabletotranslatemanyconceptsandpro…     

扭矩作用下黏弹性和正交异性半空间问题的解

采用Ｈａｎｋｅｌ变换分析半空间受扭矩作用时的响应。在获得应力和位移通式的基础上，讨论了集中扭矩作用下轴弹性和正交异性半空间问题，给出了位移和应力的解析表达．     

ANALYSIS OF THE LARGE DEFLECTION DYNAMIC RESPONSE OF RIGID-PLASTIC CIRCULAR PLATE RESTING ON FLUID

A study is presented for the large deflection dynamic response of rigid-plastic circular plate resting on potential fluid under a rectangular pressure pulse load.By virtue of Hankel integral transform technique,this interaction problem is reduced toa problem of dynamic plastic response of the plate in vacuum.The closed-formsolutions are derived for both middle and high pressure loads by solving the equationsof motion with the large deflection in the range where both bending moments andmembrane forces are important.Some numerical results are given.     

流固耦合介质轴对称动力问题解法的改进

用直接求解常微分方程组解文［１］所得的控制方程，减少了传递矩阵计算工作量，避免了子阵求逆，使问题的求解得到了简化     

饱和土地基的非轴对称固结

固结问题是土力学的基础课题之一，现有的研究主要针对饱和土的平面固结和轴对称固结问题。本文应用Fourier展开、Laplace变换和Hankel变换求解了各向同性饱和土的Blot固结方程；讨论了半空间各向同性饱和土的非轴对称固结。借助数值计算，本文的方法可以用于分析各向同性饱和土的非轴对称固结问题。     

关于Toeplitz+Hankel线性方程组的迭代解法

本文研究Toeplitz+Hankel线性方程组的预处理迭代解法.我们提出了几个新的预条件子,并分析了预处理矩阵的谱性质,当生成函数在Wiener类中时,预处理矩阵的特征值聚集在1附近.数值实验表明该预处理子比文[5]中的预处理子更有效.