Optimal algebraic multilevel preconditioning for local refinement along a line

The application of some recently proposed algebraic multilevel methods for the solution of two-dimensional finite element problems on nonuniform meshes is studied. The locally refined meshes are created by the newest vertex mesh refinement method. After the introduction of this refinement technique it is shown that, by combining levels of refinement, a preconditioner of optimal order can be constructed for the case of local refinement along a line. Its relative condition number is accurately estimated. Numerical tests demonstrating the performance of the proposed preconditioners will be reported in a forthcoming paper.     

三系数有限元向量尺度函数的构造

The aim of this paper is to present construction of finite element multiscaling function with three coefficients. In order to illuminate the result, two examples are given finally.     

Estimates for Elements of Inverse Matrices for a Class of Operators with Matrices of Special Structure

In this paper, we consider questions related to the structure of inverse matrices of linear bounded operators acting in infinite-dimensional complex Banach spaces. We obtain specific estimates of elements of inverse matrices for bounded operators whose matrices have a special structure. Matrices are introduced as special operator-valued functions on an index set. The matrix structure is described by the behavior of the given function on elements of a special partition of the index set. The method used for deriving the estimates is based on an analysis of Fourier series of strongly continuous periodic functions.     

抓好数学建模竞赛 推动数学教学改革

本文通过近几年组织数学建模教学和指导学生参加竞赛的实践 ,探索抓好数学建模竞赛 ,促进数学教学改革 ,推动数学素质教育 ,提高人才培养质量的途径、措施和方法     

牛顿弦截法预估校正迭代格式的收敛阶

研究如下形式的牛顿弦截法的预估校正(P.C.)格式:P(预估):~xk+1=xk-(xk-xk-1)f(xk)f(xk)-f(xk-1)C(校正):xk+1=xk-(~xk+1-xk)f(xk)f~(xk+1)-f(xk)证明了它的收敛阶为2.618.     

相位差与q变形广义相干叠加态的压缩特性

对于q变形的非简谐振子广义相干态的叠加态β〉+eiφβeiδ〉,其量子涨落的可能高阶压缩阶数可以表示为k≠2πn/δ,这里n是整数.当δ=π时,压缩阶数不能是偶数即只能是奇数,这正是q变形非简谐振子广义奇偶相干态的结果.由此表明参数相位差δ对决定q变形的非简谐振子广义相干态叠加态的高阶压缩阶数起决定性作用.     

简析"静止液体内部压强公式验证"实验的设计策略

“静止液体内部压强公式验证”在现行教材中有两种实验方法。通过分析实验的设计策略，说明其作用、效果及操作上的困难，指出合理的与不合理诸因素，从而提出改进实验的方法，化难为易，提高实验教学效果。     

The Properties of Light Pressure Force with High Order in Laser Fields

1　Ｉｎｔｒｏｄｕｃｔｉｏｎ　　Ｉｎｒｅｃｅｎｔｙｅａｒｓ,ｂｏｔｈｔｈｅｔｈｅｏｒｅｔｉｃａｌａｎｄｅｘｐｅｒｉｍｅｎｔａｌｉｎｖｅｓｔｉｇａｔｉｏｎｓｏｎｌａｓｅｒｃｏｏｌｉｎｇａｎｄｔｒａｐｐｉｎｇｈａｖｅｂｅｃｏｍｅｏｎｅｏｆｔｈｅｍａｊｏｒｆｉｅｌｄｓｉｎａｔｏｍｉｃ,ｍｏｌｅｃｕｌａｒａｎｄｏｐｔｉｃａｌ ｐｈｙｓｉｃｓ[1～ 8] .Ｔｈｅｄｅｖｅｌｏｐｍｅｎｔｏｆｌａｓｅｒｃｏｏｌｉｎｇａｎｄｔｒａｐｐｉｎｇｔｅｃｈｎｏｌｏｇｙｉｓｉｍｐｏｒｔａｎｔｆｏｒｔｈｅａｐｐｌｉｃａｔｉｏｎｓｓｕ…     

Electronic properties of model quantum-dot structures in zero and finite magnetic fields

We have computed electronic structures and total energies of circularly confined two-dimensional quantum dots and their lateral dimers in zero and finite uniform external magnetic fields using different theoretical schemes: the spin-density-functional theory (SDFT), the current-and-spin-density-functional theory (CSDFT), and the variational quantum Monte Carlo (VMC) method. The SDFT and CSDFT calculations employ a recently-developed, symmetry-unrestricted real-space algorithm allowing solutions which break the spin symmetry. Results obtained for a six-electron dot in the weak confinement limit and in zero magnetic field as well as in a moderate confinement and in finite magnetic fields enable us to draw conclusions about the reliability of the more approximative SDFT and CSDFT schemes in comparison with the VMC method. The same is true for results obtained for the two-electron quantum dot dimer as a function of inter-dot distance. The structure and role of the symmetry-breaking solutions appearing in the SDFT and CSDFT calculations for the above systems are discussed. Received 16 October 2001 and Received in final form 17 January 2002     

Propagation of mesons in asymmetric nuclear matter in a density-dependent coupling model

We study the propagation of the light mesons σ,ω,ρ, and a₀(980) in dense hadronic matter in an extended derivative scalar coupling model. Within the scheme proposed it is possible to unambiguously define effective density-dependent couplings at the Lagrangian level. We first apply the model to study asymmetric nuclear matter with fixed isospin asymmetry, and then we pay particular attention to hypermatter in β-equilibrium. The equation of state and the potential contribution to the symmetry coefficient arising from the mean-field approximation are investigated. Received: 16 October 2001 / Accepted: 10 January 2002