Krylov subspaces and the analytic grade

Typical behaviour of the solution of a linear system of equations obtained iteratively by Krylov methods can be characterized by three stages. Initially the residual diminishes steadily; this is followed by stagnation and finally rapid convergence near the algebraic grade. This study examines this behaviour in terms of the concepts of approximately invariant subspace and what we have called the analytic grade of a Krylov sequence. It is shown how the small Ritz values play a vital role in the convergence and how this knowledge helps in the construction of an effective preconditioner. Copyright © 2004 John Wiley & Sons, Ltd.     

微模塑法制备PMMA/SiO2二氧化硅杂化材料微结构

以摩尔比为 1∶1的甲基丙烯酸甲酯 (MMA)、甲基丙烯酸 (3 三乙氧基硅烷基 )丙酯 (ESMA)单体、0 .2 %(单体总量的质量分数 )的偶氮二异丁腈AIBN引发剂和四氢呋喃 (THF)溶剂 ,及 2 0 % (总质量分数 )的正硅酸乙酯TEOS合成出PMMA/SiO2 有机 无机杂化的杂化溶胶 .将溶胶在洗净的普通光学玻璃基片表面甩膜 .利用软刻蚀中的微模塑法 ,把有机硅弹性印章复制有精细图纹一面轻放在杂化溶胶膜上进行微模塑 ,外加 1N压力于12 0℃下处理 2h使溶胶凝胶化 .印章剥离后在基片表面就形成了PMMA/SiO2 有机 无机杂化材料的微图纹结构 .从微图纹的光学显微镜照片可以看出微模塑方法制备杂化材料复制的图纹精细度高 ,操作简单易行 ,是一类比较理想的微细图纹结构加工的方法 .     

Photoproduction of jets and heavy flavors at future polarized ep-colliders

We study photoproduction of jets and heavy flavors in a polarized collider mode of HERA and in polarized ep collisions at √S ≈ GeV. We examine the sensitivity of the cross sections and their asymmetries to the proton’s polarized gluon distribution and to the completely unknown parton distributions of longitudinally polarized photons.     

New Classes of Toda Soliton Solutions

We provide a detailed investigation of limits of N–soliton solutions of the Toda lattice as N tends to infinity. Our principal results yield new classes of Toda solutions including, in particular, new kinds of soliton–like (i.e., reflectionless) solutions. As a byproduct we solve an inverse spectral problem for one–dimensional Jacobi operators and explicitly construct tri–diagonal matrices that yield a purely absolutely continuous spectrum in (-1,1) and give rise to an eigenvalue spectrum that includes any prescribed countable and bounded subset of . Received: 16 October 1995/Accepted: 23 July 1996     

The gas dynamics of current-limiting devices during immobility time

The aim of this paper is to extend our knowledge about the gas-dynamic processes in arcs during immobility time. For this purpose, the conservation equations in a magnetohydrodynamic approximation were coupled with the thermochemical and Maxwell equations. Special features arc the introduction of dissociation and ionization of nitrogen and oxygen, and the simultaneous calculation of the distributions of current density and magnetic induction in the arc. Numerical calculations were performed with a reduced two-dimensional (2-D) time-dependent model. Results of the calculations were compared with measurements. The development in time of the measured and calculated are voltage and arc chamber pressure show very good agreement. The pumping effect of the double vortex in the arc region was confirmed by optical measurements. It is concluded that the three-layer model is a good representation for the main physical features during the immobility time, and that the presence of highly conducting gas in the downstream region of the arc is essential for its downstream movement     

ON THE UNIQUENESS OF LIMIT CYCLE FOR A GENERALIZED LINARD SYSTEM

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