Efficient Collocation Schemes for Singular Boundary Value Problems

We discuss an error estimation procedure for the global error of collocation schemes applied to solve singular boundary value problems with a singularity of the first kind. This a posteriori estimate of the global error was proposed by Stetter in 1978 and is based on the idea of Defect Correction, originally due to Zadunaisky. Here, we present a new, carefully designed modification of this error estimate which not only results in less computational work but also appears to perform satisfactorily for singular problems. We give a full analytical justification for the asymptotical correctness of the error estimate when it is applied to a general nonlinear regular problem. For the singular case, we are presently only able to provide computational evidence for the full convergence order, the related analysis is still work in progress. This global estimate is the basis for a grid selection routine in which the grid is modified with the aim to equidistribute the global error. This procedure yields meshes suitable for an efficient numerical solution. Most importantly, we observe that the grid is refined in a way reflecting only the behavior of the solution and remains unaffected by the unsmooth direction field close to the singular point.     

On Series of Ordinals and Combinatorics

This paper deals mainly with generalizations of results in finitary combinatorics to infinite ordinals. It is well-known that for finite ordinals ∑_bT<αβ is the number of 2-element subsets of an α-element set. It is shown here that for any well-ordered set of arbitrary infinite order type α, ∑_bT<αβ is the ordinal of the set M of 2-element subsets, where M is ordered in some natural way. The result is then extended to evaluating the ordinal of the set of all n-element subsets for each natural number n ≥ 2. Moreover, series ∑_β<αf(β) are investigated and evaluated, where α is a limit ordinal and the function f belongs to a certain class of functions containing polynomials with natural number coefficients. The tools developed for this result can be extended to cover all infinite α, but the case of finite α appears to be quite problematic.     

Spectrophotometric analysis, thermal analysis and gravimetric determination of some metal ions with oxime and Schiff's base derivatives of N-furoylphenylhydroxylamine

The oxime and Schiff's base of N-furoylphenylhydroxylamine form complexes with Co²⁺, Cu²⁺, Zn²⁺ and Fe³⁺. These complexes were studied by means of the UV — Vis. spectra of nujol mulls, electron spin resonance (ESR) spectra and magnetic susceptibility to determine their stereochemistry. The complexes were characterized via elemental analyses, molar conductivities and thermogravimetric analyses. Organic reagents were used for the gravimetric determination of Co²⁺, Cu²⁺ and Fe³⁺ through the precipitation of their complexes. The compounds were also used for separation of a binary mixture of Cu²⁺ and Cu²⁺. Interferences were studied.     

宇宙临界减速因子

本文证明了如果中微子具有质量,那么膨胀宇宙的临界减速因子q_c就不是通常所说的1/2而是等于1。     

建立社会主义市场经济必须首先解放思想

从传统的计划经济向社会主义市场经济的转变，必须从计划经济体制下所形成的旧的思想观念中解放出来，树立适应社会主义市场经济的新观念，这是建立社会主义市场经济的需要。我国十几年的改革开放的实践已证明，在马克思主义的指导下，打破习惯势力和主观偏见的束缚，从实际出发，解放思想，是改革开放和进行社会主义建设的首要条件。     

浅谈对学生地理基本技能的培养

地理基本技能给我们用地理的观点观察周围事物提供了一种有效工具 .培养学生地理基本技能是地理教学的主要目标之一 .本文主要谈讨了地理基本技能的构成、重要性以及地理技能的培养问题     

45钢固体粉末法稀土、硼、铬、铝共渗工艺研究

研究了RE_Mg合金对固体粉末法硼、铬、铝共渗层成分、组织和性能的影响 .发现随着RE_Mg合金加入量的增加 ,渗层中Al2 O3的量不断增多 ,当RE_Mg合金加入量为 5 %时 ,渗层中出现连续致密分布的Al2 O3黑区组织 ,对此进行了性能测试和机理探讨     

加强管理体制改革与创新努力使实验教学和管理上一个新台阶

结合化学系实验室现状 ,探讨了实验教学在实现两个重要转变的过程中 ,进行实验室体制改革等方面的思路和实践 .     

检测陀螺仪转子安装精度的一种新方法

陀螺仪转子的安装精度对其运行的稳定性和精确性有很大的影响。由于要求的安装误差很好，因此，对其误差的测量要求准则。其测量误差应经安装误差小1／10以及上，一般的检测方法很难达到要求，为此介绍了一种新型的光电检测方法，该方法利用狭缝的光学傅立叶变换提取陀螺仪转子的误差信息，采用计算机进行信息处理，从而完成陀螺仪转子的自动检测和分类，该方法也可用于其他一些精密年的自动检测处理。