Functional analysis proofs of Abel's theorems

We give alternative proofs to the classical theorems of Abel, using the concept of Berezin symbol.

     

Simultaneous Pseudo-Timestepping for PDE-Model Based Optimization Problems

In this paper we present a new method for the solution of optimization problems with PDE constraints. It is based on simultaneous pseudo-time stepping for evolution equations. The new method can be viewed as a continuous reduced SQP method in the sense that it uses a preconditioner derived from that method. The reduced Hessian in the preconditioner is approximated by a pseudo-differential operator, whose symbol can be investigated analytically. We apply our method to a boundary control model problem. The new optimization method needs 3.2-times the overall computational effort of the solution of simulation problem alone.     

液态金属流的表面张力问题中的两点边值问题解的存在性

本文讨论了在区域提纯过程中，研究液态金属流的表面张力时提出的一个带有非负参数Ｑ的两点边值问题．利用上、下解方法和Ｓｃｈａｕｄｅｒ不动点定理，证明了当０Ｑ８５１时，该问题至少有一个解，对已有结果０Ｑ＜１进行了重要的改进．     

D—^3He聚变动力可行性研究

本文首先简要地讨论D-3He聚变的物理要求并与D-T聚变作相应的比较,然后运用目前的约束定律和第一稳定区β极限,对计划的近期ETR规模装置(如CIT,TIBER,FER,NET)进行D-3He得失相当和点火实验的可行性研究,并对高径比第二稳定区D-3He托卡马克堆进行参数学研究,最后指出潜在的缩短商用化进程可能性。     

Two long-standing problems in Tsallis’ statistics

On the basis of Tsallis’ entropy and the joint probability factorization condition, two controversial problems existing in Tsallis’ statistics are investigated, where one is whether energy is extensive or not and the other is whether it is necessary to introduce the so-called generalized zeroth law of thermodynamics or not. The results obtained show clearly that like entropy, energy is also nonextensive in Tsallis’ statistics, and that the zeroth law of thermodynamics has been implicitly used in Tsallis’ statistics since 1988. Moreover, it is expounded that the standard energy additivity rule adopted by a great number of researchers is not suitable in Tsallis’ statistics, because its corollary is in contradiction with the zeroth law of thermodynamics.     

Quadratic transformations of the sixth Painlevé equation with application to algebraic solutions

In 1991, one of the authors showed the existence of quadratic transformations between the Painlevé VI equations with local monodromy differences (1/2, a, b, ±1/2) and (a, a, b, b). In the present paper we give concise forms of these transformations. They are related to the quadratic transformations obtained by Manin and Ramani–Grammaticos–Tamizhmani via Okamoto transformations. To avoid cumbersome expressions with differentiation, we use contiguous relations instead of the Okamoto transformations. The 1991 transformation is particularly important as it can be realized as a quadratic‐pull back transformation of isomonodromic Fuchsian equations. The new formulas are illustrated by derivation of explicit expressions for several complicated algebraic Painlevé VI functions. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

逆奇异值问题的相对广义牛顿法

本文用另一方法证明了非对称矩阵的奇异值是处处强半光滑的,并利用这一性质给出求解逆奇异值问题的相对广义牛顿法,该方法具有Q-二阶收敛速度.     

两种群竞争模型的奇摄动群

本文应用多重尺度法构造出非线性微分方程组的解的渐近展开式。并用微分不等式的技巧，证明原问题的解的存在性，且给出解的一致有效渐近估计．     

锥体棱镜的加工

本文简单地叙述了锥体棱镜两种加工工艺。重点介绍直接成型法加工中对角度误差~1″的控制。并提出了角度超差零件返修时的光胶方法。     

Do intramolecular halogen bonds exist? Ab initio calculations and crystal structures’ evidences

Cl···O intramolecular contacts are analysed here. Hence the Cambridge Structural Database (CSD) search was performed to find five-membered Cl–C=C–C=O pseudo-rings closed through Cl···O intramolecular contacts. Such rings were analysed and it was found that some of Cl···O distances are smaller than the corresponding sum of van der Waals radii. Additionally ab initio MP2/6-311++G(d,p) calculations and AIM analyses were carried out here on 3-chloropropenal and its fluoro derivatives to deepen the nature of intramolecular Cl···O interactions, some of findings may indicate that they are attractive and stabilizing ones. This paper is dedicated to Prof. T. M. Krygowski on the occasion of his 70th birthday