Free probability and the von Neumann algebrasof free groups

This short note summarizes the circumstances of the birth of free probability theory andsome of the recent achievements.     

The mesa problem for Neumann boundary value problem

In this paper, we study the singular limit of the Porous Medium equation u_t=Δu^m+g(x,u), as m→∞, in a bounded domain with Neumann boundary condition.     

CAP-子群与p-幂零性

设G是有限群。H是G的一个正规子群。P是|H|的一个素因子。P是H的一个Sylow p-子群。若下列条件之一满足。则H是p-幂零：1)P的极大子群都是G的CAP-子群且(|H|，P-1)=1；2)P的二次极大子群都是G的CAP-子群且(|H|，P^2-1)=1。特别地，若进一步假设G／H为P-幂零且(|G|，P-1)=1或(|G|，P^2-1)=1。则G自身亦为P-幂零。     

Generating Quadratic Pseudo-Anosov Homeomorphisms of Closed Surfaces

In this note, we show that given a closed, orientable genus-g surface S _g , any hyperbolic toral automorphism has a positive power which induces a quadratic, orientable pseudo-Anosov homeomorphism on S _g . To show this, we lift Anosov toral automorphisms through a ramified topological covering and present the lifted homeomorphism via a standard set of Lickorish twists. This construction provides a general method of producing pseudo-Anosov maps of closed surfaces with predetermined orientable foliations and quadratic dilatation. Since these lifted automorphisms have orientable foliations, this construction is a sort of converse to that of Franks and Rykken [Trans. Amer. Math. Soc. 1999], who established that one can associate to a quadratic pseudo-Anosov homeomorphism with oriented unstable foliation a hyperbolic toral automorphism.     

Liquid-phase noncatalytic butene oxidation with nitrous oxide

The kinetics and mechanism of noncatalytic liquid-phase oxidation of but-1-ene and but-2-ene with nitrous oxide in a benzene solution in the temperature range from 180 to 240°C were studied. Oxidation proceeds via the 1,3-dipolar cycloaddition mechanism to form carbonyl compounds. Both of these reactions occur with close rates and activation energies and have the first orders with respect to the alkene and N₂O. A considerable fraction (39%) of but-1-ene involved in oxidation undergoes cleavage at the double bond yielding propanal and an equivalent amount of methylene, the latter producing ethylcyclopropane and cycloheptatriene. The oxidation of but-2-ene proceeds with a minimum bond cleavage and affords methyl ethyl ketone with 84% selectivity. Regularities of the oxidation of terminal and internal alkenes C₂—C₈ with nitrous oxide were analyzed using the previously published data. __________ Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 4, pp. 925–933, April, 2005.     

A novel synthesis of 5-perfluorophenyl 4,5-dihydro-1H-pyrazoles in THF or water

5-Perfluorophenyl 4,5-dihydro-1H-pyrazoles were synthesized from 1,3-dipolar cycloaddition reaction of perfluorobenyl 2,4,6-triisopropylbenzenesulfonylhydrazone and α,β-unsaturated carbonyl compounds or acrylonitrile in THF or water. It was worthy to note that better results were obtained when water was employed as the solvent, which was considered as an effective, economic and environmentally friendly method to synthesize these pyrazole derivatives.     

Rhodium-catalyzed addition of arylstannanes to carbon-heteroatom double bond

The addition of arylstannanes to the carbon-heteroatom double bond in the presence of a catalytic amount of a cationic rhodium complex ([Rh(cod)(MeCN)₂]BF₄) was examined. The reactions of aldehydes, α-dicarbonyl compounds, and N-substituted aldimines with the arylstannanes gave corresponding alcohols, α-hydroxy carbonyl compounds, and amines, respectively. An arylrhodium complex generated by the transmetalation with the arylstannane was probably the active catalytic species.     

免疫算法在车辆调度问题中的应用

免疫算法是模仿生物体高度进化、复杂的免疫系统仿生的一种智能化启发式算法。本文根据车辆调度问题的具体情况，应用免疫算法解决车辆调度中路线安排问题，并提出了一种基于分组匹配的亲和力的计算方法。实验结果表明，免疫算法能有效地应用于车辆调度中路线安排问题。