Averages of characteristic polynomials in random matrix theory

We compute averages of products and ratios of characteristic polynomials associated with orthogonal, unitary, and symplectic ensembles of random matrix theory. The Pfaffian/determinantal formulae for these averages are obtained, and the bulk scaling asymptotic limits are found for ensembles with Gaussian weights. Classical results for the correlation functions of the random matrix ensembles and their bulk scaling limits are deduced from these formulae by a simple computation. We employ a discrete approximation method: the problem is solved for discrete analogues of random matrix ensembles originating from representation theory, and then a limit transition is performed. Exact Pfaffian/determinantal formulae for the discrete averages are proven using standard tools of linear algebra; no application of orthogonal or skew‐orthogonal polynomials is needed. © 2005 Wiley Periodicals, Inc.     

Development of shaping technologies for crystals grown from melts

The development of technologies for growing crystals with a given shape and designing the growth equipment for the Czochralski and conventional and modified Stepanov methods have been considered. The reviewed experimental data lead to the conclusion that it is possible to provide three-dimensional control of the crystal geometry with the aid of a die in the growth process.     

Proton transfer in the 1,1-dinitroethane/n-dibutylamine complex

The ¹H NMR spectra of 1,1-dinitroethane/n-dibutylamine solutions in CCl₄ have been investigated. It is shown that two types of complexes, the CH … N hydrogen bond complex and the ion pair are present in the solution simultaneously, with slow exchange through proton transfer between them. The exchange rates, activation energy and enthalpy of proton transfer are determined. It can be concluded that the act of proton transfer from carbon to nitrogen and back is kinetically determined.     

Weak invariance principle for local times

Results are found on weak convergence of some processes generated by a recurrent random walk to a Brownian local time process.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 158, pp. 14–31, 1987.     

相对论性核碰撞中φ介子增强

用强子和弦级联模型LUCIAE系统地研究了相对论性p+p和Pb+Pb碰撞中φ介子产生.在模型框架内实验测得的158AGeV/cPb+Pb碰撞中φ介子产额相对于同能量p+p碰撞的增强现象,依赖于弦发射胶子的集体效应和奇异夸克压低约化两机制,在一定程度内能得到解释.     

在RHIC的极限碎裂和Ф介子产生(英文)

利用强子和串级联模型LUCIAE研究了PHOBOS的极限碎裂等以及在PHIC进行的Au +Au碰撞中带电粒子多重性的经验标度规律 .对介子的产生机制也通过与带电粒子多重性的比较进行类似的研究 .结果似乎表明在串级碎裂模型中带电粒子和介子有共同的产生机制 .还讨论了PHOBOS经验标度规律的模型依赖性 .     

Leiterf?rmige Polymere mit einem System konjugierter Bindungen auf der Basis der Vinylacetylenverbindungen

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