Polyhedral <Emphasis Type="Italic">K</Emphasis><Subscript><Emphasis Type="Italic">2</Emphasis></Subscript>

 Using elementary graded automorphisms of polytopal algebras (essentially the coordinate rings of projective toric varieties) polyhedral versions of the group of elementary matrices and the Steinberg and Milnor groups are defined. They coincide with the usual K-theoretic groups in the special case when the polytope is a unit simplex and can be thought of as compact/polytopal substitutes for the tame automorphism groups of polynomial algebras. Relative to the classical case, many new aspects have to be taken into account. We describe these groups explicitly when the underlying polytope is 2-dimensional. Already this low-dimensional case provides interesting classes of groups. Received: 13 December 2001 / Revised version: 24 June 2002 The second author was supported by the Deutsche Forschungsgemeinschaft, INTAS grant 99-00817 and TMR grant ERB FMRX CT-97-0107 Mathematics Subject Classification (2000): 14L27, 14M25, 19C09, 52B20     

Singularity conjecture and constructions of Jacobi forms

This paper verifies the singularity conjecture for Jacobi forms with higher degree in some typical cases, and gives constructions for the Jacobi cusp forms whose Fourier coefficients can be expressed by some kind of Rankin-typeL-series.     

Instability of quark matter core in a compact newborn neutron star with moderately strong magnetic field

It is explicitly shown that if phase transition occurs at the core of a newborn neutron star with moderately strong magnetic field strength, which populates only the electron’s Landau levels, then in the β -equilibrium condition, the quark core is energetically much more unstable than the neutron matter of identical physical condition.     

贝克曼AllegraTM21R型超高速离心机故障排除一例

贝克曼Allegra^TM 21R型超高速离心机开机后，操作面板上出现错误代码“28”，离心机不旋转。离心机的电机采用无刷感应驱动，由电机驱动电源模块BSMl0GD60DN2驱动离心机的电机。故障是由于电源模块BSMl0GD60DN2损坏引起的。采用东芝三相桥式IGBT电源模块MG25Q6ES42代替BSMl0GD60DN2，并更换已烧毁的栅极电阻后。开机试验，仪器恢复正常。     

<Emphasis Type="Italic">J/Ψ</Emphasis>production

For more than 25 yearsJΨ production has helped to sharpen our understanding of QCD. In proton induced reaction some observations are rather well understood while others are still unclear. The current status of the theory ofJΨ production will be sketched, paying special attention to the issues of formation time andJΨ re-interaction in a nuclear medium.     

伽利略的自由落体定律研究——"最美丽"的十大物理实验之一

在伽利略的运动学研究中,自由落体运动是一个重要课题.他敏锐地认识到,通过打开自由落体运动这个缺口,会导致一门新科学的诞生.他在《两门新科学》(即《关于两门新科学的数学证明的对话》)一书中写道:"我的目的,是要阐述一门崭新的科学,它研究的却是非常古老的课题.也许,在自然界中最古老的课题莫过于运动了.     

Hydrophobicity-induced drying transition in alkanethiol self-assembled monolayer—water interface

During the course of our investigation of the electron transfer properties of some redox species through highly hydrophobic long chain alkanethiol molecules on gold in aqueous and non-aqueous solvents, we obtained some intriguing results such as unusually low interfacial capacitance, very high values of impedance and film resistance, all of which pointed to the possible existence of a nanometer size interfacial gap between the hydrophobic monolayer and aqueous electrolyte. We explain this phenomenon by a model for the alkanethiol monolayer—aqueous electrolyte interface, in which the extremely hydrophobic alkanethiol film repels water molecules adjacent to it and in the process creates a shield between the monolayer film and water. This effectively increases the overall thickness of the dielectric layer that is manifested as an abnormally low value of interfacial capacitance. This behaviour is very much akin to the ‘drying transition’ proposed by Lum, Chandler and Weeks in their theory of length scale dependent hydrophobicity. For small hydrophobic units consisting of apolar solutes, the water molecules can reorganize around them without sacrificing their hydrogen bonds. Since for an extended hydrophobic unit, the existence of hydrogen bonded water structure close to it is geometrically unfavourable, there is a net depletion of water molecules in the vicinity leading to the possible creation of a hydrophobic interfacial gap.     

从诺贝尔经济学奖看数学对经济学的作用

本文在分析2003年诺贝尔经济学奖学术贡献的基础上，阐述了数学思维方式和数学方法对经济问题的解决、经济理论的发展等方面的作用．     

Quantum diffusion

Basic ideas and results which characterize quantum diffusion of defects in quantum crystals like solid helium as a new phenomenon are presented. Quantum effects in such media lead to a delocalization of point defects (vacancies, impurities etc.) and they turn into quasiparticles of a new type—defectons, which are characterized not by their position in the crystal lattice but by their quasimomentum and dispersion law. Defecton-defecton and defecton-phonon scattering are considered and an interpolation formula for the diffusion coefficient valid in all interesting temperature and concentration regions is presented. A comparison with the experimental data is made. Some alternative points of view are discussed in detail and the inconsistency of the Kisvarsanyi-Sullivan theory is shown.