Cyclic vectors for Hilbert algebras

In this paper, we give a simple proof of the Stone-von Neumann theorem about the irreducible unitary representations of Heisenberg groups. First of all, we prove a result about the representations of Hilbert algebras of Hilbert-Schmidt operators on a Hilbert space. Then we use it to give a simple proof of the Stone-von Neumann theorem. Applications to theoretical physics are mentioned.     

Tropological systems are points of quantales

We address two areas in which quantales have been used. One is of a topological nature, whereby quantales or involutive quantales are seen as generalized noncommutative spaces, and its main purpose so far has been to investigate the spectrum of noncommutative C∗-algebras. The other sees quantales as algebras of abstract experiments on physical or computational systems, and has been applied to the study of the semantics of concurrent systems. We investigate connections between the two areas, in particular showing that concurrent systems, in the form of either set-theoretic or localic tropological systems, can be identified with points of quantales by means of a suitable adjunction, which indeed holds for a much larger class of so-called “tropological models”. We show that in the case of tropological models in factor quantales, which still generalize tropological systems, the identification of models and (generalized) points preserves all the information needed for describing the observable behaviour of systems. We also define a notion of morphism of models that generalizes previous definitions of morphism of systems, and show that morphisms, too, can be defined in terms of either side of the adjunction, in fact giving us isomorphisms of categories. The relation between completeness notions for tropological systems and spatiality for quantales is also addressed, and a preliminary partial preservation result is obtained.     

Playing with fidelities

The notion of partial fidelities as invented by A. Uhlmann for pairs of finite-dimensional density matrices is extended to the νN-algebraic context and is considered and thoroughly discussed in detail from a mathematical point of view. Especially, in the case of semifinite νN-algebras, formulae and estimates for the partial fidelity between the functionals of a dense cone of inner derived normal positive linear forms are obtained. Also, some generalities on the notion of fidelity in quantum physics are collected in Appendix, and another system of mathematical axioms for fidelity over density operators, which is based on the concept of relative majorization and which is intimately related to complete positivity, is proposed.     

基于单片机的全固态激光器电控系统

利用AT89C55单片机,将激光器多路控制信号整合在一起,设计并制作完成了一套结构紧凑,使用方便,操作智能,运行稳定的全固态激光器综合电控系统.     

Beta-decay studies of neutron-rich Sc- Cr nuclei

The neutron-rich nuclei ₂₁^{57, 58}Sc, ₂₂^58-60Ti, ₂₃^60-63V, ₂₄^62-66Cr have been produced at Ganil via interactions of a 61.8A MeV ⁷⁶Ge beam with a ⁵⁸Ni target. Beta-decay studies have been performed using combined - and -ray spectroscopy. Half-lives have been determined and -decay schemes are proposed for ⁵⁸Ti, ⁶¹V and ⁶²Cr. From these studies, new hints for the existence of -decaying isomers in ⁶⁰V and in ⁶²Mn are provided. These results are compared to shell model calculations. The role of the f_7/2- f_5/2 proton-neutron interaction is examined through its influence on the lifetime values.     

Precursory phenomena associated with large avalanches in the long-range connective sandpile (LRCS) model

Reduction in b-values before a large earthquake is a very popular topic for discussion. This study proposes an alternative sandpile model being able to demonstrate reduction in scaling exponents before large events through adaptable long-range connections. The distant connection between two separated cells was introduced in the sandpile model. We found that our modified long-range connective sandpile (LRCS) system repeatedly approaches and retreats from a critical state. When a large avalanche occurs in the LRCS model, accumulated energy dramatically dissipates and the system simultaneously retreats from criticality. The system quickly approaches the critical state accompanied by the increase in the slopes of the power-law frequency-size distributions of events. Afterwards, and most interestingly, the power-law slope declines before the next large event. The precursory b-value reduction before large earthquakes observed from earthquake catalogues closely mimics the evolution in power-law slopes for the frequency-size distributions of events derived in the LRCS models. Our paper, thus, provides a new explanation for declined b-values before large earthquakes.     

显微镜工作台定位系统的设计与实现

设计了一套基于AT89C52单片机的显微镜工作台定位系统。机械传动部分采用小模数齿轮实现机械运动和动力的传递,单片机电路控制部分实现计数脉冲的获取和电机的控制,上位机控制环节完成用户命令的发布。该系统可以按照预先设定的方式控制电机,实现显微镜工作台的二维运动,两方向重复定位精度±50μm,满足了多波长光存储实验的要求,同时为医疗检验提供了自动化手段。     

Coincidence Doppler shift lifetime measurements in 73,74Se and 74Br using the EUROBALL Cluster cube array

Subpicosecond lifetimes of high spin states in the rotational nuclei ⁷³Se, ⁷⁴Se and ⁷⁴Br have been measured using the ⁵⁸Ni +¹⁹F compound reaction and the Doppler Shift Attenuation method. Six EUROBALL Cluster detectors arranged in cube geometry allowed us to select the relevant transitions in γγ coincidence mode. The high counting statistics achieved in this setup also facilitated the determination of average sidefeeding times, which were found to agree rather well with the results of Monte-Carlo calculations of the particle and γ-ray evaporation process. The deduced quadrupole strengths and deformations are compared with the results of previous measurements and the predictions of Cranked Shell Model calculations. In ⁷⁴Br, a large and constant prolate deformation of β₂= 0.37(1) was found for the presumed 4⁺ and 3⁻ two-quasiparticle bands. Received: 2 July 1999