Uniform random number generation

In typical stochastic simulations, randomness is produced by generating a sequence of independent uniform variates (usually real-valued between 0 and 1, or integer-valued in some interval) and transforming them in an appropriate way. In this paper, we examine practical ways of generating (deterministic approximations to) such uniform variates on a computer. We compare them in terms of ease of implementation, efficiency, theoretical support, and statistical robustness. We look in particular at several classes of generators, such as linear congruential, multiple recursive, digital multistep, Tausworthe, lagged-Fibonacci, generalized feedback shift register, matrix, linear congruential over fields of formal series, and combined generators, and show how all of them can be analyzed in terms of their lattice structure. We also mention other classes of generators, like non-linear generators, discuss other kinds of theoretical and empirical statistical tests, and give a bibliographic survey of recent papers on the subject.     

Mersenne数$M_p$都是孤立数

设p是素数,M_P=2~P-1.本文证明了M_P都是孤立数.     

Tuning size and catalytic activity of nano-clusters of cobalt oxide

Cobalt oxides were prepared by three different methods: (1) by reacting cobalt nitrate with oxalic acid, (2) co-precipitating cobalt nitrate with sodium carbonate, and (3) using sodium dodecyl sulphate as organic surfactant. All three samples were characterized before and after calcination by solvent extraction and the resulting products examined by IR spectroscopy. In the case of method 3, the removal of surfactant was followed by TGA studies. Products from all three methods were identified by XRD. Peaks in low angle XRD indicate the porous nature of the oxides. The morphology of the pores was studied by transmission electron microscopy. Some irregular pore structures were obtained for samples from methods 1 and 2, with an average size of 4–6 nm. Only the product from method 3 using SDS as template showed ordered structure and optimum size, and Brunauer-Emmet-Teller surface areas of the as-prepared, as well as the treated samples, exhibited H3 type hysteresis. The samples from the three methods were used as catalysts in the oxidation reaction of cyclohexane under mild conditions and the catalytic efficiency of the cobalt oxide was comparable with mesoporous cobalt oxides.     

反超图的笛卡儿积的上色数

讨论反超图的笛卡儿积的着色理论 ,求出了满足一定条件的反超图的笛卡儿积的上色数 .     

n元等比级数

定义了n元等比数列、n元等比级数,给出了它们的通项公式及前n项和.并解决了多元等比级数的敛散性问题,求出了多元等比级数的和.指出了多元等比数列及多元等比级数在特殊情况下与一元等比数列及一元等比级数的一致性.     

Decomposition of organic salts of some d and f metals

The thermal decomposition in non-isothermal conditions of formates, acetates, propionates and butyrates of Mn, Co, Zn, Cd, Eu, Sm and Ni was studied. The observed compensation effect allows us to calculate the isokinetic temperature. A selective activation mechanism was suggested. This leads to a good agreement between kinetic and spectroscopic data. This revised version was published online in July 2006 with corrections to the Cover Date.     

关于艾森斯坦因判别法的间接应用

探讨了间接应用艾森斯坦因判别法判断整系数多项式在有理数域上不可约的两种途径.     

Kerr介质中级联三能级原子与压缩相干态相互作用的光子统计演化

本文研究了存在Kerr介质的高Q腔中压缩相干态与级联三能级原子相互作用的光子统计演化规律,讨论了光场参数、Kerr介质及相干振幅对平均光子数的影响.     

Topological order in the phase diagram for high-temperature superconductors with point defects

Applying a Lindemann like criterion obtained previously by Kierfeld et al. [J. Kierfeld, T. Nattermann, T. Hwa, Phys. Rev. B 55 (1997) 626], we estimate the magnetic field and temperature for a high-T_c superconductor, at which a topologically ordered vortex glass phase becomes unstable with respect to a disorder-induced formation of dislocations. The employed criterion is shown to be equivalent to a conventional phenomenological Lindemann criterion including the values for the numerical factors, i.e., for the Lindemann number. The positional correlation length of the topologically ordered vortex glass is calculated.     

组合原则回溯

从组合原则产生的背景和关键入手，分析和叙述了里兹的组合原则在光谱学上的重要意义，同时，也阐述了它与玻尔氢原子理论之间的关系。