The Choquet-Deny convolution equation μ=μ*σ for probability measures on Abelian semigroups

In this note, we characterize the regular probability measures satisfying the Choquet-Deny convolution equation =* on Abelian topological semigroups for a given probability measure .     

Statistical mechanics of probabilistic cellular automata

We investigate the behavior of discrete-time probabilistic cellular automata (PCA), which are Markov processes on spin configurations on ad-dimensional lattice, from a rigorous statistical mechanics point of view. In particular, we exploit, whenever possible, the correspondence between stationary measures on the space-time histories of PCAs on ^d and translation-invariant Gibbs states for a related Hamiltonian on ( ^d+1). This leads to a simple large-deviation formula for the space-time histories of the PCA and a proof that in a high-temperature regime the stationary states of the PCA are Gibbsian. We also obtain results about entropy, fluctuations, and correlation inequalities, and demonstrate uniqueness of the invariant state and exponential decay of correlations in a high-noise regime. We discuss phase transitions in the low-noise (or low-temperature) regime and review Toom's proof of nonergodicity of a certain class of PCAs.     

A Monte Carlo method for an objective Bayesian procedure

This paper describes a method for an objective selection of the optimal prior distribution, or for adjusting its hyper-parameter, among the competing priors for a variety of Bayesian models. In order to implement this method, the integration of very high dimensional functions is required to get the normalizing constants of the posterior and even of the prior distribution. The logarithm of the high dimensional integral is reduced to the one-dimensional integration of a cerain function with respect to the scalar parameter over the range of the unit interval. Having decided the prior, the Bayes estimate or the posterior mean is used mainly here in addition to the posterior mode. All of these are based on the simulation of Gibbs distributions such as Metropolis' Monte Carlo algorithm. The improvement of the integration's accuracy is substantial in comparison with the conventional crude Monte Carlo integration. In the present method, we have essentially no practical restrictions in modeling the prior and the likelihood. Illustrative artificial data of the lattice system are given to show the practicability of the present procedure.     

Relationships between characteristics in periodic Poisson queues

We study single server periodic queues in the day equilibrium conditions. The following characteristics of interest are considered at time of dayt: V^p(t)-the work load, L^p(t)-the number of customers and u^p(t)-the departure rate. We give relationships between E[V^p(t)], E[L^p(t)] and u^p(t). We also prove that E[V^p(t)] < and E[L^p(t)] < provided the second moment of the service time is finite.     

Likelihood estimation of soft-core interaction potentials for Gibbsian point patterns

The likelihood method is developed for the analysis of socalled regular point patterns. Approximating the normalizing factor of Gibbs canonical distribution, we simultaneously estimate two parameters, one for the scale and the other which measures the softness (or hardness), of repulsive interactions between points. The approximations are useful up to a considerably high density. Some real data are analyzed to illustrate the utility of the parameters for characterizing the regular point pattern.     

Disintegration and perfectness of measure spaces

For every finite measure space (X,A,P) we find a unique representation P=Q₁+Q₂+Q₃ such that Q₁ is compact, Q₂ is perfect and purely noncompact and Q₃ is purely nonperfect. We show that every Pachl-_O-disintegrable probability space is Ramachandran-_O-disintegrable and therefore perfect and under a certain condition we prove the equivalence between compactness and Ramachandran-_O-disintegrability.     

Evidence for the poisson distribution for quasi-energies in the quantum kicked-rotator model

A transformation on the two-dimensional torus which is related to the problem of limit distribution for the distance between the levels in the kicked-rotator model is considered. The first four moments of the r.w. which describe the numbers of visits of a point in a rectangle of measure are calculated. It is shown that when 0 they converge to the first four moments of a Poisson r.w.     

Absence of symmetry breaking for systems of rotors with random interactions

We prove that Gibbs states for the Hamiltonian , with thes _x varying on theN-dimensional unit sphere, obtained with nonrandom boundary conditions (in a suitable sense), are almost surely rotationally invariant if withJ _xy i.i.d. bounded random variables with zero average, 1 in one dimension, and 2 in two dimensions.     

高碘酸法测定水中锰的改进

介绍了一种室温下测定水中锰的方法，经检验，其显色反应可在短时间内完成，且色泽稳定，精密度和准确度均能达到分析要求。     

Influence of hydrogen bonding on the properties of water molecules adsorbed in zeolite frameworks

Three hydrated aluminosilicate frameworks—LiABW, NaNAT, and BaEDI—are partly optimized with the periodic Hartree–Fock CRYSTAL95 code. In particular, we optimized the positions of the adsorbed water molecules including the positions of the framework cations (ABW, NAT) or part of the framework atomic positions (ABW). This allowed us to compare cation–water clusters in the gas and adsorbed states and discuss the influence of hydrogen bonding to the framework oxygen atoms or to the neighbor water molecules on the atomic properties (quadrupole coupling constant, anisotropy of electric field gradient) of the adsorbed water molecules. The LiBIK structure obtained from X‐ray diffraction is also considered to illustrate the hydrogen bonds occurring between adsorbed water molecules. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003