An investigation of finite-size scaling for systems with long-range interaction: The spherical model

A method is suggested for the derivation of finite-size corrections in the thermodynamic functions of systems with pair interaction potential decaying at large distancesr asr ^{–d –} , whered is the space dimensionality and>0. It allows for a unified treatment of short-range (=2) and long-range (<2) interaction. The asymptotic analysis is illustrated by the mean spherical model of general geometryL ^d–d× ^d subject to periodic boundary conditions. The Fisher-Privman equation of state is generalized to arbitrary real values ofd, 0d. It is shown that the-expansion may be used to study the breakdown of standard finite-size scaling at the borderline dimensionalities.     

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.     

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.     

On Super-KMS functionals and entire cyclic cohomology

We formulate the super-KMS condition suggested by Connes and Kastler, in the context of entire cyclic cohomology of quantum algebras. We show that the Chern character of Jaffe, Lesniewski, and Osterwalder — associated by Kastler to a super-KMS functional — satisfies the entire growth condition. Hence, a super-KMS functional defines a cocycle for the entire cyclic cohomology of quantum algebras.Supported in part by the National Science Foundation.     

The elimination of fast variables in complex chemical reactions. III. Mesoscopic level (irreducible case)

The master equation for a complex chemical reaction cannot always be reduced to a simpler master equation, even if there are fast and slow individual reaction steps. Nevertheless the elimination of intermediates can be carried out with the help of the-expansion. This is illustrated with a well-known complex reaction: the dissociation of N₂O₅. It is shown that the intrinsic fluctuations in the N₂O₅ decay are larger than those implied by the master equation suggested by the macroscopic rate law.     

纳米二氧化钛粒子分散性能的研究

以四氯化钛为原料，采用溶胶-凝胶法技术合成路线，获得了平均粒径为63nm的二氧化钛粉末。采用分散技术，不仅可以改善粒子的分散性能，而且对粒子的生长也起到一定的抑制作用。研究表明：(1)采用SDS作为分散剂时，其极性基团和非极性基团分别与水和纳米TiO2粒子相结合，从而阻隔了TiO2粒子的团聚，起到分散作用。(2)以稀土元素La作为分散剂，其独特的轨道结构，不仅扩大了能量吸收的范围，更重要的是它与TiO2形成的络合物，使其成为相对独立的小团体，而它本身很小的固溶度使其难于形成合金化组元，结果被释放出来，从而形成更小的纳米TiO2粒子，起到分散纳米TiO2粒子的作用，并同时抑制纳米TiO2粒子的生长。     

7-氮杂-3,6-二氧杂-二环[3.3.0]辛-2-酮类化合物合成的新方法

5-甲氧基-2-（5H）-呋喃酮与氮酸硅烷基酯通过1，3-偶极环加成反应可以为7-氮杂-4-甲氧基-3，6-二氧杂-二环[3.3.0]辛-2-酮类化合物提供新的合成途径。通过元素分析、IR、^1HNMR、^13CNMR、MS等波谱分析进行了结构表征。     

Asymmetric Baeyer—Villiger oxidation: control of stereoelectronic demand

The recent development of asymmetric Baeyer—Villiger oxidation of prochiral and racemic ketones is briefly summarized, focusing on the regio- and stereocontrol of the oxidation attained by regulating the stereoelectronic demand in the step of rearrangement of the Criegee intermediate.Based on the report presented at the International Conference Modern Trends in Organoelement and Polymer Chemistry dedicated to the 50th anniversary of the A. N. Nesmeyanov Institute of Organoelement Compounds of the Russian Academy of Sciences (Moscow, May 30–June 4, 2004).Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1784–1794, September, 2004.     

[2+2]-Photocycloaddition von Cyclohexen an 2-Acetyl-5,5-dimethyl-1,3-cyclohexandion und 3-Acetyl-1,5,5-trimethyl-2,4-pyrrolidindion

Summary Irradiation of solutions of excess cyclohexene and 2-acetyl-5,5-dimethyl-1,3-cyclohexanedione (1), and 3-acetyl-1,5,5-trimethyl-2,4-pyrrolidinedione (4) results mainly in the formation of 1,5-diones2 and5. These originate from intermediate cycloadducts of cyclohexene and theexo-enols of the cyclic 1,3-diketones. The yields decrease with increasing polarity of the solvent. In solution2 and5 are in equilibrium with the cyclic hemiacetales3 and6.