Statistical mechanics of thermal diffusion

Expressions of the flows of atoms A and B of a binary system in a crystal are derived as the response to the imposed gradients of temperature and chemical potentials. The formulation is done using the pair approximation of the Path Probability Method of irreversible statistical mechanics and atomic migration is assumed to be via the vacancy mechanism. The energy carried by photons (and electrons) under the temperature gradient is assumed to be independent of the atomic flux. For the case near equilibrium, linear relations are derived among the atomic fluxes, the energy flux (associated with atomic flux) and the gradients. The Onsager reciprocal relations are proved to hold among the coefficients, including those related to energy flows. The heat of transport (energy carried by a diffusing atom) and the heat conduction due to atomic flux are thus unambigously derived.     

Infinite Divisibility for Stochastic Processes and Time Change

General results concerning infinite divisibility, selfdecomposability, and the class L _m property as properties of stochastic processes are presented. A new concept called temporal selfdecomposability of stochastic processes is introduced. Lévy processes, additive processes, selfsimilar processes, and stationary processes of Ornstein–Uhlenbeck type are studied in relation to these concepts. Further, time change of stochastic processes is studied, where chronometers (stochastic processes that serve to change time) and base processes (processes to be time-changed) are independent but do not, in general, have independent increments. Conditions for inheritance of infinite divisibility and selfdecomposability under time change are given.     

Synthesis and biological evaluation of optically active 3-H-1-carbacephem compounds

3-H-1-Carbacephem nuclei with or without a 2 alpha- or 2 beta-methyl group were prepared via 2 + 2 cycloaddition followed by intramolecular Horner-Emmons cyclization. Optically active 3-H-1-carbacephem compounds were efficiently prepared by employing a penicillin acylase-producing microorganism in two ways. That is, the 7-phenylacetamide of a racemic carbacephem nucleus was hydrolyzed enantioselectively with the enzyme to afford the optically pure nucleus, which was then acylated to give antimicrobial compounds. Alternatively, a racemic carbacephem nucleus was directly and enantioselectively phenylglycylated with the enzyme. 3-H-1-Carbacephem nuclei appeared to be better substrates for penicillin acylase than penam or cephem nuclei of natural origin. 3-H-1-Carbacephem compounds showed potent antimicrobial activity; compound 32a exhibited activity comparable to that of ceftizoxime, a cephem analog with the same acyl group. It is of interest that the 3-H-1-carbacephem compound turned out to have more potent antimicrobial activity than its 3-substituted methyl analog.     

A new efficient synthesis of the biologically potent PGD2-analogue ZK118182

A highly stereoselective and practical synthetic method for ZK118182, which is chemically and metabolically stable and a biologically potent PGD₂-analogue developed by Schering AG, is reported.