Poincaré cycles and ergodic behavior of a linear diatomic chain

The ergodic behavior of a linear diatomic chain is shown to be analogous to that of a linear monatomic chain. Starting with the expressions for the time-relaxed correlation functions between any two particles in the chain, we show that the existence of Poincaré cycles is not inconsistent with the development of an equilibrium state. Also, we show that those dynamical variables that are ergodic for the linear monoatomic chain remain ergodic in the diatomic chain. It is shown that the autocorrelation functions for particles with equal or different masses decay in time ast ^–1/2 .This work was completed when the author was associated with the Institute for Fluid Dynamics and Applied Mathematics, University of Maryland and supported by the United States Air Force through the Air Force Office of Scientific Research of the Air Research and Development Command under contract No. AF18(600)1315.     

Interaction information and Markov chain

The problem of multivariate information analysis is considered. First, the interaction information in each dimension is defined analogously according to McGill [4] and then applied to Markov chains. The property of interaction information zero deeply relates to a certain class of weakly dependent random variables. For homogeneous, recurrent Markov chains with m states, m ≥ n ≥3, the zero criterion of n-dimensional interaction information is achieved only by (n ? 2)-dependent Markov chains, which are generated by some nilpotent matrices. Further for Gaussian Markov chains, it gives the decomposition rule of the variables into mutually correlated subchains.     

1H NMR study of the catalytic system (rac-Me2Si(2-Me,4-PhInd)2ZrCl2— polymethylalumoxane)—triisobutylaluminum

The products of the reactions of polymethylalumoxane (MAO) with triisobutylaluminum (TIBA), rac-Me₂Si(2-Me,4-PhInd)₂ZrCl₂ (1) with MAO (1 + MAO), and (1 + MAO) + TIBA were studied by ¹H NMR at different molar ratios of the components. When the ratio Al_TIBA/Al_MAO is ∼6, the reaction between MAO and TIBA involves the replacement of the methyl group of MAO by isobutyl groups and the formation of isobutylmethylalumoxane or mixed isobutylmethylalumoxane structures. When the TIBA content in the system increases to 30 mol.%, these structures are rearranged to form products with a low degree of association. With the equimolar ratio of the reactants, the main reaction products are tetraisobutylalumoxane and polyisobutylalumoxane. The 1 + MAO system with the molar ratio Al_MAO/Zr = 50 affords a MAO-bonded monomethyl monochloride derivative [L₂ZrCl-μ-Me]^δ+[MAO]^δ−. An increase in this ratio to 150 produces intermediate binuclear complexes [L₂ZrCl-μ-Me-MeZrL₂]⁺[MAO]⁻ and [Me₂Al-(μ-Me)₂-ZrL₂]⁺[MAO]⁻. The addition of TIBA induces the replacement of the ZrMe groups by isobutyl groups at the first step of the interaction and formation of nonidentified reaction products at the subsequent steps. __________ Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 4, pp. 934–940, April, 2005.     

An efficient algorithm for finding the largest chain graph according to a given chain graph

Chain graph (CG) is a general model of graphical Markov models. Some different chain graphs may describe the same conditional independence structure, then we say that these CGs are Markov equivalent. In 1990 Frydenberg showed that every class of Markov equivalent CGs has a CG which is called the largest chain graph with the greatest number of lines. This paper presents an efficient algorithm for finding the largest chain graph of the corresponding Markov equivalent class of a given CG. The computational complexity of the algorithm is O(n3). It is more efficient than the complexity O(n!) of the present algorithms. Also a more intuitive graphical characterization of the largest chain graph is provided based on the algorithm in this paper.     

Group automorphisms with few and with many periodic points

For each a compact group automorphism is constructed with the property that

This may be interpreted as a combinatorial analogue of the (still open) problem of whether compact group automorphisms with any given topological entropy exist.

     

Two-component ising chain with nearest-neighbor interaction

The one-dimensional, two-component linear Ising chain with nearest-neighbor interaction is formulated by using the transfer matrix method, with emphasis placed on the case in which the two components are randomly distributed along the chain. Certain recurrence formulas appear such that themth-order partition function of one of the components is dependent on the lower-order ones. The algorithm provides a working basis for discussing the thermodynamic and magnetic functions with various concentrations of one of the components. An exact expression for the partition function is derived for a linear chain which is composed of a periodic distribution of the two components. The construction of a periodic sequence which would approximate a random distribution of the two components is briefly discussed.This study was partially supported by ARPA and monitored by ONR(N00014-17-0308).     

Review of particle properties

This review of the properties of leptons, mesons, and baryons is an updating of Review of Particle Properties, Particle Data Group [Rev. Mod. Phys. 45, No. 2, Part II, Supplement (1973)]. Data are evaluated, listed, averaged, and summarized in tables.     

Group decisions I. In arbitrary spaces of fuzzy binary relations

This article solves the problem of finding a set of group decisions that satisfy the classical Pareto unanimity principle for the case of initial data represented as fuzzy relations of individual preference. The solution proceeds from results obtained in studying the structure of convex (in the sense defined here) sets and their convex hulls. In the first part that study is carried out for spaces of arbitrary fuzzy binary relations.     

Biomethylation and biotransformation of arsenic in a freshwater food chain: Green alga (chlorella vulgaris)→shrimp (neocaridina denticulata)→killifish (oryzias iatipes)

Tolerance, bioaccumulation, biotransformation and excretion of arsenic compounds by the fresh–water shrimp (Neocaridina denticulata) and the killifish (Oryzias latipes) (collected from the natural environment) were investigated. Tolerances (LC₅₀) of the shrimp against disodium arsenate [abbreviated as As(V)], methylarsonic acid (MAA), dimethylarsinic acid (DMAA), and arsenobetaine (AB) were 1.5, 10, 40, and 150μg As ml^?1, respectively. N. denticulata accumulated arsenic from an aqueous phase containing 1 μg As ml^?1 of As(V), 10 μg As ml^?1 of MAA, 30 μg As ml^?1 of DMAA or 150 μg As ml^?1 of AB, and biotransformed and excreted part of these species. Both methylation and demethylation of the arsenicals were observed in vivo. When living N. denticulata accumulating arsenic was transferred into an arsenic–free medium, a part of the accumulated arsenic was excreted. The concentration of methylated arsenicals relative to total arsenic was higher in the excrement than in the organism. Total arsenic accumulation in each species via food in the food chain Green algae (Chlorella vulgaris) → shrimp (N. denticulata) → killifish (O. latipes) decreased by one order of magnitude or more, and the concentration of methylated arsenic relative to total arsenic accumulated increased successively with elevation in the trophic level. Only trace amounts of monomethylarsenic species were detected in the shrimp and fish tested. Dimethylarsenic species in alga and shrimp, and trimethylarsenic species in killifish, were the predominant methylated arsenic species, respectively.     

皮质激素侧链合成方法的新进展

综述了近五年来由１７－甾体酮基合成皮质激素侧链方法的进展。参考文献１４篇。