Dynamic complexity of optimal paths and discount factors for strongly concave problems

We study the relationship between the dynamical complexity of optimal paths and the discount factor in general infinite-horizon discrete-time concave problems. Given a dynamic systemx _t+1=h(x _t ), defined on the state space, we find two discount factors 0 < ^{* **} < 1 having the following properties. For any fixed discount factor 0 < < ^*, the dynamic system is the solution to some concave problem. For any discount factor ^** < < 1, the dynamic system is not the solution to any strongly concave problem. We prove that the upper bound ^** is a decreasing function of the topological entropy of the dynamic system. Different upper bounds are also discussed.This research was partially supported by MURST, National Group on Nonlinear dynamics in Economics and Social Sciences. The author would like to thank two anonymous referees for helpful comments and suggestions.     

NMR study of the stoichiometry,stability and exchange kinetics of complexation reaction between Pb2+ ion and 18-crown-6 in binary acetonitrile-water mixtures

Proton NMR was used to study the complexation reaction between lead ion and 18-crown-6 in a number of binary acetonitrile-water mixtures. Formation constant for the resulting 11 complexes in different solvent mixtures was determined by computer fitting of the chemical shift-mole ratio data. There is an inverse relationship between the complex stability and amount of water in the mixed solvent. The dissociative kinetics of the complex was studied by proton line-shape analysis. The Arrhenius plots showed a distinct isokinetic temperature at about 25°C at which the decomplexation rate is more or less independent of the solvent composition. the complexation rate and the activation parameters E _a , H and S, for the exchange have been determined and found to be strongly solvent dependent. There is actually a linear relationship between the mole fraction of acetonitrile in the mixed solvent and logarithm of the stability constant as well as activation parameters.     

Moment closure hierarchies for kinetic theories

This paper presents a systematicnonperturbative derivation of a hierarchy of closed systems of moment equations corresponding to any classical kinetic theory. The first member of the hierarchy is the Euler system, which is based on Maxwellian velocity distributions, while the second member is based on nonisotropic Gaussian velocity distributions. The closure proceeds in two steps. The first ensures that every member of the hierarchy is hyperbolic, has an entropy, and formally recovers the Euler limit. The second involves modifying the collisional terms so that members of the hierarchy beyound the second also recover the correct Navier-Stokes behavior. This is achieved through the introduction of a generalization of the BGK collision operator. The simplest such system in three spatial dimensions is a 14-moment closure, which also recovers the behavior of the Grad 13-moment system when the velocity distributions lie near local Maxwellians. The closure procedure can be applied to a general class of kinetic theories.     

Positivity of entropy production in nonequilibrium statistical mechanics

We analyze different mechanisms of entropy production in statistical mechanics, and propose formulas for the entropy production ratee() in a state . When is steady state describing the long term behavior of a system we show thate()0, and sometimes we can provee()>0.     

Convergence of distorted Brownian motions and singular Hamiltonians

We prove a convergence theorem for sequences of Diffusion Processes corresponding to Dirichlet Forms of the kind .We obtain convergence in total variation norm of the corresponding probability measures on the path space C(₊;^d) under hypotheses which, for example, are satisfied in the case of H _loc ¹ ( ^d )-convergence of the 's, but we can allow more singular situations as regards the approximating sequences. We use then these results to give a criterion of convergence for generalized Schrödinger operators in which the potential function should not necessarily exists as a measurable function. We obtain convergence not only in strong resolvent sense, but we also obtain convergence in the uniform operator topology up to sets of arbitrarily small Lebesgue measure. Applications to the problem of the approximation of ordinary Schrödinger operators by generalized ones corresponding to zero-range interactions are given.     

Spectrum of positive entropy multidimensional dynamical systems with a mixed time

It is shown that if an abelian countable group is such that is a finite group and every aperiodic positive entropy action of on a Lebesgue probability space has a countable Haar spectrum in the subspace , where denotes the Pinsker -
algebra of , then every aperiodic positive entropy action of on has the same property. A positive answer to the question of J.P. Thouvenot is obtained as a corollary.

     

Determination of thermodynamic functions of sorption for cyclohexyl-, piperidyl-, morpholyl-, and thiomorpholyl-n-alkanes by capillary gas-liquid chromatography

The values of partial molar free energy (G), enthalpy (H), and entropy (S) of sorption in the homologous series ofN-alkylpiperidines,N-alkylmorpholines,N-alkyl thiomorpholines, and alkylcyclohexanes were determined. It was found that the free energy of sorption is determined to a greater extent by the enthalpy term than by the entropy one. The free energy of sorption of the first homolog decreases when then-alkyl chain is attached directly to the carbon atom of the cycle and increases in the case ofN-alkylsubstituted heterocycles. The influence of the heteroatom nature on intermolecular interactions of homologs with the nonpolar stationary phase was quantitatively estimated on the basis of thermodynamic data.Dead time necessary for calculation of the retention factor was determined by the retention of methane injected into the column simultaneously with the sample.Translated from Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 2030–2032, August, 1996.     

Effect of aryl ligands on the chemical hardness of arylmercury cations

¹⁹F NMR spectroscopy was used to study the exchange reactions involving 4-fluorothiophenoxides, 4-nitrophenoxides, chlorides, and acetates of arylmercury and triphenylphosphinegold. The analysis of the data on equilibrium constants allows one to obtain information on the comparative chemical hardness of ArHg⁺ and Ph₃PAu⁺ cations. The increase in the electron-donating ability of aryl ligands enhances the chemical hardness of ArHg⁺ cations, their influence being best described by ⁰ constants of substituted phenyl groups.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 5, pp. 1255–1260, May, 1996.     

Aryl-bis(triorganylphosphine)nickel phenoxides

Compounds of general formulatrans-ArNi(PR₃)₂OAr' (R = Et, cyclohexyl; Ar = 2-MeC₆H₄, 2-FC₆H₄; Ar' = 4-FC₆H₄, 4-NO₂C₆H₄) were synthesized by the reaction of Ar'OK with cationic nickel complexes generated by treatment of ArNi(PR₃)₂Cl with TlBF₄. Syntheses of 4-fluorophenoxide complexes, ArNi(PR₃)₂OC₆H₄F-4, additionally give some quantities oftrans-[ArNi(PR₃)₂OC₆H₄F-4][HOC₆H₄F-4] adducts. Exchange reactions MeC₆H₄Ni(PEt₃)₂OC₆H₄F-4 + XC₆H₄OH 2-MeC₆H₄Ni(PEt₃)₂OC₆H₄X + 4-FC₆H₄OH were studied in THF. The equilibrium is shifted to the right as the acidity of ArOH increases. A linear relationship between lgK _eq and pK _a of XC₆H₄OH in DMSO was found. A conclusion concerning the strong polarization of the Ni-O bond was made on the basis of an analysis of the chemical shifts of fluorine atoms in 2-MeC₆H₄Ni(PEt₃)₂OC₆H₄F-4.Translated fromIvestiya Akademii Nauk. Seriya Khimicheskaya, No. 11, pp. 2266–2271, November, 1995.     

Magnetic exchange interactions in tetrabromocuprate compounds

Magnetic and structural data for 28 compounds containing the tetrabromocuprate ion are presented. The parameters which affect the strength and sign of the magnetic superexchange interaction via non-bonding contacts between bromide ions are described and a system for describing the topology of the interaction between tetrahedra is proposed. Analysis of the data suggests that the primary factors affecting the magnetic exchange are the Br?Br distance, the Cu-Br?Br angle and the Cu-Br?Br-Cu dihedral angle.