Boron—nitrogen compounds : LXX. Boron derivatives of 3,3′-diaminodipropylamine

The reaction of borane(3) with 3,3′-diaminodipropylamine yields BH₂B-bridge associated [3,3′-bis(dihydroborylamino)dipropylamino]dihydroborane, 1-aminopropyl-1,3,2-diazaboracyclohexane, or 1,8,10,9-triazaboradecalin (I), depending on the reaction conditions and the stoichiometry of the reactants. If tris(dimethylamino)borane is treated with 3,3′-diaminodipropylamine, only I or 1-bis-(dimethylamino)boryl-1,8,10,9-triazaboradecalin are obtained.     

Boron-Nitrogen Compounds 83 [1]. Experimental and Theoretical Studies on Monomeric Iminoboranes

Nuclear magnetic resonance and vibrational spectroscopic data support the existence of liner C?N? B skeleton in monomeric iminoboranes of the type R₂C?N? BR. This allene-like arrangement of the central moiety of the compounds does not seem to enhance the N? B bond strength by interaction of this bond with the vicinal C?N bond. Rather, in the case of R′ being a hydrocarbon group, the nature of the N? B bond is similar to that found in (monoamino) diorganyl-boranes, R₂N? Br. Similarly, (CF₃)₂C?N? B[N(CH₃)₂]₂ may ve viewed as a trisaminoborane. However, the rigid C?N? BN₂ unit makes this compound colored and the electronic structure of the species was studied; theoretical and experimental data are in good agreement.     

Association equlibria in acetonitrile solution of tetracyanoquinodimethanides

Trimetric ion (TCNQ)^2?₃ has been discovered in mixed solutions of TCNQ and LiTCNQ in acetonitrile. The estimated association constant isK_T = 5.6 × 10¹⁰ øl² mol^?2.     

On Mobility and Einstein Relation for Tracers in Time-Mixing Random Environments

In this paper we rigorously establish the existence of the mobility coefficient for a tagged particle in a simple symmetric exclusion process with adsorption/desorption of particles, in a presence of an external force field interacting with the particle. The proof is obtained using a perturbative argument. In addition, we show that, for a constant external field, the mobility of a particle equals to the self-diffusivity coefficient, the so-called Einstein relation. The method can be applied to any system where the environment has a Markovian evolution with a fast convergence to equilibrium (spectral gap property). In this context we find a necessary relation between forward and backward velocity for the validity of the Einstein relation. This relation is always satisfied by reversible systems. We provide an example of a non-reversible system, where the Einstein relation is valid.This revised version was published online in March 2005 with corrections to the page numbers.     

The study of hydronium NASICON conductivity with deuterium

The ionic conductivity of the bulk phase of bonded hydronium NASICON (Hyceram^TM) was measured at equilibrium with an H₂O/N₂ and then a D₂O/N₂ atmosphere, each at 100% relative humidity and 75% relative humidity over the temperature range 25°C to 50°C. At 100% relative humidity and 25°C, the protonic system had a bulk conductivity of 5.0×10⁻⁴ S/cm and an activation energy of 17.3kJ/mole; the same sample, when deuterated, had a bulk conductivity of 2.2×10⁻⁴ S/cm and an activation energy of 19.3kJ/mole. At 75% relative humidity and 25°C, the conductivity of the protonated system decreased to 1.4×10⁻⁴S/cm with an activation energy of 24.1 kJ/mole. The deuterated sample at 75% relative humidity had a bulk conductivity of 5.4×10⁻⁵ S/cm with an activation energy of 26.0 kJ/mole. The isotope effect suggested a proton hopping (Grotthus) mechanism as the means by which the protons pass through the lattice.     

Polarization justified Fukui functions: the theory and applications for molecules

The Fukui functions based on the computable local polarizability vector have been presented for a group of simple molecules. The necessary approximation for the density functional theory softness kernel has been supported by a theoretical analysis unifying and generalizing early concepts produced by the several authors. The exact relation between local polarizability vector and the derivative of the nonlocal part of the electronic potential over the electric field has been demonstrated. The resulting Fukui functions are unique and represent a reasonable refinement when compared to the classical ones that are calculated as the finite difference of the density in molecular ions. The new Fukui functions are strongly validated by their direct link to electron dipole polarizabilities that are reported experimentally and by other computational methods.     

On the sector condition and homogenization of diffusions with a Gaussian drift

In this paper we present the functional central limit theorem for a class of Markov processes, whose L²-generator satisfies the so-called graded sector condition. We apply the result to obtain homogenization theorems for certain classes of diffusions with a random Gaussian drift. Additionally, we present a result concerning the regularity of the effective diffusivity tensor with respect to the parameters related to the statistics of the drift. The abstract central limit theorem, see Theorem 2.2, is obtained by applying the technique used in Sethuraman et al. (Comm. Pure Appl. Math. 53 (2000) 972) to the case of infinite particle systems.     

Gas-liquid phase transition and singularities

A new model for the space of undercritical states of a gas-liquid system is proposed. Simple, physically motivated mathematical hypotheses among which stsbility plays an essential role, determine differential types of germs of pressure and temperature at the critical point. They are connected with the class D⁺₄ of Arnold's classification. The general configuration of vaporization and condensation curves is examined. As a result, Guggenheim's one-third law is obtained.     

On the Asymptotic Behavior of Solutions of the Heat Equation with a Random,Long-Range Correlated Potential

In this note we investigate the asymptotic behavior of the solutions of the heat equation with random, fast oscillating potential