Cation transport at 25°c from binary Tl+Mn+ and K+Mn+ nitrate mixtures in a H2OCHCl3H2O liquid membrane system containing a series of macrocyclic polyether carriers

Carrier-mediated cation fluxes were determined using a H₂OCHC1₃H₂O liquid merebrane system for TlNO₃ and for binary mixtures of either TlNO₃ or KNO₃ with alkali metal ions, alkaline earth metal ions, and Pb²⁺ (in the case of TlNO₃). Both macrocyclic polyether and cryptand ligands were used as carriers. In Tl⁺Mⁿ⁺ mixtures, selective transport of Tl⁺ was found over all cations studied, except in the cases of Ag⁺ by 2.2 and of Pb²⁺ by 18C6, DC18C6, ClDKP18C6, and 2.2. Generally, K⁺ was transported selectively from K⁺Mⁿ⁺ mixtures, except in the cases of K⁺Tl⁺ mixtures in which Tl⁺ was transported selectively in all cases. A model relating cation flux to log K(CH₃OH) for Mⁿ⁺—macrocycle interaction and to ion-partitioning between the organic and aqueous phases was successful in rationalizing selective cation transport in most of the systems studied.     

Fermions coupled to autonomous (λΦ 4)3+1 theory

Recent Gaussian-effective-potential results for “autonomous”λΦ ⁴ theory, an apparently nontrivial, positive-λ, 3+1 dimensional theory, are extended to include a Yukawa coupling to fermions. The formerly massless bosons of the symmetric phase acquire a mass.     

The scattering of classical waves from inhomogeneous media

By extending Kato's theory of two Hilbert space scattering, we are able to formulate both optical and accoustical scattering from inhomogeneous media as strictly elliptic problems. We use this formulation to present simple proofs of the existence and completeness of scattering states.     

The application of thermal and mass chromatography to thermal oxidative degradation of polymers

A modification of a relatively new technique (thermal and mass chromatography) is used to study the volatile products evolved in the thermal oxidative degradation of isotactic poly(1-pentene) at 115° C under 100% oxygen. This new technique allows certain data to be obtained much more easily and more reliably than before.     

Support properties of the free measure for Boson fields

Let μ be the measure onI′ (? ^d ) corresponding to the Gaussian process with mean zero and covariance (f,(?Δ+1)^?1 g) onI (? ^d ). It is proven that the set $$( - \Delta _{d - 1} + 1)^{d/4 - \tfrac{1}{2} + \alpha } (1 + x^2 )^{d/4} [\log (2 + x^2 )]^\beta L^2 (\mathbb{R}^d )$$ has μ measure one if α>0 and β>1/2 and μ measure zero if α>0 and β<1/2; here Δ _d?1 is the Laplacian in anyd?1 dimensions whend>1 and Δ₀=Δ.