Direct measurement of gas solubility and diffusivity in poly(vinylidene fluoride) with a high-pressure microbalance

We present solubility and diffusion data for the gases methane and carbon dioxide in the polymer poly(vinylidene fluoride). The polymer was cut from extruded piping intended for use in offshore oil and gas applications. Measurements were carried out using a purpose-built high-pressure microbalance. These properties were determined in the temperature range 80-120 °C and in the pressure range 50-150 bar for methane and 20-40 bar for carbon dioxide. In general, good agreement was obtained for similar measurements reported in the literature. Solubility follows a Henry’s law (linear) dependence with pressure. Diffusion coefficients for each of the gases in the polymer were also measured using the balance. Activation energies for diffusion and heats of solution for the two gases in the polymer were also determined.     

Entropy of some automorphisms of theII 1-factor of the free group in infinite number of generators

Summary LetL(F ) be theII ₁-factor defined by the free groupF in infinite number of generators. It is shown that for a class of automorphisms ofL(F ) arising from bijections of the set of generators ofF on itself, and including the free shift, the entropy is zero.Oblatum 15-III-1992     

Improved solution of displacements due to a compacting reservoir over a rigid basement

Geertsma’s analytical method is often used to compute strain and stress changes around a compacting geological reservoir. The present work extends Geertsma’s solution by adding a rigid layer beneath the compacting reservoir. Analytical formulae are presented for all the components of displacement of a point in the subsurface. Our derivation includes the correction of an error found in the paper written by Sharma in 1956.     

The Variational Principle for a Class of Asymptotically Abelian C*-Algebras

Let (A,α) be a C^*-dynamical system. We introduce the notion of pressure P _α(H) of the automorphism α at a self-adjoint operator H∈A. Then we consider the class of AF-systems satisfying the following condition: there exists a dense α-invariant *-subalgebra ? of A such that for all pairs a,b∈? the C^*-algebra they generate is finite dimensional, and there is p=p(a,b)∈ℕ such that [α ^j (a),b]= 0 for |j|≥p. For systems in this class we prove the variational principle, i.e. show that P _α(H) is the supremum of the quantities h _φ(α) −φ(H), where h _φ(α) is the Connes–Narnhofer–Thirring dynamical entropy of α with respect to the α-invariant state φ. If H∈A, and P _α(H) is finite, we show that any state on which the supremum is attained is a KMS-state with respect to a one-parameter automorphism group naturally associated with H. In particular, Voiculescu's topological entropy is equal to the supremum of h _φ(α), and any state of finite maximal entropy is a trace. Received: 19 April 2000 / Accepted: 14 June 2000     

Homogeneity of the state space of factors of type III1

A factor M is of type III₁ if and only if the action of its unitary group on its state space by inner automorphisms is topologically transitive in the norm topology.     

Ergodic Theory and Maximal Abelian Subalgebras of the Hyperfinite Factor

Let T be a free ergodic measure-preserving action of an abelian group G on (X,μ). The crossed product algebra R_T=L^∞(X,μ)? G has two distinguished masas, the image C_T of L^∞(X,μ) and the algebra S_T generated by the image of G. We conjecture that conjugacy of the singular masas S_T⁽¹⁾ and S_T⁽²⁾ for weakly mixing actions T⁽¹⁾ and T⁽²⁾ of different groups implies that the groups are isomorphic and the actions are conjugate with respect to this isomorphism. Our main result supporting this conjecture is that the conclusion is true under the additional assumption that the isomorphism γ : R_T⁽¹⁾→R_T⁽²⁾ such that γ(S_T⁽¹⁾)=S_T⁽²⁾ has the property that the Cartan subalgebras γ(C_T⁽¹⁾) and C_T⁽²⁾ of R_T⁽²⁾ are inner conjugate. We discuss a stronger conjecture about the structure of the automorphism group Aut(R_T,S_T), and a weaker one about entropy as a conjugacy invariant. We study also the Pukanszky and some related invariants of S_T, and show that they have a simple interpretation in terms of the spectral theory of the action T. It follows that essentially all values of the Pukanszky invariant are realized by the masas S_T, and there exist non-conjugate singular masas with the same Pukanszky invariant.     

Spectral Evidence for a 2:1 Complex Between Titanium Tetrachloride and Ethyl Benzoate

Abstract

Infrared spectra of codeposited ethyl benzoate with excess titanium tetrachloride at 80 K revealed a novel 2:1 complex, where the inorganic entity is proposed to be a dimeric, triple bridged titanium tetrachloride unit. The ester is complexed to one of the octahedral titanium units through the carbonyl group. Compared to the 2:2 complex there are ν_c=o' ν _α-C-Oand ν_Ti-O shifts of -40/-47, +4/+24 and +16/17 cm^?1, depending on which of the ¹⁸O-carbonyl or d⁵-ethyl isotopic congeners is considered.