Experimental investigation of liquid chromatography columns by means of computed tomography

The efficiency of packed chromatographic columns was investigated experimentally by means of computed tomography (CT) techniques. The measurements were carried out by monitoring tracer fronts in situ inside the chromatographic columns. The experimental results were fitted using the equilibrium dispersive model (EDM) and varying the so called apparent axial dispersion coefficient. The additivity of the first and second central moments was exploited to estimate column efficiency in different regions of the column. The results showed that the columns under investigation offered a higher column efficiency in the centre compared to the wall region. Furthermore the void fraction in the vicinity of the walls was lower than that in the column core. For this reason the bands were conveyed faster in the central region of the column where the permeability was higher. This result is in good agreement with earlier findings.     

Free states of the canonical anticommutation relations

Each gauge invariant generalized free state _A of the anticommutation relation algebra over a complex Hilbert spaceK is characterized by an operatorA onK. It is shown that the cyclic representations induced by two gauge invariant generalized free states _A and _B are quasi-equivalent if and only if the operatorsA ^1/2–B ^1/2 and (I–A)^1/2–(I–B)^1/2 are of Hilbert-Schmidt class. The combination of this result with results from the theory of isomorphisms of von Neumann algebras yield necessary and sufficient conditions for the unitary equivalence of the cyclic representations induced by gauge invariant generalized free states.Work supported in part by US Atomic Energy Commission, under Contract AT (30-1)-2171 and by the National Science Foundation.     

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.     

Large groups of automorphisms of C*-algebras

Groups of *-automorphisms ofC*-algebras and their invariant states are studied. We assume the groups satisfy a certain largeness condition and then obtain results which contain many of those known for asymptotically abelianC*-algebras and for inner automorphisms and traces ofC*-algebras. Our key result is the construction in certain finite cases, where the automorphisms are spatial, of an invariant linear map of theC*-algebra onto the fixed point algebra carrying with it most of the relevant information.     

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.     

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.     

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