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.     

Entropy of Bogoliubov automorphisms of the canonical anticommutation relations

We compute the entropyh _A ( _U ) in the sense of Connes, Narnhofer and Thirring of Bogoliubov automorphisms _U of the CAR-algebra with respect to invariant quasifree states _A with 0A1 having pure point spectrum.Supported in part by a grant from the National Science Foundation     

Extended UNIQUAC model for thermodynamic modeling of CO2 absorption in aqueous alkanolamine solutions

The extended UNIQUAC model [K. Thomsen, P. Rasmussen, Chem. Eng. Sci. 54 (1999) 1787–1802] was applied to the thermodynamic representation of carbon dioxide absorption in aqueous monoethanolamine (MEA), methyldiethanolamine (MDEA) and varied strength mixtures of the two alkanolamines (MEA–MDEA). For these systems, altogether 13 interaction model parameters are adjusted. Out of these parameters, 11 are temperature dependent.     

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.     

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     

EARLY CELL KINETIC EFECTS OF A SINGLE DOSE OF NARROW-BANDED ULTRAVIOLET B IRRADIATION ON THE RAT CORNEAL EPITHELUM

Abstract— The right eyes of 40 rats were exposed to a signal erythemogenic dose fo ultraviolet B irradiation (UVB) at 297nm. The irradiation was directed perpenddicualr to the center of the cornea. The left eyes served as controls. The animals were randomly assigned into 10 groups. The labelling index (LI) after pluse labeling the tritiated thymidine and the mitotic rate (MR) after Colcemid administration were registered in the corneal epithelium at predetermined intervals up to 96 h after the irradiation. A mathematical method was used to corealted corresponding corneal areas from the different animals. In the central the LI was considerably reduced up to 36h after the irradiation. The LI increased toward the peripheral cornea and reached normal values at the limbal area. The MR was also reduced up to 36h. However, this reduction was over the entire epithelium. The block in cell proliferation was followed by increased proliferation.     

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.