A class of almost C_0(K)-C*-algebras

We consider in this paper the family of exponential Lie groups Gn,µ, whose Lie algebra is an extension of the Heisenberg Lie algebra by the reals and whose quotient group by the centre of the Heisenberg group is an ax + b-like group. The C*-algebras of the groups Gn,µ give new examples of almost C0(K)-C*-algebras.

Reduced K-theory for Azumaya algebras

Abstract In the theory of central simple algebras, often we are dealing with abelian groups which arise from the kernel or co-kernel of functors which respect transfer maps (for example K-functors). Since a central simple algebra splits and the functors above are “trivial” in the split case, one can prove certain calculus on these functors. The common examples are kernel or co-kernel of the maps Ki(F)?Ki(D), where Ki are Quillen K-groups, D is a division algebra and F its center, or the homotopy fiber arising from the long exact sequence of above map, or the reduced Whitehead group SK1. In this note we introduce an abstract functor over the category of Azumaya algebras which covers all the functors mentioned above and prove the usual calculus for it. This, for example, immediately shows that K-theory of an Azumaya algebra over a local ring is “almost” the same as K-theory of the base ring. The main result is to prove that reduced K-theory of an Azumaya algebra over a Henselian ring coincides with reduced K-theory of its residue central simple algebra. The note ends with some calculation trying to determine the homotopy fibers mentioned above.

Trimethoxymethane as an alternative fuel for a direct oxidation PBI polymer electrolyte fuel cell

The oxidation of trimethoxymethane (TMM) (trimethyl orthoformate) in a direct oxidation PBI fuel cell was examined by on-line mass spectroscopy and on-line FTIR spectroscopy. The results show that TMM was almost completely hydrolyzed in a direct oxidation fuel cell which employs an acid doped polymer electrolyte to form a mixture of methylformate, methanol and formic acid. It also found that TMM was hydrolyzed in the presence of water at 120°C even without acidic catalyst. The anode performance improves in the sequence of methanol, TMM, formic acid/methanol, and methylformate solutions. Since formic acid is electrochemically more active than methanol, these results suggest that formic acid is probably a key factor for the improvement of the anode performance by using TMM instead of methanol under these conditions. © 1998 Elsevier Science Ltd. All rights reserved.

The solvable Lie group N_{6, 28}: an example of an almost C_0(\mathcal{K})-C*-algebra

Motivated by the description of the C*-algebra of the affine automorphism group N6,28 of the Siegel upper half-plane of degree 2 as an algebra of operator fields defined over the unitary dual View the MathML source of the group, we introduce a family of C*-algebras, which we call almost C0(K), and we show that the C*-algebra of the group N6,28 belongs to this class.

Contingent screening for down syndrome is an efficient alternative to non-disclosure sequential screening

Objective To present a first and second trimester Down syndrome screening strategy, whereby second-trimester marker determination is contingent on the first-trimester results. Unlike non-disclosure sequential screening (the Integrated test), which requires all women to have markers in both trimesters, this allows a large proportion of the women to complete screening in the first trimester. Methods Two first-trimester risk cut-offs defined three types of results: positive and referred for early diagnosis; negative with screening complete; and intermediate, needing second-trimester markers. Multivariate Gaussian modelling with Monte Carlo simulation was used to estimate the false-positive rate for a fixed 85% detection rate. The false-positive rate was evaluated for various early detection rates and early test completion rates. Model parameters were taken from the SURUSS trial. Results Completion of screening in the first trimester for 75% of women resulted in a 30% early detection rate and a 55% second trimester detected rate (net 85%) with a false-positive rate only 0.1% above that achievable by the Integrated test. The screen-positive rate was 0.1% in the first trimester and 4.7% for those continuing to be tested in the second trimester. If the early detection rate were to be increased to 45% or the early completion rate were to be increased to 80%, there would be a further 0.1% increase in the false-positive rate. Conclusion Contingent screening can achieve results comparable with the Integrated test but with earlier completion of screening for most women. Both strategies need to be evaluated in large-scale prospective studies particularly in relation to psychological impact and practicability.

SK1-like functors for division algebras

We investigate the group valued functor G(D) = D*/F*D' where D is a division algebra with center F and D' the commutator subgroup of D*. We show that G has the most important functorial properties of the reduced Whitehead group SK1. We then establish a fundamental connection between this group, its residue version, and relative value group when D is a Henselian division algebra. The structure of G(D) turns out to carry significant information about the arithmetic of D. Along these lines, we employ G(D) to compute the group SK1(D). As an application, we obtain theorems of reduced K-theory which require heavy machinery, as simple examples of our method.

Monitoring electrical resistance of concretes containing alternative cementitious materials to assess their resistance to chloride penetration

This is an invited contribution in a special issue of the Journal of Cement and Concrete Composites

Spectrally bounded operators from von Neumann algebras

We prove that every unital spectrally bounded operator from a properly infinite von Neumann algebra onto a semisimple Banach algebra is a Jordan homomorphism.