Normalisers, nest algebras and tensor products

We show that if $\cl A$ is the tensor product of finitely many continuous nest algebras, $\cl B$ is a CDCSL algebra and $\cl A$ and $\cl B$ have the same normaliser semi-group then either $\cl A = \cl B$ or $\cl A^* = \cl B$.

Convergence of bimodules over maximal abelian selfadjoint algebras

We prove a continuity result for the map sending a masa-bimodule to its support. We characterise the convergence of a net of weakly closed convex hulls of bilattices in terms of the convergence of the corresponding supports, and establish a lower-semicontinuity result for the map sending a support to the corresponding masa-bimodule.

Angles in C*-algebras

In this work we characterise the C*-algebras $\mathcal{A}$ generated by projections with the property that every pair of projections in $\mathcal{A}$ has positive angle, as certain extensions of abelian algebras by algebras of compact operators. We show that this property is equivalent to a lattice theoretic property of projections and also to the property that the set of finite dimensional *-subalgebras of $\mathcal{A}$ is directed.

Multipliers of multidimensional Fourier algebras

Let $G$ be a locally compact $\sigma$-compact group. Motivated by an earlier notion for discrete groups due to Effros and Ruan, we introduce the multidimensional Fourier algebra $A^n(G)$ of $G$. We characterise the completely bounded multidimensional multipliers associated with $A^n(G)$ in several equivalent ways. In particular, we establish a completely isometric embedding of the space of all $n$-dimensional completely bounded multipliers into the space of all Schur multipliers on $G^{n+1}$ with respect to the (left) Haar measure. We show that in the case $G$ is amenable the space of completely bounded multidimensional multipliers coincides with the multidimensional Fourier-Stieltjes algebra of $G$ introduced by Ylinen. We extend some well-known results for abelian groups to the multidimensional setting.

On the simplicial cohomology of Banach operator algebras

We investigate the simplicial cohomology of certain Banach operator algebras. The two main examples considered are the Banach algebra of all bounded operators on a Banach space and its ideal of approximable operators. Sufficient conditions will be given forcing Banach algebras of this kind to be simplicially trivial.

Spectral isometries on non-simple C*-algebras

We prove that unital surjective spectral isometries on certain non-simple unital C*-algebras are Jordan isomorphisms. Along the way, we establish several general facts in the setting of semisimple Banach algebras.

Response characteristics of optical sensors for oxygen: models based on a distribution in tau(o) or kappa(q)

The features of two popular models used to describe the observed response characteristics of typical oxygen optical sensors based on luminescence quenching are examined critically. The models are the 'two-site' and 'Gaussian distribution in natural lifetime, tau(o),' models. These models are used to characterise the response features of typical optical oxygen sensors; features which include: downward curving Stern-Volmer plots and increasingly non-first order luminescence decay kinetics with increasing partial pressures of oxygen, pO(2). Neither model appears able to unite these latter features, let alone the observed disparate array of response features exhibited by the myriad optical oxygen sensors reported in the literature, and still maintain any level of physical plausibility. A model based on a Gaussian distribution in quenching rate constant, k(q), is developed and, although flawed by a limited breadth in distribution, rho, does produce Stern-Volmer plots which would cover the range in curvature seen with real optical oxygen sensors. A new 'log-Gaussian distribution in tau(o) or k(q)' model is introduced which has the advantage over a Gaussian distribution model of placing no limitation on the value of rho. Work on a 'log-Gaussian distribution in tau(o)' model reveals that the Stern-Volmer quenching plots would show little degree in curvature, even at large rho values and the luminescence decays would become increasingly first order with increasing pO(2). In fact, with real optical oxygen sensors, the opposite is observed and thus the model appears of little value. In contrast, a 'log-Gaussian distribution in k(o)' model does produce the trends observed with real optical oxygen sensors; although it is technically restricted in use to those in which the kinetics of luminescence decay are good first order in the absence of oxygen. The latter model gives a good fit to the major response features of sensors which show the latter feature, most notably the [Ru(dpp)(3)(2+)(Ph4B-)(2)] in cellulose optical oxygen sensors. The scope of a log-Gaussian model for further expansion and, therefore, application to optical oxygen sensors, by combining both a log-Gaussian distribution in k(o) with one in tau(o) is briefly discussed.

Interlaboratory comparison of real-time polymerase chain reaction methods to detect Coxiella burnetii, the causative agent of Q fever

The bacterium Coxiella burnetii, which has a wide host range, causes Q fever. Infection with C burnetii can cause abortions, stillbirth, and the delivery of weak offspring in ruminants. Coxiella burnetii infection is zoonotic, and in human beings it can cause chronic, potentially fatal disease. Real-time polymerase chain reaction (PCR) is increasingly being used to detect the organism and to aid in diagnosis both in human and animal cases. Many different real-time PCR methods, which target different genes, have been described. To assess the comparability of the C. burnetii real-time PCR assays in use in different European laboratories, a panel of nucleic acid extracts was dispatched to 7 separate testing centers. The testing centers included laboratories from both human and animal health agencies. Each laboratory tested the samples using their in-house real-time PCR methods. The results of this comparison show that the most common target gene for real-time PCR assays is the IS1111 repeat element that is present in multiple copies in the C. burnetii genome. Many laboratories also use additional real-time PCR tests that target single-copy genes. The results of the current study demonstrate that the assays in use in the different laboratories are comparable, with general agreement of results for the panel of samples.

Coxiella burnetii (Q fever) seroprevalence in cattle

Human cases of Q fever appear to be common in Northern Ireland compared to the rest of the British Isles. The purpose of this study was to describe the seroepidemiology of Coxiella burnetii infection in cattle in Northern Ireland in terms of seroprevalence and determinants of infection. A total of 5182 animals (from a stratified systematic random sample of 273 herds) were tested with a commercial C. burnetii phase 2 IgG ELISA. A total of 6.2% of animals and 48.4% of herds tested positively. Results from a multilevel logistic regression model indicated that the odds of cattle being infected with Q fever increased with age, Friesian breed, being from large herds and from dairy herds. Large dairy herd animal prevalence was 12.5% compared to 2.1% for small beef herds. Preliminary seroprevalence in sheep (12.3%), goats (9.3%), pigs (0%) rats (9.7%) and mice (3.2%) using indirect immunofluorescence is reported.

Human seroprevalence to Coxiella bumetii (Q fever) in Northern Ireland

Despite the widespread prevalence of infection with Coxiella burnetii, there have been few large population-based studies examining the epidemiology of this infection. The aim of this study was to examine the distribution and determinants of C. burnetii past infection in Northern Ireland (NI). Coxiella burnetii phase II specific IgG antibodies were measured by enzyme-linked immunosorbent assay in stored serum from 2394 randomly selected subjects, aged 12-64, who had participated in population-based surveys of cardiovascular risk factors performed in 1986 and 1987. The overall prevalence of C. burnetii antibody positivity was 12.8%. The prevalence of sero-positivity was slightly higher in males than that in females (14.3% versus 11.2%, P = 0.02). Sero-positivity was low in children (

C∗-Segal algebras with order unit

We introduce the notion of a (noncommutative) C *-Segal algebra as a Banach algebra (A, {norm of matrix}{dot operator}{norm of matrix} A) which is a dense ideal in a C *-algebra (C, {norm of matrix}{dot operator}{norm of matrix} C), where {norm of matrix}{dot operator}{norm of matrix} A is strictly stronger than {norm of matrix}{dot operator}{norm of matrix} C onA. Several basic properties are investigated and, with the aid of the theory of multiplier modules, the structure of C *-Segal algebras with order unit is determined.