Conjugate Dynamical Systems on C*-algebras

Let $(A, \alpha)$ and $(B, \beta)$ be C*-dynamical systems where $\alpha$ and $\beta$ are arbitrary *-endomorphisms. When $\alpha$ is injective or surjective, we show that the semicrossed products $A \times_\alpha \mathbb{Z}$ and $B \times_\beta \mathbb{Z}$ are isometrically isomorphic if and only if $(A, \alpha)$ and $(B, \beta)$ are outer conjugate. This conclusion also holds in various other cases as well.Comment: 19 page

A screening method for ranking chemicals by their fate and behaviour in the environment and potential toxic effects in humans following non-occupational exposure

A large number of chemicals are released intentionally or unintentionally into the environment each year. These include thousands of substances that are currently listed worldwide and several hundred new substances added annually (Mücke et al., 1986). When these compounds are used, they can reach microorganisms, plants, animals and man either in their original state or in the form of reaction and degradation products via air, water, soil or foodstuffs. Hence environmental chemicals can occur in practically all environmental compartments and ecosystems. It is not feasible to conduct assessments of human exposure and possible associated health effects for all chemicals. Even if the necessary resources were available, reliable data for a quantitative evaluation are likely to be absent in most cases. This has led to the development of schemes for prioritising compounds likely to be of environmental significance. Such schemes can be used to direct future research efforts towards the prioritised compounds. This study was commissioned by the Department of Health (DH) as part of a broader research activity that aims to identify key priority chemicals of concern to human health at routine levels of environmental exposure. The main pathways of human exposure are shown in Figure 1.1. A review of the principal prioritisation schemes used by different organisations to assess the significance of chemical release into the environment has been conducted by the MRC Institute for Environment and Health (IEH, 2003). This review showed that the approaches used by different organisations vary widely, depending on the initial reasons for which the schemes were developed. The basic information presented in the review was used to develop a simple screening method for ranking chemicals. The model used in this prioritisation scheme is outlined in Figure 1.2. The main purpose in developing the prioritisation scheme for DH was to develop a dedicated priority setting method capable of identifying chemicals in air, water, soil and foodstuffs that might pose a significant risk to human health following low level environmental exposure. The methodology was developed in order to identify compounds that required further assessment and those that had data gaps. More detailed risk assessments were conducted at a later stage on those compounds prioritised as being of high importancea. The screening methodology was developed for ‘existing chemicals’ as these are of greatest concern because data on their toxicity and/or fate and behaviour are often unknownb. The production of a priority list was designed to highlight compounds that required further regulatory measures to reduce exposure of the general population and for which an in-depth risk characterisation would be necessary to assist in the evaluation and implementation of activities for reducing environmental risks. This might include an assessment of the costs of such risks to human health and the costs of reduction measures. As the scheme also aimed to identify data gaps that might warrant further investigation, the application of default categories for chemicals with no data was also considered. The overall aim was to develop a screening methodology that is quick, clear and simple to use and that can easily be revised to take into account new information on compounds as and when it becomes available. a Benzene (IEH Report on Benzene in the Environment, R12); 4,6-dichlorocresol, hexachloro-1,3-butadiene, tetrachlorobenzene, 2,4,6-trichlorophenol (reports to DH; available from MRC Institute for Environment and Health b ‘Existing Substances’ are those that were placed in the European Union (EU) market before 1981. Prior to 1981 regulatory requirements were related to products intended for certain uses (e.g. veterinary medicines) and did not require assessment of the hazardous properties of any substance before they were released into the market. For substances placed on the market after 1981 (classified as ‘New Substances’) there is a legal requirement to conduct such assessments. Regulatory agencies require the collection of extensive documentation for safety before a chemical, for example, can be used in foods or commercial products. IEH Web Report W14, posted March 2004 at http://www.le.ac.uk/ieh/ 4 This report describes how physicochemical properties and toxicological data were incorporated into a screening model to assess the potential fate and transfer of chemicals between different environmental compartments and to predict the potential human exposure to toxic chemicals through the inhalation of contaminated air and the ingestion of water and food. It must be stressed, however, that the method devised is a simple screening process and that a more detailed assessment is necessary to determine the potential transfer through the foodchain of a chemical and the full extent of any adverse health effects. Sections 2 and 4 present the physicochemical properties, toxicological data and algorithms used to screen the compounds. Section 3 summarises the groups of chemicals that were included in the screening process. The results of the prioritisation scheme and comments on their limitations and constraints are presented in Section 5

Feasibility model of a high reliability five-year tape transport. Volume 3: Appendices

Detailed drawings of the five year tape transport are presented. Analytical tools used in the various analyses are described. These analyses include: tape guidance, tape stress over crowned rollers, tape pack stress program, response (computer) program, and control system electronics description

Storing images in warm atomic vapor

Reversible and coherent storage of light in atomic medium is a key-stone of future quantum information applications. In this work, arbitrary two-dimensional images are slowed and stored in warm atomic vapor for up to 30 $\mu$s, utilizing electromagnetically induced transparency. Both the intensity and the phase patterns of the optical field are maintained. The main limitation on the storage resolution and duration is found to be the diffusion of atoms. A techniqueanalogous to phase-shift lithography is employed to diminish the effect of diffusion on the visibility of the reconstructed image

Semicrossed Products of Operator Algebras by Semigroups

We examine the semicrossed products of a semigroup action by $*$-endomorphisms on a C*-algebra, or more generally of an action on an arbitrary operator algebra by completely contractive endomorphisms. The choice of allowable representations affects the corresponding universal algebra. We seek quite general conditions which will allow us to show that the C*-envelope of the semicrossed product is (a full corner of) a crossed product of an auxiliary C*-algebra by a group action. Our analysis concerns a case-by-case dilation theory on covariant pairs. In the process we determine the C*-envelope for various semicrossed products of (possibly nonselfadjoint) operator algebras by spanning cones and lattice-ordered abelian semigroups. In particular, we show that the C*-envelope of the semicrossed product of C*-dynamical systems by doubly commuting representations of $\mathbb{Z}^n_+$ (by generally non-injective endomorphisms) is the full corner of a C*-crossed product. In consequence we connect the ideal structure of C*-covers to properties of the actions. In particular, when the system is classical, we show that the C*-envelope is simple if and only if the action is injective and minimal. The dilation methods that we use may be applied to non-abelian semigroups. We identify the C*-envelope for actions of the free semigroup $\mathbb{F}_+^n$ by automorphisms in a concrete way, and for injective systems in a more abstract manner. We also deal with C*-dynamical systems over Ore semigroups when the appropriate covariance relation is considered.Comment: 100 pages; comments and references update

Reflexivity of the translation-dilation algebras on L^2(R)

The hyperbolic algebra A_h, studied recently by Katavolos and Power, is the weak star closed operator algebra on L^2(R) generated by H^\infty(R), as multiplication operators, and by the dilation operators V_t, t \geq 0, given by V_t f(x) = e^{t/2} f(e^t x). We show that A_h is a reflexive operator algebra and that the four dimensional manifold Lat A_h (with the natural topology) is the reflexive hull of a natural two dimensional subspace.Comment: 10 pages, no figures To appear in the International Journal of Mathematic

Unitary ambiguity in the extraction of the E2/M1 ratio for the γN↔Δ\gamma N\leftrightarrow\Delta transition

The resonant electric quadrupole amplitude in the transition $\gamma N\leftrightarrow\Delta(1232)$ is of great interest for the understanding of baryon structure. Various dynamical models have been developed to extract it from the corresponding photoproduction multipole of pions on nucleons. It is shown that once such a model is specified, a whole class of unitarily equivalent models can be constructed, all of them providing exactly the same fit to the experimental data. However, they may predict quite different resonant amplitudes. Therefore, the extraction of the E2/M1($\gamma N\leftrightarrow\Delta$) ratio (bare or dressed) which is based on a dynamical model using a largely phenomenological $\pi N$ interaction is not unique.Comment: 10 pages revtex including 4 postscript figure