Time operators and shift representation of dynamical systems

We introduce and characterise time operators for unilateral shifts and exact endomorphisms. The associated shift representation of evolution is related to the spectral representation by a generalized Fourier transform. We illustrate the results for a simple exact system, namely the Renyi map.

Uptake of carbon, nitrogen and phosphorus by phytoplankton along the 20 degrees W meridian in the NE Atlantic between 57.5 degrees N and 37 degrees N

Phytoplankton biomass and rate of production were measured along a transect from 57.54 degreesN to 37.01 degreesN in the northeast Atlantic during July 1996 and at a series of stations over a 7-day period at 37 degreesN 20 degreesW. Surface nutrient concentrations ranged from 4 mu mol l(-1) NO3-, and 0.35 mu mol l(-1) PO43- at 57.54 degreesN to <10 nmol l(-1) NO3- and similar to 10 nmol l(-1) PO43- at 37.01 degreesN. The greatest phytoplankton biomass and production were measured in the vicinity of a frontal system at 50 degreesN, and there was a general decline in total phytoplankton biomass and production to the south of the transect. Production was measured in three size fractions. At the station with the highest chlorophyll concentrations (50.34 degreesN), phytoplankton cells larger than 5 mum dominated the assemblage, accounting for 72% of the chlorophyll concentration (22.9 mg m(-2)) and 51% of primary production (54.1 mmol Cm-2 d(-1)), but picophytoplankton production was also high (43%). At 57 degreesN, carbon fixation by the > 5 mum fraction accounted for 75% of the daily production of 60.75 mmol Cm-2 d(-1). At 37 degreesN, picophytoplankton was the dominant group, accounting for similar to 58% (10 mg m(-2)) of chlorophyll and similar to 64% (46 mmol Cm-2 d(-1)), of primary production. Nitrate, ammonium and phosphate uptake rates also were determined. Although high nitrate uptake rates were measured in the surface water at similar to 50 degreesN, the greatest uptake rates of both depth-integrated nitrate and ammonium were at the south of the transect. At 37 degreesN, a deep euphotic zone was present and light penetrated through the nitracline; total nitrate uptake was enhanced because of assimilation at the base of the euphotic zone. As a consequence, high values of depth-integrated f-ratio were measured in the oligotrophic waters at the south of the transect. Phosphate was predominantly incorporated into the picoplankton fraction, which included heterotrophic and autotrophic components, at all stations and a significant proportion of phosphate uptake occurred in the dark. The C:N:P assimilation ratios were variable throughout the region; phosphate uptake was generally greater than would be expected if nutrient assimilation were in proportion to the Redfield ratio. (C) 2001 Elsevier Science Ltd. All rights reserved.

Resolution of an ancient surface science anomaly: Work function change induced by N adsorption on W{100}

For many decades it has been assumed that an adsorbate centered above a metal surface and with a net negative charge should increase the work function of the surface. However, despite their electronegativity, N adatoms on W{100} cause a significant work function decrease. Here we present a resolution of this anomaly. Using density functional theory, we demonstrate that while the N atom carries a negative charge, of overriding importance is a reduction in the surface overspill electron density into the vacuum, when that charge is engaged in bonding to the adatom. This novel interpretation is fundamentally important in the general understanding of work function changes induced by atomic adsorbates.

A Context-Dependent Algorithm for Merging Uncertain Information in Possibility Theory

The need to merge multiple sources of uncertaininformation is an important issue in many application areas,especially when there is potential for contradictions betweensources. Possibility theory offers a flexible framework to represent,and reason with, uncertain information, and there isa range of merging operators, such as the conjunctive anddisjunctive operators, for combining information. However, withthe proposals to date, the context of the information to be mergedis largely ignored during the process of selecting which mergingoperators to use. To address this shortcoming, in this paper,we propose an adaptive merging algorithm which selects largelypartially maximal consistent subsets (LPMCSs) of sources, thatcan be merged through relaxation of the conjunctive operator, byassessing the coherence of the information in each subset. In thisway, a fusion process can integrate both conjunctive and disjunctiveoperators in a more flexible manner and thereby be morecontext dependent. A comparison with related merging methodsshows how our algorithm can produce a more consensual result.

Stable isomorphism of dual operator spaces

We prove that two dual operator spaces $X$ and $Y$ are stably isomorphic if and only if there exist completely isometric normal representations $phi$ and $psi$ of $X$ and $Y$, respectively, and ternary rings of operators $M_1, M_2$ such that $phi (X)= [M_2^*psi (Y)M_1]^{-w^*}$ and $psi (Y)=[M_2phi (X)M_1^*].$ We prove that this is equivalent to certain canonical dual operator algebras associated with the operator spaces being stably isomorphic. We apply these operator space results to prove that certain dual operator algebras are stably isomorphic if and only if they are isomorphic. We provide examples motivated by CSL algebra theory.