Crossed Products by Dual Coactions of Groups and Homogeneous Spaces

Mansfield showed how to induce representations of crossed products of C*-algebras by coactions from crossed products by quotient groups and proved an imprimitivity theorem characterising these induced representations. We give an alternative construction of his bimodule in the case of dual coactions, based on the symmetric imprimitivity theorem of the third author; this provides a more workable way of inducing representations of crossed products of C*-algebras by dual coactions. The construction works for homogeneous spaces as well as quotient groups, and we prove an imprimitivity theorem for these induced representations.Comment: LaTeX-2e, 19 pages, requires pb-diagram.sty ((E) University of Paderborn, Germany (K,R) University of Newcastle, Australia

Naturality and Induced Representations

We show that induction of covariant representations for C*-dynamical systems is natural in the sense that it gives a natural transformation between certain crossed-product functors. This involves setting up suitable categories of C*-algebras and dynamical systems, and extending the usual constructions of crossed products to define the appropriate functors. From this point of view, Green's Imprimitivity Theorem identifies the functors for which induction is a natural equivalence. Various spcecial cases of these results have previously been obtained on an ad hoc basis.Comment: LaTeX-2e, 24 pages, uses package pb-diagra

A Categorical Approach to Imprimitivity Theorems for C*-Dynamical Systems

Imprimitivity theorems provide a fundamental tool for studying the representation theory and structure of crossed-product C*-algebras. In this work, we show that the Imprimitivity Theorem for induced algebras, Green's Imprimitivity Theorem for actions of groups, and Mansfield's Imprimitivity Theorem for coactions of groups can all be viewed as natural equivalences between various crossed-product functors among certain equivariant categories. The categories involved have C*-algebras with actions or coactions (or both) of a fixed locally compact group G as their objects, and equivariant equivalence classes of right-Hilbert bimodules as their morphisms. Composition is given by the balanced tensor product of bimodules. The functors involved arise from taking crossed products; restricting, inflating, and decomposing actions and coactions; inducing actions; and various combinations of these. Several applications of this categorical approach are also presented, including some intriguing relationships between the Green and Mansfield bimodules, and between restriction and induction of representations.Comment: LaTeX2e, 152 pages, uses class memo-l and packages amscd, xy, and amssymb; fixed several typos and updated bibliograph

Continued Fraction Representation of Temporal Multi Scaling in Turbulence

It was shown recently that the anomalous scaling of simultaneous correlation functions in turbulence is intimately related to the breaking of temporal scale invariance, which is equivalent to the appearance of infinitely many times scales in the time dependence of time-correlation functions. In this paper we derive a continued fraction representation of turbulent time correlation functions which is exact and in which the multiplicity of time scales is explicit. We demonstrate that this form yields precisely the same scaling laws for time derivatives and time integrals as the "multi-fractal" representation that was used before. Truncating the continued fraction representation yields the "best" estimates of time correlation functions if the given information is limited to the scaling exponents of the simultaneous correlation functions up to a certain, finite order. It is worth noting that the derivation of a continued fraction representation obtained here for an operator which is not Hermitian or anti-Hermitian may be of independent interest.Comment: 7 pages, no figur

Scaling relations in large-Prandtl-number natural thermal convection

In this study we follow Grossmann and Lohse, Phys. Rev. Lett. 86 (2001), who derived various scalings regimes for the dependence of the Nusselt number $Nu$ and the Reynolds number $Re$ on the Rayleigh number $Ra$ and the Prandtl number $Pr$. We focus on theoretical arguments as well as on numerical simulations for the case of large-$Pr$ natural thermal convection. Based on an analysis of self-similarity of the boundary layer equations, we derive that in this case the limiting large-$Pr$ boundary-layer dominated regime is I$_\infty^<$, introduced and defined in [1], with the scaling relations $Nu\sim Pr^0\,Ra^{1/3}$ and $Re\sim Pr^{-1}\,Ra^{2/3}$. Our direct numerical simulations for $Ra$ from $10^4$ to $10^9$ and $Pr$ from 0.1 to 200 show that the regime I$_\infty^<$ is almost indistinguishable from the regime III$_\infty$, where the kinetic dissipation is bulk-dominated. With increasing $Ra$, the scaling relations undergo a transition to those in IV$_u$ of reference [1], where the thermal dissipation is determined by its bulk contribution

Response of Pacific-sector Antarctic ice shelves to the El Niño/Southern Oscillation.

Satellite observations over the past two decades have revealed increasing loss of grounded ice in West Antarctica, associated with floating ice shelves that have been thinning. Thinning reduces an ice-shelf's ability to restrain grounded-ice discharge, yet our understanding of the climate processes that drive mass changes is limited. Here, we use ice-shelf height data from four satellite altimeter missions (1994-2017) to show a direct link between ice-shelf-height variability in the Antarctic Pacific sector and changes in regional atmospheric circulation driven by the El Niño-Southern Oscillation. This link is strongest from Dotson to Ross ice shelves and weaker elsewhere. During intense El Niño years, height increase by accumulation exceeds the height decrease by basal melting, but net ice-shelf mass declines as basal ice loss exceeds lower-density snow gain. Our results demonstrate a substantial response of Amundsen Sea ice shelves to global and regional climate variability, with rates of change in height and mass on interannual timescales that can be comparable to the longer-term trend, and with mass changes from surface accumulation offsetting a significant fraction of the changes in basal melting. This implies that ice-shelf height and mass variability will increase as interannual atmospheric variability increases in a warming climate

Revised structure of haemoventosin

The structure of the lichen pigment haemoventosin has been revised to 3,4,6,9-tetrahydro-5,10-dihydroxy-7-methoxy-3S-methyl-1,6,9-trioxo-1H-naphtho-[2,3-c]pyran (3), mainly on the basis of long-range δC/δH correlations observed in 2D HMBC NMR experiments and long-range δH/δD isotope effects observed in partial deuteriation experiments with 10-O-acetylhaemoventosin; ortho- and para-quinonoid structures were distinguished by means of the transacetylation inferred in the sodium dithionite reduction of 10-O-acetylhaemoventosin

Energy transfer within phycocyanin trimers of Mastigocladus laminosus studied by picosecond time-resolved transient absorption spectroscopy

The transient absorption recovery induced in phycocyanin trimers by picosecond pulses of variable wavelength (570 — 620 nm) has been recorded and analyzed by applying a least-squares multi-exponential fit procedure. The results suggest that in native PC trimers the chromophores exhibit a microheterogeneity with the effect that the derived apparent lifetimes are functions of excitation and probing wavelength. It is suggested that, due to strong excitonic coupling between a-84 and ß-84 chromophores, the lifetime of the terminal acceptor state is reduced to about 900 ps; the apparent energy transfer time from chromophore β-155 to a-84 and ß-84 chromophores varies between 20—50 ps depending on the actual chromophore-protein arrangement (microheterogeneity)