Constructive Gelfand duality for C*-algebras

We present a constructive proof of Gelfand duality for C*-algebras by reducing the problem to Gelfand duality for real C*-algebras.Comment: 6page

Flooding in Southwestern Pennsylvania: Knowledge Gaps and Approaches

As southwestern Pennsylvania continues to evolve from its industrial past to become a national leader in innovation and sustainability, it has encountered a complex set of water challenges that threaten the economy, ecology, and public health of the region. In this context, over the last year, the Heinz Endowments funded the Pittsburgh Collaboratory for Water Research, Education, and Outreach at the University of Pittsburgh to hold a series of consensus-building meetings among regional academic scholars, community groups, governmental, and non-governmental organizations. These meetings (one each on green infrastructure, water quality, and flooding) aimed to identify key regional knowledge gaps and chart a collaborative research agenda to fill these gaps and enhance the region’s ability to strategically and creatively solve water problems. In June 2019, the first of the reports on Green Infrastructure and Stormwater Management was released. In October 2019, the second report on Water Quality was released. Now, in February 2020, the third report describing the research agenda on flooding arising from an April 2, 2019 meeting is being formally released. This report outlines several fundamental knowledge gaps in the region and suggests methods to span these gaps with new collaborative research

A relative double commutant theorem for hereditary sub-C*-algebras

We prove a double commutant theorem for hereditary subalgebras of a large class of C*-algebras, partially resolving a problem posed by Pedersen[8]. Double commutant theorems originated with von Neumann, whose seminal result evolved into an entire field now called von Neumann algebra theory. Voiculescu proved a C*-algebraic double commutant theorem for separable subalgebras of the Calkin algebra. We prove a similar result for hereditary subalgebras which holds for arbitrary corona C*-algebras. (It is not clear how generally Voiculescu's double commutant theorem holds.)Nous démontrons un théorème commutant double (d'après Voiculescu et von Neumann) pour des sous-C*-algèbres héréditaires dans une C*-algèbre <<corona>>, c'est a dire M(A)/A

In situ Rb-Sr dating by collision cell, multicollection inductively-coupled plasma mass-spectrometry with pre-cell mass-filter, (CC-MC-ICPMS/MS)

We document the utility for in situ Rb–Sr dating of a one-of-a-kind tribrid mass spectrometer, ‘Proteus’, coupled to a UV laser ablation system. Proteus combines quadrupole mass-filter, collision cell and sector magnet with a multicollection inductively-coupled plasma mass spectrometer (CC-MC-ICPMS/MS). Compared to commercial, single collector, tribrid inductively-coupled plasma mass spectrometers (CC-ICPMS/MS) Proteus has enhanced ion transmission and offers simultaneous collection of all Sr isotopes using an array of Faraday cups. These features yield improved precision in measured (87)Sr/(86)Sr ratios, for a given mass of Sr analysed, approximately a factor of 25 in comparison to the Thermo Scientific™ iCAP TQ™ operated under similar conditions. Using SF(6) as a reaction gas on Proteus, measurements of Rb-doped NIST SRM (standard reference material) 987 solutions, with Rb/Sr ratios from 0.01–100, yield (87)Sr/(86)Sr that are indistinguishable from un-doped NIST SRM 987, demonstrating quantitative ‘chemical resolution’ of Rb from Sr. We highlight the importance of mass-filtering before the collision cell for laser ablation (87)Sr/(86)Sr analysis, using an in-house feldspar standard and a range of glass reference materials. By transmitting only those ions with mass-to-charge ratios 82–92 u/e into the collision cell, we achieve accurate (87)Sr/(86)Sr measurements without any corrections for atomic or polyatomic isobaric interferences. Without the pre-cell mass-filtering, measured in situ(87)Sr/(86)Sr ratios are inaccurate. Combining in situ measurements of Rb/Sr and radiogenic Sr isotope ratios we obtain mineral isochrons. We utilise a sample from the well-dated Dartmoor granite (285 ± 1 Ma) as a calibrant for our in situ ages and, using the same conditions, produce accurate Rb–Sr isochron ages for samples of the Fish Canyon tuff (28 ± 2 Ma) and Shap granite pluton (397 ± 1 Ma). Analysing the same Dartmoor granite sample using identical laser conditions and number of spot analyses using the Thermo Scientific™ iCAP TQ™ yielded an isochron slope 5× less precise than Proteus. We use an uncertainty model to illustrate the advantage of using Proteus over single collector CC-ICPMS/MS for in situ Rb–Sr dating. The results of this model show that the improvement is most marked for samples that have low Rb/Sr (<10) or are young (<100 Ma). We also report the first example of an in situ, internal Rb–Sr isochron from a single potassium-feldspar grain. Using a sample from the Shap granite, we obtained accurate age and initial (87)Sr/(86)Sr with 95% confidence intervals of ±1.5% and ±0.03% respectively. Such capabilities offer new opportunities in geochronological studies

Assessing a New Clue to How Much Carbon Plants Take Up

Current climate models disagree on how much carbon dioxide land ecosystems take up for photosynthesis. Tracking the stronger carbonyl sulfide signal could help

Membrane-Protein Interactions in a Generic Coarse-Grained Model for Lipid Bilayers

We study membrane-protein interactions and membrane-mediated protein-protein interactions by Monte Carlo simulations of a generic coarse-grained model for lipid bilayers with cylindrical hydrophobic inclusions. The strength of the hydrophobic force and the hydrophobic thickness of the proteins are systematically varied. The results are compared with analytical predictions of two popular analytical theories: The Landau-de Gennes theory and the elastic theory. The elastic theory provides an excellent description of the fluctuation spectra of pure membranes and successfully reproduces the deformation profiles of membranes around single proteins. However, its prediction for the potential of mean force between proteins is not compatible with the simulation data for large distances. The simulations show that the lipid-mediated interactions are governed by five competing factors: Direct interactions, lipid-induced depletion interactions, lipid bridging, lipid packing, and a smooth long-range contribution. The mechanisms leading to "hydrophobic mismatch" interactions are critically analyzed.Comment: 16 pages, 8 figures, accepted for publication in Biophysical Journa