Quasi-exactly Solvable Lie Superalgebras of Differential Operators

In this paper, we study Lie superalgebras of $2\times 2$ matrix-valued first-order differential operators on the complex line. We first completely classify all such superalgebras of finite dimension. Among the finite-dimensional superalgebras whose odd subspace is nontrivial, we find those admitting a finite-dimensional invariant module of smooth vector-valued functions, and classify all the resulting finite-dimensional modules. The latter Lie superalgebras and their modules are the building blocks in the construction of QES quantum mechanical models for spin 1/2 particles in one dimension.Comment: LaTeX2e using the amstex and amssymb packages, 24 page

New Constraints on the Timing and Pattern of Deglaciation in the Húnaflói Bay Region of Northwest Iceland Using Cosmogenic 36CA Dating and Geomorphic Mapping

Understanding the evolution and timing of changes in ice sheet geometry and extent in Iceland during the Last Glacial Maximum (LGM) and subsequent deglaciation continues to stimulate much active research. Though many previous studies have advanced our knowledge of Icelandic ice sheet history preserved in marine and terrestrial settings (e.g., Andrews et al., 2000; Norðdahl et al., 2008), the timing of ice margin retreat remains largely unknown in several key regions. Recently published 36Cl surface exposure ages of bedrock surfaces and moraines in the West Fjords (Brynjólfsson et al., 2015) contribute important progress in establishing more precise age control of ice recession in northwest Iceland. In another recent study, the spatial pattern and style of deglaciation in northern Iceland have been revealed through geomorphic mapping and GIS analyses of glacial landforms (Principato et al., 2016). Additional insight comes from updated numerical modeling reconstructions, which now provide a series of glaciologically plausible Icelandic ice sheet configurations from the LGM through the last deglaciation (Patton et al., 2017). However, the optimization of ice sheet model simulations relies on critical comparisons with the available empirical record of glacial-geologic evidence and chronological control, which remains relatively limited and sparsely distributed throughout Iceland. Our investigation is motivated by the need for more accurate constraints on the deglacial history in northern Iceland, where dated terrestrial records of ice margin retreat are particularly scarce. (excerpt

Phytoplankton realized Niches Track changing oceanic conditions at a long-term coastal station offSydney Australia

© 2018 Ajani, McGinty, Finkel and Irwin. Phytoplankton dynamics are closely linked to the ocean-climate system with evidence that changing ocean conditions are substantially altering phytoplankton biogeography, abundance and phenology. Using phytoplankton community composition and environmental data spanning 1965 to 2013 from a long-term Pacific Ocean coastal station offshore from Sydney, Australia (Port Hacking 100 m), we used the Maximum Entropy Modelling framework (MaxEnt) to test whether phytoplankton realized niches are fixed or shift in response to changing environmental conditions. The mean niches of phytoplankton closely tracked changes in mean temperature, while the mean salinity and mixed layer depth realized niches were consistently at the extreme range of available conditions. Prior studies had shown a fixed niche for nitrate in some phytoplankton species at a site where nitrate concentration was decreasing and potentially limiting; however, at Port Hacking nitrate and silicate niches increased more rapidly than environmental conditions, apparently in response to periodic occurrences of elevated nutrient concentrations. This study provides further evidence that climate change model projections cannot assume fixed realized niches of biotic communities, whilst highlighting the importance of sustained ocean measurements from the southern hemisphere to enhance our understanding of global ocean trends

Bounded Determinization of Timed Automata with Silent Transitions

Deterministic timed automata are strictly less expressive than their non-deterministic counterparts, which are again less expressive than those with silent transitions. As a consequence, timed automata are in general non-determinizable. This is unfortunate since deterministic automata play a major role in model-based testing, observability and implementability. However, by bounding the length of the traces in the automaton, effective determinization becomes possible. We propose a novel procedure for bounded determinization of timed automata. The procedure unfolds the automata to bounded trees, removes all silent transitions and determinizes via disjunction of guards. The proposed algorithms are optimized to the bounded setting and thus are more efficient and can handle a larger class of timed automata than the general algorithms. The approach is implemented in a prototype tool and evaluated on several examples. To our best knowledge, this is the first implementation of this type of procedure for timed automata.Comment: 25 page

Automatic Verification of Erlang-Style Concurrency

This paper presents an approach to verify safety properties of Erlang-style, higher-order concurrent programs automatically. Inspired by Core Erlang, we introduce Lambda-Actor, a prototypical functional language with pattern-matching algebraic data types, augmented with process creation and asynchronous message-passing primitives. We formalise an abstract model of Lambda-Actor programs called Actor Communicating System (ACS) which has a natural interpretation as a vector addition system, for which some verification problems are decidable. We give a parametric abstract interpretation framework for Lambda-Actor and use it to build a polytime computable, flow-based, abstract semantics of Lambda-Actor programs, which we then use to bootstrap the ACS construction, thus deriving a more accurate abstract model of the input program. We have constructed Soter, a tool implementation of the verification method, thereby obtaining the first fully-automatic, infinite-state model checker for a core fragment of Erlang. We find that in practice our abstraction technique is accurate enough to verify an interesting range of safety properties. Though the ACS coverability problem is Expspace-complete, Soter can analyse these verification problems surprisingly efficiently.Comment: 12 pages plus appendix, 4 figures, 1 table. The tool is available at http://mjolnir.cs.ox.ac.uk/soter

Quasi-Exact Solvability and the direct approach to invariant subspaces

We propose a more direct approach to constructing differential operators that preserve polynomial subspaces than the one based on considering elements of the enveloping algebra of sl(2). This approach is used here to construct new exactly solvable and quasi-exactly solvable quantum Hamiltonians on the line which are not Lie-algebraic. It is also applied to generate potentials with multiple algebraic sectors. We discuss two illustrative examples of these two applications: an interesting generalization of the Lam\'e potential which posses four algebraic sectors, and a quasi-exactly solvable deformation of the Morse potential which is not Lie-algebraic.Comment: 17 pages, 3 figure

Proton decay of high-lying states in odd nuclei

In the framework of the quasiparticle-phonon model, we study the non-statistical proton decay of excited states in odd nuclei towards low-lying collective states. Partial cross sections and branching ratios for the proton decay of the high angular momentum states in $^{41}$Sc, $^{59}$Cu and $^{91}$Nb %{\it excited by means of the ($^{7}$Li,$^{6}$He) reaction} are evaluated. The calculated branching ratios predict strong direct proton decays to the low-lying vibrational states in $^{41}$Sc and $^{91}$Nb. A general agreement with existing experimental data is found.Comment: 12 pages, 2 figures, Latex, accepted for publication in Nucl. Phys.