39,094 research outputs found

    On the Global Limiting Absorption Principle for Massless Dirac Operators

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    We prove a global limiting absorption principle on the entire real line for free, massless Dirac operators H0=α⋅(−i∇)H_0 = \alpha \cdot (-i \nabla) for all space dimensions n∈Nn \in \mathbb{N}, n≥2n \geq 2. This is a new result for all dimensions other than three, in particular, it applies to the two-dimensional case which is known to be of some relevance in applications to graphene. We also prove an essential self-adjointness result for first-order matrix-valued differential operators with Lipschitz coefficients.Comment: 22 page

    An Independent Calibration of Stellar Ages: HST Observations of White Dwarfs at V=25

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    The white dwarf luminosity function of a stellar cluster will have a sharp truncation at a luminosity which is determined by the time since formation of the first white dwarfs in that cluster. Calculation of the dependence of this limiting luminosity on age requires relatively well-understood physics and is independent of stellar evolutionary models. Thus, measurement of the termination of the white dwarf luminosity function provides an independent method to determine the age of a cluster, and thereby to calibrate stellar evolutionary ages. We have obtained HST WFPC2 data in two open clusters, identified the white dwarf sequence, and proved the feasibility of this approach, by detecting white dwarfs to V=25. Much deeper data are feasible. From our present limited data, we show that degenerate cooling ages are not consistent with some published isochrone ages for clusters with ages of order 1Gyr.Comment: 5 pages plus 3 figures ps format, paper in press in MNRAS: previous attempt lost the tex

    A Case Study on Logical Relations using Contextual Types

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    Proofs by logical relations play a key role to establish rich properties such as normalization or contextual equivalence. They are also challenging to mechanize. In this paper, we describe the completeness proof of algorithmic equality for simply typed lambda-terms by Crary where we reason about logically equivalent terms in the proof environment Beluga. There are three key aspects we rely upon: 1) we encode lambda-terms together with their operational semantics and algorithmic equality using higher-order abstract syntax 2) we directly encode the corresponding logical equivalence of well-typed lambda-terms using recursive types and higher-order functions 3) we exploit Beluga's support for contexts and the equational theory of simultaneous substitutions. This leads to a direct and compact mechanization, demonstrating Beluga's strength at formalizing logical relations proofs.Comment: In Proceedings LFMTP 2015, arXiv:1507.0759

    Inextendibility of expanding cosmological models with symmetry

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    A new criterion for inextendibility of expanding cosmological models with symmetry is presented. It is applied to derive a number of new results and to simplify the proofs of existing ones. In particular it shows that the solutions of the Einstein-Vlasov system with T2T^2 symmetry, including the vacuum solutions, are inextendible in the future. The technique introduced adds a qualitatively new element to the available tool-kit for studying strong cosmic censorship.Comment: 7 page
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