39,094 research outputs found
On the Global Limiting Absorption Principle for Massless Dirac Operators
We prove a global limiting absorption principle on the entire real line for
free, massless Dirac operators for all space
dimensions , . 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
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
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
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 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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