281 research outputs found
A standardisation proof for algebraic pattern calculi
This work gives some insights and results on standardisation for call-by-name
pattern calculi. More precisely, we define standard reductions for a pattern
calculus with constructor-based data terms and patterns. This notion is based
on reduction steps that are needed to match an argument with respect to a given
pattern. We prove the Standardisation Theorem by using the technique developed
by Takahashi and Crary for lambda-calculus. The proof is based on the fact that
any development can be specified as a sequence of head steps followed by
internal reductions, i.e. reductions in which no head steps are involved.Comment: In Proceedings HOR 2010, arXiv:1102.346
Compton Scattering in Ultra-Strong Magnetic Fields: Numerical and Analytical Behavior in the Relativistic Regime
This paper explores the effects of strong magnetic fields on the Compton
scattering of relativistic electrons. Recent studies of upscattering and energy
loss by relativistic electrons that have used the non-relativistic, magnetic
Thomson cross section for resonant scattering or the Klein-Nishina cross
section for non-resonant scattering do not account for the relativistic quantum
effects of strong fields ( G). We have derived a
simplified expression for the exact QED scattering cross section for the
broadly-applicable case where relativistic electrons move along the magnetic
field. To facilitate applications to astrophysical models, we have also
developed compact approximate expressions for both the differential and total
polarization-dependent cross sections, with the latter representing well the
exact total QED cross section even at the high fields believed to be present in
environments near the stellar surfaces of Soft Gamma-Ray Repeaters and
Anomalous X-Ray Pulsars. We find that strong magnetic fields significantly
lower the Compton scattering cross section below and at the resonance, when the
incident photon energy exceeds in the electron rest frame. The cross
section is strongly dependent on the polarization of the final scattered
photon. Below the cyclotron fundamental, mostly photons of perpendicular
polarization are produced in scatterings, a situation that also arises above
this resonance for sub-critical fields. However, an interesting discovery is
that for super-critical fields, a preponderance of photons of parallel
polarization results from scatterings above the cyclotron fundamental. This
characteristic is both a relativistic and magnetic effect not present in the
Thomson or Klein-Nishina limits.Comment: AASTeX format, 31 pages included 7 embedded figures, accepted for
publication in The Astrophysical Journa
Automated Reasoning and Presentation Support for Formalizing Mathematics in Mizar
This paper presents a combination of several automated reasoning and proof
presentation tools with the Mizar system for formalization of mathematics. The
combination forms an online service called MizAR, similar to the SystemOnTPTP
service for first-order automated reasoning. The main differences to
SystemOnTPTP are the use of the Mizar language that is oriented towards human
mathematicians (rather than the pure first-order logic used in SystemOnTPTP),
and setting the service in the context of the large Mizar Mathematical Library
of previous theorems,definitions, and proofs (rather than the isolated problems
that are solved in SystemOnTPTP). These differences poses new challenges and
new opportunities for automated reasoning and for proof presentation tools.
This paper describes the overall structure of MizAR, and presents the automated
reasoning systems and proof presentation tools that are combined to make MizAR
a useful mathematical service.Comment: To appear in 10th International Conference on. Artificial
Intelligence and Symbolic Computation AISC 201
Load assessment and analysis of impacts in multibody systems
The evaluation of contact forces during an impact requires the use of continuous force-based methods. An accurate prediction of the impact force demands the identification of the contact parameters on a case-by-case basis. In this paper, the preimpact effective kinetic energy (Formula presented.) is put forward as an indicator of the intensity of the impact force along the contact normal direction. This represents a part of the total kinetic energy of the system that is associated with the subspace of constrained motion defined by the impact constraints at the moment of contact onset. Its value depends only on the mechanical parameters and the configuration of the system. We illustrate in this paper that this indicator can be used to characterize the impact force intensity. The suitability of this indicator is confirmed by numerical simulations and experimentsPostprint (author's final draft
Population study for gamma-ray pulsars with the outer gap model
Inspired by increase of population of -ray emitting pulsars by the
telescope, we perform a population study for -ray emitting
canonical pulsars. We use a Monte-Carlo technique to simulate the Galactic
population of neutron stars and the radio pulsars. For each simulated neutron
star, we consider the -ray emission from the outer gap accelerator in
the magnetosphere. In our outer gap model, we apply the gap closure mechanism
proposed by Takata et al., in which both photon-photon pair-creation and
magnetic pair-creation processes are considered. Simulating the sensitivities
of previous major radio surveys, our simulation predicts that there are radio loud and -ray-selected -ray pulsars,
which can be detected with a -ray flux . Applying the sensitivity of the six-month
observation of the telescope, 40-61 radio-selected and 36-75
-ray selected pulsars are detected within our simulation. We show that
the distributions of various pulsar parameters for the simulated -ray
pulsars can be consistent with the observed distribution of the -ray
pulsars detected by the telescope. We also predict that
radio-loud and -ray-selected pulsars irradiate the Earth
with a flux , and most of those
-ray pulsars are distributing with a distance more than 1~kpc and a
flux . The ration between the
radio-selected and -ray-selected pulsars depend on the sensitivity of
the radio surveys. We also discuss the Galactic distribution of the
unidentified sources and the canonical -ray pulsars.Comment: 45 page, 10 figures, Accepted for publication in Ap
The Geminga Fraction
Radio-quiet gamma-ray pulsars like Geminga may account for a number of the unidentified EGRET sources in the Galaxy. The number of Geminga-like pulsars is very sensitive to the geometry of both the gamma-ray and radio beams. Recent studies of the shape and polarization of pulse profiles of young radio pulsars have provided evidence that their radio emission originates in wide cone beams at altitudes that are a significant fraction (1 -10%) of their light cylinder radius. Such wide radio emission beams will be visible at a much larger range of observer angles than the narrow core components thought to originate at lower altitude. Using 3D geometrical modeling that includes relativistic effects from pulsar rotation, we study the visibility of such radio cone beams as well as that of the gamma-ray beams predicted by slot gap and outer gap models. From the results of this study one can obtain revised predictions for the fraction of Geminga-like, radio quiet pulsars present in the gamma-ray pulsar population
Magnetic fileds of coalescing neutron stars and the luminosity function of short gamma-ray burst
Coalescing neutron star binaries are believed to be the most reliable sources
for ground-based detectors of gravitational waves and likely progenitors of
short gamma-ray bursts. In the process of coalescence, magnetic fields of
neutron stars can induce interesting observational manifestations and affect
the form of gravitational wave signal. In this papaer we use the population
synthesis method to model the expected distribution of neutron star magnetic
fields during the coalescence under different assumptions on the initial
parameters of neutron stars and their magnetic field evolution. We discuss
possible elecotrmagnetic phenomena preceding the coalescence of magnetized
neutron star binaries and the effect of magnetic field on the gravitational
wave signal. We find that a log-normal (Gaussian in logarithms) distribution of
the initial magnetic fields of neutron stars, which agrees with observed
properties of radio pulsars, produces the distribution of the magnetic field
energy during the coalescence that adequately describes the observed luminosity
function of short gamma-ray bursts under different assumptions on the field
evolution and initial parameters of neutron stars. This agreement lends further
support to the model of coalescing neutron star binaries as progenitors of
gamma-ray bursts.Comment: v.2, LATEX, 25 pages, inc. 7 ps figures, Astron. Lett., in press.
Typos corrected, reference adde
Point-Free, Set-Free Concrete Linear Algebra
International audienceWe show how a simple variant of Gaussian elimination can be used to model abstract linear algebra directly, using matrices only to represent all categories of objects, with operations such as subspace intersection and sum. We can even provide effective support for direct sums and subalgebras. We have formalized this work in Coq, and used it to develop all of the group representation theory required for the proof of the Odd Order Theorem, including results such as the Jacobson Density Theorem, Clifford's Theorem, the Jordan-Holder Theorem for modules, the Wedderburn Structure Theorem for semisimple rings (the basis for character theory).On présente une formalisation en Coq de l'algèbre linéaire où tous les objets sont représentés par des matrices, y compris les sous-espaces. Ce développement a été utilisé pour élaborer la formalisation des éléments de théorie de la représentation nécessaires à la prévue du théorème de Feit-Thompson
Incidence Simplicial Matrices Formalized in Coq/SSReflect
International audienceSimplicial complexes are at the heart of Computational Algebraic Topology, since they give a concrete, combinatorial description of otherwise rather abstract objects which makes many important topological computations possible. The whole theory has many applications such as coding theory, robotics or digital image analysis. In this paper we present a formalization in the COQ theorem prover of simplicial complexes and their incidence matrices as well as the main theorem that gives meaning to the definition of homology groups and is a first step towards their computation
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