12,734 research outputs found
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
ENIGMA: Efficient Learning-based Inference Guiding Machine
ENIGMA is a learning-based method for guiding given clause selection in
saturation-based theorem provers. Clauses from many proof searches are
classified as positive and negative based on their participation in the proofs.
An efficient classification model is trained on this data, using fast
feature-based characterization of the clauses . The learned model is then
tightly linked with the core prover and used as a basis of a new parameterized
evaluation heuristic that provides fast ranking of all generated clauses. The
approach is evaluated on the E prover and the CASC 2016 AIM benchmark, showing
a large increase of E's performance.Comment: Submitted to LPAR 201
The Masses Of The B-Stars In The High Galactic Latitude Eclipsing Binary IT Lib
A number of blue stars which appear to be similar to Population I B-stars in
the star forming regions of the galactic disk are found more than 1 kpc from
the galactic plane. Uncertainties about the true distances and masses of these
high latitude B-stars has fueled a debate as to their origin and evolutionary
status. The eclipsing binary IT Lib is composed of two B-stars, is
approximately one kiloparsec above the galactic plane, and is moving back
toward the plane. Observations of the light and velocity curves presented here
lead to the conclusion that the B-stars in this system are massive young
main-sequence stars. While there are several possible explanations, it appears
most plausible that the IT Lib system formed in the disk about 30 million years
ago and was ejected on a trajectory taking it to its present position.Comment: 26 pages, 3 figures, accepted for publication in the PASP (January
2003
Natural extension of the Generalised Uncertainty Principle
We discuss a gedanken experiment for the simultaneous measurement of the
position and momentum of a particle in de Sitter spacetime. We propose an
extension of the so-called generalized uncertainty principle (GUP) which
implies the existence of a minimum observable momentum. The new GUP is directly
connected to the nonzero cosmological constant, which becomes a necessary
ingredient for a more complete picture of the quantum spacetime.Comment: 4 pages, 1 figure, v2 with added references, revised and extended as
published in CQ
Perturbation of magnetostatic modes observed by ferromagnetic resonance force microscopy
Magnetostatic modes of yttrium iron garnet (YIG) films are investigated by ferromagnetic resonance force microscopy. A thin-film "probe" magnet at the tip of a compliant cantilever introduces a local inhomogeneity in the internal field of the YIG sample. This influences the shape of the sample's magnetostatic modes, thereby measurably perturbing the strength of the force coupled to the cantilever. We present a theoretical model that explains these observations; it shows that the tip-induced variation of the internal field creates either a local "potential barrier" or "potential well" for the magnetostatic waves. The data and model together indicate that local magnetic imaging of ferromagnets is possible, even in the presence of long-range spin coupling, through the introduction of localized magnetostatic modes predicted to arise from sufficiently strong tip fields
Dark energy, antimatter gravity and geometry of the Universe
This article is based on two hypotheses. The first one is the existence of
the gravitational repulsion between particles and antiparticles. Consequently,
virtual particle-antiparticle pairs in the quantum vacuum may be considered as
gravitational dipoles. The second hypothesis is that the Universe has geometry
of a four-dimensional hyper-spherical shell with thickness equal to the Compton
wavelength of a pion, which is a simple generalization of the usual geometry of
a 3-hypersphere. It is striking that these two hypotheses lead to a simple
relation for the gravitational mass density of the vacuum, which is in very
good agreement with the observed dark energy density
Stability and Symmetry Breaking in Metal Nanowires
A general linear stability analysis of simple metal nanowires is presented
using a continuum approach which correctly accounts for material-specific
surface properties and electronic quantum-size effects. The competition between
surface tension and electron-shell effects leads to a complex landscape of
stable structures as a function of diameter, cross section, and temperature. By
considering arbitrary symmetry-breaking deformations, it is shown that the
cylinder is the only generically stable structure. Nevertheless, a plethora of
structures with broken axial symmetry is found at low conductance values,
including wires with quadrupolar, hexapolar and octupolar cross sections. These
non-integrable shapes are compared to previous results on elliptical cross
sections, and their material-dependent relative stability is discussed.Comment: 12 pages, 4 figure
Gravitational particle production in braneworld cosmology
Gravitational particle production in time variable metric of an expanding
universe is efficient only when the Hubble parameter is not too small in
comparison with the particle mass. In standard cosmology, the huge value of the
Planck mass makes the mechanism phenomenologically irrelevant. On the
other hand, in braneworld cosmology the expansion rate of the early universe
can be much faster and many weakly interacting particles can be abundantly
created. Cosmological implications are discussed.Comment: 4 pages, 1 figure, v3 with new definition of and minor text
modification
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