17,421 research outputs found
A rich hierarchy of functionals of finite types
We are considering typed hierarchies of total, continuous functionals using
complete, separable metric spaces at the base types. We pay special attention
to the so called Urysohn space constructed by P. Urysohn. One of the properties
of the Urysohn space is that every other separable metric space can be
isometrically embedded into it. We discuss why the Urysohn space may be
considered as the universal model of possibly infinitary outputs of algorithms.
The main result is that all our typed hierarchies may be topologically
embedded, type by type, into the corresponding hierarchy over the Urysohn
space. As a preparation for this, we prove an effective density theorem that is
also of independent interest.Comment: 21 page
Simulating Nonholonomic Dynamics
This paper develops different discretization schemes for nonholonomic
mechanical systems through a discrete geometric approach. The proposed methods
are designed to account for the special geometric structure of the nonholonomic
motion. Two different families of nonholonomic integrators are developed and
examined numerically: the geometric nonholonomic integrator (GNI) and the
reduced d'Alembert-Pontryagin integrator (RDP). As a result, the paper provides
a general tool for engineering applications, i.e. for automatic derivation of
numerically accurate and stable dynamics integration schemes applicable to a
variety of robotic vehicle models
Hokupa'a-Gemini Discovery of Two Ultracool Companions to the Young Star HD 130948
We report the discovery of two faint ultracool companions to the nearby
(d~17.9 pc) young G2V star HD 130948 (HR 5534, HIP 72567) using the Hokupa'a
adaptive optics instrument mounted on the Gemini North 8-meter telescope. Both
objects have the same common proper motion as the primary star as seen over a 7
month baseline and have near-IR photometric colors that are consistent with an
early-L classification. Near-IR spectra taken with the NIRSPEC AO instrument on
the Keck II telescope reveal K I lines, FeH, and water bandheads. Based on
these spectra, we determine that both objects have spectral type dL2 with an
uncertainty of 2 spectral subclasses. The position of the new companions on the
H-R diagram in comparison with theoretical models is consistent with the young
age of the primary star (<0.8 Gyr) estimated on the basis of X-ray activity,
lithium abundance and fast rotation. HD 130948 B and C likely constitute a pair
of young contracting brown dwarfs with an orbital period of about 10 years, and
will yield dynamical masses for L dwarfs in the near future.Comment: 10 pages, 3 figures, (13 total pages
Non-equilibrium dynamics of Andreev states in the Kondo regime
The transport properties of a quantum dot coupled to superconducting leads
are analyzed. It is shown that the quasiparticle current in the Kondo regime is
determined by the non-equilibrium dynamics of subgap states (Andreev states)
under an applied voltage. The current at low bias is suppressed exponentially
for decreasing Kondo temperature in agreement with recent experiments. We also
predict novel interference effects due to multiple Landau-Zener transitions
between Andreev states.Comment: Revtex4, 4 pages, 4 figure
Exact solution of the Schr\"{o}dinger equation for an hydrogen atom at the interface between the vacuum and a topologically insulating surface
When an hydrogen atom is brought near to the interface between
-media, the quantum-mechanical motion of the electron will be affected
by the electromagnetic interaction between the atomic charges and the
-interface, which is described by an axionic extension of Maxwell
electrodynamics in the presence of a boundary. In this paper we investigate the
atom-surface interaction effects upon the energy levels and wave functions of
an hydrogen atom placed at the interface between a -medium and the
vacuum. In the approximation considered, the Schr\"{o}dinger equation can be
exactly solved by separation of variables in terms of hypergeometic functions
for the angular part and hydrogenic functions for the radial part. In order to
make such effects apparent we deal with unrealistic high values of the
-parameter. We also compute the energy shifts using perturbation theory
for a particular small value of and we demonstrate that they are in a
very good agreement with the ones obtained from the exact solution.Comment: 20 pages, 17 figures, 6 tables, Accepted for publication in the
European Physics Journal
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