2,741 research outputs found
Non-power positional number representation systems, bijective numeration, and the Mesoamerican discovery of zero
Pre-Columbian Mesoamerica was a fertile crescent for the development of number systems. A form of vigesimal system seems to have been present from the first Olmec civilization on wards, to which succeeding peoples made contributions. We discuss the Maya use of the representational redundancy present in their Long Count calendar, a non-power positional number representation system with multipliers 1, 20, 18 x 20, ..., 18 x 20(n). We demonstrate that the Mesoamericans did not need to invent positional notation and discover zero at the same time because they were not afraid of using a number system in which the same number can be written indifferent ways. A Long Count number system with digits from 0 to 20 is seen later to pass to one using digits 0 to 19, which leads us to propose that even earlier there may have been an initial zeroless bijective numeration system whose digits ran from 1 to 20. Mesoamerica was able to make this conceptual leap to the concept of a cardinal zero to perform arithmetic owing to a familiarity with multiple and redundant number representation systems
Four new planets around giant stars and the mass-metallicity correlation of planet-hosting stars
CONTEXT. Exoplanet searches have demonstrated that giant planets are
preferentially found around metal-rich stars and that their fraction increases
with the stellar mass. AIMS. During the past six years, we have conducted a
radial velocity follow-up program of 166 giant stars, to detect substellar
companions, and characterizing their orbital properties. Using this
information, we aim to study the role of the stellar evolution in the orbital
parameters of the companions, and to unveil possible correlations between the
stellar properties and the occurrence rate of giant planets. METHODS. Using
FEROS and CHIRON spectra, we have computed precision radial velocities and we
have derived atmospheric and physical parameters for all of our targets.
Additionally, velocities computed from UCLES spectra are presented here. By
studying the periodic radial velocity signals, we have detected the presence of
several substellar companions. RESULTS. We present four new planetary systems
around the giant stars HIP8541, HIP74890, HIP84056 and HIP95124. Additionally,
we find that giant planets are more frequent around metal-rich stars, reaching
a peak in the detection of = 16.7% around stars with
[Fe/H] 0.35 dex. Similarly, we observe a positive correlation of the
planet occurrence rate with the stellar mass, between M 1.0 -2.1
M, with a maximum of = 13.0%, at M = 2.1
M. CONCLUSIONS. We conclude that giant planets are preferentially
formed around metal-rich stars. Also, we conclude that they are more
efficiently formed around more massive stars, in the mass range of M
1.0 - 2.1 M. These observational results confirm previous
findings for solar-type and post-MS hosting stars, and provide further support
to the core-accretion formation model.Comment: Accepted for publication in A&
Frictional Drag between Two Dilute Two-Dimensional Hole Layers
We report drag measurements on dilute double layer two-dimensional hole
systems in the regime of r_s=19~39. We observed a strong enhancement of the
drag over the simple Boltzmann calculations of Coulomb interaction, and
deviations from the T^2 dependence which cannot be explained by
phonon-mediated, plasmon-enhanced, or disorder-related processes. We suggest
that this deviation results from interaction effects in the dilute regime.Comment: 4 pages, 3 figures, accepted in Phys. Rev. Lett. Added single layer
transport dat
Absence of gap for infinite half--integer spin ladders with an odd number of legs
A proof is presented for the absence of gap for spin ladders with an
odd number of legs, in the infinite leg length limit. This result is relevant
to the current discussion of coupled one--dimensional spin systems, a physical
realization of which are vanadyl pyrophosphate, (VO)PO, and
stoichiometric Sr Cu O (with ).Comment: REVTeX, 8 page
Freezing transition of the vortex liquid in anisotropic superconductors
We study the solid-liquid transition of a model of pancake vortices in
laminar superconductors using a density functional theory of freezing. The
physical properties of the system along the melting line are discussed in
detail. We show that there is a very good agreement with experimental data in
the shape and position of the first order transition in the phase diagram and
in the magnitude and temperature dependence of the magnetic induction jump at
the transition. We analyze the validity of the Lindemann melting criterion and
the Hansen-Verlet freezing criterion. Both criteria are shown to be good to
predict the phase diagram in the region where a first order phase transition is
experimentally observed.Comment: 9 pages, 10 figure
Many-body solitons in a one-dimensional condensate of hard core bosons
A mapping theorem leading to exact many-body dynamics of impenetrable bosons
in one dimension reveals dark and gray soliton-like structures in a toroidal
trap which is phase-imprinted. On long time scales revivals appear that are
beyond the usual mean-field theory
Hole dynamics in generalized spin backgrounds in infinite dimensions
We calculate the dynamical behaviour of a hole in various spin backgrounds in
infinite dimensions, where it can be determined exactly. We consider hypercubic
lattices with two different types of spin backgrounds. On one hand we study an
ensemble of spin configurations with an arbitrary spin probability on each
sublattice. This model corresponds to a thermal average over all spin
configurations in the presence of staggered or uniform magnetic fields. On the
other hand we consider a definite spin state characterized by the angle between
the spins on different sublattices, i.e a classical spin system in an external
magnetic field. When spin fluctuations are considered, this model describes the
physics of unpaired particles in strong coupling superconductors.Comment: Accepted in Phys. Rev. B. 18 pages of text (1 fig. included) in Latex
+ 2 figures in uuencoded form containing the 2 postscripts (mailed
separately
Spin-Hall effect and spin-Coulomb drag in doped semiconductors
In this review, we describe in detail two important spin-transport phenomena:
the extrinsic spin-Hall effect (coming from spin-orbit interactions between
electrons and impurities) and the spin-Coulomb drag. The interplay of these two
phenomena is analyzed. In particular, we discuss the influence of scattering
between electrons with opposite spins on the spin current and the spin
accumulation produced by the spin-Hall effect. Future challenges and open
questions are briefly discussed.Comment: Topical revie
- …