3,816 research outputs found
Relative entropy via non-sequential recursive pair substitutions
The entropy of an ergodic source is the limit of properly rescaled 1-block
entropies of sources obtained applying successive non-sequential recursive
pairs substitutions (see P. Grassberger 2002 ArXiv:physics/0207023 and D.
Benedetto, E. Caglioti and D. Gabrielli 2006 Jour. Stat. Mech. Theo. Exp. 09
doi:10.1088/1742.-5468/2006/09/P09011). In this paper we prove that the cross
entropy and the Kullback-Leibler divergence can be obtained in a similar way.Comment: 13 pages , 2 figure
Design of SiC-Si Hybrid Interleaved 3-Phase 5-Level E-Type Back-to-Back Converter
In modern applications, such as variable frequency electric drives, aircraft propulsion, electric vehicles, and uninterruptible power supply units, high power-dense, and efficient AC-AC power converters are the key to reducing power losses, thus limiting the overall costs, and improving the system's reliability. Power electronic equipment can be enhanced thanks to the continuous evolution of conversion topologies and advancements in power semiconductor technology. The design and the optimization strategy of the AC-AC 5-Level converter, called Interleaved 3-Phase 5-Level E-Type Back-to-Back Converter (I3Φ5L BTB E-Type Converter), has been proposed in this paper. The converter is analyzed and experimentally characterized to prove the configuration's high efficiency and high-power density. An introduction to the characteristics of the I-3Φ5L BTB E-Type Converter is described, and afterward, the optimization methodology to design the multilevel converter is presented. The converter prototype is illustrated, which achieves a peak efficiency of 98.2% and a total weight of 6.18 kg using hybrid technology for power semiconductor
Orthonormal sequences in and time frequency localization
We study uncertainty principles for orthonormal bases and sequences in
. As in the classical Heisenberg inequality we focus on the product
of the dispersions of a function and its Fourier transform. In particular we
prove that there is no orthonormal basis for for which the time and
frequency means as well as the product of dispersions are uniformly bounded.
The problem is related to recent results of J. Benedetto, A. Powell, and Ph.
Jaming.
Our main tool is a time frequency localization inequality for orthonormal
sequences in . It has various other applications.Comment: 18 page
Entropy-driven cutoff phenomena
In this paper we present, in the context of Diaconis' paradigm, a general
method to detect the cutoff phenomenon. We use this method to prove cutoff in a
variety of models, some already known and others not yet appeared in
literature, including a chain which is non-reversible w.r.t. its stationary
measure. All the given examples clearly indicate that a drift towards the
opportune quantiles of the stationary measure could be held responsible for
this phenomenon. In the case of birth- and-death chains this mechanism is
fairly well understood; our work is an effort to generalize this picture to
more general systems, such as systems having stationary measure spread over the
whole state space or systems in which the study of the cutoff may not be
reduced to a one-dimensional problem. In those situations the drift may be
looked for by means of a suitable partitioning of the state space into classes;
using a statistical mechanics language it is then possible to set up a kind of
energy-entropy competition between the weight and the size of the classes.
Under the lens of this partitioning one can focus the mentioned drift and prove
cutoff with relative ease.Comment: 40 pages, 1 figur
On the velocity distributions of the one-dimensional inelastic gas
We consider the single-particle velocity distribution of a one-dimensional
fluid of inelastic particles. Both the freely evolving (cooling) system and the
non-equilibrium stationary state obtained in the presence of random forcing are
investigated, and special emphasis is paid to the small inelasticity limit. The
results are obtained from analytical arguments applied to the Boltzmann
equation along with three complementary numerical techniques (Molecular
Dynamics, Direct Monte Carlo Simulation Methods and iterative solutions of
integro-differential kinetic equations). For the freely cooling fluid, we
investigate in detail the scaling properties of the bimodal velocity
distribution emerging close to elasticity and calculate the scaling function
associated with the distribution function. In the heated steady state, we find
that, depending on the inelasticity, the distribution function may display two
different stretched exponential tails at large velocities. The inelasticity
dependence of the crossover velocity is determined and it is found that the
extremely high velocity tail may not be observable at ``experimentally
relevant'' inelasticities.Comment: Latex, 14 pages, 12 eps figure
Symmetric Informationally Complete Quantum Measurements
We consider the existence in arbitrary finite dimensions d of a POVM
comprised of d^2 rank-one operators all of whose operator inner products are
equal. Such a set is called a ``symmetric, informationally complete'' POVM
(SIC-POVM) and is equivalent to a set of d^2 equiangular lines in C^d.
SIC-POVMs are relevant for quantum state tomography, quantum cryptography, and
foundational issues in quantum mechanics. We construct SIC-POVMs in dimensions
two, three, and four. We further conjecture that a particular kind of
group-covariant SIC-POVM exists in arbitrary dimensions, providing numerical
results up to dimension 45 to bolster this claim.Comment: 8 page
Photometric Solutions for Detached Eclipsing Binaries: selection of ideal distance indicators in the SMC
Detached eclipsing binary stars provide a robust one-step distance
determination to nearby galaxies. As a by-product of Galactic microlensing
searches, catalogs of thousands of variable stars including eclipsing binaries
have been produced by the OGLE, MACHO and EROS collaborations. We present
photometric solutions for detached eclipsing binaries in the Small Magellanic
Cloud (SMC) discovered by the OGLE collaboration. The solutions were obtained
with an automated version of the Wilson-Devinney program. By fitting mock
catalogs of eclipsing binaries we find that the normalized stellar radii
(particularly their sum) and the surface brightness ratio are accurately
described by the fitted parameters and estimated standard errors, despite
various systematic uncertainties. In many cases these parameters are well
constrained. In addition we find that systems exhibiting complete eclipses can
be reliably identified where the fractional standard errors in the radii are
small. We present two quantitatively selected sub-samples of eclipsing binaries
that will be excellent distance indicators. These can be used both for
computation of the distance to the SMC and to probe its structure. One
particularly interesting binary has a very well determined solution, exhibits
complete eclipses, and is comprised of well detached G-type, class giants.Comment: 29 pages, 12 figures. To be published in Ap
Non Sequential Recursive Pair Substitution: Some Rigorous Results
We present rigorous results on some open questions on NSRPS, non sequential
recursive pairs substitution method (see Grassberger in \cite{G}). In
particular, starting from the action of NSRPS on finite strings we define a
corresponding natural action on measures and we prove that the iterated measure
becomes asymptotically Markov. This certify the effectiveness of NSRPS as a
tool for data compression and entropy estimation.Comment: 20 page
Synthetic Spectra and Color-Temperature Relations of M Giants
As part of a project to model the integrated spectra and colors of elliptical
galaxies through evolutionary synthesis, we have refined our synthetic spectrum
calculations of M giants. After critically assessing three effective
temperature scales for M giants, we adopted the relation of Dyck et al. (1996)
for our models. Using empirical spectra of field M giants as a guide, we then
calculated MARCS stellar atmosphere models and SSG synthetic spectra of these
cool stars, adjusting the band absorption oscillator strengths of the TiO bands
to better reproduce the observational data. The resulting synthetic spectra are
found to be in very good agreement with the K-band spectra of stars of the
appropriate spectral type taken from Kleinmann & Hall (1986) as well. Spectral
types estimated from the strengths of the TiO bands and the depth of the
bandhead of CO near 2.3 microns quantitatively confirm that the synthetic
spectra are good representations of those of field M giants. The broad-band
colors of the models match the field relations of K and early-M giants very
well; for late-M giants, differences between the field-star and synthetic
colors are probably caused by the omission of spectral lines of VO and water in
the spectrum synthesis calculations. Here, we present four grids of K-band
bolometric corrections and colors -- Johnson U-V and B-V; Cousins V-R and V-I;
Johnson-Glass V-K, J-K and H-K; and CIT/CTIO V-K, J-K, H-K and CO -- for models
having 3000 K < Teff < 4000 K and -0.5 < log g < 1.5. These grids, which have
[Fe/H] = +0.25, 0.0, -0.5 and -1.0, extend and supplement the color-temperature
relations of hotter stars presented in a companion paper (astro-ph/9911367).Comment: To appear in the March 2000 issue of the Astronomical Journal. 60
pages including 15 embedded postscript figures (one page each) and 6 embedded
postscript tables (10 pages total
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