1,133 research outputs found
Generators of simple Lie algebras in arbitrary characteristics
In this paper we study the minimal number of generators for simple Lie
algebras in characteristic 0 or p > 3. We show that any such algebra can be
generated by 2 elements. We also examine the 'one and a half generation'
property, i.e. when every non-zero element can be completed to a generating
pair. We show that classical simple algebras have this property, and that the
only simple Cartan type algebras of type W which have this property are the
Zassenhaus algebras.Comment: 26 pages, final version, to appear in Math. Z. Main improvements and
corrections in Section 4.
Mesoscopic modelling of financial markets
We derive a mesoscopic description of the behavior of a simple financial
market where the agents can create their own portfolio between two investment
alternatives: a stock and a bond. The model is derived starting from the
Levy-Levy-Solomon microscopic model (Econ. Lett., 45, (1994), 103--111) using
the methods of kinetic theory and consists of a linear Boltzmann equation for
the wealth distribution of the agents coupled with an equation for the price of
the stock. From this model, under a suitable scaling, we derive a Fokker-Planck
equation and show that the equation admits a self-similar lognormal behavior.
Several numerical examples are also reported to validate our analysis
Dimensional Crossover in the Effective Second Harmonic Generation of Films of Random Dielectrics
The effective nonlinear response of films of random composites consisting of
a binary composite with nonlinear particles randomly embedded in a linear host
is theoretically and numerically studied. A theoretical expression for the
effective second harmonic generation susceptibility, incorporating the
thickness of the film, is obtained by combining a modified effective-medium
approximation with the general expression for the effective second harmonic
generation susceptibility in a composite. The validity of the thoretical
results is tested against results obtained by numerical simulations on random
resistor networks. Numerical results are found to be well described by our
theory. The result implies that the effective-medium approximation provides a
convenient way for the estimation of the nonlinear response in films of random
dielectrics.Comment: 9 pages, 2 figures; accepted for publication in Phys. Rev.
Castaing Instability and Precessing Domains in Confined Alkali Gases
We explore analogy between two-component quantum alkali gases and
spin-polarized helium systems. Recent experiments in trapped gases are put into
the frame of the existing theory for Castaing instability in transverse channel
and formation of homogeneous precessing domains in spin-polarized systems.
Analogous effects have already been observed in spin-polarized and
mixtures systems. The threshold effect of the confining
potential on the instability is analyzed. New experimental possibilities for
observation of transverse instability in a trap are discussed.Comment: 6 RevTex pages, no figure
Density-Matrix functional theory of strongly-correlated lattice fermions
A density functional theory (DFT) of lattice fermion models is presented,
which uses the single-particle density matrix gamma_{ij} as basic variable. A
simple, explicit approximation to the interaction-energy functional W[gamma] of
the Hubbard model is derived from exact dimer results, scaling properties of
W[gamma] and known limits. Systematic tests on the one-dimensional chain show a
remarkable agreement with theBethe-Ansatz exact solution for all interaction
regimes and band fillings. New results are obtained for the ground-state
energyand charge-excitation gap in two dimensions. A successful description of
strong electron correlations within DFT is achieved.Comment: 15 pages, 6 figures Submitted to PR
Linear response conductance and magneto-resistance of ferromagnetic single-electron transistors
The current through ferromagnetic single-electron transistors (SET's) is
considered. Using path integrals the linear response conductance is formulated
as a function of the tunnel conductance vs. quantum conductance and the
temperature vs. Coulomb charging energy. The magneto-resistance of
ferromagnet-normal metal-ferromagnet (F-N-F) SET's is almost independent of the
Coulomb charging energy and is only reduced when the transport dwell time is
longer than the spin-flip relaxation time. In all-ferromagnetic (F-F-F) SET's
with negligible spin-flip relaxation time the magneto-resistance is calculated
analytically at high temperatures and numerically at low temperatures. The
F-F-F magneto-resistance is enhanced by higher order tunneling processes at low
temperatures in the 'off' state when the induced charges vanishes. In contrast,
in the 'on' state near resonance the magneto-resistance ratio is a
non-monotonic function of the inverse temperature.Comment: 10 pages, 6 figures. accepted for publication in Phys. Rev.
Periodic harmonic functions on lattices and points count in positive characteristic
This survey addresses pluri-periodic harmonic functions on lattices with
values in a positive characteristic field. We mention, as a motivation, the
game "Lights Out" following the work of Sutner, Goldwasser-Klostermeyer-Ware,
Barua-Ramakrishnan-Sarkar, Hunzikel-Machiavello-Park e.a.; see also 2 previous
author's preprints for a more detailed account. Our approach explores harmonic
analysis and algebraic geometry over a positive characteristic field. The
Fourier transform allows us to interpret pluri-periods of harmonic functions on
lattices as torsion multi-orders of points on the corresponding affine
algebraic variety.Comment: These are notes on 13p. based on a talk presented during the meeting
"Analysis on Graphs and Fractals", the Cardiff University, 29 May-2 June 2007
(a sattelite meeting of the programme "Analysis on Graphs and its
Applications" at the Isaac Newton Institute from 8 January to 29 June 2007
Efficacy of celecoxib in treating symptoms of viral pharyngitis: A double-blind, randomized study of celecoxib versus diclofenac
This study compared the efficacy and safety of the cyclooxygenase-2 specific inhibitor celecoxib with the conventional non-steroidal anti-inflammatory drug diclofenac in the symptomatic treatment of viral pharyngitis. Adult patients from 27 study centers in Latin America were treated with oral doses of celecoxib 200 mg once daily or 200 mg twice daily, or diclofenac 75 mg twice daily for 5 days in a double-blind, randomized study. The primary efficacy assessment was 'Throat Pain on Swallowing' on day 3. In addition, secondary quality-of-life assessments were performed on days 3 and 5. All adverse events and treatment-emergent signs and symptoms were recorded. Data from 313 patients were evaluable for efficacy (105 celecoxib 200 mg once daily, 107 celecoxib 200 mg twice daily, 101 diclofenac 75 mg twice daily). The upper 95% confidence limits for the visual analog scale of 'Throat Pain on Swallowing' on day 3 for celecoxib 200 mg once daily relative to diclofenac 75 mg twice daily, and celecoxib 200 mg twice daily relative to diclofenac 75 mg twice daily were 9.26 and 7.83, respectively. All secondary efficacy and quality-of-life measures were clinically similar for the three treatment groups, and no statistically significant differences were detected. The incidences of treatment-emergent adverse events and withdrawals due to adverse events were similar for all groups, but numerically higher among patients taking diclofenac than celecoxib. More patients in the diclofenac group reported gastrointestinal complaints (7.3%) compared with those in the celecoxib groups (4.3% in the celecoxib 200 mg once-daily group and 3.4% in the celecoxib 200 mg twice-daily group). In conclusion, 5 days of treatment with celecoxib 200 mg once daily is as effective as diclofenac 75 mg twice daily in the symptomatic treatment of viral pharyngitis. Celecoxib 200 mg once daily is also as effective as celecoxib 200 mg twice daily in this condition
Electronic Structure of Dangling Bonds in Amorphous Silicon Studied via a Density-Matrix Functional Method
A structural model of hydrogenated amorphous silicon containing an isolated
dangling bond is used to investigate the effects of electron interactions on
the electronic level splittings, localization of charge and spin, and
fluctuations in charge and spin. These properties are calculated with a
recently developed density-matrix correlation-energy functional applied to a
generalized Anderson Hamiltonian, consisting of tight-binding one-electron
terms parametrizing hydrogenated amorphous silicon plus a local interaction
term. The energy level splittings approach an asymptotic value for large values
of the electron-interaction parameter U, and for physically relevant values of
U are in the range 0.3-0.5 eV. The electron spin is highly localized on the
central orbital of the dangling bond while the charge is spread over a larger
region surrounding the dangling bond site. These results are consistent with
known experimental data and previous density-functional calculations. The spin
fluctuations are quite different from those obtained with unrestricted
Hartree-Fock theory.Comment: 6 pages, 6 figures, 1 tabl
Second Harmonic Generation for a Dilute Suspension of Coated Particles
We derive an expression for the effective second-harmonic coefficient of a
dilute suspension of coated spherical particles. It is assumed that the coating
material, but not the core or the host, has a nonlinear susceptibility for
second-harmonic generation (SHG). The resulting compact expression shows the
various factors affecting the effective SHG coefficient. The effective SHG per
unit volume of nonlinear coating material is found to be greatly enhanced at
certain frequencies, corresponding to the surface plasmon resonance of the
coated particles. Similar expression is also derived for a dilute suspension of
coated discs. For coating materials with third-harmonic (THG) coefficient,
results for the effective THG coefficients are given for the cases of coated
particles and coated discs.Comment: 11 pages, 3 figures; accepted for publication in Phys. Rev.
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