842 research outputs found
Eastern Shona : a comparative dialect study
In this paper, the speech patterns of eleven individuals living in the Eastern half of Rhodesia are described and compared. Each individual was selected as being representative of a number of localities described in the map below. The first part of the paper is concerned with the abstraction of comparable linguistic units from the dialects. These units are abstracted at various levels of analysis and unit categories include phonemes, tonemes, morphophonemes, tonomorphemes and morphemes. Each unit category is described in relation to the general structural framework of the dialects established by a sentence analysis. The units so abstracted and described constitute the distinctive attributes of each dialect. In part two the dialects are compared and classified by computer according to their correspondence to approximately one thousand selected properties
Microscopic dynamics underlying the anomalous diffusion
The time dependent Tsallis statistical distribution describing anomalous
diffusion is usually obtained in the literature as the solution of a non-linear
Fokker-Planck (FP) equation [A.R. Plastino and A. Plastino, Physica A, 222, 347
(1995)]. The scope of the present paper is twofold. Firstly we show that this
distribution can be obtained also as solution of the non-linear porous media
equation. Secondly we prove that the time dependent Tsallis distribution can be
obtained also as solution of a linear FP equation [G. Kaniadakis and P.
Quarati, Physica A, 237, 229 (1997)] with coefficients depending on the
velocity, that describes a generalized Brownian motion. This linear FP equation
is shown to arise from a microscopic dynamics governed by a standard Langevin
equation in presence of multiplicative noise.Comment: 4 pag. - no figures. To appear on Phys. Rev. E 62, September 200
Nonextensive Entropies derived from Form Invariance of Pseudoadditivity
The form invariance of pseudoadditivity is shown to determine the structure
of nonextensive entropies. Nonextensive entropy is defined as the appropriate
expectation value of nonextensive information content, similar to the
definition of Shannon entropy. Information content in a nonextensive system is
obtained uniquely from generalized axioms by replacing the usual additivity
with pseudoadditivity. The satisfaction of the form invariance of the
pseudoadditivity of nonextensive entropy and its information content is found
to require the normalization of nonextensive entropies. The proposed principle
requires the same normalization as that derived in [A.K. Rajagopal and S. Abe,
Phys. Rev. Lett. {\bf 83}, 1711 (1999)], but is simpler and establishes a basis
for the systematic definition of various entropies in nonextensive systems.Comment: 16 pages, accepted for publication in Physical Review
Nonlinear equation for anomalous diffusion: unified power-law and stretched exponential exact solution
The nonlinear diffusion equation is analyzed here, where , and , and are real parameters.
This equation unifies the anomalous diffusion equation on fractals ()
and the spherical anomalous diffusion for porous media (). Exact
point-source solution is obtained, enabling us to describe a large class of
subdiffusion (), normal diffusion () and
superdiffusion (). Furthermore, a thermostatistical basis
for this solution is given from the maximum entropic principle applied to the
Tsallis entropy.Comment: 3 pages, 2 eps figure
Option Pricing Formulas based on a non-Gaussian Stock Price Model
Options are financial instruments that depend on the underlying stock. We
explain their non-Gaussian fluctuations using the nonextensive thermodynamics
parameter . A generalized form of the Black-Scholes (B-S) partial
differential equation, and some closed-form solutions are obtained. The
standard B-S equation () which is used by economists to calculate option
prices requires multiple values of the stock volatility (known as the
volatility smile). Using which well models the empirical distribution
of returns, we get a good description of option prices using a single
volatility.Comment: final version (published
Multiplicative noise: A mechanism leading to nonextensive statistical mechanics
A large variety of microscopic or mesoscopic models lead to generic results
that accommodate naturally within Boltzmann-Gibbs statistical mechanics (based
on ). Similarly, other classes of models
point toward nonextensive statistical mechanics (based on , where the value of the entropic index depends on
the specific model). We show here a family of models, with multiplicative
noise, which belongs to the nonextensive class. More specifically, we consider
Langevin equations of the type , where
and are independent zero-mean Gaussian white noises with
respective amplitudes and . This leads to the Fokker-Planck equation
. Whenever the
deterministic drift is proportional to the noise induced one, i.e., , the stationary solution is shown to be (with and ). This distribution is
precisely the one optimizing with the constraint constant. We also
introduce and discuss various characterizations of the width of the
distributions.Comment: 3 PS figure
Anomalous diffusion and Tsallis statistics in an optical lattice
We point out a connection between anomalous quantum transport in an optical
lattice and Tsallis' generalized thermostatistics. Specifically, we show that
the momentum equation for the semiclassical Wigner function that describes
atomic motion in the optical potential, belongs to a class of transport
equations recently studied by Borland [PLA 245, 67 (1998)]. The important
property of these ordinary linear Fokker--Planck equations is that their
stationary solutions are exactly given by Tsallis distributions. Dissipative
optical lattices are therefore new systems in which Tsallis statistics can be
experimentally studied.Comment: 4 pages, 1 figur
Some Open Points in Nonextensive Statistical Mechanics
We present and discuss a list of some interesting points that are currently
open in nonextensive statistical mechanics. Their analytical, numerical,
experimental or observational advancement would naturally be very welcome.Comment: 30 pages including 6 figures. Invited paper to appear in the
International Journal of Bifurcation and Chao
Nonlinear anomalous diffusion equation and fractal dimension: Exact generalized gaussian solution
In this work we incorporate, in a unified way, two anomalous behaviors, the
power law and stretched exponential ones, by considering the radial dependence
of the -dimensional nonlinear diffusion equation where , ,
, and are real parameters and is a time-dependent
source. This equation unifies the O'Shaugnessy-Procaccia anomalous diffusion
equation on fractals () and the spherical anomalous diffusion for
porous media (). An exact spherical symmetric solution of this
nonlinear Fokker-Planck equation is obtained, leading to a large class of
anomalous behaviors. Stationary solutions for this Fokker-Planck-like equation
are also discussed by introducing an effective potential.Comment: Latex, 6 pages. To appear in Phys. Rev.
Quantum entanglement inferred by the principle of maximum Tsallis entropy
The problem of quantum state inference and the concept of quantum
entanglement are studied using a non-additive measure in the form of Tsallis
entropy indexed by the positive parameter q. The maximum entropy principle
associated with this entropy along with its thermodynamic interpretation are
discussed in detail for the Einstein-Podolosky-Rosen pair of two spin-1/2
particles. Given the data on the Bell-Clauser-Horne-Shimony-Holt observable,
the analytic expression is given for the inferred quantum entangled state. It
is shown that for q greater than unity, indicating the sub-additive feature of
the Tsalls entropy, the entangled region is small and enlarges as one goes into
super-additive regime where q is less than unity. It is also shown that quantum
entanglement can be quantified by the generalized Kullback-Leibler entropy.Comment: 15 pages, 1 figur
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