224,656 research outputs found
Painlev\'e V and time dependent Jacobi polynomials
In this paper we study the simplest deformation on a sequence of orthogonal
polynomials, namely, replacing the original (or reference) weight
defined on an interval by It is a well-known fact that under
such a deformation the recurrence coefficients denoted as and
evolve in according to the Toda equations, giving rise to the
time dependent orthogonal polynomials, using Sogo's terminology. The resulting
"time-dependent" Jacobi polynomials satisfy a linear second order ode. We will
show that the coefficients of this ode are intimately related to a particular
Painlev\'e V. In addition, we show that the coefficient of of the
monic orthogonal polynomials associated with the "time-dependent" Jacobi
weight, satisfies, up to a translation in the Jimbo-Miwa -form of
the same while a recurrence coefficient is up to a
translation in and a linear fractional transformation
These results are found
from combining a pair of non-linear difference equations and a pair of Toda
equations. This will in turn allow us to show that a certain Fredholm
determinant related to a class of Toeplitz plus Hankel operators has a
connection to a Painlev\'e equation
Strong gravitational lensing in a squashed Kaluza-Klein black hole spacetime
We investigate the strong gravitational lensing in a Kaluza-Klein black hole
with squashed horizons. We find the size of the extra dimension imprints in the
radius of the photon sphere, the deflection angle, the angular position and
magnification of the relativistic images. Supposing that the gravitational
field of the supermassive central object of the Galaxy can be described by this
metric, we estimated the numerical values of the coefficients and observables
for gravitational lensing in the strong field limit.Comment: 13pages, 5 figures, Final version appeared in PR
Computer Program for the Calculation of Multicomponent Convective Diffusion Deposition Rates from Chemically Frozen Boundary Layer Theory
The computer program based on multicomponent chemically frozen boundary layer (CFBL) theory for calculating vapor and/or small particle deposition rates is documented. A specific application to perimter-averaged Na2SO4 deposition rate calculations on a cylindrical collector is demonstrated. The manual includes a typical program input and output for users
An artificial intelligence-based structural health monitoring system for aging aircraft
To reduce operating expenses, airlines are now using the existing fleets of commercial aircraft well beyond their originally anticipated service lives. The repair and maintenance of these 'aging aircraft' has therefore become a critical safety issue, both to the airlines and the Federal Aviation Administration. This paper presents the results of an innovative research program to develop a structural monitoring system that will be used to evaluate the integrity of in-service aerospace structural components. Currently in the final phase of its development, this monitoring system will indicate when repair or maintenance of a damaged structural component is necessary
Composite-fermionization of bosons in rapidly rotating atomic traps
The non-perturbative effect of interaction can sometimes make interacting
bosons behave as though they were free fermions. The system of neutral bosons
in a rapidly rotating atomic trap is equivalent to charged bosons coupled to a
magnetic field, which has opened up the possibility of fractional quantum Hall
effect for bosons interacting with a short range interaction. Motivated by the
composite fermion theory of the fractional Hall effect of electrons, we test
the idea that the interacting bosons map into non-interacting spinless fermions
carrying one vortex each, by comparing wave functions incorporating this
physics with exact wave functions available for systems containing up to 12
bosons. We study here the analogy between interacting bosons at filling factors
with non-interacting fermions at for the ground state
as well as the low-energy excited states and find that it provides a good
account of the behavior for small , but interactions between fermions become
increasingly important with . At , which is obtained in the limit
, the fermionization appears to overcompensate for the
repulsive interaction between bosons, producing an {\em attractive}
interactions between fermions, as evidenced by a pairing of fermions here.Comment: 8 pages, 3 figures. Submitted to Phys. Rev.
Hopf Bifurcation and Chaos in Tabu Learning Neuron Models
In this paper, we consider the nonlinear dynamical behaviors of some tabu
leaning neuron models. We first consider a tabu learning single neuron model.
By choosing the memory decay rate as a bifurcation parameter, we prove that
Hopf bifurcation occurs in the neuron. The stability of the bifurcating
periodic solutions and the direction of the Hopf bifurcation are determined by
applying the normal form theory. We give a numerical example to verify the
theoretical analysis. Then, we demonstrate the chaotic behavior in such a
neuron with sinusoidal external input, via computer simulations. Finally, we
study the chaotic behaviors in tabu learning two-neuron models, with linear and
quadratic proximity functions respectively.Comment: 14 pages, 13 figures, Accepted by International Journal of
Bifurcation and Chao
The symplectic Deligne-Mumford stack associated to a stacky polytope
We discuss a symplectic counterpart of the theory of stacky fans. First, we
define a stacky polytope and construct the symplectic Deligne-Mumford stack
associated to the stacky polytope. Then we establish a relation between stacky
polytopes and stacky fans: the stack associated to a stacky polytope is
equivalent to the stack associated to a stacky fan if the stacky fan
corresponds to the stacky polytope.Comment: 20 pages; v2: To appear in Results in Mathematic
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