Subject: ICTP Preprints titles - January 1999
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1998LIST-14
This is the fourteenth list of 1998 ICTP preprints which have been
issued.
(Also available at: http://www.ictp.trieste.it/~pub_offsiedstmlrgy-list-archive/.sasianet/sasia)
+--------------------------------------------------------------+
ICTP Preprint No.IC98077
AN EQUIVALENCE OF A SYSTEM OF PARTIAL INTEGRAL EQUATIONS
TO A SYSTEM OF FREDHOLM¹S INTEGRAL EQUATIONS
by S.N. Lakaev and I.N. Khayrullaev
ABSTRACT: Two systems of partial integral equations are considered.
Under
some natural conditions the equivalence of these equations,
corresponding
to the systems of second kind of Fredholm¹s integral equations, is
proved.
ICTP Preprint No.IC98136
INDUCED REPRESENTATIONS OF THE MULTIPARAMETER HOPF
SUPERALGEBRAS U$_{u\bf q}$(gl(m/n)) AND U$_{u\bf q}$(sl(m/n))
by V.K. Dobrev and E.H. Tahri
ABSTRACT: We construct induced representations of the multiparameter
Hopf
superalgebras $U_{u\q}(gl(m/n))$ and $U_{u\q}(sl(m/n))$. The first
superalgebra we constructed earlier as the dual of the multiparameter
quantum deformation of the supergroup $GL(m/n)$. The second
superalgebra is
a Hopf subalgebra of the first for a special choice of the parameters.
The
representations are labelled by $m+n$ integer numbers, respectively
$m+n-1$
complex numbers, and act in the space of formal power series of
$(m+n)(m+n-
1)/2$ non-commuting variables, of which $mn$ are odd and the rest are
even.
These variables generate a $q$-deformation of a flag supermanifold
of the supergroup $GL(m/n)$, respectively $SL(m/n)$.
ICTP Preprint No.IC98137
TOPICS IN BAYESIAN STATISTICS AND MAXIMUM ENTROPY
by R. Mutihac, C. Stanciulescu, A. Cicuttin and A. Cerdeira
ABSTRACT: Notions of Bayesian decision theory and maximum entropy
methods
are reviewed with particular emphasis on probabilistic inference and
Bayesian modeling, The axiomatic approach is considered as the best
justification of Bayesian analysis and maximum entropy principle
applied in
natural sciences. Particular emphasis is put on solving the inverse
problem
in digital image restoration and Bayesian modeling of neural networks.
Further topics addressed briefly include language modeling, neutron
scattering, multiuser detection and channel equalization in digital
communications, genetic information, and Bayesian court
decision-making.
ICTP Preprint No.IC98138
HIDDEN SUPERSYMMETRY AND BEREZIN QUANTIZATION OF N = 2, D = 3
SPINNING SUPERPARTICLES
by I.V. Gorbunov and S.L. Lyakhovich
ABSTRACT: The first quantized theory of N=2, D=3 massive superparticles
with arbitrary fixed central charge and (half)integer or fractional
superspin is constructed. The quantum states are realized on the fields
carrying a finite dimensional, or a unitary infinite dimensional
representation of the supergroups $\rm OSp(2|2)$ or $\rm SU(1,1|2)$.
The
construction originates from quantization of a classical model of the
superparticle we suggest. The physical phase space of the classical
superparticle is embedded in a symplectic superspace $T^\ast({\rm
R}^{1,2})\times{\cal L}^{1|2}$, where the inner Kahler
supermanifold $\rm{\cal L}^{1|2}\cong OSp(2|2)/[U(1)\times U(1)]\cong
SU(1,1|2)/[U(2|2)\times U(1)]$ provides the particle with superspin
degrees
of freedom. We find the relationship between Hamiltonian generators of
the
global Poincar\'e supersymmetry and the "internal" $\rm SU(1,1|2)$ one.
Quantization of the superparticle combines the Berezin quantization
on ${\cal L}^{1|2}$ and the conventional Dirac quantization with
respect to
space-time degrees of freedom. Surprisingly, to retain the
supersymmetry,
quantum corrections are required for the classical N=2 supercharges as
compared to the conventional Berezin method. These corrections are
derived
and the Berezin correspondence principle for ${\cal L}^{1|2}$
underlying
their origin is verified. The model admits a smooth contraction to the
N=1
supersymmetry in the BPS limit.
ICTP Preprint No.IC98139
LATTICE VIBRATIONS AND ELASTIC CONSTANTS OF CRYSTALLINE $^4$He AND
$^3$He
NEAR LOW-TEMPERATURE MELTING
by V. Tozzini and M.P. Tosi
ABSTRACT: The phonon dispersion curves and the elastic constants are
evaluated for crystallinE $^4$He and $^3$He near melting at low
temperature
in the deep quantal regime. The structures considered are the hexagonal
close-packed and the body-centred and face-centred cubic ones for
$^4$He
and the body-centred cubic one for $^3$He. The calculations use a
density
functional approach to construct a field of effective force constants
in
the strongly anharmonic solid near melting from its Debye-Waller factor
and
from the linear density response function of the fluid phase at
freezing.
The results of the calculations are compared with the available
experimental evidence: good agreement is generally found for transverse
phonon frequencies and shear elastic constants, and phenomenological
adjustments of the force-constant field are proposed for a quantitative
description of the longitudinal modes. A relationship between the
dispersion curves of phonons in crystalline $^4$He and that of
elementary
collective excitations in superfluid $^4$He is displayed and discussed
in
the light of current interpretations of atomic dynamics in the
superfluid
phase, with main emphasis on the region of the roton minimum.
ICTP Preprint No.IC98140
ON THE QUANTUM SUPER VIRASORO ALGEBRA
by M. Mansour
ABSTRACT: The quantum super-algebra structure on the deformed super
Virasoro algebra is investigated. More specifically we established the
possibility of defining a non trivial Hopf super-algebra on both one
and
two-parameters deformed super Virasoro algebras.
ICTP Preprint No.IC98141
SECOND HARMONICS AND COMPENSATION EFFECT IN CERAMIC SUPERCONDUCTORS
by Mai Suan Li
ABSTRACT: The nonlinear ac susceptibility and the compensation effect
observed in ceramic superconductors which show the paramagnetic
Meissner
effect are studied by the Monte Carlo simulations on a three
dimensional
lattice model of the Josephson array with finite self-conductance. Our
study is based on the possible existence of the chiral glass phase in
these
materials. In agreement with experiments, the compensation effect is
demonstrated to be present in $d$-wave superconductors but not in the
$s$-
wave ones.
ICTP Preprint No.IC98142
AN APPLICATION OF NONLINEAR FUNDAMENTAL PROBLEMS
OF A TRANSVERSELY ISOTROPIC LAYER IN FINITE ELASTIC DEFORMATION
by Ade Akinola
ABSTRACT: We obtain the complex potentials and the accompanying
nonlinear
fundamental problems for the plane problem of a transversely-isotropic
body
under finite elastic deformation. The fundamental problem-two is
considered
for an infinite medium, with a circular hole in the initial
configuration.
It is obtained that in the current configuration the deforming contour
is
not rigidly circular, due to finite deformation effect. Variation of
the
deforming contour with respect to the parameter of finite deformation
(or
parameter of nonlinearity) is given.
ICTP Preprint No.IC98143
SUPERSYMMETRIC SINE ALGEBRA AND DEGENERACY OF LANDAU LEVELS
by A. Jellal, M. Daoud and Y. Hassouni
ABSTRACT: Two different realizations of the supersymmetric sine algebra
(SSA) are given. We show that the quantum superalgebra $sl_{q}(2/1)$ is
derived from the SSA. We discuss the relevance of the latter result to
the
study of spin-$1\over 2$ Bloch electron in a constant magnetic field.
The relation between the deformation parameter $q$ and the degeneracy
of
Landau levels is established.
ICTP Preprint No.IC98144
AN EFFECTIVE FIELD STUDY OF THE MAGNETIC PROPERTIES AND CRITICAL
BEHAVIOUR AT THE SURFACE ISING FILM
by Mouna Bengrine, Abdelilah Benyoussef, Hamid Ez-Zahraouy
and Fouad Mhirech
ABSTRACT: The influence of corrugation and disorder at the surface on
the
critical behaviour of a ferromagnetic spin-1/2 Ising film is
investigated
using mean-field theory and finite cluster approximation. It is found
that the critical surface exponent $\beta_1$ follows closely the one
of
a perfect surface, in the two cases: corrugated surface and random
equiprobable coupling surface. However, in the case of flat surface
with
random interactions the surface critical exponent $\beta_1$ depends on
the concentration $p$ of the strong interaction for $p>p_c = 0.5$,
while
for $p<