International Conference
"PIONEERS OF BULGARIAN MATHEMATICS"
A B S T R A C T S
DISPERSIVE ESTIMATES OF SOLUTIONS TO THE
WAVE EQUATION WITH A POTENTIAL IN DIMENSIONS TWO AND THREE
Fernando Cardoso
fernando@dmat.ufpe.br
Claudio Cuevas
cch@dmat.ufpe.br
Georgi Vodev
georgi.vodev@math.univnantes.fr
2000 Mathematics Subject Classification: 35L15, 35B40, 47F05.
Key words:
Wave equation, dispersive estimates.
We prove dispersive estimates
for solutions to the wave equation with a realvalued potential
V Î L^{¥}(R^{n}), n = 2 or 3, satisfying
V(x) = O(áxñ^{(n+1)/2e}), e > 0.
NECESSARY AND SUFFICIENT CONDITION FOR OSCILLATIONS OF NEUTRAL DIFFERENTIAL
EQUATION
E. M. Elabbasy
emelabbasy@mans.edu.eg
T. S. Hassan
tshassan@mans.edu.eg
S. H. Saker
shsaker@mans.edu.eg
2000 Mathematics Subject Classification: 34K15, 34C10.
Key words:
Oscillation, Characteristic equation, Neutral
delay differential equations.
We obtain necessary and sufficient conditions for the oscillation of all
solutions of neutral differential equation with mixed (delayed and advanced)
arguments

é ë

x( t) + 
m å
k = 1

r_{k}x( tm_{k}) 
ù û

¢+ 
n å
i = 1

p_{i}x( tt_{i}) = 0, 

where r_{k}, m_{k}, p_{i}, t_{i} Î R for k = 1,2,...,m
and i = 1,2,... ,n. Our results extend and improve several known results
in the literature and solve an open problem posed by Gyori and Ladas
[6].
QUASILIKELIHOOD ESTIMATION FOR ORNSTEINUHLENBECK
DIFFUSION OBSERVED AT RANDOM TIME POINTS
Michel Adès
ades.michel@uqam.ca
JeanPierre Dion
dion.jeanpierre@uqam.ca
Brenda MacGibbon
macgibbon.brenda@uqam.ca
2000 Mathematics Subject Classification:
60J60, 62M99.
Key words:
Diffusion Processes, OrnsteinUhlenbeck,
QuasiLikelihood, Poisson arrivals.
In this paper, we study the quasilikelihood estimator of the drift
parameter q in the OrnsteinUhlenbeck diffusion process, when
the process is observed at random time points, which are assumed to
be unobservable. These time points are arrival times of a Poisson
process with known rate. The asymptotic properties of the quasilikelihood
estimator (QLE) of q, as well as those of its approximations are also
elucidated. An extensive simulation study of these estimators is also
performed. As a corollary to this work, we obtain the quasilikelihood
estimator iteratively in the deterministic framework with nonequidistant
time points.
RÉTRACTES ABSOLUS DE VOISINAGE ALGÉBRIQUES
Robert Cauty
cauty@math.jussieu.fr
2000 Mathematics Subject Classification:
54C55, 54H25, 55M20.
Key words:
Algebraic ANRs, LefschetzHopf fixed point theorem.
We introduce the class of algebraic ANRs. It is defined by replacing
continuous maps by chain mappings in Lefschetz's characterization of
ANRs. To a large extent, the theory of algebraic ANRs parallels the
classical theory of ANRs. Every ANR is an algebraic ANR, but the class
of algebraic ANRs is much larger; the most striking difference between
these classes is that every locally equiconnected metrisable space is an
algebraic ANR, whereas there exist metric linear spaces which are not ARs.
This is important for applications of topological fixed point theory to
functional analysis because all known results of fixed point for compact
maps of ANRs extend to the algebraic ANRs. We prove here two such
generalizations: the LefschetzHopf fixed point theorem for compact
maps of algebraic ANRs, and the fixed point theorem for compact upper
semicontinuous multivalued maps with Qacyclic compacts point
images in a Qacyclic algebraic ANR. We stress that these
generalizations apply to all neighborhood retract of a metrisable
linear space and, more generally, of a locally contractible metrisable group.
In the frames of the celebration of
the 120 anniversary of Academician Lubomir Tschakaloff (18861963)
and the 110 anniversary of Academician Nikola Obrechkoff (18961963)
under the aegis of the Bulgarian National Committee of Mathematics,
The Department of Mathematics and Informatics
of the Sofia University St. Kliment Ohridski
is organizing an international conference
PIONEERS OF BULGARIAN MATHEMATICS
dedicated to these two anniversaries. The conference will take place in
Sofia, July 810, 2006.
The organizers have the ambition to gather in Sofia most of the
mathematicians and specialists
in computer science with Bulgarian origin from all over the world. The
scope of the conference
will cover all fields of interest of the two mathematical giants:
mathematical analysis,
theory of functions, algebra, number theory, probability, numerical
analysis, as well as computer science.
Detailed information can be found in the web site
http://profot.fmi.unisofia.bg
Proceedings of the Conference will be published as special issues of
Serdica Mathematical Journal
and Annuaire de l'Université de Sofia St. Kliment Ohridski,
Faculté de Mathèmatiques et Informatique
(Godishnik na Sofijskiya Universitet),
following the standard procedure for publishing in these journals.
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