Abstracts - Facultatea de Matematică

Providing irrigation canals with automatic controllers leads to increase the exploitation
performance.
The major part of the mathematical simulation models are based on the numerical or
analytical solution of the nonlinear equations with partial derivatives of hyperbolic type
that govern the unsteady flow in the canals equipped with the automatic regulators.
In this paper we offer an answer on how to conceive and use an analytical model
for the design of the automatic irrigation canals for practical important situations. The
model was obtained by analytical integration of the linearized equations based on the
hypothesis of small oscillation theory and the properties of the Fourier transforms. It
can be used to predict the behavior of the system under the perturbation factors.
Semi-cardinal models for multivariable interpolation
Aurelian BEJANCU
Kuwait University
abejancu@yahoo.co.uk
Schoenberg’s ‘semi-cardinal interpolation’ (SCI) model in univariate spline theory
constructs a polynomial spline function that interpolates values given on the grid Z+ of
non-negative integers. We present an overview of recent multivariable extensions of the
SCI model, focusing on the complete results obtained for interpolation on the semi-plane
grid Z+ × Z from a space of triangular box-splines. The box-spline SCI schemes employ
boundary conditions that extend the ‘natural’ and ‘not-a-knot’ end-point conditions of
cubic spline interpolation. The analysis of the localization and polynomial reproduction
properties of the bivariate SCI schemes proves that the ‘natural’-type boundary conditions
induce a halving effect in accuracy, while the ‘not-a-knot’-type conditions achieve
maximal accuracy (Bejancu A., J. Comput. Appl. Math., to appear; Bejancu A., Sabin
M.A., Adv. Comput. Math. 22 (2005), 275-298).
A Viability Result for Semilinear Reaction-Diffusion Sytems
Monica BURLICĂ and Daniela ROS¸U
Chair of Mathematics, “Gheorghe Asachi” Technical University of Ia¸si, Romania
monicaburlica@yahoo.com, rosudaniela100@yahoo.com
Using some some topological assumptions, expressed by the Kuratowski measure of
noncompactness, we establish several necessary and sufficient conditions for viability for
various classes of semilinear reaction-diffusion systems.
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