




Contributed Papers Session / Communications libres (Patrick Browne, Organizer)
 KHALID ELYASSINI
Some interiorexterior points methods for linear programming

We describe different interiorexterior algorithms for linear
programming problem and we specially present our recent algorithm based
on path following idea. The algorithm uses a two parameter mixed
penalty function. Each iteration updates the penalty parameters. An
approximate solution, of KarushKuhnTucker system of equations which
characterizes a solution of the mixed penalty function, is computed by
using only one Newton direction or by using the predictorcorrector
method. The approximate solution obtained gives a dual and a
pseudofeasible primal points. Since the primal solution is non
feasible, a new pseudogap definition is introduced to characterize
primal and dual solutions. Finally, Some numerical results will be
presented.
 ILHAN IZMIRLI, Strayer University, Washington, D.C. 20005, USA
On some generalizations of an indeterminate problem of
Ibn Hamza

In this paper, I will talk about some of the contributions of the
famous Middle Eastern mathematician Ibn Hamza to mathematics. I will
mostly concentrate on a problem posed and solved by him around 1590's,
along with some interesting generalizations of this rather elegant
solution.
 JOHN H. URSELL, P.O. Box 761, Kingston, Ontario K7L 4X6
An elementary proof of the second case of Fermat's last
theorem

Fermat's Last Theorem is divided into exactly two cases for odd prime
exponent p. This talk gives an elementary proof of the second case.
The present author believes that Pierre de Fermat had this proof.
 YOUCHEN ZHOU, Zhejian University
On Moeckellike boundary of the local Siegel disk

For a family of simple closed curves in the local Siegel Disk (defined
by J. T. Rogers, Jr.) that converges to the boundary of the disk, we
get a simple and clear condition on it that is sufficient and necessary
to the boundary being Moeckellike. It is also proven that third and
fourth kinds of prime ands are empty for Moeckellike boundary.

