Guest editorial

Citation

Cherruault, Y. (2009), "Guest editorial", Kybernetes, Vol. 38 No. 5. https://doi.org/10.1108/k.2009.06738eaa.002

Guest editorial

Article Type: Guest editorial From: Kybernetes, Volume 38, Issue 5

The contributions that are included in this special issue have been selected from those presented at the important first conference on “Models and Mathematical Methods and their Applications to Biology and Industry”. This event was indeed the first of what is hoped will be a series of such events. As a result of its success we were pleased to have been invited by the Editorial Advisory Board of Kybernetes to compile this issue which has been carefully prepared to show the range of contributions that were given at this conference which was held in La Roche sur Yon (Vendee, France) in December 2007. All the papers included here have been updated and double-refereed after the event so that they reflect the discussions which took place after their presentation and in the main discussion held at the end of the presented works.

A scientific report of this first conference was published in this journal’s Technical Reports (Cherruault, 2008), where it was emphasized that the aim of the conference was to present mathematical and numerical methods for solving problems arising from biology, medicine, the food industry and more generally from the industrial field. As a result most of the presentations were related to modelling, identification, optimisation, optimal control and algorithms for solving functional equations. In this compilation, we have chosen papers for publication that specifically follow those guidelines. An example of this strategy is the inclusion of contributions by Yves Cherruault, Jean Claude Mazza, and Gaspar Mora, who devoted their presentations to the theory of α-dense curves and their applications to industrial processes. These authors were intent on proving the power of this method applied to global optimization involving continuous or integer variables. It is believed that generally, industrial problems can be easily and completely solved by means α-dense curves. This is shown by Professor Gaspar Mora who has developed a theory of V-dense curves in topological vector spaces with application to industrial problems. By using this approach he has been able to obtain a solution for ill-posed problems. Also selected for inclusion in this issue is a paper by Feyed Ben Zitoun and Yves Cherruault who describe a new algorithm designed to solve non-linear boundary value problems. Another new method is introduced by Yves Cherruault to resolve industrial problems This is a method which proved to be both simple and universal in its usage.

Said Guellal and his colleagues Alain Meulemans and Salim Khelifa, have developed and mathematically studied an enzymatic model of neuronal NO-synthase. It should be noted that Alain Meulemans claims to have detected a neurophysical error in some recent scientific publications.

One of the last presenters at the conference was Ngarkodje Ngarasta of the Universite de Ndjamena au TCHAD (Chad) who applied the Adomian decomposition methods to the resolution of non-linear integral equations. This has been selected for publication in this issue and it illustrates some of the previous works of Yves Cherruault and colleagues

Bekhaled Hebri with Salim Khelifa and Yves Cherruault, offer another new approach concerning the stability of the linearization method in compartmental analysis. Whilst Armand Caron explains, the new results on the approximate solution of the non-linear partial derivative equation system of corona-electrical separation.

There is no doubt that the “First Conference” offered many important contributions to studies in modelling and using mathematical methods in both biology and in industry. The updated papers included in this special issue will also continue not only to offer new initiatives and new methodologies but also contribute substantially to the existing studies in this important and expanding field.

Yves CherruaultGuest Editor