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Sommation effective d’une somme de Borel par séries de factorielles

Eric Delabaere, Jean-Marc Rasoamanana (2007)

Annales de l’institut Fourier

Nous abordons dans cet article la question de la sommation effective d’une somme de Borel d’une série par la série de factorielles associée. Notre approche fournit un contrôle de l’erreur entre la somme de Borel recherchée et les sommes partielles de la série de factorielles. Nous généralisons ensuite cette méthode au cadre des séries de puissances fractionnaires, après avoir démontré un analogue d’un théorème de Nevanlinna de sommation de Borel fine pour ce cadre.

Space-time caustics.

Gorman, Arthur D. (1986)

International Journal of Mathematics and Mathematical Sciences

Spatiotemporal Dynamics in a Spatial Plankton System

R. K. Upadhyay, W. Wang, N. K. Thakur (2010)

Mathematical Modelling of Natural Phenomena

In this paper, we investigate the complex dynamics of a spatial plankton-fish system with Holling type III functional responses. We have carried out the analytical study for both one and two dimensional system in details and found out a condition for diffusive instability of a locally stable equilibrium. Furthermore, we present a theoretical analysis of processes of pattern formation that involves organism distribution and their interaction of spatially...

Spatio-Temporal Modelling of the p53–mdm2 Oscillatory System

K. E. Gordon, I. M.M. van Leeuwen, S. Laín, M. A.J. Chaplain (2009)

Mathematical Modelling of Natural Phenomena

In this paper we investigate the role of spatial effects in determining the dynamics of a subclass of signalling pathways characterised by their ability to demonstrate oscillatory behaviour. To this end, we formulate a simple spatial model of the p53 network that accounts for both a negative feedback and a transcriptional delay. We show that the formation of protein density patterns can depend on the shape of the cell, position of the nucleus, and the protein diffusion rates. The temporal...

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