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Does Atkinson-Wilcox Expansion Converges for any Convex Domain?

Arnaoudov, I., Georgiev, V., Venkov, G. (2007)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 35C10, 35C20, 35P25, 47A40, 58D30, 81U40.The Atkinson-Wilcox theorem claims that any scattered field in the exterior of a sphere can be expanded into a uniformly and absolutely convergent series in inverse powers of the radial variable and that once the leading coefficient of the expansion is known the full series can be recovered uniquely through a recurrence relation. The leading coefficient of the series is known as the scattering amplitude or the far...

Dynamics of Erythroid Progenitors and Erythroleukemia

N. Bessonov, F. Crauste, I. Demin, V. Volpert (2009)

Mathematical Modelling of Natural Phenomena

The paper is devoted to mathematical modelling of erythropoiesis, production of red blood cells in the bone marrow. We discuss intra-cellular regulatory networks which determine self-renewal and differentiation of erythroid progenitors. In the case of excessive self-renewal, immature cells can fill the bone marrow resulting in the development of leukemia. We introduce a parameter characterizing the strength of mutation. Depending on its value, leukemia will or will not develop. The simplest...

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