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Krzysztof Jan Nowak (2011)
Annales Polonici Mathematici
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We demonstrate that the composite function theorems of Bierstone-Milman-Pawłucki and of Glaeser carry over to any polynomially bounded, o-minimal structure which admits smooth cell decomposition. Moreover, the assumptions of the o-minimal versions can be considerably relaxed compared with the classical analytic ones.
Daniel A. Moran (1975)
Commentationes Mathematicae Universitatis Carolinae
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Zofia Ambroży, Wiesław Pawłucki (2015)
Banach Center Publications
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A local-global version of the implicit function theorem in o-minimal structures and a generalization of the theorem of Wilkie on covering open sets by open cells are proven.
P. Speissegger (1995)
Manuscripta mathematica
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Małgorzata Czapla, Wiesław Pawłucki (2016)
Annales Polonici Mathematici
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A version of Michael's theorem for multivalued mappings definable in o-minimal structures with M-Lipschitz cell values (M a common constant) is proven. Uniform equi-LCⁿ property for such families of cells is checked. An example is given showing that the assumption about the common Lipschitz constant cannot be omitted.
E. D. Tymchatyn (1972)
Colloquium Mathematicae
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A. Szabó, A. Czirók (2010)
Mathematical Modelling of Natural Phenomena
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Collective cell motility and its guidance via cell-cell contacts is instrumental in several morphogenetic and pathological processes such as vasculogenesis or tumor growth. Multicellular sprout elongation, one of the simplest cases of collective motility, depends on a continuous supply of cells streaming along the sprout towards its tip. The phenomenon is often explained as leader cells pulling the rest of the sprout forward via cell-cell adhesion. Building on an empirically demonstrated...