Square-free and overlap-free words
A. J. Kfoury (1988)
Banach Center Publications
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A. J. Kfoury (1988)
Banach Center Publications
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R. Z. Buzyakova, A. Chigogidze (2011)
Fundamenta Mathematicae
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Our main result states that every fixed-point free continuous self-map of ℝⁿ is colorable. This result can be reformulated as follows: A continuous map f: ℝⁿ → ℝⁿ is fixed-point free iff f̃: βℝⁿ → βℝⁿ is fixed-point free. We also obtain a generalization of this fact and present some examples
Caro, Yair (1990)
International Journal of Mathematics and Mathematical Sciences
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Jean Berstel (1985)
Publications du Département de mathématiques (Lyon)
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Karl Dilcher, Lutz G. Lucht (2006)
Acta Arithmetica
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Tomasz Schoen (2001)
Acta Arithmetica
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B. Tilson (1972)
Semigroup forum
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Ekhad, Shalosh B., Zeilberger, Doron (1998)
Journal of Integer Sequences [electronic only]
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A. Kumar, P. K. Pathak (1976)
Colloquium Mathematicae
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Calkin, Neil J., Finch, Steven R. (1996)
Experimental Mathematics
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F. Levin, G. Rosenberger, B. Baumslag (1993)
Mathematische Zeitschrift
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Ruimei Gao, Xiupeng Cui, Zhe Li (2017)
Open Mathematics
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In this paper, we define the supersolvable order of hyperplanes in a supersolvable arrangement, and obtain a class of inductively free arrangements according to this order. Our main results improve the conclusion that every supersolvable arrangement is inductively free. In addition, we assert that the inductively free arrangement with the required induction table is supersolvable.
Henry Francis Joseph Löwig (1968)
Czechoslovak Mathematical Journal
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Frank Levin, Benjamin Baumslag (1976)
Mathematische Zeitschrift
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Walter Thirring (1972)
Recherche Coopérative sur Programme n°25
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Xavier Ros-Oton, Joaquim Serra (2019)
Matematica, Cultura e Società. Rivista dell'Unione Matematica Italiana
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Free boundary problems are those described by PDEs that exhibit a priori unknown (free) interfacesor boundaries. The most classical example is the melting of ice to water (the Stefan problem). In this case, the freeboundary is the liquid-solid interface between ice and water. A central mathematical challenge in this context is to understand the regularity and singularities of free boundaries. In this paper we provide a gentle introduction to this topic by presenting some classical results...