On affine geometric product objects
Józef Joachim Telega (1977)
Annales Polonici Mathematici
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Józef Joachim Telega (1977)
Annales Polonici Mathematici
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Janko Marovt (2006)
Studia Mathematica
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Let 𝒳 be a compact Hausdorff space which satisfies the first axiom of countability, I = [0,1] and 𝓒(𝒳,I) the set of all continuous functions from 𝒳 to I. If φ: 𝓒(𝒳,I) → 𝓒(𝒳,I) is a bijective affine map then there exists a homeomorphism μ: 𝒳 → 𝒳 such that for every component C in 𝒳 we have either φ(f)(x) = f(μ(x)), f ∈ 𝓒(𝒳,I), x ∈ C, or φ(f)(x) = 1-f(μ(x)), f ∈ 𝓒(𝒳,I), x ∈ C.
Paweł Urbański (2003)
Banach Center Publications
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An affine Cartan calculus is developed. The concepts of special affine bundles and special affine duality are introduced. The canonical isomorphisms, fundamental for Lagrangian and Hamiltonian formulations of the dynamics in the affine setting are proved.
Veldsman, Stefan (1992)
Mathematica Pannonica
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Cruceanu, Vasile (2005)
Balkan Journal of Geometry and its Applications (BJGA)
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Takashi Sano (1999)
Banach Center Publications
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We study affine invariants of plane curves from the view point of the singularity theory of smooth functions. We describe how affine vertices and affine inflexions are created and destroyed.
Christoph Bandt, Mathias Mesing (2009)
Banach Center Publications
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In the class of self-affine sets on ℝⁿ we study a subclass for which the geometry is rather tractable. A type is a standardized position of two intersecting pieces. For a self-affine tiling, this can be identified with an edge or vertex type. We assume that the number of types is finite. We study the topology of such fractals and their boundary sets, and we show how new finite type fractals can be constructed. For finite type self-affine tiles in the plane we give an algorithm which...
Varga, Adrienn (2008)
Banach Journal of Mathematical Analysis [electronic only]
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Udo Simon, An-Mi Li, Luc Vrancken (1991)
Mathematische Zeitschrift
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Papi, Paolo (1997)
The Electronic Journal of Combinatorics [electronic only]
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Takashi Kurose (1990)
Mathematische Zeitschrift
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Joachim Schmid (1995)
Manuscripta mathematica
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Bach, Andrea K. (1997)
Beiträge zur Algebra und Geometrie
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John Smillie (1981)
Inventiones mathematicae
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Michał Sadowski (1990)
Colloquium Mathematicae
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Agata, Smoktunowicz (2001)
Serdica Mathematical Journal
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The Köthe conjecture states that if a ring R has no nonzero nil ideals then R has no nonzero nil one-sided ideals. Although for more than 70 years significant progress has been made, it is still open in general. In this paper we survey some results related to the Köthe conjecture as well as some equivalent problems.