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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Frederick M. Goodman, Holly Hauschild (2006)
Fundamenta Mathematicae
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The affine Birman-Wenzl-Murakami algebras can be defined algebraically, via generators and relations, or geometrically as algebras of tangles in the solid torus, modulo Kauffman skein relations. We prove that the two versions are isomorphic, and we show that these algebras are free over any ground ring, with a basis similar to a well known basis of the affine Hecke algebra.
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.
R.V. Gurjahr (1980)
Inventiones mathematicae
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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.
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...
Bobenko, Alexander I., Schief, Wolfgang K. (1999)
Experimental Mathematics
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Ivan Kolář, Marco Modugno (1990)
Czechoslovak Mathematical Journal
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T. Bisztriczky, J.W. Lorimer (1994)
Aequationes mathematicae
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Cruceanu, Vasile (2005)
Balkan Journal of Geometry and its Applications (BJGA)
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Varga, Adrienn (2008)
Banach Journal of Mathematical Analysis [electronic only]
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Takashi Kurose (1990)
Mathematische Zeitschrift
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T. Bisztriczky, J.W. Lorimer (1994)
Aequationes mathematicae
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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.