Affine invariants of annuli
Waldemar Cieślak, Elzbieta Szczygielska (2012)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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A family of regular annuli is considered. Affine invariants of annuli are introduced.
Waldemar Cieślak, Elzbieta Szczygielska (2012)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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A family of regular annuli is considered. Affine invariants of annuli are introduced.
Nadjafikhah, Mehdi (2002)
Balkan Journal of Geometry and its Applications (BJGA)
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Yang, Jianwei, Chen, Zirun, Chen, Wen-Sheng, Chen, Yunjie (2011)
Mathematical Problems in Engineering
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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.
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.
T.Y. Thomas (1929)
Mathematische Annalen
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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.
Udo Simon, An-Mi Li, Luc Vrancken (1991)
Mathematische Zeitschrift
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Peter Giblin (2008)
Banach Center Publications
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The classical medial axis and symmetry set of a smooth simple plane curve M, depending as they do on circles bitangent to M, are invariant under euclidean transformations. This article surveys the various ways in which the construction has been adapted to be invariant under affine transformations. They include affine distance and area constructions, and also the 'centre symmetry set' which generalizes central symmetry. A connexion is also made with the tricentre set of a convex plane...
Cruceanu, Vasile (2005)
Balkan Journal of Geometry and its Applications (BJGA)
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Marcin Bownik, Eric Weber (2003)
Studia Mathematica
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We show that if the canonical dual of an affine frame has the affine structure, with the same number of generators, then the core subspace V₀ is shift invariant. We demonstrate, however, that the converse is not true. We apply our results in the setting of oversampling affine frames, as well as in computing the period of a Riesz wavelet, answering in the affirmative a conjecture of Daubechies and Han. Additionally, we completely characterize when the canonical dual of a quasi-affine...
Varga, Adrienn (2008)
Banach Journal of Mathematical Analysis [electronic only]
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Sam Nelson (2014)
Fundamenta Mathematicae
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We define ambient isotopy invariants of oriented knots and links using the counting invariants of framed links defined by finite racks. These invariants reduce to the usual quandle counting invariant when the rack in question is a quandle. We are able to further enhance these counting invariants with 2-cocycles from the coloring rack's second rack cohomology satisfying a new degeneracy condition which reduces to the usual case for quandles.
Jung R. Cho, Józef Dudek (2002)
Colloquium Mathematicae
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In [7] and [8], two sets of regular identities without finite proper models were introduced. In this paper we show that deleting one identity from any of these sets, we obtain a set of regular identities whose models include all affine spaces over GF(p) for prime numbers p ≥ 5. Moreover, we prove that this set characterizes affine spaces over GF(5) in the sense that each proper model of these regular identities has at least 13 ternary term functions and the number 13 is attained if and...
Makeev, V.V. (2005)
Journal of Mathematical Sciences (New York)
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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...
Papi, Paolo (1997)
The Electronic Journal of Combinatorics [electronic only]
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Michał Sadowski (1990)
Colloquium Mathematicae
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