### On affine subspaces that illuminate a convex set.

Bezdek, Károly (1994)

Beiträge zur Algebra und Geometrie

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Bezdek, Károly (1994)

Beiträge zur Algebra und Geometrie

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Zhao, Chang-Jian, Leng, Gangsong, Debnath, Lokenath (2005)

International Journal of Mathematics and Mathematical Sciences

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Cheung, Wing-Sum, Zhao, Chang-Jian (2008)

Banach Journal of Mathematical Analysis [electronic only]

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Lin, Si, Bin, Xiong, Wuyang, Yu (2006)

Journal of Inequalities and Applications [electronic only]

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Eric L. Grinberg (1991)

Mathematische Annalen

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Fenghong, Lu, Weihong, Mao, Gangsong, Leng (2007)

Journal of Inequalities and Applications [electronic only]

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Martini, Horst, Mustafaev, Zokhrab (2010)

Journal of Inequalities and Applications [electronic only]

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Yu, Wuyang (2009)

Journal of Inequalities and Applications [electronic only]

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Józef Joachim Telega (1977)

Annales Polonici Mathematici

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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...

Janusz Matkowski (2003)

Colloquium Mathematicae

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The class of all functions f:(0,∞) → (0,∞) which are continuous at least at one point and affine with respect to the logarithmic mean is determined. Some related results concerning the functions convex with respect to the logarithmic mean are presented.

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.

Cruceanu, Vasile (2005)

Balkan Journal of Geometry and its Applications (BJGA)

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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.

Karáné, G.S. (1994)

Beiträge zur Algebra und Geometrie

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Leichtweiss, Kurt (1999)

Beiträge zur Algebra und Geometrie

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