EuDML | Browse

Suppose $A \in G l_{d} (ℤ)$ has a 2-dimensional expanding subspace $E^{u}$ , satisfies a regularity condition, called “good star”, and has $A^{*} \geq 0$ , where $A^{*}$ is an oriented compound of $A$ . A morphism $θ$ of the free group on ${1, 2, \dots, d}$ is called a non-abelianization of $A$ if it has structure matrix $A$ . We show that there is a tiling substitution $Θ$ whose “boundary substitution” $θ = \partial Θ$ is a non-abelianization of $A$ . Such a tiling substitution $Θ$ leads to a self-affine tiling of $E^{u} \sim ℝ^{2}$ with $A_{u} {: = A |}_{E_{u}} \in G L_{2} (ℝ)$ as its expansion. In the last section we find conditions on $A$ so...

Tilings in topological spaces.

Arenas, F.G. (1999)

International Journal of Mathematics and Mathematical Sciences

Tilings of convex polygons

Richard Kenyon (1997)

Annales de l'institut Fourier

Call a polygon rational if every pair of side lengths has rational ratio. We show that a convex polygon can be tiled with rational polygons if and only if it is itself rational. Furthermore we give a necessary condition for an arbitrary polygon to be tileable with rational polygons: we associate to any polygon $P$ a quadratic form $q (P)$ , which must be positive semidefinite if $P$ is tileable with rational polygons.The above results also hold replacing the rationality condition with the following: a polygon...

Tilings of the Square with Similar Rectangles.

G. Szekeres, M. Laczkovich (1995)

Discrete & computational geometry

Tilings with the neighborhood property.

Fosnaugh, Linda S., Kramer, Earl S. (1996)

International Journal of Mathematics and Mathematical Sciences

Topological criteria for $𝐤$ -formal arrangements.

Tohǎneanu, Stefan O. (2007)

Beiträge zur Algebra und Geometrie

Topological Order Complexes and Resolutions of Discriminant Sets

V. A. Vassiliev (1999)

Publications de l'Institut Mathématique

Topological order complexes and resolutions of discriminant sets.

Vassiliev, V.A. (1999)

Publications de l'Institut Mathématique. Nouvelle Série

Topological proper separation theorems

Ulrich Meyer zu Hörste (1982)

Commentationes Mathematicae Universitatis Carolinae

Topological Representation of Dual Pairs of Oriented Matroids.

G.M. Ziegler, J. Richter-Gebert (1993)

Discrete & computational geometry

Topological Structure of Non-separable Sigma-locally Compact Convex Sets

Iryna Banakh, Taras Banakh, Katsuhisa Koshino (2013)

Bulletin of the Polish Academy of Sciences. Mathematics

Topologies faciales dans les convexes compacts. Calcul fonctionnel et décomposition spectrale dans le centre d’un espace $A (X)$

Marc Rogalski (1972)

Annales de l'institut Fourier

Cet article étudie, sur l’ensemble $𝒮 (X)$ des points extrémaux d’un convexe compact $X$ , des topologies faciales dont les fermés sont les traces de faces $F$ “parallélisables” (il existe une plus grande face $F^{'}$ disjointe de $F$ , et tout $x$ de $X$ s’écrit $x = λ y + (1 - λ) y^{'}, y \in F, y^{'} \in F^{'}$ , avec $λ$ unique). Les topologies faciales uniformisables sont en bijection avec les sous-espaces réticulés fermés et contenant 1 de l’espace $A (X)$ des fonctions affines continues sur $X$ . Ceci redonne des résultats classiques sur les simplexes, et permet une étude...

Topology and geometry of nontrivial rank-one convex hulls for two-by-two matrices

Carl-Friedrich Kreiner, Johannes Zimmer (2006)

ESAIM: Control, Optimisation and Calculus of Variations

Continuing earlier work by Székelyhidi, we describe the topological and geometric structure of so-called T4-configurations which are the most prominent examples of nontrivial rank-one convex hulls. It turns out that the structure of T4-configurations in $ℝ^{2 \times 2}$ is very rich; in particular, their collection is open as a subset of ${(ℝ^{2 \times 2})}^{4}$ . Moreover a previously purely algebraic criterion is given a geometric interpretation. As a consequence, we sketch an improved algorithm to detect T4-configurations. ...

Currently displaying 161 – 180 of 219

Previous Page 9 Next