Ara
Toplam kayıt 40, listelenen: 1-10
Chaotic n-dimensional euclidean and hyperbolic open billiards and chaotic spinning planar billiards
(Siam Publications, 2008)
We propose a new method to handle the n-dimensional billiard problem in the exterior of a finite mutually disjoint union of convex ( but not necessarily strictly convex) smooth obstacles without eclipse in the Euclidean ...
On the Minkowski measurability of self-similar fractals in R-d
(Scientific Technical Research Council Turkey-Tubitak, 2013)
The question of Minkowski measurability of fractals is investigated for different situations by various authors, notably by M. Lapidus. In dimension one it is known that the attractor of an IFS consisting of similitudes ...
A notion of robustness and stability of manifolds
(Academic Press Inc Elsevier Science, 2008)
Starting from the notion of thickness of Parks we define a notion of robustness for arbitrary subsets of R-k and we investigate its relationship with the notion of positive reach of Federer. We prove that if a set M is ...
Tube volumes via functional equations
(Springer Basel Ag, 2015)
Tube formulas for convex sets and for smooth submanifolds of Euclidean spaces have long been of interest for geometers. In the last two decades there has been great progress on tube formulas for badly behaved spaces such ...
Tight span of subsets of the plane with the maximum metric
(Academic Press Inc Elsevier Science, 2016)
We prove that a nonempty closed and geodesically convex subset of the l(infinity) plane R-infinity(2) is hyperconvex and we characterize the tight spans of arbitrary subsets of R-infinity(2) via this property: Given any ...
An equivalence class decomposition of finite metric spaces via Gromov products
(Elsevier Science BV, 2017)
Let (X, d) be a finite metric space with elements P-i, i = 1,..., n and with the distance functions d(ij) The Gromov Product of the "triangle" (P-i, P-j, P-k) with vertices P-t, P-j and P-k at the vertex Pi is defined by ...
A Fractal Representation of the Complex Clifford Algebra Equivalent to the Fock Representation
(Birkhauser Verlag Ag, 2012)
We construct a representation of the infinite dimensional complex Clifford algebra on the Hilbert space of square-integrable complex-valued functions on the Cantor set, which we show to be equivalent to the classical Fock ...
Fractal interpolation on the Sierpinski Gasket
(Academic Press Inc Elsevier Science, 2008)
We prove for the Sierpinski Gasket (SG) an analogue of the fractal interpolation theorem of Barnsley. Let V-0 = [p(1), p(2), p(3)) be the set of vertices of SG and u(i) (x) = 1/2 (x + p(i)) the three contractions of the ...
Representations of Clifford Algebras on Function Spaces on the Cantor Set
(Birkhauser Verlag Ag, 2011)
We give a representation of the (infinite-dimensional) complex Clifford algebra on the Hilbert space of square-integrable complexvalued functions on the Cantor set.
Graph-directed sprays and their tube volumes via functional equations
(European Mathematical Soc, 2017)
The notion of sprays introduced by Lapidus and his co-workers has proved useful in the context of fractal tube formulas. In the present note, we define a notion of a graph-directed spray, associated with a weighted directed ...