Kurum Yazarı "Koçak, Şahin" WoS İndeksli Yayınlar Koleksiyonu İçin Listeleme
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Canonical bases for real representations of Clifford algebras
Bilge, Ayşe Hümeyra; Koçak, Şahin; Uguz, S. (Elsevier Science Inc, 2006)The well-known classification of the Clifford algebras Cl(r, s) leads to canonical forms of complex and real representations which are essentially unique by virtue of the Wedderburn theorem. For s >= 1 representations of ... -
Chaos in product maps
Değirmenci, Nedim; Koçak, Şahin (Scientific Technical Research Council Turkey-Tubitak, 2010)We discuss how chaos conditions on maps carry over to their products First we give a counterexample showing that the product of two chaotic maps (in the sense of Devaney) need not be chaotic We then remark that if two maps ... -
Chaotic n-dimensional euclidean and hyperbolic open billiards and chaotic spinning planar billiards
Deniz, Ali; Kennedy, Judy; Koçak, Şahin; Ratiu, Andrei V.; Üstün, Cevat; Yorke, James A. (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 ... -
The circle as an attractor of an iterated function system on the plane
Demir, Bünyamin; Dzhafarov, Vakif; Koçak, Şahin; Üreyen, Mehmet (Academic Press Inc Elsevier Science, 2007)We give an iterated function system (IFS) on the plane with the circle as attractor. In doing this, we also give a sufficient condition for radially contracting functions on the plane (or on R-n) to be a contraction. A ... -
Degenerate Spin Groups as Semi-Direct Products
Dereli, Tekin; Koçak, Şahin; Limoncu, Murat (Birkhauser Verlag Ag, 2010)Let Q be a symmetric bilinear form on R(n)=R(p+q+r) with corank r, rank p+q and signature type (p, q), p resp. q denoting positive resp. negative dimensions. We consider the degenerate spin group Spin(Q) = Spin(p, q, r) ... -
Derivatives of the restrictions of harmonic functions on the Sierpinski gasket to segments
Demir, Bünyamin; Dzhafarov, Vakif; Koçak, Şahin; Üreyen, Mehmet (Academic Press Inc Elsevier Science, 2007)We give an explicit derivative computation for the restriction of a harmonic function on SG to segments at specific points of the segments: The derivative is zero at points dividing the segment in ratio 1:3. This shows ... -
An equivalence class decomposition of finite metric spaces via Gromov products
Bilge, Ayşe Hümeyra; Çelik, Derya; Koçak, Şahin (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 ... -
Existence of a dense orbit and topological transitivity: When are they equivalent?
Değirmenci, Nedim; Koçak, Şahin (Akademiai Kiado, 2003)Topological transitivity and existence of a dense orbit are two notions which play an important role in every definition of chaos [2], [4]. Unfortunately, in the literature there are often misunderstandings (or even false ... -
Finite-monotonicity of eigenfunctions of the Laplacian on the Sierpinski Gasket
Demir, B; Dzhafarov, V; Koçak, Şahin; Üreyen, Mehmet (World Scientific Publ Co Pte LTD, 2005)We show that the restriction of an eigenfunction of the Laplacian on the Sierpinski Gasket (SG) to any segment inside the SG is monotone on finite pieces, i.e. there is a subdivision of the segment, such that the function ... -
Fractal interpolation on the Sierpinski Gasket
Çelik, Derya; Koçak, Şahin; Özdemir, Yunus (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 ... -
A Fractal Representation of the Complex Clifford Algebra Equivalent to the Fock Representation
Çelik, Derya; Koçak, Şahin (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 ... -
The geometry of self-dual two-forms
Bilge, Ayşe Hümeyra; Dereli, Tekin; Koçak, Şahin (Amer Inst Physics, 1997)We show that self-dual two-forms in 2n-dimensional spaces determine a n(2)-n+1-dimensional manifold S-2n and the dimension of the maximal linear subspaces of S-2n is equal To the (Radon-Hurwitz) number of linearly independent ... -
Graph-directed sprays and their tube volumes via functional equations
Çelik, Derya; Koçak, Şahin; Özdemir, Yunus; Üreyen, Adem Ersin (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 ... -
Inner Tube Formulas for Polytopes
Koçak, Şahin; Ratiu, Andrei V. (Amer Mathematical Soc, 2012)We show that the volume of the inner r-neighborhood of a polytope in the d-dimensional Euclidean space is a pluriphase Steiner-like function, i.e. a continuous piecewise polynomial function of degree d, thus proving a ... -
Linear connections on light-like manifolds
Dereli, Tekin; Koçak, Şahin; Limoncu, Murat (Scientific Technical Research Council Turkey-Tubitak, 2008)It is well-known that a torsion-free linear connection on a light-like manifold (M, g) compatible with the degenerate metric g exists if and only if Rad(TM) is a Killing distribution. In case of existence, there is an ... -
Maximal linear subspaces of strong self-dual 2-forms and the Bonan 4-form
Bilge, Ayşe Hümeyra; Dereli, Tekin; Koçak, Şahin (Elsevier Science Inc, 2011)The notion of self-duality of 2-forms in 4-dimensions plays an eminent role in many areas of mathematics and physics, but although the 2-forms have a genuine meaning related to curvature and gauge-field-strength in higher ... -
Monopole equations on 8-manifolds with spin(7) holonomy
Bilge, Ayşe Hümeyra; Dereli, Tekin; Koçak, Şahin (Springer Verlag, 1999)We construct a consistent set of monopole equations on eight-manifolds with Spin(7) holonomy. These equations are elliptic and admit non-trivial solutions including all the 4-dimensional Seiberg-Witten solutions as a special case. -
A note on a theorem of Rantzer
Dzhafarov, Vakif; Koçak, Şahin; Azcan, Hüseyin (John Wiley & Sons LTD, 2002)In this note we fill the missing cases of a theorem of Rantzer on the relationship between n-convex directions and the growth condition. We mainly show that if a second or a third order polynomial is a 3-convex direction, ... -
A note on positive Lyapunov exponent and sensitive dependence on initial conditions
Demir, Bünyamin; Koçak, Şahin (Pergamon-Elsevier Science LTD, 2001)In this note, we give two examples of discrete dynamics (Functions) on intervals C R, the first having a positive Lyapunov exponent at a point but not being sensitive-dependent on initial conditions at that point; and the ...