Yazar "Koçak, Şahin" için Matematik Bölümü listeleme
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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. -
Monopole Equations on R8: The Energy Integral
Bilge, Ayşe Hümeyra; Dereli, Tekin; Koçak, Şahin (2000)We discuss the Seiberg-Witten theory in four dimensions and possible generalizations to eight dimensions. We propose an action which is minimized by a set of monopole equations, previously obtained as a generalization of ... -
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 ... -
A notion of robustness and stability of manifolds
Deniz, Ali; Koçak, Şahin; Ratiu, Andrei V. (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 ... -
On Products of Uniquely Geodesic Spaces
Kılıç, Mehmet; Koçak, Şahin (Mathematical Assoc Amer, 2015)After introducing the geodesic spaces, we prove that the product of two complete, uniquely geodesic spaces with respect to the product metric d(p) is again a uniquely geodesic space for 1 < p < infinity. -
On the Minkowski measurability of self-similar fractals in R-d
Deniz, Ali; Koçak, Şahin; Özdemir, Yunus; Ratiu, Andrei; Üreyen, Adem Ersin (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 ... -
On the Minkowski measurability of self-similar fractals in Rd
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 ... -
Representations of Clifford Algebras on Function Spaces on the Cantor Set
Çelik, Derya; Koçak, Şahin; Özdemir, Yunus (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. -
Seiberg-Witten equations on R8
Bilge, Ayşe Hümeyra; Dereli, Tekin; Koçak, Şahin (1997)[No abstract available] -
Seiberg-Witten type monopole equations on 8-manifolds with Spin(7) holonomy as minimizers of a quadratic action
Bilge, Ayşe Hümeyra; Dereli, Tekin; Koçak, Şahin (Springer, 2003)We obtain an elliptic system of monopole equations on 8-manifolds with Spin(7) holonomy by minimizing an action involving negative spinors coupled to an abelian gauge field. -
Self-dual gauge fields in eight dimensions
Bilge, Ayşe Hümeyra; Dereli, Tekin; Koçak, Şahin (1997)Self-dual gauge fields in even dimensional spaces are characterised by a set of constraints on the eigenvalues of F. We derive a new topological bound (Latin small letter esh sign)M(F, F)2 ? ?M P12 on a compact 8-manifold ... -
Stability of Graphs
Demir, Bünyamin; Deniz, Ali; Koçak, Şahin (Electronic Journal Of Combinatorics, 2009)Positively weighted graphs have a natural intrinsic metric. We consider finite, positively weighted graphs with a positive lower bound for their minimal weights and show that any two such graphs, which are close enough ... -
Strong 2-Calibrations on R-2N
Koçak, Şahin; Özdemir, Yunus (Kinokuniya Co LTD, 2011)Most of the classical calibrations possess a property which does not seem to be recognized. Making this property explicit, we define what we call the strong calibrations and prove that a strong 2-calibration field on R-2n ... -
Strong 2-calibrations on R2n
Koçak, Şahin; Özdemir, Y. (2011)Most of the classical calibrations possess a property which does not seem to be recognized. Making this property explicit, we define what we call the strong calibrations and prove that a strong 2-calibration field on R2n ... -
Tight span of subsets of the plane with the maximum metric
Kılıç, Mehmet; Koçak, Şahin (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 ... -
Tube Formulas for Graph-Directed Fractals
Demir, Bünyamin; Deniz, Ali; Koçak, Şahin; Üreyen, Adem Ersin (World Scientific Publ Co Pte LTD, 2010)Lapidus and Pearse proved recently an interesting formula about the volume of tubular neighborhoods of fractal sprays, including the self-similar fractals. We consider the graph-directed fractals in the sense of graph ... -
Tube volumes via functional equations
Deniz, Ali; Koçak, Şahin; Özdemir, Yunus; Üreyen, Adem Ersin (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 ...