Browsing by Author "Koçak, Şahin"
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An equivalence class decomposition of finite metric spaces via Gromov products
Authors:Bilge, Ayşe Hümeyra; Çelik, Derya; Koçak, Şahin
Publisher and Date:(Elsevier Science Bv, 2017)Let (X, d) be a finite metric space with elements Pi, i = 1,..., n and with the distance functions d(ij) The Gromov Product of the "triangle" (Pi, Pj, Pk) with vertices Pt, Pj and Pk at the vertex Pi is defined by Delta(ijk) = 1/2(d(ij) + d(ik)  d(jk)). We show that the collection of Gromov products determines the metric. We call a metric space Deltageneric, if the set of all Gromov products at a fixed vertex Pi has a unique smallest element (for i = 1,., n). We consider the function ...

Gromov product structures, quadrangle structures and split metric spaces
Authors:Bilge, Ayşe Hümeyra; Çelik, Derya; Koçak, Şahin; Rezaeinazhad, Arash Mohammadian
Publisher and Date:(Elsevier B.V., 202106)Let (X,d) be a finite metric space with elements Pi, i=1,…,n and with distances dij≔d(Pi,Pj) for i,j=1,…,n. The “Gromov product” Δijk, is defined as [Formula presented]. (X,d) is called Δgeneric, if, for each fixed i, the set of Gromov products Δijk has a unique smallest element, Δijiki. The Gromov product structure on a Δgeneric finite metric space (X,d) is the map that assigns the edge Ejiki to Pi. A finite metric space is called “quadrangle generic”, if for all 4point subsets {Pi,Pj,Pk,Pl}, ...

Maximal linear subspaces of strong selfdual 2forms and the Bonan 4form
Authors:Bilge, Ayşe Hümeyra; Dereli, Tekin; Koçak, Şahin
Publisher and Date:(Elsevier Science Inc, 2011)The notion of selfduality of 2forms in 4dimensions plays an eminent role in many areas of mathematics and physics, but although the 2forms have a genuine meaning related to curvature and gaugefieldstrength in higher dimensions also, their "selfduality" is something which is almost avoided above 4dimensions. We show that selfduality of 2forms is a very natural notion in higher (even) dimensions also and we prove the equivalence of some scattered and rarely used definitions in the literature. ...

Selfduality in higher dimensions
Authors:Bilge, Ayşe Hümeyra; Dereli, Tekin; Koçak, Şahin
Publisher and Date:(IOP Publishing Ltd, 2017)Let w be a 2form on a 2n dimensional manifold. In previous work, we called w "strong selfdual, if the eigenvalues of its matrix with respect to an orthonormal frame are equal in absolute value. In a series of papers, we showed that strong selfduality agrees with previous definitions; in particular if w is strong selfdual, then, in 2n dimensions, w(n) is proportional to its Hodge dual w and in 4n dimensions, w(n) is Hodge selfdual. We also obtained a local expression of the Bonan 4form on 8 ...