Mathematics / Matematik
Permanent URI for this collectionhttps://hdl.handle.net/11147/8
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Article Parity of an Odd Dominating Set(2022) Batal, AhmetFor a simple graph $G$ with vertex set $V(G)={v_1,...,v_n}$, we define the closed neighborhood set of a vertex $u$ as $N[u]={v in V(G) ; | ; v ; text{is adjacent to} ; u ; text{or} ; v=u }$ and the closed neighborhood matrix $N(G)$ as the matrix whose $i$th column is the characteristic vector of $N[v_i]$. We say a set $S$ is odd dominating if $N[u]cap S$ is odd for all $uin V(G)$. We prove that the parity of the cardinality of an odd dominating set of $G$ is equal to the parity of the rank of $G$, where rank of $G$ is defined as the dimension of the column space of $N(G)$. Using this result we prove several corollaries in one of which we obtain a general formula for the nullity of the join of graphs.Article Some Properties of Rickart Modules(Ankara Üniversitesi, 2012) Üngör, Burcu; Kafkas, Gizem; Halıcıoğlu, Sait; Harmancı, AbdullahR birimli bir halka, M saº g R-mod¸l ve M nin endomorÖzma halkas¨ S = EndR(M) olsun. Her f 2 S iÁin rM(f) = eM olacak biÁimde e2 = e 2 S varsa (denk olarakKerf,Mmod¸l¸n¸nbirdirekttoplanan¨ise)MyeRickartmod¸lad¨verilmi?stir[8]. BuÁal¨?smadaRickartmod¸llerinˆzellikleriincelenmeyedevamedilmi?stir. M birRickart mod¸l olmak ¸zere, M nin S-kat¨ (s¨ras¨yla S-indirgenmi?s, S-simetrik, S-yar¨ deºgi?smeli, S-Armendariz)mod¸l olmas¨ iÁin gerek ve yeter ?sart¨n S nin kat¨ (s¨ras¨yla indirgenmi?s, simetrik, yar¨ deºgi?smeli, Armendariz) halka olduºgu gˆsterilmi?stir. M[x], S[x] halkas¨na gˆre Rickart mod¸l iken M nin de Rickart mod¸l oldugu,tersinin M nin S-Armendariz olmas¨ durumunda doºgru olduºgu ispatlanm¨?st¨r. Ayrıca bir M mod¸l¸n¸n Rickart ol- mas¨iÁingerekveyeter?sart¨nhersaºgmod¸l¸nM-temelprojektifolduºgueldeedilmi?stir.Article Citation - WoS: 1Citation - Scopus: 1Recursion Formula for the Green's Function of a Hamiltonian for Several Types of Dirac Delta-Function Potentials in Curved Spaces(TUBITAK, 2016) Erman, FatihIn this short article, we nonperturbatively derive a recursive formula for the Green's function associated with finitely many point Dirac delta potentials in one dimension. We extend this formula to the one for the Dirac delta potentials supported by regular curves embedded in two-dimensional manifolds and for the Dirac delta potentials supported by two-dimensional compact manifolds embedded in three-dimensional manifolds. Finally, this formulation allows us to find the recursive formula of the Green's function for the point Dirac delta potentials in two- and three-dimensional Riemannian manifolds, where the renormalization of coupling constant is required.Article Citation - WoS: 1Citation - Scopus: 1Casimir energies for some single cavities(TUBITAK, 2006) Ahmedov, Hacı; Duru, İsmail HakkıCasimir energies for some single cavities. Casimir energies are discussed for some cavities.