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Now showing 1 - 8 of 8

Citation - WoS: 5
Citation - Scopus: 5
Convergence Analysis and Numerical Solution of the Benjamin-Bona Equation by Lie-Trotter Splitting
(TUBITAK, 2018) Zürnacı, Fatma; Gücüyenen Kaymak, Nurcan; Seydaoğlu, Muaz; Tanoğlu, Gamze
In this paper, an operator splitting method is used to analyze nonlinear Benjamin-Bona-Mahony-type equations. We split the equation into an unbounded linear part and a bounded nonlinear part and then Lie-Trotter splitting is applied to the equation. The local error bounds are obtained by using the approach based on the differential theory of operators in a Banach space and the quadrature error estimates via Lie commutator bounds. The global error estimate is obtained via Lady Windermere's fan argument. Finally, to confirm the expected convergence order, numerical examples are studied.
Citation - WoS: 1
Corrigendum: on Density Theorems for Rings of Krull Type With Zero Divisors
(TUBITAK, 2017) Ay Saylam, Başak
This corrigendum is written to correct some parts of the paper "On density theorems for rings of Krull type with zero divisors". The proofs of Proposition 2.4 and Proposition 4.3 are incorrect and the current note makes the appropriate corrections.
Citation - WoS: 1
Citation - Scopus: 1
Recursion Formula for the Green's Function of a Hamiltonian for Several Types of Dirac Delta-Function Potentials in Curved Spaces
(TUBITAK, 2016) Erman, Fatih
In 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.
Citation - Scopus: 2
On Density Theorems for Rings of Krull Type With Zero Divisors
(TUBITAK, 2014) Ay Saylam, Başak
Let R be a commutative ring and I(R) denote the multiplicative group of all invertible fractional ideals of R, ordered by A ≥ B if and only if B ⊆ A. If R is a Marot ring of Krull type, then R(Pi), where {Pi}i∈I are a collection of prime regular ideals of R, is a valuation ring and R = ∩ R(Pi) . We denote by Gi the value group of the valuation associated with R(Pi). We prove that there is an order homomorphism from I(R) into the cardinal direct sum ∐i∈I Gi and we investigate the conditions that make this monomorphism onto for R.
Citation - WoS: 17
Citation - Scopus: 19
Lebesgue-Stieltjes Measure on Time Scales
(TUBITAK, 2009) Deniz, Aslı; Ufuktepe, Ünal
The theory of time scales was introduced by Stefan Hilger in his Ph. D. thesis in 1988, supervised by Bernd Auldbach, in order to unify continuous and discrete analysis [5]. Measure theory on time scales was first constructed by Guseinov [4], then further studies were made by Guseinov-Bohner [1], Cabada-Vivero [2] and Rzezuchowski [6]. In this article, we adapt the concept of Lebesgue-Stieltjes measure to time scales. We define Lebesgue-Stieltjes Δ and ▶-measures and by using these measures, we define an integral adapted to time scales, specifically Lebesgue-Stieltjes Δ-integral. We also establish the relation between Lebesgue-Stieltjes measure and Lebesgue-Stieltjes Δ-measure, consequently between Lebesgue-Stieltjes integral and Lebesgue-Stieltjes Δ-integral.
Citation - WoS: 19
Citation - Scopus: 15
When Δ-Semiperfect Rings Are Semiperfect
(TUBITAK, 2010) Büyükaşık, Engin; Lomp, Christian
Zhou defined δ -semiperfect rings as a proper generalization of semiperfect rings. The purpose of this paper is to discuss relative notions of supplemented modules and to show that the semiperfect rings are precisely the semilocal rings which are δ -supplemented. Module theoretic version of our results are obtained. © TÜBİTAK.
Citation - WoS: 1
Citation - Scopus: 1
Casimir energies for some single cavities
(TUBITAK, 2006) Ahmedov, Hacı; Duru, İsmail Hakkı
Casimir energies for some single cavities. Casimir energies are discussed for some cavities.
Citation - Scopus: 2
Inequalities for the Vibrating Clamped Plate Problem
(TUBITAK, 2001) Mchale, K. P.; Ufuktepe, Ünal
We study the eigenvalues of the vibrating clamped plate problem. We have made improvements on the bounds of the ratios of the eigenvalues of the biharmonic operator (clamped plate) using the methods of Payne, Polya, and Weinberger. The difference in our proof lies mainly with the trial functions and the orthogonality arguments. While Payne, Polya, and Weinberger and Hile and Yeh project away components along u1, u2,...,uk to meet the orthogonality conditions, we use a translation/rotation argument to meet these conditions.

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