Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
Permanent URI for this collectionhttps://hdl.handle.net/11147/7148
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Article Citation - WoS: 1Citation - Scopus: 2Nondegeneracy of the Ground State for Nonrelativistic Lee Model(American Institute of Physics, 2014) Erman, Fatih; Malkoç, Berkin; Turgut, Osman TeomanIn the present work, we first briefly sketch the construction of the nonrelativistic Lee model on Riemannian manifolds, introduced in our previous works. In this approach, the renormalized resolvent of the system is expressed in terms of a well-defined operator, called the principal operator, so as to obtain a finite formulation. Then, we show that the ground state of the nonrelativistic Lee model on compact Riemannian manifolds is nondegenerate using the explicit expression of the principal operator that we obtained. This is achieved by combining heat kernel methods with positivity improving semi-group approach and then applying these tools directly to the principal operator, rather than the Hamiltonian, without using cut-offs.Article Citation - Scopus: 1Inequalities for Buckling of a Clamped Plate(Taylor and Francis Ltd., 2002) Ufuktepe, Ünal; Mchale, K. P.We study the eigenvalue problems for the buckling of a clamped plate. The previous upper bound on low eigenvalues due to Payne, Pólya, and Weinberger, and Rile and Yeh are reviewed. Using methods similar to those used in bounding ratios of eigenvalues of the membrance problem, bounds for ratios of eigenvalues are found for the buckling of a clamped piateArticle Citation - Scopus: 2Inequalities for the Vibrating Clamped Plate Problem(TUBITAK, 2001) Mchale, K. P.; Ufuktepe, ÜnalWe 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.