Diss.--Cologne.

Inaug.-dis.--Marburg. / Vita.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1995. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliography.

Thesis (M. S.)--Electrical and Computer Engineering, Georgia Institute of Technology, 2007. / Lee, Robert, Committee Member ; Egerstedt, Magnus, Committee Member ; Ting, Lena, Committee Chair.

The variation of the eigenvalues and eigenfunctions of an ordinary linear self-adjoint differential operator L is considered under perturbations of the domain of L. The basic problem is defined as a suitable singular eigenvalue problem for L on the open interval ω_ < a < ω+ and is assumed to have at least one real eigenvalue λ of multiplicity k. The perturbed problem is a regular self-adjoint problem defined for L on a closed subinterval [a,b] of (ω_,ω+). It is proved under suitable conditions on the boundary operators of the perturbed problem that exactly k perturbed eigenvalues [ Formula omitted ] as a,b ⇢ ω_,ω+. Further, asymptotic estimates are obtained for [ Formula omitted ] as a,b ⇢ ω_,ω+. The other results are refinements which lead to asymptotic estimates for the eigenfunctions and variational formulae for the eigenvalues. The conditions on the limiting behaviour of the boundary operators depend strongly on the nature of the singularities ω_,ω+. If for some numberℓ⃘, ℓ⃘not an eigenvalue, linearly independent solutions of Lx = ℓ⃘x exist which are asymptotically ordered at ω_, then ω_ is palled a class 1 singularity. In the case that both ω_,ω+ are class 1 singularities, very general boundary operators permit the convergence of [ Formula omitted ], Class 2 singularities are defined as follows: If all solutions of Lx = ℓ⃘x are square-integrable on (ω_, c] for any c satisfying ω_ < c < ω+, then ω_ is called a class 2 singularity. An asymptotic ordering of the solutions is not assumed in this case. Since the behaviour of the solutions of Lx = ℓ⃘x is essentially arbitrary when both ω_,ω+ are class 2 singularities, the generality of the boundary operators has to be sacrificed to ensure that [ Formula omitted ]. Certain one end perturbation problems and examples also are considered. / Science, Faculty of / Mathematics, Department of / Graduate

Many novel materials, such as the vanadates MgV 2O5, the cuprates SrCu 2O3, conducting polymers and organic salts which involve longer-range Coulomb interactions, can be modeled by the extended Hubbard model. In this thesis, we applied the strong-coupling perturbation theory to study a generalized extended Hubbard model characterized by the inter-chain electron hopping t' and the inter-chain nearest-neighbor interaction V' as well as the on-site interaction U, the intra-chain nearest-neighbor interaction V and the intra-chain electron hopping t at strong coupling limit for quarter and half band fillings. / The early strong coupling perturbation expansion was only up to the fourth order in t/U and t/V expansion, which is good for the large values of interaction, U/t > 10. However, for real physical systems, the reasonable range of U/t should be from 4 to 10. In order to investigate the physical systems more accurately, we worked out a perturbation expansion up to the sixth order, hence obtained an effective Hamiltonian in t/U, t/V, t/V', t'/U, t'/V and t'/V' expansion for the extended Hubbard model in half and quarter band filings. The effective Hamiltonian obtained only contains the spin-spin correlation terms. For the half-filled band, we calculated the four spin-spin correlation terms and applied the first and second nearest-neighbor correlation of the linear Heisenberg model obtained by Hulthen and Takahashi and the third nearest-neighbor correlation obtained by Kazumitsu Sakai's group to calculate the ground state energy for the 1-D extended Hubbard chain with the realistic Coulomb interactions, U/t ranges from 4 to 14 and V/t ranges from 0 to 2 respectively. For the quarter-filled case, we worked out the effective Hamiltonian for the 1-D and the 2-D cases and calculated the spin-spin correlation functions by the spin-wave theory. We calculated the ground state energy with the same ranges of the on-site interaction input in the half-filled case and the V/t ranges from 1.5 to 4.0 for the 1-D, the quasi 2-D (t > t', t'/V &sim; t/V) and the isotropic 2-D (t = t', V = V') case respectively. In order to check the validity of the perturbation expansion, we proceeded numerical calculations of the ground state energy by exact diagonalization for the same values of U, V, t, V' and t' for both the half-filled and the quarter-filled cases. / Lee Wing Fai = 強耦合擴展 Hubbard模型之微擾計算 / 李榮輝. / "August 2005." / Adviser: Lin Hai Qing. / Source: Dissertation Abstracts International, Volume: 67-01, Section: B, page: 0323. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (p. 157-160). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / School code: 1307. / Lee Wing Fai = Qiang ou he kuo zhan Hubbard mo xing zhi wei rao ji suan / Li Ronghui.

Pang Kam Moon. / "June 2000." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (p. 134-137). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese. / Pang Kam Moon.

Thesis (Ph. D.)--University of Chicago, Dept. of Mathematics, December 2003. / Includes bibliographical references. Also available on the Internet.

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