UTokyo Repository カテゴリ: Graduate School of Mathematical Sciences
http://hdl.handle.net/2261/153
Graduate School of Mathematical Sciences2017-03-25T04:04:06ZThe Euler Characteristic Formula for Logarithmic Minimal Degenerations of Surfaces with Kodaira Dimension Zero
http://hdl.handle.net/2261/42813
タイトル: The Euler Characteristic Formula for Logarithmic Minimal Degenerations of Surfaces with Kodaira Dimension Zero
著者: Ohno, Koji
内容記述: 報告番号: 乙14765 ; 学位授与年月日: 2000-07-14 ; 学位の種別: 論文博士 ; 学位の種類: 博士(数理科学) ; 学位記番号: 第14765号 ; 研究科・専攻: 数理科学研究科2000-07-14T00:00:00ZBlow-Up of Finite-Difference Solutions to Nonlinear Wave Equations
http://hdl.handle.net/2261/61488
タイトル: Blow-Up of Finite-Difference Solutions to Nonlinear Wave Equations
著者: Saito, Norikazu; Sasaki, Takiko
抄録: Finite-difference schemes for computing blow-up solutions of one dimensional nonlinear wave equations are presented. By applying time increments control technique, we can introduce a numerical blow-up time which is an approximation of the exact blowup time of the nonlinear wave equation. After having verified the convergence of our proposed schemes, we prove that solutions of those finite-difference schemes actually blow up in the corresponding numerical blow-up times.Then, we prove that the numerical blow-up time converges to the exact blow-up time as the discretization parameters tend to zero.Sev eral numerical examples that confirm the validity of our theoretical results are also offered.2016-01-25T00:00:00ZOn a Tower of Good Affinoids in X0(pn) and the Inertia Action on the Reduction
http://hdl.handle.net/2261/61487
タイトル: On a Tower of Good Affinoids in X0(pn) and the Inertia Action on the Reduction
著者: Tsushima, Takahiro
抄録: Coleman and McMurdy calculate the stable reduction of X0(p3) for any prime number p ≥ 13, on the basis of rigid geometry in [CM]. Further, in [CM2], they compute also the inertia action on the stable reduction of X0(p3). In [T], we have determined the stable model of X0(p4) for any prime p ≥ 13. In this paper, we calculate the reductions of some “good” affinoids in X0(pn) and determine the inertia action on them. As a result, we study the middle cohomology of the reductions in terms of the type theory for GL2(Qp) given in [BH].2016-01-25T00:00:00ZRenormalization Group Analysis of Multi-Band Many-Electron Systems at Half-Filling
http://hdl.handle.net/2261/61486
タイトル: Renormalization Group Analysis of Multi-Band Many-Electron Systems at Half-Filling
著者: Kashima, Yohei
抄録: Renormalization group analysis for multi-band manyelectron systems at half-filling at positive temperature is presented. The analysis includes the Matsubara ultra-violet integration and the infrared integration around the zero set of the dispersion relation. The multi-scale integration schemes are implemented in a finitedimensional Grassmann algebra indexed by discrete position-time variables. In order that the multi-scale integrations are justified inductively, various scale-dependent estimates on Grassmann polynomials are established. We apply these theories in practice to prove that for the half-filled Hubbard model with nearest-neighbor hopping on a square lattice the infinite-volume, zero-temperature limit of the free energy density exists as an analytic function of the coupling constant in a neighborhood of the origin if the system contains the magnetic flux π (mod 2π) per plaquette and 0 (mod 2π) through the large circles around the periodic lattice. Combined with Lieb’s result on the flux phase problem ([Lieb, E. H., Phys. Rev. Lett. 73 (1994), 2158]), this theorem implies that the minimum free energy density of the fluxphase problem converges to an analytic function of the coupling constant in the infinite-volume, zero-temperature limit. The proof of the theorem is based on a four-band formulation of the model Hamiltonian and an extension of Giuliani-Mastropietro’s renormalization designed for the half-filled Hubbard model on the honeycomb lattice ([Giuliani, A. and V. Mastropietro, Commun. Math. Phys. 293 (2010), 301–346]).2016-01-25T00:00:00Z