Decay of correlations in nearest-neighbor self-avoiding walk, percolation, lattice trees and animals

We consider nearest-neighbor self-avoiding walk, bond percolation, lattice trees, and bond lattice animals on ${\mathbb{Z}}^d$. The two-point functions of these models are respectively the generating function for self-avoiding walks from the origin to $x\in{\mathbb{Z}}^d$, the probability of a connection from the origin to $x$, and the generating functions for lattice trees or lattice animals containing the origin and $x$. Using the lace expansion, we prove that the two-point function at the critical point is asymptotic to $\mathit{const.}|x|^{2-d}$ as $|x|\to\infty$, for $d\geq 5$ for self-avoiding walk, for $d\geq19$ for percolation, and for sufficiently large $d$ for lattice trees and animals. These results are complementary to those of [Ann. Probab. 31 (2003) 349--408], where spread-out models were considered. In the course of the proof, we also provide a sufficient (and rather sharp if $d>4$) condition under which the two-point function of a random walk on ${{\mathbb{Z}}^d}$ is asymptotic to $\mathit{const.}|x|^{2-d}$ as $|x|\to\infty$.Comment: Published in at http://dx.doi.org/10.1214/009117907000000231 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Inductive construction of the p-adic zeta functions for non-commutative p-extensions of totally real fields with exponent p

We construct the p-adic zeta function for a one-dimensional (as a p-adic Lie extension) non-commutative p-extension of a totally real number field such that the finite part of its Galois group is a pgroup with exponent p. We first calculate the Whitehead groups of the Iwasawa algebra and its canonical Ore localisation by using Oliver-Taylor's theory upon integral logarithms. This calculation reduces the existence of the non-commutative p-adic zeta function to certain congruence conditions among abelian p-adic zeta pseudomeasures. Then we finally verify these congruences by using Deligne-Ribet's theory and certain inductive technique. As an application we shall prove a special case of (the p-part of) the non-commutative equivariant Tamagawa number conjecture for critical Tate motives. The main results of this paper give generalisation of those of the preceding paper of the author.Comment: 52 page

Iwasawa theory of totally real fields for certain non-commutative pp-extensions

In this paper, we prove the Iwasawa main conjecture of totally real fields for certain specific non-commutative $p$-adic Lie extensions, using the integral logarithms introduced by Oliver and Taylor. Our result gives certain generalization of Kazuya Kato's proof of the main conjecture for Galois extensions of Heisenberg type.Comment: 77page

透析間体重増加がヘモグロビン濃度と心血管イベントとの関連に与える影響について

京都大学新制・課程博士博士(医学)甲第23416号医博第4761号新制||医||1052(附属図書館)京都大学大学院医学研究科医学専攻(主査)教授 柳田 素子, 教授 木村 剛, 教授 近藤 尚己学位規則第4条第1項該当Doctor of Medical ScienceKyoto UniversityDFA

Dynamic response property of cooling tower structures

Reinforced concrete (R/C) cooling tower structures have been used for cooling down the hot water produced by power or chemical plants. These structures are designed to prevent against the failure under a self-weight and a wind loading, as well as an earthquake loading. In this paper, the numerical scheme under parallel processing is introduced and the dynamic evaluation of the cooling tower under an earthquake loading is examined. In numerical analyses, the cooling tower is assumed to have two types of conventional column system, i.e., V-column and I-column systems. Both R/C shell portion and column system are modeled by use of solid elements. From the numerical analyses, the higher stress concentrations are arisen between the junctions of R/C shell and columns for I-column than those for V-column. Also, it is concluded that the additional reinforcements should be placed around the junction considering the seismic effects