Project/Area Number  10640032 
Research Category 
GrantinAid for Scientific Research (C).

Section  一般 
Research Field 
Algebra

Research Institution  NAGASAKI UNIVERSITY 
Principal Investigator 
KUDO Aichi Nagasaki Univ., Fac. of Engineering, Professor, 工学部, 教授 (00112285)

CoInvestigator(Kenkyūbuntansha) 
森川 良三 長崎大学, 工学部, 教授 (90087081)
MARUYAMA Yukihiro Nagasaki Univ., Fac. of Economics, Professor, 経済学部, 教授 (30229629)
SUGAWARA Tamio Nagasaki Univ., Fac. of Education, Professor, 教育学部, 教授 (10034711)
WASHIO Tadashi Nagasaki Univ., Fac. of Education, Professor, 教育学部, 教授 (60039435)

Project Fiscal Year 
1998 – 1999

Project Status 
Completed(Fiscal Year 1999)

Budget Amount *help 
¥2,400,000 (Direct Cost : ¥2,400,000)
Fiscal Year 1999 : ¥900,000 (Direct Cost : ¥900,000)
Fiscal Year 1998 : ¥1,500,000 (Direct Cost : ¥1,500,000)

Keywords  Bernoulli number / padic Lfunction / padic zeta function / padic Euler constant / shortest path problems / associative path / routing problems / duality theorem / ベルヌイ数 / P進L関数 / P進ゼータ関数 / P進オイラー定数 / 最短経路問題 / 結合型経路 / ルーチング関数 / 双対理論 / P進デデキント和 / 一般ベルヌイ数 / 結合型最適経路問題 / 双対定理 / 単位半群 / 有向グラフ / P進解析学 
Research Abstract 
In this research, a part of padic analysis discrete optimization problems were mainly treated. A. Kudo investigated padic congruence properties of ordinary and generalized Bernoulli numbers for the character of the first kind. 1. For padic Lfunction attached to Dirichlet character of the first kind, he improved a padic approximation formula of generalized Bernoulli number by character sum, and derived an exact padic congruence which gives the FerreroGreenberg formula as padic limit. 2. For ordinary Bernoulli number and generalized Bernoulli number with a power of Teichmuller character, he obtained a padic congruence containing its degree. As application, padic approximative values of padic Euler constant and defferential coefficients of padic zeta function at some nonpositive integers are given. Y. Maruyama investigated associative optimal path problems. 1. Using an invariant imbedding technique, he derived a parameterized recursive equation for the class of associative shortest path problems, proved the uniqueness of the solution of it and proposed a sequence which converges to the solution. 2. For every multiobjective routing problem, he associated another closely related problem and derived a duality theorem between the primal problem and the dual one. 3. Solving a system of two interrelated recursive equations, he found both the shortest and the longest path lengths simultaneously. He proved the existence and uniqueness of the solution of the system. An algorithm which solves the class of shortest path problems was given.
