1999 Fiscal Year Final Research Report Summary
p-adic method in discrete mathematics and its application
| Project/Area Number |
10640032
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| 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)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
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 Period (FY) |
1998 – 1999
|
| Keywords | Bernoulli number / p-adic L-function / p-adic zeta function / p-adic Euler constant / shortest path problems / associative path / routing problems / duality theorem |
|---|
| Research Abstract |
In this research, a part of p-adic analysis discrete optimization problems were mainly treated.
A. Kudo investigated p-adic congruence properties of ordinary and generalized Bernoulli numbers for the character of the first kind.
1. For p-adic L-function attached to Dirichlet character of the first kind, he improved a p-adic approximation formula of generalized Bernoulli number by character sum, and derived an exact p-adic congruence which gives the Ferrero-Greenberg formula as p-adic limit.
2. For ordinary Bernoulli number and generalized Bernoulli number with a power of Teichmuller character, he obtained a p-adic congruence containing its degree. As application, p-adic approximative values of p-adic Euler constant and defferential coefficients of p-adic zeta function at some non-positive 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.
|
