4 research outputs found
On the Spectral Gap of a Quantum Graph
We consider the problem of finding universal bounds of "isoperimetric" or
"isodiametric" type on the spectral gap of the Laplacian on a metric graph with
natural boundary conditions at the vertices, in terms of various analytical and
combinatorial properties of the graph: its total length, diameter, number of
vertices and number of edges. We investigate which combinations of parameters
are necessary to obtain non-trivial upper and lower bounds and obtain a number
of sharp estimates in terms of these parameters. We also show that, in contrast
to the Laplacian matrix on a combinatorial graph, no bound depending only on
the diameter is possible. As a special case of our results on metric graphs, we
deduce estimates for the normalised Laplacian matrix on combinatorial graphs
which, surprisingly, are sometimes sharper than the ones obtained by purely
combinatorial methods in the graph theoretical literature
A Study of the Railway Network Critical Evaluation by Multiple Criteria: Case Studies of Inter-city and Urban Railway Networks in Japan
13301甲第5591号博士(学術)金沢大学博士論文本文Full 以下に掲載:Asian Transport Studies 8(100074) pp.1-12 2022. Elsevier . 共著者:Pongwit PROMSUWAN, Shoichiro NAKAYAMA, Hiromichi YAMAGUCHI, Shun-ichi KOBAYASH