| Author | Blanco-Ferro, Antonio A.| Lopez Lopez, Miguel A.| |
|---|---|
| Published Date | 1986-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume28 |
| Issue | issue1 |
| Content Type | Journal Article |
| JaLCDOI | 10.18926/mjou/33945 |
| Author | Wakimoto, Kazumasa| |
|---|---|
| Published Date | 1974-12 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume17 |
| Issue | issue1 |
| Content Type | Journal Article |
| JaLCDOI | 10.18926/mjou/33910 |
| Author | Shitanda, Yoshimi| |
|---|---|
| Published Date | 2017-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume59 |
| Issue | issue1 |
| Content Type | Journal Article |
| JaLCDOI | 10.18926/mjou/54712 |
| FullText URL | mjou_063_153_165.pdf |
|---|---|
| Author | Seita, Kohei| |
| Abstract | Let G be a finite group and let V and W be real G-modules. We call V and W dim-equivalent if for each subgroup H of G, the H-fixed point sets of V and W have the same dimension. We call V and W are Smith equivalent if there is a smooth G-action on a homotopy sphere Σ with exactly two G-fixed points, say a and b, such that the tangential G-representations at a and b of Σ are respectively isomorphic to V and W . Moreover, We call V and W are d-Smith equivalent if they are dim-equivalent and Smith equivalent. The differences of d-Smith equivalent real G-modules make up a subset, called the d-Smith set, of the real representation ring RO(G). We call V and W P(G)-matched if they are isomorphic whenever the actions are restricted to subgroups with prime power order of G. Let N be a normal subgroup. For a subset F of G, we say that a real G-module is F-free if the H-fixed point set of the G-module is trivial for all elements H of F. We study the d-Smith set by means of the submodule of RO(G) consisting of the differences of dim-equivalent, P(G)-matched, {N}-free real G-modules. In particular, we give a rank formula for the submodule in order to see how the d-Smith set is large. |
| Keywords | Real G-module Smith equivalence representation ring Oliver group |
| Published Date | 2021-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume63 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 153 |
| End Page | 165 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright©2021 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_064_013_029.pdf |
|---|---|
| Author | Seita, Kohei| |
| Abstract | Let G be a finite group. In 1970s, T. Petrie defined the Smith equivalence of real G-modules. The Smith set of G is the subset of the real representation ring consisting of elements obtained as differences of Smith equivalent real G-modules. Various results of the topic have been obtained. The d-Smith set of G is the set of all elements [V ]−[W] in the Smith set of G such that the H-fixed point sets of V and W have the same dimension for all subgroups H of G. The results of the Smith sets of the alternating groups and the symmetric groups are obtained by E. Laitinen, K. Pawa lowski and R. Solomon. In this paper, we give the calculation results of the d-Smith sets of the alternating groups and the symmetric groups. In addition, we give the calculation results of the d-Smith sets of Cartesian products of the alternating groups and finite elementary abelian 2-groups. |
| Keywords | Real G-module Smith equivalence Oliver group alternating group |
| Published Date | 2022-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume64 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 13 |
| End Page | 29 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright ©2022 by the Editorial Board of Mathematical Journal of Okayama University |
| Author | Abe, Koji| |
|---|---|
| Published Date | 1986-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume28 |
| Issue | issue1 |
| Content Type | Journal Article |
| JaLCDOI | 10.18926/mjou/33931 |
| Author | Komatsu, Hiroaki| |
|---|---|
| Published Date | 1986-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume28 |
| Issue | issue1 |
| Content Type | Journal Article |
| JaLCDOI | 10.18926/mjou/33950 |
| FullText URL | mjou_064_031_045.pdf |
|---|---|
| Author | Yamagishi, Hiroyuki| |
| Abstract | We have the best constants of three kinds of discrete Sobolev inequalities on the complete bipartite graph with 2N vertices, that is, KN,N. We introduce a discrete Laplacian A on KN,N. A is a 2N ×2N real symmetric positive-semidefinite matrix whose eigenvector corresponding to zero eigenvalue is 1 = t(1, 1, … , 1)∈ C2N. A discrete heat kernel, a Green’s matrix and a pseudo Green’s matrix play important roles in giving the best constants. |
| Keywords | Discrete Sobolev inequality Discrete Laplacian Green’s matrix Reproducing relation |
| Published Date | 2022-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume64 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 31 |
| End Page | 45 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright ©2022 by the Editorial Board of Mathematical Journal of Okayama University |
| Author | Singh, Y. P.| |
|---|---|
| Published Date | 1971-12 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume15 |
| Issue | issue1 |
| Content Type | Journal Article |
| JaLCDOI | 10.18926/mjou/33542 |
| Author | Salim, Mohamed A.M.| Sandling, Robert| |
|---|---|
| Published Date | 1995-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume37 |
| Issue | issue1 |
| Content Type | Journal Article |
| JaLCDOI | 10.18926/mjou/33786 |
| Author | Miljojkovic, Gradimir| |
|---|---|
| Published Date | 1997-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume39 |
| Issue | issue1 |
| Content Type | Journal Article |
| JaLCDOI | 10.18926/mjou/33578 |
| Author | Nakajima, Masumi| |
|---|---|
| Published Date | 1987-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume29 |
| Issue | issue1 |
| Content Type | Journal Article |
| JaLCDOI | 10.18926/mjou/33278 |
| Author | Hikida, Mizuho| |
|---|---|
| Published Date | 1997-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume39 |
| Issue | issue1 |
| Content Type | Journal Article |
| JaLCDOI | 10.18926/mjou/33587 |
| Author | Kishi, Yasuhiro| |
|---|---|
| Published Date | 2005-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume47 |
| Issue | issue1 |
| Content Type | Journal Article |
| JaLCDOI | 10.18926/mjou/33603 |
| Author | Mukai, Juno| |
|---|---|
| Published Date | 1982-12 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume24 |
| Issue | issue2 |
| Content Type | Journal Article |
| JaLCDOI | 10.18926/mjou/33980 |
| Author | Barros, Tomas Edson| Rigas, Alcibiades| |
|---|---|
| Published Date | 2001-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume43 |
| Issue | issue1 |
| Content Type | Journal Article |
| JaLCDOI | 10.18926/mjou/33251 |
| Author | Yosimura, Zen-Ichi| |
|---|---|
| Published Date | 1993-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume35 |
| Issue | issue1 |
| Content Type | Journal Article |
| JaLCDOI | 10.18926/mjou/33479 |
| Author | Nishimura, Yasuzo| Yosimura, Zen-ichi| |
|---|---|
| Published Date | 1998-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume40 |
| Issue | issue1 |
| Content Type | Journal Article |
| JaLCDOI | 10.18926/mjou/33678 |
| Author | Kutami, Mamoru| |
|---|---|
| Published Date | 1996-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume38 |
| Issue | issue1 |
| Content Type | Journal Article |
| JaLCDOI | 10.18926/mjou/33101 |
| Author | Kutami, Mamoru| Inoue, Ichiro| |
|---|---|
| Published Date | 1993-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume35 |
| Issue | issue1 |
| Content Type | Journal Article |
| JaLCDOI | 10.18926/mjou/33473 |
