| FullText URL | mjou_064_143_151.pdf |
|---|---|
| Author | Aokage, Kazuya | Tabata, Sumitaka | Yamada, Hiro-Fumi| |
| Abstract | A quantum version of classical Sylvester-Franke theorem is presented. After reviewing some representation theory of the quantum group GLq (n, C), the commutation relations of the matrix elements are verified. Once quantum determinant of the representation matrix is defined, the theorem follows naturally |
| Keywords | Quantum general linear group Sylvester-Franke theorem |
| 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 | 143 |
| End Page | 151 |
| 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 |
| FullText URL | mjou_064_153_186.pdf |
|---|---|
| Author | Nishiyama, Yuta| |
| Abstract | In this article, we introduce some identities obtained from the inner products of some symmetric polynomials including the Macdonald polynomials. These identities are obtained not only from the inner products, but also by constructing certain bijections. The bijections are constructed through transforming the Young diagrams of partitions. |
| Keywords | Macdonald polynomials Young diagram bijective proof |
| 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 | 153 |
| End Page | 186 |
| 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 |
| FullText URL | mjou_064_187_190.pdf |
|---|---|
| Author | Puthenpurakal, Tony J. | |
| Abstract | Let K be a field and consider the standard grading on A = K[X1, ... ,Xd]. Let I, J be monomial ideals in A. Let In(J) = (In : J∞) be the nth symbolic power of I with respect to J. It is easy to see that the function fI J (n) = e0(In(J)/In) is of quasi-polynomial type, say of period g and degree c. For n ≫ 0 say fIJ (n) = ac(n)nc + ac−1(n)nc−1 + lower terms, where for i = 0, ... , c, ai : N → Q are periodic functions of period g and ac ≠0. In [4, 2.4] we (together with Herzog and Verma) proved that dim In(J)/In is constant for n ≫ 0 and ac(−) is a constant. In this paper we prove that if I is generated by some elements of the same degree and height I ≥ 2 then ac−1(−) is also a constant. |
| Keywords | quasi-polynomials monomial ideals symbolic powers |
| 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 | 187 |
| End Page | 190 |
| 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 |
| FullText URL | mjou_064_191_213.pdf |
|---|---|
| Author | Suzuki, Takeshi| Toyosawa, Yoshitaka| |
| Abstract | We present a conjectural hook formula concerning the number of the standard tableaux on "cylindric" skew diagrams. Our formula can be seen as an extension of Naruse's hook formula for skew diagrams. Moreover, we prove our conjecture in some special cases. |
| 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 | 191 |
| End Page | 213 |
| 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 |
| FullText URL | mjou_064_215_225.pdf |
|---|---|
| Author | Hyodo, Fumitake| |
| Abstract | This paper focuses on the theory of the Hecke rings associated with the general linear groups originally studied by Hecke and Shimura et al., and moreover generalizes its notions to Hecke rings associated with the automorphism groups of certain algebras. Then, in the case of the Heisenberg Lie algebra, we show an analog of the classical theory. |
| Keywords | Hecke rings noncommutative rings |
| 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 | 215 |
| End Page | 225 |
| 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 |
| FullText URL | mjou_065_001_022.pdf |
|---|---|
| Author | Koike, Kazutoshi| |
| Abstract | There are many characterizations of Harada rings. In this paper, we characterize right co-Harada rings by giving a characterization of the class of basic right co-Harada rings. |
| Keywords | Harada rings QF rings |
| Published Date | 2023-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume65 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 1 |
| End Page | 22 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright ©2023 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_065_023_034.pdf |
|---|---|
| Author | Kato, Ryo| |
| Abstract | Let E(2) be the second Johnson-Wilson spectrum at the prime 3. In this paper, we show that some beta elements exist in the homotopy groups of the E(2)-localized sphere spectrum with a grading over the Picard group of the stable homotopy category of E(2)-local spectra. |
| Keywords | Stable homotopy of spheres Picard group |
| Published Date | 2023-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume65 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 23 |
| End Page | 34 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright ©2023 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_065_035_081.pdf |
|---|---|
| Author | Morita, Jun| Pianzola, Arturo| Shibata, Taiki| |
| Abstract | We provide explicit generators and relations for the affine Kac-Moody groups, as well as a realization of them as (twisted) loop groups by means of Galois descent considerations. As a consequence, we show that the affine Kac-Moody group of type X(r) N is isomorphic to the fixed-point subgroup of the affine Kac-Moody group of type X(1) N under an action of the Galois group. |
| Keywords | Affine Kac-Moody groups Loop groups Twisted Chevalley groups |
| Published Date | 2023-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume65 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 35 |
| End Page | 81 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright ©2023 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_065_083_096.pdf |
|---|---|
| Author | Kinjo, Toshiteru| |
| Abstract | Pavel Guerzhoy show that the Kaneko-Zagier equation for SL2(Z) has mixed mock mock modular solutions in certain weights. In this paper, we show that the Kaneko-Zagier equations for the Fricke groups of level 2 and 3 also have mixed mock modular solutions in certain weights. |
| Keywords | mixed mock modular forms weak harmonic Maass forms Kaneko-Zagier equation |
| Published Date | 2023-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume65 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 83 |
| End Page | 96 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright ©2023 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_065_097_116.pdf |
|---|---|
| Author | Kusuoka, Seiichiro| |
| Abstract | This is a remark paper for the Φ43 -measure and the associated flow on the torus which are constructed in [1] by the limit of the stationary processes of the stochastic quantization equations of approximation measures. We improve the integrability of the state space of the Φ43 -process and the support of the Φ43 -measure. For the improvement, we improve the estimates of the Hölder continuity in time of the solutions to approximation equations. In the present paper, we only discuss the estimates different from those in [1]. |
| Keywords | stochastic quantization quantum field theory singular SPDE |
| Published Date | 2023-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume65 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 97 |
| End Page | 116 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright ©2023 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_065_117_123.pdf |
|---|---|
| Author | Hoshi, Yuichiro| |
| Abstract | In the present paper, we study fields generated by Jacobi sums. In particular, we completely determine the field obtained by adjoining, to the field of rational numbers, all of the Jacobi sums “of two variables” with respect to a fixed maximal ideal of the ring of integers of a fixed prime-power cyclotomic field. |
| Keywords | Jacobi sum |
| Published Date | 2023-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume65 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 117 |
| End Page | 123 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright ©2023 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_065_125_143.pdf |
|---|---|
| Author | Wah, Wah| TANIGUCHI, Masaharu| |
| Abstract | Traveling front solutions have been studied for reaction-diffusion equations with various kinds of nonlinear terms. One of the interesting subjects is the existence and non-existence of them. In this paper, we prove that, if a traveling front solution exists for a reaction-diffusion equation with a nonlinear term, it also exists for a reaction-diffusion equation with a perturbed nonlinear term. In other words, a traveling front is robust under perturbation on a nonlinear term. |
| Keywords | traveling front existence perturbation reaction-diffusion equation |
| Published Date | 2023-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume65 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 125 |
| End Page | 143 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright ©2023 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_065_145_173.pdf |
|---|---|
| Author | Kametaka, Yoshinori| Watanabe, Kohtaro| Nagai, Atsushi| Takemura, Kazuo| Yamagishi, Hiroyuki| |
| Abstract | We consider the boundary value problem for fourth order linear ordinary differential equation in a half line (0,∞), which represents bending of a beam on an elastic foundation under a tension. A tension is relatively stronger than a spring constant of elastic foundation. We here treat four self-adjoint boundary conditions, clamped, Dirichlet, Neumann and free edges, at x = 0. We show the positivity and the hierarchical structure of four Green functions. |
| Keywords | Green function boundary value problem positivity hierarchical structure |
| Published Date | 2023-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume65 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 145 |
| End Page | 173 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright ©2023 by the Editorial Board of Mathematical Journal of Okayama University |
| Author | Nasu, Yasuo| |
|---|---|
| Published Date | 1961-03 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume10 |
| Issue | issue2 |
| Content Type | Journal Article |
| JaLCDOI | 10.18926/mjou/33080 |
| Author | Otsuki, Tominosuke| |
|---|---|
| Published Date | 1961-03 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume10 |
| Issue | issue2 |
| Content Type | Journal Article |
| JaLCDOI | 10.18926/mjou/33081 |
| Author | Koseki, Ken'iti| |
|---|---|
| Published Date | 1961-03 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume10 |
| Issue | issue2 |
| Content Type | Journal Article |
| JaLCDOI | 10.18926/mjou/33082 |
| Author | Koseki, Ken'iti| |
|---|---|
| Published Date | 1961-03 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume10 |
| Issue | issue2 |
| Content Type | Journal Article |
| JaLCDOI | 10.18926/mjou/33083 |
| Author | Nagahara, Takashi| Tominaga, Hisao| |
|---|---|
| Published Date | 1961-03 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume10 |
| Issue | issue2 |
| Content Type | Journal Article |
| JaLCDOI | 10.18926/mjou/33084 |
| Author | Tashiro, Yoshihiro| |
|---|---|
| Published Date | 1960-10 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume10 |
| Issue | issue1 |
| Content Type | Journal Article |
| JaLCDOI | 10.18926/mjou/33085 |
| Author | Nagahara, Takasi| |
|---|---|
| Published Date | 1960-10 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume10 |
| Issue | issue1 |
| Content Type | Journal Article |
| JaLCDOI | 10.18926/mjou/33086 |
