| 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 |
| FullText URL | mjou_066_001_030.pdf |
|---|---|
| Author | Horie, Madoka| |
| Abstract | Let N be a positive integer. For any positive integer L ≤ N and any positive divisor r of N, we enumerate the equivalence classes of dessins d’enfants with N edges, L faces and two vertices whose representatives have automorphism groups of order r. Further, for any non-negative integer h, we enumerate the equivalence classes of dessins with N edges, h faces of degree 2 with h ≤ N, and two vertices whose representatives have automorphism group of order r. Our arguments are essentially based upon a natural one-to-one correspondence between the equivalence classes of all dessins with N edges and the equivalence classes of all pairs of permutations whose entries generate a transitive subgroup of the symmetric group of degree N. |
| Keywords | dessin d’enfants symmetric group combinatorics Riemann surface |
| Published Date | 2024-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume66 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 1 |
| End Page | 30 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright ©2024 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_066_031_044.pdf |
|---|---|
| Author | Motegi, Yuki| |
| Abstract | Multiple Hook Removing Game (MHRG for short) introduced in [1] is an impartial game played in terms of Young diagrams. In this paper, we give a characterization of the set of all game positions in MHRG. As an application, we prove that for t ∈ Z≥0 and m, n ∈ N such that t ≤ m ≤ n, and a Young diagram Y contained in the rectangular Young diagram Yt,n of size t × n, Y is a game position in MHRG with Ym,n the starting position if and only if Y is a game position in MHRG with Yt,n−m+t the starting position, and also that the Grundy value of Y in the former MHRG is equal to that in the latter MHRG. |
| Keywords | Young diagram hook combinatorial game Grundy value |
| Published Date | 2024-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume66 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 31 |
| End Page | 44 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright ©2024 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_066_045_061.pdf |
|---|---|
| Author | Nakamura, Tomoya| |
| Abstract | We define Dirac pairs on Jacobi algebroids, which is a generalization of Dirac pairs on Lie algebroids introduced by Kosmann-Schwarzbach. We show the relationship between Dirac pairs on Lie and on Jacobi algebroids, and that Dirac pairs on Jacobi algebroids characterize several compatible structures on Jacobi algebroids. |
| Keywords | Dirac pair Dirac structure Jacobi algebroid Lie algebroid |
| Published Date | 2024-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume66 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 45 |
| End Page | 61 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright ©2024 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_066_063_069.pdf |
|---|---|
| Author | Kishi, Yasuhiro| Yamada, Mei| |
| Abstract | In this article, we give two families of dihedral quintic polynomials by using the Weber sextic resolvent and a certain elliptic curve. |
| Keywords | Quintic polynomials Galois group |
| Published Date | 2024-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume66 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 63 |
| End Page | 69 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright ©2024 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_066_071_083.pdf |
|---|---|
| Author | Jinzenji, Masao| Tajima, Yu| |
| Abstract | In this paper, we first propose a cohomological derivation of the celebrated Euler’s Pentagonal Number Theorem. Then we prove an identity that corresponds to a bosonic extension of the theorem. The proof corresponds to a cohomological re-derivation of Euler’s another celebrated identity. |
| Keywords | partitions of integers cohomology Euler number Euler’s pentagonal number theorem |
| Published Date | 2024-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume66 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 71 |
| End Page | 83 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright ©2024 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_066_085_102.pdf |
|---|---|
| Author | Akorede, Moses B.| Arawomo, Peter O.| |
| Abstract | In this paper, we discuss the existence and uniqueness of positive solutions to a singular boundary value problem of fractional differential equations with three-point integral boundary conditions. The nonlinear term f possesses singularity and also depends on the first-order derivative u′. Our approach is based on Leray-Schauder fixed point theorem and Banach contraction principle. Examples are presented to confirm the application of the main results. |
| Keywords | Fractional derivative positive solutions singularity three-point boundary value problem cone |
| Published Date | 2024-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume66 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 85 |
| End Page | 102 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright ©2024 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_066_103_113.pdf |
|---|---|
| Author | Puthenpurakal, Tony J.| |
| Abstract | Let (A,m) be an excellent Henselian Cohen-Macaulay local ring of finite representation type. If the AR-quiver of A is known then by a result of Auslander and Reiten one can explicity compute G(A) the Grothendieck group of finitely generated A-modules. If the AR-quiver is not known then in this paper we give estimates of G(A)Q = G(A) ⊗Z Q when k = A/m is perfect. As an application we prove that if A is an excellent equi-characteristic Henselian Gornstein local ring of positive even dimension with char A/m ≠ 2, 3, 5 (and A/m perfect) then G(A)Q ≅ Q. |
| Keywords | Grothendieck group finite representation type AR sequence |
| Published Date | 2024-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume66 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 103 |
| End Page | 113 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright ©2024 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_066_115_124.pdf |
|---|---|
| Author | Maruyama, Takashi| Seto, Tatsuki| |
| Abstract | In this paper, we generalize the Cantor function to 2-dimensional cubes and construct a cyclic 2-cocycle on the Cantor dust. This cocycle is non-trivial on the pullback of the smooth functions on the 2-dimensional torus with the generalized Cantor function while it vanishes on the Lipschitz functions on the Cantor dust. The cocycle is calculated through the integration of 2-forms on the torus by using a combinatorial Fredholm module. |
| Keywords | Fredholm module Cantor dust cyclic cocycle |
| Published Date | 2024-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume66 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 115 |
| End Page | 124 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright ©2024 by the Editorial Board of Mathematical Journal of Okayama University |
