フルテキストURL mjou_064_031_045.pdf
著者 Yamagishi, Hiroyuki|
抄録 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.
キーワード Discrete Sobolev inequality Discrete Laplacian Green’s matrix Reproducing relation
発行日 2022-01
出版物タイトル Mathematical Journal of Okayama University
64巻
1号
出版者 Department of Mathematics, Faculty of Science, Okayama University
開始ページ 31
終了ページ 45
ISSN 0030-1566
NCID AA00723502
資料タイプ 学術雑誌論文
言語 英語
著作権者 Copyright ©2022 by the Editorial Board of Mathematical Journal of Okayama University
フルテキストURL mjou_064_047_061.pdf
著者 Yamanaka, Satoshi|
抄録 The notion of weakly separable extensions was introduced by N. Hamaguchi and A. Nakajima as a generalization of separable extensions. The purpose of this article is to give a characterization of weakly separable polynomials in skew polynomial rings. Moreover, we shall show the relation between separability and weak separability in skew polynomial rings of derivation type.
キーワード separable extension weakly separable extension skew polynomial ring derivation
発行日 2022-01
出版物タイトル Mathematical Journal of Okayama University
64巻
1号
出版者 Department of Mathematics, Faculty of Science, Okayama University
開始ページ 47
終了ページ 61
ISSN 0030-1566
NCID AA00723502
資料タイプ 学術雑誌論文
言語 英語
著作権者 Copyright ©2022 by the Editorial Board of Mathematical Journal of Okayama University
フルテキストURL mjou_064_063_073.pdf
著者 Tasaka, Koji|
抄録 A partial answer to a conjecture about the rank of the matrix CN,r introduced by Francis Brown in the study of totally odd multiple zeta values is given.
キーワード Multiple zeta values Period polynomials
発行日 2022-01
出版物タイトル Mathematical Journal of Okayama University
64巻
1号
出版者 Department of Mathematics, Faculty of Science, Okayama University
開始ページ 63
終了ページ 73
ISSN 0030-1566
NCID AA00723502
資料タイプ 学術雑誌論文
言語 英語
著作権者 Copyright ©2022 by the Editorial Board of Mathematical Journal of Okayama University
フルテキストURL mjou_064_075_107.pdf
著者 Nagamachi, Ippei|
抄録 We give good reduction criteria for hyperbolic polycurves, i.e., successive extensions of families of curves, under some assumptions. These criteria are higher dimensional versions of the good reduction criterion for hyperbolic curves given by Oda and Tamagawa.
キーワード good reduction, hyperbolic curve, polyucurve, ètale fundamental group.
発行日 2022-01
出版物タイトル Mathematical Journal of Okayama University
64巻
1号
出版者 Department of Mathematics, Faculty of Science, Okayama University
開始ページ 75
終了ページ 107
ISSN 0030-1566
NCID AA00723502
資料タイプ 学術雑誌論文
言語 英語
著作権者 Copyright ©2022 by the Editorial Board of Mathematical Journal of Okayama University
フルテキストURL mjou_064_109_116.pdf
著者 Yagita, Nobuaki|
抄録 Let p be a prime number. For a given finite group G, let gr*γ(BG) be the associated ring of the gamma filtration of the topological K-theory for the classifying space BG. In this paper, we study gr*γ(BG) when G are abelian p-groups which are not elementary. In particular, we extend related Chetard’s results for such 2-groups to p-groups for odd p.
キーワード K-theory gamma fitration abelian p-group
発行日 2022-01
出版物タイトル Mathematical Journal of Okayama University
64巻
1号
出版者 Department of Mathematics, Faculty of Science, Okayama University
開始ページ 109
終了ページ 116
ISSN 0030-1566
NCID AA00723502
資料タイプ 学術雑誌論文
言語 英語
著作権者 Copyright ©2022 by the Editorial Board of Mathematical Journal of Okayama University
フルテキストURL mjou_064_117_141.pdf
著者 Wang, Qi|
抄録 As the first attempt to classify τ-tilting finite two-point algebras, we have determined the τ-tilting finiteness for minimal wild two-point algebras and some tame two-point algebras.
キーワード Support τ-tilting modules τ-tilting finite two-point algebras
発行日 2022-01
出版物タイトル Mathematical Journal of Okayama University
64巻
1号
出版者 Department of Mathematics, Faculty of Science, Okayama University
開始ページ 117
終了ページ 141
ISSN 0030-1566
NCID AA00723502
資料タイプ 学術雑誌論文
言語 英語
著作権者 Copyright ©2022 by the Editorial Board of Mathematical Journal of Okayama University
フルテキストURL mjou_064_143_151.pdf
著者 Aokage, Kazuya | Tabata, Sumitaka | Yamada, Hiro-Fumi|
抄録 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
キーワード Quantum general linear group Sylvester-Franke theorem
発行日 2022-01
出版物タイトル Mathematical Journal of Okayama University
64巻
1号
出版者 Department of Mathematics, Faculty of Science, Okayama University
開始ページ 143
終了ページ 151
ISSN 0030-1566
NCID AA00723502
資料タイプ 学術雑誌論文
言語 英語
著作権者 Copyright ©2022 by the Editorial Board of Mathematical Journal of Okayama University
フルテキストURL mjou_064_153_186.pdf
著者 Nishiyama, Yuta|
抄録 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.
キーワード Macdonald polynomials Young diagram bijective proof
発行日 2022-01
出版物タイトル Mathematical Journal of Okayama University
64巻
1号
出版者 Department of Mathematics, Faculty of Science, Okayama University
開始ページ 153
終了ページ 186
ISSN 0030-1566
NCID AA00723502
資料タイプ 学術雑誌論文
言語 英語
著作権者 Copyright ©2022 by the Editorial Board of Mathematical Journal of Okayama University
フルテキストURL mjou_064_187_190.pdf
著者 Puthenpurakal, Tony J. |
抄録 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.
キーワード quasi-polynomials monomial ideals symbolic powers
発行日 2022-01
出版物タイトル Mathematical Journal of Okayama University
64巻
1号
出版者 Department of Mathematics, Faculty of Science, Okayama University
開始ページ 187
終了ページ 190
ISSN 0030-1566
NCID AA00723502
資料タイプ 学術雑誌論文
言語 英語
著作権者 Copyright ©2022 by the Editorial Board of Mathematical Journal of Okayama University
フルテキストURL mjou_064_191_213.pdf
著者 Suzuki, Takeshi| Toyosawa, Yoshitaka|
抄録 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.
発行日 2022-01
出版物タイトル Mathematical Journal of Okayama University
64巻
1号
出版者 Department of Mathematics, Faculty of Science, Okayama University
開始ページ 191
終了ページ 213
ISSN 0030-1566
NCID AA00723502
資料タイプ 学術雑誌論文
言語 英語
著作権者 Copyright ©2022 by the Editorial Board of Mathematical Journal of Okayama University
フルテキストURL mjou_064_215_225.pdf
著者 Hyodo, Fumitake|
抄録 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.
キーワード Hecke rings noncommutative rings
発行日 2022-01
出版物タイトル Mathematical Journal of Okayama University
64巻
1号
出版者 Department of Mathematics, Faculty of Science, Okayama University
開始ページ 215
終了ページ 225
ISSN 0030-1566
NCID AA00723502
資料タイプ 学術雑誌論文
言語 英語
著作権者 Copyright ©2022 by the Editorial Board of Mathematical Journal of Okayama University
フルテキストURL mjou_065_001_022.pdf
著者 Koike, Kazutoshi|
抄録 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.
キーワード Harada rings QF rings
発行日 2023-01
出版物タイトル Mathematical Journal of Okayama University
65巻
1号
出版者 Department of Mathematics, Faculty of Science, Okayama University
開始ページ 1
終了ページ 22
ISSN 0030-1566
NCID AA00723502
資料タイプ 学術雑誌論文
言語 英語
著作権者 Copyright ©2023 by the Editorial Board of Mathematical Journal of Okayama University
フルテキストURL mjou_065_023_034.pdf
著者 Kato, Ryo|
抄録 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.
キーワード Stable homotopy of spheres Picard group
発行日 2023-01
出版物タイトル Mathematical Journal of Okayama University
65巻
1号
出版者 Department of Mathematics, Faculty of Science, Okayama University
開始ページ 23
終了ページ 34
ISSN 0030-1566
NCID AA00723502
資料タイプ 学術雑誌論文
言語 英語
著作権者 Copyright ©2023 by the Editorial Board of Mathematical Journal of Okayama University
フルテキストURL mjou_065_035_081.pdf
著者 Morita, Jun| Pianzola, Arturo| Shibata, Taiki|
抄録 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.
キーワード Affine Kac-Moody groups Loop groups Twisted Chevalley groups
発行日 2023-01
出版物タイトル Mathematical Journal of Okayama University
65巻
1号
出版者 Department of Mathematics, Faculty of Science, Okayama University
開始ページ 35
終了ページ 81
ISSN 0030-1566
NCID AA00723502
資料タイプ 学術雑誌論文
言語 英語
著作権者 Copyright ©2023 by the Editorial Board of Mathematical Journal of Okayama University
フルテキストURL mjou_065_083_096.pdf
著者 Kinjo, Toshiteru|
抄録 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.
キーワード mixed mock modular forms weak harmonic Maass forms Kaneko-Zagier equation
発行日 2023-01
出版物タイトル Mathematical Journal of Okayama University
65巻
1号
出版者 Department of Mathematics, Faculty of Science, Okayama University
開始ページ 83
終了ページ 96
ISSN 0030-1566
NCID AA00723502
資料タイプ 学術雑誌論文
言語 英語
著作権者 Copyright ©2023 by the Editorial Board of Mathematical Journal of Okayama University
フルテキストURL mjou_065_097_116.pdf
著者 Kusuoka, Seiichiro|
抄録 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].
キーワード stochastic quantization quantum field theory singular SPDE
発行日 2023-01
出版物タイトル Mathematical Journal of Okayama University
65巻
1号
出版者 Department of Mathematics, Faculty of Science, Okayama University
開始ページ 97
終了ページ 116
ISSN 0030-1566
NCID AA00723502
資料タイプ 学術雑誌論文
言語 英語
著作権者 Copyright ©2023 by the Editorial Board of Mathematical Journal of Okayama University
フルテキストURL mjou_065_117_123.pdf
著者 Hoshi, Yuichiro|
抄録 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.
キーワード Jacobi sum
発行日 2023-01
出版物タイトル Mathematical Journal of Okayama University
65巻
1号
出版者 Department of Mathematics, Faculty of Science, Okayama University
開始ページ 117
終了ページ 123
ISSN 0030-1566
NCID AA00723502
資料タイプ 学術雑誌論文
言語 英語
著作権者 Copyright ©2023 by the Editorial Board of Mathematical Journal of Okayama University
フルテキストURL mjou_065_125_143.pdf
著者 Wah, Wah| TANIGUCHI, Masaharu|
抄録 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.
キーワード traveling front existence perturbation reaction-diffusion equation
発行日 2023-01
出版物タイトル Mathematical Journal of Okayama University
65巻
1号
出版者 Department of Mathematics, Faculty of Science, Okayama University
開始ページ 125
終了ページ 143
ISSN 0030-1566
NCID AA00723502
資料タイプ 学術雑誌論文
言語 英語
著作権者 Copyright ©2023 by the Editorial Board of Mathematical Journal of Okayama University
フルテキストURL mjou_065_145_173.pdf
著者 Kametaka, Yoshinori| Watanabe, Kohtaro| Nagai, Atsushi| Takemura, Kazuo| Yamagishi, Hiroyuki|
抄録 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.
キーワード Green function boundary value problem positivity hierarchical structure
発行日 2023-01
出版物タイトル Mathematical Journal of Okayama University
65巻
1号
出版者 Department of Mathematics, Faculty of Science, Okayama University
開始ページ 145
終了ページ 173
ISSN 0030-1566
NCID AA00723502
資料タイプ 学術雑誌論文
言語 英語
著作権者 Copyright ©2023 by the Editorial Board of Mathematical Journal of Okayama University
著者 Sakai, Yuichi| Shimizu, Kenichi|
発行日 2015-01
出版物タイトル Mathematical Journal of Okayama University
57巻
1号
資料タイプ 学術雑誌論文
JaLCDOI 10.18926/mjou/53038