| FullText URL | mjou_067_133_147.pdf |
|---|---|
| Author | Nakagawa, Yuto| Nakano, Fumihiko| |
| Abstract | K. Brown [1] studied the random to top shuffle (the Tsetlin libary) by semigroup method. In this paper, (i) we extend his results to the colored permutation groups, and (ii) we consider a q-analogue of Tsetlin library which is different from what is studied in [1]. In (i), the results also extends those results for the top to random shuffle [4],[5], [6] to arbitrary distribution of choosing cards, but we still have derangement numbers in the multiplicity of each eigenvalues. In (ii), a version of q-analogue of derangement numbers by Chen-Rota [3] appears in the multiplicity of eigenvalues. |
| Keywords | Tsetlin library Left Regular Band colored permutation group |
| Published Date | 2025-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume67 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 133 |
| End Page | 147 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright ©2025 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_067_101_131.pdf |
|---|---|
| Author | Ohmoto, Toyokazu| |
| Abstract | An alternating sign matrix (ASM for short) is a square matrix which consists of 0, 1 and −1. In this paper, we characterize an ASM by showing a bijection between alternating sign matrix and six vertex model, and a bijection between six vertex model and height function. In order to show these bijections, we define a triplet (ai,j , ci,j , ri,j) for each entry of an ASM. We also define a track for each index of height function, and state more properties of height function. |
| Keywords | Alternating sign matrix six vertex model height function |
| Published Date | 2025-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume67 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 101 |
| End Page | 131 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright ©2025 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_067_075_099.pdf |
|---|---|
| Author | Yamagishi, Hiroyuki| Kametaka, Yoshinori| |
| Abstract | The Sobolev inequality shows that the supremum of a function defined on a whole line is estimated from the above by constant multiples of the potential energy. Among such constants, the smallest constant is the best constant. If we replace a constant by the best constant in the Sobolev inequality, then the equality holds for the best function. The aim of this paper is to find the best constant and the best function. In the background, there is a bending problem of a string with a rectangular spring constant. The Green function is an important function because the best constant and the best function consist of the Green function. |
| Keywords | Sobolev inequality Green function reproducing kernel |
| Published Date | 2025-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume67 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 75 |
| End Page | 99 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright ©2025 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_067_067_074.pdf |
|---|---|
| Author | Honda, Masanobu| Sakamoto, Takanori| |
| Abstract | We assume that a basic field k has zero characteristic. We show that any Fitting class is serially coalescent for locally finite Lie algebras. We also show that any class X satisfying N ≤ X ≤ ˆGr (e.g. Ft, B, Z, Gr, lN, rN, `e(◁)ˆA, ˆe(◁)ˆA, `Gr) is locally serially coalescent for locally finite Lie algebras, and, for any locally finite Lie algebra L, the X-ser radical of L is locally nilpotent. |
| Keywords | Lie algebra serial subalgebra locally coalescent class |
| Published Date | 2025-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume67 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 67 |
| End Page | 74 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright ©2025 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_067_053_065.pdf |
|---|---|
| Author | Harrington, Joshua| Jones, Lenny| |
| Abstract | A polynomial f(x) ∈ Z[x] of degree N is called monogenic if f(x) is irreducible over Q and {1, θ, θ2, . . . , θN−1} is a basis for the ring of integers of Q(θ), where f(θ) = 0. Define F(x) := xm+Axm−1+B. In this article, we determine sets of conditions on m, A, and B, such that the power-compositional trinomial F(xpn) is monogenic for all integers n ≥ 0 and a given prime p. Furthermore, we prove the actual existence of infinite families of such trinomials F(x). |
| Keywords | irreducible monogenic power-compositional trinomial |
| Published Date | 2025-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume67 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 53 |
| End Page | 65 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright ©2025 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_067_029_051.pdf |
|---|---|
| Author | Haraguchi, Tadayuki| Shimakawa, Kazuhisa| |
| Abstract | We construct on the category of diffeological spaces a Quillen model structure having smooth weak homotopy equivalences as the class of weak equivalences. |
| Keywords | Diffeological space Homotopy theory Model category |
| Published Date | 2025-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume67 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 29 |
| End Page | 51 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright ©2025 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_067_001_028.pdf |
|---|---|
| Author | Wakabayashi, Yasuhiro| |
| Abstract | The present paper aims to generalize a result by H. Kaji on Gauss maps in positive characteristic and establish an interaction with the study of dormant opers and Frobenius-projective structures. We prove a correspondence between dormant opers on a smooth projective variety and closed immersions into a projective space with purely inseparable Gauss map. By using this, we determine the subfields of the function field of a smooth curve in positive characteristic induced by Gauss maps. Moreover, this correspondence gives us a Frobenius-projective structure on a Fermat hypersurface. |
| Keywords | Gauss map Frobenius-projective structure dormant indigenous bundle oper |
| Published Date | 2025-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume67 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 1 |
| End Page | 28 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright ©2025 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_066_171_187.pdf |
|---|---|
| Author | Tarmidi, Rani Sasmita| |
| Abstract | In this work, we provide explicit conditions for the coeffi-cients of a symmetric truncated cubic to give a smooth tropical curve. We also examine non-smooth cases corresponding to some specific sub-division types. |
| Keywords | tropical curves smooth tropical curves symmetric truncated cubic |
| 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 | 171 |
| End Page | 187 |
| 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_159_169.pdf |
|---|---|
| Author | Shiraishi, Densuke| |
| Abstract | In this paper, we derive formulas of complex and ℓ-adic multiple polylogarithms, which have two aspects: a duality in terms of indexes and a reflection in terms of variables. We provide an algebraic proof of these formulas by using algebraic relations between associators arising from the S3-symmetry of the projective line minus three points. |
| Keywords | multiple polylogarithm ℓ-adic Galois multiple polylogarithm duality-reflection formula |
| 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 | 159 |
| End Page | 169 |
| 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_135_157.pdf |
|---|---|
| Author | Davis, Daniel G.| |
| Abstract | Let n ≥ 1, p a prime, and T(n) any representative of the Bousfield class of the telescope v−1n F(n) of a finite type n complex. Also, let En be the Lubin-Tate spectrum, K(En) its algebraic K-theory spectrum, and Gn the extended Morava stabilizer group, a profinite group. Motivated by an Ausoni-Rognes conjecture, we show that there are two spectral sequences IEs,t2 ⇒ πt−s((LT(n+1)K(En))hGn) ⇐ IIEs,t2 with common abutment π∗(−) of the continuous homotopy fixed points of LT(n+1)K(En), where IEs,t2 is continuous cohomology with coefficients in a certain tower of discrete Gn-modules. If the tower satisfies the Mittag-Leffler condition, then there are isomorphisms with continuous cochain cohomology groups: IE∗,∗2 ≅ H∗cts(Gn, π∗(LT(n+1)K(En))) ≅ IIE∗,∗2. We isolate two hypotheses, the first of which is true when (n, p) = (1, 2), that imply (LT(n+1)K(En))hGn ≃ LT(n+1)K(LK(n)S0). Also, we show that there is a spectral sequence Hscts(Gn, πt(K(En) ⊗ T(n + 1))) ⇒ πt−s((K(En) ⊗ T(n + 1))hGn). |
| Keywords | Algebraic K-theory spectrum continuous homotopy fixed point spectrum Lubin-Tate spectrum Morava stabilizer group homotopy fixed point spectral sequence telescopic localization |
| 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 | 135 |
| End Page | 157 |
| 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_125_133.pdf |
|---|---|
| Author | Singh, Gagandeep| Singh, Gurcharanjit| |
| Abstract | The aim of this paper is to introduce a new subclass of strongly close-to-convex functions by subordinating to Janowski function. Certain properties such as coefficient estimates, distortion theorem, argument theorem, inclusion relations and radius of convexity are established for this class. The results obtained here will generalize various earlier known results. |
| Keywords | Analytic functions Subordination Janowski-type function Close-to-convex functions Distortion theorem Argument theorem Coefficient bounds |
| 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 | 125 |
| End Page | 133 |
| 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 |
| 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_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_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_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_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_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_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_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 |
