| FullText URL | mjou_068_183_204.pdf |
|---|---|
| Author | Horiuchi, Ryo| |
| Abstract | In this note, we investigate a mixture of combinatorial spectra and stratified simplicial sets, which would be thought of as a model of the spectrum objects of (∞,∞)-categories. |
| Published Date | 2026-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume68 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 183 |
| End Page | 204 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright ©2026 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_068_175_181.pdf |
|---|---|
| Author | Puthenpurakal, Tony J. | |
| Abstract | Let R be a regular ring of dimension d containing a field K of characteristic zero. If E is an R-module let Assi E = {Q ∈ AssE | heightQ = i}. Let P be a prime ideal in R of height g. We show that if R/P satisfies Serre’s condition Ri then Assg+i+1 Hg+1P(R) is a finite set. As an application of our techniques we prove that if P is a prime ideal in R such that (R/P)q is regular for any non-maximal prime ideal q then HiP(R) has finitely many associate primes for all i. |
| Keywords | local cohomology regular rings Rn condition |
| Published Date | 2026-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume68 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 175 |
| End Page | 181 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright ©2026 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_068_147_174.pdf |
|---|---|
| Author | Hagiwara, Tomomichi| |
| Abstract | This paper aims at providing a new fundamental framework for the Wronskian theory by paying attention to the null space of the Wronski matrix. It is first shown that identical vanishing of the Wronskian leads to two different representations of vector-valued functions that lie in the null space of the Wronski matrix. It is further shown that they are algebraically linearly dependent, by which we are immediately led to a key identity in the Wronskian theory, derived only through very simple linear algebraic arguments. Most fundamental results on the Wronskian theory available in the literature can thus be obtained in a quite straightforward fashion with a very clear perspective, and hence the relevant arguments are believed to be of pedagogical value, too. Some further issues relevant to the null space viewpoint are also discussed, where some other results available in the literature are derived through the null space viewpoint in a somewhat strengthened form. |
| Keywords | linear independence of functions Wronski matrix eigenspace determinants minors |
| Published Date | 2026-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume68 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 147 |
| End Page | 174 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright ©2026 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_068_139_146.pdf |
|---|---|
| Author | Horiuchi, Jun| Shimomoto, Kazuma| |
| Abstract | The aim of this article is to investigate interrelated structures lying among three notable problems in commutative algebra. These are Lifting problem, Ascent/descent along associated graded rings, and Matijevic-Roberts type problem. |
| Keywords | Associated graded ring integral closure Rees ring seminormality weak normality |
| Published Date | 2026-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume68 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 139 |
| End Page | 146 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright ©2026 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_068_113_137.pdf |
|---|---|
| Author | Ohara, Mariko| |
| Abstract | The main objective is showing a variant of resolution theorem of connective Waldhausen K-theory in suitable situations. We construct two sequences of subcategories, one is consisting of finitely generated symmetric module spectra which satisfy the condition of the resolution theorem and the other is consisting of the corresponding ∞-subcategories of certain finitely generated module spectra. As an application, we construct a sequence of subcategories consisting of certain DG-modules satisfying the condition of a resolution theorem. |
| Keywords | K-theory projective modules E∞-rings infinity category |
| Published Date | 2026-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume68 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 113 |
| End Page | 137 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright ©2026 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_068_089_111.pdf |
|---|---|
| Author | Kato, Ryo| |
| Abstract | In [3], Hovey and Palmieri proved many interesing results around the Bousfield lattice of the stable homotopy caregory of spectra. In [4], the author, Shimomura and Tatehara defined monoidally distributive posets as a generalization of the Bousfield lattice. In this paper, we consider the retract problem and a subset admitting complete Boolean algebra structure of monoidally distributive posets. In the last section, we see that some results in [3] are given by our results in this paper. |
| Keywords | Bousfield lattice Monoidal poset Retract problem |
| Published Date | 2026-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume68 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 89 |
| End Page | 111 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright ©2026 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_068_077_087.pdf |
|---|---|
| Author | Chikunji, Chiteng’a John| |
| Abstract | Let R be a commutative completely primary finite ring with unique maximal ideal J such that J3 = {0} and J2 ̸= {0}. In this paper, we investigate and determine the structure of the group of units U(R) of the ring R of characteristic p3 without giving any conditions on the generators for the maximal ideal J or on the invariants of the ring R. |
| Keywords | commutative finite rings unit groups |
| Published Date | 2026-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume68 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 77 |
| End Page | 87 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright ©2026 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_068_063_075.pdf |
|---|---|
| Author | Nosaka, Takefumi| |
| Abstract | Given a 3-cocycle ψ in the cohomology of a finite group G, we can define the Dijkgraaf-Witten invariant of closed 3-manifolds. In this paper, we focus on the case where ψ is a 3-cocycle systematically transferred from the second Chern class of a complex representation of G, and show some procedures for computing the invariant, and clarify its topological interpretation under some conditions. |
| Keywords | Group cohomology 3-manifold Chern classes splitting principle |
| Published Date | 2026-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume68 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 63 |
| End Page | 75 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright ©2026 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_068_013_062.pdf |
|---|---|
| Author | Gaucher, Philippe| |
| Abstract | We identify Grandis’ directed spaces as a full reflective subcategory of the category of multipointed d-spaces. When the multipointed d-space realizes a precubical set, its reflection coincides with the standard realization of the precubical set as a directed space. The reflection enables us to extend the construction of the natural system of topological spaces in Baues-Wirsching’s sense from directed spaces to multipointed d-spaces. In the case of a cellular multipointed d-space, there is a discrete version of this natural system which is proved to be bisimilar up to homotopy. We also prove that these constructions are invariant up to homotopy under globular subdivision. These results are the globular analogue of Dubut’s results. Finally, we point the apparent incompatibility between the notion of bisimilar natural systems and the q-model structure of multipointed d-spaces and we give some suggestions for future works. |
| Keywords | multipointed d-space globular subdivision directed path natural system bisimulation open map |
| Published Date | 2026-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume68 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 13 |
| End Page | 62 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright ©2026 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_068_001_012.pdf |
|---|---|
| Author | Komatsu, Toru| |
| Abstract | In this paper we present an algorithm to make a generator of the quadratic subextension of an odd dihedral extension. As an application we solve the Galois group problem for the quintic polynomials given by Kishi and Yamada. |
| Keywords | Dihedral extension quadratic subextension Galois theory |
| Published Date | 2026-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume68 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 1 |
| End Page | 12 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright ©2026 by the Editorial Board of Mathematical Journal of Okayama University |
| 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 |
