| FullText URL | mjou_063_001_014.pdf |
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| Author | Graef, John R.| Beldjerd, Djamila| Remili, Moussadek| |
| Abstract | In this paper, sufficient conditions are established for the stability, boundedness and square integrability of solutions for some non-linear neutral delay differential equations of third order. Lyapunov’s direct method is used to obtain the results. |
| Keywords | boundedness stability square integrability |
| Published Date | 2021-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume63 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 1 |
| End Page | 14 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | 英語 |
| Copyright Holders | Copyright©2021 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_063_061_086.pdf |
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| Author | Itaba, Ayako| Matsuno, Masaki| |
| Abstract | Classification of AS-regular algebras is one of the main interests in non-commutative algebraic geometry. Recently, a complete list of superpotentials (defining relations) of all 3-dimensional AS-regular algebras which are Calabi-Yau was given by Mori-Smith (the quadratic case) and Mori-Ueyama (the cubic case), however, no complete list of defining relations of all 3-dimensional AS-regular algebras has not appeared in the literature. In this paper, we give all possible defining relations of 3-dimensional quadratic AS-regular algebras. Moreover, we classify them up to isomorphism and up to graded Morita equivalence in terms of their defining relations in the case that their point schemes are not elliptic curves. In the case that their point schemes are elliptic curves, we give conditions for isomorphism and graded Morita equivalence in terms of geometric data. |
| Keywords | AS-regular algebras geometric algebras quadratic algebras nodal cubic curves elliptic curves Hesse form Sklyanin algebras |
| Published Date | 2021-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume63 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 61 |
| End Page | 86 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | 英語 |
| Copyright Holders | Copyright©2021 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_063_087_105.pdf |
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| Author | Zdzisław, Wojtkowiak| |
| Abstract | The fact that the double zeta values ζ(n, m) can be written in terms of zeta values, whenever n+m is odd is attributed to Euler. We shall show the weak version of this result for the l-adic Galois realization. |
| Keywords | multiple zeta values Galois groups fundamental groups |
| Published Date | 2021-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume63 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 87 |
| End Page | 105 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | 英語 |
| Copyright Holders | Copyright©2021 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_063_107_122.pdf |
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| Author | Kato, Ryo| Shimomura, katsumi| |
| Abstract | In recent years, Liu and his collaborators found many non-trivial products of generators in the homotopy groups of the sphere spectrum. In this paper, we show a result which not only implies most of their results, but also extends a result of theirs. |
| Keywords | Stable homotopy of spheres Adams spectral sequence May spectral sequence |
| Published Date | 2021-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume63 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 107 |
| End Page | 122 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | 英語 |
| Copyright Holders | Copyright©2021 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_063_123_131.pdf |
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| Author | Lee, Min Ho| |
| Abstract | Given Jacobi forms, we determine associated Jacobi-like forms, whose coefficients are quasimodular forms. We then use these quasimodular forms to construct differential operators on modular forms, which are expressed in terms of the Fourier coefficients of the given Jacobi forms. |
| Keywords | Jacobi forms Jacobi-like forms modular forms quasimodular forms |
| Published Date | 2021-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume63 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 123 |
| End Page | 131 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | 英語 |
| Copyright Holders | Copyright©2021 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_063_133_151.pdf |
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| Author | Aokage, Kazuya| |
| Abstract | We derive the Schur function identities coming from the tensor products of the spin representations of the symmetric group Sn. We deal with the tensor products of the basic spin representation V (n) and any spin representation V λ (λ ∈ SP (n)). The characteristic map of the tensor product ζn ⊗ ζλ is described by Stembridge[4] for the case of odd n. We consider the case n is even. |
| Keywords | symmetric group symmetric function projective representation |
| Published Date | 2021-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume63 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 133 |
| End Page | 151 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | 英語 |
| Copyright Holders | Copyright©2021 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_063_153_165.pdf |
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| Author | Seita, Kohei| |
| Abstract | Let G be a finite group and let V and W be real G-modules. We call V and W dim-equivalent if for each subgroup H of G, the H-fixed point sets of V and W have the same dimension. We call V and W are Smith equivalent if there is a smooth G-action on a homotopy sphere Σ with exactly two G-fixed points, say a and b, such that the tangential G-representations at a and b of Σ are respectively isomorphic to V and W . Moreover, We call V and W are d-Smith equivalent if they are dim-equivalent and Smith equivalent. The differences of d-Smith equivalent real G-modules make up a subset, called the d-Smith set, of the real representation ring RO(G). We call V and W P(G)-matched if they are isomorphic whenever the actions are restricted to subgroups with prime power order of G. Let N be a normal subgroup. For a subset F of G, we say that a real G-module is F-free if the H-fixed point set of the G-module is trivial for all elements H of F. We study the d-Smith set by means of the submodule of RO(G) consisting of the differences of dim-equivalent, P(G)-matched, {N}-free real G-modules. In particular, we give a rank formula for the submodule in order to see how the d-Smith set is large. |
| Keywords | Real G-module Smith equivalence representation ring Oliver group |
| Published Date | 2021-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume63 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 153 |
| End Page | 165 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | 英語 |
| Copyright Holders | Copyright©2021 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_063_167_173.pdf |
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| Author | Puthenpurakal, Tony J.| |
| Abstract | Let (A, m) be an excellent normal domain of dimension two. We define an m-primary ideal I to be a pg -ideal if the Rees algebra A[It] is a Cohen-Macaulay normal domain. If A has infinite residue field then it follows from a result of Rees that the product of two pg ideals is pg . When A contains an algebraically closed field k ∼= A/m then Okuma, Watanabe and Yoshida proved that A has pg -ideals and furthermore product of two pg -ideals is a pg ideal. In this article we show that if A is an excellent normal domain of dimension two containing a field k ∼= A/m of characteristic zero then also A has pg -ideals. |
| Keywords | pg -ideal normal Rees rings Cohen-Macaulay rings stable ideals |
| Published Date | 2021-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume63 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 167 |
| End Page | 173 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | 英語 |
| Copyright Holders | Copyright©2021 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_063_175_182.pdf |
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| Author | Chinen, Koji| |
| Abstract | In this note, we establish an analog of the Mallows-Sloane bound for Type III formal weight enumerators. This completes the bounds for all types (Types I through IV) in synthesis of our previous results. Next we show by using the binomial moments that there exists a family of polynomials divisible by three, which are not related to linear codes but are invariant under the MacWilliams transform for the value 3/2. We also discuss some properties of the zeta functions for such polynomials. |
| Keywords | Binomial moment Divisible code Invariant polynomial ring Zeta function for codes Riemann hypothesis |
| Published Date | 2021-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume63 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 175 |
| End Page | 182 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | 英語 |
| Copyright Holders | Copyright©2021 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_063_183_199.pdf |
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| Author | Baba, Yoshitomo| |
| Abstract | In [8] M. Harada studied a left artinian ring R such that every non-small left R-module contains a non-zero injective submodule. And in [13] K. Oshiro called the ring a left Harada ring (abbreviated left H-ring). We can see many results on left Harada rings in [6] and many equivalent conditions in [4, Theorem B]. In this paper, to characterize two-sided Harada rings, we intruduce new concepts “co-H-sequence” and “H-epimorphism” and study them. |
| Keywords | Harada ring Artinian ring |
| Published Date | 2021-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume63 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 183 |
| End Page | 199 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | 英語 |
| Copyright Holders | Copyright©2021 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_063_201_217.pdf |
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| Author | Kojima, Takuya| Oshita, Yoshihito| |
| Abstract | We show linear stability or instability for radially symmet-ric equilibrium solutions to the system of interface equation and two parabolic equations arising in the singular limit of three-component activator-inhibitor models. |
| Keywords | singular limit problem equilibrium solutions linear stability |
| Published Date | 2021-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume63 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 201 |
| End Page | 217 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | 英語 |
| Copyright Holders | Copyright©2021 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_062_001_025.pdf |
|---|---|
| Author | Ohara, Mariko| |
| Abstract | In this paper, we study K-theory of spectral schemes by using locally free sheaves. Let us regard the K-theory as a functor K on affine spectral schemes. Then, we prove that the group completion ΩB<sup>G</sup>(B<sup>G</sup>GL) represents the sheafification of K with respect to Zariski (resp. Nisnevich) topology G, where B<sup>G</sup>GL is a classifying space of a colimit of affine spectral schemes GLn. |
| Keywords | Infinity category Derived algebraic geometry K-theory |
| Published Date | 2020-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume62 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 1 |
| End Page | 25 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | 英語 |
| Copyright Holders | Copyright©2020 by the Editorial Board of Mathematical Journal of Okayama University |
| Author | Oshima, Hideaki| Oshima, Katsumi| |
|---|---|
| Keywords | Toda bracket Unstable higher Toda bracket Higher composition Cofibration Coextension Extension |
| Published Date | 2020-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume62 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 27 |
| End Page | 86 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | 英語 |
| Copyright Holders | Copyright©2020 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_062_087_178.pdf |
|---|---|
| Author | Hiroshima, Toya| |
| Abstract | The branching coefficients of the tensor product of finite-dimensional irreducible Uq(g)-modules, where g is so(2n + 1, C) (Bn-type), sp(2n,C) (Cn-type), and so(2n,C) (Dn-type), are expressed in terms of Littlewood-Richardson (LR) coefficients in the stable region. We give an interpretation of this relation by Kashiwara’s crystal theory by providing an explicit surjection from the LR crystal of type Cn to the disjoint union of Cartesian product of LR crystals of An−1-type and by proving that LR crystals of types Bn and Dn are identical to the corresponding LR crystal of type Cn in the stable region. |
| Keywords | Kashiwara crystals Littlewood-Richardson crystals Kashiwara-Nakashima tableaux Branching rule |
| Published Date | 2020-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume62 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 87 |
| End Page | 178 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | 英語 |
| Copyright Holders | Copyright©2020 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_062_179_195.pdf |
|---|---|
| Author | Fujimori, Shoichi| Kawakami, Yu| Kokubu, Masatoshi| Rossman, Wayne| Umehara, Masaaki| Yamada, Kotaro| |
| Abstract | Catenoids in de Sitter 3-space S<sup>3</sup><sub>1</sub> belong to a certain class of space-like constant mean curvature one surfaces. In a previous work, the authors classified such catenoids, and found that two different classes of countably many exceptional elliptic catenoids are not realized as closed subsets in S<sup>3</sup><sub>1</sub> . Here we show that such exceptional catenoids have closed analytic extensions in S<sup>3</sup><sub>1</sub> with interesting properties. |
| Keywords | constant mean curvature de Sitter space analytic extension |
| Published Date | 2020-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume62 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 179 |
| End Page | 195 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | 英語 |
| Copyright Holders | Copyright©2020 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_062_197_210.pdf |
|---|---|
| Author | Amy Poh Ai Ling| Taniguchi, Masaharu| |
| Abstract | The existence and stability of the Allen–Cahn equation discretized in space and time are studied in a finite spatial interval. If a parameter is less than or equals to a critical value, the zero solution is the only stationary solution. If the parameter is larger than the critical value, one has a positive stationary solution and this positive stationary solution is asymptotically stable. |
| Keywords | Allen–Cahn equation stationary solution comparison theorem discretized |
| Published Date | 2020-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume62 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 197 |
| End Page | 210 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | 英語 |
| Copyright Holders | Copyright©2020 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_061_001_018.pdf |
|---|---|
| Author | Yang, Yu| |
| Abstract | Let R be a complete discrete valuation ring with algebraically residue field of characteristic p > 0 and X a stable curve over R. In the present paper, we study the geometry of coverings of X. Under certain assumptions, we prove that, by replacing R by a finite extension of R, there exists a morphism of stable curves f : Y → X over R such that the morphism fη : Yη → Xη induced by f on generic fibers is finite étale and the morphism fs : Ys → Xs induced by f on special fibers is non-finite. |
| Keywords | stable curve stable covering vertical point admissible covering |
| Published Date | 2019-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume61 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 1 |
| End Page | 18 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | 英語 |
| Copyright Holders | Copyright©2019 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_061_019_035.pdf |
|---|---|
| Author | Cahen, Benjamin| |
| Abstract | We introduce a Schr¨odinger model for the generic representations of a Heisenberg motion group and we construct adapted Weyl correspondences for these representations by adapting the method introduced in [ B. Cahen, Weyl quantization for semidirect products, Differential Geom. Appl. 25 (2007), 177-190]. |
| Keywords | Weyl correspondence Berezin quantization Heisenberg motion group Schr¨odinger representation Bargmann-Fock representation Segal-Bargmann transform unitary representation coadjoint orbit |
| Published Date | 2019-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume61 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 19 |
| End Page | 35 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | 英語 |
| Copyright Holders | Copyright©2019 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_061_037_073.pdf |
|---|---|
| Author | Higashiyama, Kazumi| |
| Abstract | In the present paper, we study configuration space groups. The goal of this paper is to reconstruct group-theoretically the inertia groups associated to various types of log divisors of a log configuration space of a smooth log curve from the associated configuration space group equipped with its collection of log-full subgroups. |
| Keywords | anabelian geometry configuration space log divisor log-full subgroup |
| Published Date | 2019-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume61 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 37 |
| End Page | 73 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | 英語 |
| Copyright Holders | Copyright©2019 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_061_075_084.pdf |
|---|---|
| Author | Izadi, Farzali| Baghalaghdam, Mehdi| |
| Keywords | Diophantine equations Cubes Quintics Elliptic curves Rank |
| Published Date | 2019-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume61 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 75 |
| End Page | 84 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | 英語 |
| Copyright Holders | Copyright©2019 by the Editorial Board of Mathematical Journal of Okayama University |
