フルテキストURL mjou_063_167_173.pdf
著者 Puthenpurakal, Tony J.|
抄録 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.
キーワード pg -ideal normal Rees rings Cohen-Macaulay rings stable ideals
発行日 2021-01
出版物タイトル Mathematical Journal of Okayama University
63巻
1号
出版者 Department of Mathematics, Faculty of Science, Okayama University
開始ページ 167
終了ページ 173
ISSN 0030-1566
NCID AA00723502
資料タイプ 学術雑誌論文
言語 English
著作権者 Copyright©2021 by the Editorial Board of Mathematical Journal of Okayama University
フルテキストURL mjou_063_001_014.pdf
著者 Graef, John R.| Beldjerd, Djamila| Remili, Moussadek|
抄録 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.
キーワード boundedness stability square integrability
発行日 2021-01
出版物タイトル Mathematical Journal of Okayama University
63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 14
ISSN 0030-1566
NCID AA00723502
資料タイプ 学術雑誌論文
言語 English
著作権者 Copyright©2021 by the Editorial Board of Mathematical Journal of Okayama University
フルテキストURL mjou_063_053_060.pdf
著者 Iokibe, Gaku|
抄録 In this paper, we refine the method introduced by Izadi and Baghalaghdam to search integer solutions to the Diophantine equation<img src="http://www.lib.okayama-u.ac.jp/www/mjou/mjou_63_53.png">. We show that the Diophantine equation has infinitely many positive solutions.
キーワード Diophantine equations Elliptic Curves
発行日 2021-01
出版物タイトル Mathematical Journal of Okayama University
63巻
1号
出版者 Department of Mathematics, Faculty of Science, Okayama University
開始ページ 53
終了ページ 60
ISSN 0030-1566
NCID AA00723502
資料タイプ 学術雑誌論文
言語 English
著作権者 Copyright©2021 by the Editorial Board of Mathematical Journal of Okayama University
フルテキストURL mjou_063_061_086.pdf
著者 Itaba, Ayako| Matsuno, Masaki|
抄録 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.
キーワード AS-regular algebras geometric algebras quadratic algebras nodal cubic curves elliptic curves Hesse form Sklyanin algebras
発行日 2021-01
出版物タイトル Mathematical Journal of Okayama University
63巻
1号
出版者 Department of Mathematics, Faculty of Science, Okayama University
開始ページ 61
終了ページ 86
ISSN 0030-1566
NCID AA00723502
資料タイプ 学術雑誌論文
言語 English
著作権者 Copyright©2021 by the Editorial Board of Mathematical Journal of Okayama University
フルテキストURL mjou_063_123_131.pdf
著者 Lee, Min Ho|
抄録 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.
キーワード Jacobi forms Jacobi-like forms modular forms quasimodular forms
発行日 2021-01
出版物タイトル Mathematical Journal of Okayama University
63巻
1号
出版者 Department of Mathematics, Faculty of Science, Okayama University
開始ページ 123
終了ページ 131
ISSN 0030-1566
NCID AA00723502
資料タイプ 学術雑誌論文
言語 English
著作権者 Copyright©2021 by the Editorial Board of Mathematical Journal of Okayama University
フルテキストURL mjou_063_107_122.pdf
著者 Kato, Ryo| Shimomura, katsumi|
抄録 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.
キーワード Stable homotopy of spheres Adams spectral sequence May spectral sequence
発行日 2021-01
出版物タイトル Mathematical Journal of Okayama University
63巻
1号
出版者 Department of Mathematics, Faculty of Science, Okayama University
開始ページ 107
終了ページ 122
ISSN 0030-1566
NCID AA00723502
資料タイプ 学術雑誌論文
言語 English
著作権者 Copyright©2021 by the Editorial Board of Mathematical Journal of Okayama University
フルテキストURL mjou_063_175_182.pdf
著者 Chinen, Koji|
抄録 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.
キーワード Binomial moment Divisible code Invariant polynomial ring Zeta function for codes Riemann hypothesis
発行日 2021-01
出版物タイトル Mathematical Journal of Okayama University
63巻
1号
出版者 Department of Mathematics, Faculty of Science, Okayama University
開始ページ 175
終了ページ 182
ISSN 0030-1566
NCID AA00723502
資料タイプ 学術雑誌論文
言語 English
著作権者 Copyright©2021 by the Editorial Board of Mathematical Journal of Okayama University
フルテキストURL mjou_063_087_105.pdf
著者 Zdzisław, Wojtkowiak|
抄録 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.
キーワード multiple zeta values Galois groups fundamental groups
発行日 2021-01
出版物タイトル Mathematical Journal of Okayama University
63巻
1号
出版者 Department of Mathematics, Faculty of Science, Okayama University
開始ページ 87
終了ページ 105
ISSN 0030-1566
NCID AA00723502
資料タイプ 学術雑誌論文
言語 English
著作権者 Copyright©2021 by the Editorial Board of Mathematical Journal of Okayama University
フルテキストURL mjou_063_015_052.pdf
著者 da Silva, Luiz C. B.|
抄録 We study invariant surfaces generated by one-parameter subgroups of simply and pseudo isotropic rigid motions. Basically, the simply and pseudo isotropic geometries are the study of a three-dimensional space equipped with a rank 2 metric of index zero and one, respectively. We show that the one-parameter subgroups of isotropic rigid motions lead to seven types of invariant surfaces, which then generalizes the study of revolution and helicoidal surfaces in Euclidean and Lorentzian spaces to the context of singular metrics. After computing the two fundamental forms of these surfaces and their Gaussian and mean curvatures, we solve the corresponding problem of prescribed curvature for invariant surfaces whose generating curves lie on a plane containing the degenerated direction.
キーワード Simply isotropic space pseudo-isotropic space singular metric invariant surface prescribed Gaussian curvature prescribed mean curvature
発行日 2021-01
出版物タイトル Mathematical Journal of Okayama University
63巻
1号
出版者 Department of Mathematics, Faculty of Science, Okayama University
開始ページ 15
終了ページ 52
ISSN 0030-1566
NCID AA00723502
資料タイプ 学術雑誌論文
言語 English
著作権者 Copyright©2021 by the Editorial Board of Mathematical Journal of Okayama University
フルテキストURL mjou_063_133_151.pdf
著者 Aokage, Kazuya|
抄録 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.
キーワード symmetric group symmetric function projective representation
発行日 2021-01
出版物タイトル Mathematical Journal of Okayama University
63巻
1号
出版者 Department of Mathematics, Faculty of Science, Okayama University
開始ページ 133
終了ページ 151
ISSN 0030-1566
NCID AA00723502
資料タイプ 学術雑誌論文
言語 English
著作権者 Copyright©2021 by the Editorial Board of Mathematical Journal of Okayama University
フルテキストURL mjou_063_183_199.pdf
著者 Baba, Yoshitomo|
抄録 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.
キーワード Harada ring Artinian ring
発行日 2021-01
出版物タイトル Mathematical Journal of Okayama University
63巻
1号
出版者 Department of Mathematics, Faculty of Science, Okayama University
開始ページ 183
終了ページ 199
ISSN 0030-1566
NCID AA00723502
資料タイプ 学術雑誌論文
言語 English
著作権者 Copyright©2021 by the Editorial Board of Mathematical Journal of Okayama University
フルテキストURL mjou_063_201_217.pdf
著者 Kojima, Takuya| Oshita, Yoshihito|
抄録 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.
キーワード singular limit problem equilibrium solutions linear stability
発行日 2021-01
出版物タイトル Mathematical Journal of Okayama University
63巻
1号
出版者 Department of Mathematics, Faculty of Science, Okayama University
開始ページ 201
終了ページ 217
ISSN 0030-1566
NCID AA00723502
資料タイプ 学術雑誌論文
言語 English
著作権者 Copyright©2021 by the Editorial Board of Mathematical Journal of Okayama University
フルテキストURL mjou_063_153_165.pdf
著者 Seita, Kohei|
抄録 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.
キーワード Real G-module Smith equivalence representation ring Oliver group
発行日 2021-01
出版物タイトル Mathematical Journal of Okayama University
63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 165
ISSN 0030-1566
NCID AA00723502
資料タイプ 学術雑誌論文
言語 English
著作権者 Copyright©2021 by the Editorial Board of Mathematical Journal of Okayama University
フルテキストURL mjou_062_087_178.pdf
著者 Hiroshima, Toya|
抄録 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.
キーワード Kashiwara crystals Littlewood-Richardson crystals Kashiwara-Nakashima tableaux Branching rule
発行日 2020-01
出版物タイトル Mathematical Journal of Okayama University
62巻
1号
出版者 Department of Mathematics, Faculty of Science, Okayama University
開始ページ 87
終了ページ 178
ISSN 0030-1566
NCID AA00723502
資料タイプ 学術雑誌論文
言語 English
著作権者 Copyright©2020 by the Editorial Board of Mathematical Journal of Okayama University
フルテキストURL mjou_062_179_195.pdf
著者 Fujimori, Shoichi| Kawakami, Yu| Kokubu, Masatoshi| Rossman, Wayne| Umehara, Masaaki| Yamada, Kotaro|
抄録 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.
キーワード constant mean curvature de Sitter space analytic extension
発行日 2020-01
出版物タイトル Mathematical Journal of Okayama University
62巻
1号
出版者 Department of Mathematics, Faculty of Science, Okayama University
開始ページ 179
終了ページ 195
ISSN 0030-1566
NCID AA00723502
資料タイプ 学術雑誌論文
言語 English
著作権者 Copyright©2020 by the Editorial Board of Mathematical Journal of Okayama University
フルテキストURL mjou_062_197_210.pdf
著者 Amy Poh Ai Ling| Taniguchi, Masaharu|
抄録 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.
キーワード Allen–Cahn equation stationary solution comparison theorem discretized
発行日 2020-01
出版物タイトル Mathematical Journal of Okayama University
62巻
1号
出版者 Department of Mathematics, Faculty of Science, Okayama University
開始ページ 197
終了ページ 210
ISSN 0030-1566
NCID AA00723502
資料タイプ 学術雑誌論文
言語 English
著作権者 Copyright©2020 by the Editorial Board of Mathematical Journal of Okayama University
フルテキストURL mjou_062_001_025.pdf
著者 Ohara, Mariko|
抄録 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.
キーワード Infinity category Derived algebraic geometry K-theory
発行日 2020-01
出版物タイトル Mathematical Journal of Okayama University
62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 25
ISSN 0030-1566
NCID AA00723502
資料タイプ 学術雑誌論文
言語 English
著作権者 Copyright©2020 by the Editorial Board of Mathematical Journal of Okayama University
著者 Oshima, Hideaki| Oshima, Katsumi|
キーワード Toda bracket Unstable higher Toda bracket Higher composition Cofibration Coextension Extension
発行日 2020-01
出版物タイトル Mathematical Journal of Okayama University
62巻
1号
出版者 Department of Mathematics, Faculty of Science, Okayama University
開始ページ 27
終了ページ 86
ISSN 0030-1566
NCID AA00723502
資料タイプ 学術雑誌論文
言語 English
著作権者 Copyright©2020 by the Editorial Board of Mathematical Journal of Okayama University
フルテキストURL mjou_061_075_084.pdf
著者 Izadi, Farzali| Baghalaghdam, Mehdi|
キーワード Diophantine equations Cubes Quintics Elliptic curves Rank
発行日 2019-01
出版物タイトル Mathematical Journal of Okayama University
61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 84
ISSN 0030-1566
NCID AA00723502
資料タイプ 学術雑誌論文
言語 English
著作権者 Copyright©2019 by the Editorial Board of Mathematical Journal of Okayama University
フルテキストURL mjou_061_019_035.pdf
著者 Cahen, Benjamin|
抄録 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].
キーワード Weyl correspondence Berezin quantization Heisenberg motion group Schr¨odinger representation Bargmann-Fock representation Segal-Bargmann transform unitary representation coadjoint orbit
発行日 2019-01
出版物タイトル Mathematical Journal of Okayama University
61巻
1号
出版者 Department of Mathematics, Faculty of Science, Okayama University
開始ページ 19
終了ページ 35
ISSN 0030-1566
NCID AA00723502
資料タイプ 学術雑誌論文
言語 English
著作権者 Copyright©2019 by the Editorial Board of Mathematical Journal of Okayama University