FullText URL mjou_061_159_166.pdf
Author Tasaka, Fuminori|
Abstract A 2-block of a finite group having a Klein four hyperfocal subgroup has the same number of irreducible Brauer characters as the corresponding 2-block of the normalizer of the hyperfocal subgroup.
Keywords group theory modular representation hyperfocal 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 159
End Page 166
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_167_172.pdf
Author Brown, Stephen C.| Davis, Chad T.|
Abstract Due to a theorem of Dedekind, factoring ideals generated by prime numbers in number fields is easily done given that said prime number does not divide the index of the field. In this paper, we determine the prime ideal factorizations of both 2 and 3 in cyclic quartic fields whose index is divisible by one of or both of these primes.
Keywords Cyclic quartic field Prime ideal factorization
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 167
End Page 172
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_173_186.pdf
Author Sato, Yuichiro|
Abstract This paper gives, in generic situations, a complete classification of ruled minimal surfaces in pseudo-Euclidean space with arbitrary index. In addition, we discuss the condition for ruled minimal surfaces to exist, and give a counter-example on the problem of Bernstein type.
Keywords minimal surface ruled surface pseudo-Euclidean space
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 173
End Page 186
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_187_198.pdf
Author Rashid, M.H.M.|
Abstract A Banach space operator satisfies property (Bw) if the complement of its B-Weyl spectrum in its the spectrum is the set of finite multiplicity isolated eigenvalues of the operator. Property (Bw) does not transfer from operators T and S to their tensor product T ⊗ S. We give necessary and /or sufficient conditions ensuring the passage of property (Bw) from T and S to T ⊗ S. Perturbations by Riesz operators are considered.
Keywords property (Bw) SVEP tensor product
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 187
End Page 198
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_199_204.pdf
Author Hamid, Nur| Oura, Manabu|
Abstract The Terwilliger algebra plays an important role in the theory of association schemes. The present paper gives the explicit structures of the Terwilliger algebras of the group association schemes of the finite groups PSL(2, 7), A6, and S6.
Keywords Terwilliger algebragroup association scheme
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 199
End Page 204
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_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_063_001_014.pdf
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_015_052.pdf
Author da Silva, Luiz C. B.|
Abstract 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.
Keywords Simply isotropic space pseudo-isotropic space singular metric invariant surface prescribed Gaussian curvature prescribed mean curvature
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 15
End Page 52
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_053_060.pdf
Author Iokibe, Gaku|
Abstract 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.
Keywords Diophantine equations Elliptic Curves
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 53
End Page 60
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
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
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
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
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
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
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
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