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_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_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_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
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_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_175_182.pdf
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
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_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