| 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 | English |
| 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 | English |
| 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 | English |
| 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 | English |
| 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 | English |
| 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 | English |
| 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 | English |
| 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 | English |
| 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 | English |
| 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 | English |
| 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 . 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 | English |
| Copyright Holders | Copyright©2021 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_064_031_045.pdf |
|---|---|
| Author | Yamagishi, Hiroyuki| |
| Abstract | We have the best constants of three kinds of discrete Sobolev inequalities on the complete bipartite graph with 2N vertices, that is, KN,N. We introduce a discrete Laplacian A on KN,N. A is a 2N ×2N real symmetric positive-semidefinite matrix whose eigenvector corresponding to zero eigenvalue is 1 = t(1, 1, … , 1)∈ C2N. A discrete heat kernel, a Green’s matrix and a pseudo Green’s matrix play important roles in giving the best constants. |
| Keywords | Discrete Sobolev inequality Discrete Laplacian Green’s matrix Reproducing relation |
| Published Date | 2022-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume64 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 31 |
| End Page | 45 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright ©2022 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_064_047_061.pdf |
|---|---|
| Author | Yamanaka, Satoshi| |
| Abstract | The notion of weakly separable extensions was introduced by N. Hamaguchi and A. Nakajima as a generalization of separable extensions. The purpose of this article is to give a characterization of weakly separable polynomials in skew polynomial rings. Moreover, we shall show the relation between separability and weak separability in skew polynomial rings of derivation type. |
| Keywords | separable extension weakly separable extension skew polynomial ring derivation |
| Published Date | 2022-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume64 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 47 |
| End Page | 61 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright ©2022 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_064_063_073.pdf |
|---|---|
| Author | Tasaka, Koji| |
| Abstract | A partial answer to a conjecture about the rank of the matrix CN,r introduced by Francis Brown in the study of totally odd multiple zeta values is given. |
| Keywords | Multiple zeta values Period polynomials |
| Published Date | 2022-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume64 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 63 |
| End Page | 73 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright ©2022 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_064_075_107.pdf |
|---|---|
| Author | Nagamachi, Ippei| |
| Abstract | We give good reduction criteria for hyperbolic polycurves, i.e., successive extensions of families of curves, under some assumptions. These criteria are higher dimensional versions of the good reduction criterion for hyperbolic curves given by Oda and Tamagawa. |
| Keywords | good reduction, hyperbolic curve, polyucurve, ètale fundamental group. |
| Published Date | 2022-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume64 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 75 |
| End Page | 107 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright ©2022 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_064_109_116.pdf |
|---|---|
| Author | Yagita, Nobuaki| |
| Abstract | Let p be a prime number. For a given finite group G, let gr*γ(BG) be the associated ring of the gamma filtration of the topological K-theory for the classifying space BG. In this paper, we study gr*γ(BG) when G are abelian p-groups which are not elementary. In particular, we extend related Chetard’s results for such 2-groups to p-groups for odd p. |
| Keywords | K-theory gamma fitration abelian p-group |
| Published Date | 2022-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume64 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 109 |
| End Page | 116 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright ©2022 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_064_117_141.pdf |
|---|---|
| Author | Wang, Qi| |
| Abstract | As the first attempt to classify τ-tilting finite two-point algebras, we have determined the τ-tilting finiteness for minimal wild two-point algebras and some tame two-point algebras. |
| Keywords | Support τ-tilting modules τ-tilting finite two-point algebras |
| Published Date | 2022-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume64 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 117 |
| End Page | 141 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright ©2022 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_064_143_151.pdf |
|---|---|
| Author | Aokage, Kazuya | Tabata, Sumitaka | Yamada, Hiro-Fumi| |
| Abstract | A quantum version of classical Sylvester-Franke theorem is presented. After reviewing some representation theory of the quantum group GLq (n, C), the commutation relations of the matrix elements are verified. Once quantum determinant of the representation matrix is defined, the theorem follows naturally |
| Keywords | Quantum general linear group Sylvester-Franke theorem |
| Published Date | 2022-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume64 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 143 |
| End Page | 151 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright ©2022 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_064_153_186.pdf |
|---|---|
| Author | Nishiyama, Yuta| |
| Abstract | In this article, we introduce some identities obtained from the inner products of some symmetric polynomials including the Macdonald polynomials. These identities are obtained not only from the inner products, but also by constructing certain bijections. The bijections are constructed through transforming the Young diagrams of partitions. |
| Keywords | Macdonald polynomials Young diagram bijective proof |
| Published Date | 2022-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume64 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 153 |
| End Page | 186 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright ©2022 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_064_187_190.pdf |
|---|---|
| Author | Puthenpurakal, Tony J. | |
| Abstract | Let K be a field and consider the standard grading on A = K[X1, ... ,Xd]. Let I, J be monomial ideals in A. Let In(J) = (In : J∞) be the nth symbolic power of I with respect to J. It is easy to see that the function fI J (n) = e0(In(J)/In) is of quasi-polynomial type, say of period g and degree c. For n ≫ 0 say fIJ (n) = ac(n)nc + ac−1(n)nc−1 + lower terms, where for i = 0, ... , c, ai : N → Q are periodic functions of period g and ac ≠0. In [4, 2.4] we (together with Herzog and Verma) proved that dim In(J)/In is constant for n ≫ 0 and ac(−) is a constant. In this paper we prove that if I is generated by some elements of the same degree and height I ≥ 2 then ac−1(−) is also a constant. |
| Keywords | quasi-polynomials monomial ideals symbolic powers |
| Published Date | 2022-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume64 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 187 |
| End Page | 190 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright ©2022 by the Editorial Board of Mathematical Journal of Okayama University |
