Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 67 1 2025 Tsetlin library on p-colored permutations and q-analogue 133 147 EN Yuto Nakagawa Mathematical Institute, Tohoku University Fumihiko Nakano Mathematical Institute, Tohoku University K. Brown [1] studied the random to top shuffle (the Tsetlin libary) by semigroup method. In this paper, (i) we extend his results to the colored permutation groups, and (ii) we consider a q-analogue of Tsetlin library which is different from what is studied in [1]. In (i), the results also extends those results for the top to random shuffle [4],[5], [6] to arbitrary distribution of choosing cards, but we still have derangement numbers in the multiplicity of each eigenvalues. In (ii), a version of q-analogue of derangement numbers by Chen-Rota [3] appears in the multiplicity of eigenvalues. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 67 1 2025 The characterizations of an alternating sign matrices using a triplet 101 131 EN Toyokazu Ohmoto Department of Mathematics, Faculty of Science, Okayama University An alternating sign matrix (ASM for short) is a square matrix which consists of 0, 1 and −1. In this paper, we characterize an ASM by showing a bijection between alternating sign matrix and six vertex model, and a bijection between six vertex model and height function. In order to show these bijections, we define a triplet (ai,j , ci,j , ri,j) for each entry of an ASM. We also define a track for each index of height function, and state more properties of height function. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 67 1 2025 The best constant of the Sobolev inequality corresponding to a bending problem of a string with a rectangular spring constant 75 99 EN Hiroyuki Yamagishi Tokyo Metropolitan College of Industrial Technology Yoshinori Kametaka Faculty of Engineering Science, Osaka University The Sobolev inequality shows that the supremum of a function defined on a whole line is estimated from the above by constant multiples of the potential energy. Among such constants, the smallest constant is the best constant. If we replace a constant by the best constant in the Sobolev inequality, then the equality holds for the best function. The aim of this paper is to find the best constant and the best function. In the background, there is a bending problem of a string with a rectangular spring constant. The Green function is an important function because the best constant and the best function consist of the Green function. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 67 1 2025 Locally serially coalescent classes of Lie algebras 67 74 EN Masanobu Honda Faculty of Pharmaceutical Sciences, Niigata University of Pharmacy and Medical and Life Sciences Takanori Sakamoto Department of Mathematics, University of Teacher Education Fukuoka We assume that a basic field k has zero characteristic. We show that any Fitting class is serially coalescent for locally finite Lie algebras. We also show that any class X satisfying N ≤ X ≤ ˆGr (e.g. Ft, B, Z, Gr, lN, rN, `e(◁)ˆA, ˆe(◁)ˆA, `Gr) is locally serially coalescent for locally finite Lie algebras, and, for any locally finite Lie algebra L, the X-ser radical of L is locally nilpotent. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 67 1 2025 The irreducibility and monogenicity of power-compositional trinomials 53 65 EN Joshua Harrington Department of Mathematics, Cedar Crest College Lenny Jones Department of Mathematics, Shippensburg University A polynomial f(x) ∈ Z[x] of degree N is called monogenic if f(x) is irreducible over Q and {1, θ, θ2, . . . , θN−1} is a basis for the ring of integers of Q(θ), where f(θ) = 0. Define F(x) := xm+Axm−1+B. In this article, we determine sets of conditions on m, A, and B, such that the power-compositional trinomial F(xpn) is monogenic for all integers n ≥ 0 and a given prime p. Furthermore, we prove the actual existence of infinite families of such trinomials F(x). No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 67 1 2025 The Quillen model structure on the category of diffeological spaces 29 51 EN Tadayuki Haraguchi Faculty of Education for Human Growth, Nara Gakuen University Kazuhisa Shimakawa Okayama University We construct on the category of diffeological spaces a Quillen model structure having smooth weak homotopy equivalences as the class of weak equivalences. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 67 1 2025 Inseparable Gauss maps and dormant opers 1 28 EN Yasuhiro Wakabayashi Graduate School of Information Science and Technology, Osaka University The present paper aims to generalize a result by H. Kaji on Gauss maps in positive characteristic and establish an interaction with the study of dormant opers and Frobenius-projective structures. We prove a correspondence between dormant opers on a smooth projective variety and closed immersions into a projective space with purely inseparable Gauss map. By using this, we determine the subfields of the function field of a smooth curve in positive characteristic induced by Gauss maps. Moreover, this correspondence gives us a Frobenius-projective structure on a Fermat hypersurface. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 66 1 2024 Note on smoothness condition on tropical elliptic curves of symmetric truncated cubic forms 171 187 EN Rani Sasmita Tarmidi Department of Mathematics, Graduate School of Science, Osaka University In this work, we provide explicit conditions for the coeffi-cients of a symmetric truncated cubic to give a smooth tropical curve. We also examine non-smooth cases corresponding to some specific sub-division types. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 66 1 2024 Duality-reflection formulas of multiple polylogarithms and their ℓ-adic Galois analogues 159 169 EN Densuke Shiraishi Department of Mathematics, Graduate School of Science, Osaka University In this paper, we derive formulas of complex and ℓ-adic multiple polylogarithms, which have two aspects: a duality in terms of indexes and a reflection in terms of variables. We provide an algebraic proof of these formulas by using algebraic relations between associators arising from the S3-symmetry of the projective line minus three points. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 66 1 2024 Several homotopy fixed point spectral sequences in telescopically localized algebraic K-theory 135 157 EN Daniel G. Davis Department of Mathematics, University of Louisiana at Lafayette Let n ≥ 1, p a prime, and T(n) any representative of the Bousfield class of the telescope v−1n F(n) of a finite type n complex. Also, let En be the Lubin-Tate spectrum, K(En) its algebraic K-theory spectrum, and Gn the extended Morava stabilizer group, a profinite group. Motivated by an Ausoni-Rognes conjecture, we show that there are two spectral sequences<br> IEs,t2 ⇒ πt−s((LT(n+1)K(En))hGn) ⇐ IIEs,t2<br> with common abutment π∗(−) of the continuous homotopy fixed points of LT(n+1)K(En), where IEs,t2 is continuous cohomology with coefficients in a certain tower of discrete Gn-modules. If the tower satisfies the Mittag-Leffler condition, then there are isomorphisms with continuous cochain cohomology groups:<br> IE∗,∗2 ≅ H∗cts(Gn, π∗(LT(n+1)K(En))) ≅ IIE∗,∗2.<br> We isolate two hypotheses, the first of which is true when (n, p) = (1, 2), that imply (LT(n+1)K(En))hGn ≃ LT(n+1)K(LK(n)S0). Also, we show that there is a spectral sequence<br> Hscts(Gn, πt(K(En) ⊗ T(n + 1))) ⇒ πt−s((K(En) ⊗ T(n + 1))hGn). No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 66 1 2024 A subclass of strongly close-to-convex functions associated with Janowski function 125 133 EN Gagandeep Singh Department of Mathematics, Khalsa College Gurcharanjit Singh Department of Mathematics, G.N.D.U. College The aim of this paper is to introduce a new subclass of strongly close-to-convex functions by subordinating to Janowski function. Certain properties such as coefficient estimates, distortion theorem, argument theorem, inclusion relations and radius of convexity are established for this class. The results obtained here will generalize various earlier known results. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 66 1 2024 A combinatorial integration on the Cantor dust 115 124 EN Takashi Maruyama Department of Engineering, Stanford University Tatsuki Seto General Education and Research Center, Meiji Pharmaceutical University In this paper, we generalize the Cantor function to 2-dimensional cubes and construct a cyclic 2-cocycle on the Cantor dust. This cocycle is non-trivial on the pullback of the smooth functions on the 2-dimensional torus with the generalized Cantor function while it vanishes on the Lipschitz functions on the Cantor dust. The cocycle is calculated through the integration of 2-forms on the torus by using a combinatorial Fredholm module. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 66 1 2024 On G(A)Q of rings of finite representation type 103 113 EN Tony J. Puthenpurakal Department of Mathematics, IIT Bombay Let (A,m) be an excellent Henselian Cohen-Macaulay local ring of finite representation type. If the AR-quiver of A is known then by a result of Auslander and Reiten one can explicity compute G(A) the Grothendieck group of finitely generated A-modules. If the AR-quiver is not known then in this paper we give estimates of G(A)Q = G(A) ⊗Z Q when k = A/m is perfect. As an application we prove that if A is an excellent equi-characteristic Henselian Gornstein local ring of positive even dimension with char A/m ≠ 2, 3, 5 (and A/m perfect) then G(A)Q ≅ Q. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 66 1 2024 Positive solutions to a nonlinear three-point boundary value problem with singularity 85 102 EN Moses B. Akorede Department of Mathematics, Faculty of Science, University of Ibadan Peter O. Arawomo Department of Mathematics, Faculty of Science, University of Ibadan In this paper, we discuss the existence and uniqueness of positive solutions to a singular boundary value problem of fractional differential equations with three-point integral boundary conditions. The nonlinear term f possesses singularity and also depends on the first-order derivative u′. Our approach is based on Leray-Schauder fixed point theorem and Banach contraction principle. Examples are presented to confirm the application of the main results. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 66 1 2024 Harmonic partitions of positive integers and bosonic extension of Euler’s pentagonal number theorem 71 83 EN Masao Jinzenji Department of Mathematics, Okayama University Yu Tajima Division of Mathematics, Graduate School of Science, Hokkaido University In this paper, we first propose a cohomological derivation of the celebrated Euler’s Pentagonal Number Theorem. Then we prove an identity that corresponds to a bosonic extension of the theorem. The proof corresponds to a cohomological re-derivation of Euler’s another celebrated identity. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 66 1 2024 Construction of families of dihedral quintic polynomials 63 69 EN Yasuhiro Kishi Department of Mathematics, Faculty of Education, Aichi University of Education Mei Yamada Department of Mathematics, Faculty of Education, Aichi University of Education In this article, we give two families of dihedral quintic polynomials by using the Weber sextic resolvent and a certain elliptic curve. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 66 1 2024 Dirac pairs on Jacobi algebroids 45 61 EN Tomoya Nakamura Academic Support Center, Kogakuin University We define Dirac pairs on Jacobi algebroids, which is a generalization of Dirac pairs on Lie algebroids introduced by Kosmann-Schwarzbach. We show the relationship between Dirac pairs on Lie and on Jacobi algebroids, and that Dirac pairs on Jacobi algebroids characterize several compatible structures on Jacobi algebroids. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 66 1 2024 Game positions of multiple hook removing game 31 44 EN Yuki Motegi Graduate School of Pure and Applied Sciences, University of Tsukuba Multiple Hook Removing Game (MHRG for short) introduced in [1] is an impartial game played in terms of Young diagrams. In this paper, we give a characterization of the set of all game positions in MHRG. As an application, we prove that for t ∈ Z≥0 and m, n ∈ N such that t ≤ m ≤ n, and a Young diagram Y contained in the rectangular Young diagram Yt,n of size t × n, Y is a game position in MHRG with Ym,n the starting position if and only if Y is a game position in MHRG with Yt,n−m+t the starting position, and also that the Grundy value of Y in the former MHRG is equal to that in the latter MHRG. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 66 1 2024 Equivalence classes of dessins d’enfants with two vertices 1 30 EN Madoka Horie Graduate School of Science, Tohoku University Let N be a positive integer. For any positive integer L ≤ N and any positive divisor r of N, we enumerate the equivalence classes of dessins d’enfants with N edges, L faces and two vertices whose representatives have automorphism groups of order r. Further, for any non-negative integer h, we enumerate the equivalence classes of dessins with N edges, h faces of degree 2 with h ≤ N, and two vertices whose representatives have automorphism group of order r. Our arguments are essentially based upon a natural one-to-one correspondence between the equivalence classes of all dessins with N edges and the equivalence classes of all pairs of permutations whose entries generate a transitive subgroup of the symmetric group of degree N. No potential conflict of interest relevant to this article was reported.

Acta Medica Okayama 2022 Traveling Front Solutions to Reaction-Diffusion Equations and Their Robustness for Perturbation on Reaction Terms EN Wah Wah Graduate School of Natural Science and Technology, Okayama university No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 65 1 2023 Positivity and Hierarchical Structure of four Green Functions Corresponding to a Bending Problem of a Beam on a half line 145 173 EN Yoshinori Kametaka Faculty of Engineering Science, Osaka University Kohtaro Watanabe Department of Computer Science, National Defense Academy Atsushi Nagai Department of Computer Sciences, College of Liberal Arts, Tsuda University Kazuo Takemura College of Science and Technology, Nihon University Hiroyuki Yamagishi Tokyo Metropolitan College of Industrial Technology We consider the boundary value problem for fourth order linear ordinary differential equation in a half line (0,∞), which represents bending of a beam on an elastic foundation under a tension. A tension is relatively stronger than a spring constant of elastic foundation. We here treat four self-adjoint boundary conditions, clamped, Dirichlet, Neumann and free edges, at x = 0. We show the positivity and the hierarchical structure of four Green functions. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 65 1 2023 Traveling front solutions for perturbed reaction-diffusion equations 125 143 EN Wah Wah Research Institute for Interdisciplinary Science, Okayama University Masaharu TANIGUCHI Research Institute for Interdisciplinary Science, Okayama University Traveling front solutions have been studied for reaction-diffusion equations with various kinds of nonlinear terms. One of the interesting subjects is the existence and non-existence of them. In this paper, we prove that, if a traveling front solution exists for a reaction-diffusion equation with a nonlinear term, it also exists for a reaction-diffusion equation with a perturbed nonlinear term. In other words, a traveling front is robust under perturbation on a nonlinear term. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 65 1 2023 A Note on Fields Generated by Jacobi Sums 117 123 EN Yuichiro Hoshi Research Institute for Mathematical Sciences, Kyoto University In the present paper, we study fields generated by Jacobi sums. In particular, we completely determine the field obtained by adjoining, to the field of rational numbers, all of the Jacobi sums “of two variables” with respect to a fixed maximal ideal of the ring of integers of a fixed prime-power cyclotomic field. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 65 1 2023 An improvement of the integrability of the state space of the Φ43-process and the support of the Φ43-measure constructed by the limit of stationary processes of approximating stochastic quantization equations 97 116 EN Seiichiro Kusuoka Department of Mathematics, Graduate School of Science, Kyoto University This is a remark paper for the Φ⁴₃ -measure and the associated flow on the torus which are constructed in [1] by the limit of the stationary processes of the stochastic quantization equations of approximation measures. We improve the integrability of the state space of the Φ⁴₃ -process and the support of the Φ⁴₃ -measure. For the improvement, we improve the estimates of the H&#246;lder continuity in time of the solutions to approximation equations. In the present paper, we only discuss the estimates different from those in [1]. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 65 1 2023 Non-Modular Solution of the Kaneko-Zagier Equations with respect to Fricke Groups of Low Levels 83 96 EN Toshiteru Kinjo Graduate School of Mathematics, Kyushu University Pavel Guerzhoy show that the Kaneko-Zagier equation for SL2(Z) has mixed mock mock modular solutions in certain weights. In this paper, we show that the Kaneko-Zagier equations for the Fricke groups of level 2 and 3 also have mixed mock modular solutions in certain weights. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 65 1 2023 Affine Kac-Moody Groups as Twisted Loop Groups obtained by Galois Descent Considerations 35 81 EN Jun Morita Institute of Mathematics, University of Tsukuba Arturo Pianzola Department of Mathematical and Statistical Sciences, University of Alberta Taiki Shibata Department of Applied Mathematics, Okayama University of Science We provide explicit generators and relations for the affine Kac-Moody groups, as well as a realization of them as (twisted) loop groups by means of Galois descent considerations. As a consequence, we show that the affine Kac-Moody group of type X(r) N is isomorphic to the fixed-point subgroup of the affine Kac-Moody group of type X(1) N under an action of the Galois group. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 65 1 2023 E(2)-local Picard graded beta elements at the prime three 23 34 EN Ryo Kato Faculty of Fundamental Science National Institute of Technology, Niihama college Let E(2) be the second Johnson-Wilson spectrum at the prime 3. In this paper, we show that some beta elements exist in the homotopy groups of the E(2)-localized sphere spectrum with a grading over the Picard group of the stable homotopy category of E(2)-local spectra. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 65 1 2023 A characterization of the class of Harada rings 1 22 EN Kazutoshi Koike National Institute of Technology, Okinawa College There are many characterizations of Harada rings. In this paper, we characterize right co-Harada rings by giving a characterization of the class of basic right co-Harada rings. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 64 1 2022 A note on a Hecke ring associated with the Heisenberg Lie algebra 215 225 EN Fumitake Hyodo Department of Health Informatics Faculty of Health and Welfare Services Administration Kawasaki University of Medical Welfare This paper focuses on the theory of the Hecke rings associated with the general linear groups originally studied by Hecke and Shimura et al., and moreover generalizes its notions to Hecke rings associated with the automorphism groups of certain algebras. Then, in the case of the Heisenberg Lie algebra, we show an analog of the classical theory. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 64 1 2022 On Hook Formulas for Cylindric Skew Diagrams 191 213 EN Takeshi Suzuki Department of Mathematics, Faculty of Science, Okayama University Yoshitaka Toyosawa Graduate School of Natural Science and Technology, Okayama University We present a conjectural hook formula concerning the number of the standard tableaux on "cylindric" skew diagrams. Our formula can be seen as an extension of Naruse's hook formula for skew diagrams. Moreover, we prove our conjecture in some special cases. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 64 1 2022 Symbolic powers of monomial ideals 187 190 EN Tony J. Puthenpurakal Let K be a field and consider the standard grading on A = K[X₁, ... ,X_d]. Let I, J be monomial ideals in A. Let I_n(J) = (Iⁿ : J^&infin;) be the n^th symbolic power of I with respect to J. It is easy to see that the function f^I _J (n) = e₀(I_n(J)/Iⁿ) is of quasi-polynomial type, say of period g and degree c. For n ≫ 0 say<br> <br> f^I_J (n) = a_c(n)n^c + a_c−1(n)n^c−1 + lower terms,<br> <br> where for i = 0, ... , c, a_i : N → Q are periodic functions of period g and a_c &ne;0. In [4, 2.4] we (together with Herzog and Verma) proved that dim I_n(J)/Iⁿ is constant for n ≫ 0 and a_c(−) 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 a_c−1(−) is also a constant. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 64 1 2022 Bijective proofs of the identities on the values of inner products of the Macdonald polynomials 153 186 EN Yuta Nishiyama Graduate School of Science and Technology, Kumamoto University 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. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 64 1 2022 Quantum Sylvester-Franke Theorem 143 151 EN Kazuya Aokage Department of Mathematics, National Institute of Technology, Ariake College Sumitaka Tabata Department of Mathematics, Kumamoto University Hiro-Fumi Yamada Department of Mathematics, Kumamoto University A quantum version of classical Sylvester-Franke theorem is presented. After reviewing some representation theory of the quantum group GL_q (n, C), the commutation relations of the matrix elements are verified. Once quantum determinant of the representation matrix is defined, the theorem follows naturally No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 64 1 2022 τ-tilting finiteness of two-point algebras I 117 141 EN Qi Wang Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University 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. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 64 1 2022 Notes on the filtration of the K-theory for abelian p-groups 109 116 EN Nobuaki Yagita Department of Mathematics Faculty of Education Ibaraki University Let p be a prime number. For a given finite group G, let gr^*_&gamma;(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^*_&gamma;(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. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 64 1 2022 Criteria for good reduction of hyperbolic polycurves 75 107 EN Ippei Nagamachi Research Institute for Mathematical Sciences, Kyoto University 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. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 64 1 2022 Note on totally odd multiple zeta values 63 73 EN Koji Tasaka A partial answer to a conjecture about the rank of the matrix C_N,_r introduced by Francis Brown in the study of totally odd multiple zeta values is given. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 64 1 2022 On Weakly Separable Polynomials in skew polynomial rings 47 61 EN Satoshi Yamanaka Department of Integrated Science and Technology National Institute of Technology, Tsuyama College 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. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 64 1 2022 The best constant of the discrete Sobolev inequalities on the complete bipartite graph 31 45 EN Hiroyuki Yamagishi Tokyo Metropolitan College of Industrial Technology We have the best constants of three kinds of discrete Sobolev inequalities on the complete bipartite graph with 2N vertices, that is, K_N,_N. We introduce a discrete Laplacian A on K_N,_N. A is a 2N ×2N real symmetric positive-semidefinite matrix whose eigenvector corresponding to zero eigenvalue is 1 = ^t(1, 1, … , 1)&isin; C^2N. A discrete heat kernel, a Green’s matrix and a pseudo Green’s matrix play important roles in giving the best constants. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 64 1 2022 The d-Smith sets of Cartesian products of the alternating groups and finite elementary abelian 2-groups 13 29 EN Kohei Seita Department of Mathematics, Graduate School of Natural Science and Technology, Okayama University Let G be a finite group. In 1970s, T. Petrie defined the Smith equivalence of real G-modules. The Smith set of G is the subset of the real representation ring consisting of elements obtained as differences of Smith equivalent real G-modules. Various results of the topic have been obtained. The d-Smith set of G is the set of all elements [V ]−[W] in the Smith set of G such that the H-fixed point sets of V and W have the same dimension for all subgroups H of G. The results of the Smith sets of the alternating groups and the symmetric groups are obtained by E. Laitinen, K. Pawa lowski and R. Solomon. In this paper, we give the calculation results of the d-Smith sets of the alternating groups and the symmetric groups. In addition, we give the calculation results of the d-Smith sets of Cartesian products of the alternating groups and finite elementary abelian 2-groups. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 64 1 2022 A Note on Torsion Points on Ample Divisors on Abelian Varieties 1 11 EN Yuichiro Hoshi Research Institute for Mathematical Sciences, Kyoto University In the present paper, we consider torsion points on ample divisors on abelian varieties. We prove that, for each integer n &le; 2, an effective divisor of level n on an abelian variety does not contain the subgroup of n-torsion points. Moreover, we also discuss an application of this result to the study of the p-rank of cyclic coverings of curves in positive characteristic. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 8 2 1958 Galois theory of simple rings IV 189 194 EN Takasi Nagahara Nobuo Nobusawa Hisao Tominaga No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 8 2 1958 On generating elements of Galois extensions of division rings IV 181 188 EN Takashi Nagahara No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 8 2 1958 Tangent bundles of order 2 and general connections 143 179 EN Tominosuke Otsuki No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 8 2 1958 On normal basis theorems and strictly Galois extensions 133 142 EN Takasi Nagahara Takesi Onodera Hisao Tominaga No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 8 2 1958 Some remarks on homotopy equivalences and H-spaces 125 131 EN Masahiro Sugawara No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 8 2 1958 A note on Galois theory of primary rings 117 123 EN Hisao Tominaga No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 8 2 1958 Note on curvature of Finsler manifolds 107 116 EN Tominosuke Ōtsuki No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 8 1 1958 Poincarésche Vermutung in Topologie 1 106 EN Ken'iti Koseki No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 63 1 2021 Linear stability of radially symmetric equilibrium solutions to the singular limit problem of three-component activator-inhibitor model 201 217 EN Takuya Kojima Graduate school of Natural Science and Technology, Okayama University Yoshihito Oshita Department of Mathematics, Okayama University 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. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 63 1 2021 On H-epimorphisms and co-H-sequences in two-sided Harada rings 183 199 EN Yoshitomo Baba Department of Mathematics Education Osaka Kyoiku University 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. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 63 1 2021 On some families of invariant polynomials divisible by three and their zeta functions 175 182 EN Koji Chinen Department of Mathematics, School of Science and Engineering, Kindai University 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. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 63 1 2021 On pg-ideals 167 173 EN Tony J. Puthenpurakal Department of Mathematics, IIT Bombay 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. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 63 1 2021 The d-Smith sets of direct products of dihedral groups 153 165 EN Kohei Seita Department of Mathematics, Graduate School of Natural Science and Technology, Okayama University 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. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 63 1 2021 Rectangular Hall-Littlewood symmetric functions and a specific spin character 133 151 EN Kazuya Aokage Department of Mathematics, National Institute of Technology, Ariake College 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. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 63 1 2021 Differential operators on modular forms associated to Jacobi forms 123 131 EN Min Ho Lee Department of Mathematics, University of Northern Iowa 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. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 63 1 2021 A note on products in stable homotopy groups of spheres via the classical Adams spectral sequence 107 122 EN Ryo Kato Faculty of Fundamental Science, National Institute of Technology, Niihama College katsumi Shimomura Department of Mathematics, faculty of Science and Technology, Kochi University 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. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 63 1 2021 A weak Euler formula for l-adic Galois double zeta values 87 105 EN Wojtkowiak Zdzisław Université de Nice-Sophia Antipolis, Déartement de Math ématiques Laboratoire Jean Alexandre Dieudonné 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. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 63 1 2021 Defining relations of 3-dimensional quadratic AS-regular algebras 61 86 EN Ayako Itaba Department of Mathematics, faculty of Science, Tokyo University of Science Masaki Matsuno Graduate School of Science and Technology, Shizuoka University 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. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 63 1 2021 Remark on a Paper by Izadi and Baghalaghdam about Cubes and Fifth Powers Sums 53 60 EN Gaku Iokibe Department of Mathematics, Graduate School of Science, Osaka University 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. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 63 1 2021 Differential geometry of invariant surfaces in simply isotropic and pseudo-isotropic spaces 15 52 EN Luiz C. B. da Silva Department of Physics of Complex Systems, Weizmann Institute of Science 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. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 63 1 2021 On the stability, boundedness, and square integrability of solutions of third order neutral delay differential equations 1 14 EN John R. Graef Department of Mathematics, University of Tennessee at Chattanooga Djamila Beldjerd Oran’s High School of Electrical Engineering and Energetics Moussadek Remili Department of Mathematics, University of Oran 1 Ahmed Ben Bella 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. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 62 1 2020 Existence and stability of stationary solutions to the Allen-Cahn equation discretized in space and time 197 210 EN Amy Poh Ai Ling Division of Mathematics and Physics, Graduate School of Natural Science and Technology, Okayama University Masaharu Taniguchi Research Institute for Interdisciplinary Science, Okayama University 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. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 62 1 2020 Analytic extension of exceptional constant mean curvature one catenoids in de Sitter 3-space 179 195 EN Shoichi Fujimori Department of Mathematics, Hiroshima University Yu Kawakami Graduate School of Natural Science and Technology, Kanazawa University Masatoshi Kokubu Department of Mathematics, School of Engineering, Tokyo Denki University Wayne Rossman Department of Mathematics, Faculty of Science, Kobe University Masaaki Umehara Department of Mathematical and Computing Sciences, Tokyo Institute of Technology Kotaro Yamada Department of Mathematics, Tokyo Institute of Technology Catenoids in de Sitter 3-space S³₁ 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 S³₁ . Here we show that such exceptional catenoids have closed analytic extensions in S³₁ with interesting properties. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 62 1 2020 Crystal interpretation of a formula on the branching rule of types Bn, Cn, and Dn 87 178 EN Toya Hiroshima Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University 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. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 62 1 2020 Unstable higher Toda brackets 27 86 EN Hideaki Oshima Ibaraki University Katsumi Oshima No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 62 1 2020 A representation for algebraic K-theory of quasi-coherent modules over affine spectral schemes 1 25 EN Mariko Ohara Department of Mathematical Sciences Shinshu University 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^G(B^GGL) represents the sheafification of K with respect to Zariski (resp. Nisnevich) topology G, where B^GGL is a classifying space of a colimit of affine spectral schemes GLn. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 61 1 2019 Terwilliger Algebras of Some Group Association Schemes 199 204 EN Nur Hamid Faculty of Mathematics and Physics, Kanazawa University Manabu Oura Faculty of Mathematics and Physics, Kanazawa University 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. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 61 1 2019 Passage of property (Bw) from two operators to their tensor product 187 198 EN M.H.M. Rashid Department of Mathematics& Statistics Faculty of Science P.O.Box(7) Mu’tah University 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. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 61 1 2019 On the classification of ruled minimal surfaces in pseudo-Euclidean space 173 186 EN Yuichiro Sato Department of Mathematical Sciences Tokyo Metropolitan University 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. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 61 1 2019 The Factorization of 2 and 3 in Cyclic Quartic Fields 167 172 EN Stephen C. Brown Department of Computer Science, Mathematics, Physics and Statistics I.K. Barber School of Arts and Sciences University of British Columbia Chad T. Davis Department of Computer Science, Mathematics, Physics and Statistics I.K. Barber School of Arts and Sciences University of British Columbia 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. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 61 1 2019 The number of simple modules in a block with Klein four hyperfocal subgroup 159 166 EN Fuminori Tasaka National Institute of Technology Tsuruoka College 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. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 61 1 2019 Cesaro Orlicz sequence spaces and their Kothe-Toeplitz duals 141 158 EN Kuldip Raj School of Mathematics Shri Mata Vaishno Devi University Renu Anand School of Mathematics Shri Mata Vaishno Devi University Suruchi Pandoh School of Mathematics Shri Mata Vaishno Devi University The present paper focus on introducing certain classes of Cesàro Orlicz sequences over n-normed spaces. We study some topological and algebraic properties of these spaces. Further, we examine relevant relations among the classes of these sequences. We show that these spaces are made n-BK-spaces under certain conditions. Finally, we compute the Köthe-Toeplitz duals of these spaces. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 61 1 2019 A limit transition from the Heckman-Opdam hypergeometric functions to the Whittaker functions associated with root systems 129 139 EN Nobukazu Shimeno School of Science and Technology Kwansei Gakuin University We prove that the radial part of the class one Whittaker function on a split semisimple Lie group can be obtained as an appropriate limit of the Heckman-Opdam hypergeometric function. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 61 1 2019 Complex interpolation of smoothness Triebel-Lizorkin-Morrey spaces 99 128 EN Denny Ivanal Hakim Department of Mathematics and Information Sciences, Tokyo Metropolitan University Toru Nogayama Department of Mathematics and Information Sciences, Tokyo Metropolitan University Yoshihiro Sawano Department of Mathematics and Information Sciences, Tokyo Metropolitan University This paper extends the result in [8] to Triebel-Lizorkin-Morrey spaces which contains 4 parameters p, q, r, s. This paper reinforces our earlier paper [8] by Nakamura, the first and the third authors in two different directions. First, we include the smoothness parameter s and the second smoothness parameter r. In [8] we assumed s = 0 and r = 2. Here we relax the conditions on s and r to s ∈ R and 1 < r ≤ ∞. Second, we apply a formula obtained by Bergh in 1978 to prove our main theorem without using the underlying sequence spaces. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 61 1 2019 On the structure of the profile of finite connected quandles 85 98 EN Taisuke Watanabe We verify some cases of a conjecture by C. Hayashi on the structure of the profile of a finite connected quandle. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 61 1 2019 On the Diophantine equation in the form that a sum of cubes equals a sum of quintics 75 84 EN Farzali Izadi Mehdi Baghalaghdam Department of Mathematics Faculty of Science Azarbaijan Shahid Madani University Mehdi Baghalaghdam Mehdi Baghalaghdam Department of Mathematics Faculty of Science Azarbaijan Shahid Madani University No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 61 1 2019 Reconstruction of inertia groups associated to log divisors from a configuration space group equipped with its collection of log-full subgroups 37 73 EN Kazumi Higashiyama Research Institute for Mathematical Sciences Kyoto University 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. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 61 1 2019 Berezin-Weyl quantization of Heisenberg motion groups 19 35 EN Benjamin Cahen D´epartement de math´ematiques Universit´e de Lorraine 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]. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 61 1 2019 On the existence of non-finite coverings of stable curves over complete discrete valuation rings 1 18 EN Yu Yang Research Institute for Mathematical Sciences Kyoto University 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. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 60 1 2018 On the profinite abelian Beckmann-Black problem 233 240 EN Nour Ghazi University of Damascus, Faculty of Sciences, Department of Mathematics The main topic of this paper is to generalize the problem of Beckmann-Black for pro�nite groups. We introduce the Beckmann-Black problem for complete systems of �finite groups and for unramified extensions. We prove that every Galois extension of profi�nite abelian group over a ψ-free fi�eld is the specialization of some tower of regular Galois extensions of the same group. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 60 1 2018 A binomial-coefficient identity arising from the middle discrete series of SU(2,2) 221 231 EN Takahiro Hayata Graduate School of Science and Engineering, Yamagata University Masao Ishikawa Graduate School of Natural Science and Technology, Okayama University The aim of this paper is to answer the question in Remark 8.2 of Takahiro Hayata, Harutaka Koseki, and Takayuki Oda, Matrix coefficients of the middle discrete series of SU(2; 2), J. Funct. Anal. 185 (2001), 297{341, by giving an elementary proof of certain identities on binomials. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 60 1 2018 Necessary and sufficient Tauberian conditions for the A^r method of summability 209 219 EN Özer Talo Department of Mathematics Faculty of Science and Letters Manisa Celal Bayar University Feyzi Bas̨ar İnönü University Móricz and Rhoades determined the necessary and sufficient Tauberian conditions for certain weighted mean methods of summability in [Acta. Math. Hungar. 102(4) (2004), 279{285]. In the present paper, we deal with the necessary and sufficient Tauberian conditions for the Ar method which was introduced by Bas̨ar in [Fırat Üniv. Fen & Müh. Bil. Dergisi 5(1)(1993), 113{117]. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 60 1 2018 Indecomposability of various profinite groups arising from hyperbolic curves 175 208 EN Arata Minamide Research Institute for Mathematical Sciences Kyoto University In this paper, we prove that the etale fundamental group of a hyperbolic curve over an arithmetic field [e.g., a finite extension field of Q or Qp] or an algebraically closed field is indecomposable [i.e., cannot be decomposed into the direct product of nontrivial profinite groups]. Moreover, in the case of characteristic zero, we also prove that the etale fundamental group of the configuration space of a curve of the above type is indecomposable. Finally, we consider the topic of indecomposability in the context of the comparison of the absolute Galois group of Q with the Grothendieck-Teichmuller group GT and pose the question: Is GT indecomposable? We give an affirmative answer to a pro-l version of this question No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 60 1 2018 An alternative proof of some results on the framed bordism classes of low rank simple Lie groups 165 173 EN Haruo Minami Nara University of Education We present a uni�ed proof of some known results on the framed bordism classes of low rank simple Lie groups. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 60 1 2018 Arithmetic of positive integers having prime sums of complementary divisors 155 164 EN Kenichi Shimizu We study a class of integers called SP numbers (Sum Prime numbers). An SP number is by de�nition a positive integer d that gives rise to a prime number (a + b)=gcd(4; 1 + d) from every factorization d = ab. We also discuss properties of SP numbers in relations with arithmetic of imaginary quadratic �elds (least split primes, exponents of ideal class groups). Further we point out that special cases of SP numbers provide the problems of distribution of prime numbers (twin primes, Sophi-Germain primes, quadratic progressions). Finally, we consider the problem whether there exist in�nitely many SP numbers. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 60 1 2018 A non-symmetric diffusion process on the Wiener space 137 153 EN Ichiro Shigekawa Department of Mathematics Graduate School of Science Kyoto University We discuss a non-symmetric diffusion process on the Wiener space. The process we consider is generated by A = L + b, L being the Ornstein-Uhlenbeck operator and b being a vector �eld. Under suitable integrability condition for b, we show the existence of associated diffusion process. We also investigate the domain of the generator. Further we consider a similar problem in the �nite dimensional Euclidean space. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 60 1 2018 A remark on a central limit theorem for non-symmetric random walks on crystal lattices 109 135 EN Ryuya Namba Graduate School of Natural Sciences, Okayama University Recently, Ishiwata, Kawabi and Kotani [4] proved two kinds of central limit theorems for non-symmetric random walks on crystal lattices from the view point of discrete geometric analysis developed by Kotani and Sunada. In the present paper, we establish yet another kind of the central limit theorem for them. Our argument is based on a measure-change technique due to Alexopoulos [1]. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 60 1 2018 Primary decompositions in abelian R-categories 91 108 EN Kenichi Sato Graduate School of Natural Science and Technology Okayama University Yuji Yoshino Graduate School of Natural Science and Technology Okayama University We shall generalize the theory of primary decomposition and associated prime ideals of �nitely generated modules over a noetherian ring to general objects in an abelian R-category where R is a noetherian commutative ring. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 60 1 2018 Stable splittings of the complex connective K-theory of BSO(2n+1) 73 89 EN Tsung-Hsuan Wu Department of Mathematics National Tsing Hua University We give the stable splittings of the complex connective K-theory of the classifying space BSO(2n + 1), n≥1. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 60 1 2018 Absolute continuity of the representing measures of the transmutation operators attached to the root system of type BC2 59 72 EN Khalifa Trimẻche Department of Mathematics Faculty of sciences of Tunis University We prove in this paper the absolute continuity of the representing measures of the transmutation operators Vk, tVk and VkW, tVkW associated respectively to the Cherednik operators and the Heckman-Opdam theory attached to the root system of type BC2. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 60 1 2018 Tomita-Takesaki theory and its application to the structure theory of factors of type III 37 58 EN Toshihiko Masuda Graduate School of Mathematics, Kyushu University We give a survey of Tomita-Takesaki theory and the development of analysis of structure of type III factors, which started from Tomita-Takesaki theory. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 60 1 2018 Review on higher homotopies in the theory of H-spaces 1 36 EN Yutaka Hemmi Department of Mathematics Faculty of Science and Technology Kochi University Higher homotopy in the theory of H-spaces started from the works by Sugawara in the 1950th. In this paper we review the development of the theory of H-spaces associated with it. Mainly there are two types of higher homotopies, homotopy associativity and homotopy commutativity. We give explanations of the polytopes used as the parameter spaces of those higher forms. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 59 1 2017 Blowup and global existence of a solution to a semilinear reaction-diffusion system with the fractional Laplacian 175 218 EN Tomoyuki Kakehi Department of Mathematics, Okayama University Yoshihito Oshita Department of Mathematics, Okayama University 10.18926/mjou/54723 In this paper, we deal with the semilinear reaction diffusion system with the fractional Laplacian.<br> <img src="http://www.lib.okayama-u.ac.jp/www/mjou/mjou_59_175.png"><br> where <i>p,q</i> &gt; 1 and 0 &lt; <i>&alpha;</i> &lt; 1. We study the existence of a global in time solution, the blowup of a solution, and the life span of the blowup solution to the above reaction-diffusion system for sufficiently small initial data. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 59 1 2017 Scattering and semi-classical asymptotics for periodic Schr&ouml;dinger operators with oscillating decaying potential 149 174 EN Mouez Dimassi Universit´e Bordeaux I, Institut de Math´ematiques de Bordeaux Anh Tuan Duong Department of Mathematics, Hanoi National University of Education 10.18926/mjou/54721 In the semi-classical regime (i.e., <i>h</i> &searr; 0), we study the effect of an oscillating decaying potential <i>V</i> (<i>hy, y</i>) on the periodic Schr&ouml;dinger operator <i>H</i>. The potential <i>V</i> (<i>x, y</i>) is assumed to be smooth, periodic with respect to <i>y</i> and tends to zero as |<i>x</i>| &rarr; &infin;. We prove the existence of <i>O</i>(<i>h⁻ⁿ</i>) eigenvalues in each gap of the operator <i>H</i> + <i>V</i> (<i>hy, y</i>). We also establish a Weyl type asymptotics formula of the counting function of eigenvalues with optimal remainder estimate. We give a weak and pointwise asymptotic expansions in powers of <i>h</i> of the spectral shift function corresponding to the pair (<i>H</i> + <i>V</i> (<i>hy, y</i>),<i>H</i>). Finally, under some analytic assumption on the potential V we prove the existence of shape resonances, and we give their asymptotic expansions in powers of <i>h^1/2</i>. All our results depend on the Floquet eigenvalues corresponding to the periodic Schr&ouml;dinger operator <i>H</i> +<i>V</i> (<i>x, y</i>), (here <i>x</i> is a parameter). No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 59 1 2017 On the (1 − C₂) condition 141 147 EN Le Van An Department of Natural Education, Ha Tinh University Nguyen Thi Hai Anh Department of Natural Education, Ha Tinh University Ngo Sy Tung Department of Mathematics, Vinh University 10.18926/mjou/54720 In this paper, we give some results on (1 − C₂)−modules and 1−continuous modules. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 59 1 2017 Higher-dimensional absolute versions of symmetric, Frobenius, and quasi-Frobenius algebras 131 140 EN Mitsuyasu Hashimoto Department of Mathematics Faculty of Science, Okayama University 10.18926/mjou/54719 In this paper, we define and discuss higher-dimensional and absolute versions of symmetric, Frobenius, and quasi-Frobenius algebras. In particular, we compare these with the relative notions defined by Scheja and Storch. We also prove the validity of codimension two-argument for modules over a coherent sheaf of algebras with a 2-canonical module, generalizing a result of the author. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 59 1 2017 A note on balance equations for doubly periodic minimal surfaces 117 130 EN Peter Connor Department of Mathematical Sciences, Indiana University South Bend 10.18926/mjou/54718 Most known examples of doubly periodic minimal surfaces in R³ with parallel ends limit as a foliation of R³ by horizontal noded planes, with the location of the nodes satisfying a set of balance equations. Conversely, for each set of points providing a balanced configuration, there is a corresponding three-parameter family of doubly periodic minimal surfaces. In this note we derive a differential equation that is equivalent to the balance equations for doubly periodic minimal surfaces. This allows for the generation of many more solutions to the balance equations, enabling the construction of increasingly complicated surfaces. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 59 1 2017 A remark on the Lavallee-Spearman-Williams-Yang family of quadratic fields 113 116 EN Kwang-Seob Kim School of Mathematics, Korea Institute for Advanced Study Yasuhiro Kishi Department of Mathematics, Aichi University of Education 10.18926/mjou/54717 In [4], M. J. Lavallee, B. K. Spearman, K. S. Williams and Q. Yang introduced a certain parametric D5-quintic polynomial and studied its splitting field. The present paper gives an infinite family of quadratic fields with class number divisible by 5 by using properties of its polynomial. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 59 1 2017 Gauss maps of cuspidal edges in hyperbolic 3-space, with application to flat fronts 93 111 EN Yuta Ogata Department of Mathematics, Graduate School of Science, Kobe University Keisuke Teramoto Department of Mathematics, Graduate School of Science, Kobe University 10.18926/mjou/54716 We study singularities of de Sitter Gauss map images of cuspidal edges in hyperbolic 3-space. We show relations between singularities of de Sitter Gauss map images and differential geometric properties of cuspidal edges. Moreover, we apply this result to flat fronts in hyperbolic 3-space. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 59 1 2017 An arithmetic function arising from the Dedekind &psi; function 81 92 EN Colin Defant Department of Mathematics, University of Florida 10.18926/mjou/54715 We define &psi;&oline; to be the multiplicative arithmetic function that satisfies<br> <img src="http://www.lib.okayama-u.ac.jp/www/mjou/mjou_59_81.png"><br> for all primes <i>p</i> and positive integers &alpha;. Let <i>&lambda;(n)</i> be the number of iterations of the function <i>&psi;&oline;</i> needed for <i>n</i> to reach 2. It follows from a theorem due to White that <i>&lambda;</i> is additive. Following Shapiro's work on the iterated <i>&phi;</i> function, we determine bounds for <i>&lambda;</i>. We also use the function <i>&lambda;</i> to partition the set of positive integers into three sets <i>S₁, S₂, S₃</i> and determine some properties of these sets. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 59 1 2017 Evaluation of convolution sums and some remarks on cusp forms of weight 4 and level 12 71 79 EN B. Ramakrishhan Harish-Chandra Research Institute Brundaban Sahu School of Mathematical Sciences National Institute of Science Education and Research 10.18926/mjou/54714 In this note, we evaluate certain convolution sums and make some remarks about the Fourier coefficients of cusp forms of weight 4 for &Gamma;₀(12). We express the normalized newform of weight 4 on &Gamma;₀(12) as a linear combination of the (quasimodular) Eisenstein series (of weight 2) <i>E₂(dz)</i>, <i>d</i>|12 and their derivatives. Now, by comparing the work of Alaca-Alaca-Williams [1] with our results, as a consequence, we express the coefficients <i>c_1,12(n)</i> and <i>c_3,4(n)</i> that appear in [1, Eqs.(2.7) and (2.12)] in terms of linear combination of the Fourier coefficients of newforms of weight 4 on &Gamma;₀(6) and &Gamma;₀(12). The properties of <i>c_1,12(n)</i> and <i>c_3,4(n)</i> that are derived in [1] now follow from the properties of the Fourier coefficients of the newforms mentioned above. We also express the newforms as a linear combination of certain eta-quotients and obtain an identity involving eta-quotients. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 59 1 2017 On a non-abelian generalization of the Bloch–Kato exponential map 41 70 EN Kenji Sakugawa Department of Mathematics Graduate School of Science, Osaka University 10.18926/mjou/54713 The present paper establishes a non-abelian generalization of the Bloch–Kato exponential map. Then, we relate p-adic polylogarithms introduced by Coleman to `-adic polylogarithms introduced by Wojtkowiak. This formula is another analog of the Coleman–Ihara formula obtained by Nakamura, Wojtkowiak, and the author. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 59 1 2017 The degree of set-valued mappings from ANR spaces to homology spheres 27 40 EN Yoshimi Shitanda School of political science and economics, Meiji University 10.18926/mjou/54712 An admissible mapping is a set-valued mapping which has a selected pair of continuous mappings. In this paper, we study the degree of admissible mappings from ANR spaces to homology spheres and prove the uniqueness of the degree under some conditions. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 59 1 2017 Some examples of non-tidy spaces 21 25 EN Takahiro Matsushita Graduate School of Mathematical Sciences, The University of Tokyo 10.18926/mjou/54711 We construct a free Z₂-space <i>X_n</i> for a positive integer <i>n</i> such that <i>w₁(X_n)ⁿ</i> &ne; 0 but there is no Z₂-map from <i>S</i>² to <i>X_n</i>. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 59 1 2017 Categorical characterization of strict morphisms of fs log schemes 1 19 EN Yuichiro Hoshi Research Institute for Mathematical Sciences, Kyoto University Chikara Nakayama Department of Economics, Hitotsubashi University 10.18926/mjou/54710 In the present paper, we study a categorical characterization of strict morphisms of fs log schemes. In particular, we prove that strictness of morphisms of fs log schemes is preserved by an arbitrary equivalence of categories between suitable categories of fs log schemes. The main result of the present paper leads us to a relatively simple alternative proof of a result on a categorical representation of fs log schemes proved by S. Mochizuki. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 58 1 2016 The positivity of the transmutation operators associated to the Cherednik operators for the root system $BC_2$ 183 198 EN Khalifa TRIMÈCHE 10.18926/mjou/53925 We consider the transmutation operators V_k, ^tV_k and V ^W _k , ^tV ^W _k associated respectively with the Cherednik operators and the Heckman-Opdam theory attached to the root system BC2, called also in [8, 9, 10] the trigonometric Dunkl intertwining operators, and their dual. In this paper we prove that the operators V_k, ^tV_k and V^W_k , ^tV^W_k are positivity preserving and allows positive integral representations. In particular we deduce that the Opdam-Cherednik and the Heckman-Opdam kernels are positive definite. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 58 1 2016 On weakly separable polynomials and weakly quasi-separable polynomials over rings 169 182 EN Satoshi Yamanaka 10.18926/mjou/53924 Separable extensions of noncommutative rings have already been studied extensively. Recently, N. Hamaguchi and A. Nakajima introduced the notions of weakly separable extensions and weakly quasiseparable extensions. They studied weakly separable polynomials and weakly quasi-separable polynomials in the case that the coefficient ring is commutative. The purpose of this paper is to give some improvements and generalizations of Hamaguchi and Nakajima's results. We shall characterize a weakly separable polynomial f(X) over a commutative ring by using its derivative f′(X) and its discriminant δ(f(X)). Further, we shall try to give necessary and sufficient conditions for weakly separable polynomials in skew polynomial rings in the case that the coefficient ring is noncommutative. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 58 1 2016 Restriction on Galois groups by prime inert condition 159 167 EN Toru Komatsu 10.18926/mjou/53923 In this paper, we study number fields K with the property that every prime factor of the degree of K remains prime in K. We determine all types of Galois groups of such K up to degree nine and find that Wang's non-existence in cyclic octic case is exceptionally undetermined by our group-theoretic criterion. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 58 1 2016 Alternative approach for Siegel's lemma 141 158 EN Makoto Nagata 10.18926/mjou/53922 In this article, we present an alternative approach to show a generalization of Siegel's lemma which is an essential tool in Diophantine problems. Our main statement contains the so-called analytic Siegel's lemma as well as the Bombieri-Vaaler lemma. Our proof avoids relying on the ordinary geometry of numbers. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 58 1 2016 On finite rings over which every free codes is splitting 133 140 EN Yasuyuki Hirano 10.18926/mjou/53921 In this paper, we study the structure of finite rings over which all free codes are splitting. In particular, we show that over the matrix rings over finite local rings all free codes are splitting. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 58 1 2016 On a duality of Gras between totally positive and primary cyclotomic units 125 132 EN Humio Ichimura 10.18926/mjou/53920 Let K be a real abelian field of odd degree over Q, and C the group of cyclotomic units of K. We denote by C+ and C0 the totally positive and primary elements of C, respectively. G. Gras found a duality between the Galois modules C+/C2 and C0/C2 by some ingenious calculation on cyclotomic units. We give an alternative proof using a consequence (=“Gras conjecture”) of the Iwasawa main conjecture and the standard reflection argument. We also give some related topics. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 58 1 2016 Another description of quasi tertiary composition 109 123 EN Hideaki Ōshima Katsumi Ōshima 10.18926/mjou/53919 We give another description of quasi tertiary composition in terms of horizontal and vertical compositions. As an application of the description and a modified result of Hardie-Kamps-Marcum-Oda, we see that any quasi tertiary composition has an indeterminacy. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 58 1 2016 Aharonov--Bohm effect in resonances of magnetic Schrödinger operators in two dimensions III 79 108 EN Hideo Tamura 10.18926/mjou/53918 We study the Aharonov–Bohm effect (AB effect) in quantum resonances for magnetic scattering in two dimensions. The system consists of four scatters, two obstacles and two scalar potentials with compact support, which are largely separated from one another. The obstacles by which the magnetic fields are completely shielded are vertically placed between the supports of the two potentials. The system yields a two dimensional model of a toroidal scattering system in three dimensions. The resonances are shown to be generated near the real axis by the trajectories trapped between two supports of the scalar potentials as the distances between the scatterers go to infinity. We analyze how the AB effect influences the location of resonances. The result heavily depends on the width between the two obstacles as well as on the magnetic fluxes. The critical case is that the width is comparable to the square root of the distance between the supports of the two potentials. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 58 1 2016 Aharonov--Bohm effect in resonances of magnetic Schrödinger operators in two dimensions II 41 78 EN Hideo Tamura 10.18926/mjou/53917 We study the Aharonov–Bohm effect (AB effect) in quantum resonances for magnetic scattering in two dimensions. The system consists of four scatters, two obstacles and two scalar potentials with compact support, which are largely separated from one another. The obstacles by which the magnetic fields are completely shielded are horizontally placed between the supports of the two potentials. The fields do not influence particles from a classical mechanical point of view, but quantum particles are influenced by the corresponding vector potential which does not necessarily vanish outside the obstacle. This quantum phenomenon is called the AB effect. The resonances are shown to be generated near the real axis by the trajectories trapped between two supports of the scalar potentials as the distances between the scatterers go to infinity. We analyze how the AB effect influences the location of resonances. The result is described in terms of the backward amplitudes for scattering by each of the scalar potentials, and it depends heavily on the ratios of the distances between the four scatterers as well as on the magnetic fluxes of the fields. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 58 1 2016 Asymptotic properties in forward directions of resolvent kernels of magnetic Schrödinger operators in two dimensions 1 39 EN Hideo Tamura 10.18926/mjou/53916 We study the asymptotic properties in forward directions of resolvent kernels with spectral parameters in the lower half plane (unphysical sheet) of the complex plane for magnetic Schrödinger operators in two dimensions. The asymptotic formula obtained has an application to the problem of quantum resonances in magnetic scattering, and it is especially helpful in studying how the Aharonov–Bohm effect influences the location of resonances. Here we mention only the results without proofs. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 57 1 2015 ZERO MEAN CURVATURE SURFACES IN LORENTZ-MINKOWSKI 3-SPACE AND 2-DIMENSIONAL FLUID MECHANICS 173 200 EN Shoichi Fujimori Young Wook Kim Sung-Eun Koh Wayne Rossman Heayong Shin Masaaki Umehara Kotaro Yamada Seong-Deog Yang 10.18926/mjou/53048 Space-like maximal surfaces and time-like minimal surfaces in Lorentz-Minkowski 3-space R³₁ are both characterized as zero mean curvature surfaces. We are interested in the case where the zero mean curvature surface changes type from space-like to time-like at a given non-degenerate null curve. We consider this phenomenon and its interesting connection to 2-dimensional fluid mechanics in this expository article. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 57 1 2015 ENUMERATIVE COMBINATORICS ON DETERMINANTS AND SIGNED BIGRASSMANNIAN POLYNOMIALS 159 172 EN Masato Kobayashi 10.18926/mjou/53047 As an application of linear algebra for enumerative combinatorics, we introduce two new ideas, signed bigrassmannian polynomials and bigrassmannian determinant. First, a signed bigrassmannian polynomial is a variant of the statistic given by the number of bigrassmannian permutations below a permutation in Bruhat order as Reading suggested (2002) and afterward the author developed (2011). Second, bigrassmannian determinant is a q-analog of the determinant with respect to our statistic. It plays a key role for a determinantal expression of those polynomials. We further show that bigrassmannian determinant satisfies weighted condensation as a generalization of Dodgson, Jacobi-Desnanot and Robbins-Rumsey (1986). No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 57 1 2015 ON &empty;-RECURRENT CONTACT METRIC MANIFOLDS 149 158 EN Esmaeil Peyghan Hassan Nasrabadi Akbar Tayebi 10.18926/mjou/53046 In this paper, we prove that evry 3-dimensional manifold M is a &empty;-recurrent N(k)-contact metric manifold if and only if it is flat. Then we classify the &empty;-recurrent contact metric manifolds of constant curvature. This implies that there exists no &empty;-recurrent N(k)-contact metric manifold, which is neither symmetric nor locally &empty;-symmetric. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 57 1 2015 AN EXPLICIT EFFECT OF NON-SYMMETRY OF RANDOM WALKS ON THE TRIANGULAR LATTICE 129 148 EN Satoshi Ishiwata Hiroshi Kawabi Tsubasa Teruya 10.18926/mjou/53045 In the present paper, we study an explicit effect of non-symmetry on asymptotics of the n-step transition probability as n → &infin; for a class of non-symmetric random walks on the triangular lattice. Realizing the triangular lattice into R² appropriately, we observe that the Euclidean distance in R² naturally appears in the asymptotics. We characterize this realization from a geometric view point of Kotani-Sunada’s standard realization of crystal lattices. As a corollary of the main theorem, we obtain that the transition semigroup generated by the non-symmetric random walk approximates the heat semigroup generated by the usual Brownian motion on R². No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 57 1 2015 THE EQUIVARIANT SIMPLICIAL DE RHAM COMPLEX AND THE CLASSIFYING SPACE OF A SEMI-DIRECT PRODUCT GROUP 123 128 EN Naoya Suzuki 10.18926/mjou/53044 We show that the cohomology group of the total complex of the equivariant simplicial de Rham complex is isomorphic to the cohomology group of the classifying space of a semi-direct product group. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 57 1 2015 THE CANONICAL LINE BUNDLES OVER EQUIVARIANT REAL PROJECTIVE SPACES 111 122 EN Yan Qi 10.18926/mjou/53043 A generator of the reduced KO-group of the real projective space of dimension n is related to the canonical line bundle &gamma;. In the present paper, we will prove that for a finite group G of odd order and a real G-representation U of dimension 2n, in the reduced G-equivariant KO-group of the real projective space associated with the G-representation R ⊕ U, the element 2ⁿ⁺²[&gamma;] is equal to zero. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 57 1 2015 SUPPLEMENTED MORPHISMS 99 110 EN Arda Kör Truong Cong Quynh Serap Şahinkaya Muhammet Tamer Koşan 10.18926/mjou/53042 In the present paper, left R-modules M and N are studied under the assumptions that Hom_R(M,N) is supplemented. It is shown that Hom(M,N) is (⊕, G*, amply)-supplemented if and only if N is (⊕, G*, amply)-supplemented. Some applications to cosemisimple modules, refinable modules and UCC-modules are presented. Finally, the relationship between the Jacobson radical J[M,N] of Hom_R(M,N) and Hom_R(M,N) is supplemented are investigated. Let M be a finitely generated, self-projective left R-module and N ∈ Gen(M). We show that if Hom(M,N) is supplemented and N has GD2 then Hom(M,N)/J(M,N) is semisimple as a left E_M-module. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 57 1 2015 STEENROD-ČECH HOMOLOGY-COHOMOLOGY THEORIES ASSOCIATED WITH BIVARIANT FUNCTORS 85 98 EN Kohei Yoshida 10.18926/mjou/53041 Let NG₀ denote the category of all pointed numerically generated spaces and continuous maps preserving base-points. In [SYH], we described a passage from bivariant functors NG₀^op × NG₀ → NG₀ to generalized homology and cohomology theories. In this paper, we construct a bivariant functor such that the associated cohomology is the Čech cohomology and the homology is the Steenrod homology (at least for compact metric spaces). No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 57 1 2015 ON MODEL STRUCTURE FOR COREFLECTIVE SUBCATEGORIES OF A MODEL CATEGORY 79 84 EN Tadayuki Haraguchi 10.18926/mjou/53040 No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 57 1 2015 QUASI TERTIARY COMPOSITIONS AND A TODA BRACKET IN HOMOTOPY GROUPS OF SU(3) 13 78 EN Hideaki Ōshima Katsumi Ōshima 10.18926/mjou/53039 We revise the theories of tertiary compositions studied by &Ocirc;guchi and Mimura. As a byproduct, we determine a Toda bracket in homotopy groups of SU(3) which solves an ambiguity in a previous paper of Maruyama and the first author. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 57 1 2015 MODULAR DIFFERENTIAL EQUATIONS WITH REGULAR SINGULARITIES AT ELLIPTIC POINTS FOR THE HECKE CONGRUENCE SUBGROUPS OF LOW-LEVELS 1 12 EN Yuichi Sakai Kenichi Shimizu 10.18926/mjou/53038 In this paper, we give explicit expressions of modular differential equations with regular singularities at elliptic points for the Hecke subgroups of level 2, 3, and 4, and their solutions expressed in terms of the Gauss hypergeometric series. We also give quasimodular-form solutions for some modular differential equations. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 56 1 2014 ON THE SOLVABILITY OF CERTAIN (SSIE) WITH OPERATORS OF THE FORM B(r, s) 179 198 EN Bruno de Malafosse Eberhard Malkowsky 10.18926/mjou/52077 Given any sequence z = (z_n)_n≥1 of positive real numbers and any set E of complex sequences, we write Ez for the set of all sequences y = (y_n)_n≥1 such that y/z = (y_n/z_n)_n≥1 ∈ E; in particular, s_z^(c) denotes the set of all sequences y such that y/z converges. In this paper we deal with sequence spaces inclusion equations (SSIE), which are determined by an inclusion each term of which is a sum or a sum of products of sets of sequences of the form Xa(T) and Xx(T) where a is a given sequence, the sequence x is the unknown, T is a given triangle, and Xa(T) and Xx(T) are the matrix domains of T in the set X . Here we determine the set of all positive sequences x for which the (SSIE) s_x^(c) (B(r, s)) s_x^(c)⊂ (B(r', s')) holds, where r, r', s' and s are real numbers, and B(r, s) is the generalized operator of the first difference defined by (B(r, s)y)_n = ry_n+sy_n−1 for all n ≥ 2 and (B(r, s)y)₁ = ry₁. We also determine the set of all positive sequences x for which ry_n + sy_n−1 /x_n → l implies r'y_n + s'y_n−1 /x_n → l (n → ∞) for all y and for some scalar l. Finally, for a given sequence a, we consider the a–Tauberian problem which consists of determining the set of all x such that s_x^(c) (B(r, s)) ⊂ s_a^(c) . No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 56 1 2014 CONVEXITY PROPERTIES OF A NEW GENERAL INTEGRAL OPERATOR OF p-VALENT FUNCTIONS 171 178 EN Serap Bulut 10.18926/mjou/52076 In this paper, we introduce a new general integral operator and obtain the order of convexity of this integral operator. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 56 1 2014 STUDY OF A PARABOLIC PROBLEM IN A CONICAL DOMAIN 157 169 EN Boubaker-Khaled Sadallah 10.18926/mjou/52075 In this paper we consider the heat equation with Dirichlet boundary conditions in a conical domain. We look for a sufficient condition on the lateral surface of the cone in order to have the optimal regularity of the solution in an anisotropic Sobolev space when the right hand side of the equation is in a Lebesgue space. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 56 1 2014 THE BEST CONSTANT OF L^p SOBOLEV INEQUALITY CORRESPONDING TO DIRICHLET-NEUMANN BOUNDARY VALUE PROBLEM 145 155 EN Hiroyuki Yamagishi Kohtaro Watanabe Yoshinori Kametaka 10.18926/mjou/52074 We have obtained the best constant of the following L^p Sobolev inequality sup _0≤y≤1| u^(j)(y)| ≤C (∫ <doubleint>₀¹ </doubleint> | u^(M)(x)| ^p dx)^1/p , where u is a function satisfying u^(M) ∈ L^p(0, 1), u⁽²ⁱ⁾(0) = 0 (0 ≤i ≤ [(M − 1)/2]) and u⁽²ⁱ⁺¹⁾(1) = 0 (0 ≤ i ≤ [(M − 2)/2]), where u⁽ⁱ⁾ is the abbreviation of (d/dx)ⁱu(x). In [9], the best constant of the above inequality was obtained for the case of p = 2 and j = 0. This paper extends the result of [9] under the conditions p > 1 and 0 ≤ j ≤ M −1. The best constant is expressed by Bernoulli polynomials. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 56 1 2014 GROWTH OF SOLUTIONS OF HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS 129 143 EN Abdallah El Farissi Benharrat Belaïdi 10.18926/mjou/52073 This paper is devoted to studying the growth of solutions of the higher order nonhomogeneous linear differential equation f^(k) + A_k−1f^(k−1) + ... + A₂f " + (D₁ (z) + A₁ (z) e^P(z)) f ' + (D₀ (z) + A₀ (z)e ^Q(z)) f = F (k ≥ 2) , where P (z) , Q(z) are nonconstant polynomials such that deg P = degQ = n and Aj (z) (j = 0, 1, ..., k − 1) , F (z) are entire functions with max{p(Aj) (j = 0, 1, ..., k − 1) , p(Dj) (j = 0, 1)} < n. We also investigate the relationship between small functions and the solutions of the above equation. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 56 1 2014 WEIL ALGEBRAS ASSOCIATED TO FUNCTORS OF THIRD ORDER SEMIHOLONOMIC VELOCITIES 117 127 EN Miroslav Kureš 10.18926/mjou/52072 The structure of Weil algebras associated to functors of third order semiholonomic velocities is completely described including the explicit expression of widths. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 56 1 2014 EQUIVARIANT STABLE HOMOTOPY THEORY FOR PROPER ACTIONS OF DISCRETE GROUPS 91 115 EN Noé Bárcenas 10.18926/mjou/52071 Following ideas of Graeme Segal [Segal(1973)], [Segal(1968)], Christian Schlichtkrull [Schlichtkrull(2007)] and Kazuhisa Shimakawa [Shimakawa(1989)] we construct equivariant stable homotopy groups for proper equivariant CW complexes with an action of a discrete group. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 56 1 2014 A MODEL FOR THE WHITEHEAD PRODUCT IN RATIONAL MAPPING SPACES 75 89 EN Takahito Naito 10.18926/mjou/52070 We describe the Whitehead products in the rational homo- topy group of a connected component of a mapping space in terms of the André-Quillen cohomology. As a consequence, an upper bound for the Whitehead length of a mapping space is given. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 56 1 2014 PRIME, MAXIMAL AND PRIMITIVE IDEALS IN SOME SUBRINGS OF POLYNOMIAL RINGS 65 74 EN Miguel Ferrero Edilson Soares Miranda 10.18926/mjou/52069 In this paper we describe prime, maximal and primitive ideals in some graded subrings of polynomial rings. As applications the corresponding radicals are determined. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 56 1 2014 SUMS OF TWO BIQUADRATES AND ELLIPTIC CURVES OF RANK ≥ 4 51 63 EN F.A. Izadi F. Khoshnam K. Nabardi 10.18926/mjou/52068 If an integer n is written as a sum of two biquadrates in two different ways, then the elliptic curve y² = x³ − nx has positive rank. We utilize Euler’s parametrization to introduce some homoge- neous equations to prove that En has rank ≥ 3. If moreover n is odd and the parity conjecture is true, then the curve has even rank ≥ 4. Finally, some examples of ranks equal to 4, 5, 6, 7, 8 and 10, are also obtained. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 56 1 2014 ON POSITIVE INTEGERS OF MINIMAL TYPE CONCERNED WITH THE CONTINUED FRACTION EXPANSION 35 50 EN Yasuhiro Kishi Sayaka Tajiri Ken-ichiro Yoshizuka 10.18926/mjou/52067 No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 56 1 2014 INTERSECTIVE POLYNOMIALS WITH GALOIS GROUP D₅ 27 33 EN Melisa J. Lavallee Blair K. Spearman Qiduan Yang 10.18926/mjou/52066 We give an infinite family of intersective polynomials with Galois group D₅, the dihedral group of order 10. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 56 1 2014 A CHARACTERIZATION OF THE GLAUBERMAN-WATANABE CORRESPONDING BLOCKS AS BIMODULES 17 26 EN Fuminori Tasaka 10.18926/mjou/52065 We give a characterization of the Glauberman-Watanabe corresponding blocks viewed as bimodules as a direct summand of a restricted or an induced module from the block in terms of a vertex and a multiplicity. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 56 1 2014 MUTATING BRAUER TREES 1 16 EN Takuma Aihara 10.18926/mjou/52064 In this paper we introduce mutation of Brauer trees. We show that our mutation of Brauer trees explicitly describes the tilting mutation of Brauer tree algebras introduced by Okuyama and Rickard. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 55 1 2013 ON HYPERBOLIC AREA OF THE MODULI OF θ－ACUTE TRIANGLES 191 200 EN Naomi Kanesaka Hiroaki Nakamura 10.18926/mjou/49105 A θ-acute triangle is a Euclidean triangle on the plane whose three angles are less than a given constant θ. In this note, we shall give an explicit formula computing the hyperbolic area A(θ) of the moduli region of θ-acute triangles on the Poincar´e disk. It turns out that A(θ) is a period in the sense of Kontsevich-Zagier if cot θ is a nonnegative algebraic number. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 55 1 2013 AN ALGEBRAIC APPROACH TO THE CAMERON-MARTIN-MARUYAMA-GIRSANOV FORMULA 167 190 EN Jirô Akahori Takafumi Amaba Sachiyo Uraguchi 10.18926/mjou/49104 In this paper, we will give a new perspective to the Cameron- Martin-Maruyama-Girsanov formula by giving a totally algebraic proof to it. It is based on the exponentiation of the Malliavin-type differenti- ation and its adjointness. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 55 1 2013 UNIFORM STABILITY AND BOUNDEDNESS OF SOLUTIONS OF NONLINEAR DELAY DIFFERENTIAL EQUATIONS OF THE THIRD ORDER 157 166 EN Ademora Adeleke Timothy Arawamo Peter Olutola 10.18926/mjou/49103 In this paper, a complete Lyapunov functional was con- structed and used to obtain criteria (when p = 0) for uniform asymptotic stability of the zero solution of the nonlinear delay differential equation (1.1). When p ≠ 0, sufficient conditions are also established for uni- form boundedness and uniform ultimate boundedness of solutions of this equation. Our results improve and extend some well known results in the literature. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 55 1 2013 MULTIPLICITY-FREE PERMUTATION CHARACTERS OF COVERING GROUPS OF SPORADIC SIMPLE GROUPS 145 155 EN S. A. Linton Z. E. Mpono 10.18926/mjou/49102 In this paper we classify all multiplicity-free faithful per- mutation representations of the covering groups of the sporadic simple groups. These results were obtained computationally, making extensive use of the GAP library of character tables. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 55 1 2013 PURITY AND GORENSTEIN FILTERED RINGS 131 143 EN Hiroki Miyahara 10.18926/mjou/49101 In this paper, we discuss on the existence of filtrations of modules having good properties. In particular, we focus on filtered homomorphisms called strict, and show that there exists a filtration which makes a filtered homomorphism a strict filtered homomorphism. Moreover, by using this result, we study purity for filtered modules over a Gorenstein filtered ring. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 55 1 2013 ON MONO-INJECTIVE MODULES AND MONO-OJECTIVE MODULES 117 129 EN Derya Keskin Tütüncü Yosuke Kuratomi 10.18926/mjou/49099 In [5] and [6], we have introduced a couple of relative generalized epi-projectivities and given several properties of these projectivities. In this paper, we consider relative generalized injectivities that are dual to these relative projectivities and apply them to the study of direct sums of extending modules. Firstly we prove that for an extending module N, a module M is N-injective if and only if M is mono-Ninjective and essentially N-injective. Then we define a mono-ojectivity that plays an important role in the study of direct sums of extending modules. The structure of (mono-)ojectivity is complicated and hence it is difficult to determine whether these injectivities are inherited by finite direct sums and direct summands even in the case where each module is quasi-continuous. Finally we give several characterizations of these injectivities and find necessary and sufficient conditions for the direct sums of extending modules to be extending. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 55 1 2013 A MODEL STRUCTURE ON THE CATEGORY OF SMALL CATEGORIES FOR COVERINGS 95 116 EN Kohei Tanaka 10.18926/mjou/49098 We consider a model structure on the category of small categories, which is intimately related to the notion of coverings and fundamental groups of small categories. Fibrant objects coincide with groupoids, and the fibrant replacement is the groupoidification. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 55 1 2013 NOTE ON THE COHOMOLOGICAL INVARIANT OF PFISTER FORMS 87 93 EN Michishige Tezuka Nobuaki Yagita 10.18926/mjou/49097 The cohomological invariant ring of the n-Pfister forms is isomorphic to the invariant ring under a GLn(Z/2)-action in that of an elementary abelian 2-group of rank n. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 55 1 2013 THE BLOCK APPROXIMATION THEOREM 53 85 EN Dan Haran Moshe Jarden Florian Pop 10.18926/mjou/49096 The block approximation theorem is an extensive general- ization of both the well known weak approximation theorem from valu- ation theory and the density property of global fields in their henseliza- tions. It guarantees the existence of rational points of smooth affine varieties that solve approximation problems of local-global type (see e.g. [HJP07]). The theorem holds for pseudo real closed fields, by [FHV94]. In this paper we prove the block approximation for pseudo-F- closed fields K, where F is an ´etale compact family of valuations of K with bounded residue fields (Theorem 4.1). This includes in particular the case of pseudo p-adically closed fields and generalizations of these like the ones considered in [HJP05]. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 55 1 2013 EXPLICIT ASSOCIATOR RELATIONS FOR MULTIPLE ZETA VALUES 1 52 EN Ismaël Soudères 10.18926/mjou/49095 Associators were introduced by Drinfel’d in [Dri91] as a monodromy representation of a Knizhnik-Zamolodchikov equation. Associators can be briefly described as formal series in two non-commutative variables satisfying three equations. These three equations yield a large number of algebraic relations between the coefficients of the series, a situation which is particularly interesting in the case of the original Drinfel’d associator, whose coefficients are multiple zetas values. In the first part of this paper, we work out these algebraic relations among multiple zeta values by direct use of the defining relations of associators. While well-known for the first two relations, the algebraic relations we obtain for the third (pentagonal) relation, which are algorithmically explicit although we do not have a closed formula, do not seem to have been previously written down. The second part of the paper shows that if one has an explicit basis for the bar-construction of the moduli space M0,5 of genus zero Riemann surfaces with 5 marked points at one’s disposal, then the task of writing down the algebraic relations corresponding to the pentagon relation becomes significantly easier and more economical compared to the direct calculation above. We discuss the explicit basis described by Brown and Gangl, which is dual to the basis of the enveloping algebra of the braids Lie algebra UB5. In order to write down the relation between multiple zeta values, we then remark that it is enough to write down the relations associated to elements that generate the bar construction as an algebra. This corresponds to looking at the bar construction modulo shuffle, which is dual to the Lie algebra of 5-strand braids. We write down, in the appendix, the associated algebraic relations between multiple zeta values in weights 2 and 3. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 41 1 1999 Universal Factorization Equalities for Quaternion Matrices and Their Applications 45 62 EN Yongge Tian 10.18926/mjou/48176 No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 41 1 1999 Semi-Convergence of Filters and Nets 103 109 EN R. M. Latif 10.18926/mjou/48175 No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 41 1 1999 Irreducibilities of the Induced Characters of Cyclic p-Groups 27 36 EN Katsusuke Sekiguchi 10.18926/mjou/48174 No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 41 1 1999 A Generalization of the Dade's Theorem on Localization of Injective Modules 75 79 EN Kazuhiko Hirata U Syu 10.18926/mjou/48173 No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 54 1 2012 ON MEANS OF BANACH-SPACE-VALUED FUNCTIONS 145 211 EN Ryotaro Sato 10.18926/mjou/47199 We continue to study relations among exponential and polynomial growth orders of the γ-th order Cesàro means (γ≥0) and of the Abel mean for a Banach-space-valued function u on the interval [0,∞). We have already studied the problem for a continuous function u. Now we assume that u is a locally integrable function in a Banach space or an improperly locally integrable positive function in a Banach lattice. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 54 1 2012 CONTROLLABILITY OF FRACTIONAL INTEGRODIFFERENTIAL SYSTEMS VIA SEMIGROUP THEORY IN BANACH SPACES 133 143 EN Mohammed Hazi Mabrouk Bragdi 10.18926/mjou/47198 This paper focuses on controllability results of fractional integrodifferential systems in Banach spaces. We obtain sufficient conditions for the controllability results by using fractional calculus, semi-group theory and the fixed point theorem. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 54 1 2012 HOMOGENIZATION OF NON-LINEAR VARIATIONAL PROBLEMS WITH THIN INCLUSIONS 97 131 EN Abdelaziz Aït Moussa Loubna Zlaïji 10.18926/mjou/47197 We are concerned in this work with the asymptotic behavior of an assemblage whose components are a thin inclusion with higher rigidity modulus included into an elastic body. We aim at finding the approximating energy functional of the above structure in a Γ-convergence framework, and making use also of the subadditive theorem and the blow-up method. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 54 1 2012 THE TANGENT BUNDLES OVER EQUIVARIANT REAL PROJECTIVE SPACES 87 96 EN Yan Qi 10.18926/mjou/47196 let G be a nontrivial cyclic group of odd order. In the present paper, we will prove that the fourfold Whitney sum of the tangent bundle of real projective plane of any three dimensional nontrivial real G-representation is equivariantly a product bundle. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 54 1 2012 NOTE ON THE HOMOTOPY OF THE SPACE OF MAPS BETWEEN REAL PROJECTIVE SPACES 77 86 EN Kohhei Yamaguchi 10.18926/mjou/47195 We study the homotopy types of the space consisting of all base-point preseving continuous maps from the m dimensional real projective space into the n dimensional real projective space. When 2 ≤ m < n, it has two path connected components and we investigate whether these two path-components have the same homotopy type or not. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 54 1 2012 ON A GENERALIZATION OF CQF-3′ MODULES AND COHEREDITARY TORSION THEORIES 65 76 EN Yasuhiko Takehana 10.18926/mjou/47194 Throughout this paper we assume that R is a right perfect ring with identity and let Mod-R be the category of right R-modules. Let M be a right R-module. We denote by 0 → K(M) → P(M) → M → 0 the projective cover of M. M is called a CQF-3′ module, if P(M) is M-generated, that is, P(M) is isomorphic to a homomorphic image of a direct sum ⊕M of some copies of M. A subfunctor of the identity functor of Mod-R is called a preradical. For a preradical σ, T_σ := {M ∈ Mod-R : σ(M) = M} is called the class of σ-torsion right R-modules, and F_σ := {M ∈ Mod-R : σ(M) = 0} is called the class of σ-torsionfree right R-modules. A right R-module M is called σ-projective if the functor Hom_R(M,−) preserves the exactness for any exact sequence 0 → A → B → C → 0 with A ∈ F_σ. We put P_σ(M) = P(M)/σ(K(M)) for a module M. We call a right R-module M a σ-CQF-3′ module if P_σ(M) is M-generated. In this paper, we characterize σ-CQF-3′ modules and give some related facts. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 54 1 2012 ON A GENERALIZATION OF QF-3′ MODULES AND HEREDITARY TORSION THEORIES 53 63 EN Yasuhiko Takehana 10.18926/mjou/47193 Let R be a ring with identity, and let Mod-R be the category of right R-modules. Let M be a right R-module. We denote by E(M) the injective hull of M. M is called QF-3′ module, if E(M) is M-torsionless, that is, E(M) is isomorphic to a submodule of a direct product ΠM of some copies of M. A subfunctor of the identity functor of Mod-R is called a preradical. For a preradical σ, T_σ := {M ∈ Mod-R : σ(M) = M} is the class of σ-torsion right R-modules, and F_σ := {M ∈ Mod-R : σ(M) = 0} is the class of σ-torsionfree right R-modules. A right R-module M is called σ-injective if the functor Hom_R(−,M) preserves the exactness for any exact sequence 0 → A → B → C → 0 with C ∈ T_σ. A right R-module M is called σ-QF-3′ module if E_σ(M) is M-torsionless, where E_σ(M) is defined by E_σ(M)/M := σ(E(M)/M). In this paper, we characterize σ-QF-3′ modules and give some related facts. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 54 1 2012 ON THE STRUCTURE OF THE MORDELL-WEIL GROUPS OF THE JACOBIANS OF CURVES DEFINED BY yn = f(x) 49 52 EN Hyunsuk Moon 10.18926/mjou/47192 Let A be an abelian variety defined over a number field K. It is proved that for the composite field K_n of all Galois extensions over K of degree dividing n, the torsion subgroup of the Mordell-Weil group A(K_n) is finite. This is a variant of Ribet’s result ([7]) on the finiteness of torsion subgroup of A(K(ζ_∞)). It is also proved that for the Jacobians of superelliptic curves yⁿ = f(x) defined over K the Mordell-Weil group over the field generated by all nth roots of elements of K is the direct sum of a finite torsion group and a free ℤ-module of infinite rank. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 54 1 2012 HILBERT-SPEISER NUMBER FIELDS AND STICKELBERGER IDEALS; THE CASE p = 2 33 48 EN Humio Ichimura 10.18926/mjou/47191 We say that a number field F satisfies the condition (H′_2^m) when any abelian extension of exponent dividing 2^m has a normal basis with respect to rings of 2-integers. We say that it satisfies (H′ _2^∞) when it satisfies (H′ _2^m) for all m. We give a condition for F to satisfy (H'_2^m), and show that the imaginary quadratic fields F = Q(√−1) and Q(√−2) satisfy the very strong condition (H′ _2^∞) if the conjecture that h⁺_2^m = 1 for all m is valid. Here, h⁺_2^m) is the class number of the maximal real abelian field of conductor 2^m. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 54 1 2012 SOME REMARKS ON LUCAS PSEUDOPRIMES 1 32 EN Noriyuki Suwa 10.18926/mjou/47190 We present a way of viewing Lucas pseudoprimes, Euler-Lucas pseudoprimes and strong Lucas pseudoprimes in the context of group schemes. This enables us to treat the Lucas pseudoprimalities in parallel to establish pseudoprimes, Euler pseudoprimes and strong pseudoprimes. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 53 1 2011 TRIANGLE CENTERS DEFINED BY QUADRATIC POLYNOMIALS 185 216 EN Yoshio Agaoka 10.18926/mjou/41406 We consider a family of triangle centers whose barycentric coordinates are given by quadratic polynomials, and determine the lines that contain an infinite number of such triangle centers. We show that for a given quadratic triangle center, there exist in general four principal lines through this center. These four principal lines possess an intimate connection with the Nagel line. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 53 1 2011 THE UNIFORM EXPONENTIAL STABILITY OF LINEAR SKEW-PRODUCT SEMIFLOWS ON REAL HILBERT SPACE 173 183 EN Pham Viet Hai Le Ngoc Thanh 10.18926/mjou/41405 The goal of the paper is to present some characterizations for the uniform exponential stability of linear skew-product semiflows on real Hilbert space. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 53 1 2011 A CAUCHY-KOWALEVSKI THEOREM FOR INFRAMONOGENIC FUNCTIONS 167 172 EN Helmuth R. Malonek Dixan Peña Peña Frank Sommen 10.18926/mjou/41404 In this paper we prove a Cauchy-Kowalevski theorem for the functions satisfying the system ∂_xf∂_x = 0 (called inframonogenic functions). No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 53 1 2011 AN EXPLICIT PSp₄(3)-POLYNOMIAL WITH 3 PARAMETERS OF DEGREE 40 155 165 EN Hidetaka Kitayama 10.18926/mjou/41403 We will give an explicit polynomial over ℚ with 3 parameters of degree 40 as a result of the inverse Galois problem. Its Galois group over ℚ (resp. ℚ(√-3)) is isomorphic to PGSp₄(3) (resp. PSp₄(3)) and it is a regular PSp₄(3)-polynomial over ℚ(p√−3). To construct the polynomial and prove its properties above we use some results of Siegel modular forms and permutation group theory. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 53 1 2011 ABSTRACT LOCAL COHOMOLOGY FUNCTORS 129 154 EN Yuji Yoshino Takeshi Yoshizawa 10.18926/mjou/41402 We propose to define the notion of abstract local cohomology functors. The ordinary local cohomology functor RΓ_I with support in the closed subset defined by an ideal I and the generalized local cohomology functor RΓ_I,J defined in [16] are characterized as elements of the set of all the abstract local cohomology functors. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 53 1 2011 NOTE ON SYMMETRIC HILBERT SERIES 111 127 EN Yuji Kamoi 10.18926/mjou/41401 No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 53 1 2011 ON ALMOST N-SIMPLE-PROJECTIVES 101 109 EN Yoshitomo Baba Takeshi Yamazaki 10.18926/mjou/41400 The concept of almost N-projectivity is defined in [5] by M. Harada and A. Tozaki to translate the concept "lifting module" in terms of homomorphisms. In [6, Theorem 1] M. Harada defined a little weaker condition "almost N-simple-projecive" and gave the following relationship between them: For a semiperfect ring R and R-modules M and N of finite length, M is almost N-projective if and only if M is almost N-simple-projective. We remove the assumption "of finite length" and give the result in Theorem 5 as follows: For a semiperfect ring R, a finitely generated right R-module M and an indecomposable right R-module N of finite Loewy length, M is almost N-projective if and only if M is almost N-simple-projective. We also see that, for a semiperfect ring R, a finitely generated R-module M and an R-module N of finite Loewy length, M is N-simple-projective if and only if M is N-projective. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 53 1 2011 FP-GR-INJECTIVE MODULES 83 100 EN Xiaoyan Yang Zhongkui Liu 10.18926/mjou/41399 In this paper, we give some characterizations of FP-grinjective R-modules and graded right R-modules of FP-gr-injective dimension at most n. We study the existence of FP-gr-injective envelopes and FP-gr-injective covers. We also prove that (1) (^⊥gr-FI, gr-FI) is a hereditary cotorsion theory if and only if R is a left gr-coherent ring, (2) If R is right gr-coherent with FP-gr-id(R_R) ≤ n, then (gr-FI_n, gr-F _n^⊥) is a perfect cotorsion theory, (3) (^⊥gr-FI_n, gr-FI_n) is a cotorsion theory, where gr-FI denotes the class of all FP-gr-injective left R-modules, gr-FI_n is the class of all graded right R-modules of FP-gr-injective dimension at most n. Some applications are given. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 53 1 2011 TORSION OF ELLIPTIC CURVES OVER QUADRATIC CYCLOTOMIC FIELDS 75 82 EN Filip Najman 10.18926/mjou/41398 In this paper we study the possible torsions of elliptic curves over ℚ(i) and ℚ(√−3). No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 53 1 2011 PROJECTIVE STRUCTURES AND AUTOMORPHIC PSEUDODIFFERENTIAL OPERATORS 55 74 EN Min Ho Lee 10.18926/mjou/41397 Automorphic pseudodifferential operators are pseudodifferential operators that are invariant under an action of a discrete subgroup Γ of SL(2,ℝ), and they are closely linked to modular forms. In particular, there is a lifting map from modular forms to automorphic pseudodifferential operators, which can be interpreted as a lifting morphism of sheaves over the Riemann surface X associated to the given discrete subgroup Γ. One of the questions raised in a paper by Cohen, Manin, and Zagier is whether the difference in the images of a local section of a sheaf under such lifting morphisms corresponding to two projective structures on X can be expressed in terms of certain Schwarzian derivatives. The purpose of this paper is to provide a positive answer to this question for some special cases. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 53 1 2011 LIFTED CODES OVER FINITE CHAIN RINGS 39 53 EN Steven T. Dougherty Hongwei Liu Young Ho Park 10.18926/mjou/41396 In this paper, we study lifted codes over finite chain rings. We use γ-adic codes over a formal power series ring to study codes over finite chain rings. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 53 1 2011 ASYMPTOTIC ANALYSIS FOR GREEN FUNCTIONS OF AHARONOV-BOHM HAMILTONIAN WITH APPLICATION TO RESONANCE WIDTHS IN MAGNETIC SCATTERING 1 37 EN Hideo Tamura 10.18926/mjou/41395 The Aharonov–Bohm Hamiltonian is the energy operator which governs quantum particles moving in a solenoidal field in two dimensions. We analyze asymptotic properties of its Green function with spectral parameters in the unphysical sheet. As an application, we discuss the lower bound on resonance widths for scattering by two magnetic fields with compact supports at large separation. The bound is evaluated in terms of backward scattering amplitudes by a single magnetic field. A special emphasis is placed on analyzing how a trajectory oscillating between two magnetic fields gives rise to resonances near the real axis, as the distance between two supports goes to infinity. We also refer to the relation to the semiclassical resonance theory for scattering by two solenoidal fields. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 24 1 1982 An application of certain multiplicities of C∞ map germs 25 35 EN Yoshifumi Ando 10.18926/mjou/33994 No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 24 1 1982 Subgroup SU(8)/Z2 of compact simple Lie group E7 and non-compact simple Lie group E{7(7)} of type E7 53 71 EN Ichiro Yokota 10.18926/mjou/33993 No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 24 1 1982 Note on groups with isomorphic group algebras 1 6 EN Tôru Furukawa 10.18926/mjou/33992 No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 24 1 1982 On a theorem of M. S. Putcha and A. Yaqub 21 23 EN Hiroaki Komatsu 10.18926/mjou/33991 No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 24 1 1982 Some remarks on bisimple rings 15 19 EN Yasuyuki Hirano Hisao Tominaga 10.18926/mjou/33990 No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 24 1 1982 Surgery obstruction of twisted products 73 97 EN Tomoyoshi Yoshida 10.18926/mjou/33989 No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 24 1 1982 Some polynomial identities and commutativity of s-unital rings 7 13 EN Yasuyuki Hirano Yuji Kobayashi Hisao Tominaga 10.18926/mjou/33988 No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 24 1 1982 On J-groups of S^l(RP(t-l)/RP(n-l)) 45 51 EN Susumu Kôno Akie Tamamura 10.18926/mjou/33987 No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 24 1 1982 On the iterated Samelson product 37 44 EN Hideyuki Kachi 10.18926/mjou/33986 No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 24 2 1982 A certain type of commutative Hopf Galois extensions and their groups 137 152 EN Atsushi Nakajima 10.18926/mjou/33985 No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 24 2 1982 Notes on stable equivariant maps 167 178 EN Syuichi Izumiya 10.18926/mjou/33984 No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 24 2 1982 On right p.p. rings 99 109 EN Yasuyuki Hirano Motoshi Hongan Masayuki Ôhori 10.18926/mjou/33983 No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 24 2 1982 On the equational definability of addition in rings 133 136 EN Hiroaki Komatsu 10.18926/mjou/33982 No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 24 2 1982 On strongly prime modules and related topics 117 132 EN Motoshi Hongan 10.18926/mjou/33981 No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 24 2 1982 The S^1-transfer map and homotopy groups of suspended complex projective spaces 179 200 EN Juno Mukai 10.18926/mjou/33980 No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 24 2 1982 Some polynomial identities and commutativity of s-unital rings. II 111 115 EN Yasuyuki Hirano Hisao Tominaga Adil Yaqub 10.18926/mjou/33979 No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 24 2 1982 A construction of spaces with general connections which have points swallowing geodesics 157 165 EN Tominosuke Otsuki 10.18926/mjou/33978 No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 24 2 1982 On an individual ergodic theorem 153 156 EN Ryotaro Sato 10.18926/mjou/33977 No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 20 1 1978 Notes on a conjecture of P. Erdös. II 41 49 EN Masataka Yorinaga Saburô Uchiyama 10.18926/mjou/33976 No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 20 1 1978 Two commutativity theorems for rings 67 72 EN Yasuyuki Hirano Hisao Tominaga 10.18926/mjou/33975 No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 20 1 1978 Restricted semiprimary group rings 77 82 EN J. B. Srivastava Vishnu Gupta 10.18926/mjou/33974 No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 20 1 1978 On the fixed point set of S^1-actions on the complex flag manifolds 1 16 EN Kenji Hokama Susumu Kôno 10.18926/mjou/33973 No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 20 1 1978 Simply connected smooth 4-manifolds which admit nontrivial smooth S^1 actions 25 40 EN Tomoyoshi Yoshida 10.18926/mjou/33972 No potential conflict of interest relevant to this article was reported.