Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666612024Note on smoothness condition on tropical elliptic curves of symmetric truncated cubic forms171187ENRani SasmitaTarmidiDepartment of Mathematics, Graduate School of Science, Osaka UniversityIn 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 UniversityActa Medica Okayama0030-15666612024Duality-reflection formulas of multiple polylogarithms and their ℓ-adic Galois analogues159169ENDensukeShiraishiDepartment of Mathematics, Graduate School of Science, Osaka UniversityIn 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 UniversityActa Medica Okayama0030-15666612024Several homotopy fixed point spectral sequences in telescopically localized algebraic K-theory135157ENDaniel G.DavisDepartment of Mathematics, University of Louisiana at LafayetteLet 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 UniversityActa Medica Okayama0030-15666612024A subclass of strongly close-to-convex functions associated with Janowski function125133ENGagandeepSinghDepartment of Mathematics, Khalsa CollegeGurcharanjitSinghDepartment of Mathematics, G.N.D.U. CollegeThe 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 UniversityActa Medica Okayama0030-15666612024A combinatorial integration on the Cantor dust115124ENTakashiMaruyamaDepartment of Engineering, Stanford UniversityTatsukiSetoGeneral Education and Research Center, Meiji Pharmaceutical UniversityIn 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 UniversityActa Medica Okayama0030-15666612024On G(A)Q of rings of finite representation type103113ENTony J.PuthenpurakalDepartment of Mathematics, IIT BombayLet (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 UniversityActa Medica Okayama0030-15666612024Positive solutions to a nonlinear three-point boundary value problem with singularity85102ENMoses B.AkoredeDepartment of Mathematics, Faculty of Science, University of IbadanPeter O.ArawomoDepartment of Mathematics, Faculty of Science, University of IbadanIn 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 UniversityActa Medica Okayama0030-15666612024Harmonic partitions of positive integers and bosonic extension of Euler’s pentagonal number theorem7183ENMasaoJinzenjiDepartment of Mathematics, Okayama UniversityYuTajimaDivision of Mathematics, Graduate School of Science, Hokkaido UniversityIn 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 UniversityActa Medica Okayama0030-15666612024Construction of families of dihedral quintic polynomials6369ENYasuhiroKishiDepartment of Mathematics, Faculty of Education, Aichi University of EducationMeiYamadaDepartment of Mathematics, Faculty of Education, Aichi University of EducationIn 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 UniversityActa Medica Okayama0030-15666612024Dirac pairs on Jacobi algebroids4561ENTomoyaNakamuraAcademic Support Center, Kogakuin UniversityWe 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 UniversityActa Medica Okayama0030-15666612024Game positions of multiple hook removing game3144ENYukiMotegiGraduate School of Pure and Applied Sciences, University of TsukubaMultiple 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 UniversityActa Medica Okayama0030-15666612024Equivalence classes of dessins d’enfants with two vertices130ENMadokaHorieGraduate School of Science, Tohoku UniversityLet 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.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665912017Blowup and global existence of a solution to a semilinear reaction-diffusion system with the fractional Laplacian175218ENTomoyukiKakehiDepartment of Mathematics, Okayama UniversityYoshihitoOshitaDepartment of Mathematics, Okayama University10.18926/mjou/54723In 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> > 1 and 0 < <i>α</i> < 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 UniversityActa Medica Okayama0030-15665912017Scattering and semi-classical asymptotics for periodic Schrödinger operators with oscillating decaying potential149174ENMouezDimassiUniversit´e Bordeaux I, Institut de Math´ematiques de BordeauxAnh Tuan DuongDepartment of Mathematics, Hanoi National University of Education10.18926/mjou/54721In the semi-classical regime (i.e., <i>h</i> ↘ 0), we study the effect of an oscillating decaying potential <i>V</i> (<i>hy, y</i>) on the periodic Schrödinger 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>| → ∞. We prove the existence of <i>O</i>(<i>h<sup>−n</sup></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<sup>1/2</sup></i>. All our results depend on the Floquet eigenvalues corresponding to the periodic Schrödinger 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 UniversityActa Medica Okayama0030-15665912017On the (1 − C<sub>2</sub>) condition141147ENLe Van AnDepartment of Natural Education, Ha Tinh UniversityNguyen Thi Hai AnhDepartment of Natural Education, Ha Tinh UniversityNgo Sy TungDepartment of Mathematics, Vinh University10.18926/mjou/54720In this paper, we give some results on (1 − C<sub>2</sub>)−modules and 1−continuous modules.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665912017Higher-dimensional absolute versions of symmetric, Frobenius, and quasi-Frobenius algebras131140ENMitsuyasuHashimotoDepartment of Mathematics Faculty of Science, Okayama University10.18926/mjou/54719In 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 UniversityActa Medica Okayama0030-15665912017A note on balance equations for doubly periodic minimal surfaces117130ENPeterConnorDepartment of Mathematical Sciences, Indiana University South Bend10.18926/mjou/54718Most known examples of doubly periodic minimal surfaces in R<sup>3</sup> with parallel ends limit as a foliation of R<sup>3</sup> 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 UniversityActa Medica Okayama0030-15665912017A remark on the Lavallee-Spearman-Williams-Yang family of quadratic fields113116ENKwang-SeobKimSchool of Mathematics, Korea Institute for Advanced StudyYasuhiroKishiDepartment of Mathematics, Aichi University of Education10.18926/mjou/54717In [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 UniversityActa Medica Okayama0030-15665912017Gauss maps of cuspidal edges in hyperbolic 3-space, with application to flat fronts93111ENYutaOgataDepartment of Mathematics, Graduate School of Science, Kobe UniversityKeisukeTeramotoDepartment of Mathematics, Graduate School of Science, Kobe University10.18926/mjou/54716We 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 UniversityActa Medica Okayama0030-15665912017An arithmetic function arising from the Dedekind ψ function8192ENColinDefantDepartment of Mathematics, University of Florida10.18926/mjou/54715We define ψ‾ 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 α. Let <i>λ(n)</i> be the number of iterations of the function <i>ψ‾</i> needed for <i>n</i> to reach 2. It follows from a theorem due to White that <i>λ</i> is additive. Following Shapiro's work on the iterated <i>φ</i> function, we determine bounds for <i>λ</i>. We also use the function <i>λ</i> to partition the set of positive integers into three sets <i>S<sub>1</sub>, S<sub>2</sub>, S<sub>3</sub></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 UniversityActa Medica Okayama0030-15665912017Evaluation of convolution sums and some remarks on cusp forms of weight 4 and level 127179ENB.RamakrishhanHarish-Chandra Research InstituteBrundabanSahuSchool of Mathematical Sciences National Institute of Science Education and Research10.18926/mjou/54714In this note, we evaluate certain convolution sums and make some remarks about the Fourier coefficients of cusp forms of weight 4 for Γ<sub>0</sub>(12). We express the normalized newform of weight 4 on Γ<sub>0</sub>(12) as a linear combination of the (quasimodular) Eisenstein series (of weight 2) <i>E<sub>2</sub>(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<sub>1,12</sub>(n)</i> and <i>c<sub>3,4</sub>(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 Γ<sub>0</sub>(6) and Γ<sub>0</sub>(12). The properties of <i>c<sub>1,12</sub>(n)</i> and <i>c<sub>3,4</sub>(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 UniversityActa Medica Okayama0030-15665912017On a non-abelian generalization of the Bloch–Kato exponential map4170ENKenjiSakugawaDepartment of Mathematics Graduate School of Science, Osaka University10.18926/mjou/54713The 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 UniversityActa Medica Okayama0030-15665912017The degree of set-valued mappings from ANR spaces to homology spheres2740ENYoshimiShitandaSchool of political science and economics, Meiji University10.18926/mjou/54712An 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 UniversityActa Medica Okayama0030-15665912017Some examples of non-tidy spaces2125ENTakahiroMatsushitaGraduate School of Mathematical Sciences, The University of Tokyo10.18926/mjou/54711We construct a free Z<sub>2</sub>-space <i>X<sub>n</sub></i> for a positive integer <i>n</i> such that <i>w<sub>1</sub>(X<sub>n</sub>)<sup>n</sup></i> ≠ 0 but there is no Z<sub>2</sub>-map from <i>S</i><sup>2</sup> to <i>X<sub>n</sub></i>.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665912017Categorical characterization of strict morphisms of fs log schemes119ENYuichiroHoshiResearch Institute for Mathematical Sciences, Kyoto UniversityChikaraNakayamaDepartment of Economics, Hitotsubashi University10.18926/mjou/54710In 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 UniversityActa Medica Okayama0030-15665812016The positivity of the transmutation operators associated to the Cherednik operators for the root system $BC_2$183198ENKhalifaTRIMÈCHE10.18926/mjou/53925We consider the transmutation operators V<sub>k</sub>, <sup>t</sup>V<sub>k</sub> and V <sup>W</sup> <sub>k</sub> , <sup>t</sup>V <sup>W</sup> <sub>k</sub> 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<sub>k</sub>, <sup>t</sup>V<sub>k</sub> and V<sup>W</sup><sub>k</sub> , <sup>t</sup>V<sup>W</sup><sub>k</sub> 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 UniversityActa Medica Okayama0030-15665812016On weakly separable polynomials and weakly quasi-separable polynomials over rings169182ENSatoshiYamanaka10.18926/mjou/53924Separable 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 UniversityActa Medica Okayama0030-15665812016Restriction on Galois groups by prime inert condition159167ENToruKomatsu10.18926/mjou/53923In 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 UniversityActa Medica Okayama0030-15665812016Alternative approach for Siegel's lemma141158ENMakotoNagata10.18926/mjou/53922In 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 UniversityActa Medica Okayama0030-15665812016On finite rings over which every free codes is splitting133140ENYasuyukiHirano10.18926/mjou/53921In 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 UniversityActa Medica Okayama0030-15665812016On a duality of Gras between totally positive and primary cyclotomic units125132ENHumioIchimura10.18926/mjou/53920Let 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 UniversityActa Medica Okayama0030-15665812016Another description of quasi tertiary composition109123ENHideakiŌshimaKatsumiŌshima10.18926/mjou/53919We 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 UniversityActa Medica Okayama0030-15665812016Aharonov--Bohm effect in resonances of magnetic Schrödinger operators in two dimensions III79108ENHideoTamura10.18926/mjou/53918We 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 UniversityActa Medica Okayama0030-15665812016Aharonov--Bohm effect in resonances of magnetic Schrödinger operators in two dimensions II4178ENHideoTamura10.18926/mjou/53917We 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 UniversityActa Medica Okayama0030-15665812016Asymptotic properties in forward directions of resolvent kernels of magnetic Schrödinger operators in two dimensions139ENHideoTamura10.18926/mjou/53916We 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 UniversityActa Medica Okayama0030-15665712015ZERO MEAN CURVATURE SURFACES IN LORENTZ-MINKOWSKI 3-SPACE AND 2-DIMENSIONAL FLUID MECHANICS173200ENShoichiFujimoriYoung WookKimSung-EunKohWayneRossmanHeayongShinMasaakiUmeharaKotaroYamadaSeong-DeogYang10.18926/mjou/53048Space-like maximal surfaces and time-like minimal surfaces
in Lorentz-Minkowski 3-space R<sup>3</sup><sub>1</sub> 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 UniversityActa Medica Okayama0030-15665712015ENUMERATIVE COMBINATORICS ON DETERMINANTS AND SIGNED BIGRASSMANNIAN POLYNOMIALS159172ENMasatoKobayashi10.18926/mjou/53047As 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 UniversityActa Medica Okayama0030-15665712015ON ∅-RECURRENT CONTACT METRIC MANIFOLDS149158ENEsmaeilPeyghanHassanNasrabadiAkbarTayebi10.18926/mjou/53046In this paper, we prove that evry 3-dimensional manifold
M is a ∅-recurrent N(k)-contact metric manifold if and only if it is flat.
Then we classify the ∅-recurrent contact metric manifolds of constant
curvature. This implies that there exists no ∅-recurrent N(k)-contact
metric manifold, which is neither symmetric nor locally ∅-symmetric.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665712015AN EXPLICIT EFFECT OF NON-SYMMETRY OF RANDOM WALKS ON THE TRIANGULAR LATTICE129148ENSatoshiIshiwataHiroshiKawabiTsubasaTeruya10.18926/mjou/53045In the present paper, we study an explicit effect of non-symmetry on asymptotics of the n-step transition probability as n → ∞
for a class of non-symmetric random walks on the triangular lattice. Realizing the triangular lattice into R<sup>2</sup> appropriately, we observe that the
Euclidean distance in R<sup>2</sup> 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 R<sup>2</sup>.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665712015THE EQUIVARIANT SIMPLICIAL DE RHAM COMPLEX AND THE CLASSIFYING SPACE OF A SEMI-DIRECT PRODUCT GROUP123128ENNaoyaSuzuki10.18926/mjou/53044We 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 UniversityActa Medica Okayama0030-15665712015THE CANONICAL LINE BUNDLES OVER EQUIVARIANT REAL PROJECTIVE SPACES111122ENYanQi10.18926/mjou/53043A generator of the reduced KO-group of the real projective space of dimension n is related to the canonical line bundle γ. 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 2<sup>n+2</sup>[γ] is equal to zero.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665712015SUPPLEMENTED MORPHISMS99110ENArdaKörTruong CongQuynhSerapŞahinkayaMuhammet TamerKoşan10.18926/mjou/53042In the present paper, left R-modules M and N are studied
under the assumptions that Hom<sub>R</sub>(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<sub>R</sub>(M,N) and
Hom<sub>R</sub>(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<sub>M</sub>-module.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665712015STEENROD-ČECH HOMOLOGY-COHOMOLOGY THEORIES ASSOCIATED WITH BIVARIANT FUNCTORS8598ENKoheiYoshida10.18926/mjou/53041Let NG<sub>0</sub> denote the category of all pointed numerically
generated spaces and continuous maps preserving base-points. In [SYH],
we described a passage from bivariant functors NG<sub>0</sub><sup>op</sup>
× NG<sub>0</sub> → NG<sub>0</sub>
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 UniversityActa Medica Okayama0030-15665712015ON MODEL STRUCTURE FOR COREFLECTIVE SUBCATEGORIES OF A MODEL CATEGORY7984ENTadayukiHaraguchi10.18926/mjou/53040No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665712015QUASI TERTIARY COMPOSITIONS AND A TODA BRACKET IN HOMOTOPY GROUPS OF SU(3)1378ENHideakiŌshimaKatsumiŌshima10.18926/mjou/53039We revise the theories of tertiary compositions studied by
Ôguchi 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 UniversityActa Medica Okayama0030-15665712015MODULAR DIFFERENTIAL EQUATIONS WITH REGULAR SINGULARITIES AT ELLIPTIC POINTS FOR THE HECKE CONGRUENCE SUBGROUPS OF LOW-LEVELS112ENYuichiSakaiKenichiShimizu10.18926/mjou/53038In 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 UniversityActa Medica Okayama0030-15665612014ON THE SOLVABILITY OF CERTAIN (SSIE) WITH OPERATORS OF THE FORM B(r, s)179198ENBruno deMalafosseEberhardMalkowsky10.18926/mjou/52077Given any sequence z = (z<sub>n</sub>)<sub>n≥1</sub> of positive real numbers
and any set E of complex sequences, we write Ez for the set of all
sequences y = (y<sub>n</sub>)<sub>n≥1</sub> such that y/z = (y<sub>n</sub>/z<sub>n</sub>)<sub>n≥1</sub> ∈ E; in particular,
s<sub>z</sub><sup>(c)</sup>
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<sub>x</sub><sup>(c)</sup>
(B(r, s)) s<sub>x</sub><sup>(c)</sup>⊂
(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)<sub>n</sub> = ry<sub>n</sub>+sy<sub>n−1</sub> for all n ≥ 2 and (B(r, s)y)<sub>1</sub> = ry<sub>1</sub>.
We also determine the set of all positive sequences x for which
ry<sub>n</sub> + sy<sub>n−1</sub> /x<sub>n</sub>
→ l implies
r'y<sub>n</sub> + s'y<sub>n−1</sub>
/x<sub>n</sub>
→ 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<sub>x</sub><sup>(c)</sup> (B(r, s)) ⊂ s<sub>a</sub><sup>(c)</sup> .No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665612014CONVEXITY PROPERTIES OF A NEW GENERAL INTEGRAL OPERATOR OF p-VALENT FUNCTIONS171178ENSerapBulut10.18926/mjou/52076In 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 UniversityActa Medica Okayama0030-15665612014STUDY OF A PARABOLIC PROBLEM IN A CONICAL DOMAIN157169ENBoubaker-KhaledSadallah10.18926/mjou/52075In 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 UniversityActa Medica Okayama0030-15665612014THE BEST CONSTANT OF L<sup>p</sup> SOBOLEV INEQUALITY CORRESPONDING TO DIRICHLET-NEUMANN BOUNDARY VALUE PROBLEM145155ENHiroyukiYamagishiKohtaroWatanabeYoshinoriKametaka10.18926/mjou/52074We have obtained the best constant of the following L<sup>p</sup>
Sobolev inequality
sup
<sub>0≤y≤1</sub>|
u<sup>(j)</sup>(y)|
≤C (∫ <doubleint><sub>0</sub><sup>1</sup>
</doubleint> |
u<sup>(M)</sup>(x)|
<sup>p</sup>
dx)<sup>1/p</sup>
,
where u is a function satisfying u<sup>(M)</sup> ∈ L<sup>p</sup>(0, 1), u<sup>(2i)</sup>(0) = 0 (0 ≤i ≤
[(M − 1)/2]) and u<sup>(2i+1)</sup>(1) = 0 (0 ≤ i ≤ [(M − 2)/2]), where u<sup>(i)</sup> is
the abbreviation of (d/dx)<sup>i</sup>u(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 UniversityActa Medica Okayama0030-15665612014GROWTH OF SOLUTIONS OF HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS129143ENAbdallah ElFarissiBenharratBelaïdi10.18926/mjou/52073This paper is devoted to studying the growth of solutions
of the higher order nonhomogeneous linear differential equation
f<sup>(k)</sup> + A<sub>k−1</sub>f<sup>(k−1)</sup> + ... + A<sub>2</sub>f
"
+ (D<sub>1</sub> (z) + A<sub>1</sub> (z) e<sup>P(z)</sup>) f
'
+ (D<sub>0</sub> (z) + A<sub>0</sub> (z)e <sup>Q(z)</sup>) 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 UniversityActa Medica Okayama0030-15665612014WEIL ALGEBRAS ASSOCIATED TO FUNCTORS OF THIRD ORDER SEMIHOLONOMIC VELOCITIES117127ENMiroslavKureš10.18926/mjou/52072The 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 UniversityActa Medica Okayama0030-15665612014EQUIVARIANT STABLE HOMOTOPY THEORY FOR PROPER ACTIONS OF DISCRETE GROUPS91115ENNoéBárcenas10.18926/mjou/52071Following 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 UniversityActa Medica Okayama0030-15665612014A MODEL FOR THE WHITEHEAD PRODUCT IN RATIONAL MAPPING SPACES7589ENTakahitoNaito10.18926/mjou/52070We 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 UniversityActa Medica Okayama0030-15665612014PRIME, MAXIMAL AND PRIMITIVE IDEALS IN SOME SUBRINGS OF POLYNOMIAL RINGS6574ENMiguelFerreroEdilson SoaresMiranda10.18926/mjou/52069In 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 UniversityActa Medica Okayama0030-15665612014SUMS OF TWO BIQUADRATES AND ELLIPTIC CURVES OF RANK ≥ 45163ENF.A.IzadiF.KhoshnamK.Nabardi10.18926/mjou/52068If an integer n is written as a sum of two biquadrates in
two different ways, then the elliptic curve y<sup>2</sup> = x<sup>3</sup> − 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 UniversityActa Medica Okayama0030-15665612014ON POSITIVE INTEGERS OF MINIMAL TYPE CONCERNED WITH THE CONTINUED FRACTION EXPANSION3550ENYasuhiroKishiSayakaTajiriKen-ichiroYoshizuka10.18926/mjou/52067No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665612014INTERSECTIVE POLYNOMIALS WITH GALOIS GROUP D<sub>5</sub>2733ENMelisa J.LavalleeBlair K.SpearmanQiduanYang10.18926/mjou/52066We give an infinite family of intersective polynomials with
Galois group D<sub>5</sub>, the dihedral group of order 10.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665612014A CHARACTERIZATION OF THE GLAUBERMAN-WATANABE CORRESPONDING BLOCKS AS BIMODULES1726ENFuminoriTasaka10.18926/mjou/52065We 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 UniversityActa Medica Okayama0030-15665612014MUTATING BRAUER TREES116ENTakumaAihara10.18926/mjou/52064In 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 UniversityActa Medica Okayama0030-15665512013ON HYPERBOLIC AREA OF THE MODULI OF θ-ACUTE TRIANGLES191200ENNaomiKanesakaHiroakiNakamura10.18926/mjou/49105A 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 UniversityActa Medica Okayama0030-15665512013AN ALGEBRAIC APPROACH TO THE CAMERON-MARTIN-MARUYAMA-GIRSANOV FORMULA167190ENJirôAkahoriTakafumiAmabaSachiyoUraguchi10.18926/mjou/49104In 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 UniversityActa Medica Okayama0030-15665512013UNIFORM STABILITY AND BOUNDEDNESS OF SOLUTIONS OF NONLINEAR DELAY DIFFERENTIAL EQUATIONS OF THE THIRD ORDER157166ENAdemoraAdeleke TimothyArawamoPeter Olutola10.18926/mjou/49103In 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 UniversityActa Medica Okayama0030-15665512013MULTIPLICITY-FREE PERMUTATION CHARACTERS OF COVERING GROUPS OF SPORADIC SIMPLE GROUPS145155ENS. A.LintonZ. E.Mpono10.18926/mjou/49102In 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 UniversityActa Medica Okayama0030-15665512013PURITY AND GORENSTEIN FILTERED RINGS131143ENHirokiMiyahara10.18926/mjou/49101In 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 UniversityActa Medica Okayama0030-15665512013ON MONO-INJECTIVE MODULES AND MONO-OJECTIVE MODULES117129ENDeryaKeskin TütüncüYosukeKuratomi10.18926/mjou/49099In [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 UniversityActa Medica Okayama0030-15665512013A MODEL STRUCTURE ON THE CATEGORY OF SMALL CATEGORIES FOR COVERINGS95116ENKoheiTanaka10.18926/mjou/49098We 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 UniversityActa Medica Okayama0030-15665512013NOTE ON THE COHOMOLOGICAL INVARIANT OF PFISTER FORMS8793ENMichishigeTezukaNobuakiYagita10.18926/mjou/49097The 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 UniversityActa Medica Okayama0030-15665512013THE BLOCK APPROXIMATION THEOREM5385ENDanHaranMosheJardenFlorianPop10.18926/mjou/49096The 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 UniversityActa Medica Okayama0030-15665512013EXPLICIT ASSOCIATOR RELATIONS FOR MULTIPLE ZETA VALUES152ENIsmaëlSoudères10.18926/mjou/49095Associators 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 UniversityActa Medica Okayama0030-15664111999Universal Factorization Equalities for Quaternion Matrices and Their Applications4562ENYonggeTian10.18926/mjou/48176No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664111999Semi-Convergence of Filters and Nets103109ENR. M.Latif10.18926/mjou/48175No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664111999Irreducibilities of the Induced Characters of Cyclic p-Groups2736ENKatsusukeSekiguchi10.18926/mjou/48174No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664111999A Generalization of the Dade's Theorem on Localization of Injective Modules7579ENKazuhikoHirataUSyu10.18926/mjou/48173No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665412012ON MEANS OF BANACH-SPACE-VALUED FUNCTIONS145211ENRyotaroSato10.18926/mjou/47199We 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 UniversityActa Medica Okayama0030-15665412012CONTROLLABILITY OF FRACTIONAL INTEGRODIFFERENTIAL SYSTEMS VIA SEMIGROUP THEORY IN BANACH SPACES133143ENMohammedHaziMabroukBragdi10.18926/mjou/47198This 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 UniversityActa Medica Okayama0030-15665412012HOMOGENIZATION OF NON-LINEAR VARIATIONAL PROBLEMS WITH THIN INCLUSIONS97131ENAbdelaziz AïtMoussaLoubnaZlaïji10.18926/mjou/47197We 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 UniversityActa Medica Okayama0030-15665412012THE TANGENT BUNDLES OVER EQUIVARIANT REAL PROJECTIVE SPACES8796ENYanQi10.18926/mjou/47196let 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 UniversityActa Medica Okayama0030-15665412012NOTE ON THE HOMOTOPY OF THE SPACE OF MAPS BETWEEN REAL PROJECTIVE SPACES7786ENKohheiYamaguchi10.18926/mjou/47195We 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 UniversityActa Medica Okayama0030-15665412012ON A GENERALIZATION OF CQF-3′ MODULES AND COHEREDITARY TORSION THEORIES6576ENYasuhikoTakehana10.18926/mjou/47194Throughout 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<sub>σ</sub> := {M ∈ Mod-R : σ(M) = M} is called the class of σ-torsion right R-modules, and F<sub>σ</sub> := {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<sub>R</sub>(M,−) preserves the exactness for any exact sequence 0 → A → B → C → 0 with A ∈ F<sub>σ</sub>. We put P<sub>σ</sub>(M) = P(M)/σ(K(M)) for a module M. We call a right R-module M a
σ-CQF-3′ module if P<sub>σ</sub>(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 UniversityActa Medica Okayama0030-15665412012ON A GENERALIZATION OF QF-3′ MODULES AND HEREDITARY TORSION THEORIES5363ENYasuhikoTakehana10.18926/mjou/47193Let 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<sub>σ</sub> := {M ∈ Mod-R : σ(M) = M} is the class of σ-torsion right R-modules, and F<sub>σ</sub> := {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<sub>R</sub>(−,M) preserves the exactness for any exact sequence 0 → A → B → C → 0 with C ∈ T<sub>σ</sub>. A right R-module M is called σ-QF-3′ module if E<sub>σ</sub>(M) is M-torsionless, where E<sub>σ</sub>(M) is defined by E<sub>σ</sub>(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 UniversityActa Medica Okayama0030-15665412012ON THE STRUCTURE OF THE MORDELL-WEIL GROUPS OF THE JACOBIANS OF CURVES DEFINED BY y<sup>n</sup> = f(x)4952ENHyunsukMoon10.18926/mjou/47192Let A be an abelian variety defined over a number field K. It is proved that for the composite field K<sub>n</sub> of all Galois extensions over K of degree dividing n, the torsion subgroup of the Mordell-Weil group A(K<sub>n</sub>) is finite. This is a variant of Ribet’s result ([7]) on the finiteness of torsion subgroup of A(K(ζ<sub>∞</sub>)). It is also proved that for the Jacobians of superelliptic curves y<sup>n</sup> = 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 UniversityActa Medica Okayama0030-15665412012HILBERT-SPEISER NUMBER FIELDS AND STICKELBERGER IDEALS; THE CASE p = 23348ENHumioIchimura10.18926/mjou/47191We say that a number field F satisfies the condition (H′<sub>2<sup>m</sup></sub>) when any abelian extension of exponent dividing 2<sup>m </sup> has a normal basis with respect to rings of 2-integers. We say that it satisfies (H′
<sub>2<sup>∞</sup></sub>) when it satisfies (H′
<sub>2<sup>m</sup></sub>) for all m. We give a condition for F to satisfy (H'<sub>2<sup>m</sup></sub>), and show that the imaginary quadratic fields F = Q(√−1) and Q(√−2) satisfy the very strong condition (H′
<sub>2<sup>∞</sup></sub>) if the conjecture that h<sup>+</sup><sub>2<sup>m</sup></sub> = 1 for all m is valid. Here, h<sup>+</sup><sub>2<sup>m</sup></sub>) is the class number of the maximal real abelian field of conductor 2<sup>m</sup>.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665412012SOME REMARKS ON LUCAS PSEUDOPRIMES132ENNoriyukiSuwa10.18926/mjou/47190We 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 UniversityActa Medica Okayama0030-15665312011TRIANGLE CENTERS DEFINED BY QUADRATIC POLYNOMIALS185216ENYoshioAgaoka10.18926/mjou/41406We 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 UniversityActa Medica Okayama0030-15665312011THE UNIFORM EXPONENTIAL STABILITY OF LINEAR SKEW-PRODUCT SEMIFLOWS ON REAL HILBERT SPACE173183ENPham VietHaiLe NgocThanh10.18926/mjou/41405The 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 UniversityActa Medica Okayama0030-15665312011A CAUCHY-KOWALEVSKI THEOREM FOR INFRAMONOGENIC FUNCTIONS167172ENHelmuth R.MalonekDixan PeñaPeñaFrankSommen10.18926/mjou/41404In this paper we prove a Cauchy-Kowalevski theorem for the functions satisfying the system ∂<sub>x</sub>f∂<sub>x</sub> = 0 (called inframonogenic functions).No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665312011AN EXPLICIT PSp<sub>4</sub>(3)-POLYNOMIAL WITH 3 PARAMETERS OF DEGREE 40155165ENHidetakaKitayama10.18926/mjou/41403We 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 PGSp<sub>4</sub>(3) (resp. PSp<sub>4</sub>(3)) and it is a regular PSp<sub>4</sub>(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 UniversityActa Medica Okayama0030-15665312011ABSTRACT LOCAL COHOMOLOGY FUNCTORS129154ENYujiYoshinoTakeshiYoshizawa10.18926/mjou/41402We propose to define the notion of abstract local cohomology functors. The ordinary local cohomology functor RΓ<sub>I</sub> with support in the closed subset defined by an ideal I and the generalized local cohomology functor RΓ<sub>I,J</sub> 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 UniversityActa Medica Okayama0030-15665312011NOTE ON SYMMETRIC HILBERT SERIES111127ENYujiKamoi10.18926/mjou/41401No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665312011ON ALMOST N-SIMPLE-PROJECTIVES101109ENYoshitomoBabaTakeshiYamazaki10.18926/mjou/41400The 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 UniversityActa Medica Okayama0030-15665312011FP-GR-INJECTIVE MODULES83100ENXiaoyanYangZhongkuiLiu10.18926/mjou/41399In 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) (<sup>⊥</sup>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<sub>R</sub>) ≤ n, then (gr-FI<sub>n</sub>, gr-F <sub>n</sub><sup>⊥</sup>) is a perfect cotorsion theory, (3) (<sup>⊥</sup>gr-FI<sub>n</sub>, gr-FI<sub>n</sub>) is a cotorsion theory, where gr-FI denotes the class of all FP-gr-injective left R-modules, gr-FI<sub>n</sub> 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 UniversityActa Medica Okayama0030-15665312011TORSION OF ELLIPTIC CURVES OVER QUADRATIC CYCLOTOMIC FIELDS7582ENFilipNajman10.18926/mjou/41398In 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 UniversityActa Medica Okayama0030-15665312011PROJECTIVE STRUCTURES AND AUTOMORPHIC PSEUDODIFFERENTIAL OPERATORS5574ENMin HoLee10.18926/mjou/41397Automorphic 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 UniversityActa Medica Okayama0030-15665312011LIFTED CODES OVER FINITE CHAIN RINGS3953ENSteven T.DoughertyHongweiLiuYoung HoPark10.18926/mjou/41396In 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 UniversityActa Medica Okayama0030-15665312011ASYMPTOTIC ANALYSIS FOR GREEN FUNCTIONS OF AHARONOV-BOHM HAMILTONIAN WITH APPLICATION TO RESONANCE WIDTHS IN MAGNETIC SCATTERING137ENHideoTamura10.18926/mjou/41395The 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 UniversityActa Medica Okayama0030-15662411982An application of certain multiplicities of C∞ map germs2535ENYoshifumiAndo10.18926/mjou/33994No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662411982Subgroup SU(8)/Z2 of compact simple Lie group E7 and non-compact simple Lie group E{7(7)} of type E75371ENIchiroYokota10.18926/mjou/33993No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662411982Note on groups with isomorphic group algebras16ENTôruFurukawa10.18926/mjou/33992No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662411982On a theorem of M. S. Putcha and A. Yaqub2123ENHiroakiKomatsu10.18926/mjou/33991No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662411982Some remarks on bisimple rings1519ENYasuyukiHiranoHisaoTominaga10.18926/mjou/33990No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662411982Surgery obstruction of twisted products7397ENTomoyoshiYoshida10.18926/mjou/33989No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662411982Some polynomial identities and commutativity of s-unital rings713ENYasuyukiHiranoYujiKobayashiHisaoTominaga10.18926/mjou/33988No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662411982On J-groups of S^l(RP(t-l)/RP(n-l))4551ENSusumuKônoAkieTamamura10.18926/mjou/33987No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662411982On the iterated Samelson product3744ENHideyukiKachi10.18926/mjou/33986No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662421982A certain type of commutative Hopf Galois extensions and their groups137152ENAtsushiNakajima10.18926/mjou/33985No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662421982Notes on stable equivariant maps167178ENSyuichiIzumiya10.18926/mjou/33984No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662421982On right p.p. rings99109ENYasuyukiHiranoMotoshiHonganMasayukiÔhori10.18926/mjou/33983No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662421982On the equational definability of addition in rings133136ENHiroakiKomatsu10.18926/mjou/33982No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662421982On strongly prime modules and related topics117132ENMotoshiHongan10.18926/mjou/33981No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662421982The S^1-transfer map and homotopy groups of suspended complex projective spaces179200ENJunoMukai10.18926/mjou/33980No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662421982Some polynomial identities and commutativity of s-unital rings. II111115ENYasuyukiHiranoHisaoTominagaAdilYaqub10.18926/mjou/33979No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662421982A construction of spaces with general connections which have points swallowing geodesics157165ENTominosukeOtsuki10.18926/mjou/33978No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662421982On an individual ergodic theorem153156ENRyotaroSato10.18926/mjou/33977No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662011978Notes on a conjecture of P. Erdös. II4149ENMasatakaYorinagaSaburôUchiyama10.18926/mjou/33976No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662011978Two commutativity theorems for rings6772ENYasuyukiHiranoHisaoTominaga10.18926/mjou/33975No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662011978Restricted semiprimary group rings7782ENJ. B.SrivastavaVishnuGupta10.18926/mjou/33974No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662011978On the fixed point set of S^1-actions on the complex flag manifolds116ENKenjiHokamaSusumuKôno10.18926/mjou/33973No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662011978Simply connected smooth 4-manifolds which admit nontrivial smooth S^1 actions2540ENTomoyoshiYoshida10.18926/mjou/33972No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662011978Note on commutativity of rings2124ENIsaoMogamiMotoshiHongan10.18926/mjou/33971No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662011978Note on the n-center of an algebra7376ENShûichiIkehata10.18926/mjou/33970No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662011978On rings satisfying some polynomial identities1720ENArifKaya10.18926/mjou/33969No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662011978On the p'-section sum in a finite group ring8386ENYukioTsushima10.18926/mjou/33968No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662011978On a theorem of S. Koshitani5965ENKaoruMotose10.18926/mjou/33967No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662011978Numerical investigation of some equations involving Euler's φ-function5158ENMasatakaYorinaga10.18926/mjou/33966No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662011978On the p-rationality of lifted characters8789ENYoshiyasuNobusato10.18926/mjou/33965No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662021978On powers of artinian rings without identity131140ENIchiroMuraseHisaoTominaga10.18926/mjou/33964No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662021978The monoid structure of Galois H-dimodule algebras induced by the smash product165177ENAtsushiNakajima10.18926/mjou/33963No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662021978Direct sums of nonsingular indecomposable injective modules9199ENMamoruKutamiKiyoichiOshiro10.18926/mjou/33962No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662021978On generalizations of V-rings and regular rings123129ENRogerYue Chi Ming10.18926/mjou/33961No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662021978Covers of abelian groups115121ENJohn D.O'neill10.18926/mjou/33960No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662021978Commutativity of certain rings179181ENKazuoKishimotoIsaoMogami10.18926/mjou/33959No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662021978On some sums involving farey fractions101113ENShigeruKanemitus10.18926/mjou/33958No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662021978Numerical computation of Carmichael numbers151163ENMasatakaYorinaga10.18926/mjou/33957No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662021978Some studies on strongly π-regular rings141149ENYasuyukiHirano10.18926/mjou/33956No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662811986Equivalence of module categories147150ENShojiKyuno10.18926/mjou/33955No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662811986SI-modules133146ENMohamed F.Yousif10.18926/mjou/33954No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662811986Products of Galois objects and the Picard invariant map2936ENLindsay N.Childs10.18926/mjou/33953No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662811986An O theorem for a class of Dirichlet series151158ENDonRedmond10.18926/mjou/33952No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662811986An algebraic proof of a theorem of Warfield on algebraically compact modules5360ENGoroAzumaya10.18926/mjou/33951No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662811986The category of s-unital modules6591ENHiroakiKomatsu10.18926/mjou/33950No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662811986A characterization of quadratic residue codes15ENNoboruIto10.18926/mjou/33949No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662811986On Jacobson's conjecture115118ENYasuyukiHiranoHiroakiKomatsuIsaoMogami10.18926/mjou/33948No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662811986On periodic rings and related rings101103ENHoward E.BellHisaoTominaga10.18926/mjou/33947No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662811986A remark on the ergodic Hilbert transform159163ENRyotaroSato10.18926/mjou/33946No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662811986The group of Galois H-dimodule algebras2127ENAntonio A.Blanco-FerroMiguel A.Lopez Lopez10.18926/mjou/33945No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662811986Notes on biquadratic cyclic extensions of a commutative ring1520ENKazuoKishimoto10.18926/mjou/33944No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662811986A ring topology based on submodules over an Asano order of a ring6164ENKentaroMurata10.18926/mjou/33943No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662811986On some Cohen-Macaulay subsets of a partially ordered abelian group713ENAndrzejNowickiKazuoKishimotoTakasiNagahara10.18926/mjou/33942No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662811986Derivations algebriques sur un ideal dans les anneaux semi-premiers109113ENAndrzejTrzepizur10.18926/mjou/33941No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662811986On restricted anti-Hopfian modules119131ENYasuyukiHiranoIsaoMogami10.18926/mjou/33940No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662811986Identification of the ratio ergodic limit for an invertible positive isometry on L1165171ENRyotaroSato10.18926/mjou/33939No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662811986On commutativity of s-unital rings105108ENHiroakiKomatsuHisaoTominaga10.18926/mjou/33938No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662811986On the fixed point set of S¹-actions on the space whose rational cohomology ring is generated by elements of degree 2191206ENKenjiHokamaSusumuKôno10.18926/mjou/33937No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662811986On commutativity conditions for rings105108ENWalterStreb10.18926/mjou/33936No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662811986On Azumaya's exact rings4151ENVictor P.CamilloKent R.FullerJoel K.Haack10.18926/mjou/33935No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662811986Cozzens domains are hereditary3739ENCarlFaith10.18926/mjou/33934No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662811986Families of geodesics which distinguish flat tori207217ENNobuhiroInnami10.18926/mjou/33933No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662811986Some conditions for commutativity of rings97100ENHisaoTominaga10.18926/mjou/33932No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662811986The classification of homogeneous structures on 3-dimensional space forms173189ENKojiAbe10.18926/mjou/33931No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664612004The Perron Problem for C-Semigroups141152ENPetrePradaAlinPoganCiprianPreda10.18926/mjou/33930<p><p>Characterizations of Perron-type for the exponential stability of exponentially bounded C-semigroups are given. Also, some applications for the asymptotic behavior of the integrated semigroups are obtained.</p></p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664612004Results on prime near-ring with (σ,τ)-derivation18ENOznurGolbasiNesetAydin10.18926/mjou/33929<p>Let N be a prime left near-ring with multiplicative centerZ; and D be a (α, γ)derivation such that δD = Dδ and ΓD = DΓ(i)If D(N)⊂ Z; or [D(N);D(N)] = 0 or [D(N);D(N)]σ, γ= 0; then (N; +)is abelian. (ii) If N is 2-torsion free, d1 is a (α, γ)-derivation and d2 is a derivation on N such that d1d2(N) = 0, then d1 = 0 or d2 = 0.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664612004Some Metric Invariants of Spheres and Alexandrov Spaces I163182ENNobuyukiSochi10.18926/mjou/33928<p>A metric invariant a<sub>k</sub> is defined, and we have that a<sub>k</sub>(X)≤a<sub>k</sub>(S<sup>n</sup>) holds in an Alexandrov space X with curvature ≥ 1. And the
borderline case when a3(X) = a3(S<sup>n</sup>) and ak(S<sup>1</sup>) are studied.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664612004On Strong Approximation of Functions by Certain Linear Operators153162ENLucynaRempulskaMariolaSkorupka10.18926/mjou/33927<p>This note is motivated by the results on the strong approximation of 2Π-periodic functions by means of trigonometric Fourier series.In this note is investigated certain class of positive linear operators in the polynomial weighted spaces. We introduce the strong differences of functions and their operators and we give the Jackson type theorems for them. We give also some corollaries.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664612004A Note on Commutative Gelfand Theory for Real Banach Algebras121130ENSin-EiTakahashiTakeshiMiuraOsamuHatori10.18926/mjou/33926<p>Pfaffenberger and Phillips [2] consider a real and unital case of the classical commutative Gelfand theorem and obtain two representation theorems. One is to represent a unital real commutative Banach algebra A as an algebra of continuous functions on the unital homomorphism space ΦA. The other is to represent A as an algebra of continuous sections on the maximal ideal space MA. In this note, we point out that similar theorems for non-unital case hold and show that two representation theorems are essentially identical.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664612004A Study of Fq-Functions Connected with Ramanujan's Tenth Order Mock Theta Functions131140ENBhaskarSrivastava10.18926/mjou/33925<p><P>We have defined generalized functions which reduce to Ramanujan's mock theta functions of order ten. We have shown that they are Fq-functions. We have given their integral representation and multibasic expansions.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664612004On Simple-Injective Modules916ENTakashiSumiokaTakashiTokashiki10.18926/mjou/33924No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664612004Remark on Cup-Products115120ENKohheiYamaguchi10.18926/mjou/33923No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664612004Igusa Local Zeta Functions of Regular 2-Simple Prehomogeneous Vector Spaces of Type I with Universally Transitive Open Orbits85104ENSatoshiWakatsuki10.18926/mjou/33922No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664612004Principal Ideals in Ore Extensions7784ENWagnerCortesMiguelFerrero10.18926/mjou/33921<p>In this paper we prove that if R is a prime ring and I is an R-disjoint ideal of an Ore extension R[χ, δ,d], then I is closed and principal generated by a normal polynomial of minimal degree if and only if I contains a Sharma polynomial of minimal degree.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664612004Noncritical Belyi Maps105114ENShinichiMochizuki10.18926/mjou/33920<p>In the present paper, we present a slightly strengthened version of a well-known theorem of Belyi on the existence of "Belyi maps".
Roughly speaking, this strengthened version asserts that there exist Belyi maps which are unramified at [cf.Theorem 2.5] - or even near [cf.Corollary 3.2] - a prescribed finite set of points.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664612004Eigenloci of 5 Point Configurations on the Riemann Sphere and the Grothendieck-Teichm・ler Group3976ENPierreLochakHiroakiNakamuraLeilaSchneps10.18926/mjou/33919No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664612004Hasse Principle" for Finite p-Groups with Cyclic Subgroups of Index p23138ENMichitakuFumaYasushiNinomiya10.18926/mjou/33918No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664612004Upper Cohen-Macaulay Dimension1730ENTokujiArayaRyoTakahashiYujiYoshino10.18926/mjou/33917<p>In this paper, we define a homological invariant for finitely generated modules over a commutative noetherian local ring, which we call upper Cohen-Macaulay dimension. This invariant is quite similar to Cohen-Macaulay dimension that has been introduced by Gerko. Also we
define a homological invariant with respect to a local homomorphism of local rings. This invariant links upper Cohen-Macaulay dimension with Gorenstein dimension.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661711974Imbeddings of some separable extensions in Galois extensions5965ENTakasiNagahara10.18926/mjou/33916No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661711974On Ricci curvatures and equivalence of Riemannian manifolds117ENToshioNasu10.18926/mjou/33915No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661711974On separable polynomials over a commutative ring IV4958ENTakasiNagaharaAtsushiNakajima10.18926/mjou/33914No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661711974On isomorphisms of weakly Galois extensions3947ENMiguel A.Ferrero10.18926/mjou/33913No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661711974On minimal suraces in a Riemannian manifold of constant curvature1938ENTakehiroItoh10.18926/mjou/33912No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661711974g-adical analogues of some arithmetical functions7594ENIekataShiokawa10.18926/mjou/33911No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661711974The estimation of multiple correlation coefficient in stratified random sampling6774ENKazumasaWakimoto10.18926/mjou/33910No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661721975On generalized Harrison cohomology and Galois object135148ENAtsushiNakajima10.18926/mjou/33909No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661721975On two theorems of A. Abian165170ENIsaoMogami10.18926/mjou/33908No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661721975Remarks on manifolds of negative curvature177180ENRyosukeIchida10.18926/mjou/33907No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661721975On the true maximum order of a class of arithmetical functions95101END.SuryanarayanaR. Sita RamaChandra Rao10.18926/mjou/33906No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661721975On Riemannian manifolds of non-positive sectional curvature admitting a killing vector field131134ENRyosukeIchida10.18926/mjou/33905No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661721975On coprimary decomposition theory for modules125130ENIsaoMogamiHisaoTominaga10.18926/mjou/33904No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661721975On the subgroups H of a group G such that J(KH)KG ⊃ J(KG)171176ENKaoruMotoseYasushiNinomiya10.18926/mjou/33903No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661721975Centralizers of a module over a quasi-Frobenius extension103123ENYoshimiKitamura10.18926/mjou/33902No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661721975On the fixed point set of S¹-actions on CP^m×CP^n181186ENKenjiHokama10.18926/mjou/33901No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661721975On decompositions into simple rings159163ENHisaoTominaga10.18926/mjou/33900No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661721975On a generalized p-vector curvature and its applications149158ENToshioNasu10.18926/mjou/33899No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662211980On the Blum-Hanson theorem in Lp2732ENRyotaroSato10.18926/mjou/33898No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662211980Note on commutativity of rings. II5154ENIsaoMogami10.18926/mjou/33897No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662211980A note on separable polynomials in skew polynomial rings of derivation type5960ENShûichiIkehata10.18926/mjou/33896No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662211980A note on commutative separable algebras13ENStuart Sui-ShengWang10.18926/mjou/33895No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662211980A note on separable polynomials in skew polynomial rings of automorphism type7376ENTakasiNagahara10.18926/mjou/33894No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662211980On automorphisms of skew polynomial rings of derivation type2126ENMiguelFerreroKazuoKishimoto10.18926/mjou/33893No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662211980On QF-2 algebras with commutative radicals1720ENShigemotoAsanoKaoruMotose10.18926/mjou/33892No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662211980Equational definability of addition in rings satisfying polynomial identities5557ENHazarAbu-KhuzamHisaoTominagaAdilYaqub10.18926/mjou/33891No potential conflict of interest relevant to this article was reported.