Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666212020Existence and stability of stationary solutions to the Allen-Cahn equation discretized in space and time197210ENAmy Poh Ai LingDivision of Mathematics and Physics, Graduate School of Natural Science and Technology, Okayama UniversityMasaharuTaniguchiResearch Institute for Interdisciplinary Science, Okayama University The existence and stability of the Allen–Cahn equation discretized in space and time are studied in a finite spatial interval. If a parameter is less than or equals to a critical value, the zero solution is the only stationary solution. If the parameter is larger than the critical value, one has a positive stationary solution and this positive stationary solution is asymptotically stable.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666212020Analytic extension of exceptional constant mean curvature one catenoids in de Sitter 3-space179195ENShoichiFujimoriDepartment of Mathematics, Hiroshima UniversityYuKawakamiGraduate School of Natural Science and Technology, Kanazawa UniversityMasatoshiKokubuDepartment of Mathematics, School of Engineering, Tokyo Denki UniversityWayneRossmanDepartment of Mathematics, Faculty of Science, Kobe UniversityMasaakiUmeharaDepartment of Mathematical and Computing Sciences, Tokyo Institute of TechnologyKotaroYamadaDepartment of Mathematics, Tokyo Institute of Technology Catenoids in de Sitter 3-space S<sup>3</sup><sub>1</sub> belong to a certain class of
space-like constant mean curvature one surfaces. In a previous work, the authors
classified such catenoids, and found that two different classes of countably many exceptional elliptic catenoids are not realized as closed subsets in S<sup>3</sup><sub>1</sub> . Here we show that such exceptional catenoids have closed analytic extensions in S<sup>3</sup><sub>1</sub> with interesting properties.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666212020Unstable higher Toda brackets2786ENHideakiOshimaIbaraki UniversityKatsumiOshimaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666212020A representation for algebraic K-theory of quasi-coherent modules over affine spectral schemes125ENMarikoOharaDepartment of Mathematical Sciences Shinshu University In this paper, we study K-theory of spectral schemes by using locally free sheaves. Let us regard the K-theory as a functor K on affine spectral schemes. Then, we prove that the group completion
ΩB<sup>G</sup>(B<sup>G</sup>GL) represents the sheafification of K with respect to Zariski (resp. Nisnevich) topology G, where B<sup>G</sup>GL is a classifying space of a colimit of affine spectral schemes GLn.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666212020Crystal interpretation of a formula on the branching rule of types Bn, Cn, and Dn87178ENToyaHiroshimaDepartment of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka UniversityThe branching coefficients of the tensor product of finite-dimensional irreducible Uq(g)-modules, where g is so(2n + 1, C) (Bn-type), sp(2n,C) (Cn-type), and so(2n,C) (Dn-type), are expressed in
terms of Littlewood-Richardson (LR) coefficients in the stable region. We give an interpretation of this relation by Kashiwara’s crystal theory by providing an explicit surjection from the LR crystal of type Cn to the disjoint union of Cartesian product of LR crystals of An−1-type and by proving that LR crystals of types Bn and Dn are identical to the corresponding LR crystal of type Cn in the stable region.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666112019Reconstruction of inertia groups associated to log divisors from a configuration space group equipped with its collection of log-full subgroups3773ENKazumiHigashiyamaResearch Institute for Mathematical Sciences Kyoto University In the present paper, we study configuration space groups. The goal of this paper is to reconstruct group-theoretically the inertia groups associated to various types of log divisors of a log configuration space of a smooth log curve from the associated configuration space group equipped with its collection of log-full subgroups.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666112019Passage of property (Bw) from two operators to their tensor product187198ENM.H.M.RashidDepartment of Mathematics& Statistics Faculty of Science P.O.Box(7) Mu’tah University A Banach space operator satisfies property (Bw) if the complement of its B-Weyl spectrum in its the spectrum is the set of finite multiplicity isolated eigenvalues of the operator. Property (Bw) does not transfer from operators T and S to their tensor product T ⊗ S. We give necessary and /or sufficient conditions ensuring the passage of property (Bw) from T and S to T ⊗ S. Perturbations by Riesz operators are considered.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666112019The number of simple modules in a block with Klein four hyperfocal subgroup159166ENFuminoriTasakaNational Institute of Technology Tsuruoka College A 2-block of a finite group having a Klein four hyperfocal subgroup has the same number of irreducible Brauer characters as the corresponding 2-block of the normalizer of the hyperfocal subgroup.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666112019Berezin-Weyl quantization of Heisenberg motion groups1935ENBenjaminCahenD´epartement de math´ematiques Universit´e de Lorraine We introduce a Schr¨odinger model for the generic representations of a Heisenberg motion group and we construct adapted Weyl correspondences for these representations by adapting the method introduced in [ B. Cahen, Weyl quantization for semidirect products, Differential Geom. Appl. 25 (2007), 177-190].No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666112019On the Diophantine equation in the form that a sum of cubes equals a sum of quintics7584ENFarzaliIzadiMehdi Baghalaghdam Department of Mathematics Faculty of Science Azarbaijan Shahid Madani UniversityMehdiBaghalaghdamMehdi Baghalaghdam Department of Mathematics Faculty of Science Azarbaijan Shahid Madani UniversityNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666112019On the classification of ruled minimal surfaces in pseudo-Euclidean space173186ENYuichiroSatoDepartment of Mathematical Sciences Tokyo Metropolitan University This paper gives, in generic situations, a complete classification of ruled minimal surfaces in pseudo-Euclidean space with arbitrary index. In addition, we discuss the condition for ruled minimal surfaces to exist, and give a counter-example on the problem of Bernstein type.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666112019Terwilliger Algebras of Some Group Association Schemes199204ENNurHamidFaculty of Mathematics and Physics, Kanazawa UniversityManabuOuraFaculty of Mathematics and Physics, Kanazawa University The Terwilliger algebra plays an important role in the theory of association schemes. The present paper gives the explicit structures of the Terwilliger algebras of the group association schemes of the finite groups PSL(2, 7), A6, and S6.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666112019On the existence of non-finite coverings of stable curves over complete discrete valuation rings118ENYuYangResearch Institute for Mathematical Sciences Kyoto UniversityLet R be a complete discrete valuation ring with algebraically residue field of characteristic p > 0 and X a stable curve over R. In the present paper, we study the geometry of coverings of X. Under certain assumptions, we prove that, by replacing R by a finite extension of R, there exists a morphism of stable curves f : Y → X over R such that the morphism fη : Yη → Xη induced by f on generic fibers is finite étale and the morphism fs : Ys → Xs induced by f on special fibers is non-finite.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666112019A limit transition from the Heckman-Opdam hypergeometric functions to the Whittaker functions associated with root systems129139ENNobukazuShimenoSchool of Science and Technology Kwansei Gakuin University We prove that the radial part of the class one Whittaker function on a split semisimple Lie group can be obtained as an appropriate limit of the Heckman-Opdam hypergeometric function.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666112019Cesaro Orlicz sequence spaces and their Kothe-Toeplitz duals141158ENKuldipRajSchool of Mathematics Shri Mata Vaishno Devi UniversityRenuAnandSchool of Mathematics Shri Mata Vaishno Devi UniversitySuruchiPandohSchool of Mathematics Shri Mata Vaishno Devi UniversityThe present paper focus on introducing certain classes of Cesàro Orlicz sequences over n-normed spaces. We study some topological and algebraic properties of these spaces. Further, we examine relevant relations among the classes of these sequences. We show that these spaces are made n-BK-spaces under certain conditions. Finally, we compute the Köthe-Toeplitz duals of these spaces.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666112019The Factorization of 2 and 3 in Cyclic Quartic Fields167172ENStephen C.BrownDepartment of Computer Science, Mathematics, Physics and Statistics I.K. Barber School of Arts and Sciences University of British ColumbiaChad T.DavisDepartment of Computer Science, Mathematics, Physics and Statistics I.K. Barber School of Arts and Sciences University of British Columbia Due to a theorem of Dedekind, factoring ideals generated by prime numbers in number fields is easily done given that said prime number does not divide the index of the field. In this paper, we determine the prime ideal factorizations of both 2 and 3 in cyclic quartic fields whose index is divisible by one of or both of these primes.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666112019Complex interpolation of smoothness Triebel-Lizorkin-Morrey spaces99128ENDenny IvanalHakimDepartment of Mathematics and Information Sciences, Tokyo Metropolitan UniversityToruNogayamaDepartment of Mathematics and Information Sciences, Tokyo Metropolitan UniversityYoshihiroSawanoDepartment of Mathematics and Information Sciences, Tokyo Metropolitan University This paper extends the result in [8] to Triebel-Lizorkin-Morrey spaces which contains 4 parameters p, q, r, s. This paper reinforces our earlier paper [8] by Nakamura, the first and the third authors in two different directions. First, we include the smoothness parameter s and the second smoothness parameter r. In [8] we assumed s = 0 and r = 2. Here we relax the conditions on s and r to s ∈ R and 1 < r ≤ ∞. Second, we apply a formula obtained by Bergh in 1978 to prove our main theorem without using the underlying sequence spaces.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666112019On the structure of the profile of finite connected quandles8598ENTaisukeWatanabe We verify some cases of a conjecture by C. Hayashi on the structure of the profile of a finite connected quandle.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666012018Necessary and sufficient Tauberian conditions for the A^r method of summability209219ENÖzerTaloDepartment of Mathematics Faculty of Science and Letters Manisa Celal Bayar UniversityFeyziBas̨arİnönü UniversityMóricz and Rhoades determined the necessary and sufficient Tauberian conditions for certain weighted mean methods of summability in [Acta. Math. Hungar. 102(4) (2004), 279{285]. In the present paper, we deal with the necessary and sufficient Tauberian conditions for the Ar method which was introduced by Bas̨ar in [Fırat Üniv. Fen & Müh. Bil. Dergisi 5(1)(1993), 113{117].No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666012018Tomita-Takesaki theory and its application to the structure theory of factors of type III3758ENToshihikoMasudaGraduate School of Mathematics, Kyushu UniversityWe give a survey of Tomita-Takesaki theory and the development of analysis of structure of type III factors, which started from Tomita-Takesaki theory.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666012018Stable splittings of the complex connective K-theory of BSO(2n+1)7389ENTsung-HsuanWuDepartment of Mathematics National Tsing Hua UniversityWe give the stable splittings of the complex connective K-theory of the classifying space BSO(2n + 1), n≥1.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666012018Indecomposability of various profinite groups arising from hyperbolic curves175208ENArataMinamideResearch Institute for Mathematical Sciences Kyoto UniversityIn this paper, we prove that the etale fundamental group of a hyperbolic curve over an arithmetic field [e.g., a finite extension field of Q or Qp] or an algebraically closed field is indecomposable [i.e., cannot be decomposed into the direct product of nontrivial profinite groups]. Moreover, in the case of characteristic zero, we also prove that the etale fundamental group of the configuration space of a curve of the above type is indecomposable. Finally, we consider the topic of indecomposability in the context of the comparison of the absolute Galois group of Q with the Grothendieck-Teichmuller group GT and pose the question: Is GT indecomposable? We give an affirmative answer to a pro-l version of this questionNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666012018Primary decompositions in abelian R-categories91108ENKenichiSatoGraduate School of Natural Science and Technology Okayama UniversityYujiYoshinoGraduate School of Natural Science and Technology Okayama UniversityWe shall generalize the theory of primary decomposition and associated prime ideals of �nitely generated modules over a noetherian ring to general objects in an abelian R-category where R is a noetherian commutative ring.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666012018Arithmetic of positive integers having prime sums of complementary divisors155164ENKenichiShimizuWe study a class of integers called SP numbers (Sum Prime numbers). An SP number is by de�nition a positive integer d that gives rise to a prime number (a + b)=gcd(4; 1 + d) from every factorization d = ab. We also discuss properties of SP numbers in relations with arithmetic of imaginary quadratic �elds (least split primes, exponents of ideal class groups). Further we point out that special cases of SP numbers provide the problems of distribution of prime numbers (twin primes, Sophi-Germain primes, quadratic progressions). Finally, we consider the problem whether there exist in�nitely many SP numbers.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666012018On the profinite abelian Beckmann-Black problem233240ENNourGhaziUniversity of Damascus, Faculty of Sciences, Department of MathematicsThe main topic of this paper is to generalize the problem of Beckmann-Black for pro�nite groups. We introduce the Beckmann-Black problem for complete systems of �finite groups and for unramified extensions. We prove that every Galois extension of profi�nite abelian group over a ψ-free fi�eld is the specialization of some tower of regular Galois extensions of the same group.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666012018Absolute continuity of the representing measures of the transmutation operators attached to the root system of type BC25972ENKhalifaTrimẻcheDepartment of Mathematics Faculty of sciences of Tunis UniversityWe prove in this paper the absolute continuity of the representing measures of the transmutation operators Vk, tVk and VkW, tVkW associated respectively to the Cherednik operators and the Heckman-Opdam theory attached to the root system of type BC2.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666012018A binomial-coefficient identity arising from the middle discrete series of SU(2,2)221231ENTakahiroHayataGraduate School of Science and Engineering, Yamagata UniversityMasaoIshikawaGraduate School of Natural Science and Technology, Okayama UniversityThe aim of this paper is to answer the question in Remark 8.2 of Takahiro Hayata, Harutaka Koseki, and Takayuki Oda, Matrix coefficients of the middle discrete series of SU(2; 2), J. Funct. Anal. 185 (2001), 297{341, by giving an elementary proof of certain identities on binomials.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666012018A non-symmetric diffusion process on the Wiener space137153ENIchiroShigekawaDepartment of Mathematics Graduate School of Science Kyoto UniversityWe discuss a non-symmetric diffusion process on the Wiener space. The process we consider is generated by A = L + b, L being the Ornstein-Uhlenbeck operator and b being a vector �eld. Under suitable integrability condition for b, we show the existence of associated diffusion process. We also investigate the domain of the generator. Further we consider a similar problem in the �nite dimensional Euclidean space.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666012018A remark on a central limit theorem for non-symmetric random walks on crystal lattices109135ENRyuyaNambaGraduate School of Natural Sciences, Okayama UniversityRecently, Ishiwata, Kawabi and Kotani [4] proved two kinds of central limit theorems for non-symmetric random walks on crystal lattices from the view point of discrete geometric analysis developed by Kotani and Sunada. In the present paper, we establish yet another kind of the central limit theorem for them. Our argument is based on a measure-change technique due to Alexopoulos [1].No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666012018Review on higher homotopies in the theory of H-spaces136ENYutakaHemmiDepartment of Mathematics Faculty of Science and Technology Kochi UniversityHigher homotopy in the theory of H-spaces started from the works by Sugawara in the 1950th. In this paper we review the development of the theory of H-spaces associated with it. Mainly there are two types of higher homotopies, homotopy associativity and homotopy commutativity. We give explanations of the polytopes used as the parameter spaces of those higher forms.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666012018An alternative proof of some results on the framed bordism classes of low rank simple Lie groups165173ENHaruoMinamiNara University of EducationWe present a uni�ed proof of some known results on the framed bordism classes of low rank simple Lie groups.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665912017Higher-dimensional absolute versions of symmetric, Frobenius, and quasi-Frobenius algebras131140ENMitsuyasuHashimotoDepartment of Mathematics Faculty of Science, Okayama UniversityIn 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 Okayama0030-15665912017On 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 UniversityIn 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 Okayama0030-15665912017The degree of set-valued mappings from ANR spaces to homology spheres2740ENYoshimiShitandaSchool of political science and economics, Meiji UniversityAn 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 Okayama0030-15665912017Scattering 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 EducationIn 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 Okayama0030-15665912017Categorical characterization of strict morphisms of fs log schemes119ENYuichiroHoshiResearch Institute for Mathematical Sciences, Kyoto UniversityChikaraNakayamaDepartment of Economics, Hitotsubashi UniversityIn 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 Okayama0030-15665912017An arithmetic function arising from the Dedekind ψ function8192ENColinDefantDepartment of Mathematics, University of FloridaWe 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 Okayama0030-15665912017A remark on the Lavallee-Spearman-Williams-Yang family of quadratic fields113116ENKwang-SeobKimSchool of Mathematics, Korea Institute for Advanced StudyYasuhiroKishiDepartment of Mathematics, Aichi University of EducationIn [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 Okayama0030-15665912017A note on balance equations for doubly periodic minimal surfaces117130ENPeterConnorDepartment of Mathematical Sciences, Indiana University South BendMost 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 Okayama0030-15665912017Gauss 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 UniversityWe 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 Okayama0030-15665912017Some examples of non-tidy spaces2125ENTakahiroMatsushitaGraduate School of Mathematical Sciences, The University of TokyoWe 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 Okayama0030-15665912017Evaluation 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 ResearchIn 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 UniversityThe 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 Okayama0030-15665912017Blowup and global existence of a solution to a semilinear reaction-diffusion system with the fractional Laplacian175218ENTomoyukiKakehiDepartment of Mathematics, Okayama UniversityYoshihitoOshitaDepartment of Mathematics, Okayama UniversityIn 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 Okayama0030-15665812016Asymptotic properties in forward directions of resolvent kernels of magnetic Schrödinger operators in two dimensions139ENHideoTamuraWe 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 Okayama0030-15665812016On finite rings over which every free codes is splitting133140ENYasuyukiHiranoIn 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 Okayama0030-15665812016Aharonov--Bohm effect in resonances of magnetic Schrödinger operators in two dimensions II4178ENHideoTamuraWe 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 Okayama0030-15665812016Another description of quasi tertiary composition109123ENHideakiŌshimaKatsumiŌshimaWe 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 Okayama0030-15665812016On a duality of Gras between totally positive and primary cyclotomic units125132ENHumioIchimuraLet 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 Okayama0030-15665812016Aharonov--Bohm effect in resonances of magnetic Schrödinger operators in two dimensions III79108ENHideoTamuraWe 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 Okayama0030-15665812016The positivity of the transmutation operators associated to the Cherednik operators for the root system $BC_2$183198ENKhalifaTRIMÈCHEWe 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 Okayama0030-15665812016Alternative approach for Siegel's lemma141158ENMakotoNagataIn 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 Okayama0030-15665812016Restriction on Galois groups by prime inert condition159167ENToruKomatsuIn 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 Okayama0030-15665812016On weakly separable polynomials and weakly quasi-separable polynomials over rings169182ENSatoshiYamanakaSeparable 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 Okayama0030-15665712015THE EQUIVARIANT SIMPLICIAL DE RHAM COMPLEX AND THE CLASSIFYING SPACE OF A SEMI-DIRECT PRODUCT GROUP123128ENNaoyaSuzukiWe 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 Okayama0030-15665712015STEENROD-ČECH HOMOLOGY-COHOMOLOGY THEORIES ASSOCIATED WITH BIVARIANT FUNCTORS8598ENKoheiYoshidaLet 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 Okayama0030-15665712015SUPPLEMENTED MORPHISMS99110ENArdaKörTruong CongQuynhSerapŞahinkayaMuhammet TamerKoşanIn 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 Okayama0030-15665712015ENUMERATIVE COMBINATORICS ON DETERMINANTS AND SIGNED BIGRASSMANNIAN POLYNOMIALS159172ENMasatoKobayashiAs 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 Okayama0030-15665712015ZERO MEAN CURVATURE SURFACES IN LORENTZ-MINKOWSKI 3-SPACE AND 2-DIMENSIONAL FLUID MECHANICS173200ENShoichiFujimoriYoung WookKimSung-EunKohWayneRossmanHeayongShinMasaakiUmeharaKotaroYamadaSeong-DeogYangSpace-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 Okayama0030-15665712015AN EXPLICIT EFFECT OF NON-SYMMETRY OF RANDOM WALKS ON THE TRIANGULAR LATTICE129148ENSatoshiIshiwataHiroshiKawabiTsubasaTeruyaIn 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 Okayama0030-15665712015ON ∅-RECURRENT CONTACT METRIC MANIFOLDS149158ENEsmaeilPeyghanHassanNasrabadiAkbarTayebiIn 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 Okayama0030-15665712015ON MODEL STRUCTURE FOR COREFLECTIVE SUBCATEGORIES OF A MODEL CATEGORY7984ENTadayukiHaraguchiNo 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 SPACES111122ENYanQiA 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 Okayama0030-15665712015QUASI TERTIARY COMPOSITIONS AND A TODA BRACKET IN HOMOTOPY GROUPS OF SU(3)1378ENHideakiŌshimaKatsumiŌshimaWe 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-LEVELS112ENYuichiSakaiKenichiShimizuIn 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 Okayama0030-15665612014THE BEST CONSTANT OF L<sup>p</sup> SOBOLEV INEQUALITY CORRESPONDING TO DIRICHLET-NEUMANN BOUNDARY VALUE PROBLEM145155ENHiroyukiYamagishiKohtaroWatanabeYoshinoriKametakaWe 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 Okayama0030-15665612014A CHARACTERIZATION OF THE GLAUBERMAN-WATANABE CORRESPONDING BLOCKS AS BIMODULES1726ENFuminoriTasakaWe 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 Okayama0030-15665612014INTERSECTIVE POLYNOMIALS WITH GALOIS GROUP D<sub>5</sub>2733ENMelisa J.LavalleeBlair K.SpearmanQiduanYangWe 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 Okayama0030-15665612014WEIL ALGEBRAS ASSOCIATED TO FUNCTORS OF THIRD ORDER SEMIHOLONOMIC VELOCITIES117127ENMiroslavKurešThe 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 Okayama0030-15665612014ON POSITIVE INTEGERS OF MINIMAL TYPE CONCERNED WITH THE CONTINUED FRACTION EXPANSION3550ENYasuhiroKishiSayakaTajiriKen-ichiroYoshizukaNo 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-KhaledSadallahIn 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 Okayama0030-15665612014SUMS OF TWO BIQUADRATES AND ELLIPTIC CURVES OF RANK ≥ 45163ENF.A.IzadiF.KhoshnamK.NabardiIf 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 Okayama0030-15665612014A MODEL FOR THE WHITEHEAD PRODUCT IN RATIONAL MAPPING SPACES7589ENTakahitoNaitoWe 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 Okayama0030-15665612014CONVEXITY PROPERTIES OF A NEW GENERAL INTEGRAL OPERATOR OF p-VALENT FUNCTIONS171178ENSerapBulutIn 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 Okayama0030-15665612014ON THE SOLVABILITY OF CERTAIN (SSIE) WITH OPERATORS OF THE FORM B(r, s)179198ENBruno deMalafosseEberhardMalkowskyGiven 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 Okayama0030-15665612014PRIME, MAXIMAL AND PRIMITIVE IDEALS IN SOME SUBRINGS OF POLYNOMIAL RINGS6574ENMiguelFerreroEdilson SoaresMirandaIn 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 Okayama0030-15665612014EQUIVARIANT STABLE HOMOTOPY THEORY FOR PROPER ACTIONS OF DISCRETE GROUPS91115ENNoéBárcenasFollowing 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 Okayama0030-15665612014GROWTH OF SOLUTIONS OF HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS129143ENAbdallah ElFarissiBenharratBelaïdiThis 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 Okayama0030-15665612014MUTATING BRAUER TREES116ENTakumaAiharaIn 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 TRIANGLES191200ENNaomiKanesakaHiroakiNakamuraA 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 FORMULA167190ENJirôAkahoriTakafumiAmabaSachiyoUraguchiIn 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 OlutolaIn 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.MponoIn 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 Okayama0030-15665512013EXPLICIT ASSOCIATOR RELATIONS FOR MULTIPLE ZETA VALUES152ENIsmaëlSoudèresAssociators 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 Okayama0030-15665512013PURITY AND GORENSTEIN FILTERED RINGS131143ENHirokiMiyaharaIn 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 Okayama0030-15665512013THE BLOCK APPROXIMATION THEOREM5385ENDanHaranMosheJardenFlorianPopThe 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 Okayama0030-15665512013NOTE ON THE COHOMOLOGICAL INVARIANT OF PFISTER FORMS8793ENMichishigeTezukaNobuakiYagitaThe 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 Okayama0030-15665512013A MODEL STRUCTURE ON THE CATEGORY OF SMALL CATEGORIES FOR COVERINGS95116ENKoheiTanakaWe 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 Okayama0030-15665512013ON MONO-INJECTIVE MODULES AND MONO-OJECTIVE MODULES117129ENDeryaKeskin TütüncüYosukeKuratomiIn [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 Okayama0030-15665412012NOTE ON THE HOMOTOPY OF THE SPACE OF MAPS BETWEEN REAL PROJECTIVE SPACES7786ENKohheiYamaguchiWe 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 Okayama0030-15665412012THE TANGENT BUNDLES OVER EQUIVARIANT REAL PROJECTIVE SPACES8796ENYanQilet 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 Okayama0030-15665412012HILBERT-SPEISER NUMBER FIELDS AND STICKELBERGER IDEALS; THE CASE p = 23348ENHumioIchimuraWe 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 Okayama0030-15665412012ON THE STRUCTURE OF THE MORDELL-WEIL GROUPS OF THE JACOBIANS OF CURVES DEFINED BY y<sup>n</sup> = f(x)4952ENHyunsukMoonLet 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 Okayama0030-15665412012ON A GENERALIZATION OF QF-3′ MODULES AND HEREDITARY TORSION THEORIES5363ENYasuhikoTakehanaLet 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 Okayama0030-15665412012SOME REMARKS ON LUCAS PSEUDOPRIMES132ENNoriyukiSuwaWe 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 Okayama0030-15665412012CONTROLLABILITY OF FRACTIONAL INTEGRODIFFERENTIAL SYSTEMS VIA SEMIGROUP THEORY IN BANACH SPACES133143ENMohammedHaziMabroukBragdiThis 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 Okayama0030-15665412012ON MEANS OF BANACH-SPACE-VALUED FUNCTIONS145211ENRyotaroSatoWe 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 Okayama0030-15665412012HOMOGENIZATION OF NON-LINEAR VARIATIONAL PROBLEMS WITH THIN INCLUSIONS97131ENAbdelaziz AïtMoussaLoubnaZlaïjiWe 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 Okayama0030-15665412012ON A GENERALIZATION OF CQF-3′ MODULES AND COHEREDITARY TORSION THEORIES6576ENYasuhikoTakehanaThroughout 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 Okayama0030-15665312011PROJECTIVE STRUCTURES AND AUTOMORPHIC PSEUDODIFFERENTIAL OPERATORS5574ENMin HoLeeAutomorphic 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 HoParkIn 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 Okayama0030-15665312011TORSION OF ELLIPTIC CURVES OVER QUADRATIC CYCLOTOMIC FIELDS7582ENFilipNajmanIn 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 Okayama0030-15665312011THE UNIFORM EXPONENTIAL STABILITY OF LINEAR SKEW-PRODUCT SEMIFLOWS ON REAL HILBERT SPACE173183ENPham VietHaiLe NgocThanhThe 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 Okayama0030-15665312011TRIANGLE CENTERS DEFINED BY QUADRATIC POLYNOMIALS185216ENYoshioAgaokaWe 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 Okayama0030-15665312011ABSTRACT LOCAL COHOMOLOGY FUNCTORS129154ENYujiYoshinoTakeshiYoshizawaWe 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 Okayama0030-15665312011ASYMPTOTIC ANALYSIS FOR GREEN FUNCTIONS OF AHARONOV-BOHM HAMILTONIAN WITH APPLICATION TO RESONANCE WIDTHS IN MAGNETIC SCATTERING137ENHideoTamuraThe 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 Okayama0030-15665312011FP-GR-INJECTIVE MODULES83100ENXiaoyanYangZhongkuiLiuIn 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 Okayama0030-15665312011AN EXPLICIT PSp<sub>4</sub>(3)-POLYNOMIAL WITH 3 PARAMETERS OF DEGREE 40155165ENHidetakaKitayamaWe 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 Okayama0030-15665312011ON ALMOST N-SIMPLE-PROJECTIVES101109ENYoshitomoBabaTakeshiYamazakiThe 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 Okayama0030-15665312011A CAUCHY-KOWALEVSKI THEOREM FOR INFRAMONOGENIC FUNCTIONS167172ENHelmuth R.MalonekDixan PeñaPeñaFrankSommenIn 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 Okayama0030-15665312011NOTE ON SYMMETRIC HILBERT SERIES111127ENYujiKamoiNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665212010CORRECTION: RESULTS ON PRIME NEAR-RINGS WITH (σ,τ)- DERIVATIONENÖznurGölbaşiNeşetAydinNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665212010ARITHMETIC ELLIPTIC CURVES IN GENERAL POSITIONENShinichiMochizuki<p>We combine various well-known techniques from the theory of heights, the theory of “noncritical Belyi maps”, and classical analytic number theory to conclude that the “ABC Conjecture”, or, equivalently, the so-called “Effective Mordell Conjecture”, holds for arbitrary rational points of the projective line minus three points if and only if it holds for rational points which are in “sufficiently general position” in the sense that the following properties are satisfied: (a) the rational point under
consideration is bounded away from the three points at infinity at a given finite set of primes; (b) the Galois action on the l-power torsion points of the corresponding elliptic curve determines a surjection onto
GL<sub>2</sub>(Zl), for some prime number l which is roughly of the order of the sum of the height of the elliptic curve and the logarithm of the discriminant of the minimal field of definition of the elliptic curve, but does not divide the conductor of the elliptic curve, the rational primes
that are absolutely ramified in the minimal field of definition of the elliptic curve, or the local heights [i.e., the orders of the q-parameter at primes of [bad] multiplicative reduction] of the elliptic curve.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665212010SOME PROPERTIES OF EF-EXTENDING RINGSENTruong CongQuynhLe VanThuyet<p>In [16], Thuyet and Wisbauer considered the extending property for the class of (essentially) finitely generated submodules. A module M is called ef-extending if every closed submodule which contains essentially a finitely generated submodule is a direct summand of M. A ring R is called right ef-extending if R<sub>R</sub> is an ef-extending module. We show that a ring R is right ef-extending and the R-dual of every simple left R-module is simple if and only if R is semiperfect right continuous with Sl = Sl ≤<sup>e</sup> R<sub>R</sub>. We also prove that a ring R is a QF-ring if and only if R is left Kasch and R<sub>R</sub><sup>(ω)</sup>
is ef-extending if and only if R is right AGP-injective satisfying DCC on right (or left) annihilators and (R ⊕ R)<sub>R</sub> is ef-extending.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665212010TRIANGULAR MATRIX REPRESENTATIONS OF SKEW MONOID RINGSENLiuZhongkuiYangXiaoyan<p>Let R be a ring and S a u.p.-monoid. Assume that there is a monoid homomorphism α : S → Aut (R). Suppose that α is weakly　rigid and l<sub>R</sub>(Ra) is pure as a left ideal of R for every element a ∈ R. Then the skew monoid ring R*S induced by α has the same triangulating dimension as R. Furthermore, if R is a PWP ring, then so is R*S.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665212010ON FUCHSIAN GROUPS WITH THE SAME SET OF FIXED POINTS OF PARABOLIC ELEMENTSENTaeMaeda<p>There is an open question whether Fuchsian groups having
the same set of the axes of hyperbolic elements are commensurable or
not. In this note, we consider an analogous question where the axes are
replaced with the fixed points of parabolic elements.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665212010INFINITE MATRICES ASSOCIATED WITH POWER SERIES AND APPLICATION TO OPTIMIZATION AND MATRIX TRANSFORMATIONSENBruno deMalafosseAdnanYassine<p>In this paper we first recall some properties of triangle Toeplitz matrices of the Banach algebra S<sub>r </sub> associated with power series. Then for boolean Toeplitz matrices M we explicitly calculate the product M<sup>N</sup> that gives the number of ways with N arcs associated with M. We compute the matrix B<sup>N</sup> (i, j), where B (i, j) is an infinite matrix whose the nonzero entries are on the diagonals m − n = i or m − n = j. Next among other things we consider the infinite boolean
matrix B<sup>+</sup><sub>∞</sub> that have infinitely many diagonals with nonzero entries and we explicitly calculate (B<sup>+</sup><sub>∞</sub>)<sup>N</sup>. Finally we give necessary and sufficient conditions for an infinite matrix M to map c (B<sup>N</sup> (i, 0)) to c.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665212010TRADING DEGREE FOR DIMENSION IN THE SECTION CONJECTURE: THE NON-ABELIAN SHAPIRO LEMMAENJakobStix<p>This note aims at providing evidence for the section conjecture of anabelian geometry by establishing its behaviour under Weil restriction of scalars. In particular, the étale fundamental group of the Weil restriction is determined by means of a Shapiro Lemma for nonabelian group cohomology.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665212010ON GENERALIZED EPI-PROJECTIVE MODULESENDerya KeskinTütüncüYosukeKuratomi<p>A module M is said to be generalized N-projective (or N-dual ojective) if, for any epimorphism g : N → X and any homomorphism f : M → X, there exist decompositions M = M<sub>1</sub> ⊕ M<sub>2</sub>, N = N<sub>1</sub> ⊕ N<sub>2</sub>, a homomorphism h<sub>1</sub> : M<sub>1</sub> → N<sub>1</sub> and an epimorphism h<sub>2</sub> : N<sub>2</sub> → M<sub>2</sub> such that g ◦ h<sub>1</sub> = f|<sub>M<sub>1</sub></sub> and f ◦ h<sub>2</sub> = g|<sub>N<sub>2</sub></sub> . This relative projectivity is very useful for the study on direct sums of lifting modules (cf. [5], [7]). In the definition, it should be noted that we may often consider the case when f to be an epimorphism. By this reason, in this paper we define relative (strongly) generalized epi-projective modules and show several results on this generalized epi-projectivity. We apply our results to the known problem when finite direct sums M<sub>1</sub>⊕· · ·⊕M<sub>n</sub> of lifting modules M<sub>i</sub> (i = 1, · · · , n) is lifting.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665212010A NOTE ON QUASI-ARMENDARIZ RINGSENLiuZhongkuiZhangWenhui<p>A ring R is called a quasi-Armendariz ring if whenever elements α = a<sub>0</sub>+a<sub>1</sub>x+a<sub>2</sub>x<sup>2</sup>+· · ·+a<sub>n</sub>x<sup>n</sup>, β = b<sub>0</sub>+b<sub>1</sub>x+b<sub>2</sub>x<sup>2</sup>+· · ·+b<sub>m</sub>x<sup>m</sup>
∈ R[x] satisfy αR[x]β = 0, then a<sub>i</sub>Rb<sub>j</sub> = 0 for each i, j. In this note we consider quasi-Armendariz property of a special subring of the infinite upper triangular matrix ring over a ring R.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665212010ON SELF MAPS OF HP<sup>n</sup> FOR n = 4 AND 5ENKazuyoshiKatōgi<p>We determine the cardinality of the set of the homotopy classes of self maps of HP<sup>4</sup> with degree 0. And we shall determine the nilpotency of HP<sup>5</sup>.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665212010EXPONENTIAL GENERALIZED DISTRIBUTIONSENM.GordonL.Loura<p>In this paper we generalize the Fourier transform from the space of tempered distributions to a bigger space called exponential generalized distributions. For that purpose we replace the Schwartz space S by a smaller space X<sub>0</sub> of smooth functions such that, among other properties, decay at infinity faster than any exponential. The construction of X<sub>0</sub> is such that this space of test functions is closed for derivatives, for Fourier transform and for translations. We equip X<sub>0</sub> with an appropriate locally convex topology and we study it’s dual X'<sub>0</sub>; we call X′<sub>0</sub> the space of exponential generalized distributions. The space X′<sub>0</sub> contains all the Schwartz tempered distributions, is closed for derivatives, and both, translations and Fourier transform, are vector and topological automorphisms in X′<sub>0</sub>. As non trivial examples of elements
in X′<sub>0</sub>, we show that some multipole series appearing in physics are
convergent in this space.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665212010BELYI FUNCTION ON X<sub>0</sub>(49) OF DEGREE 7ENKenjiHoshinoHiroakiNakamuraNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665212010A GENERAL INEQUALITY FOR DOUBLY WARPED PRODUCT SUBMANIFOLDSENAndreeaOlteanu<p>In this paper, we consider doubly warped product manifolds and we establish a general inequality for doubly warped products isometrically immersed in arbitrary Riemannian manifolds. Some aplications are derived.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665212010THE BELYI FUNCTIONS AND DESSIN D’ENFANTS CORRESPONDING TO THE NON-NORMAL INCLUSIONS OF TRIANGLE GROUPSENKenjiHoshino<p>We present the Belyi functions, dessin d’enfants, and monodromy permutations corresponding to the non-normal inclusions of triangle groups.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665212010SERIALLY COALESCENT CLASSES OF LIE ALGEBRASENMasanobuHondaTakanoriSakamoto<p>We introduce the concept of serially coalescent classes of Lie algebras corresponding to those of coalescent classes and ascendantly coalescent
classes. We show that the class of finite-dimensional and nilpotent, the class of finite-dimensional and the class of finite-dimensional and soluble Lie algebras, are serially coalescent classes for locally finite Lie algebras over any field of characteristic zero. We also introduce the
concept of locally serially coalescent classes of Lie algebras and find some
locally serially coalescent classes for locally finite Lie algebras.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665212010SOME APPLICATIONS OF DIFFERENTIAL SUBORDINATION FOR A GENERAL CLASS OF MULTIVALENTLY ANALYTIC FUNCTIONS INVOLVING A CONVOLUTION STRUCTUREENJ. K.PrajapatR. K.Raina<p>In the present paper we investigate a class of multivalently analytic functions which essentially involves a Hadamard product of two multivalent functions. We apply the techniques of differential subordination and derive some useful characteristics of this function class. The
applications to generalized hypergeometric functions and various consequences of the main results exhibiting also relevant connections with
some of the known (and new) results (including also an improved version
of a known result) are also pointed out.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665112009COMMUTATIVE GROUP ALGEBRAS OF ABELIAN GROUPS WITH UNCOUNTABLE POWERS AND LENGTHSENPeterDanchev<p>Let F be a field of char(F) = p > 0 and G an abelian group
with p-component G<sub>p</sub> of cardinality at most ℵ<sub>1</sub> and length at most ω<sub>1</sub>. The main affirmation on the Direct Factor Problem is that S(FG)/G<sub>p</sub> is totally projective whenever F is perfect. This extends results due to May (Contemp. Math., 1989) and Hill-Ullery (Proc. Amer. Math. Soc., 1990). As applications to the Isomorphism Problem, suppose that for any group H the F-isomorphism FH ≅ FG holds. Then if G<sub>p</sub> is totally projective, H<sub>p</sub> ≅ G<sub>p</sub>. This partially solves a problem posed by May (Proc. Amer. Math. Soc., 1988). In particular, H ≅ G provided G is
p-mixed of torsion-free rank one so that G<sub>p</sub> is totally projective. The same isomorphism H ≅ G is fulfilled when G is p-local algebraically compact too. Besides if F<sub>p</sub> is the simple field with p-elements and G<sub>p</sub> F<sub>p</sub>H
is a coproduct of torsion complete groups, F<sub>p</sub>H ≅ F<sub>p</sub>G as F<sub>p</sub> F<sub>p</sub>-algebras implies H<sub>p</sub> ≅ G<sub>p</sub>. This expands the central theorem obtained by us in (Rend. Sem. Mat. Univ. Padova, 1999) and partly settles the generalized version of a question raised by May (Proc. Amer. Math. Soc.,1979) as well. As a consequence, when G<sub>p</sub> is torsion complete and G is p-mixed of torsion-free rank one, H ≅ G. Moreover, if G is a coproduct of p-local algebraically compact groups then H ≅ G. The last
attainment enlarges an assertion of Beers-Richman-Walker (Rend. Sem. Mat. Univ. Padova, 1983).
Each of the reported achievements strengthens our statements in this direction (Southeast Asian Bull. Math., 2001-2002) and also continues own studies in this aspect (Hokkaido Math. J., 2000) and (Kyungpook Math. J., 2004).</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665112009NAKAYAMA ISOMORPHISMS FOR THE MAXIMAL QUOTIENT RING OF A LEFT HARADA RINGENKazuakiNonomura<p>From several results of Kado and Oshiro, we see that if
the maximal quotient ring of a given left Harada ring R of type (*) has a Nakayama automorphism, then R has a Nakayama isomorphism. This result poses a question whether if the maximal quotient ring of a given left Harada ring R has a Nakayama isomorphism, then R has a
Nakayama isomorphism. In this paper, we shall show that a basic ring of the maximal quotient ring of a given Harada ring has a Nakayama isomorphism if and only if its Harada ring has a Nakayama isomorphism.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665112009SOME IDENTITIES RELATING MOCK THETA FUNCTIONS WHICH ARE DERIVED FROM DENOMINATOR IDENTITYENYukariSanada<p>We show that there exists a new connection between identities satisfied by mock theta functions and special case of denominator identities for affine Lie superalgebras.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665112009THE SPACE L<sub>q</sub> OF DOUBLE SEQUENCESENFeyziBasarYurdalSever<p>The spaces BS, BS(t), CS<sub>p</sub>, CS<sub>bp</sub>, CS<sub>r</sub> and BV of double
sequences have recently been studied by Altay and Ba¸sar [J. Math. Anal. Appl. 309(1)(2005), 70–90]. In this work, following Altay and Ba¸sar [1], we introduce the Banach space L<sub>q</sub> of double sequences corresponding to the well-known space ℓ<sub>q</sub> of single sequences and examine some properties
of the space L<sub>q</sub>. Furthermore, we determine the β(υ)-dual of the space
and establish that the α- and γ-duals of the space L<sub>q</sub> coincide with the β(υ)-dual; where 1 ≤ q < ∞ and υ 2 {p, bp, r}.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665112009ON THE FUNDAMENTAL GROUPS OF LOG CONFIGURATION SCHEMESENYuichiroHoshi<p>In the present paper, we study the cuspidalization problem for the fundamental group of a curve by means of the log geometry of the log configuration scheme, which is a natural compactification of the usual configuration space of the curve. The goal of this paper is to show
that the fundamental group of the configuration space is generated by the images from morphisms from a group extension of the fundamental groups of the configuration spaces of lower dimension, and that the fundamental group of the configuration space can be partially reconstructed from a collection of data concerning the fundamental groups of the configuration spaces of lower dimension.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665112009LINKAGE AND DUALITY OF MODULESENKenjiNishida<p>Martsinkovsky and Strooker [13] recently introduced module theoretic linkage using syzygy and transpose. This generalization brings possibility of much application of linkage, especially, to homological
theory of modules. In the present paper, we connect linkage of modules to certain duality of modules. We deal with Gorenstein dimension, Cohen-Macaulay modules over a Gorenstein local ring using linkage and generalize the results to non-commutative algebras.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665112009ON ι-ADIC ITERATED INTEGRALS, IV -Ramification and generators of Galois actions on fundamental groups and torsors of pathsENZdzislawWojtkowiak<p>We are studying Galois representations on fundamental groups and on torsors of paths of a projective line minus a finite number of points. We reprove by explicit calculations some known results about
ramification properties of such representations. We calculate the number
of generators in degree 1 of the images of these Galois representations. We show also that the number of linearly independent generators in degree greater than 1 is equal &franc12 φ(n) for the action of G<sub>Q(μ5)</sub> on the fundamental group of P<sup>1</sup><sub>¯Q</sub>
\ ({0,∞} ∪ μ<sub>n</sub>). Finally we show that the graded Lie algebra associated with the action of G<sub>Q(μ5)</sub> on the fundamental
group of P<sup>1</sup><sub>¯Q</sub>
\ ({0,∞} ∪ μ<sub>5</sub>) is not free.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665112009ON THE JORDAN DECOMPOSITION OF TENSORED MATRICES OF JORDAN CANONICAL FORMSENKei-ichiroIimaRyoIwamatsu<p>Let κ be an algebraically closed field of characteristic p ≥ 0. We shall consider the problem of finding out a Jordan canonical form of
J(α , s)⊗<sub>κ</sub>J(β , t), where J(α, s) means the Jordan block with eigenvalue
α ∈ κ and size s.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665112009RADIAL HEAT OPERATORS ON JACOBI-LIKE FORMSENMinHoLEE<p>We consider a differential operator D<sup>X</sup> <sub>λ</sub> associated to an
integer λ acting on the space of formal power series, which may be
regarded as the heat operator with respect to the radial coordinate in the 2λ-dimensional space for λ > 0. We show that D<sup>X</sup> <sub>λ</sub> carries Jacobilike
forms of weight λ to ones of weight λ+2 and obtain the formula for the m-fold composite (D<sup>X</sup> <sub>λ</sub> )<sup>[m]</sup> of such operators. We then determine the
corresponding operators on modular series and as well as on automorphic pseudodifferential operators.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665112009LOCALLY AND COLOCALLY FACTORABLE BANACH SPACESENF. B.H.JamjoomH. M.Jebreen<p>We generalize the concept of locality (resp. colocality) to the concept of locally factorable (resp. colocally factorable) such that Theorem 2 of [2] and Theorems 1.7 and 1.16 of [11] are still valid for the new concepts. In addition we show that locally factorable and colocally factorable are inherited by complemented subspace, then we present some examples and establish relations between locally factorable and colocally factorable. We prove some relations between being finitely (resp. cofinitely) represented in a Banach space and being locally factorable (resp. colocally factorable) some family of finite dimensional Banach spaces.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665112009A NOTE ON CERTAIN METRICS ON R<sup>4</sup><sub>+</sub>ENTominosukeOtsukiNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665112009ON LIE IDEALS AND LEFT JORDAN σ-CENTRALIZERS OF 2-TORSION-FREE RINGSENWagnerCortesClausHaetinger<p>B. Zalar proved that any left (resp. right) Jordan centralizer on a 2-torsion-free semiprime ring is a left (resp. right) centralizer. We prove this question changing the semiprimality condition on R. The main result of this paper is the following. Let R be a 2-torsionfree ring which has a commutator right (resp. left) nonzero divisor and
let G: R → R be left (resp. right) Jordan σ-centralizer mapping of , where σ is an automorphism of R. Then G is a left (resp. right) -centralizer mapping of R.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665112009A NOTE ON ALMOST INJECTIVE MODULESENAdelAlahmadiSurender K.Jain<p>We give some new properties of almost injective modules and their endomorphism rings, and also provide conditions as to when a direct sum of almost injective (or CS) modules is again almost injective (or CS) in some special cases..</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665112009MULTIPLE POISSON KERNELSENMauroSpreaficoNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665012008Strong Convergence Theorems for Nonexpansive Mappings by Viscosity Approximation Methods in Banach SpacesENXiaolongQinYongfuSuChangqunWu<p>In this paper, we introduce a modified Ishikawa iterative process for a pair of nonexpansive mappings and obtain a strong convergence theorem in the framework of uniformly Banach spaces. Our results improve and extend the recent ones announced by Kim and Xu [T.H. Kim, H.K. Xu, Strong convergence of modified Mann iterations, Nonlinear Anal. 61 (2005) 51-60], Xu [H.K. Xu, Viscosity approximation methods for nonexpansive mappings. J. Math. Anal. Appl. 298 (2004) 279-291] and some others.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665012008On Unit Groups of Completely Primary Finite RingsENChiteng'a JohnChikunji<p>Let R be a commutative completely primary finite ring with the unique maximal ideal J such that J3 = (0) and J2 ≠ (0): Then R⁄J ≅ GF(pr) and the characteristic of R is pk, where 1 ≤ k ≤ 3, for
some prime p and positive integers k, r. Let Ro = GR (pkr,pk) be a galois subring of R so that R = Ro ⊕ U ⊕ V ⊕ W, where U, V and W are finitely generated Ro-modules. Let non-negative integers s, t and be numbers of elements in the generating sets for U, V and W, respectively. In this work, we determine the structure of the subgroup 1+W of the unit group R* in general, and the structure of the unit group R* of R when s = 3, t = 1; ≥ 1 and characteristic of R is p. We then generalize the solution of the cases when s = 2, t = 1; t = s(s +1)⁄2 for a fixed s; for all the characteristics of R ; and when s = 2, t = 2, and characteristic of R is p to the case when the annihilator ann(J ) = J2 + W, so that ≥ 1. This complements the author's earlier solution of the problem in the case when the annihilator of the radical coincides with the square of the radical.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665012008K-semimetrizabilities and C-stratifiabilities of SpacesENIwaoYoshiokaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665012008A New Class of Quasicyclic Complex Vector Functional EquationsENIce B.Risteski<p>For the first time in the literature a quasicyclic complex vector functional equation is introduced in the present paper. By a matrix method the general quasicyclic complex vector functional equation is solved, as well as its particular case for n = 3. This case is completely solved in an explicit form, and for every step of the solution examples are provided. Using a simple spectral property of compound matrices, a necessary and sufficient condition for stability of the quasicyclic complex vector functional equation considered is proved.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665012008On Φ-recurrent N(k)-contact Metric ManifoldsENUday ChandDeAboul KalamGazi<p>In this paper we prove that a Φ-recurrent N(k)-contact metric manifold is an η-Einstein manifold with constant coefficients. Next, we prove that a 3-dimensional Φ-recurrent N(k)-contact metric manifold
is of constant curvature. The existence of a Φ-recurrent N(k)-contact metric manifold is also proved.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665012008Imaginary Quadratic Fields whose Exponents are Less Than or Equal To TwoENKenichiShimizu<p>We give a necessary condition for an imaginary quadratic
field to have exponent less than or equal to two. Further we discuss relations of this condition with other necessary conditions studied by Möller and Mollin, and conjecture that these conditions are equivalent.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665012008On Fox Spaces and Jacobi IdentitiesENMarekGolasinskiDaciberg LimaGonçalvesPeterWong<p>In 1945, R. Fox introduced the so-called Fox torus homo-
topy groups in which the usual homotopy groups are embedded and their Whitehead products are expressed as commutators. A modern treatment of Fox torus homotopy groups and their generalization has been given and studied. In this note, we further explore these groups
and their properties. We discuss co-multiplications on Fox spaces and Jacobi identities for the generalized Whitehead products and the T- Whitehead products.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665012008On Central Gap Numbers of Symmetric GroupsENHirotakakikyo<p>g(G) denotes the central gap number of a group G. We
show that for n ≥ 8, g(Sn) ≥ n and g(An) ≥ n-2. We give exact values of g(Sn) and g(An) for small n's. In particular, g(S9) = 9 and g(A9) = 7. Therefore, for any positive integer n ≠ 1, 3, 5 there is a group G such that n = g(G). G can be finite or infinite.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665012008A Lower Bound for the Rational LS-category of a Coformal Elliptic SpaceENToshihiroYamaguchi<p>We give a lower bound for the rational LS-category of certain spaces, including the coformal elliptic ones, in terms of the dimension of its total rational cohomology.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665012008The Fine Spectra of the Cesàro Operator C 1 over the Sequence Space bvp, (1 ≤ p ∞)ENAli M.AkhmedovFeyziBasar<p>The sequence space bvp consisting of all sequences (xk) such that (xk - xk-1) in the sequence space lp has recently been introduced by Basar and Altay [Ukrainian Math. J. 55(1)(2003), 136-147]; where 1 ≤ p ≤ ∞. In the present paper, the norm of the Cesàro operator C1 acting on the sequence space bvp has been found and the fine spectrum of the Cesàro operator C1 over the sequence space bvp has been determined, where 1 ≤ p < ∞.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665012008Inverse Limits of Spaces with the Weak B-PropertyENZhaoBinNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664912007A Generalized Primitive Element TheoremENDirceuBagioAntonioPaques<p>We deal with the following variant of the primitive element theorem: any commutative strongly separable extension of a commutative ring can be embedded in another one having primitive element. This statement holds for connected strongly separable extension of commutative rings which are either local or connected semilocal. We show that it holds for a more general family of rings, that is, for connected commutative rings whose quotient ring by the corresponding Jacobson radical is von Neumann regular and locally uniform. Some properties of the (connected) separable closure of such rings are also given as an application of this result.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664912007A Characterization of δ-quasi-Baer RingsENEbrahimHashemi<p>Let δ be a derivation on R. A ring R is called δ-quasi-Baer (resp. quasi-Baer) if the right annihilator of every δ-ideal (resp. ideal) of R is generated by an idempotent of R. In this note first we give a positive answer to the question posed in Han et al. [7], then we show that R is δ-quasi-Baer iff the differential polynomial ring S = R[x; δ] is quasi-Baer iff S is δ‾-quasi-Baer for every extended derivation δ‾ on S of δ. This results is a generalization of Han et al. [7], to the case where R
is not assumed to be δ-semiprime.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664912007Galois Covers of Degree p and Semi-stable Reduction of Curves in Equal Characteristic p>0ENMohamedSaïdi<p>In this paper we study the semi-stable reduction of Galois covers of degree p above curves over a complete discrete valuation ring of equal characteristic p.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664912007Evaluation of the Convolution Sums ∑ l+24m=n σ(l) σ(m) and ∑ 3l+8m=n σ(l) σ(m)ENAyseAlacaSabanAlacaKenneth S.WilliamsNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664912007Elliptic Curves y²=x³-px of Rank TwoENBlair K.Spearman<p>A class of prime numbers p is given for which the elliptic curve y² =x³-px has rank two. This extends a theorem of Kudo and Motose.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664912007Cut Loci and Distance FunctionsENJin-ichiItohTakashiSakaiNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664912007Generalized Derivations with Commutativity and Anti-commutativity ConditionsENHoward E.BellNadeem-urRehman<p>Let R be a prime ring with 1, with char(R) ≠ 2; and let F : R → R be a generalized derivation. We determine when one of the following holds for all x,y ∈ R: (i) [F(x); F(y)] = 0; (ii) F(x)ΟF(y) = 0;
(iii) F(x) Ο F(y) = x Ο y .</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664912007Privalov Space on the Upper Half PlaneENYasuoIida<p>In this paper, we shall consider Privalov space Np 0 (D) (p > 1) which consists of holomorphic functions f on the upper half plane D := {z ∈ C|Imz > 0} such that (log+ |f(z)|)p has a harmonic majorant on D. We shall give some properties of Np 0 (D).</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664912007Character Values and Dade's ConjectureENRyoNarasakiNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664912007Some Questions on the Ideal Class Group of Imaginary Abelian FieldsENTsuyoshiItoh<p>Let k be an imaginary quadratic field. Assume that the
class number of k is exactly an odd prime number p, and p splits into two distinct primes in k. Then it is known that a prime ideal lying above p is not principal. In the present paper, we shall consider a question whether a similar result holds when the class number of k is 2p. We
also consider an analogous question for the case that k is an imaginary quartic abelian field.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664912007Some Results on (σ,τ)-Lie IdealsENEvrimGüvenKazimKayaMuharremSoytürk<p>In this note we give some basic results on one sided(σ,τ)-Lie ideals of prime rings with characteristic not 2.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664912007On Ideals and Orthogonal Generalized Derivations of Semiprime RingsENEmineAlbas<p>In this paper, some results concerning orthogonal generalized derivations are generalized for a nonzero ideal of a semiprime ring. These results are a generalization of results of M. Brešar and J. Vukman
in [3], which are related to a theorem of E. Posner for the product of derivations on a prime ring.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664912007Higher Weights of Codes from Projective Planes and BiplanesENSteven T.DoughertyReshmaRamadurai<p>We study the higher weights of codes formed from planes
and biplanes. We relate the higher weights of the Hull and the code of a plane and biplane. We determine all higher weight enumerators of planes and biplanes of order less or equal to 4.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664912007Sums and Partial Sums of Double Power Series associated with the Generalized Zeta Function and Their N-fractional CalculusSums and Partial Sums of Double Power Series associated with the Generalized Zeta Function and Their N-fractional CalculusENMaged G.Bin-Saad<p>An attempt is made here to introduce and study a pair of
double power series associated with the generalized zeta function due to Erdélyi Φ(x; z; a) together with related sums, integral representations,
generating relations and N-fractional calculus. A number of (known and
new) results shown to follow as special cases of our theorems.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664812006Self-homotopy of the Double Suspension of the Real 7-projective SpaceENToshiyukiMiyauchi<p>We determine the group structure of the self-homotopy set of the double suspension of the real 7-dimensionnal projective space.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664812006Stickelberger Ideals and Normal Bases of Rings of p-integersENHumioIchimuraNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664812006Multipliers and Cyclic Vectors on the Weighted Bloch SpaceENShanliYeNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664812006Characterization of Frobenius Groups of Special TypeENArun S.Muktibodh<p>We define a Con-Cos group G to be one having a proper
normal subgroup N whose cosets other than N itself are conjugacy classes. It follows easily that N = G’, the derived group of G. Most of the paper is devoted to trying to classify finite Con-Cos groups satisfying the additional requirement that N has just two conjugacy classes. We show that for such groups the center Z(G) has order at most 2, and if Z(G) = {1}, then G is a Frobenius group of a rather special type.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664812006On Higher Syzygies of Projective Toric VarietiesENShoetsuOgata<p>Let A be an ample line bundle on a projective toric variety X of dimension n (≥ 2). It is known that the d-th tensor power A⊗d embedds X as a projectively normal variety in Pr := P(H0(X,L⊗d)) if d ≥ n − 1. In this paper first we show that when dimX = 2 the line bundle A⊗d satisfies the property Np for p ≤ 3d − 3. Second we show that when dimX = n ≥ 3 the bundle A⊗d satisfies the property Np for p ≤ d − n + 2 and d ≥ n − 1.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664812006The Prime Ideal Factorization of 2 in Pure Quartic Fields with Index 2ENBlair K.SpearmanKenneth S.Williams<p>The prime ideal decomposition of 2 in a pure quartic field with field index 2 is determined explicitly.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664812006Bott's Theorem on Samelson ProductsENKeiSugataNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664812006The Geometry and Topology on Grassmann ManifoldsENZhouJianwei<p>This paper shows that the Grassmann Manifolds GF(n,N)
can all be imbedded in an Euclidean space MF(N) naturally and the imbedding can be realized by the eigenfunctions of Laplacian Δ on GF(n,N). They are all minimal submanifolds in some spheres of MF(N) respectively. Using these imbeddings, we construct some degenerate Morse functions on Grassmann Manifolds, show that the homology of
the complex and quaternion Grassmann Manifolds can be computed easily.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664812006Some Homotopy Groups of Homogeneous SpacesENTomohisaInoue<p>The symplectic group is embedded in the rotation group
and the quotient set equipped with the identification topology is a homogeneous space. The purpose of this paper is to determine some homotopy groups of the homogeneous space. Exact sequences induced from fibrations are frequently used, and homotopy groups of Lie groups and other homogeneous spaces which are obtained by several authors are referred heavily.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664812006Mutually Orthogonal Latin Squares and Self-complementary DesignsENHiroyukiNakasora<p>Suppose that n is even and a set of n/2 -1 mutually orthogonal
Latin squares of order n exists. Then we can construct a strongly
regular graph with parameters (n², n/2 (n-1), n/2 ( n/2-1), n/2 ( n/2 -1)), which
is called a Latin square graph. In this paper, we give a sufficient condition
of the Latin square graph for the existence of a projective plane of
order n. For the existence of a Latin square graph under the condition,
we will introduce and consider a self-complementary 2-design (allowing
repeated blocks) with parameters (n, n/2 , n/2 ( n/2 -1)). For n ≡ 2 (mod 4),
we give a proof of the non-existence of the design.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664812006Almost Periodic Solutions of C-well-posed Evolution EquationsENNguyen VanMinh<p>This paper is concerned with the existence and uniqueness of almost periodic mild solutions of evolution equations of the form u(t) = Au(t) + ƒ(t) where A is the generator of a holomorphic Csemigroup on a Banach space and ƒ is an almost periodic function. A sufficient condition in terms of spectral properties of A and ƒ is obtained that extends a well known result in this subject.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664812006On Regular Rings Satisfying Weak Chain ConditionENMamoruKutami<p>In this paper, we shall study regular rings satisfying weak chain condition. As main results, we show that regular rings satisfying weak chain condition are unit-regular, and show that these rings have the unperforation and power cancellation properties for the family of finitely generated projective modules.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664812006A New Generalization of the Poisson KernelENSerapBulut<p>The purpose of this paper is to give a new generalization of the Poisson Kernel in two dimensions and discuss an integral formula for this.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664812006Global Solvably Closed Anabelian GeometryENShinichiMochizuki<p>In this paper, we study the pro-Σ anabelian geometry of hyperbolic curves, where Σ is a nonempty set of prime numbers, over Galois groups of “solvably closed extensions” of number fields — i.e., infinite extensions of number fields which have no nontrivial abelian extensions. The main results of this paper are, in essence, immediate corollaries of the following three ingredients: (a) classical results concerning the structure of Galois groups of number fields; (b) an anabelian result of Uchida concerning Galois groups of solvably closed extensions of number fields; (c) a previous result of the author concerning the pro-Σ anabelian geometry of hyperbolic curves over nonarchimedean local fields.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664812006Note on the Vector-valued Cohomology Equation f=ho T-hENShigeruHasegawaRyotaroSatoNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664812006New Ultimate Boundedness and Periodicity Results for Certain Third-order Nonlinear Vector Differential EquationsENCemilTuncErcanTunc<p>The principle aim of this paper is to present some new
results related to the ultimate boundedness and existence of periodic of solutions a certain non-linear ordinary vector differential equation of third order. Our results improve some well-known results in the literature.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664812006On Euclidean AlgorithmENKaoruMotoseNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664812006Quaternionic Line Bundles over Quaternionic Projective SpacesENDaciberg L.GoncalvesMauroSpreaficoNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664712005Connective Coverings of a Few Cell ComplexesENKohheiYamaguchi<p>We shall determine the 2-connective coverings of a few cell complexes of the form S<sup>2</sup> ∪f e<sup>n</sup> for n ≥ 4 and 0 ≠ f ∈ π<sub>n-1</sub>(S<sup>2</sup>).</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664712005Appendix to ``Some Metric Invariants of Spheres and Alexandrov Spaces II''ENKazuyoshiKiyoharaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664712005Dihedral Quintic Fields with a Power BasisENMelissa J.LavalleeBlair K.SpearmanKenneth S.WilliamsQiduanYang<p>It is shown that there exist infinitely many dihedral quintic fields with a power basis.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664712005On Group Structures of Some Special Elliptic CurvesENTakehiroKudoKaoruMotoseNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664712005A Lower Bound for the LS Category of a Formal Elliptic SpaceENYasusukeKotaniToshihiroYamaguchi<p>We give a lower bound for the LS category of a formal elliptic space in terms of its rational cohomology.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664712005A Note on Quotients of Orthogonal GroupsENAkihiroOhsita<p>We discuss the mod 2 cohomology of the quotient of a compact classical Lie group by its maximal 2-torus. In particular, the case of the orthogonal group is treated. The case of the spinor group is not included.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664712005Ramanujan's Sums and Cyclotomic PolynomialsENKaoruMotoseNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664712005Some Metric Invariants of Spheres and Alexandrov Spaces IIENNobuyukiSochi<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([So]). And the borderline case when a<sub>2p-1</sub>(X) = a<sub>2p-1</sub>(S<sup>n</sup>) and a<sub>k</sub>(S<sup>n</sup>) are studied.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664712005Quadratic Twists of an Elliptic Curve and Maps from a Hyperelliptic CurveENMasatoKuwata<p>For an elliptic curve E over a number field k, we look for a polynomial f(t) such that rankE<sup>f(t)</sup>(k(t)) is at least 3. To do so, we construct a family of hyperelliptic curves C : s² = f(t) over k of genus 3
such that J(C) is isogenous to E<sub>1</sub> × E<sub>2</sub> × E<sub>3</sub>, and we give an example of C and E such that J(C) is isogenous to E × E × E over Q(√−3).</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664712005Modifications of the Limited Memory BFGS Algorithm for Large-scale Nonlinear OptimizationENLeong WahJuneMalik AbuHassan<p>In this paper we present two new numerical methods for unconstrained large-scale optimization. These methods apply update formulae, which are derived by considering different techniques of approximating the objective function. Theoretical analysis is given to show the advantages of using these update formulae. It is observed that these update formulae can be employed within the framework of limited memory strategy with only a modest increase in the linear algebra cost. Comparative results with limited memory BFGS (L-BFGS) method are presented.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664712005The Spiegelungssatz for p=5 from a Constructive ApproachENYasuhiroKishi<p>We describe explicitly the relation between the 5-ranks of the ideal class groups of two quadratic fields with conductors m and 5m, respectively, and that of the associated cyclic quartic field.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664712005Belyi Function whose Grothendieck Dessin is a Flower Tree with Two Ramification IndicesENToruKomatsu<p>In this paper we present an explicit construction of Belyi functions whose dessins are flower trees (i.e., graphs of diameter 4) with two ramification indices. We also give a method for obtaining Belyi functions defined over the moduli fields of the dessins.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664712005Symplectic Invariants Arising from a Grassmann Quotient and Trivalent GraphsENHirokiAkazawa<p>In this paper, we study the sp-invariant graded algebra arising in a specific quotient of a Grassmann algebra, and identify it with an algebra generated by trivalent graphs.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664712005Unit Groups of a Certain Class of Completely Primary Finite RingsENChiteng’a JohnChikunji<p>A completely primary finite ring is a ring R with identity 1 ≠ 0 whose subset of all its zero-divisors forms the unique maximal ideal J. Let R be a commutative completely primary finite ring with the unique maximal ideal J such that J<sup>3</sup> = (0) and J<sup>2</sup> ≠ (0). Then R/J ≒ GF(ρ<sup>γ</sup>) and the characteristic of R is ρ<sup>γ</sup>, where 1 ≤ k ≤ 3, for
some prime ρ and positive integer γ. Let R<sub>o</sub> = GR(p<sup>kr</sup>, p<sup>k</sup>) be a Galois
subring of R and let the annihilator of J be J<sup>2</sup> so that R = R<sub>o</sub> ⊕U ⊕V , where U and V are finitely generated R<sub>o</sub>-modules. Let non-gative
integers s and t be numbers of elements in the generating sets for U and V , respectively. When s = 2, t = 1 and the characteristic of R is p<sup>2</sup> and p<sup>3</sup>; and when s = 2, t = 2 and the characteristic of R is p, the structure of the group of units R<sup>*</sup> of the ring R and its generators have been determined; these depend on the structural matrices (a<sup>l</sup><sub>ij</sub>) and on
the parameters p, k, r, s and t.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664712005The Galois Action on the Torsor of Homotopy Classes of Paths on a Projective Line minus a Finite Number of PointsENZdzisÃlawWojtkowiakNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664712005Derivations and Automorphisms on the Algebra of Non-commutative Power SeriesENKentaroIhara<p><Motivated by the study of multiple zeta values, we discuss several linear operators on the algebra of non-commutative formal power series k<<x,y>> over a field k of characteristic zero. Especially a family of derivations whose elements commute with each other is defined and automorphisms which correspond to these derivations via exponential map are described explicitly./p></p>
No potential conflict of interest relevant to this article was reported.