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 Okayama0030-15666012018Tomita-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 Okayama0030-15666012018Absolute 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 Okayama0030-15666012018Stable 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 Okayama0030-15666012018Primary 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 Okayama0030-15666012018A 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 Okayama0030-15666012018A 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 Okayama0030-15666012018Arithmetic 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 Okayama0030-15666012018An 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 Okayama0030-15666012018Indecomposability 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 Okayama0030-15666012018Necessary 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 Okayama0030-15666012018A 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 Okayama0030-15666012018On 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 ƒÕ-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 Okayama0030-15666112019On 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 fƒÅ : YƒÅ ¨ XƒÅ 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 Okayama0030-15666112019Berezin-Weyl quantization of Heisenberg motion groups1935ENBenjaminCahenDLepartement de mathLematiques UniversitLe de Lorraine We introduce a SchrNodinger 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 Okayama0030-15666112019Reconstruction 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 Okayama0030-15666112019On 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 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 Okayama0030-15666112019Complex 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 Okayama0030-15666112019A 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 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 Okayama0030-15666112019The 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 Okayama0030-15666112019On 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 Okayama0030-15666112019Passage of property (Bw) from two operators to their tensor product187198ENM.H.M.RashidDepartment of Mathematics& Statistics Faculty of Science P.O.Box(7) Muftah 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 Okayama0030-15666112019Terwilliger 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 Okayama0030-15666212020A 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 Okayama0030-15666212020Unstable higher Toda brackets2786ENHideakiOshimaIbaraki UniversityKatsumiOshimaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666212020Crystal 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 Kashiwarafs 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 Okayama0030-15666212020Analytic 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 Okayama0030-15666212020Existence 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 Okayama0030-15666312021On the stability, boundedness, and square integrability of solutions of third order neutral delay differential equations114ENJohn R.GraefDepartment of Mathematics, University of Tennessee at ChattanoogaDjamilaBeldjerdOranfs High School of Electrical Engineering and EnergeticsMoussadekRemiliDepartment of Mathematics, University of Oran 1 Ahmed Ben BellaIn this paper, sufficient conditions are established for the stability, boundedness and square integrability of solutions for some non-linear neutral delay differential equations of third order. Lyapunovfs direct method is used to obtain the results.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666312021Differential geometry of invariant surfaces in simply isotropic and pseudo-isotropic spaces1552ENLuiz C. B.da SilvaDepartment of Physics of Complex Systems, Weizmann Institute of ScienceWe study invariant surfaces generated by one-parameter subgroups of simply and pseudo isotropic rigid motions. Basically, the simply and pseudo isotropic geometries are the study of a three-dimensional space equipped with a rank 2 metric of index zero and one, respectively. We show that the one-parameter subgroups of isotropic rigid motions lead to seven types of invariant surfaces, which then generalizes the study of revolution and helicoidal surfaces in Euclidean and Lorentzian spaces to the context of singular metrics. After computing the two fundamental forms of these surfaces and their Gaussian and mean curvatures, we solve the corresponding problem of prescribed curvature for invariant surfaces whose generating curves lie on a plane containing the degenerated direction.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666312021Remark on a Paper by Izadi and Baghalaghdam about Cubes and Fifth Powers Sums5360ENGakuIokibeDepartment of Mathematics, Graduate School of Science, Osaka University In this paper, we refine the method introduced by Izadi and Baghalaghdam to search integer solutions to the Diophantine equation<img src="http://www.lib.okayama-u.ac.jp/www/mjou/mjou_63_53.png">. We show that the Diophantine equation has infinitely many positive solutions.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666312021Defining relations of 3-dimensional quadratic AS-regular algebras6186ENAyakoItabaDepartment of Mathematics, faculty of Science, Tokyo University of ScienceMasakiMatsunoGraduate School of Science and Technology, Shizuoka UniversityClassification of AS-regular algebras is one of the main interests in non-commutative algebraic geometry. Recently, a complete list of superpotentials (defining relations) of all 3-dimensional AS-regular algebras which are Calabi-Yau was given by Mori-Smith (the quadratic case) and Mori-Ueyama (the cubic case), however, no complete list of defining relations of all 3-dimensional AS-regular algebras has not appeared in the literature. In this paper, we give all possible defining relations of 3-dimensional quadratic AS-regular algebras. Moreover, we classify them up to isomorphism and up to graded Morita equivalence in terms of their defining relations in the case that their point schemes are not elliptic curves. In the case that their point schemes are elliptic curves, we give conditions for isomorphism and graded Morita equivalence in terms of geometric data.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666312021A weak Euler formula for l-adic Galois double zeta values87105ENWojtkowiakZdzisławUniversité de Nice-Sophia Antipolis, Déartement de Math ématiques Laboratoire Jean Alexandre DieudonnéThe fact that the double zeta values ƒÄ(n, m) can be written in terms of zeta values, whenever n+m is odd is attributed to Euler. We shall show the weak version of this result for the l-adic Galois realization.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666312021A note on products in stable homotopy groups of spheres via the classical Adams spectral sequence107122ENRyoKatoFaculty of Fundamental Science, National Institute of Technology, Niihama CollegekatsumiShimomuraDepartment of Mathematics, faculty of Science and Technology, Kochi UniversityIn recent years, Liu and his collaborators found many non-trivial products of generators in the homotopy groups of the sphere spectrum. In this paper, we show a result which not only implies most of their results, but also extends a result of theirs.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666312021Differential operators on modular forms associated to Jacobi forms123131ENMin HoLeeDepartment of Mathematics, University of Northern IowaGiven Jacobi forms, we determine associated Jacobi-like forms, whose coefficients are quasimodular forms. We then use these quasimodular forms to construct differential operators on modular forms, which are expressed in terms of the Fourier coefficients of the given Jacobi forms.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666312021Rectangular Hall-Littlewood symmetric functions and a specific spin character133151ENKazuyaAokageDepartment of Mathematics, National Institute of Technology, Ariake CollegeWe derive the Schur function identities coming from the tensor products of the spin representations of the symmetric group Sn. We deal with the tensor products of the basic spin representation V (n) and any spin representation V ƒÉ (ƒÉ ¸ SP (n)). The characteristic map
of the tensor product ƒÄn ⊗ ƒÄƒÉ is described by Stembridge[4] for the case of odd n. We consider the case n is even.
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666312021The d-Smith sets of direct products of dihedral groups153165ENKoheiSeitaDepartment of Mathematics, Graduate School of Natural Science and Technology, Okayama UniversityLet G be a finite group and let V and W be real G-modules. We call V and W dim-equivalent if for each subgroup H of G, the H-fixed point sets of V and W have the same dimension. We call V and W are Smith equivalent if there is a smooth G-action on a homotopy sphere ƒ° with exactly two G-fixed points, say a and b, such that the tangential G-representations at a and b of ƒ° are respectively isomorphic to V and W . Moreover, We call V and W are d-Smith equivalent if they are dim-equivalent and Smith equivalent. The differences of d-Smith equivalent real G-modules make up a subset, called the d-Smith set, of the real representation ring RO(G). We call V and W P(G)-matched if they are isomorphic whenever the actions are restricted to subgroups with prime power order of G. Let N be a normal subgroup. For a subset F of G, we say that a real G-module is F-free if the H-fixed point set of the G-module is trivial for all elements H of F. We study the d-Smith set by means of the submodule of RO(G) consisting of the differences of dim-equivalent, P(G)-matched, {N}-free real G-modules. In particular, we give a rank formula for the submodule in order to see how the d-Smith set is large.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666312021On pg-ideals167173ENTony J.PuthenpurakalDepartment of Mathematics, IIT BombayLet (A, m) be an excellent normal domain of dimension two. We define an m-primary ideal I to be a pg -ideal if the Rees algebra A[It] is a Cohen-Macaulay normal domain. If A has infinite residue field then it follows from a result of Rees that the product of two pg ideals is pg . When A contains an algebraically closed field k ∼= A/m then Okuma, Watanabe and Yoshida proved that A has pg -ideals and furthermore product of two pg -ideals is a pg ideal. In this article we show that if A is an excellent normal domain of dimension two containing a field k ∼= A/m of characteristic zero then also A has pg -ideals.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666312021On some families of invariant polynomials divisible by three and their zeta functions175182ENKojiChinenDepartment of Mathematics, School of Science and Engineering, Kindai UniversityIn this note, we establish an analog of the Mallows-Sloane bound for Type III formal weight enumerators. This completes the bounds for all types (Types I through IV) in synthesis of our previous results. Next we show by using the binomial moments that there exists a family of polynomials divisible by three, which are not related to linear codes but are invariant under the MacWilliams transform for the value 3/2. We also discuss some properties of the zeta functions for such polynomials.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666312021On H-epimorphisms and co-H-sequences in two-sided Harada rings183199ENYoshitomoBabaDepartment of Mathematics Education Osaka Kyoiku UniversityIn [8] M. Harada studied a left artinian ring R such that every non-small left R-module contains a non-zero injective submodule. And in [13] K. Oshiro called the ring a left Harada ring (abbreviated left H-ring). We can see many results on left Harada rings in [6] and many equivalent conditions in [4, Theorem B]. In this paper, to characterize two-sided Harada rings, we intruduce new concepts gco-H-sequenceh and gH-epimorphismh and study them.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666312021Linear stability of radially symmetric equilibrium solutions to the singular limit problem of three-component activator-inhibitor model201217ENTakuyaKojimaGraduate school of Natural Science and Technology, Okayama UniversityYoshihitoOshitaDepartment of Mathematics, Okayama UniversityWe show linear stability or instability for radially symmet-ric equilibrium solutions to the system of interface equation and two parabolic equations arising in the singular limit of three-component activator-inhibitor models.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566811958Poincarésche Vermutung in Topologie1106ENKen'itiKosekiNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566821958Note on curvature of Finsler manifolds107116ENTominosukeŌtsukiNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566821958A note on Galois theory of primary rings117123ENHisaoTominagaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566821958Some remarks on homotopy equivalences and H-spaces125131ENMasahiroSugawaraNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566821958On normal basis theorems and strictly Galois extensions133142ENTakasiNagaharaTakesiOnoderaHisaoTominagaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566821958Tangent bundles of order 2 and general connections 143179ENTominosukeOtsukiNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566821958On generating elements of Galois extensions of division rings IV181188ENTakashiNagaharaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566821958Galois theory of simple rings IV189194ENTakasiNagaharaNobuoNobusawaHisaoTominagaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666412022A Note on Torsion Points on Ample Divisors on Abelian Varieties111ENYuichiroHoshiResearch Institute for Mathematical Sciences, Kyoto UniversityIn the present paper, we consider torsion points on ample divisors on abelian varieties. We prove that, for each integer n ≤ 2, an effective divisor of level n on an abelian variety does not contain the subgroup of n-torsion points. Moreover, we also discuss an application of this result to the study of the p-rank of cyclic coverings of curves in positive characteristic.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666412022The d-Smith sets of Cartesian products of the alternating groups and finite elementary abelian 2-groups1329ENKoheiSeitaDepartment of Mathematics, Graduate School of Natural Science and Technology, Okayama UniversityLet G be a finite group. In 1970s, T. Petrie defined the Smith equivalence of real G-modules. The Smith set of G is the subset of the real representation ring consisting of elements obtained as differences of Smith equivalent real G-modules. Various results of the topic have been obtained. The d-Smith set of G is the set of all elements [V ]|[W] in the Smith set of G such that the H-fixed point sets of V and W have the same dimension for all subgroups H of G. The results of the Smith sets of the alternating groups and the symmetric groups are obtained by E. Laitinen, K. Pawa lowski and R. Solomon. In this paper, we give the calculation results of the d-Smith sets of the alternating groups and the symmetric groups. In addition, we give the calculation results of the d-Smith sets of Cartesian products of the alternating groups and finite elementary abelian 2-groups.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666412022The best constant of the discrete Sobolev inequalities on the complete bipartite graph3145ENHiroyukiYamagishiTokyo Metropolitan College of Industrial TechnologyWe have the best constants of three kinds of discrete Sobolev inequalities on the complete bipartite graph with 2N vertices, that is, K<sub>N</sub>,<sub>N</sub>. We introduce a discrete Laplacian A on K<sub>N</sub>,<sub>N</sub>. A is a 2N ~2N real symmetric positive-semidefinite matrix whose eigenvector corresponding to zero eigenvalue is 1 = <sup>t</sup>(1, 1, c , 1)∈ C<sup>2N</sup>. A discrete heat kernel, a Greenfs matrix and a pseudo Greenfs matrix play important roles in giving the best constants.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666412022On Weakly Separable Polynomials in skew polynomial rings4761ENSatoshiYamanakaDepartment of Integrated Science and Technology National Institute of Technology, Tsuyama CollegeThe notion of weakly separable extensions was introduced by N. Hamaguchi and A. Nakajima as a generalization of separable extensions. The purpose of this article is to give a characterization of weakly separable polynomials in skew polynomial rings. Moreover, we shall show the relation between separability and weak separability in skew polynomial rings of derivation type.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666412022Note on totally odd multiple zeta values6373ENKojiTasakaA partial answer to a conjecture about the rank of the matrix C<sub>N</sub>,<sub>r</sub> introduced by Francis Brown in the study of totally odd multiple zeta values is given.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666412022Criteria for good reduction of hyperbolic polycurves75107ENIppeiNagamachiResearch Institute for Mathematical Sciences, Kyoto UniversityWe give good reduction criteria for hyperbolic polycurves, i.e., successive extensions of families of curves, under some assumptions. These criteria are higher dimensional versions of the good reduction criterion for hyperbolic curves given by Oda and Tamagawa.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666412022Notes on the filtration of the K-theory for abelian p-groups109116ENNobuakiYagitaDepartment of Mathematics Faculty of Education Ibaraki UniversityLet p be a prime number. For a given finite group G, let gr<sup>*</sup><sub>γ</sub>(BG) be the associated ring of the gamma filtration of the topological K-theory for the classifying space BG. In this paper, we study gr<sup>*</sup><sub>γ</sub>(BG) when G are abelian p-groups which are not elementary. In particular, we extend related Chetardfs results for such 2-groups to p-groups for odd p.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666412022ƒÑ-tilting finiteness of two-point algebras I117141ENQiWangDepartment of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka UniversityAs the first attempt to classify ƒÑ-tilting finite two-point algebras, we have determined the ƒÑ-tilting finiteness for minimal wild two-point algebras and some tame two-point algebras.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666412022Quantum Sylvester-Franke Theorem143151ENKazuya AokageDepartment of Mathematics, National Institute of Technology, Ariake CollegeSumitaka TabataDepartment of Mathematics, Kumamoto UniversityHiro-FumiYamadaDepartment of Mathematics, Kumamoto UniversityA quantum version of classical Sylvester-Franke theorem is presented. After reviewing some representation theory of the quantum group GL<sub>q</sub> (n, C), the commutation relations of the matrix elements are verified. Once quantum determinant of the representation matrix is defined, the theorem follows naturallyNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666412022Bijective proofs of the identities on the values of inner products of the Macdonald polynomials153186ENYutaNishiyamaGraduate School of Science and Technology, Kumamoto UniversityIn this article, we introduce some identities obtained from the inner products of some symmetric polynomials including the Macdonald polynomials. These identities are obtained not only from the inner products, but also by constructing certain bijections. The bijections are constructed through transforming the Young diagrams of partitions.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666412022Symbolic powers of monomial ideals187190ENTony J. PuthenpurakalLet K be a field and consider the standard grading on A = K[X<sub>1</sub>, ... ,X<sub>d</sub>]. Let I, J be monomial ideals in A. Let I<sub>n</sub>(J) = (I<sup>n</sup> : J<sup>∞</sup>) be the n<sup>th</sup> symbolic power of I with respect to J. It is easy to see that the function f<sup>I</sup> <sub>J</sub> (n) = e<sub>0</sub>(I<sub>n</sub>(J)/I<sup>n</sup>) is of quasi-polynomial type, say of period g and degree c. For n â 0 say<br>
<br>
f<sup>I</sup><sub>J</sub> (n) = a<sub>c</sub>(n)n<sup>c</sup> + a<sub>c|1</sub>(n)n<sup>c|1</sup> + lower terms,<br>
<br>
where for i = 0, ... , c, a<sub>i</sub> : N ¨ Q are periodic functions of period g and a<sub>c</sub> ≠0. In [4, 2.4] we (together with Herzog and Verma) proved that dim I<sub>n</sub>(J)/I<sup>n</sup> is constant for n â 0 and a<sub>c</sub>(|) is a constant. In this paper we prove that if I is generated by some elements of the same degree and height I ≥ 2 then a<sub>c|1</sub>(|) is also a constant.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666412022On Hook Formulas for Cylindric Skew Diagrams191213ENTakeshiSuzukiDepartment of Mathematics, Faculty of Science, Okayama UniversityYoshitakaToyosawaGraduate School of Natural Science and Technology, Okayama UniversityWe present a conjectural hook formula concerning the number of the standard tableaux on "cylindric" skew diagrams. Our formula can be seen as an extension of Naruse's hook formula for skew diagrams. Moreover, we prove our conjecture in some special cases.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666412022A note on a Hecke ring associated with the Heisenberg Lie algebra215225ENFumitakeHyodoDepartment of Health Informatics Faculty of Health and Welfare Services Administration Kawasaki University of Medical WelfareThis paper focuses on the theory of the Hecke rings associated with the general linear groups originally studied by Hecke and Shimura et al., and moreover generalizes its notions to Hecke rings associated with the automorphism groups of certain algebras. Then, in the case of the Heisenberg Lie algebra, we show an analog of the classical theory.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666512023A characterization of the class of Harada rings122ENKazutoshiKoikeNational Institute of Technology, Okinawa CollegeThere are many characterizations of Harada rings. In this paper, we characterize right co-Harada rings by giving a characterization of the class of basic right co-Harada rings.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666512023E(2)-local Picard graded beta elements at the prime three2334ENRyoKatoFaculty of Fundamental Science National Institute of Technology, Niihama collegeLet E(2) be the second Johnson-Wilson spectrum at the prime 3. In this paper, we show that some beta elements exist in the homotopy groups of the E(2)-localized sphere spectrum with a grading over the Picard group of the stable homotopy category of E(2)-local spectra.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666512023Affine Kac-Moody Groups as Twisted Loop Groups obtained by Galois Descent Considerations3581ENJunMoritaInstitute of Mathematics, University of TsukubaArturoPianzolaDepartment of Mathematical and Statistical Sciences, University of AlbertaTaikiShibataDepartment of Applied Mathematics, Okayama University of ScienceWe provide explicit generators and relations for the affine Kac-Moody groups, as well as a realization of them as (twisted) loop groups by means of Galois descent considerations. As a consequence, we show that the affine Kac-Moody group of type X(r) N is isomorphic to the
fixed-point subgroup of the affine Kac-Moody group of type X(1) N under an action of the Galois group.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666512023Non-Modular Solution of the Kaneko-Zagier Equations with respect to Fricke Groups of Low Levels8396ENToshiteruKinjoGraduate School of Mathematics, Kyushu UniversityPavel Guerzhoy show that the Kaneko-Zagier equation for SL2(Z) has mixed mock mock modular solutions in certain weights. In this paper, we show that the Kaneko-Zagier equations for the Fricke groups of level 2 and 3 also have mixed mock modular solutions in certain weights.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666512023An improvement of the integrability of the state space of the ƒ³43-process and the support of the ƒ³43-measure constructed by the limit of stationary processes of approximating stochastic quantization equations97116ENSeiichiroKusuokaDepartment of Mathematics, Graduate School of Science, Kyoto UniversityThis is a remark paper for the ƒ³<sup>4</sup><sub>3</sub> -measure and the associated flow on the torus which are constructed in [1] by the limit of the stationary processes of the stochastic quantization equations of approximation measures. We improve the integrability of the state space of the ƒ³<sup>4</sup><sub>3</sub> -process and the support of the ƒ³<sup>4</sup><sub>3</sub> -measure. For the improvement, we improve the estimates of the Hölder continuity in time of the solutions to approximation equations. In the present paper, we only discuss the estimates different from those in [1].No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666512023A Note on Fields Generated by Jacobi Sums117123ENYuichiroHoshiResearch Institute for Mathematical Sciences, Kyoto UniversityIn the present paper, we study fields generated by Jacobi sums. In particular, we completely determine the field obtained by adjoining, to the field of rational numbers, all of the Jacobi sums gof two variablesh with respect to a fixed maximal ideal of the ring of integers of a fixed prime-power cyclotomic field.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666512023Traveling front solutions for perturbed reaction-diffusion equations125143ENWahWahResearch Institute for Interdisciplinary Science, Okayama UniversityMasaharuTANIGUCHIResearch Institute for Interdisciplinary Science, Okayama UniversityTraveling front solutions have been studied for reaction-diffusion equations with various kinds of nonlinear terms. One of the interesting subjects is the existence and non-existence of them. In this paper, we prove that, if a traveling front solution exists for a reaction-diffusion equation with a nonlinear term, it also exists for a reaction-diffusion equation with a perturbed nonlinear term. In other words, a traveling front is robust under perturbation on a nonlinear term.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666512023Positivity and Hierarchical Structure of four Green Functions Corresponding to a Bending Problem of a Beam on a half line145173ENYoshinoriKametakaFaculty of Engineering Science, Osaka UniversityKohtaroWatanabeDepartment of Computer Science, National Defense AcademyAtsushiNagaiDepartment of Computer Sciences, College of Liberal Arts, Tsuda UniversityKazuoTakemuraCollege of Science and Technology, Nihon UniversityHiroyukiYamagishiTokyo Metropolitan College of Industrial TechnologyWe consider the boundary value problem for fourth order linear ordinary differential equation in a half line (0,‡), which represents bending of a beam on an elastic foundation under a tension. A tension is relatively stronger than a spring constant of elastic foundation. We here treat four self-adjoint boundary conditions, clamped, Dirichlet, Neumann and free edges, at x = 0. We show the positivity and the hierarchical structure of four Green functions.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661021961On Hilbert geometry101112ENYasuoNasu10.18926/mjou/33080No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661021961On general connections II113124ENTominosukeOtsuki10.18926/mjou/33081No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661021961Über die Koeffizienten der schlichten Funktionen (II)125142ENKen'itiKoseki10.18926/mjou/33082No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661021961Über die p-wertigen Funktionen8799ENKen'itiKoseki10.18926/mjou/33083No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661021961On Galois and locally Galois extensions of simple rings143166ENTakashiNagaharaHisaoTominaga10.18926/mjou/33084No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661011960On conformal collineations7585ENYoshihiroTashiro10.18926/mjou/33085No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661011960On generating elements of Galois extensions of division rings V1117ENTakasiNagahara10.18926/mjou/33086No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661011960Spectral theory of operator algebras II1960ENMinoruTomita10.18926/mjou/33087No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661011960On some properties of group characters II6166ENMasaruOsima10.18926/mjou/33088No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661011960Beiträge zur Theorie der schlichten Funktionen19ENKen'itiKoseki10.18926/mjou/33089No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661011960On Galois theory of division rings III6773ENNobuoNobusawaHisaoTominaga10.18926/mjou/33090No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663811996Self Maps of Suspension of Sphere Bundles over Spheres155158ENHideoTakahashi10.18926/mjou/33091No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663811996Anti-Intergral Elements and Coefficients of their Minimal Polynomials8391ENSusumuOdaKen-ichiYoshida10.18926/mjou/33092No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663811996Theta Functions, II93108ENTakashiTasaka10.18926/mjou/33093No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663811996Hopf Maps and Triality197208ENA.RigasLucas M.Chaves10.18926/mjou/33094No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663811996Multiplicative Elements in Morava K-Theory of BZ/p145154ENK.Kordzaya10.18926/mjou/33095No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663811996On the Differential Submodules of Modules1324ENMamoruFuruyaHiroshiNiitsuma10.18926/mjou/33096No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663811996On Values of Cyclotomic Polynomials. III115122ENKaoruMotose10.18926/mjou/33097No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663811996Orthogonality in the Category of Complexes2546ENEdger E.EnochsOvertoun M. G.JendaJinzhongXu10.18926/mjou/33098No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663811996Weakly Henselian Rings4751ENThomasMckenzie10.18926/mjou/33099No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663811996Note on Homotopy Classes of Self Maps; [ƒ°HP³, ƒ°HP³]159196ENHideoTakahashi10.18926/mjou/33100No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663811996The Property Special (DF) for Unit-Regular Rings111ENMamoruKutami10.18926/mjou/33101No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663811996Panes, Nets, and Codes123143ENSteven T.Dougherty10.18926/mjou/33102No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663811996A Remark on Torsion-Free Subgroups in Group Rings109114ENTôruFurukawa10.18926/mjou/33103No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663811996Infinite Galois Theory of Semisimple Rings5382ENKazuyukiTanabe10.18926/mjou/33104No 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 Two183184ENBlair K.Spearman10.18926/mjou/33105<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 Okayama0030-15664912007Evaluation of the Convolution Sums ‡” l+24m=n ƒÐ(l) ƒÐ(m) and ‡”3l+8m=n ƒÐ(l) ƒÐ(m)93111ENAyseAlacaSabanAlacaKenneth S.Williams10.18926/mjou/33106No 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>0113138ENMohamedSaïdi10.18926/mjou/33107<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 Okayama0030-15664912007A Characterization of ƒÂ-quasi-Baer Rings197200ENEbrahimHashemi10.18926/mjou/33108<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 Okayama0030-15664912007A Generalized Primitive Element Theorem171181ENDirceuBagioAntonioPaques10.18926/mjou/33109<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 Okayama0030-15664912007Sums 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 Calculus3752ENMaged G.Bin-Saad10.18926/mjou/33110<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 Okayama0030-15664912007Higher Weights of Codes from Projective Planes and Biplanes149161ENSteven T.DoughertyReshmaRamadurai10.18926/mjou/33111<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 Okayama0030-15664912007On Ideals and Orthogonal Generalized Derivations of Semiprime Rings5358ENEmineAlbas10.18926/mjou/33112<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 Okayama0030-15664912007Some Results on (ƒÐ,ƒÑ)-Lie Ideals5964ENEvrimGüvenKazimKayaMuharremSoytürk10.18926/mjou/33113<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 Okayama0030-15664912007Some Questions on the Ideal Class Group of Imaginary Abelian Fields185196ENTsuyoshiItoh10.18926/mjou/33114<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 Okayama0030-15664912007Character Values and Dade's Conjecture136ENRyoNarasaki10.18926/mjou/33115No 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 Plane163169ENYasuoIida10.18926/mjou/33116<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 Okayama0030-15664912007Generalized Derivations with Commutativity and Anti-commutativity Conditions139147ENHoward E.BellNadeem-urRehman10.18926/mjou/33117<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 Okayama0030-15664912007Cut Loci and Distance Functions6592ENJin-ichiItohTakashiSakai10.18926/mjou/33118No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664412002A Representation of Ring Homomorphisms on Unital Regular Commutative Banach Algebras143154ENTakeshiMiura10.18926/mjou/33119<p>We give a complete representation of a ring homomorphism from a unital semisimple regular commutative Banach algebra into a unital semisimple commutative Banach algebra, which need not be regular. As a corollary we give a sufficient condition in order that a ring homomorphism is automatically linear or conjugate linear.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664412002On the Nilpotency Index of the Radical of a Group Algebra. XI5156ENKaoruMotose10.18926/mjou/33120No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664412002Hopf Algebra Structure of Morava K-Theory of the Exceptional Lie Groups, II57122ENTetsuNishimoto10.18926/mjou/33121No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664412002Note on the Relation between S-reducibility, S-coreducibility and Stable Homotopy Types of Some Stunted Lens Spaces131136ENYasusukeKotani10.18926/mjou/33122No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664412002Ladder Index of Groups3742ENKazuhiroIshikawaHiroshiTanakaKatsumiTanaka10.18926/mjou/33123No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664412002On Commutativity of Rings with Generalized Derivations4350ENNadeem urRehman10.18926/mjou/33124<p>The concept of derivations as well as of generalized inner derivations have been generalized as an additive function F : R → R satisfying F(xy) = F(x)y + xd(y) for all x, y ∈ R, where d is a derivation on R, such a function F is said to be a generalized derivation. In the present paper we have discussed the commutativity of prime rings admitting a generalized derivation F satisfying (i) [F(x), x] = 0, (ii) F([x, y]) = [x, y], and (iii) F(x ◦ y) = x ◦ y for all x, y in some appropriate subset of R.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664412002On the Group ƒÎ(ƒ°A ~ B, X)123130ENSeiyaSasao10.18926/mjou/33125No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664412002Decomposition of Spinor Groups by the Involution ƒÐŒ in Exceptional Lie Groups128ENToshikazuMiyashita10.18926/mjou/33126No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664412002Semigroups of Locally Lipschitz Operators155170ENYoshikazuKobayashiNaokiTanaka10.18926/mjou/33127No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664412002Geometry on Grassmann Manifolds G(2,8) and G(3,8)171179ENZhouJianweiHuangHui10.18926/mjou/33128<p>In this paper, we use the Clifford algebra Cℓ<sub>8</sub> to construct fibre bundles ¿<sub>1</sub> : G(2; 8) → S<sup>6</sup>, ¿'<sub>1</sub> : G(2; 7) → S<sup>6</sup> and ¿<sub>2</sub> : G(3; 8) → S<sup>7</sup>, the fibres are CP<sup>3</sup>, CP<sup>2</sup> and ASSOC = G<sub>2</sub>=SO(4) respectively. We show that G(2; 5), CP<sup>3</sup> and S<sup>6</sup> are the homologically volume minimizing submanifolds of G(2; 8) by calibrations and they generate the homology group H<sub>6</sub>(G(2; 8)). The submanifolds S<sup>7</sup> and ASSOC of G(3; 8) generate H<sub>7</sub>(G(3; 8)) and H<sub>8</sub>(G(3; 8)) respectively.</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-Property127133ENZhaoBin10.18926/mjou/33129No 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 ∞)135147ENAli M.AkhmedovFeyziBasar10.18926/mjou/33130<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 Okayama0030-15665012008A Lower Bound for the Rational LS-category of a Coformal Elliptic Space201203ENToshihiroYamaguchi10.18926/mjou/33131<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 Okayama0030-15665012008On Central Gap Numbers of Symmetric Groups6384ENHirotakaKikyo10.18926/mjou/33132<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 Okayama0030-15665012008On Fox Spaces and Jacobi Identities161176ENMarekGolasinskiDaciberg LimaGonçalvesPeterWong10.18926/mjou/33133<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 Okayama0030-15665012008Imaginary Quadratic Fields whose Exponents are Less Than or Equal To Two8599ENKenichiShimizu10.18926/mjou/33134<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 ƒ³-recurrent N(k)-contact Metric Manifolds101112ENUday ChandDeAboul KalamGazi10.18926/mjou/33135<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 Okayama0030-15665012008A New Class of Quasicyclic Complex Vector Functional Equations161ENIce B.Risteski10.18926/mjou/33136<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 Okayama0030-15665012008K-semimetrizabilities and C-stratifiabilities of Spaces177199ENIwaoYoshioka10.18926/mjou/33137No 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 Rings149160ENChiteng'a JohnChikunji10.18926/mjou/33138<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 Okayama0030-15665012008Strong Convergence Theorems for Nonexpansive Mappings by Viscosity Approximation Methods in Banach Spaces113125ENXiaolongQinYongfuSuChangqunWu10.18926/mjou/33139<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 Okayama0030-15663411992Some Examples of Benford Sequences225232ENKazuoGoto10.18926/mjou/33140No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663411992On Derivations in Near-rings and Rings135144ENHoward E.BellGordonMason10.18926/mjou/33141No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663411992Curvature Forms and Einstein-like Metrics on Sasakian Manifolds241248ENElsaAbbenaSergioGarbiero10.18926/mjou/33142No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663411992Degree Equations for p-blocks of Finite Group, II6773ENKazuokiIkeda10.18926/mjou/33143No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663411992Generalized Tilting Modules and Applications to Module Theory7598ENYoichiMiyashita10.18926/mjou/33144No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663411992Subrings Containing Ideals149151ENShalomFeigelstock10.18926/mjou/33145No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663411992Real Hypersurfaces in Pn(C) with Constant Principal Curvatures233240ENU-HangKiRyoichiTakagi10.18926/mjou/33146No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663411992On Commutativity of a Certain Class of Rings131134ENHiroakiKomatsuTsunekazuNishinakaAdilYaqub10.18926/mjou/33147No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663411992Uncoutably Many Infinite Loop Spaces of the Same N-type for all N217223ENYoshimiShitanda10.18926/mjou/33148No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663411992Some Characterizations of Right co-H-rings165174ENDinh VanHuynhPhanDan10.18926/mjou/33149No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663411992ƒÎ-regular Rings Satisfying the Converse of Schur's Lemma153156ENChol OnKimChanHuh10.18926/mjou/33150No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663411992Primitive Elements for Cyclic p^n -extensions of Commutative Rings1320ENAnnetta G.Aramova10.18926/mjou/33151No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663411992Prime Ideals in Strongly Graded Rings by Polycyclic-by-finite Groups II115124ENHidetoshiMarubayashiHaruoMiyamoto10.18926/mjou/33152No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663411992Pseudo-riemannian Submanifolds with Pointwise Planar Normal Sections249257ENYoung HoKim10.18926/mjou/33153No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663411992Finite Posets P and P-galois Extensions of Rings2147ENKazuoKishimoto10.18926/mjou/33154No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663411992On H-separable Polynomials in Skew Polynomial Rings of Automorphism Type4955ENShoichiIkehataGeorgeSzeto10.18926/mjou/33155No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663411992Degrees of Self-maps205216ENAkiraSasao10.18926/mjou/33156No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663411992On Jordan Left Derivations145147ENQingDeng10.18926/mjou/33157No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663411992Global Dimension of 2x2 Generic Trace Zero Matrices and Invariants of 2x2 Generic Matrices157163ENChanHuh10.18926/mjou/33158No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663411992On the (2,3)-closures of Ideals112ENSusumuOdaKen-IchiYoshida10.18926/mjou/33159No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663411992An Example of an Indecomposable Module which is not Injective125129ENShojiMorimotoTakefumiShudo10.18926/mjou/33160No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663411992Signatures on a Ring99114ENTeruoKanzaki10.18926/mjou/33161No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663411992On Some Products of ƒÀ-elements in the Homotopy of the Moore Spectrum195204ENMihoMabuchiKatsumiShimomura10.18926/mjou/33162No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663411992On the Nilpotency Index of the Radical of a Group Algebra. X5766ENKaoruMotose10.18926/mjou/33163No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663411992A Note on the Lie Group G2 as a Framed Boundary175179ENMasaakiYokotani10.18926/mjou/33164No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663411992The Integral Cohomology Rings of F4/Spin(n) and E6/Spin(m)181193ENMasaakiYokotani10.18926/mjou/33165No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566221953Notes on Basic Rings103110ENMasaruOshima10.18926/mjou/33166No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566221953Theorie der Derivationen und Körperdifferenten111148ENMikaoMoriya10.18926/mjou/33167No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566221953Contribution à la Topologie II149184ENTakeshiInagaki10.18926/mjou/33168<p>On croit en général que la théorie topologique dans un espace
se développe en relation avec la propriété topologique de l'espace
considéré. Cependant, si l'on envisage les notions utilisées pour
établir la théorie, on voit sans peine qu'il y a deux espéces de notions,
c.-á-d. que les unes sont en relations intimes avec la topologie de l'espace
et les autres, presque indépendantes de la topologie de l'espace. Par
exemple, la notion d'un ensemble fermé est bien définie en relation
intime avec la topologie de l'espace considéré et la notion de l'ensemble
mesurable ß se rapporte certainement á la puissance ℵ<sub>0</sub> ,
mais il sera plus naturel de dire qu'elle est presque indépendante de
la topologie de l'espace.
Pour mettre en lumière ce que nous avons rapporté plus haut,
nous montrons un exemple. Si l'on regard l'ensemble dit homogenen
Normaltypus η<sub>ξ</sub> comme un espace dans lequel, comme toujours, les
voisinages d'un point x sont d'intervalles ouverts contenant le point
x, alors, comme on le voit sans peine, la SQ1nme de nombre dénombrable
d'ensembles fermés l'est également; par conséquent, dans cet
espace la notion de l'ensemble F<sub>σ</sub> au sens usuel n'a aucun sens essentiel,
et on voit que dans cet espace l'ensemble correspondant à
l'ensemble F<sub>σ</sub> doit être défini comme une somme de la puissance ℵ<sub>ξ</sub>
d'ensembles fermés.
Originellement, la topologie prend sa source à la notion de la.
limite et il me semble donc qu'il est naturel de développer sa théorie
en relation avec la structure de la limite dans l'espace que nous
avons en question.
Soient R un espace υ introduit par M. Fréchet et χ un point de·
R. Alors, il y a plusieurs familles de voisinages du point χ telles
qu'elles sont équivalentes deux à deux, et de plus il y a une famille
telle que sa puissance est la plus petite parmi celles de toutes les
familles. Désignons respectivement par {V(χ)} et ℵ(χ), la famille
et sa puissance. Cela posé, si un système ordonné de points {χ<sub>χ</sub>}
converge vers le point χ, alors, comme on le sait, on peut convenablement
extraire un système {χ<sub>v(χ)</sub>}, se composant de points de {χ<sub>χ</sub>}
et ordonné suivant l'ordre de l'ensemble {V(χ)} de leurs suffixes, tel
qu'il converge vers le point χ; ce qui Inontre que la convergence
vers le point x peut être écrite par le mot de la convergence d'un
système ordonné de la puissance ℵ<sub>ξ</sub>(χ). Par conséquent, si la puissance
ℵ<sub>ξ</sub>(χ) est indépendante du point x de l'espace considéré, nous
pouvons écrire la topologie dans l'espace par le mot de la conver,
gence d'un système ordonné de la puissance ℵ<sub>ξ</sub>. Ainsi, on peut dire
que l'espace jouit en un sens de la structure uniforme par rapport à
la limite.
De plus, quoiqu'un espace considéré R ne soit pas à structure
uniforlne en ce sens enoncé plus haut, s'il est quantitatif, la puissance
d'ensemble de suffixes de voisinages est indépendante de points
de l'espace et, par suite, on peut considérer que l'espace est à structure
unifonne par rapport à la lilnite. Ainsi, il sera naturel que,
dans l'espace quantitatif, la notion ayant des relations avec une puissance
doit être définie en relation avec la puissance de 1'ensemble
des suffixes, et, en effet, on pourra voir dans ˜ 5 que la puissance
joura un rôle important dans tel espace.
Dans ce travail, nous traitons principalement pour abréger les
espaces quantitatifs dans lesquels chaque voisinage est ouvert. Le
premier objet de cet article est d'excepter des notions ayant des
relations avec la puissance ℵ<sub>0</sub> dans le sens conventionnel, et le
deuxième, de démontrer un traitement naturel sur quelques affaires
fondaInentales dans la topologie. Nous traiterons les espaces quantitatifs
dans ˜ 5 et les espaces à structure uniforme dans ˜ 6.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566221953Sur un Ensemble De Capacité Nulle et L'infini D'un Potentiel99101ENNobuyukiNinomiya10.18926/mjou/33169No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566221953Quelques Généralisations des Théorémes Concernant aux Produits Directs Des Espaces Linéaires Localement Convexes185189ENIchiroAmemiya10.18926/mjou/33170<p>Les deux théorèmes, qui sont établis dans "Sur les espaces
linéaires localement convexes" par O. Takenouchi (qui a paru dans
ce même Journal, tom. 2, n‹1, pp. 57-84), et qui insistent que le
produit direct des espaces de chacune de deux espèces c.-à-d. "bornologique"
et "tonnelé" est encore l'un de la même espèce, sont
vrais sous les conditions moins restrictives. À savoir,
Concernant au théorème 14: La restriction d'être complet n'est
pas nécessaire.
Concernant au théorème 15: La puissance d'ensemble des composants
du produit peut être tenue encore plus grand.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566211952On Families of Continuous Vector Fields Over Spheres4955ENMasahiroSugawara10.18926/mjou/33171No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566211952Sur les Espaces Lineaires Localement Convexes5784ENOsamuTakenouchi10.18926/mjou/33172No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566211952On the Cartan Invariants of Algebras912ENMasaruOsima10.18926/mjou/33173No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566211952Eine notwendige Bedingung für die Gültigkeit der Klassenkörpertheorie im Kleinen1320ENMikaoMoriya10.18926/mjou/33174No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566211952On The Spaces With Normal Projective Connexions And Some Imbedding Problem Of Riemannian Spaces II2140ENTominosukeOtsuki10.18926/mjou/33175<p>In the present paper, we shall investigate the conditions under
which a given Riemannian space V<sub>n</sub> can be imbedded, as a hypersurface,
into a Riemannian space V<sub>n+1</sub> which has the following properties
I) and II).
I) The group of holonomy of the space with a normal projective
.connexion corresponding to V<sub>n+1</sub> fixes a hyperquadric and V<sub>n</sub> is its
image in V<sub>n+1</sub> , that is, the locus of points lying on the parallel displaced
hyperquadrics, regarded as points in the tangent projective spaces.
If V<sub>n+1</sub> has the property above, there exist a scalar y such that
the hypersurface is given by the relation y -= 0.
II) The orthogonal trajectories of the family of the hypersurfaces
on which y is constant are geodesics in V<sub>n+1</sub>.
If the group of holonomy of the space with a normal projective
eonnexion corresponding to a V<sub>n+1</sub> fixes a hyperquadric, it is projectively
equivalent to an Einstein space2
). In the previous paper,
the author have studied the problem of the same kind as this under
the conditions I) and
II') V<sub>n+1</sub> is an Einstein space.
The imbedding problem of V<sub>n</sub> into V<sub>n+1</sub> under the only condition
I) is very complicated in structure. The purpose of the present paper
is also to search for the methods dealing with the problem, as the previous one.
</p>No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566211952Sur Une Suite Convergente de Distributions de Masses et Leurs Potentiels Correspondants17ENNobuyukiNinomiya10.18926/mjou/33176No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566211952Compactification of Topological Spaces8597ENTakashiInagakiMasahiroSugawara10.18926/mjou/33177No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566211952Sur le Caractère Fonctionelle de la Solution du Probléme de Dirichlet4148ENNobuyukiNinomiya10.18926/mjou/33178No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566321954Some remarks on radical ideals139142ENHisaoTominaga10.18926/mjou/33179No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566321954On the regularly convex hull of a set in a conjugate Banach space143145ENMinoruTomita10.18926/mjou/33180No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566321954Some studies on Frobenius algebras, II109119ENMasaruOsima10.18926/mjou/33181No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566321954Sur les anneaux des fonctions continues à support compact175184ENKaichiroFujiwara10.18926/mjou/33182No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566321954Notes on basic rings, II121127ENMasaruOsima10.18926/mjou/33183No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566321954Some remarks on homotopy groups of rotation groups129133ENMasahiroSugawara10.18926/mjou/33184No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566321954A construction of closed surfaces of negative curvature in E^495108ENTominosukeOtsuki10.18926/mjou/33185No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566321954Representations of operator algebras147173ENMinoruTomita10.18926/mjou/33186No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566321954Supplement to my previous paper "On primary ideal decompositions in non-commutative rings"135138ENHisaoTominaga10.18926/mjou/33187No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566311953On primary ideal decompositions in non-commutative rings3946ENHisaoTominaga10.18926/mjou/33188No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566311953On the induced characters of groups of finite order4764ENMasaruOsima10.18926/mjou/33189No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566311953Necessary conditions for local class field theory510ENO. F. G.Schilling10.18926/mjou/33190No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566311953Some theorems on a system of matrices and a geometrical application8994ENTominosukeOtsuki10.18926/mjou/33191No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566311953On the homotopy groups of rotation groups1121ENMasahiroSugawara10.18926/mjou/33192No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566311953Inverses in Euclidean mobs2328ENA. D.Wallace10.18926/mjou/33193No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566311953Indecomposable semigroups13ENA. D.Wallace10.18926/mjou/33194No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566311953On some Riemann spaces6588ENTominosukeOtsuki10.18926/mjou/33195No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566311953Charakterisierung der nicht-archimedischen Bewertungen durch Grössenordnungen2938ENMikaoMoriya10.18926/mjou/33196No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663611994The Atiyah-Singer Index Theorem for G-Equivariant Real Elliptic Families145177ENKenjiTsuboi10.18926/mjou/33197No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663611994Anti-Integral Extensions and Unramified Extensions5162ENMitsuoKanemitsuKen-ichiYoshida10.18926/mjou/33198No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663611994On R-Automorphisms of R[X]6375ENMiguelFerreroAntonioPaques10.18926/mjou/33199No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663611994On Some Products of ƒÀ-Elements in the Homotopy of the Moore Spectrum II185197ENHiromiInoueYoshikoOsakadaKatsumiSimomura10.18926/mjou/33200No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663611994The Element \bar{kappa} is not in the Image of the S¹-Transfer133143ENJunoMukai10.18926/mjou/33201No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663611994A Generalization of the Bott-Taubes Rigidity Theorem199208ENShuichiTsukuda10.18926/mjou/33202No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663611994On commutative group algebras. II2327ENKaoruMotose10.18926/mjou/33203No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663611994Structure of Rings Satisfying Certain Polynomial Identities and Commutativity Theorems85103ENIsaoMogami10.18926/mjou/33204No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663611994Note on the Generalized Euler Constants2934ENTakashiTasaka10.18926/mjou/33205No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663611994Theta Functions. I3544ENTakashiTasaka10.18926/mjou/33206No potential conflict of interest relevant to this article was reported.