Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661311967Über den Fatouschen Satz (I)8589ENKen'itiKoseki10.18926/mjou/33465No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662911987(, )-derivations in prime rings173177ENNurcanArgaçArifKayaAlevKisir10.18926/mjou/33267No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-156614219703-primary components of stable homotopies of K(Z3,1) and HP^129134ENTetsuyaAikawa10.18926/mjou/33646No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-156614219703-primary components of stable homotopies of CP^8796ENTetsuyaAikawa10.18926/mjou/33653No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665312011A CAUCHY-KOWALEVSKI THEOREM FOR INFRAMONOGENIC FUNCTIONS167172ENHelmuth R.MalonekDixan PeñaPeñaFrankSommen10.18926/mjou/41404In this paper we prove a Cauchy-Kowalevski theorem for the functions satisfying the system <sub>x</sub>f<sub>x</sub> = 0 (called inframonogenic functions).No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665612014A CHARACTERIZATION OF THE GLAUBERMAN-WATANABE CORRESPONDING BLOCKS AS BIMODULES1726ENFuminoriTasaka10.18926/mjou/52065We give a characterization of the Glauberman-Watanabe
corresponding blocks viewed as bimodules as a direct summand of a
restricted or an induced module from the block in terms of a vertex and
a multiplicity.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663711995A Characterization of Anti-Integral Extensions5558ENJunroSatoSusumuOdaKen-IchiYoshida10.18926/mjou/33795No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664212000A Characterization of One Dimensional N-Graded Gorenstein Rings of Finite Cohen-Macaulay Representation Type6166ENTokujiAraya10.18926/mjou/33288No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664912007A Characterization of -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 Okayama0030-15665212010A GENERAL INEQUALITY FOR DOUBLY WARPED PRODUCT SUBMANIFOLDS133142ENAndreeaOlteanu10.18926/mjou/33495<p>In this paper, we consider doubly warped product manifolds and we establish a general inequality for doubly warped products isometrically immersed in arbitrary Riemannian manifolds. Some aplications are derived.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663611994A 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 Okayama0030-15664111999A Generalization of the Dade's Theorem on Localization of Injective Modules7579ENKazuhikoHirataUSyu10.18926/mjou/48173No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663911997A Generalization of the Whitehead Product113133ENNobuyukiOda10.18926/mjou/33579No 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 Okayama0030-15664011998A Generation of the Hopf Construction99111ENToshiyukiShimizu10.18926/mjou/33675No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664712005A Lower Bound for the LS Category of a Formal Elliptic Space141146ENYasusukeKotaniToshihiroYamaguchi10.18926/mjou/33590<p>We give a lower bound for the LS category of a formal elliptic space in terms of its rational cohomology.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665012008A 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 Okayama0030-15665612014A MODEL FOR THE WHITEHEAD PRODUCT IN RATIONAL MAPPING SPACES7589ENTakahitoNaito10.18926/mjou/52070We describe the Whitehead products in the rational homo-
topy group of a connected component of a mapping space in terms of
the André-Quillen cohomology. As a consequence, an upper bound for
the Whitehead length of a mapping space is given.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665512013A MODEL STRUCTURE ON THE CATEGORY OF SMALL CATEGORIES FOR COVERINGS95116ENKoheiTanaka10.18926/mjou/49098We consider a model structure on the category of small
categories, which is intimately related to the notion of coverings and
fundamental groups of small categories. Fibrant objects coincide with
groupoids, and the fibrant replacement is the groupoidification.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665112009A NOTE ON ALMOST INJECTIVE MODULES101109ENAdelAlahmadiSurender K.Jain10.18926/mjou/33213<p>We give some new properties of almost injective modules and their endomorphism rings, and also provide conditions as to when a direct sum of almost injective (or CS) modules is again almost injective (or CS) in some special cases..</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665112009A NOTE ON CERTAIN METRICS ON R<sup>4</sup><sub>+</sub>193201ENTominosukeOtsuki10.18926/mjou/33215No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665212010A NOTE ON QUASI-ARMENDARIZ RINGS8995ENLiuZhongkuiZhangWenhui10.18926/mjou/33493<p>A ring R is called a quasi-Armendariz ring if whenever elements α = a<sub>0</sub>+a<sub>1</sub>x+a<sub>2</sub>x<sup>2</sup>+· · ·+a<sub>n</sub>x<sup>n</sup>, β = b<sub>0</sub>+b<sub>1</sub>x+b<sub>2</sub>x<sup>2</sup>+· · ·+b<sub>m</sub>x<sup>m</sup>
∈ R[x] satisfy αR[x]β = 0, then a<sub>i</sub>Rb<sub>j</sub> = 0 for each i, j. In this note we consider quasi-Armendariz property of a special subring of the infinite upper triangular matrix ring over a ring R.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665012008A 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 Okayama0030-15664812006A New Generalization of the Poisson Kernel173180ENSerapBulut10.18926/mjou/33351<p>The purpose of this paper is to give a new generalization of the Poisson Kernel in two dimensions and discuss an integral formula for this.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663711995A Non-immersion Result for Lens Spaces Ln(2m)137151ENBernardJunod10.18926/mjou/33790No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663211990A Note on Anderson-Anderson-Johnson Questions711ENRyukiMatsuda10.18926/mjou/33303No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664612004A Note on Commutative Gelfand Theory for Real Banach Algebras121130ENSin-EiTakahashiTakeshiMiuraOsamuHatori10.18926/mjou/33926<p>Pfaffenberger and Phillips [2] consider a real and unital case of the classical commutative Gelfand theorem and obtain two representation theorems. One is to represent a unital real commutative Banach algebra A as an algebra of continuous functions on the unital homomorphism space ΦA. The other is to represent A as an algebra of continuous sections on the maximal ideal space MA. In this note, we point out that similar theorems for non-unital case hold and show that two representation theorems are essentially identical.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663211990A Note on Derivations8388ENMatejBrešar10.18926/mjou/33312No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663111989A Note on Fixed Rings8591ENYoshimiKitamura10.18926/mjou/33244No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664512003A Note on Geodesics and Curvatures of Certain 4-spaces145162ENTominosukeOtsuki10.18926/mjou/33731<p>This work is a continuation of the papers [3] and [4], in which we studied the metrics (1.1) and (1.2) on R<sup>4</sup><sub>+</sub>. The metric (1.1) with a = 0: ds<sup>2</sup> = dx1dx1 + dx2dx2 + dx3dx3 − dx4dx4
x4x4
is analogous to the metric of the hyperbolic 4-space. We considered fundamentally metrics on R<sup>4</sup><sub>+</sub> based on this hyperbolic type metric, not Euclidean or Minkowsky types.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664111999A Note on Osofsky-Smith Theorem1519ENLiuZhongkui10.18926/mjou/33620No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664712005A Note on Quotients of Orthogonal Groups159162ENAkihiroOhsita10.18926/mjou/33593<p>We discuss the mod 2 cohomology of the quotient of a compact classical Lie group by its maximal 2-torus. In particular, the case of the orthogonal group is treated. The case of the spinor group is not included.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663211990A Note on Zero Commutative and Duo Rings7376ENJebrel M.Habeb10.18926/mjou/33313No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664212000A Note on the Degenerate Morse Inequalities153160ENZhouJianwei10.18926/mjou/33291<p>In this paper we give an analytic proof of the degenerate Morse inequalities in the spirit of E. Witten. The max-min methods are used to estimate the number of esmallf eigenvalues of Wittenfs deformed Laplacian.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663611994A Note on the K-Theory of Constructible Sheves over a Curve179184ENTetsuoSasaki10.18926/mjou/33207No 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 Okayama0030-15664011998A Remark on Localization of Injective Modules3943ENUSyu10.18926/mjou/33674No 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 Okayama0030-15664412002A 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 Okayama0030-15664612004A Study of Fq-Functions Connected with Ramanujan's Tenth Order Mock Theta Functions131140ENBhaskarSrivastava10.18926/mjou/33925<p><P>We have defined generalized functions which reduce to Ramanujan's mock theta functions of order ten. We have shown that they are Fq-functions. We have given their integral representation and multibasic expansions.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663211990A Theorem on Radicals in Functor Categories with Application to Torsion Theories147151ENYaoMusheng10.18926/mjou/33317No 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 Okayama0030-15662421982A certain type of commutative Hopf Galois extensions and their groups137152ENAtsushiNakajima10.18926/mjou/33985No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662711985A characterization of boolean rings (III)3334ENYasuyukiHiranoHiroakiKomatsu10.18926/mjou/33450No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662811986A characterization of quadratic residue codes15ENNoboruIto10.18926/mjou/33949No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661411969A characterization of quaternion algebras3536ENHisaoTominaga10.18926/mjou/33670No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662321981A classification of abelian extensions of rings117124ENMiguelFerreroKazuoKishimoto10.18926/mjou/33847No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661921977A classification of free extensions of rings of a automorphism type and derivation type163169ENKazuoKishimoto10.18926/mjou/33411No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661821976A classification of free quadratic extensions of rings139148ENKazuoKishimoto10.18926/mjou/33798No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662611984A commutativity theorem for one-sided s-unital rings125128ENHisaoTominagaAdilYaqub10.18926/mjou/33328No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662221980A commutativity theorem for rings with constraints involving an additive subsemigroup. II107109ENHazarAbu-KhuzamHisaoTominagaAdilYaqub10.18926/mjou/33880No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662611984A commutativity theorem for rings109111ENHiroakiKomatsu10.18926/mjou/33324No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662511983A commutativity theorem for s-unital rings. II1922ENMotoshiHongan10.18926/mjou/33386No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662111979A commutativity theorem for s-unital rings1114ENMotoshiHonganHisaoTominaga10.18926/mjou/33832No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663011988A commutativity theorem for semiprime rings with constraints involving a derivation4144ENAndrzejTrzepizur10.18926/mjou/33547No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566721957A condition that a space is group-like123149ENMasahiroSugawara10.18926/mjou/33632No 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 Okayama0030-15662421982A construction of spaces with general connections which have points swallowing geodesics157165ENTominosukeOtsuki10.18926/mjou/33978No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661221966A fixpoint theorem on Sp(n)/U(n)91105ENToshiyukiMaebashi10.18926/mjou/33511No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663311991A generalization of a theorem of Posner97101ENMotoshiHongan10.18926/mjou/33700No 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 Okayama0030-15666012018A 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 Okayama0030-15663311991A note on E(HPn) for n≤4163176ENNorioIwaseKen-IchiMaruyamaShichiroOka10.18926/mjou/33697No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566721957A note on Galois extensions of division rings179183ENNobuoNobusawa10.18926/mjou/33631No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661611973A note on Galois theory1116ENMiguelFerrero10.18926/mjou/33771No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566711957A note on Galois theory of division rings8388ENMikaoMoriyaTakasiNagaharaHisaoTominaga10.18926/mjou/33641No 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 Okayama0030-15661921977A note on Morita equivalence of polynomial rings121122ENKatsuoChiba10.18926/mjou/33409No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661411969A note on Schauder basis1721ENOsamuKatsumata10.18926/mjou/33666No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665912017A note on balance equations for doubly periodic minimal surfaces117130ENPeterConnorDepartment of Mathematical Sciences, Indiana University South Bend10.18926/mjou/54718Most known examples of doubly periodic minimal surfaces in R<sup>3</sup> with parallel ends limit as a foliation of R<sup>3</sup> by horizontal noded planes, with the location of the nodes satisfying a set of balance equations. Conversely, for each set of points providing a balanced configuration, there is a corresponding three-parameter family of doubly periodic minimal surfaces. In this note we derive a differential equation that is equivalent to the balance equations for doubly periodic minimal surfaces. This allows for the generation of many more solutions to the balance equations, enabling the construction of increasingly complicated surfaces.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662211980A note on commutative separable algebras13ENStuart Sui-ShengWang10.18926/mjou/33895No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662321981A note on commutative separable algebras. II115116ENDavid E.DobbsStuart Sui-ShengWang10.18926/mjou/33853No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662321981A note on commutativity of rings141145ENYujiKobayashi10.18926/mjou/33841No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566711957A note on conjugates7576ENHisaoTominaga10.18926/mjou/33639No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566911959A note on conjugates II13ENHisaoTominaga10.18926/mjou/33400No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661321968A note on group rings of p-groups107109ENAtsushiNakajimaHisaoTominaga10.18926/mjou/33459No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662311981A note on isomorphism invariants of a modular group algebra15ENTôruFurukawa10.18926/mjou/33867No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566421955A note on matrix rings189191ENHisaoTominaga10.18926/mjou/33749No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661411969A note on nets15ENW. E.Pfeffer10.18926/mjou/33668No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661411969A note on normal basis elements2728ENHisaoTominaga10.18926/mjou/33658No 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 Okayama0030-15661521972A note on quotient rings over Frobenius extensions141147ENYoshimiKitamura10.18926/mjou/33520No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661811975A note on quotient rings over a quasi-Frobenius extension5767ENYoshimiKitamura10.18926/mjou/33810No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661411969A note on separable extensions of commutative rings1315ENMotoshiHonganTakasiNagahara10.18926/mjou/33665No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662211980A note on separable polynomials in skew polynomial rings of automorphism type7376ENTakasiNagahara10.18926/mjou/33894No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662211980A note on separable polynomials in skew polynomial rings of derivation type5960ENShûichiIkehata10.18926/mjou/33896No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661321968A note on the differential equations with relay-hysteresis183198ENMasatakaYorinaga10.18926/mjou/33458No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662711985A note on the number of prime factors of integers in short intervals159171ENGosukeYamano10.18926/mjou/33436No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661321968A note on uniform integrability175182ENShozoKoshi10.18926/mjou/33462No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663011988A note on universally going-down14ENDavid E.Dobbs10.18926/mjou/33558No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661411969A radical and a subcategory in an exact category5967ENAtsushiNakajima10.18926/mjou/33667No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661411969A remark on Lyapunov-Halmos-Blackwell's convexity theorem2933ENShozoKoshi10.18926/mjou/33659No 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 Okayama0030-15665912017A remark on the Lavallee-Spearman-Williams-Yang family of quadratic fields113116ENKwang-SeobKimSchool of Mathematics, Korea Institute for Advanced StudyYasuhiroKishiDepartment of Mathematics, Aichi University of Education10.18926/mjou/54717In [4], M. J. Lavallee, B. K. Spearman, K. S. Williams and Q. Yang introduced a certain parametric D5-quintic polynomial and studied its splitting field. The present paper gives an infinite family of quadratic fields with class number divisible by 5 by using properties of its polynomial.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662811986A remark on the ergodic Hilbert transform159163ENRyotaroSato10.18926/mjou/33946No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666212020A 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 Okayama0030-15662811986A ring topology based on submodules over an Asano order of a ring6164ENKentaroMurata10.18926/mjou/33943No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662521983A simple proof of a theorem on abelian regular right ideals123ENYasuyukiHirano10.18926/mjou/33370No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662121979A study on Artinian rings115123ENHisaoTominagaIchiroMurase10.18926/mjou/33822No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661911976A technique of numerical production of a sequence of pseudo-prime numbers14ENMasatakaYorinaga10.18926/mjou/33423No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566911959A theorem on rings912ENHisaoTominaga10.18926/mjou/33398No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662711985A theorem on semi-centralizing derivations of prime rings1112ENArifKaya10.18926/mjou/33443No 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 (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 Okayama0030-15665312011ABSTRACT LOCAL COHOMOLOGY FUNCTORS129154ENYujiYoshinoTakeshiYoshizawa10.18926/mjou/41402We propose to define the notion of abstract local cohomology functors. The ordinary local cohomology functor R<sub>I</sub> with support in the closed subset defined by an ideal I and the generalized local cohomology functor R<sub>I,J</sub> defined in [16] are characterized as elements of the set of all the abstract local cohomology functors.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665512013AN ALGEBRAIC APPROACH TO THE CAMERON-MARTIN-MARUYAMA-GIRSANOV FORMULA167190ENJirôAkahoriTakafumiAmabaSachiyoUraguchi10.18926/mjou/49104In this paper, we will give a new perspective to the Cameron-
Martin-Maruyama-Girsanov formula by giving a totally algebraic proof
to it. It is based on the exponentiation of the Malliavin-type differenti-
ation and its adjointness.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665712015AN EXPLICIT EFFECT OF NON-SYMMETRY OF RANDOM WALKS ON THE TRIANGULAR LATTICE129148ENSatoshiIshiwataHiroshiKawabiTsubasaTeruya10.18926/mjou/53045In the present paper, we study an explicit effect of non-symmetry on asymptotics of the n-step transition probability as n ∞
for a class of non-symmetric random walks on the triangular lattice. Realizing the triangular lattice into R<sup>2</sup> appropriately, we observe that the
Euclidean distance in R<sup>2</sup> naturally appears in the asymptotics. We characterize this realization from a geometric view point of Kotani-Sunadafs
standard realization of crystal lattices. As a corollary of the main theorem, we obtain that the transition semigroup generated by the non-symmetric random walk approximates the heat semigroup generated by
the usual Brownian motion on R<sup>2</sup>.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665312011AN EXPLICIT PSp<sub>4</sub>(3)-POLYNOMIAL WITH 3 PARAMETERS OF DEGREE 40155165ENHidetakaKitayama10.18926/mjou/41403We will give an explicit polynomial over ℚ with 3 parameters of degree 40 as a result of the inverse Galois problem. Its Galois group over ℚ (resp. ℚ(-3)) is isomorphic to PGSp<sub>4</sub>(3) (resp. PSp<sub>4</sub>(3)) and it is a regular PSp<sub>4</sub>(3)-polynomial over ℚ(p|3). To construct the polynomial and prove its properties above we use some results of Siegel modular forms and permutation group theory.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665212010ARITHMETIC ELLIPTIC CURVES IN GENERAL POSITION128ENShinichiMochizuki10.18926/mjou/33503<p>We combine various well-known techniques from the theory of heights, the theory of gnoncritical Belyi mapsh, and classical analytic number theory to conclude that the gABC Conjectureh, or, equivalently, the so-called gEffective Mordell Conjectureh, holds for arbitrary rational points of the projective line minus three points if and only if it holds for rational points which are in gsufficiently general positionh in the sense that the following properties are satisfied: (a) the rational point under
consideration is bounded away from the three points at infinity at a given finite set of primes; (b) the Galois action on the l-power torsion points of the corresponding elliptic curve determines a surjection onto
GL<sub>2</sub>(Zl), for some prime number l which is roughly of the order of the sum of the height of the elliptic curve and the logarithm of the discriminant of the minimal field of definition of the elliptic curve, but does not divide the conductor of the elliptic curve, the rational primes
that are absolutely ramified in the minimal field of definition of the elliptic curve, or the local heights [i.e., the orders of the q-parameter at primes of [bad] multiplicative reduction] of the elliptic curve.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665312011ASYMPTOTIC ANALYSIS FOR GREEN FUNCTIONS OF AHARONOV-BOHM HAMILTONIAN WITH APPLICATION TO RESONANCE WIDTHS IN MAGNETIC SCATTERING137ENHideoTamura10.18926/mjou/41395The Aharonov–Bohm Hamiltonian is the energy operator which governs quantum particles moving in a solenoidal field in two dimensions. We analyze asymptotic properties of its Green function with spectral parameters in the unphysical sheet. As an application, we discuss
the lower bound on resonance widths for scattering by two magnetic fields with compact supports at large separation. The bound is evaluated in terms of backward scattering amplitudes by a single magnetic field. A special emphasis is placed on analyzing how a trajectory oscillating between two magnetic fields gives rise to resonances near the real axis, as the distance between two supports goes to infinity. We also refer to the relation to the semiclassical resonance theory for scattering
by two solenoidal fields.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666012018Absolute 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 Okayama0030-15664011998Actions on Spaces of Polynomials141145ENKohheiYamaguchi10.18926/mjou/33677No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664312001Adjoint Orbit Types of Compact Exceptional Lie Group G<sub>2</sub> in its Lie Algebra 1724ENTakashiMiyasaka10.18926/mjou/33257No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665812016Aharonov--Bohm effect in resonances of magnetic Schrödinger operators in two dimensions III79108ENHideoTamura10.18926/mjou/53918We study the Aharonov–Bohm effect (AB effect) in quantum resonances for magnetic scattering in two dimensions. The system consists of four scatters, two obstacles and two scalar potentials with compact support, which are largely separated from one another. The obstacles by which the magnetic fields are completely shielded are vertically placed between the supports of the two potentials. The system yields a two dimensional model of a toroidal scattering system in three dimensions. The resonances are shown to be generated near the real axis by the trajectories trapped between two supports of the scalar potentials as the distances between the scatterers go to infinity. We analyze how the AB effect influences the location of resonances. The result heavily depends on the width between the two obstacles as well as on the magnetic fluxes. The critical case is that the width is comparable to the square root of the distance between the supports of the two potentials.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665812016Aharonov--Bohm effect in resonances of magnetic Schrödinger operators in two dimensions II4178ENHideoTamura10.18926/mjou/53917We study the Aharonov–Bohm effect (AB effect) in quantum resonances for magnetic scattering in two dimensions. The system consists of four scatters, two obstacles and two scalar potentials with compact support, which are largely separated from one another. The obstacles by which the magnetic fields are completely shielded are horizontally placed between the supports of the two potentials. The fields do not influence particles from a classical mechanical point of view, but quantum particles are influenced by the corresponding vector potential which does not necessarily vanish outside the obstacle. This quantum phenomenon is called the AB effect. The resonances are shown to be generated near the real axis by the trajectories trapped between two supports of the scalar potentials as the distances between the scatterers go to infinity. We analyze how the AB effect influences the location of resonances. The result is described in terms of the backward amplitudes for scattering by each of the scalar potentials, and it depends heavily on the ratios of the distances between the four scatterers as well as on the magnetic fluxes of the fields.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662111979Algebra der hyperkomplexen Zahlensysteme (Algebren)5389ENRichardBrauer10.18926/mjou/33837No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663911997Algebraic Loops on Fibrewise Pointed Spaces135145ENRusakoFujino10.18926/mjou/33575No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661311967Algebraic extensions of simple rings I1522ENTakasiNagaharaAtsushiNakajimaHisaoTominaga10.18926/mjou/33468No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661311967Algebraic extensions of simple rings II2328ENTakasiNagaharaHisaoTominaga10.18926/mjou/33469No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661911976Algebras with only finitely many subalgebras4546ENHisaoTominaga10.18926/mjou/33425No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663211990Almost Hermitian Geometry, Geodesic Spheres and Symmetries187206ENM.DjoricL.Vanhecke10.18926/mjou/33292No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664812006Almost Periodic Solutions of C-well-posed Evolution Equations145158ENNguyen VanMinh10.18926/mjou/33352<p>This paper is concerned with the existence and uniqueness of almost periodic mild solutions of evolution equations of the form u(t) = Au(t) + ƒ(t) where A is the generator of a holomorphic Csemigroup on a Banach space and ƒ is an almost periodic function. A sufficient condition in terms of spectral properties of A and ƒ is obtained that extends a well known result in this subject.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661821976Almost commutative rings and their integral extensions105111ENEdward T.Wong10.18926/mjou/33801No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665812016Alternative approach for Siegel's lemma141158ENMakotoNagata10.18926/mjou/53922In this article, we present an alternative approach to show a generalization of Siegel's lemma which is an essential tool in Diophantine problems. Our main statement contains the so-called analytic Siegel's lemma as well as the Bombieri-Vaaler lemma. Our proof avoids relying on the ordinary geometry of numbers.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663211990An Anti-Homomorphism for the Brauer-Long Group4352ENFrancisTilborghs10.18926/mjou/33315No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663511993An Exact Sequence for the Brauer Group of Dimodule Azumaya Algebras6388ENKarl-H.Ulbrich10.18926/mjou/33475No 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 Okayama0030-15663611994An Integral Involving the Error Term of the Mean Square of the Riemann Zeta-Function in the Critical Strip5162ENIsaoKiuchi10.18926/mjou/33211No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662811986An O theorem for a class of Dirichlet series151158ENDonRedmond10.18926/mjou/33952No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662811986An algebraic proof of a theorem of Warfield on algebraically compact modules5360ENGoroAzumaya10.18926/mjou/33951No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666012018An 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 Okayama0030-15662411982An application of certain multiplicities of C map germs2535ENYoshifumiAndo10.18926/mjou/33994No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665912017An arithmetic function arising from the Dedekind ψ function8192ENColinDefantDepartment of Mathematics, University of Florida10.18926/mjou/54715We define ψ‾ to be the multiplicative arithmetic function that satisfies<br>
<img src="http://www.lib.okayama-u.ac.jp/www/mjou/mjou_59_81.png"><br>
for all primes <i>p</i> and positive integers α. Let <i>λ(n)</i> be the number of iterations of the function <i>ψ‾</i> needed for <i>n</i> to reach 2. It follows from a theorem due to White that <i>λ</i> is additive. Following Shapiro's work on the iterated <i>φ</i> function, we determine bounds for <i>λ</i>. We also use the function <i>λ</i> to partition the set of positive integers into three sets <i>S<sub>1</sub>, S<sub>2</sub>, S<sub>3</sub></i> and determine some properties of these sets.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663011988An elementary proof of a theorem of Margulis for Kleinian groups177186ENTomioInada10.18926/mjou/33550No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661521972An equivalence relation in topology113123ENNormanLevine10.18926/mjou/33525No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662911987An extension of a theorem of D. Gromoll and J. A. Wolf245248ENNobuhiroInnami10.18926/mjou/33259No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662711985An ore extension over a v-HC order107120ENKazuoKishimotoHidetoshiMarubayashiAkiraUeda10.18926/mjou/33437No 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 Okayama0030-15665812016Another description of quasi tertiary composition109123ENHideakiŌshimaKatsumiŌshima10.18926/mjou/53919We give another description of quasi tertiary composition in terms of horizontal and vertical compositions. As an application of the description and a modified result of Hardie-Kamps-Marcum-Oda, we see that any quasi tertiary composition has an indeterminacy.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661521972Another proof of the invariance of Ulm's functions in commutative modular group rings137139ENPaul F.DuboisSudarshan K.Sehgal10.18926/mjou/33519No 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 Okayama0030-15663811996Anti-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 Okayama0030-15664712005Appendix to "Some Metric Invariants of Spheres and Alexandrov Spaces II''189192ENKazuyoshiKiyohara10.18926/mjou/33595No 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 Okayama0030-1566511955Associated Riemannian manifolds and motions1342ENTominosukeOtsuki10.18926/mjou/33571No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663111989Asymptotic Behavior of a Certain Multiplicative Function207212ENIsaoKiuchi10.18926/mjou/33245No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665812016Asymptotic properties in forward directions of resolvent kernels of magnetic Schrödinger operators in two dimensions139ENHideoTamura10.18926/mjou/53916We study the asymptotic properties in forward directions of resolvent kernels with spectral parameters in the lower half plane (unphysical sheet) of the complex plane for magnetic Schrödinger operators in two dimensions. The asymptotic formula obtained has an application to the problem of quantum resonances in magnetic scattering, and it is especially helpful in studying how the Aharonov–Bohm effect influences the location of resonances. Here we mention only the results without proofs.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661211963Automorphisms of algebras and a theorem concerning norms3947ENKatsuhikoMasuda10.18926/mjou/33515No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662311981Azumaya algebras and skew polynomial rings1932ENShûichiIkehata10.18926/mjou/33870No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662611984Azumaya algebras and skew polynomial rings. II4957ENShûichiIkehata10.18926/mjou/33341No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665212010BELYI FUNCTION ON X<sub>0</sub>(49) OF DEGREE 76163ENKenjiHoshinoHiroakiNakamura10.18926/mjou/33500No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566421955Banach algebras generated by a bounded linear operator97102ENMinoruTomita10.18926/mjou/33753No 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 Okayama0030-15664712005Belyi Function whose Grothendieck Dessin is a Flower Tree with Two Ramification Indices119132ENToruKomatsu10.18926/mjou/33604<p>In this paper we present an explicit construction of Belyi functions whose dessins are flower trees (i.e., graphs of diameter 4) with two ramification indices. We also give a method for obtaining Belyi functions defined over the moduli fields of the dessins.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566921960Bemerkung zu meiner Arbeit "Poincarésche Vermutung"165172ENKen'itiKoseki10.18926/mjou/33392No 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 Okayama0030-15661311967Beziehung zwischen dem Thullenschen Satz und dem Runge-Besseschen Satz9192ENKen'itiKoseki10.18926/mjou/33471No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663311991Bialgebras and Galois extensions3746ENAtsushiNakajima10.18926/mjou/33709No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665912017Blowup and global existence of a solution to a semilinear reaction-diffusion system with the fractional Laplacian175218ENTomoyukiKakehiDepartment of Mathematics, Okayama UniversityYoshihitoOshitaDepartment of Mathematics, Okayama University10.18926/mjou/54723In this paper, we deal with the semilinear reaction diffusion system with the fractional Laplacian.<br>
<img src="http://www.lib.okayama-u.ac.jp/www/mjou/mjou_59_175.png"><br>
where <i>p,q</i> > 1 and 0 < <i>α</i> < 1. We study the existence of a global in time solution, the blowup of a solution, and the life span of the blowup solution to the above reaction-diffusion system for sufficiently small initial data.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663011988Bordism theory with reality and duality theorem of Poincaré type151160ENMichikazuFujii10.18926/mjou/33551No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664812006Bott's Theorem on Samelson Products113124ENKeiSugata10.18926/mjou/33346No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663111989C-Totally Real Submanifolds of S^7(1) with Non-Negative Sectional Curvature227242ENFrankiDillenLucVrancken10.18926/mjou/33226No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665112009COMMUTATIVE GROUP ALGEBRAS OF ABELIAN GROUPS WITH UNCOUNTABLE POWERS AND LENGTHS179192ENPeterDanchev10.18926/mjou/33221<p>Let F be a field of char(F) = p > 0 and G an abelian group
with p-component G<sub>p</sub> of cardinality at most ℵ<sub>1</sub> and length at most ω<sub>1</sub>. The main affirmation on the Direct Factor Problem is that S(FG)/G<sub>p</sub> is totally projective whenever F is perfect. This extends results due to May (Contemp. Math., 1989) and Hill-Ullery (Proc. Amer. Math. Soc., 1990). As applications to the Isomorphism Problem, suppose that for any group H the F-isomorphism FH ≅ FG holds. Then if G<sub>p</sub> is totally projective, H<sub>p</sub> ≅ G<sub>p</sub>. This partially solves a problem posed by May (Proc. Amer. Math. Soc., 1988). In particular, H ≅ G provided G is
p-mixed of torsion-free rank one so that G<sub>p</sub> is totally projective. The same isomorphism H ≅ G is fulfilled when G is p-local algebraically compact too. Besides if F<sub>p</sub> is the simple field with p-elements and G<sub>p</sub> F<sub>p</sub>H
is a coproduct of torsion complete groups, F<sub>p</sub>H ≅ F<sub>p</sub>G as F<sub>p</sub> F<sub>p</sub>-algebras implies H<sub>p</sub> ≅ G<sub>p</sub>. This expands the central theorem obtained by us in (Rend. Sem. Mat. Univ. Padova, 1999) and partly settles the generalized version of a question raised by May (Proc. Amer. Math. Soc.,1979) as well. As a consequence, when G<sub>p</sub> is torsion complete and G is p-mixed of torsion-free rank one, H ≅ G. Moreover, if G is a coproduct of p-local algebraically compact groups then H ≅ G. The last
attainment enlarges an assertion of Beers-Richman-Walker (Rend. Sem. Mat. Univ. Padova, 1983).
Each of the reported achievements strengthens our statements in this direction (Southeast Asian Bull. Math., 2001-2002) and also continues own studies in this aspect (Hokkaido Math. J., 2000) and (Kyungpook Math. J., 2004).</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665412012CONTROLLABILITY OF FRACTIONAL INTEGRODIFFERENTIAL SYSTEMS VIA SEMIGROUP THEORY IN BANACH SPACES133143ENMohammedHaziMabroukBragdi10.18926/mjou/47198This paper focuses on controllability results of fractional integrodifferential systems in Banach spaces. We obtain sufficient conditions for the controllability results by using fractional calculus, semi-group theory and the fixed point theorem.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665612014CONVEXITY PROPERTIES OF A NEW GENERAL INTEGRAL OPERATOR OF p-VALENT FUNCTIONS171178ENSerapBulut10.18926/mjou/52076In this paper, we introduce a new general integral operator
and obtain the order of convexity of this integral operator.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665212010CORRECTION: RESULTS ON PRIME NEAR-RINGS WITH (,)-DERIVATION199200ENÖznurGölbaşiNeşetAydin10.18926/mjou/33502No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662221980Carmichael numbers with many prime factors169184ENMasatakaYorinaga10.18926/mjou/33876No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665912017Categorical characterization of strict morphisms of fs log schemes119ENYuichiroHoshiResearch Institute for Mathematical Sciences, Kyoto UniversityChikaraNakayamaDepartment of Economics, Hitotsubashi University10.18926/mjou/54710In the present paper, we study a categorical characterization of strict morphisms of fs log schemes. In particular, we prove that strictness of morphisms of fs log schemes is preserved by an arbitrary equivalence of categories between suitable categories of fs log schemes. The main result of the present paper leads us to a relatively simple alternative proof of a result on a categorical representation of fs log schemes proved by S. Mochizuki.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661721975Centralizers of a module over a quasi-Frobenius extension103123ENYoshimiKitamura10.18926/mjou/33902No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664512003Certain Metrics on R<sup>4</sup><sub>+</sub> (III)163186ENTominosukeOhtsuki10.18926/mjou/33730No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664212000Certain Metrics on R<sup>4</sup><sub>+</sub> 161182ENTominosukeOtsuki10.18926/mjou/33282<p>We studied the pseudo-Riemannian metric
on R<sup>3</sup> ~ R<sub>+</sub>, where γ<sup>2</sup> = Σ<sup>3</sup><sub>b=1</sub>x<sub>b</sub>x<sub>b</sub> and a = constant, which satisfies the Einstein condition (in [1], [2], [3] ). The purpose of this work is to find Einstein metrics including the above metric as a special one, which is analogous to the relation between the Schwarzschild metric and the Kerr one in the theory of relativity.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664312001Certain Metrics on R<sup>4</sup>+(II)143184ENTominosukeOtsuki10.18926/mjou/33256<p>This paper is a continuation of the one with the same title([4]), in which we obtained a special solution for a system of differential equations on metric tensors on R<sup>4</sup>+ satisfying the Einstein condition for Case I generalizing the Ot-metric:
in Theorem 1, and proved that there exist no solutions for Case II in Theorem 2. In this work, we shall show that we can obtain more general solutions for Case I which depend on the latitude parameter. We use the results in [4], so the section numbers start from 5.
1. Preliminaries and curvature tensor
2. Ricci tensor
3. Solutions for Case I
4. Analysis and a conclusion for Case II</p>
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 Okayama0030-15663111989Chacron's Condition and Commutativity Theorems101120ENHiroakiKomatsuHisaoTominaga10.18926/mjou/33243No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663011988Chain conditions and quotient rings of p.p. rings7178ENMasayukiÔhori10.18926/mjou/33549No 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 Okayama0030-15664812006Characterization of Frobenius Groups of Special Type7376ENArun S.Muktibodh10.18926/mjou/33361<p>We define a Con-Cos group G to be one having a proper
normal subgroup N whose cosets other than N itself are conjugacy classes. It follows easily that N = Gf, the derived group of G. Most of the paper is devoted to trying to classify finite Con-Cos groups satisfying the additional requirement that N has just two conjugacy classes. We show that for such groups the center Z(G) has order at most 2, and if Z(G) = {1}, then G is a Frobenius group of a rather special type.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663911997Characterizations of Hereditary Modules and V-modules716ENWeiminXue10.18926/mjou/33581No 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 Okayama0030-15662911987Closed ideals in non-unital matrix rings147152ENShojiKyunoMi-Soo B.SmithNobuoNobusawa10.18926/mjou/33264No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661821976Cobordism theory with reality171188ENMichikazuFujii10.18926/mjou/33806No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662211980Cohomology for comodules515ENAtsushiNakajima10.18926/mjou/33890No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664011998Commutative Group Algebras of Abelian Σ -groups7790ENPeterDanchev10.18926/mjou/33672No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664512003Commutative Group Algebras of Direct Sums of σ-Summables Abelian p-Groups116ENPeterDanchev10.18926/mjou/33725No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662611984Commutativity of Hopf Galois extensions with Hopf algebras of derivation type9199ENAtsushiNakajimaKenjiYokogawa10.18926/mjou/33319No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663911997Commutativity of Rings With Powers Commuting on Subsets4556ENHiroakiKomatsu10.18926/mjou/33589No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662021978Commutativity of certain rings179181ENKazuoKishimotoIsaoMogami10.18926/mjou/33959No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663311991Commutativity theorems for algebras and rings7195ENHiroakiKomatsuHisaoTominaga10.18926/mjou/33707No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662211980Commutativity theorems for certain rings6572ENYasuyukiHiranoMotoshiHonganHisaoTominaga10.18926/mjou/33884No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662611984Commutativity theorems for rings with a commutative subset or a nil subset119124ENHisaoTominagaAdilYaqub10.18926/mjou/33338No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662221980Commutativity theorems for s-unital rings satisfying polynomial identities111114ENHazarAbu-KhuzamHisaoTominagaAdilYaqub10.18926/mjou/33875No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662111979Commutativity theorems of Outcalt-Yaqub type2124ENYasuyukiHiranoShûichiIkehataHisaoTominaga10.18926/mjou/33835No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566521956Compact mob with a unique left unit115119ENNaokiKimuraTakayukiTamura10.18926/mjou/33566No 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 Okayama0030-15666112019Complex 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 Okayama0030-1566621957Compositions of linear topological spaces191208ENMinoruTomita10.18926/mjou/33738No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662511983Conditions for elements to be central in certain rings16ENMohamed N.DaifMohamed H.Fahmy10.18926/mjou/33388No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664312001Configuration Spaces with Partially Summable Labels and Homology Theories 4372ENKazuhisaShimakawa10.18926/mjou/33252<p>It is shown that any subset of a topological abelian monoid gives rise to a generalized homology theory that is closely related to the notion of labeled configuration space. Applications of the main theorem include generalizations of the classical Dold-Thom and the Barratt-
Priddy-Quillen-Segal theorems.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664712005Connective Coverings of a Few Cell Complexes133140ENKohheiYamaguchi10.18926/mjou/33594<p>We shall determine the 2-connective coverings of a few cell complexes of the form S<sup>2</sup> ∪f e<sup>n</sup> for n ≥ 4 and 0 ≠ f ∈ π<sub>n-1</sub>(S<sup>2</sup>).</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661411969Continuity of additive functionals8386ENOsamuKatsumataShozoKoshi10.18926/mjou/33662No 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.