{"title":"On the structure space of a direct product of rings","authors":"Kanroku Aoyama","doi":"10.32917/HMJ/1206138227","DOIUrl":"https://doi.org/10.32917/HMJ/1206138227","url":null,"abstract":"","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"49 1","pages":"339-353"},"PeriodicalIF":0.0,"publicationDate":"1970-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75997664","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the structure of bialgebras attached to group varieties","authors":"H. Yanagihara","doi":"10.32917/HMJ/1206138378","DOIUrl":"https://doi.org/10.32917/HMJ/1206138378","url":null,"abstract":"","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"6 1","pages":"29-58"},"PeriodicalIF":0.0,"publicationDate":"1970-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82489142","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Notes on derivations of higher order","authors":"Shizuka Sato","doi":"10.32917/HMJ/1206138584","DOIUrl":"https://doi.org/10.32917/HMJ/1206138584","url":null,"abstract":"","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"5 1","pages":"41-46"},"PeriodicalIF":0.0,"publicationDate":"1969-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77658466","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the odd order non-singular immersions of real projective spaces.","authors":"Teiichi Kobayashi","doi":"10.32917/HMJ/1206138528","DOIUrl":"https://doi.org/10.32917/HMJ/1206138528","url":null,"abstract":"","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"71 1","pages":"197-207"},"PeriodicalIF":0.0,"publicationDate":"1969-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85756933","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A generalization of Kuhn's theorem for an infinite game","authors":"Masayuki Takahashi","doi":"10.32917/HMJ/1206138533","DOIUrl":"https://doi.org/10.32917/HMJ/1206138533","url":null,"abstract":"An extensive ^-person game is usually described in terms of a finite tree in an oriented plane. The game involves in its structure the mixed and behavior strategies of each player closely related to some specified information sets. Under the assumption that each move possesses at least two alternatives, H.W. Kuhn [1] proved the theorem that the game has perfect recall if and only if, given any mixed strategies μu β2, •••, βn, there may be associated with them behavior strategies βu /32, •••, /?», each /?,depending only on the corresponding mixed strategy /*,-, so that they give rise to the equalities,","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"106 1","pages":"237-242"},"PeriodicalIF":0.0,"publicationDate":"1969-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87895301","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the decomposition of a linearly connected manifold with torsion.","authors":"M. Kikkawa","doi":"10.32917/HMJ/1206138581","DOIUrl":"https://doi.org/10.32917/HMJ/1206138581","url":null,"abstract":"Let M be a differentiable manifold with a linear connection, and let Φx be the homogeneous holonomy group at a point % e M. If the tangent vector space at x is decomposed into a direct sum of subspaces which are invariant under Φx, then by the parallel displacements along curves on M, parallel distributions are defined on M corresponding to those subspaces. If M is a Riemannian manifold and its connection is Riemannian, then by the de Rham decomposition theorem (Q7] or [_4Γ p. 185) the above parallel distributions are completely integrable and, at any point, M is locally isometric to the direct product of leaves through the point. Moreover, if M is simply connected and complete, it is globally isometric to the direct product of those leaves (see also [7] or [4] p. 192). The above local and global decomposition theorems of de Rham are generalized to the case of pseudo-Riemannian manifold by H. Wu ([9]). On the other hand, in [2], S. Kashiwabara generalized the global decomposition theorem to the case of linearly connected manifold without torsion, under the assumption of local decomposability. In the present paper, a linearly connected manifold with torsion will be treated and a condition of local decomposition will be given in terms of curvature and torsion (Theorem 1). Next, in §4, the results will be applied to a reductive homogeneous space with the canonical connection of the second kind, using the notion of algebra introduced by A. A. Sagle in [8]. Finally, in § 5, we shall remark about the decomposition of a local loop with any point in M as its origin (£3]), corresponding to the local decomposition of the linearly connected manifold M. The author wishes to express his hearty thanks to Prof. K. Morinaga for his kind suggestions and encouragement during the preparation of this paper at Hiroshima University.","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"26 1","pages":"1-9"},"PeriodicalIF":0.0,"publicationDate":"1969-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76885504","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A remark on the homeomorphism group of a manifold","authors":"Y. Nomura","doi":"10.32917/HMJ/1206138587","DOIUrl":"https://doi.org/10.32917/HMJ/1206138587","url":null,"abstract":"","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"100 1","pages":"71-72"},"PeriodicalIF":0.0,"publicationDate":"1969-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79494390","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Multiplication rings containing only finitely many minimal prime ideals","authors":"J. L. Mott","doi":"10.32917/HMJ/1206138588","DOIUrl":"https://doi.org/10.32917/HMJ/1206138588","url":null,"abstract":"","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"108 1","pages":"73-83"},"PeriodicalIF":0.0,"publicationDate":"1969-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80710233","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Relations between capacities and maximum principle","authors":"M. Yamasaki","doi":"10.32917/HMJ/1206138586","DOIUrl":"https://doi.org/10.32917/HMJ/1206138586","url":null,"abstract":"There are various definitions of capacities in potential theory. These capacities are usually used to determine potential theoretic exceptional sets. The aim of this paper is to study some properties of these capacities as set functions. More precisely, let Ω be a locally compact Hausdorff space and Φ be a kernel, i. e., a lower semicontinuous function on Ω x Ω which takes values in (0, + oo]. The adjoint kernel Φ is defined by Φ(x, y) = Φ(y, x). Φ is called symmetric if Φ = Φ. A measure μ will always be a non-negative Radon measure with compact support Sμ. The ^-potential of μ is defined by","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"96 1","pages":"59-69"},"PeriodicalIF":0.0,"publicationDate":"1969-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91034615","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}