Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry最新文献

{"title":"Composition of some series of association algebras","authors":"Sumiyasu Yamamoto, Y. Fujii, N. Hamada","doi":"10.32917/HMJ/1206139234","DOIUrl":"https://doi.org/10.32917/HMJ/1206139234","url":null,"abstract":"","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"42 4","pages":"181-215"},"PeriodicalIF":0.0,"publicationDate":"1965-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91442969","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":"Note on Miller's recurrence algorithm","authors":"Hisayoshi Shintani","doi":"10.32917/HMJ/1206139318","DOIUrl":"https://doi.org/10.32917/HMJ/1206139318","url":null,"abstract":"","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"2 1","pages":"121-133"},"PeriodicalIF":0.0,"publicationDate":"1965-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83070187","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 support theorems","authors":"S. Tôgô","doi":"10.32917/hmj/1206139313","DOIUrl":"https://doi.org/10.32917/hmj/1206139313","url":null,"abstract":"We denote by ^ _ i the 7z—1 dimensional space consisting of elements ξ'. Let 2), S? and 0 M be the spaces of all C°°-functions with compact supports, all rapidly decreasing C°°-functions and all slowly increasing C°°-functions on Rn respectively. These spaces are provided with usual topologies of L. Schwartz JΓ. Let 2X and έf be the strong duals of 2) and Sf respectively and let O'c be the space of all rapidly decreasing distributions. We shall denote by Quiβn-x) the space 0M considered on Ξn-i. By the partial Fourier transform of T e Sf' we understand the Fourier transform of T with respect to the first n—1 variables which will be denoted by t(ξ t). For any A(ξ') e O M ( ^ _ I ) , we define the operator A(DX,) on y\" as follows: The partial Fourier transform of A(DX,) T, Γ e / , is A(ξ') f(ξ t). In this paper we are concerned with the operator of the following form :","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"22 1","pages":"43-49"},"PeriodicalIF":0.0,"publicationDate":"1965-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81565857","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 connectedness theorem on schemes over local domains","authors":"H. Yanagihara","doi":"10.32917/HMJ/1206139233","DOIUrl":"https://doi.org/10.32917/HMJ/1206139233","url":null,"abstract":"The Connectedness Theorem in algebraic geometry was first proved by Zariski, using the theory of holomorphic functions on an algebraic variety, and it was applied to show the Principle of Degeneration in [7]. Later on, Chow gave \"a general Connectedness Theorem\" which asserts essentially that the Connectedness Theorem on a protective scheme over a complete local domain holds true. Precisely let X be a protective scheme over Γ=Spec(O), where O is a complete local domain. Then if X is connected, the fiber of X at the closed point of Y is also connected. On the other hand Grothendieck gave a generalization of this theorem to a proper prescheme over a locally noetherian prescheme Y with structure morphism /. He treated the case where the direct image f*(Oχ) is isomorphic to 0Y and applied it to the case where Y is the spectrum of a \"unibranche\" local domain (cf. (Ill, 4.3.) in [2]). In this paper we shall also give a generalization of the Connectedness Theorem on schemes over a complete local domain (Theorem 3). Although a complete local domain is \"unibranche\", our result is not merely a special case of his results but covers a little more, and moreover our method is direct and elementary compared with the elaborate one adopted in [2]. The first section is devoted to a summary of some basic results on proper schemes over a local domain. In §2 we shall show the equivalence of the following two properties (Pi) and (P2) of a local domain O: (Pi) Let Xbe any integral scheme, proper and dominant over F=Spec(O). Then the fiber XyQ of X at the dosed point γ0 of Y is connected. (P2) Let X be any integral scheme of finite type and dominant over Y. Then X is proper over Y if the fiber XyQ of Y at y0 is non-empty and proper over Spec (O/m), where m is the maximal ideal of O. In other words (Pi) means that \"the Connectedness Theorem\" on a proper scheme over Y holds true, and (P2) means that proper morphisms to Y are characterized by the fiber over the closed point γ0 of Y. Next we shall show that any complete local domain satisfies these two properties (Pi) and (P2), using Chow's generalization of the Connectedness Theorem mentioned as above. From these results we shall obtain a generalization of the Connectedness Theorem to schemes over a local domain in §3. Lastly in §4 we shall generalize","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"1558 1","pages":"171-179"},"PeriodicalIF":0.0,"publicationDate":"1965-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87859502","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":"An application of the minimax theorem to the theory of capacity","authors":"M. Ohtsuka","doi":"10.32917/HMJ/1206139235","DOIUrl":"https://doi.org/10.32917/HMJ/1206139235","url":null,"abstract":"","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"176 ","pages":"217-221"},"PeriodicalIF":0.0,"publicationDate":"1965-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91447282","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":"Approximate computation of errors in numerical integration of ordinary differential equations by one-step methods","authors":"Hisayoshi Shintani","doi":"10.32917/HMJ/1206139317","DOIUrl":"https://doi.org/10.32917/HMJ/1206139317","url":null,"abstract":"where f(x, y) is assumed to be a sufficiently smooth function. In numerous papers [1 — 16], various methods are obtained for bounding or approximating the errors in numerical integration of (1.1) by one-step methods with the aids of the functions that bound or approximate the function fy (#, y), the truncation error and so on. To avoid the use of such functions for practical purposes, in this paper, n steps of integration with a fixed step-size are considered as one step and a simple method is obtained for approximating the errors without computing explicitly any function other than f(x, y). The method is illustrated by two numerical examples. Since usually the step-size is not changed so often and the estimate of the error is not always necessary for each step of integration, it will not be a serious restriction to fix the step-size for the n steps of integration, and this method may be used as an integration method with a check on the accuracy of the numerical solution.","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"230 1","pages":"97-120"},"PeriodicalIF":0.0,"publicationDate":"1965-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79120103","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 a certain $G$-structure","authors":"T. Nasu","doi":"10.32917/hmj/1206139239","DOIUrl":"https://doi.org/10.32917/hmj/1206139239","url":null,"abstract":"Since the notion of G-struetures on a differentiable manifold M was introduced by S. S. Chern [2] ( 1 ) in 1953, a number of papers on this subject have been published by many writers, such as D. Bernard, R. S. Clark and M. Bruckheimer. Many structures which appear in differential geometry are closely related to the G-structures defined by certain special tensor fields whose components relative to some covering of M by moving frames are constants. Especially, among the G-structures defined by special vector 1-forms one finds the almost product, the almost complex and the almost tangent structures, etc.. As is well known, for such a G-structure we can define two tensors, that is, the Chern invariant and the Nijenhuis tensor. These two tensors play an impotant role in the theory of connections and the integrability of the Gstructures. So far, however, we have known of the relation between them only in some special cases. For example, the Chern invariant vanishes if and only if the Nijenhuis tensor vanishes for almost product, almost complex and almost tangent structures [3]. The main purpose of this paper is to investigate how such a relation will be generalized in the case of the real G-structure defined by any special vector 1-form whose eigenvalues are all real. As usual, we assume that all the objects we encounter in this paper are of class C°°.","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"14 1","pages":"253-270"},"PeriodicalIF":0.0,"publicationDate":"1965-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83625105","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":"Note on $F$-operators in locally convex spaces","authors":"S. Tôgô, R. Shiraishi","doi":"10.32917/HMJ/1206139238","DOIUrl":"https://doi.org/10.32917/HMJ/1206139238","url":null,"abstract":"The theory of F-operators in Banach spaces has been developed by several authors (cf. the references in [ΊΓ], IΓC)According to [5J, SL closed, normally solvable, linear mapping with finite ^-characteristic is called an F-operator. It is the purpose of this paper to generalize this notion of F-operator to locally convex spaces so that we may maintain a number of the basic results known in the case of Banach spaces. For the continuous F-operators, such an attempt has been made by H. Schaefer [9] and then by A. Deprit [4]. Our main concern here is the discussion of a general theory of F-operators: characterization of F-operators, the index theorem for a product, and so on.","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"448 1","pages":"243-251"},"PeriodicalIF":0.0,"publicationDate":"1965-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82896038","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":"Proof of Ohtsuka's theorem on the value of matrix games","authors":"H. Nikaidô","doi":"10.32917/HMJ/1206139236","DOIUrl":"https://doi.org/10.32917/HMJ/1206139236","url":null,"abstract":"","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"22 2 1","pages":"223-224"},"PeriodicalIF":0.0,"publicationDate":"1965-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77993125","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 symmetry of the modular relation in atomic lattices","authors":"S. Maeda","doi":"10.32917/HMJ/1206139232","DOIUrl":"https://doi.org/10.32917/HMJ/1206139232","url":null,"abstract":"","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"192 1","pages":"165-170"},"PeriodicalIF":0.0,"publicationDate":"1965-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83489757","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}