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

{"title":"Asymptotic behavior of solutions of parabolic differential equations with bounded coefficients","authors":"T. Kusano","doi":"10.32917/HMJ/1206138526","DOIUrl":"https://doi.org/10.32917/HMJ/1206138526","url":null,"abstract":"","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"17 1","pages":"151-159"},"PeriodicalIF":0.0,"publicationDate":"1969-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85681651","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":"Some properties of the Kuramochi boundary","authors":"F. Maeda","doi":"10.32917/HMJ/1206138531","DOIUrl":"https://doi.org/10.32917/HMJ/1206138531","url":null,"abstract":"It has been shown that the Kuramochi boundary of a Riemann surface or of a Green space has many useful potential-theoretic properties (see Q9], [_4~], C H I etc.). In this paper, we shall give a few more properties of the Kuramochi boundary. We consider a Green space Ω in the sense of Brelot-Choquet [3] and denote by i2* its Kuramochi compactification of Ω (see [_4Γ, [9J and [_14Γ for the definition). Let Γ be the harmonic boundary on J = Ω* — Ω, i.e., the support of a harmonic measure ω = ωXQ (x0 e Ω). By definition, Γ is a non-empty closed subset of Δ. Let KQ be a fixed compact ball in Ω. For any resolutive function φ on J, let Hφ be the Dirichlet solution on Ω—Ko with boundary values φ on Δ and 0 on dK0 ( = t h e relative boundary of Ko). For the existence of Hφ9 see e.g. [11H. If φ is a function on Γ and is the restriction of a resolutive function φ on Δ, then H~ψ is uniquely determined by φ we denote it also by Hφ. With this convention, we consider the space RD(Γ) of functions φ on Γ which are restrictions of resolutive functions on Δ and for which Hφ e HD0. Here, HD0 is the space of all harmonic functions u on Ω — Ko having finite Dirichlet integral D[_υΓ on Ω — Ko and vanishing on dK0. Identifying two functions which are equal ω-almost everywhere, we can define a norm || || on RD(Γ) by","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"7 1","pages":"223-229"},"PeriodicalIF":0.0,"publicationDate":"1969-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82969339","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 overrings of a domain","authors":"H. Butts, N. Vaughan","doi":"10.32917/HMJ/1206138590","DOIUrl":"https://doi.org/10.32917/HMJ/1206138590","url":null,"abstract":"Throughout this paper D will denote an integral domain with 1^0 and quotient field X, and by an overring of D will be meant a ring / such that DczJczK. An ideal A of D is called a valuation ideal provided there exists a valuation overring Dv of D such that ADV nD = A ([22; 340], [10]). If 77 is a general ring property, then we shall refer to an ideal A of D as a Π-ideal provided there exists an overring / of D such that / is a 77-domain (i.e. / has the property 77) and A = AJπD. It is shown in [10] that if every principal ideal of D is a valuation ideal, then D is a valuation ring. Furthermore, if every proper ideal of D is a Dedekind ideal, then D is a Dedekind domain [2] and if every proper ideal of D is a Prufer ideal, then D is a Prufer domain [7], [10; 238]. In this paper we are mainly concerned with the following question. When does the statement (a) \"there exists a collection d of 77-ideals of 7)\" imply the statement (b) \"D is a 77-domain\" (i.e. D has property 77)? Our main result in this direction is that (a) implies (b) when \"77-domain\" = \"Krull domain\" and d is the collection of proper principal ideals of 7), i.e. if every proper principal ideal is a Krull ideal, then D is a Krull domain. The same result holds in case \"Krull domain is replaced by either \"integrally closed domain\" or \"completely integrally closed domain\". In addition we show that (a) implies (b) when d is the collection of proper finitely generated ideals of D and 77 is any of the following ring properties: Prufer, 1-dim. Prufer, almost Dedekind, or Dedekind. We remark that (a) does not always imply (b), even in the case that d is the set of all ideals of D (e.g. if 77 is one of P.I.D., Bezout, or (λR-propertysee Section 5). In general we use the notation and terminology of [21] and [22]. In particular, c denotes containment, while < denotes proper containment and A is a proper ideal of D provided (0)<A<D. The theorems considered in this paper are trivial in case D is a field, so we assume throughout that D has at least one proper ideal. We wish to thank Paul M. Eakin Jr. for suggesting Lemma 3.1 (allowing us to shorten some proofs in Section 3) and Proposition 5.1 to us.","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"33 1","pages":"95-104"},"PeriodicalIF":0.0,"publicationDate":"1969-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89497973","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 homotopy groups of sphere bundles over spheres","authors":"Shichirô Oka","doi":"10.32917/HMJ/1206138527","DOIUrl":"https://doi.org/10.32917/HMJ/1206138527","url":null,"abstract":"","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"37 1","pages":"161-195"},"PeriodicalIF":0.0,"publicationDate":"1969-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86849568","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":"Relative Dirichlet problems on Riemann surfaces","authors":"Hiroshi Tanaka","doi":"10.32917/HMJ/1206138585","DOIUrl":"https://doi.org/10.32917/HMJ/1206138585","url":null,"abstract":"","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"30 1","pages":"47-57"},"PeriodicalIF":0.0,"publicationDate":"1969-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78157866","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":"Duality theorems for continuous linear programming problems","authors":"A. Murakami, M. Yamasaki","doi":"10.32917/HMJ/1206138530","DOIUrl":"https://doi.org/10.32917/HMJ/1206138530","url":null,"abstract":"Continuous linear programmings were first considered by W.F. Tyndall [7~] as a generalization of \"bottle-neck problems\" in dynamic programming. N. Levinson Q6], M. A. Hanson Q3] and M. A. Hanson and B. Mond Q4] generalized the results in [7]. In this paper we shall apply the theory of infinite linear programming studied by K.S. Kretschmer [J5Γ and M. Yamasaki [8] to the investigation of the continuous linear programmings. Our main purpose is to improve the duality theorems in Q6[] and [7J obtained by approximation from the classical finite duality theorem. In order to state the continuous linear programmings, we shall introduce some notation. If D(t) is a matrix on the interval [0, TJ (0< Γ<c>o) in the real line with entries dij(t) and g(t) is a scalar on [0, T~} such that every entry satisfies","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"34 1","pages":"213-221"},"PeriodicalIF":0.0,"publicationDate":"1969-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74116850","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":"Comparison of the classes of Wiener functions","authors":"F. Maeda","doi":"10.32917/HMJ/1206138532","DOIUrl":"https://doi.org/10.32917/HMJ/1206138532","url":null,"abstract":"For a harmonic space satisfying the axioms of M. Brelot [ΊΓ|, one can define the notion of Wiener functions as a generalization of that for a Riemann surface or a Green space (see [2]). The class of Wiener functions may be used to see global properties of the harmonic space in particular, in order to show that a compactification of the base space be resolutive with respect to the Dirichlet problem, it is enough to verify that every continuous function on the compactification is a Wiener function (see Theorem 4.4 in [2]). Thus, given two harmonic structures ξ>i and ξ>2 on the same base space Ω, it may be useful to know when the inclusion BWCBW holds, where BW(i = l, 2) is the class of bounded Wiener functions with respect to φ, (ϊ = l, 2). In this paper, we shall give a sufficient condition for the above inclusion, which includes the conditions given in [4] and [5] for special cases.","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"1 1","pages":"231-235"},"PeriodicalIF":0.0,"publicationDate":"1969-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78506940","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 outer derivations of Lie algebras","authors":"S. Tôgô","doi":"10.32917/HMJ/1206138583","DOIUrl":"https://doi.org/10.32917/HMJ/1206138583","url":null,"abstract":"Let O be the set of Lie algebras L over a field Φ satisfying the conditions that LφL and Z(L)Φ(0 where Z(L) denotes the center of L. Clearly every non-trivial nilpotent Lie algebra belongs to O. It is known ([4], [6], [8], [13]) that every Le Ό has an outer derivation. In [13] we have introduced the notion of Lie algebras of type (Γ) and shown that every Lie algebra L of type (T) such that LΦL admits an outer derivation belonging to 3ΐ, the radical of the derivation algebra ®(Z). It has been also shown that if L e Ό is not of type (Γ) there exists an abelίan ideal of ©(£) containing an outer derivation. From these observations it seems to be interesting to study the case where L is of type (T) such that L = L. The main purpose of this note is to give a detailed consideration to the case just mentioned. Some additional remarks will be also given. In Section 2 we shall show that a Lie algebra L of type (Γ) such that dim Z(L)Φ1 or Φ is of characteristic 2 admits an outer derivation in 3ΐ and that a Lie algebra L of type (T) such that L = L dim Z{L) — and Φ is of characteristic Φ 2 admits an outer derivation in 9ΐ if and only if L does (Theorem 2.2). In Section 35 we shall show that a Lie algebra L over a field of characteristic 0 admits a semisimple outer derivation in 9ΐ if the radical of L does (Proposition 3.1), and based on this result, for a Lie algebra L of type (Γ) such that L = L and dim Z(£) = l, we shall give several properties of the radical of L each of which ensures the existence of a semisimple outer derivation in 31 (Theorem 3.6). In [12] we have studied the existence of the automorphisms of L, when Φ is of characteristic 0, outside the connected algebraic group such that the corresponding Lie algebra is the algebraic hull 3KL)* of $(L), the ideal of ®(£) consisting of all inner derivations of Z. The final section 4 will be devoted to the discussions about the existence of the derivations of L e O which are contained in 9ΐ but not in","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"8 1","pages":"29-40"},"PeriodicalIF":0.0,"publicationDate":"1969-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88932304","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":"The rank of the incidence matrix of points and $d$-flats in finite geometries","authors":"N. Hamada","doi":"10.32917/HMJ/1206138660","DOIUrl":"https://doi.org/10.32917/HMJ/1206138660","url":null,"abstract":"The concept of majority decoding and, more generally, threshold decoding was introduced by Massey (ΊQ. In order to obtain majority decodable codes such as (i) a d-th order Projective Geometry code (whose parity check matrix is the incidence matrix of points and d-flats in PG(ί, p)) and (ii) a d-th order Affine Geometry code (whose parity check matrix is the incidence matrix of points other than the origin and J-flats not passing through the origin in EG(ί, p) it is necessary to investigate the rank of the incidence matrix of points and d-flats in PG(ί, p) and in EG(ί, p) over GF(p). An exact formula for the rank of the incidence matrix of points and hyperplanes ((ί — l)-flats) has been obtained by Graham and Mac Williams [_2~] for the case t = 2 and has been independently obtained by Smith [5~] and by Goethals and Delsarte [ΛΓ for general t. An exact formula for the rank of the incidence matrix of points and d-flats in a special case n = 1 has been obtained by Smith [5]. For general n, although an upper bound for the rank has been obtained by Smith, an explicit formula for the rank has not yet been obtained.*) The purpose of this paper is to derive an explicit formula for the rank of the incidence matrix of points and d-flats in PG(ί, p) and in EG(ί, p) for the general case, by extending the methods used by Smith. The main results are as follows.","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"57 1","pages":"381-396"},"PeriodicalIF":0.0,"publicationDate":"1968-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79410696","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":"Modules over $({rm qa})$-rings","authors":"H. Harui","doi":"10.32917/HMJ/1206138651","DOIUrl":"https://doi.org/10.32917/HMJ/1206138651","url":null,"abstract":"","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"56 1","pages":"247-257"},"PeriodicalIF":0.0,"publicationDate":"1968-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77871303","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}