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

{"title":"Chordal limits of holomorphic functions at Plessner points","authors":"F. Bagemihl","doi":"10.32917/HMJ/1206139102","DOIUrl":"https://doi.org/10.32917/HMJ/1206139102","url":null,"abstract":"The purpose of this paper is to construct an example of a holomorphic function in the open unit disk D of the complex plane that has a certain kind of boundary behavior at every point of the unit circle Γ. Before describing our example, we introduce some notation and terminology, and then discuss some results of Kurt Meier to which our work is closely related, in order to place it in its proper setting. Let / be a meromorphic function whose domain is D and whose range is a subset of the Riemann sphere Ω. We assume that the reader is familiar with some of the elementary notions of cluster set theory (see [5J). Thus, the cluster set of / at a point ζ e Γ is denoted by C(/, ζ). If X is a chord at C, then Cχ(f9 C) denotes the corresponding chordal cluster set of / at C We say that / has a chordal limit at ζ provided that there exists a chord X at ζ and a value ω e Ω such that Cχ(f, ζ)=α>; if, in particular, X is the radius at C, then α) is called the radial limit of / at ζ. We suppose that the reader knows what is meant when we say that / has an angular limit at a point ζ e Γ. We define the chordal principal cluster set of / at a point ζ e Γ as the set","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"60 1","pages":"109-115"},"PeriodicalIF":0.0,"publicationDate":"1966-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81262454","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 duality theorem in the theory of linear programming","authors":"M. Ohtsuka","doi":"10.32917/HMJ/1206139186","DOIUrl":"https://doi.org/10.32917/HMJ/1206139186","url":null,"abstract":"The well-known duality theorem in the theory of linear programming asserts that, if Jίφ0 and M<oo, then Jί'Φtf and M=M'. We shall generalize this theorem in the present paper. Let X and Y be compact Hausdorff spaces and Φ(x, γ) a universally measurable function on XxY which is bounded below. Let g(χ) be a universally measurable function on X which is bounded below and /(γ) a universally measurable function on Y which is bounded above. Under these general circumstances let Jί be the class of all non-negative Radon measures μ on Y satisfying","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"47 1","pages":"31-39"},"PeriodicalIF":0.0,"publicationDate":"1966-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80872116","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 semigroups, semirings, and rings of quotients","authors":"D. Smith","doi":"10.32917/HMJ/1206139104","DOIUrl":"https://doi.org/10.32917/HMJ/1206139104","url":null,"abstract":"There are many theorems known about the imbedding of algebraic structures in quotient structures, that is, structures with all the properties of the original ones in which suitable candidates (cancellable elements) become invertible, and such that every element of the larger structure is a quotient of elements of the original structure. The best-known classical theorem of this sort asserts that an integral domain may be imbedded in a field of quotients. The construction of such a field, using equivalence classes of ordered pairs, has been adapted to prove a number of generalizations, such as those of Ore [1(Γ] and Asano [1J for rings and Vandiver [14] for semigroups and semirings. In a negative direction, we have the theorem of Malcev ΊΓ that not every ring without zero divisors can be imbedded in a division ring. On the other hand, if one is willing to give up associativity, such an imbedding can always be accomplished (Neumann H9H). We will confine our attention to associative structures. In [2J, Asano generalized his own work with a different kind of construction of quotients using partial endomorphisms (which he called simply \"operators\"). This in turn was extensively generalized by Findlay and Lambek [3]. In recent years there have been many papers devoted to the subject of rings of quotients: see, for example, [7, 113 a n d references listed in these. For the purposes of ring theory, constructions via partial homomorphisms and related ideas are surely more elegant and efficient than the old-fashioned, but more concrete, constructions via equivalence classes of ordered pairs. For example, the verifications of associativity and distributivity are trivial when one uses mappings as elements of the quotient structure. However, the student is usually introduced first (perhaps solely) to the more concrete construction. Thus it is of interest to see this construction in perhaps its most general form, where only the essential ideas are present at each step. In the process, it becomes clear that for purposes of extending a multiplicative structure to include quotients, the accompanying additive structure (if any) is of little or no consequence. Hence imbedding theorems","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"78 1","pages":"123-130"},"PeriodicalIF":0.0,"publicationDate":"1966-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83775886","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":"Axiomatic treatment of full-superharmonic functions","authors":"F. Maeda","doi":"10.32917/HMJ/1206139109","DOIUrl":"https://doi.org/10.32917/HMJ/1206139109","url":null,"abstract":"","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"26 1","pages":"197-215"},"PeriodicalIF":0.0,"publicationDate":"1966-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73521701","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":"Direct methods for the numerical solution of partial difference equations for a rectangle","authors":"Hisayoshi Shintani","doi":"10.32917/HMJ/1206139190","DOIUrl":"https://doi.org/10.32917/HMJ/1206139190","url":null,"abstract":"","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"9 1","pages":"75-90"},"PeriodicalIF":0.0,"publicationDate":"1966-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74571904","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 theory of the multiplicative products of distributions","authors":"Mitsuyuki Itano","doi":"10.32917/HMJ/1206139107","DOIUrl":"https://doi.org/10.32917/HMJ/1206139107","url":null,"abstract":"","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"6 1","pages":"151-181"},"PeriodicalIF":0.0,"publicationDate":"1966-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76963399","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":"Order of the identity class of a loop space","authors":"M. Sugawara","doi":"10.32917/hmj/1206139105","DOIUrl":"https://doi.org/10.32917/hmj/1206139105","url":null,"abstract":"","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"25 1","pages":"131-136"},"PeriodicalIF":0.0,"publicationDate":"1966-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81694265","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 a capacitability problem raised in connection with linear programming","authors":"M. Yamasaki","doi":"10.32917/HMJ/1206139189","DOIUrl":"https://doi.org/10.32917/HMJ/1206139189","url":null,"abstract":"in the case that Jίκ is not empty. This quantity has a potential theoretic meaning. In fact, Fuglede Q2] considered it in case Φ^>0, g—1 and / = 1 and denoted it by capiC We shall call it Fuglede's capacity in §11. For any set A C F, we define in § 1 an inner quantity M{(A) and an outer quantity Me(A) from M(K) in the same way as the inner capacity cap*A and the outer capacity cap*̂ 4 were defined from cap K in [2] . Ohtsuka orally raised the question as to when M{(A) is equal to Me(A). We shall give an answer to this question in the present paper. Kishi Q3] examined this problem in the case that X= Y, Φ(x, y) = Φ(y, x) >0 for all x, ye X, Φ is lower semicontinuous and g=f=l. His main result","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"18 1","pages":"57-73"},"PeriodicalIF":0.0,"publicationDate":"1966-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79426544","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 finite geometries and cyclically generated incomplete block designs","authors":"Sumiyasu Yamamoto, Teijiro Fukuda, N. Hamada","doi":"10.32917/HMJ/1206139106","DOIUrl":"https://doi.org/10.32917/HMJ/1206139106","url":null,"abstract":"","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"13 1","pages":"137-149"},"PeriodicalIF":0.0,"publicationDate":"1966-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83530576","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":"Supplement to ``Weak domination principle''","authors":"Masanori Kishi","doi":"10.32917/HMJ/1206139320","DOIUrl":"https://doi.org/10.32917/HMJ/1206139320","url":null,"abstract":"Lemma 4 in the previous paper \"weak domination principle\" in the volume 28 of this journal is true without the assumption on non-degeneracy. Namely, if G is a positive kernel on Ω = {xu x2, X3} satisfying the weak domination principle, then it satisfies the ordinary domination principle or the inverse domination principle. To see this, let 7Ί2 = 0. Since ϊ23 = 0 implies 7*31 = 0, it is sufficient to notice the imcompatibility of ϊ23 > 0 and Tsi < 0. Thus the main theorems in the paper are to be stated without assuming non-degeneracy as follows.","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"58 1","pages":"147-147"},"PeriodicalIF":0.0,"publicationDate":"1965-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85683162","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}