Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry最新文献_第5页

Rings Satisfying the Three Noether Axioms. 满足三诺特公理的环。

Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry Pub Date : 1968-01-01 DOI: 10.32917/HMJ/1206138646

J. Gilbert, H. Butts

引用次数: 2

On Kuramochi's function-theoretic separative metrics on Riemann surfaces 黎曼曲面上Kuramochi的泛函分离度量

Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry Pub Date : 1968-01-01 DOI: 10.32917/HMJ/1206138656

Hiroshi Tanaka

{"title":"On Kuramochi's function-theoretic separative metrics on Riemann surfaces","authors":"Hiroshi Tanaka","doi":"10.32917/HMJ/1206138656","DOIUrl":"https://doi.org/10.32917/HMJ/1206138656","url":null,"abstract":"In order to extend Fatou's and Beurling's theorems to arbitrary Riemann surfaces, Z. Kuramochi introduced ([4]; also see [5] and [7]) two notions of function-theoretic separative metrics, i.e., H. B. and H. D. separative metrics. Since extended Fatou's and Beurling's theorems are stated in terms of compactifications of an open Riemann surface, we shall define separative compactifications rather than separative metrics. In this paper we shall give necessary and sufficient conditions for a compactification to be H. B. or H. D. separative, in terms of the Wiener or the Royden compactification, respectively. Our characterizations are given in a simple form compared with the original definition by Z. Kuramochi and may make it easier to comprehend the meaning of these notions. In §1, we shall discuss compactifications of a hyperbolic Riemann surface R. §2 (resp. §3) is devoted to the study of harmonic measures (resp. capacitary potentials) which were defined by Z. Kuramochi (Q3]). We shall investigate their properties on the Wiener or the Royden boundary of R. In §4 (resp. §5), we shall give our main theorems en H. B. (resp. H. D.) separative compactifications and study the relation between H. B. and H. D. separative compactifications (§5). As an application, we shall show in §6: 1) for Fatou's theorem, Kuramochi's result ([4], [5], [7]) and Constantinescu and Cornea's result (Satz 14.4 in [2J) are equivalent; 2) for Beurling's theorem, Kuramochi's result ( M , [5], [7]) is independent of a similar result by Constantinescu and Cornea (Satz 18.1 in [2]).","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"7 1","pages":"309-330"},"PeriodicalIF":0.0,"publicationDate":"1968-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80337741","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}

引用次数: 3

Direct solution of partial difference equations for a rectangle 矩形偏差分方程的直接解

Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry Pub Date : 1968-01-01 DOI: 10.32917/HMJ/1206138804

Hisayoshi Shintani

引用次数: 8

Evaluation of Hausdorff measures of generalized Cantor sets 广义Cantor集的Hausdorff测度的评价

Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry Pub Date : 1968-01-01 DOI: 10.32917/HMJ/1206138659

K. Hatano

{"title":"Evaluation of Hausdorff measures of generalized Cantor sets","authors":"K. Hatano","doi":"10.32917/HMJ/1206138659","DOIUrl":"https://doi.org/10.32917/HMJ/1206138659","url":null,"abstract":"The problem how a Hausdorff measure of a product set AxB is related to Hausdorff measures of A and B is not completely solved. This problem was first investigated by F. Hausdorff himself Q3] and later by A. S. Besicovitch and P. A. P. Moran [1], J. M. Marstrand ΊΓ and others. Their works and investigations of similar problem for capacity (e.g. [6], [7]) show that evaluation of Hausdorff measures of generalized Cantor sets supplies many clues to this problem. In this paper we first evaluate the α-Hausdorff measure of generalized Cantor sets in the Euclidean space R. As a concequence we see the existence of a compact set in R which has infinite α-Hausdorff measure but zero incapacity (0<a<n). Next we estimate Hausdorff measures of product sets of one-dimensional generalized Cantor sets and then give examples which show that in case the α-Hausdorff measure of £Ί is infinite and the ^-Hausdorff measure of E2 is zero, the (a + β)-Hausdorff measure of Ex x E2 may either be zero, positive finite or infinite. Also these examples answer M. Ohtsuka's question in [_7J (p. 114) in the negative. The author wishes to express his deepest gratitude to Professor M. Ohtsuka for his suggesting the problem and his valuable comments.","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"58 1","pages":"371-379"},"PeriodicalIF":0.0,"publicationDate":"1968-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88498562","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}

引用次数: 3

On Lanczos' algorithm for tri-diagonalization 关于三对角化的Lanczos算法

Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry Pub Date : 1968-01-01 DOI: 10.32917/HMJ/1206138652

Tetsuro Yamamoto

{"title":"On Lanczos' algorithm for tri-diagonalization","authors":"Tetsuro Yamamoto","doi":"10.32917/HMJ/1206138652","DOIUrl":"https://doi.org/10.32917/HMJ/1206138652","url":null,"abstract":"The Lanczos algorithm transforming a given matrix into a tri-diagonal form is well known in numerical analysis and is discussed in many literatures. The possibility of this algorithm is shown in Rutishauser's excellent paper [ΊΓ]. However it seems to the author that no further theoretical consideration has been made since then. The process starts from a pair of trial vectors x and yλ. A pair of the ί-th iterated vectors x{ and y{ can be constructed successively if γj*χjφθ ( l ^ y ^ i —1). Hence, if yp+ι*xp+ι = 0 for somep<Ln — 1, we must modify the algorithm so as to continue. This is possible in case where xp+ί = 0 or 7̂ +1 = 0, while any method of modification is not known in case where Λ ^ + I ^ O and yP+ιφΰ. We shall call the former case \"lucky\" and the latter \"unlucky\". The only thing for us to do in \"unlucky\" case is to choose new starting vectors xu j i and begin again in the hope that this case will not happen later. Rutishauser's result (Q8[] Satz 1) guarantees this possibility. In practical computation, however, \"unlucky\" case may occur after repeated modifications in \"lucky\" cases. Once we encountered with \"unlucky\" case, we have to abandon all the efforts made before and start again with new trial vectors (if we stick to the old knowledge). Then a question arises naturally: Is it actually necessary to go back to the first step? In this paper we shall treat this problem. Roughly speaking, the answer is as follows: It is sufficient to go back to the latest modification. As a special case of this result, we can show that one of the initial vectors can be chosen arbitrarily to avoid \"unlucky\" case. Further it will be shown that there exists a vector x such that the algorithm starting from xι = jι = x can be continued so that \"unlucky\" case may not occur. These results will be stated in Theorems 3-6 of §2 and a new procedure will be proposed at p. 279. Finally, in connection with the Lanczos algorithm, we shall give, in Appendix, some properties concerning the location of the eigenvalues of tri-diagonal matrices.","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"32 1","pages":"259-284"},"PeriodicalIF":0.0,"publicationDate":"1968-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79131852","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}

引用次数: 4

Non-immersion theorems for lens spaces. II 透镜空间的非浸没定理。2

Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry Pub Date : 1968-01-01 DOI: 10.32917/HMJ/1206138653

Teiichi Kobayashi

引用次数: 1

Boundary value problems for the equation $triangle u-qu=0$ with respect to an ideal boundary 方程$三角形u-qu=0$关于理想边界的边值问题

Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry Pub Date : 1968-01-01 DOI: 10.32917/HMJ/1206138806

F. Maeda

引用次数: 4

Integral domains which are almost-Krull 几乎是krull的积分域

Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry Pub Date : 1968-01-01 DOI: 10.32917/HMJ/1206138662

Elbert M. Pirtle

引用次数: 20

On a class of Lie algebras 关于一类李代数

Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry Pub Date : 1968-01-01 DOI: 10.32917/HMJ/1206138805

S. Tôgô

{"title":"On a class of Lie algebras","authors":"S. Tôgô","doi":"10.32917/HMJ/1206138805","DOIUrl":"https://doi.org/10.32917/HMJ/1206138805","url":null,"abstract":"In the previous paper [T], we have given an estimate for the dimensionality of the derivation algebra of a Lie algebra L satisfying the condition that (ad x) = 0 for x e L implies ad x = 0. Such a Lie algebra will be referred to as an (A2)-algebra in this paper according to the definition given in Jδichi pΓ|, which investigates the (A^)-algebras, k I> 2, with intention to obtain the analogues to the (A)-algebras. He showed that the (A2)-algebras have a different situation from the other classes of (A^)-algebras, k 2>3. But the problem of characterizing the (A2)-algebras remains unsolved. The purpose of this paper is to make a detailed study of this class of Lie algebras. It is known [3] that every semisimple Lie algebra over the field of complex numbers contains no non-zero element x with (ad x) = 0. We shall show that every Lie algebra over a field Φ of characteristic Φ 2 whose Killing form is non-degenerate has the same property. By making use of this result we shall show that, when the basic field Φ is of characteristic 0, L is an (A2> algebra if and only if every element x of the nil radical iVsuch that (ad#) = 0 belongs to the center Z(L), and if and only if L is either reductive, or L^N^Z(N)=Z(L)^Nφ(0) and (ad #)SM) for any xeNZ(L). This characterization will be used in classifying certain types of solvable (A2)-algebras. A solvable (A2)-algebra is not generally abelian. We shall show that if Φ is an algebraically closed field of characteristic 0, then every solvable (A2> algebra over a field Φ is abelian. The latter half of the paper will be devoted to the study of solvable (A2)-algebras, in particular, to the study of solvable (A2)-algebras L such that dim N/Z(L) is 2 or 3 and of solvable (A2)-algebras of low dimensionalities.","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"2 1","pages":"55-83"},"PeriodicalIF":0.0,"publicationDate":"1968-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85980049","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}

引用次数: 3

Corrections to the paper ``Roots of scalar operator-valued analytic functions and their functional calculus'' 对“标量算子值解析函数的根及其泛函演算”一文的修正

Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry Pub Date : 1968-01-01 DOI: 10.32917/HMJ/1206138663

C. Apostol

引用次数: 1