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

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Relatively complemented Lie algebras 相对补李代数
Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry Pub Date : 1967-01-01 DOI: 10.32917/HMJ/1206139051
B. Kolman
{"title":"Relatively complemented Lie algebras","authors":"B. Kolman","doi":"10.32917/HMJ/1206139051","DOIUrl":"https://doi.org/10.32917/HMJ/1206139051","url":null,"abstract":"","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"8 1","pages":"1-11"},"PeriodicalIF":0.0,"publicationDate":"1967-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87934951","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: 17
Note on Kishi's theorem for capacitability 关于Kishi的能力定理的注解
Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry Pub Date : 1966-01-01 DOI: 10.32917/HMJ/1206139110
M. Yamasaki
{"title":"Note on Kishi's theorem for capacitability","authors":"M. Yamasaki","doi":"10.32917/HMJ/1206139110","DOIUrl":"https://doi.org/10.32917/HMJ/1206139110","url":null,"abstract":"","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"55 1","pages":"217-226"},"PeriodicalIF":0.0,"publicationDate":"1966-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82251240","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: 1
Some examples related to duality theorem in linear programming 线性规划中有关对偶定理的几个例子
Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry Pub Date : 1966-01-01 DOI: 10.32917/HMJ/1206139187
Michio Yoshida
{"title":"Some examples related to duality theorem in linear programming","authors":"Michio Yoshida","doi":"10.32917/HMJ/1206139187","DOIUrl":"https://doi.org/10.32917/HMJ/1206139187","url":null,"abstract":"The duality problems in linear programming may read as follows. Suppose an m x n matrix A —{aij), a column vector 6 = (όi, • •-, bm) and a row vector c — (ci, , cn) are given. The primal problem: Find a column vector u = (uu •••,un) which maximizes the linear form cu subject to the conditions Au<,b and M^>0. The dual problem: Find a row vector v — (vu ,vn) which minimizes the linear form vb subject to the conditions vA^>c and v^>0. In each problem a vector satisfying the required conditions is called feasible, and if it attains the maximum or minimum it is called optimal. These problems can be represented by the following tableau:","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"42 1","pages":"41-43"},"PeriodicalIF":0.0,"publicationDate":"1966-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83065726","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: 7
Two-step processes by one-step methods of order 3 and of order 4 用3阶和4阶的一步法进行两步过程
Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry Pub Date : 1966-01-01 DOI: 10.32917/HMJ/1206139108
Hisayoshi Shintani
{"title":"Two-step processes by one-step methods of order 3 and of order 4","authors":"Hisayoshi Shintani","doi":"10.32917/HMJ/1206139108","DOIUrl":"https://doi.org/10.32917/HMJ/1206139108","url":null,"abstract":"and the initial condition y(χo) = jo, where /(#, y) is assumed to be a sufficiently smooth function. We are concerned with the case where the equation (1.1) is integrated numerically by one-step methods of order 3 and of order 4. It is well known that the one-step methods of order 3 such as Kutta method and those of order 4 such as Runge-Kutta method require three and four evaluations of the derivative respectively. It is also known that, if the same step-size is used twice in succession, an approximate value of the truncation error can be obtained by integrating again with the double step-size. This method of approximating the truncation error requires, per two steps of integration, eight and eleven evaluations of f(x, y) for any one-step method of order 3 and for that of order 4 respectively. In our previous paper C19], it has been shown that there exists a onestep formula of order 4 such that, after two steps of integration with the same step-size, only one additional evaluation of the derivative makes/it possible to approximate the truncation error. In that formula, however, four values of f(χ, y) evaluated in the first step of integration are not used explicitly in the second step. Thus there remains a possibility of reducing the number of evaluations of the derivative by utilizing all the values of the derivative computed already. In this paper, it is shown that there exist one-step integration formulas of order 3 and those of of order 4 such that approximate values zx and z2 of y(χo + h) and y(xo--2h) and an approximation to their truncation errors can be obtained with five and seven evaluations of f(x, y) respectively. Finally two numerical examples are presented.","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"185 1","pages":"183-195"},"PeriodicalIF":0.0,"publicationDate":"1966-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76423930","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: 10
On the integral closure of a domain 论域的积分闭包
Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry Pub Date : 1966-01-01 DOI: 10.32917/HMJ/1206139103
H. Butts, W. W. Smith
{"title":"On the integral closure of a domain","authors":"H. Butts, W. W. Smith","doi":"10.32917/HMJ/1206139103","DOIUrl":"https://doi.org/10.32917/HMJ/1206139103","url":null,"abstract":"","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"46 1","pages":"117-122"},"PeriodicalIF":0.0,"publicationDate":"1966-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77257064","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: 7
On a capacitability problem raised in connection with the Gauss variational problem 关于与高斯变分问题有关的一个能力问题
Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry Pub Date : 1966-01-01 DOI: 10.32917/hmj/1206139111
M. Yamasaki
{"title":"On a capacitability problem raised in connection with the Gauss variational problem","authors":"M. Yamasaki","doi":"10.32917/hmj/1206139111","DOIUrl":"https://doi.org/10.32917/hmj/1206139111","url":null,"abstract":"In a locally compact Hausdorff space, there are many ways to consider a set function for compact sets which is similar to the capacity in the classical sense. Starting from such a set function, we can define an inner quantity and an outer quantity. The problem of capacitability is to discuss when they coincide. A very useful tool is the general theory of capacitability which was estabilished by G. Choquet [2Γ. In this paper we shall examine the capacitability problem in relation to the Gauss variational problem. More precisely, let Ω be a locally compact Hausdorff space and Φ(χ, γ) be a lower semicontinuous function on ΩxΩ. Throughout this paper, we shall assume that Φ takes values in Q0, + oo], A measure μ will be always a non-negative Radon measure and Sμ the support of μ. The potential of μ is defined by","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"20 1","pages":"227-244"},"PeriodicalIF":0.0,"publicationDate":"1966-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83770297","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: 0
On a one-step method of order 4 在阶为4的一步法上
Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry Pub Date : 1966-01-01 DOI: 10.32917/HMJ/1206139191
Hisayoshi Shintani
{"title":"On a one-step method of order 4","authors":"Hisayoshi Shintani","doi":"10.32917/HMJ/1206139191","DOIUrl":"https://doi.org/10.32917/HMJ/1206139191","url":null,"abstract":"","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"29 1","pages":"91-107"},"PeriodicalIF":0.0,"publicationDate":"1966-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80649090","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: 7
Generalized capacity and duality theorem in linear programming 线性规划中的广义容量与对偶定理
Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry Pub Date : 1966-01-01 DOI: 10.32917/HMJ/1206139188
M. Ohtsuka
{"title":"Generalized capacity and duality theorem in linear programming","authors":"M. Ohtsuka","doi":"10.32917/HMJ/1206139188","DOIUrl":"https://doi.org/10.32917/HMJ/1206139188","url":null,"abstract":"Recently certain results in the theory of games and linear programming have been applied to potential theory. We mention M. Nakai [2], B. Fuglede [1] and M. Ohtsuka [4]. Our paper is along this line. More precisely, the minimax theorem in the theory of games was applied to the theory of capacity in [4]. For a compact Hausdorff space K and an extended real-valued lower semicontinuous function Φ on K x K which is bounded below, the author established","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"17 1","pages":"45-56"},"PeriodicalIF":0.0,"publicationDate":"1966-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91553807","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: 16
On a trace theorem for the space $Hsp{mu },(RspN)$ 空间$Hsp{mu}，(RspN)$的迹定理
Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry Pub Date : 1966-01-01 DOI: 10.32917/HMJ/1206139185
Mitsuyuki Itano
{"title":"On a trace theorem for the space $Hsp{mu },(RspN)$","authors":"Mitsuyuki Itano","doi":"10.32917/HMJ/1206139185","DOIUrl":"https://doi.org/10.32917/HMJ/1206139185","url":null,"abstract":"","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"61 1","pages":"11-29"},"PeriodicalIF":0.0,"publicationDate":"1966-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73823432","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
A note on normal ideals 关于正常理想的注解
Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry Pub Date : 1966-01-01 DOI: 10.32917/HMJ/1206139184
M. Janowitz
{"title":"A note on normal ideals","authors":"M. Janowitz","doi":"10.32917/HMJ/1206139184","DOIUrl":"https://doi.org/10.32917/HMJ/1206139184","url":null,"abstract":"","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"40 1","pages":"1-9"},"PeriodicalIF":0.0,"publicationDate":"1966-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78830221","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: 10
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