Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry最新文献_第6页

Two-way classification designs with unequal cell frequencies 不相等小区频率的双向分类设计

Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry Pub Date : 1968-01-01 DOI: 10.32917/HMJ/1206138658

Sumiyasu Yamamoto, Y. Fujikoshi

{"title":"Two-way classification designs with unequal cell frequencies","authors":"Sumiyasu Yamamoto, Y. Fujikoshi","doi":"10.32917/HMJ/1206138658","DOIUrl":"https://doi.org/10.32917/HMJ/1206138658","url":null,"abstract":"In a two-way classification design on two factors, say A and B, we apply each factor on varying levels to various experimental units. We assume that this application yields for each unit a quantity which we call the yield of this unit. We denote by ??(/, /) the mean value of the yield obtained when the factor A is applied at level / and the factor B at level /. These levels may be qualitative or quantitative and could assume discrete or continuous values. Usually they are chosen deterministically by the experimenter. In some cases, however, they are selected randomly according to a probability scheme. Even when the levels vary continuously, the experimenter can calibrate or can group them into a finite number of discrete values. We, therefore, assume that / and /can take the values 1, 2, •••, r and 1, 2, •••, s, respectively. The object of a two-way classification design is to make some inferences on the behavior of the mean yield function τ/(I, /). For such purpose, the function ??(/, /) is usually broken up into a general mean /*, a main effect a(I) of the factor A, a main effect /?(/) of the factor B, and an interaction effect γ(I, /) ascribed to the combination of level I of the factor A with level / of the factor B, i.e.,","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"5 1","pages":"357-370"},"PeriodicalIF":0.0,"publicationDate":"1968-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72601888","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: 6

On certain classes of algebras 在某些代数类上

Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry Pub Date : 1968-01-01 DOI: 10.32917/HMJ/1206138647

T. Ravisankar

引用次数: 1

Dimensions of the derivation algebras of Lie algebras 李代数的导数代数的维数

Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry Pub Date : 1967-01-01 DOI: 10.32917/HMJ/1206139053

S. Tôgô

引用次数: 7

On atomistic lattices with the covering property 关于具有覆盖性质的原子格

Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry Pub Date : 1967-01-01 DOI: 10.32917/HMJ/1206138963

S. Maeda

引用次数: 10

On some properties of ${germ t}(n,,Phi )$ and ${germ f}{germ t}(n,,Phi )$ 关于${germ t}(n,,Phi )$和的一些性质 ${germ f}{germ t}(n,,Phi )$

Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry Pub Date : 1967-01-01 DOI: 10.32917/HMJ/1206139055

S. Tôgô

引用次数: 0

The linear hypotheses and constraints 线性假设和约束

Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry Pub Date : 1967-01-01 DOI: 10.32917/HMJ/1206138972

Sumiyasu Yamamoto, Y. Fujikoshi

{"title":"The linear hypotheses and constraints","authors":"Sumiyasu Yamamoto, Y. Fujikoshi","doi":"10.32917/HMJ/1206138972","DOIUrl":"https://doi.org/10.32917/HMJ/1206138972","url":null,"abstract":"of the n dimensional Euclidean space Em and e is an n x 1 vector of random errors which has the multivariate normal distribution with mean 0 and covariance matrix (J2In, (J 2 times the unit matrix In. It is worthwhile to note that in our unified treatment no restriction is imposed on the known n x m matrix A and the known Ixm matrix B. The matrix A may be called a design matrix. The matrix equation Bτ = 0 is a set of constraints imposed on the parameter vector r. Bτ — 0 is in some cases a set of identifiability constraints of the parameter vector r, a set of hypotheses to be tested and a set of more complex constraints. The matrices A and B and the parameter vector τ jointly specify the linear subspace Ξ of E». The least squares estimate of the parameter τ in the extended sense and the projection operator to the space Ξ obtained by using the generalized inverse matrices are given in the Theorem of section 2. Some properties of the generalized inverse matrices and the projection operators are also given in section 2. Our general formula given in the Theorem contains as its special cases the following three cases (i), (ii) and (iii):","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"18 1","pages":"211-219"},"PeriodicalIF":0.0,"publicationDate":"1967-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82498341","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: 2

Geometrical association schemes and fractional factorial designs 几何关联方案和分数阶乘设计

Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry Pub Date : 1967-01-01 DOI: 10.32917/HMJ/1206138971

Y. Fujii

引用次数: 2

Remarks on the conditional Gauss variational problem 关于条件高斯变分问题的评述

Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry Pub Date : 1967-01-01 DOI: 10.32917/hmj/1206139057

M. Yamasaki

引用次数: 1

Idempotent ideals and unions of nets of Prüfer domains 优选域网的幂等理想与并

Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry Pub Date : 1967-01-01 DOI: 10.32917/HMJ/1206138965

J. T. Arnold, R. Gilmer

{"title":"Idempotent ideals and unions of nets of Prüfer domains","authors":"J. T. Arnold, R. Gilmer","doi":"10.32917/HMJ/1206138965","DOIUrl":"https://doi.org/10.32917/HMJ/1206138965","url":null,"abstract":"In this paper, all rings considered are assumed to be commutative rings with an identity element. It is known that an integral domain D may contain an idempotent proper ideal A. But when this occurs, A is not finitely generated [21, p. 215], so that D is not Noetherian. Also, it is easy to show that for any positive integer k there exists a ring R which is not a domain and such that R contains an ideal A with the property that A^)A^) •-•^)A = A=. .. Whether an integral domain R with this property exists is a heretofore open question which we answer affirmatively in §2. Nakano in [16] has considered the problem of determining when an ideal of D is idempotent, where D is the integral closure of Z, the domain of ordinary integers, in an infinite algebraic number field. In fact, the paper [16] is one of a series of papers which Nakano has written concerning the ideal structure of D. In [18], Ohm has generalized and simplified many of Nakano's results from [16] and [17], showing that as far as the structure of the set of primary ideals of D is concerned, the assumption that D is the integral closure of Z in an algebraic number field is superfluous the essential requirement on D being that it is a Prύfer domain according to the following definition: The integral domain / is a Prϋfer domain if for each proper prime ideal P of /, JP is a valuation ring; equivalently, / is a Prϋfer domain if each nonzero finitely generated ideal of / is invertible [10, p. 554]. Following Ohm's example, we show in §3 that most of Nakano's results in [16] carry over to the case when D is the integral closure of a fixed Prϋfer domain Do in an algebraic extension of the quotient field of Do. If / is an integral domain with quotient field K, a domain /0 between / and K will be called an overrίng of /. In case /0 is a valuation ring, we call /o a valuation overring of /. We say that / is an almost Dedekind domain if for each maximal ideal M of /, JM is a rank one discrete valuation ring [5], in","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"55 1","pages":"131-145"},"PeriodicalIF":0.0,"publicationDate":"1967-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89684553","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

An example of non-minimal Kuramochi boundary points 非极小Kuramochi边界点的一个例子

Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry Pub Date : 1967-01-01 DOI: 10.32917/HMJ/1206139056

F. Maeda

引用次数: 0