Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics最新文献_第6页

The bridge tournament problem and calibration designs for comparing pairs of objects 桥牌比武问题及对物体比较的标定设计

Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics Pub Date : 1965-10-01 DOI: 10.6028/JRES.069B.033

R. C. Bose, J. M. Cameron

{"title":"The bridge tournament problem and calibration designs for comparing pairs of objects","authors":"R. C. Bose, J. M. Cameron","doi":"10.6028/JRES.069B.033","DOIUrl":"https://doi.org/10.6028/JRES.069B.033","url":null,"abstract":"The classical tournament problem caiJs for arranging v individuals into teams of /) players so that a player is teamed the same number of times with each of the other players and also that each player is pitted equally often against each of the other players. The play of the tuurnament results in the determination of difference in performance of the various pairings of the groups. In the special case when p = 2 each team consists of two players and the desigris are called bridge tournament designs. In high precisiun calibration one can measure only the difference between two nominally equal groups S(l that if u objects are to be inte rcompared in groups of fJ objects, then the solutions tu the tour nament proble m provide schedules for the gl'lluping. These designs are useful in weighing a nd any othe r measul'emcnts where the objects tu be measured can be combined intu gl'llups without loss of precision or accuracy ill the comparisons. Tilis paper presents general methuds fill' constructing of bridge lournament designs, i.e., for Lht' case whcn p = 2, fur all /1 ~ 50. Key Wurds: Calibration, calibration designs. combinatorial analysis, difference sets, experiment designs', incomplete block designs, tourname nts, weighing designs.","PeriodicalId":408709,"journal":{"name":"Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1965-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129609365","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: 29

Error analysis of phase-integral methods. I. General theory for simple turning points 相位积分法的误差分析。1 .简单拐点的一般理论

Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics Pub Date : 1965-10-01 DOI: 10.6028/JRES.069B.028

F. Olver

引用次数: 12

A generalization of a result of Newman on multipliers of difference sets 差分集乘子的纽曼结果的推广

Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics Pub Date : 1965-10-01 DOI: 10.6028/JRES.069B.032

R. McFarland

引用次数: 0

On Kirchhoff's law and its generalized application to absorption and emission by cavities 基尔霍夫定律及其在空腔吸收和发射中的推广应用

Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics Pub Date : 1965-07-01 DOI: 10.6028/JRES.069B.019

F. Kelly

引用次数: 11

On a relation between two-dimensional Fourier integrals and series of Hankel transforms 二维傅里叶积分与汉克尔变换级数的关系

Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics Pub Date : 1965-07-01 DOI: 10.6028/JRES.069B.020

J. Cornacchio, R. P. Soni

{"title":"On a relation between two-dimensional Fourier integrals and series of Hankel transforms","authors":"J. Cornacchio, R. P. Soni","doi":"10.6028/JRES.069B.020","DOIUrl":"https://doi.org/10.6028/JRES.069B.020","url":null,"abstract":"In the theore ti cal solution rece ntly obtained for stationary spati al-cohere nce functions over radiating apertures, [I]' the evaluation of the two-dime nsional Fourie r integral of the far-fi eld inte nsity di s tribution is required. Since the appearance of s uc h integrals is also quite common in other areas of mathe matical physics, it would be useful to render their evaluation amenable to the application of ex tensively tabulated result s available in the literature. (For examples of suc h sources see [2] , [4] , [5], and [6].) For fun ctions of one variable, comprehe nsive tables of Fourier tran sforms exis t [2], and although it is possible to reduce the k dimensional Fourier tran sform of radial functions 2 [3] to Hankel transforms [3 , p. 69] for which extensive tables [5] are available , there are no tables giving the Fourier transform for k > 1 of arbitrary functions (i. e., nonradi al) even in the case of k = 2. In this paper, the two-dimensional Fourier tran sform is reduced to a form which facilitates its evaluation by th e use of existing tables [4 , 5] and also yields a result which is an extension of that given in Bochner and Chandrasekharan [3], for the case k=2, to functions which are not necessarily radial. It will be shown that if g(a, (3 ) is the two-dimensional Fourier transform of fix, y), i.e.,","PeriodicalId":408709,"journal":{"name":"Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics","volume":"689 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1965-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126511160","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: 13

A development of theory of errors with reference to economy of time 关于时间节约的误差理论的发展

Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics Pub Date : 1965-07-01 DOI: 10.6028/JRES.069B.015

M. D. Hersey

引用次数: 4

Transversals and Matroid Partition 截线和矩阵划分

Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics Pub Date : 1965-07-01 DOI: 10.6028/JRES.069B.016

J. Edmonds, D. R. Fulkerson

引用次数: 251

Some Theorems on the Permanent 关于恒量的几个定理

Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics Pub Date : 1965-07-01 DOI: 10.6028/JRES.069B.018

R. Brualdi, M. Newman

引用次数: 10

Some extensions of Banach's contraction theorem 巴拿赫收缩定理的一些推广

Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics Pub Date : 1965-07-01 DOI: 10.6028/JRES.069B.022

P. R. Meyers

引用次数: 7

Some L2 Markoff inequalities 一些L2马尔科夫不等式

Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics Pub Date : 1965-07-01 DOI: 10.6028/JRES.069B.017

L. Shampine

引用次数: 11