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Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences最新文献

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Partitioning of interaction in analysis of variance 方差分析中相互作用的划分
Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences Pub Date : 1969-10-01 DOI: 10.6028/JRES.073B.031
J. Mandel
{"title":"Partitioning of interaction in analysis of variance","authors":"J. Mandel","doi":"10.6028/JRES.073B.031","DOIUrl":"https://doi.org/10.6028/JRES.073B.031","url":null,"abstract":"A method is presented for the analysis of data representing functions of two variables, when the response can be tabulated in a rectangular array. The procedure is based on a partitioning of the row by column interaction effects into a sum of terms, each of which is the product of a row factor by a column factor. the factors in each term are estimated by a method involving the extraction of characteristic roots. The method contains as special cases a number of procedures used for the handling of non- additivity in two way arrays. It is very useful for the fitting of empirical surfaces, but is also applicable to cases in which the data depend on qualitative rather than quantitative factors. Comparisons with other techniques are made and an illustrative example is given.","PeriodicalId":166823,"journal":{"name":"Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences","volume":"133 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1969-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130494458","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: 174
Highly restricted partitions 高度受限分区
Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences Pub Date : 1969-10-01 DOI: 10.6028/JRES.073B.032
H. Gupta
{"title":"Highly restricted partitions","authors":"H. Gupta","doi":"10.6028/JRES.073B.032","DOIUrl":"https://doi.org/10.6028/JRES.073B.032","url":null,"abstract":"","PeriodicalId":166823,"journal":{"name":"Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1969-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125793537","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
A theorem on convex hulls 关于凸包的一个定理
Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences Pub Date : 1969-10-01 DOI: 10.6028/jres.073b.030
W. A. Horn
{"title":"A theorem on convex hulls","authors":"W. A. Horn","doi":"10.6028/jres.073b.030","DOIUrl":"https://doi.org/10.6028/jres.073b.030","url":null,"abstract":"Let p be a point in the interior KO of the convex hull K = K(S) of a bounded point-set S in a real Hilbert space. A quantity R (p) is determined such that every closed ball of radius > R (p) , if it con tains p, must also meet S.","PeriodicalId":166823,"journal":{"name":"Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1969-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126786398","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
Minimax Error Selection of a Univariate Distribution With Prescribed Componentwise Bounds and Ranking 具有规定分量界和排序的单变量分布的极大极小误差选择
Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences Pub Date : 1969-07-01 DOI: 10.6028/JRES.073B.022
A. J. Goldman
{"title":"Minimax Error Selection of a Univariate Distribution With Prescribed Componentwise Bounds and Ranking","authors":"A. J. Goldman","doi":"10.6028/JRES.073B.022","DOIUrl":"https://doi.org/10.6028/JRES.073B.022","url":null,"abstract":"The top ic treated is that of fi nding a re producib le, plaus ible and computationall y s imple method of selecting a di screte frequency di s tribution with a prescr ib ed rankin g of its components and pre· scrib ed upper and lowe r bounds on these compone nt. s . The problem is s hown to be tract.ab le when a minimax error selection c rit e ri on is e mployed, and \"error \" is measure d by maximum absolut e devia­ ti on a mong co mpone nts. In thi s case one obt.ains a lin ea r progra m of a specia l form ad mittin g expli c it solutio n.","PeriodicalId":166823,"journal":{"name":"Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1969-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131231069","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
Principal ideals in matrix rings 矩阵环中的主理想
Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences Pub Date : 1969-07-01 DOI: 10.6028/jres.073b.020
M. Newman, S. Pierce
{"title":"Principal ideals in matrix rings","authors":"M. Newman, S. Pierce","doi":"10.6028/jres.073b.020","DOIUrl":"https://doi.org/10.6028/jres.073b.020","url":null,"abstract":"Let R be a ring with a unity 1, and let n be a positive integer. It is well-known [3, p. 37]1 that every two-sided ideal of R\" (the complete matrix ring of order n over R) is necessarily of the form M\", where M is a two-sided ideal of R. Simple examples show that this result no longer holds for one-sided ideals. In this note we investigate the left ideals of R\" in the case when R is a principal ideal ring (an integral domain in which every ideal is principal). We shall prove THEOREM 1: IfR is a principal ideal ring, then every left ,ideal ofRn is principal_ The proof of Theorem 1 depends upon the fact that if A is any p X q matrix over R, then a unit matrix V of Rp exists such that the p X q matrix VA is upper triangular [2 , p. 32]_ We also establish the following partial converse to Theorem 1: THEOREM 2: If R is not Noetherian or if R is a Dedekind ring but not a principal ideal ring, then Rn contains a nonprincipalleft ideal_ For general information on rings , see [3]. For information on Dedekind rings, see [1 , p. 101].","PeriodicalId":166823,"journal":{"name":"Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1969-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122411021","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
The second orthogonality conditions in the theory of proper and improper rotations.IV. Solution of the trace and secular equations 正常转动和不正常转动理论中的第二正交性条件。轨迹方程和长期方程的解
Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences Pub Date : 1969-07-01 DOI: 10.6028/JRES.073B.021
H. Gelman
{"title":"The second orthogonality conditions in the theory of proper and improper rotations.IV. Solution of the trace and secular equations","authors":"H. Gelman","doi":"10.6028/JRES.073B.021","DOIUrl":"https://doi.org/10.6028/JRES.073B.021","url":null,"abstract":"The equation which connects the trace of a rotation matrix and that of its square, and the secular equation for a rotation matrix , both of which are direct res ults of the second orthogonality conditions, are solved by purely analytic methods based on the group property and the periodicity property of rotation matrices. The point is thus made that the well known formulas for the trace of a rotation matrix in terms of the angle of rotation and for the rotation matrix itself in terms of the axis and angle of rotation, are closely related to the algebraic properties of rotation matrices.","PeriodicalId":166823,"journal":{"name":"Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1969-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114376205","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
Commutator groups and algebras 交换子群与代数
Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences Pub Date : 1969-07-01 DOI: 10.6028/JRES.073B.025
L. Greenberg
{"title":"Commutator groups and algebras","authors":"L. Greenberg","doi":"10.6028/JRES.073B.025","DOIUrl":"https://doi.org/10.6028/JRES.073B.025","url":null,"abstract":"Let Hand K be connected, Lie subgroups of a Lie group C. The group [H , K] , generated by all commutators hkh1k l(h€H, k€K) is arcwise connected. Therefore, by a theorem of Yamabe, LH, K] is a Lie subgroup. If ~, Sl' denote the Lie algebras of Hand K , respectively , then the Lie algebra of [H , K] is the s mallest algebra containing [~ , S ], which is invariant underad~ andadSl'. An immediate consequ ence is that if Hand K are complex Lie subgroups, then [H , K] is also complex.","PeriodicalId":166823,"journal":{"name":"Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1969-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132695099","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 class of nonlinear transformations and their applications to the evaluation of infinite series 一类非线性变换及其在无穷级数求值中的应用
Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences Pub Date : 1969-07-01 DOI: 10.6028/JRES.073B.026
H. L. Gray, W. D. Clark
{"title":"On a class of nonlinear transformations and their applications to the evaluation of infinite series","authors":"H. L. Gray, W. D. Clark","doi":"10.6028/JRES.073B.026","DOIUrl":"https://doi.org/10.6028/JRES.073B.026","url":null,"abstract":"In this paper the problem of increasing the rate of convergence of infinite sequences and series is considered by means of a class of nonlinear transformations. The transformations employed are the discrete analogue of the so called C-transformations and the theory surrounding them is investigated in some detail. The theoretical results are demonstrated by numerous examples.","PeriodicalId":166823,"journal":{"name":"Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences","volume":"63 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1969-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128381550","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: 18
An evaluation of linear least squares computer programs 线性最小二乘计算机程序的评价
Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences Pub Date : 1969-04-01 DOI: 10.6028/JRES.073B.009
Roy H. Wampler
{"title":"An evaluation of linear least squares computer programs","authors":"Roy H. Wampler","doi":"10.6028/JRES.073B.009","DOIUrl":"https://doi.org/10.6028/JRES.073B.009","url":null,"abstract":"Two linear least squ a res tes t p roblems, both fifth degree polyno mi a ls, have bee n run on more th an twe nJ y d iffe rent co mput e r progra ms in orde r to assess th e ir num erica l acc uracy. Among the progra ms tes ted were re presentati ves f ro m vari ous sta ti sti ca l pac kages as we ll as some from th e S HA RE libra ry. Essenti a ll y fi ve diffe re nt algorithm s were used in the va ri ous progra ms to obta in the coeffi c ients of the leas t squ a res fit s. The tests were run on severa l diffe rent comput e rs, in doubl e prec i io n as we ll as s ingle precis ion. By co mpa ring the coe ffi c ie nts re port ed , it was found th at those programs us in g orthogona l Householde r transform ations or Gra m-Schmidt orthonorm aliza tion we re much more accura te th an those us ing e liminatio n a lgo rithms. P rogra ms us ing orthogo na l polyno mi als (s uit a bl e onl y for po lynomi a l fit s) a lso pro ved to be superior to those us ing e limin ation a lgo rithm s_ O ne program , us ing congru enti a l me thods and int eger a rithme ti c, obt a ined exac t so lutions. In a number of progra ms , the coeffi cie nts re port ed in one tes t probl e m were sometim es co mple te ly e rroneous, cont aining not even one co rrec t s ignificant digit.","PeriodicalId":166823,"journal":{"name":"Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1969-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114454593","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: 36
A digital computer technique for calculating the step response of lumped or distributed networks 一种计算集总或分布式网络阶跃响应的数字计算机技术
Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences Pub Date : 1969-04-01 DOI: 10.6028/JRES.073B.017
J. Andrews, N. Nahman
{"title":"A digital computer technique for calculating the step response of lumped or distributed networks","authors":"J. Andrews, N. Nahman","doi":"10.6028/JRES.073B.017","DOIUrl":"https://doi.org/10.6028/JRES.073B.017","url":null,"abstract":"This pa per d isc usses a tec llniqu e to so lve ste p res pon se probl e ms for lumped or di stribut ed ne twor ks with the a id of a d ig it a l comput e r. Th e Rosenbroc k g ra ph ic a l c urso r tec hni qu e for obt ainin g th e s te l) res pon se from the fre qu e nc y res pon se through th e in ve rse Laplace Tra ns format io n was a dapt ed fo r c ompu te r use. In add iti on, it was Illodifi ed to inc re ase it s acc uracy wh e n used wit h a digital compu te r. Th e re s po nse of a se ri es HLC lum pe d ne t work is compu te d a nd the num e ri ca l so lution is co mpared to the a na lyti c a l so lution. Also , a n ume ri ca l so lution i give n for th e s te p res pon se of a t ra ns miss ion lin c possess in g s kin -cffect me ta l loss a nd De b ye di e lec tric loss.","PeriodicalId":166823,"journal":{"name":"Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences","volume":"416 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1969-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117311555","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
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