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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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The structure of higher degree symmetry classes of tensors 高次对称张量类的结构
Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences Pub Date : 1976-04-01 DOI: 10.6028/JRES.080B.026
R. Merris
{"title":"The structure of higher degree symmetry classes of tensors","authors":"R. Merris","doi":"10.6028/JRES.080B.026","DOIUrl":"https://doi.org/10.6028/JRES.080B.026","url":null,"abstract":"The pape r is concerned with sy mm et ry c lasses of te nso rs whic h a ri se fro m a pe rmut ation gro up C a nd irred uc ible c ha racte r X of C . In case X is o f degree 1, a we ll-kno wn a lgo rith m is ava ilab le fo r induc ing a bas is of the sym me try c lass from the unde rl ying vecto r s pace. Whe n the degree of X is grea te r than 1, no com pa ra ble construc tion has been di scove red . The diffi c ulties are d isc ussed and result s obt a ined in some spec ia l cases.","PeriodicalId":166823,"journal":{"name":"Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences","volume":"62 51","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1976-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134226367","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
Two submatrix properties of certain induced norms 某些诱导模的两个子矩阵性质
Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences Pub Date : 1975-07-01 DOI: 10.6028/JRES.079B.009
Charles R. Johnson
{"title":"Two submatrix properties of certain induced norms","authors":"Charles R. Johnson","doi":"10.6028/JRES.079B.009","DOIUrl":"https://doi.org/10.6028/JRES.079B.009","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":"1975-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115304119","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
Properties of neighboring sequences in stratifiable spaces 可分层空间中邻近序列的性质
Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences Pub Date : 1975-07-01 DOI: 10.6028/JRES.079B.010
Ralph R. Sabella
{"title":"Properties of neighboring sequences in stratifiable spaces","authors":"Ralph R. Sabella","doi":"10.6028/JRES.079B.010","DOIUrl":"https://doi.org/10.6028/JRES.079B.010","url":null,"abstract":"","PeriodicalId":166823,"journal":{"name":"Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1975-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115647272","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
Maximin facility location Maximin设施位置
Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences Pub Date : 1975-07-01 DOI: 10.6028/JRES.079B.011
P. Slater
{"title":"Maximin facility location","authors":"P. Slater","doi":"10.6028/JRES.079B.011","DOIUrl":"https://doi.org/10.6028/JRES.079B.011","url":null,"abstract":"","PeriodicalId":166823,"journal":{"name":"Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences","volume":"28 2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1975-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116711822","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: 65
Similarity of partitioned matrices 分块矩阵的相似性
Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences Pub Date : 1975-07-01 DOI: 10.6028/JRES.079B.012
R. Feinberg
{"title":"Similarity of partitioned matrices","authors":"R. Feinberg","doi":"10.6028/JRES.079B.012","DOIUrl":"https://doi.org/10.6028/JRES.079B.012","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":"1975-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131120027","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: 11
On the dimension group of classical physics 论经典物理的维群
Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences Pub Date : 1975-07-01 DOI: 10.6028/JRES.079B.013
C. Page
{"title":"On the dimension group of classical physics","authors":"C. Page","doi":"10.6028/JRES.079B.013","DOIUrl":"https://doi.org/10.6028/JRES.079B.013","url":null,"abstract":"The bas ic principles of the group properti es of physical quantities are reviewed. The proble ms assoc iated with th e dimensions of angle and logarithm are solved by using functional equations, ins tead of a nalytic express ions , for de fining functions of non numerical quantities. It is concluded that the neper and radian are related by Np= j rad , so that when the radian is considered as a base unit . the neper becomes a derived unit, and is the 5 I unit for logarithmic quantiti es .","PeriodicalId":166823,"journal":{"name":"Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1975-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125257102","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: 5
Automatic computing methods for special functions. Part II. The exponential integral En(x) 特殊功能的自动计算方法。第二部分。指数积分En(x)
Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences Pub Date : 1974-10-01 DOI: 10.6028/JRES.078B.025
I. A. Stegun, R. Zucker
{"title":"Automatic computing methods for special functions. Part II. The exponential integral En(x)","authors":"I. A. Stegun, R. Zucker","doi":"10.6028/JRES.078B.025","DOIUrl":"https://doi.org/10.6028/JRES.078B.025","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":"1974-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121025923","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: 12
Field of values and spectra of positive definite multiples 正定倍数的值域和谱
Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences Pub Date : 1974-10-01 DOI: 10.6028/JRES.078B.024
Charles R. Johnson
{"title":"Field of values and spectra of positive definite multiples","authors":"Charles R. Johnson","doi":"10.6028/JRES.078B.024","DOIUrl":"https://doi.org/10.6028/JRES.078B.024","url":null,"abstract":"the \"field of values\" of A. In [1, 2, 4] 1 the H -stable matrices were characterized. (A matrix A EM II (C) is called H -stable if AECT (HA) implies Re(A) > 0 for all H * = H > 0.) The simplest version of the characterization is that A is H-stable if and only if A is nonsingular and AEF (A) implies Re(A) > 0 or A = O. In this note we give a simple characterization of those AECT (HA) for some H * = H > 0 and the theorem on H -stability, for example, is an easy corollary. The characterization is constructive in that a specific class of positive definite matrices H for which AECT (H A) is produced. Let L == {H EM il (C) :H* = H > O} . We first make two observations: (I) OECT (HA) for some H E'i if and only if Ow' (KA) for all KE'i if and only if OECT (A);","PeriodicalId":166823,"journal":{"name":"Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1974-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114224124","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
Maximizing the number of spanning trees in a graph with n nodes and m edges 在有n个节点和m条边的图中最大化生成树的数量
Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences Pub Date : 1974-10-01 DOI: 10.6028/JRES.078B.023
D. Shier
{"title":"Maximizing the number of spanning trees in a graph with n nodes and m edges","authors":"D. Shier","doi":"10.6028/JRES.078B.023","DOIUrl":"https://doi.org/10.6028/JRES.078B.023","url":null,"abstract":"Consider the class of undirected graphs hav ing 11. nodes and m edges. The proble m to be addressed here is that of finding specific configurations of III edges on the given n nodes so that the resulting graph will contain the largest number of spanning trees. In particular, an explicit solution to this problem will be exhibited for graphs which have \"enough\" edges. To be specific, let the set E of k edges be deleted from the comp lete graph KII on 11. nodes: KII has an edge between every pair of distinct nodes and thus contains 11.(11.-1)/2 edges. For th e case when k ~ 11./2, we will demonstrate that the number of spanning trees T(n, E) in the res ulting graph is maximized by choosing the k deleted edges to be mutually nonadjacent. The (apparently more complicated) cases with k > 11./2 await resolution. Let Pic denote a set of k nonadjacent (\"parallel\") edges in K II , where k ~ n/2. We will show that lEI = k implies T(n, E) ~ T(n, Pic). First the case when the edge set E is disconnected will be di sposed of. This will be done in the context of the inductive hypothesis that if i < k and 151 = i, then T(n, S) ~ T(n, Pi) whether or not 5 is connected. Suppose lEI = k and that E can be decomposed into connected edge sets C I , C 2, •.• , C p with p 3 2. Certainly, when k = 2 the only disconnected set E possible consists of two nonadjacent edges, so that the inductive hypothesis holds. More generally, if lEI = k then IC,I < k and n 3 2k > 21C 11, whence 0 ~ T(n, C d ~ T(n, Pa ), (X= IC d, by the inductive hypothesis. Similarly, we have O~T(n, C,)~T(n, P(3), {3=IC ,I, where CI = C2 U ... U Co in the decomposition E=C 1 U C2 U ... U C/!. From [2, p. 106] it is known that ( 2)i T(n,P j )=nn2 1-;; ,","PeriodicalId":166823,"journal":{"name":"Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences","volume":"173 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1974-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132536175","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: 33
Saddlepoints in p-pivot classes of skew matrices 偏矩阵p-主类中的鞍点
Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences Pub Date : 1974-10-01 DOI: 10.6028/jres.078b.022
M. Stein
{"title":"Saddlepoints in p-pivot classes of skew matrices","authors":"M. Stein","doi":"10.6028/jres.078b.022","DOIUrl":"https://doi.org/10.6028/jres.078b.022","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":"1974-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121136933","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
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