Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences最新文献_第2页

A more tractable solution to a singular integral equation obtained by solving a related Hilbert problem for two unknowns 通过求解两个未知数的相关希尔伯特问题而得到的奇异积分方程的更易于处理的解

Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences Pub Date : 1976-07-01 DOI: 10.6028/JRES.080B.040

J. A. Pennline

引用次数: 2

Automatic computing methods for special functions. Part III. The sine, cosine, exponential integrals, and related functions 特殊功能的自动计算方法。第三部分。正弦，余弦，指数积分，及相关函数

Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences Pub Date : 1976-04-01 DOI: 10.6028/JRES.080B.031

I. Stegun, R. Zucker

引用次数: 9

Matrix algebra and eigenvalues for the bead/spring model of polymer solutions 聚合物溶液的头/弹簧模型的矩阵代数和特征值

Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences Pub Date : 1976-04-01 DOI: 10.6028/JRES.080B.029

J. Fong, A. Peterlin

引用次数: 7

Definite integrals of the complete elliptic integral K 完全椭圆积分K的定积分

Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences Pub Date : 1976-04-01 DOI: 10.6028/JRES.080B.032

M. Glasser

引用次数: 23

Inverting sparse matrices by tree partitioning 用树划分法反演稀疏矩阵

Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences Pub Date : 1976-04-01 DOI: 10.6028/JRES.080B.025

D. Shier

引用次数: 0

A minimax-measure intersection problem 一个极小极大交集问题

Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences Pub Date : 1976-04-01 DOI: 10.6028/JRES.080B.024

P. R. Meyers

{"title":"A minimax-measure intersection problem","authors":"P. R. Meyers","doi":"10.6028/JRES.080B.024","DOIUrl":"https://doi.org/10.6028/JRES.080B.024","url":null,"abstract":"Some years ago, NBS colleague S. Haber communicated the following proble m: To select n subsets of the unit interval, each of mea sw'e 112, so a s to minimize the maximum of the measures of the pairwise inte rsections of these subse ts. The problem is suggested by a paper [1]1 of Gilli s which, settling \"an unpubli shed conjec ture of Erdos,\" proves that for denumerably infinite collections of sets of measure a, the value corresponding to the maximum pairwise-inte rsection meas ure has infimum a 2 • (Collections with higher transfinit e cardinality are treated by Gillis in [2].) Here we provide an explicit solution for collections of finite cardinalities n. Further, and also corresponding to [1], we consider as well the case of p-fold intersections with 2 Sop Son, and provide the corresponding explicit solution. (As noted in [2], the argument of [1] easily extend s to show that aT' is the limiting value for a denumerably infinite collection.) As preliminary, we introduce a second minimization and point out its relationship to our minimax problem, to wit: Select n subsets A 10 A2 , • . , A 1/ of the unit inte rval, eac h of measure a, so that the sum of the measures of their p-fold inte rsections is minimum. If now X = {Slo . . \" SI/}' a solution to this minimum proble m, can be chose n so that aU its p-fold intersections have the same measure s, and if M is the maximum of the measures of the p-fold intersections of an arbitrary collection A to A 2, . , \" A n with all fL(A J = a, then","PeriodicalId":166823,"journal":{"name":"Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1976-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124928004","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

Predictable Regular Continued Cotangent Expansions 可预测的规则连续余切展开

Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences Pub Date : 1976-04-01 DOI: 10.6028/JRES.080B.030

J. Shallit

引用次数: 1

The dependence of inspection-system performance on levels of penalties and inspection resources 检查系统绩效对处罚水平和检查资源的依赖性

Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences Pub Date : 1976-04-01 DOI: 10.6028/JRES.080B.020

A. J. Goldman, M. Pearl

引用次数: 18

The Kronecker power of a permutation 排列的克罗内克幂

Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences Pub Date : 1976-04-01 DOI: 10.6028/JRES.080B.027

R. Merris

引用次数: 1

On Iohvidov's proofs of the Fischer-Frobenius theorem 论Iohvidov对费雪-弗罗本纽斯定理的证明

Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences Pub Date : 1976-04-01 DOI: 10.6028/jres.080b.028

R. C. Thompson

{"title":"On Iohvidov's proofs of the Fischer-Frobenius theorem","authors":"R. C. Thompson","doi":"10.6028/jres.080b.028","DOIUrl":"https://doi.org/10.6028/jres.080b.028","url":null,"abstract":"then jT\"_1 is a Hankel matrix for all Toeplitz matrices TnI' Thi s proced ure, howe ver, does not carry Hermitian ToepLitz matrices to Hermitian (i.e., real) Hankel matrices. The theore m of FischerFroebenius asserts that a class of tran sformation s exist each of which uniformly carries Toeplitz matrices to Hankel matrices in such a way that Hermitian Toeplitz matrices are carried to Hermitian Hankel matrices. Recently I. C. Iohvidov has publi shed three proofs of this result. One of these proofs is a direct but somewhat intricate calculation; it may be found on pages 211-213 of [1]1. A second proof, to be found on page 217 of [1] and also in [2], makes a preliminary reduction to the case of positive definite ToepLitz matrices, then takes advantage of a decomposition of definite Toeplitz matrices known from the theory of the trigonometric moment problem. The third proof, in [2], avoids the .reduction to the positive definite case, and uses instead a more co mplicated decomposition of Toeplitz matrices due to Iohvidov and Krein [3, p. 338]. The purpose of this paper is to give a short and direct proof of the Fischer-Frobe nius theorem. Our proof is based on a simple decomposition of arbitrary Toeplitz matrices, for which the proof is almost a triviality and whic h was apparently not noticed in [1] and [2]. See equation (3). Iohvidov's techniques then may be applied to (3) to produce the des ired result rapidly.","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":"1976-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124697894","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