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Discrete complex functions with prescribed boundary values and residues 具有规定边值和残数的离散复函数
Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics Pub Date : 1967-04-01 DOI: 10.6028/JRES.071B.017
E. Peterson
{"title":"Discrete complex functions with prescribed boundary values and residues","authors":"E. Peterson","doi":"10.6028/JRES.071B.017","DOIUrl":"https://doi.org/10.6028/JRES.071B.017","url":null,"abstract":"","PeriodicalId":408709,"journal":{"name":"Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics","volume":"71 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1967-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116062649","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
E-transforms (II) E-transforms (2)
Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics Pub Date : 1967-04-01 DOI: 10.6028/JRES.071B.015
F. M. Ragab
{"title":"E-transforms (II)","authors":"F. M. Ragab","doi":"10.6028/JRES.071B.015","DOIUrl":"https://doi.org/10.6028/JRES.071B.015","url":null,"abstract":"","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":"1967-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131185778","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
Poincare's conjecture is implied by a conjecture on free groups 庞加莱猜想是由一个关于自由群的猜想所隐含的
Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics Pub Date : 1967-04-01 DOI: 10.6028/JRES.071B.009
R. Traub
{"title":"Poincare's conjecture is implied by a conjecture on free groups","authors":"R. Traub","doi":"10.6028/JRES.071B.009","DOIUrl":"https://doi.org/10.6028/JRES.071B.009","url":null,"abstract":"","PeriodicalId":408709,"journal":{"name":"Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics","volume":"90 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1967-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126296463","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
Construction of EPr generalized inverses by inversion of nonsingular matrices 用非奇异矩阵的逆构造EPr广义逆
Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics Pub Date : 1967-04-01 DOI: 10.6028/JRES.071B.010
J. Hearon
{"title":"Construction of EPr generalized inverses by inversion of nonsingular matrices","authors":"J. Hearon","doi":"10.6028/JRES.071B.010","DOIUrl":"https://doi.org/10.6028/JRES.071B.010","url":null,"abstract":"Any matrix 8 s uc h that A8A = A is ca ll ed a C,·inve rse of A and a C,-inverse of A such that BA8 = B is ca ll ed a C,-inverse of A. Some properties of such inverses are es tabli s hed. It is shown that if A is p-square of ra nk q < p and P is any pos itive semide finit e matrix , whose rank is the nullity of A, such that U = A + Pis nonsin gular , then B = UIAUI is a C, ·inverse of A with the property that null space 8 = null s pace 8 *. That s uc h a P exis ts for a rbitrary squ are A is shown. The relation be tween thi s res ult and th e work of Go ldm an a nd Zelen is discussed.","PeriodicalId":408709,"journal":{"name":"Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics","volume":"86 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1967-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131474885","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: 9
Stable evaluation of polynomials. 多项式的稳定评价。
Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics Pub Date : 1967-03-01 DOI: 10.6028/JRES.071B.003
C. Mesztenyi, C. Witzgall
{"title":"Stable evaluation of polynomials.","authors":"C. Mesztenyi, C. Witzgall","doi":"10.6028/JRES.071B.003","DOIUrl":"https://doi.org/10.6028/JRES.071B.003","url":null,"abstract":"Stable evaluation algorithm for polynomials, discussing minimal Newton forms, error estimation, etc","PeriodicalId":408709,"journal":{"name":"Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics","volume":"126 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1967-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114060864","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: 19
A random walk model of chain polymer adsorption at a surface .3. Mean square end-to-end distance 链式聚合物在表面吸附的随机游走模型。端到端均方距离
Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics Pub Date : 1966-10-01 DOI: 10.6028/JRES.070B.022
R. Rubin
{"title":"A random walk model of chain polymer adsorption at a surface .3. Mean square end-to-end distance","authors":"R. Rubin","doi":"10.6028/JRES.070B.022","DOIUrl":"https://doi.org/10.6028/JRES.070B.022","url":null,"abstract":"A 6·c hoice s imple c ubic latti ce model of ad sorptio n of an isolated polymer c ha in a t a so luti on surface is inves ti gated. T he mean square co mpone nts (x2(N) and (Z2(N) of th e end· to·e nd di s· tance a re compu ted as a fun c tion of the adsorption e ne rgy pe r monomer unit in the limit of a ve ry long polymer c ha in . In the c alc ul at ion, one end of th e po lymer c ha in cons is ting of N monom er unit s is cons tra ined to li e in the surface ; and (x2(N) and (Z2(N) a re , respec ti ve ly, the mea n square di s· p lace me nt of the free end of Ith e cha in para ll e l to the solution s urface in one of th e latt ice direc tio ns and normal to the sol ut ion surface. The limiting va lue of (x 2(N» /N as N ---> 00 is a co ntinuou s fun c· ti on of 8 , the d ime ns io nless adsorpt ion ene rgy pe r monom er unit , a nd is equa l to 1/3 fo r 8 .;; In (6/5) and (1/2) (i + (1/4) (eO 1)1] 1/Z for II ;;;. In (6/5). The limiting vaJu e of (zZ(N) /N as N ---> 00 is a d is· con tinuous fun c tion of 8 a nd is equal to 2/3 for 8 < In (6/5), 1/3 for 8 = In (6/5) , and 0 for 0 > In (6/5) . The re latio n of these res ults to earli e r investigat ions and the gene ra lization of these results to othe r cubic lattice mode ls is di sc ussed.","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":"1966-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128966636","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: 22
Functions for thermal stress calculation near a transient heat source on a flat surface 平面上瞬态热源附近的热应力计算函数
Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics Pub Date : 1966-10-01 DOI: 10.6028/JRES.070B.025
S. Jarvis, G. Hardy
{"title":"Functions for thermal stress calculation near a transient heat source on a flat surface","authors":"S. Jarvis, G. Hardy","doi":"10.6028/JRES.070B.025","DOIUrl":"https://doi.org/10.6028/JRES.070B.025","url":null,"abstract":"Whe n an initiall y unstressed elastic so lid at uniform te mperature is subject to a transient, locally two-dime nsional heat flux on a flat surface, the two-dime nsional total stress field near the wall is locally dete rmin ed for short times and may be constructed from the functions described in this report; Fortran programs are available for their computation. In particular, maximum total stress and total stress fi e ld s for initiaIJy large heat fluxes are readily obtained for es timations of yield probability.","PeriodicalId":408709,"journal":{"name":"Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1966-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132533333","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
Abscissas and weights for Gaussian quadrature for n=2 to 100, and n=125, 150, 175, and 200 对于n=2到100，以及n=125、150、175和200，高斯正交的横坐标和权值
Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics Pub Date : 1966-10-01 DOI: 10.6028/JRES.070B.023
C. Love
{"title":"Abscissas and weights for Gaussian quadrature for n=2 to 100, and n=125, 150, 175, and 200","authors":"C. Love","doi":"10.6028/JRES.070B.023","DOIUrl":"https://doi.org/10.6028/JRES.070B.023","url":null,"abstract":"The a bsc issas a nd we ights fo r Ga uss ia n Q uadra ture of orde r N = 2 to 100, a nd N = 125, 150 , 175 , a nd 200 a re g ive n. Th e a bscissas a re giv en to twent y· four pl aces a nd the e rror is est.im a ted to be no more th a n 1 unit in th e las t. pl ace. Th e we ights a re give n to t we nty·three pl aces and the e rror is es tim a te d to be no more tha n 1 unit in th e las t pl ace. Key Vo rd s: Ga uss ia n qu a dra ture, integ ra l equ a ti ons, num e ri ca l integr a tion , zeros of Lege ndre po lyno mi a ls.","PeriodicalId":408709,"journal":{"name":"Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1966-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123508383","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: 9
Transverse impact of a linear three-element spring and dashpot model filament: theory 线性三元弹簧和阻尼器模型丝的横向冲击:理论
Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics Pub Date : 1966-10-01 DOI: 10.6028/JRES.070B.024
Jack C. Smith
{"title":"Transverse impact of a linear three-element spring and dashpot model filament: theory","authors":"Jack C. Smith","doi":"10.6028/JRES.070B.024","DOIUrl":"https://doi.org/10.6028/JRES.070B.024","url":null,"abstract":"The mathe matics of wave propagation in a viscoelastic filament subjec ted to cons tant veloc ity trans verse impact is di scussed. The equations gove rning the s tress·strain·time be hav io r a re as· s umed to be those for a linear model cons is ting of a spring coupled in parallel with a sp ring a nd dash· pot in ser ies . The nature of the solution is di scussed, and a method is desc ribed for calculating the configuration , and the s tress, s train, a nd particle ve locity di s tribut.ions along the impacted fil ament. The me thod used consists of a n integration along the cha racteri s tics of the s ys tem of differe nti al equations describing th e probl em.","PeriodicalId":408709,"journal":{"name":"Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1966-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131160503","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 the approximation of functions of several variables 关于多变量函数的近似
Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics Pub Date : 1966-07-01 DOI: 10.6028/JRES.070B.019
B. Mond, O. Shisha
{"title":"On the approximation of functions of several variables","authors":"B. Mond, O. Shisha","doi":"10.6028/JRES.070B.019","DOIUrl":"https://doi.org/10.6028/JRES.070B.019","url":null,"abstract":"1. The purpose of this note is to point out how a certain type of approximation to fun ctions of one real variable, gives rise to similar approximations to functions of several variables. In fact, we show how information on the rapidity of cOQvergence of the approximation in the one dimensional case, yields at once corresponding information for the multidimensional case. 2. Let -oo < a < b <oo, and for n=l, 2, . .. , let c~,), cln), . •• , c!') be points of [a, b], and Kbn)(X), Kn)(x), ... , K~n)(x) polynomials which are ;;:z,: ° throughout [a , b], and such that","PeriodicalId":408709,"journal":{"name":"Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1966-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115052960","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
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