{"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}
{"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}
{"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}
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.
{"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}
Stable evaluation algorithm for polynomials, discussing minimal Newton forms, error estimation, etc
多项式的稳定评估算法，讨论最小牛顿形式，误差估计等
{"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}
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.
{"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}
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.
{"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}
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.
The a平衡计分卡issas nd we ights fo r的Ga号uss ia Q uadra of成群结队r n = 2到100,na n = 125、150、175、nd 200号g的Th和bscissas giv国王en to twent y·东nd The和rror is four pl integra。im ted to be no more Th a n 1单位在Th和las t . pl ace。我们给了你三张王牌，而我们得到的回报是，我们再也没有一个单位了。关键的发展方向是:你可以选择你想要的，你想要的，你想要的，你想要的，你想要的，你想要的，你想要的，你想要的，你想要的，你想要的，你想要的，你想要的，你想要的，你想要的，你想要的，你想要的，你想要的，你想要的，你想要的，你想要的，你想要的。
{"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}
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.
{"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}
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
1. 这篇笔记的目的是指出，对一个真实变量的有趣函数的某种近似如何产生对多个变量函数的类似近似。事实上，我们展示了一维情况下近似的coq收敛速度的信息如何立即产生多维情况下的相应信息。2. 令-oo < a < b
{"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}
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