Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics最新文献

{"title":"Selected bibliography of statistical literature: Supplement, 1958-1960","authors":"L. S. Deming","doi":"10.6028/JRES.067B.010","DOIUrl":"https://doi.org/10.6028/JRES.067B.010","url":null,"abstract":"","PeriodicalId":408709,"journal":{"name":"Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics","volume":"227 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1963-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116401261","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":"Effect of Molecular Weight on Viscoelastic Properties of Polymers as Predicted by a Molecular Theory","authors":"H. Oser, R. Marvin","doi":"10.6028/JRES.067B.009","DOIUrl":"https://doi.org/10.6028/JRES.067B.009","url":null,"abstract":"Calculations have been made covering the predictions of a model re presenting the vi s­ coelastic behavior of rubberlike polymers for molecular weights greater than 111., M. being the lower limit of t he range in which the viscosity is proportional to 1113.4. A pronounced diff erence in the character of G\" is predicted for polymers with molecu lar we ights between five and ten times 1 11. as compared with those whose molecular weights are outside this range. In a recent publication [1]1 we presented the steady state and transient behavior predicted by a model designed to repl'~sent the mechani~al behav:ior, in shear, of rubberhke polymers. ThIs model IS very similar to the molecular theor:v of Rouse [2], except that it includes directly the effect of entanglements found in long polymer chains. Our model assumes an entropy-type elasticity as the origin of t he relaxing force observed in it stress­ relaxation experiment. It involves a resistance coefficient per unit segment of a polymer chain which is evalu ated from the steady state viscous be­ havior, and the molecular weight of the polymer, expressed as the ratio of molecular weight to critical molecular weight, Me, defined as the lower limit of the range in which the viscosity is proportional to M 3. 4. For the particular example we presented in reference 1 this ratio was 60, and at the time we prepared this previous paper we did not have system­ atic calculations showing the predictions of the model for a range of molecular wei ghts. I'Ve made an effort (sec. 3, p . 176 of reference (1)) to relate the extrema of G\" and J\" to the molecular weight through the use of various approximate relationships, since the full expressions can only be treated numeril cally. We have now carried out further numerical calculations covering a range of molecular weights, and find that our previous approximate relations were completely inadequate to represent t he posi­ tions of these extrema as functions of molecular weight. In addition, we have found certain quite unexpected qualitative features of the predicted curves when the molecular weight is varied between one and ten times the critical molecular weight. I Since these quabtative features ma~T present the possibility of a rather critical test of the validity of this model, we pres en t the results here in some I detail. The results of our previous paper may be rep­ rf'sentf'd in terms of normalized functions. the","PeriodicalId":408709,"journal":{"name":"Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics","volume":"75 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1963-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114151603","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":"Estimation of dispersion parameters","authors":"W. A. Thompson","doi":"10.6028/JRES.066B.016","DOIUrl":"https://doi.org/10.6028/JRES.066B.016","url":null,"abstract":"This paper deals with a topi c in multivariate a nalys is. Consider that a sample of size n+ 1 has been collected from a p-variate normal distribution having dispersion matrix (CT ii'). Let a;r/n denote the usual unbiased estimate of CTW. Further, let O< l<u be constants such that all cha racteristic roots of a matrix having t he Wishart distribution lie in t he interval [I, u] with probability I a . A t heorem of Roy, Bose, and Gnanadesikan [A nn . Math. Stat. 24. 513536 (1953); Biometrika 44, 399410 (1957)] may be stated as follows: The probability is 1a t hat every principal minor determinant of II (aii ') (CT jj') and of (CTii,)ul(a jj') is nonnegat ive. The previous result may be used to prove t he main theorem of the p resent paper. Theorem: T he probability is at least 1a t hat t he following system of re lat ions hold simultaneo us ly : ulai i ~CT 'i ~I-laii; j = l , ... , p and ICT ii,-}f (11-1 + 11)0 ii·1 ~7WI -1,1) (a iiai';') ! ~' j r= j'.","PeriodicalId":408709,"journal":{"name":"Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1962-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130921649","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":"Bounds on ratios of means","authors":"G. T. Cargo, O. Shisha","doi":"10.6028/JRES.066B.018","DOIUrl":"https://doi.org/10.6028/JRES.066B.018","url":null,"abstract":"","PeriodicalId":408709,"journal":{"name":"Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1962-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125593381","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":"A model for the viscoelastic behavior of rubberlike polymers including entanglement effects","authors":"R. Marvin, H. Oser","doi":"10.6028/JRES.066B.019","DOIUrl":"https://doi.org/10.6028/JRES.066B.019","url":null,"abstract":"A model r epresen ting t he mechanical response of a rubberlike polym er is derived , using t he same molecular concep ts of ent ropy elasticity and a viscous parameter expressing interactions between polymer molecul es employed by R ouse, Bueche, and Zimm in thei r molec ular theories. Since t he model developed here r epresents the mechanical response of a chain, rather t han representing t he chain itself, it can be modifi ed more easily t han t hese strict molecular t heories to includ e effects due to entanglements between chains which modify the cha racter of the viscosity-molecular weight relat ionship at a crit ical molecu lar weight. This m odifi cation is in trod uced, t he results for both steady-state and transient response funct ions are calcu lated , and t hese result s compared wit h experiment for t he \" standard \" polyisobutyle ne. The agreement ind icates t hat the same \"entanglements,\" whatever t heir precise natu re, a re responsible for the proportionality of viscosity to M 3 .• for a high molecular weight polymer, the s teady-s tate elastic compli ance, a nd t he pseudo-equ ilibr ium co mplia nce at intermed iate t im es or frequencies.","PeriodicalId":408709,"journal":{"name":"Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics","volume":"417 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1962-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133269914","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":"Black box maximization of circular coverage","authors":"C. T. Zahn","doi":"10.6028/JRES.066B.020","DOIUrl":"https://doi.org/10.6028/JRES.066B.020","url":null,"abstract":"","PeriodicalId":408709,"journal":{"name":"Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics","volume":"92 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1962-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116184598","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":"An application of information theory to the analysis of contingency tables, with a table of 2n ln, n=1(1)10,000","authors":"S. Kullback, M. Kupperman, H. H. Ku","doi":"10.6028/JRES.066B.021","DOIUrl":"https://doi.org/10.6028/JRES.066B.021","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":"1962-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129937328","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":"Laguerre expansions for successive generations of a renewal process","authors":"G. Weiss","doi":"10.6028/JRES.066B.017","DOIUrl":"https://doi.org/10.6028/JRES.066B.017","url":null,"abstract":"","PeriodicalId":408709,"journal":{"name":"Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics","volume":"63 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1962-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122950705","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":"Reliability of a System in Which Spare Parts Deteriorate in Storage","authors":"G. Weiss","doi":"10.6028/JRES.066B.015","DOIUrl":"https://doi.org/10.6028/JRES.066B.015","url":null,"abstract":"Tile proble m. considered is t hat of determining the failure statistics for a syste m cons isting of a singl e p ar t a nd n spares, in which i t is assumed t hat t hat failure occurs at different rates in use a nd in stor age. The r es ul tin g equations can be solved explicitly when both ty pes of failures follow a Poisson la w. Otherwise algorithms are given for t he calcu lation of t he failur e p ro babili t ies .","PeriodicalId":408709,"journal":{"name":"Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1962-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121557953","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":"Mill's ratio for multivariate normal distributions","authors":"I. R. Savage","doi":"10.6028/JRES.066B.011","DOIUrl":"https://doi.org/10.6028/JRES.066B.011","url":null,"abstract":"","PeriodicalId":408709,"journal":{"name":"Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1962-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116522019","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}