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A primal (all-integer) integer programming algorithm 一个原始(全整数)整数规划算法
Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics Pub Date : 1965-07-01 DOI: 10.6028/JRES.069B.025
R. D. Young
{"title":"A primal (all-integer) integer programming algorithm","authors":"R. D. Young","doi":"10.6028/JRES.069B.025","DOIUrl":"https://doi.org/10.6028/JRES.069B.025","url":null,"abstract":"The algorithm is most closely related to three existing procedures: the simplex method of G. B. Dantzig for linear programming problems, the Gumory all-integer integer programming algurithm, and the direct algorithm for integer prugramming uf Ben-Israel and Charnes. The algorithm is similar to the Gomory all·integer algorithm in these respects: (i) it is an all-integcr algorithm; (ii) it uses t he same c ut generation proccdure; (iii) it uses the cut row as the pivot row; and (iv) the pivot coefficient always has unit value. While the dual method provides the vehicle for moving from tableau to tableau in the Gomory all-integer algorithm. the simplex method has the analag()us role in the primal algorithm. Thus in a general sense this algorithm is a primal analog t() the (dual) Comory all-integer algo rithm. The direct algorithm of Be n-Israel and Charnes also has the above similarities to the Gomory all-integer al~orithm, but has one significant difference: an iteration or cycle of the direct algorithm must frequently include the solution of an \"auxiliary problem\" (which is itself an int eger prugramming problem) or a determination that no solution to the \"auxiliary problem\" exists. In contrasl. the cycles of the primal algorithm include only the adjoining of a ComUl'y cut and the executiun of the change of basis procedure of the simplex method. The procedure uf the algorithm and the proof of finit eness are founded on a classification of cycles of the algorithm and on two theore ms. Two types of prorf'dural restrictions are imposed as a basis for proving fin iteness: (a) selection of the incoming variable is subjected to regulation (beyond that required by t he simplex met hod). and t he rules applied are a function uf the type of cycle being executed; (b) selection of the row Llsed as the source of the data for the","PeriodicalId":408709,"journal":{"name":"Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1965-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127990860","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: 37
The use of finite polynomial rings in the factorization of the general polynomial 有限多项式环在一般多项式分解中的应用
Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics Pub Date : 1965-07-01 DOI: 10.6028/JRES.069B.024
D. Lloyd
{"title":"The use of finite polynomial rings in the factorization of the general polynomial","authors":"D. Lloyd","doi":"10.6028/JRES.069B.024","DOIUrl":"https://doi.org/10.6028/JRES.069B.024","url":null,"abstract":"","PeriodicalId":408709,"journal":{"name":"Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1965-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128449767","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
On convex metrics 关于凸度量
Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics Pub Date : 1965-07-01 DOI: 10.6028/JRES.069B.021
C. Witzgall
{"title":"On convex metrics","authors":"C. Witzgall","doi":"10.6028/JRES.069B.021","DOIUrl":"https://doi.org/10.6028/JRES.069B.021","url":null,"abstract":"Given a finit e number of points PI, ., PI.\" in th e plane, consider the proble m of findin g a point x that minimizes the sum of Euclidean distances 'Ld(p; , x) . More general versions of thi s proble m arise in s patial economics, concerning opti mal locations for a central office , plant, or ware ho use (compare [3]). Mos t of these will be based on me trics d more general than th e Euclidean metric. Among them, th e class of metri cs that are convex fun ctions in each variable co mmand partic ular interest: in thi s case, local minima are automati cally global minima, facilitating minimization decisively. We s hall show in thi s paper that convex metrics are invariant under translation, and therefore arise from a norm. For th e concepts of topologies, metrics , and norms in linear spaces see, for instance, [1)2 and [2]. 1. Metrics and norms. Le t L be a linear s pace over the fi eld R of real numbers. A fun ction f: L -7 R is convex if","PeriodicalId":408709,"journal":{"name":"Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1965-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114721518","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: 8
A variant of the two-dimensional Riemann integral 二维黎曼积分的一种变体
Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics Pub Date : 1965-07-01 DOI: 10.6028/JRES.069B.023
A. J. Goldman
{"title":"A variant of the two-dimensional Riemann integral","authors":"A. J. Goldman","doi":"10.6028/JRES.069B.023","DOIUrl":"https://doi.org/10.6028/JRES.069B.023","url":null,"abstract":"For a va riant of the two-d imensional Ri e mann int egra l suggested by S. Marcus , it is shown that the only integrab le fun c tions which are continuous (o r merely continuou s se parately in one of th e variables) are the cons ta nt fun ctions . The int egrab le di scontinuou s functions a re proven to be cons ta nt except poss ib ly on a se t which is \"s ma ll\" in a sense made precise in the paper.","PeriodicalId":408709,"journal":{"name":"Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics","volume":"114 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1965-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116040186","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
Weak generalized inverses and minimum variance linear unbiased estimation 弱广义逆和最小方差线性无偏估计
Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics Pub Date : 1964-10-01 DOI: 10.6028/JRES.068B.021
A. J. Goldman, M. Zelen
{"title":"Weak generalized inverses and minimum variance linear unbiased estimation","authors":"A. J. Goldman, M. Zelen","doi":"10.6028/JRES.068B.021","DOIUrl":"https://doi.org/10.6028/JRES.068B.021","url":null,"abstract":"This paper presents a unified account of the theory of least squares and its adaptations to statis· tic al models more complicated than the classical one. Firs t comes a developme nt of the properties of weak general ized matrix inverses, a useful variant of the more familiar pseudo·inverse. These properties are e mployed in a proof of the usual Gauss theorem, and in analyzin g the case in which known linear res traints are obeyed by the para me ters. Anothe r s itu ation treated is that of a s ingular variance-co variance matrix for the observations . Applications include the case of equi-correlated variables (i ncluding es timation despite ignorance of the corre lation), linear \" res tra ints\" subject to random error, and step wise linear es timation.","PeriodicalId":408709,"journal":{"name":"Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1964-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115041056","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: 90
Equivalence of Certain Inequalities Complementing Those of Cauchy-Schwarz and Holder Cauchy-Schwarz与Holder的等价互补
Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics Pub Date : 1964-10-01 DOI: 10.6028/JRES.068B.020
J. B. Díaz, A. J. Goldman, F. Metcalf
{"title":"Equivalence of Certain Inequalities Complementing Those of Cauchy-Schwarz and Holder","authors":"J. B. Díaz, A. J. Goldman, F. Metcalf","doi":"10.6028/JRES.068B.020","DOIUrl":"https://doi.org/10.6028/JRES.068B.020","url":null,"abstract":"","PeriodicalId":408709,"journal":{"name":"Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1964-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122915501","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
Hydrodynamic Fluctuations and Stokes' Law Friction 流体动力波动与斯托克斯定律摩擦
Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics Pub Date : 1964-10-01 DOI: 10.6028/JRES.068B.019
R. Zwanzig
{"title":"Hydrodynamic Fluctuations and Stokes' Law Friction","authors":"R. Zwanzig","doi":"10.6028/JRES.068B.019","DOIUrl":"https://doi.org/10.6028/JRES.068B.019","url":null,"abstract":"The fri ctional forc e on a Brownian motion particle can be expressed by means of the time· correlation of the flu ctuating force on the particle . We s how that this method, applied to a spherical particle in a vi scous in compressibl e fluid , leads to Stokes ' Law. The c al culation is based on the theory of hydrodynamic flu ctuations due to Landau and Lifs hitz, and on a hydrodynamic theorem due to Faxe n. The subj ect of thi s article is th e connecti on be tween two diffe rent me th ods for calculating th e fri cti onal force on a Brownia n moti on particle. One method is based on th e s tati s ti cal mech ani cal th eory of irre­ ve r sible processes, and involv es evalua ti on of a certain time-correlati on formula. The other me thod is based on macroscopi c hydrodynami cs, and requires solution of th e N avi er- S tokes equ a ti on. F or simplicity we r estri c t the di scussion to the s pecial case of a spheri cal p article of radiu s a moving slowly through a vi scous in compressible fluid. The vi scosity coeffi cient is T/ . In the hydrodynamic theor y, th e fri c ti onal force F on a sphere movin g with constant velocity v is giv e n by Stokes' law,","PeriodicalId":408709,"journal":{"name":"Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1964-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124683069","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: 52
Thermodynamics of perfect elastic fluids 完全弹性流体热力学
Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics Pub Date : 1964-07-01 DOI: 10.6028/JRES.068B.016
B. Bernstein, E. Kearsley, L. J. Zapas
{"title":"Thermodynamics of perfect elastic fluids","authors":"B. Bernstein, E. Kearsley, L. J. Zapas","doi":"10.6028/JRES.068B.016","DOIUrl":"https://doi.org/10.6028/JRES.068B.016","url":null,"abstract":"A simple non.equilibrium thermodynamics is developed and a particular example is studied. The theory is formulated to describe a viscoelastic fluid, capable of finite deformation, which need not be locally in or near a state of thermodynamic equilibrium. This fluid may support shear stresses only when away from local thermodynamic equilibrium _ A notion of time-temperature superposition is contained in the formulation of the constitutive equations. Conservation of energy is obeyed and the second law of thermudynamics is satisfied as a consequence of simple requirements on the constitutive relations. In an adiabatic isochoric motion the temperature increases when work is done on the material and decreases when the material does work. For given volume and temperature, e ntropy decrea ses whe n the mate rial is deformed from equ il ibrium . It is s hown in what general way viscos it y depends upon te mperature . For infinites imal s train, the special form of the stress-s train relations are derived in order to de termine how t.e mpe rature and t ime-t e mperature supe rpos ition e nte r in thi s case.","PeriodicalId":408709,"journal":{"name":"Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1964-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117213247","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: 55
Generation and composition of functions 生成和组合函数
Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics Pub Date : 1964-07-01 DOI: 10.6028/JRES.068B.015
A. J. Goldman
{"title":"Generation and composition of functions","authors":"A. J. Goldman","doi":"10.6028/JRES.068B.015","DOIUrl":"https://doi.org/10.6028/JRES.068B.015","url":null,"abstract":"","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":"1964-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116300890","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
Theory of radiation from sources immersed in anisotropic media 浸没在各向异性介质中的辐射源理论
Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics Pub Date : 1964-07-01 DOI: 10.6028/JRES.068B.018
James R. Wait
{"title":"Theory of radiation from sources immersed in anisotropic media","authors":"James R. Wait","doi":"10.6028/JRES.068B.018","DOIUrl":"https://doi.org/10.6028/JRES.068B.018","url":null,"abstract":"The electromagnetic fields produced by an electric dipole immersed in an aniso tropic medium are considered. Various approaches to the problem are outlined with special reference to a cold plasma. An attempt is made to show the close relationship between previously published work on this subject. It is shown that information on the radiation field in an anisotrop ic media may be obtained directly from the shape of the refractive index surface.","PeriodicalId":408709,"journal":{"name":"Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics","volume":"129 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1964-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132024646","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: 10
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