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

{"title":"The characterizations of (Aq(U))","authors":"M. Sheingorn","doi":"10.6028/JRES.077B.009","DOIUrl":"https://doi.org/10.6028/JRES.077B.009","url":null,"abstract":"For q > J Be rs. Iefin es a Banach s pa ce A,,(U) = {/EH(U) 1 I.1 /(1I)1(1-lnl\")q~2dxdy < 00 } a nd s how s th a t a ny bou nd e d lin ea r fun c tion al on A ,,(U) may b e rep!\"esen ted a,; \"(I) = j l(n)C(u)(1-,. InI2)2q ~ 2dxdy where CEB ,,(V) = {hE H (U) 1 s up Ih (I1)I(1-lul,)q < co } and is uniqu e. T hi s work is IIE/ ' do n e in [1 p. Duren , R o mbe rg, a nd S hi e ld s. purs uant to th e ir work 4Jn H\" for p < l , d efi ne a B a n ac h s pa ce B\"(P < 1) = {/E H (V) I J,2~J,, ' I/(rei!J)I (l-r) I /\" 'drd(J <oo }. Th ey s how th a i a bllund e d lin ea r fun ('t ill n a l A lin B\" lIla y be uniqu e ly re prese nt e d as \"(f) = lim f'j, .(ei!J)g(eiO)dlJ whe re r-+ I J o (i) 1 ,(eiO) = I,(re ill) _ (ii)/i EA = {hE H (U) 1 g is co ntinu llus lin V} and gin I). a nd II-l 5t d e riv a ti ve of g, is in i ,, = {hEH(U)l h'(reiO) = O(l-r) \" 'n. (Il e re (y= l /p-1I where 1I < I /p < II+1 , Sll a ¥ O. If l /p = II + l , th e co ndition s on g a re : gEA, gin-ilEA = {hdl (V)l h\"(reiO) = 0«(1-r) ~ I)}.) Thi s work appears in [2J, * In Ihi s paper. afte r s l,., inl(th a t B\" =\" A,,(U) itll l /p= q, e d e riv e Ih e re latitlnsll ip bete('n C a lld (:{, nalllel y: 211 + I C(z) = 2: Ak·/f\"·+I)(z) ·z2!·\", (izi < 1) where Ai are C4J ns tant s, A'n+1 \"'\" O. (in thi s case q= l /p is a n int ege r. Th e Th eo re m is s li ghtl y rliffere nl if q is nol an int ege r.) { III 0-lu I2)Q-2dXdy =.l.... J I 1/1(1-r2) q-2rdrdO ~ max 0 , 2'1-2) (27T …","PeriodicalId":166823,"journal":{"name":"Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1973-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128495057","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":"Remarks on a problem of Rademacher in the theory of modular forms","authors":"M. Knopp","doi":"10.6028/JRES.077B.008","DOIUrl":"https://doi.org/10.6028/JRES.077B.008","url":null,"abstract":"","PeriodicalId":166823,"journal":{"name":"Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1973-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121701722","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":"Character induced subgroups","authors":"R. Merris, W. Watkins","doi":"10.6028/JRES.077B.010","DOIUrl":"https://doi.org/10.6028/JRES.077B.010","url":null,"abstract":"One easil y sees that Cx is the norm al s ubgroup of C co ns is ting of those ele me nts represe nted by scalars in {A (g )}. Moreove r, A = xlx(l) is a linear c haracte r on Cx whi ch is in vari a nt under conjugation b y eleme nts of C . we call C x the subgroup induced by X. THEOREM 1 : We have X (1) 2 :s:; [G : Gx], with equality if and only if X is the only irreducible character of G whose restriction to Gx contains A as a component. PROOF: Let '11.(; be the charac te r of C induced b y A. The n, b y the Froben ius Reciprocity Theore m, X occurs in '11.(; exactly x(l) tim es. Moreover , if'Y/ is a n irreduc ible charac te r on C whose restri ction to C x conta ins A, th en 'Y/ E '11. (;. But, the degree of '11.. (; is [G : G xl W e might point out th a t if'Y/ is an irredu c ible charac ter on C such that A E 'Y/ I Cx, then 'Y/ I Cx = 'Y/ (1) '11.[8 , p. 53J. In partic ular , Cx C CT) . COROLLARY 1: Let g E G be arbitrary. Then A can be extended to a character of < Gx, g), the group generatedbyG x and g.lfX(I )2 = [ G: Gx > 1,thenA cannot beextendedtoG. PROOF: T he firs t s ta te me nt follows because Gx is normal and A is invariant. The second follows from Theore m l. W e now give another proof of Theore m 1 whic h leads to an appa re ntl y diffe re nt case of equality. First, define th e support of X to be supp X = {g E C : X(g ) 0/= O}. TH EOREM 1': We have X (l) 2 :s:; [G : Gx], with equality if and only if supp X = Gx.","PeriodicalId":166823,"journal":{"name":"Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1973-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126445328","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 Schurs' lemma on irreducible sets of matrices in continuum mechanics","authors":"J. Fong","doi":"10.6028/JRES.077B.007","DOIUrl":"https://doi.org/10.6028/JRES.077B.007","url":null,"abstract":"","PeriodicalId":166823,"journal":{"name":"Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences","volume":"77 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1973-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127254575","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":"The Stieltjes Constants","authors":"J. Liang, J. Todd","doi":"10.6028/JRES.076B.012","DOIUrl":"https://doi.org/10.6028/JRES.076B.012","url":null,"abstract":"The Stieltjes Constants are the coefficients in the Laurent expansion of the Riemann Zeta function g(z) about its simple pole at z= l. They can be represented as the limit of the difference between the sum of the first n terms of a series and the integral of its n-th term. The first 20 coefficients have been computed to 15 D using the Euler-Maclaurin method. As a by-product the sums of the series ~ T\"=+ (-1)k(logk)\"lk have been obtained to 15 D for n = 1 (l) 20.","PeriodicalId":166823,"journal":{"name":"Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1972-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128628023","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":"Scheduling a time-shared server to minimize aggregate delay","authors":"A. J. Goldman","doi":"10.6028/JRES.076B.008","DOIUrl":"https://doi.org/10.6028/JRES.076B.008","url":null,"abstract":"A 1967 paper by Rangarajan and Oliver [1)1 contains a formulation and analysis of the two problems described below, which pertain to the allocation of servicing times among N incoming streams requiring \"processing\" of some kind by a single \"server.\" The server might for example be a switching point or a congestion point (e.g., a tunnel entrance) in a transport network, in which case \"processing\" an item (vehicle) simply means letting it through. Or, the server might be a computer handling reservations from several ticket offices, or exercising real-time control over vehicle movements on several network links, or performing some other tasks on a time·shared basis. The streams are treated as continuous flows. During each service cycle, of duration T, the server handles stream 1 for time Ct , switches (with associated known switch-over or \"dead\" time) to handle stream 2 for time C2 , etc. The arrivals in each stream are assumed nonrandom, with a known uniform rate (possibly different for different streams). The server's processing rate, when serving a particular stream, is also assumed nonrandom and constant (possibly different for different streams). Each Ci is constrained to be at least large enough so that no queue remains in the i th stream when one of that stream's service periods ends. The two problems formulated and analyzed are these: PROBLEM 1: For given cycle time T, what allocation Ct , C2·, ••• , CN of service times among the various streams is optimal, in the sense of minimizing total waiting time per cycle? PROBLEM 2: What value of the cycle time T will minimize average waiting time? Subsequently Horn [2] showed that the more general case, in which all streams are served equally often (possibly more than once) per cycle, can be reduced to PROBLEM 1. This provides additional reason for offering an alternative analysis, which is more self-contained and (at least to the writer) simpler than that of reference [1]. In addition, a mild generalization will be introduced by permitting the penalties for delay to be different for different streams.","PeriodicalId":166823,"journal":{"name":"Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1972-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130914469","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":"On regular sets of polynomials whose zeros lie in prescribed domains","authors":"M. Farag, M. Nassif","doi":"10.6028/JRES.076B.011","DOIUrl":"https://doi.org/10.6028/JRES.076B.011","url":null,"abstract":"","PeriodicalId":166823,"journal":{"name":"Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences","volume":"63 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1972-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125085407","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":"Confidence limits for the abscissa of intersection of two linear regressions","authors":"J. Filliben, J. McKinney","doi":"10.6028/JRES.076B.013","DOIUrl":"https://doi.org/10.6028/JRES.076B.013","url":null,"abstract":"","PeriodicalId":166823,"journal":{"name":"Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1972-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128100476","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":"Product solutions and separation of variables","authors":"A. J. Goldman","doi":"10.6028/JRES.076B.015","DOIUrl":"https://doi.org/10.6028/JRES.076B.015","url":null,"abstract":"","PeriodicalId":166823,"journal":{"name":"Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences","volume":"40 33","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1972-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133390078","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":"Weighting methods for Monte-Carlo calculation of polymer configurations","authors":"F. McCrackin","doi":"10.6028/JRES.076B.014","DOIUrl":"https://doi.org/10.6028/JRES.076B.014","url":null,"abstract":"In the Rosenbluth and Rosenbluth method of computing polymer configurations, the configurations are weighted in order to remove bias of the estimated parameters of the configurations. This weighting method is investigated and generalized for importance sampling and Boltzmann factors. The estimates are found to be unbiased in the limit for an infinite sample of configurations, but to have a bias for a finite sam pit'. The standard deviations of the estimates are also derived.","PeriodicalId":166823,"journal":{"name":"Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1972-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123524784","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}