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

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Hecke basis theorems for groups of genus 0 属0群的Hecke基定理
Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences Pub Date : 1970-07-01 DOI: 10.6028/JRES.074B.013
M. Knopp, J. R. Smart
{"title":"Hecke basis theorems for groups of genus 0","authors":"M. Knopp, J. R. Smart","doi":"10.6028/JRES.074B.013","DOIUrl":"https://doi.org/10.6028/JRES.074B.013","url":null,"abstract":"A Hecketype basis theorem is established for the cusp forms of negative even integral degree (m ultiplier syste m 1) on the class of Hecke groups. Hecke established the result for the classical modular group , which is the first of the Hecke groups. A second result is a parametrization theorem for en tire automorphic forms of negative real degree (with arbitrary multiplier systems) on certain discrete groups of real linear fractional transformations of genus zero.","PeriodicalId":166823,"journal":{"name":"Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences","volume":"102 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1970-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123556988","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: 4
Expansions with coefficient algorithms for time domain responses of skin effect lossy coaxial cables 集肤效应损耗同轴电缆时域响应的系数展开算法
Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences Pub Date : 1970-07-01 DOI: 10.6028/JRES.074B.015
D. Holt
{"title":"Expansions with coefficient algorithms for time domain responses of skin effect lossy coaxial cables","authors":"D. Holt","doi":"10.6028/JRES.074B.015","DOIUrl":"https://doi.org/10.6028/JRES.074B.015","url":null,"abstract":"","PeriodicalId":166823,"journal":{"name":"Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1970-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131739764","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
The Distribution of Eigenvalues of Covariance Matrices of Residuals in Analysis of Variance 方差分析中残差协方差矩阵特征值的分布
Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences Pub Date : 1970-07-01 DOI: 10.6028/JRES.074B.014
J. Mandel
{"title":"The Distribution of Eigenvalues of Covariance Matrices of Residuals in Analysis of Variance","authors":"J. Mandel","doi":"10.6028/JRES.074B.014","DOIUrl":"https://doi.org/10.6028/JRES.074B.014","url":null,"abstract":"A rigorous definition is given for the concept of an interaction matrix (Z* lij*s) where i=1 to m and j=1 to n, in terms of two idempotent matrices A*lr*s and B*ls*s of rank r and s, respectively. It is then shown that the frequency distribution of the eigenvalues of (Z)(Z)' depends only on r and s. Applications are given to matrices of residuals arising from two-way data, either by removing row and/or column-means, or by applying any number of sweeps of the vacuum cleaner. The theorems are important in the theory of the analysis of two-way tables of nonadditive data.","PeriodicalId":166823,"journal":{"name":"Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1970-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117320748","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
Automatic computing methods for special functions 特殊功能的自动计算方法
Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences Pub Date : 1970-07-01 DOI: 10.6028/JRES.074B.019
I. Stegun, R. Zucker
{"title":"Automatic computing methods for special functions","authors":"I. Stegun, R. Zucker","doi":"10.6028/JRES.074B.019","DOIUrl":"https://doi.org/10.6028/JRES.074B.019","url":null,"abstract":"AMS55[1)1 the Handbook of Mathematical Func tion s -in add ition to definin g fu nctions in te rms of their integrals, power series, asymptotic expansion s, e tc., also suppli es tables a nd approximating polynomial s as welJ as methods of co mputing values both within and outside th e tabular range. With the present trend to large scale co mputer sys tems, questions frequently arise concerning methods of co mputing the tabular values th emselves. In many, if not most cases, the method used for computing th e table is certainly not the bes t method for computing discrete values. While many specialized me thods and programs exis t [3,6,7,8 1, as a supple ment to the Handbook and to satisfy general need s, a sys l.ematic effort is being made to supply methods of computing special func60ns, accurate within machine precision, valid throughout the entire range of th e fun ction , efficient , and readily programmable and adaptable for varying precision and computers. Part I of the present paper is devoted to the error , probability, and related fun ctions.","PeriodicalId":166823,"journal":{"name":"Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1970-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131404479","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
Derivatives of the Grneisen and Einstein Functions 格尼森和爱因斯坦函数的导数
Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences Pub Date : 1970-07-01 DOI: 10.6028/jres.074b.016
A. Cezairliyan
{"title":"Derivatives of the Grneisen and Einstein Functions","authors":"A. Cezairliyan","doi":"10.6028/jres.074b.016","DOIUrl":"https://doi.org/10.6028/jres.074b.016","url":null,"abstract":"The function CO(8/T) is frequently referred to as the Griineisen fu nction. This fun ction is approximately unity for T P 8, which indicates that at high temperatures electrical resistivity increases linearly with temperature. At very low temperatures where T ~ 8, the Griineisen function can be expressed approximately by CO(8/T) = B (T/8) which indicates that at very low temperatures electrical resistivity increases with the fifth power of temperature. For various calculations, the successive derivatives of the electrical resistivity function may be needed_ This req uires a knowledge of the derivatives of the Griineisen function. Also, it may be possible to make further refinem ents in the electrical resistivity expression by expanding the resistivity fun ction in the derivatives of the Griineisen function. It was observed that the derivatives of the Griine isen function contain th e Einstein function and its successive derivatives. The objective of this writing is to obtain expressions for the successive derivatives of the Griineisen and the Einstein fun c tions.","PeriodicalId":166823,"journal":{"name":"Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1970-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127497315","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
On some indefinite integrals of confluent hypergeometric functions 关于合流超几何函数的不定积分
Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences Pub Date : 1970-06-01 DOI: 10.6028/JRES.074B.009
E. W. Ng, M. Geller
{"title":"On some indefinite integrals of confluent hypergeometric functions","authors":"E. W. Ng, M. Geller","doi":"10.6028/JRES.074B.009","DOIUrl":"https://doi.org/10.6028/JRES.074B.009","url":null,"abstract":"Confluent hypergeometric functions indefinite integrals analytic expressions and reduction formulas","PeriodicalId":166823,"journal":{"name":"Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences","volume":"115 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1970-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127177438","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: 6
On contractive semigroups and uniform asymptotic stability 关于收缩半群与一致渐近稳定性
Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences Pub Date : 1970-04-01 DOI: 10.6028/JRES.074B.011
P. R. Meyers
{"title":"On contractive semigroups and uniform asymptotic stability","authors":"P. R. Meyers","doi":"10.6028/JRES.074B.011","DOIUrl":"https://doi.org/10.6028/JRES.074B.011","url":null,"abstract":"Th is paper call s attention to the equ ivalence be twee n two we ll-known ma th e ma t.i ca l ideas : cont .. ac ti on mappings (in the sense of Banach) and asy mptoti c s tab ili t. y. The equiva le nce is form a li zed by de fin ing a Aow (represe nting the poss ible movements ove r tim e of some sys te m through it s s tat e s pace) as a co nt inuou s o ne-pa ra me te r semigroup of operators on a me tri c s pace, and the n showing th at these opera to rs a re all contrac tions (in suitab ly re vi se d me tri cs) if and o n ly if the re is a un iform ly asympt.otic a ll y s tab le equ ili brium point. Gene ra liza t. ions to o.the r ope rator se mi grollps a re a lso given.","PeriodicalId":166823,"journal":{"name":"Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences","volume":"486 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1970-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132790437","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: 4
Acoustic propagation and stability within an inviscid, heat-conducting fluid 无粘性导热流体中的声传播和稳定性
Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences Pub Date : 1970-04-01 DOI: 10.6028/JRES.074B.008
J. McKinney, H. Oser
{"title":"Acoustic propagation and stability within an inviscid, heat-conducting fluid","authors":"J. McKinney, H. Oser","doi":"10.6028/JRES.074B.008","DOIUrl":"https://doi.org/10.6028/JRES.074B.008","url":null,"abstract":"Propagation of acoustic waves within a continuum of in viscid, compressible, heat-conducting fluid is evaluated in detail in terms of both frequency (steady-state) and time dependent (transient) functions. The analysis reveals that when the value of the ratio of specific heats, y , lies between one and two, the apparent steady-state solutions are conjugate to unstable, or regenerative, \"transient\" solutions, and, thus, are unacceptable. Propagation is stable for other values (y= 1, y ;;. 2). The common assumption that the steady-state phase velocity varies continuously with increasing frequency from adiabatic to isothermal values is shown to be invalid, except when y = 2.","PeriodicalId":166823,"journal":{"name":"Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences","volume":"78 3-4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1970-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114121340","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
Normal subgroups of the modular group 模群的正规子群
Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences Pub Date : 1970-04-01 DOI: 10.6028/JRES.074B.012
L. Greenberg, M. Newman
{"title":"Normal subgroups of the modular group","authors":"L. Greenberg, M. Newman","doi":"10.6028/JRES.074B.012","DOIUrl":"https://doi.org/10.6028/JRES.074B.012","url":null,"abstract":"A numbe r of res ults o n the normal s ubgroup stru cture of th e class ical modul ar group is a nn o un ced. A t ypi cal res ult is th at a normal subgroup of squ are-free ind ex is necessaril y of ge nu s 1, a pa rt from 4 excep ti ons.","PeriodicalId":166823,"journal":{"name":"Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1970-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115801342","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: 13
On complementary polar conical sets 关于互补的极圆锥集
Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences Pub Date : 1970-04-01 DOI: 10.6028/JRES.074B.010
C. Witzgall
{"title":"On complementary polar conical sets","authors":"C. Witzgall","doi":"10.6028/JRES.074B.010","DOIUrl":"https://doi.org/10.6028/JRES.074B.010","url":null,"abstract":"Abstract : Tucker has formulated the Duality Theorem of Linear Programming in terms of orthogonality properties of a pair of complementary orthogonal linear manifolds with respect to the positive orthant. This theorem is generalized by substituting complementary polar conical sets for complementary orthogonal linear manifolds, and proved under simple stability assumptions. Equivalence to Feuchel's Duality Theorem for conjugate convex functions is established. There are strong parallelisms to work by Kretschmer. (Author)","PeriodicalId":166823,"journal":{"name":"Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences","volume":"62 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1970-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134232957","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: 1
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