{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T07:48:19Z","timestamp":1773388099822,"version":"3.50.1"},"reference-count":54,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[1980,1,1]],"date-time":"1980-01-01T00:00:00Z","timestamp":315532800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Scientometrics"],"published-print":{"date-parts":[[1980,1]]},"DOI":"10.1007\/bf02016597","type":"journal-article","created":{"date-parts":[[2005,8,5]],"date-time":"2005-08-05T11:00:30Z","timestamp":1123239630000},"page":"3-34","source":"Crossref","is-referenced-by-count":66,"title":["On fundamental regularities of the distribution of scientific productivity"],"prefix":"10.1007","volume":"2","author":[{"given":"A. I.","family":"Yablonsky","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"BF02016597_CR1","first-page":"109","volume":"1","author":"J. Vlach\u00fd","year":"1978","unstructured":"J. VLACH\u00dd, Frequency distributions of scientific performance. A bibliography of Lotka's law and related fenomena,Scientometrics, 1 (1978) 109\u2013131.","journal-title":"Scientometrics"},{"key":"BF02016597_CR2","first-page":"109","volume":"1","author":"J. Vlach\u00fd","year":"1978","unstructured":"For the growth statistics see:.","journal-title":"Scientometrics"},{"key":"BF02016597_CR3","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1007\/BF00353144","volume":"4","author":"J. J. Hubert","year":"1977","unstructured":"J. J. HUBERT, Bibliometric models for journal productivity,Social Indicators Research, 4 (1977) 441\u2013473.","journal-title":"Social Indicators Research"},{"key":"BF02016597_CR4","unstructured":"A. I. YABLONSKI, Models and Methods of Mathematical Studies of Science (a scientific-analytical review), Moscow, 1977."},{"key":"BF02016597_CR5","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1086\/258792","volume":"71","author":"B. Mandelbrot","year":"1963","unstructured":"B. MANDELBROT, New methods in statistical economies,Journal of Political Economy, 71 (1963) 421\u2013440.","journal-title":"Journal of Political Economy"},{"key":"BF02016597_CR6","first-page":"317","volume":"16","author":"A. J. Lotka","year":"1926","unstructured":"A. J. LOTKA, The frequency distribution of scientific productivity,Journal of the Washington Academy of Science, 16 (1926) 317\u2013323.","journal-title":"Journal of the Washington Academy of Science"},{"key":"BF02016597_CR7","unstructured":"J. VLACH\u00dd, Variable factors in scientific communities (Observations on Lotka's law),Theorie a metoda, Praha, IV\/I, 1972."},{"key":"BF02016597_CR8","unstructured":"B. N. PETROV, G. M. ULANOV, S. V. UL'YANOV, E. M. KHAZEN, Information-Semantic Problems in Organization and Control, Moscow, 1977."},{"key":"BF02016597_CR9","unstructured":"A. I. YABLONSKY, Statistical models of scientific activity. In:Systems Research Yearbook \u2014 1975, Moscow, 1976."},{"issue":"No. 2","key":"BF02016597_CR10","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1177\/030631277600600205","volume":"6","author":"P. D. Allison","year":"1976","unstructured":"P. D. ALLISON, D. de S. PRICE, B. C. GRIFFITH, M. J. MORAVCSIK, J. A. STEWART, Lotka's law: a problem in its interpretation and application,Social Studies of Science, 6 (1976), No. 2, 269\u2013276.","journal-title":"Social Studies of Science"},{"key":"BF02016597_CR11","unstructured":"Even if one considers only the scientific output measured, for instance, not by publications but by the number of new ideas, according toCrane's results concerning the spreading of innovations in agriculture (See: D. CRANE,Invisible Colleges. Diffusion of Knowledge in Scientific Communities, Chicago, 1972), the distribution of the number of innovations advanced by various scientists is also governed by Lotka's law. The author of the lawA. J. Lotka who analyzed no only the chemical abstract journal butF. Auerbach's Geschichtstafeln der Physik for 1600\u20131900 and obtained an agreement between the corresponding distributions of scientific output (as judged by publications and discoveries) noted the same."},{"key":"BF02016597_CR12","unstructured":"A. J. YABLONSKY. Models and Methods of Mathematical Studies of Science (a scientific-analytical review), Moscow, 1977."},{"key":"BF02016597_CR13","unstructured":"See. A. J. YABLONSKY,op. cit., note 9, Statistical models of scientific activity. In:Systems Research Yearbook \u2014 1975, Moscow, 1976, for details of randomization of branching processes."},{"key":"BF02016597_CR14","unstructured":"A. I. YABLONSKY, Structure and dynamics of modern science (certain methodological problems). In:Systems Research Yearbook \u2014 1976, Moscow, 1977."},{"issue":"No. 3683","key":"BF02016597_CR15","doi-asserted-by":"crossref","first-page":"510","DOI":"10.1126\/science.149.3683.510","volume":"149","author":"D. de S. Price","year":"1965","unstructured":"D. de S. PRICE, Networks of scientific papers,Science, 149 (1965) No. 3683, 510\u2013515.","journal-title":"Science"},{"key":"BF02016597_CR16","doi-asserted-by":"crossref","unstructured":"D. Dieks, H. Chang, Difference in impact of scientific publications: Some indices derived from a citation analysis,Social Studies of Science, 6 (1976) No. 2.","DOI":"10.1177\/030631277600600204"},{"issue":"No. 3","key":"BF02016597_CR17","doi-asserted-by":"crossref","first-page":"335","DOI":"10.2307\/2092499","volume":"34","author":"D. Crane","year":"1969","unstructured":"Note also the sociological studies of the scientific effect that were conducted, for instance, by D.Crane by means of questionnaire distribution among the members of the \u201cinvisible college\u201d in one of the problematic fields of rural sociology (the distribution of innovations in agriculture), in order to determine the influence of other scientists on the results of representatives of the given \u201ccollege\u201d [See: D. CRANE, Social structure in a grop of scientists: a test of the \u201cInvisible College\u201d hypothesis,American Sociological Review, 34 (June 1969) No. 3, 335\u2013352]. Of interest is that the distribution of \u201cinfluencing\u201d scientists with respect to the number of them being chosen by the examination participants is also governed (qualitatively) by a law similar to that of Lotka: the small number of scientists was given by many participants and vice versa, the basic number of \u201cinfluencing\u201d scientists was mentioned only once.","journal-title":"American Sociological Review"},{"key":"BF02016597_CR18","doi-asserted-by":"crossref","unstructured":"D. Dicks, H. Chang,op cit., note 16. Difference in impact of scientific publications: Some indices derived from a citation analysis,Social Studies of Science, 6 (1976) No. 2.","DOI":"10.1177\/030631277600600204"},{"issue":"No. 2","key":"BF02016597_CR19","first-page":"261","volume":"6","author":"D. Dicks","year":"1976","unstructured":". p. 261.","journal-title":"Social Studies of Science"},{"issue":"No. 4","key":"BF02016597_CR20","doi-asserted-by":"crossref","first-page":"377","DOI":"10.2307\/2111839","volume":"43","author":"J. R. Cole","year":"1970","unstructured":"e.g. J. R. COLE Patterns of intellectual influence in scientific research,Sociology of Education, 43 (1970) No. 4, 377\u2013403; I. V. MARSHAKOVA prospective connection in the system of scientific publications. In:Systems Research Yearbook \u2014 1976, Moscow, 1977.","journal-title":"Sociology of Education"},{"key":"BF02016597_CR21","unstructured":"S. C. BRADFORD,Documentation, London, 1948."},{"issue":"No. 1","key":"BF02016597_CR22","first-page":"18","volume":"1","author":"A. Avramescu","year":"1975","unstructured":"An important feature of this case is exactly that the corresponding set of journals should reflect with sufficient completeness the sphere of knowledge under study. \u201cThe law of dispersal of papers in the journals is valid only after a certain time interval has elapsed during which the mass of publications pertaining to a given topic will be formed, in other words, on the expiration of time required for the general spread of interest in a given subject\u201d. [A. AVRAMESCU, The modelling of scientific information transfer,Mezhdunarodnyi forum po informatsii i dokumentatsii, 1 (1975) No. 1, 18]. For this reason, by the way, the validity of Bradford's law for a given information data base can serve as an indication of a sufficiently well formed scientific field.","journal-title":"Mezhdunarodnyi forum po informatsii i dokumentatsii"},{"issue":"No. 5223","key":"BF02016597_CR23","doi-asserted-by":"crossref","first-page":"953","DOI":"10.1038\/224953a0","volume":"224","author":"B. C. Brookes","year":"1969","unstructured":"B. C. BROOKES, Bradford's law and the bibliography of science,Nature, 224 (1969) No. 5223, 953\u2013956.","journal-title":"Nature"},{"key":"BF02016597_CR24","volume-title":"Understanding Scientific Literatures \u2014 a Bibliometric Approach","author":"J. S. Donohue","year":"1973","unstructured":"J. S. DONOHUE,Understanding Scientific Literatures \u2014 a Bibliometric Approach. The MIT press, Cambridge (Mass.), London, 1973."},{"key":"BF02016597_CR25","unstructured":"The empirical parameter S equals one for very \u201cnarrow\u201d scientific fields and grows with the increase of the range of problems treated in a given field. Therefore, its definition can be used in order to estimate quantitatively the degree of broadness of the discipline under study. For example, A.Pope [see: A. Pope, Bradford's law and the periodical literature of information science.Journal of the American Society for Information Science, 26 (1975) No. 4] having analyzed the corresponding bibliographical data bases, arrived at a conclusion that information science (S=2.6) occupies an intermediate position between library science (S=1) and computational science (S=3.4), i.c., the set of its subjects is broader than the former but narrower than the latter which agrees, by the way, also with the intuitive concepts about the broadness of the set of subjects in these three disciplines."},{"key":"BF02016597_CR26","unstructured":"S. C. BRADFORD,op. cit., note 21.Documentation, London. 1948."},{"key":"BF02016597_CR27","doi-asserted-by":"crossref","unstructured":"E. A. Wilkinson, The ambiguity of Bradford's law,Journal of Documentation, 28 (1972) No. 2.","DOI":"10.1108\/eb026534"},{"key":"BF02016597_CR28","doi-asserted-by":"crossref","unstructured":"Note that such peculiar feature of representing scientific information as its quantization in the form of papers, books, unification of papers into discrete quantization units (journals), etc. exercise informational structure, its stability, the formation of Bradford's law, etc. For instance, it is noted that a peculiar feature of Bradford's law which consists in the presence of a \u201cnucleus\u201d in a collection with its own dynamics of scientific information can be explained by \u201csuch specific form of quantization as periodicals\u201d (A. I. MIKHAILOV, A. I. CHERNYI, R. C. GILYAREVSKY,Scientific Communications and Informatics, Moscow, 1976, p. 184). For this reson the \u201cquantum\u201d approach to the study of regularities of the organizing of the information base is of interest, and not only for informatics but for the science of sciences as well, for instance, in connection with the analysis of scienfitic communication. Recent papers of A.Hill et al. [B. HILL, Zipf's law and prior distributions for the composition of a population,Journal of the American Statistical Association, 65 (331) (1970) 1220 B. HILL, Rank frequency forms of Zipf's law,Journal of the American Statistical Association, 69 (348) (1974) 1017; B. HILL, M. WOODROOFE, Stronger forms of Zipf's law,Journal of the American Statistical Association, 70 (349) (1975) 212; M. WOODROOFE, B. HILL, On Zipf's law,Journal of Applied Probability, 12 (1975) 425\u2013434], in which Bose-Einstein statistics (see, e.g., W. FELLER,An Introduction to Probability Theory and its Applications, Wiley & Sons, Inc., London, Chapman & Hall Ltd., 1957) is used for derivation of Zipf's law, the ranks and analog of Lotka's law (Bradford's law representing the cumulative form of Zipf's law), provide an interesting example of the application of quantum statistics.","DOI":"10.1080\/01621459.1970.10481157"},{"key":"BF02016597_CR29","unstructured":"See, e.g., D. CRANE,op. cit., note 11; Even if one considers only the scientific output measured, for instance, not by publications but by the number of new ideas, according toCrane's results concerning the spreading of innovations in agriculture (See: D. CRANE,Invisible Colleges. Diffusion of Knowledge in Scientific Communities, Chicago, 1972), the distribution of the number of innovations advanced by various scientists is also governed by Lotka's law. The author of the lawA. J. Lotka who analyzed no only the chemical abstract journal butF. Auerbach's Geschichtstafeln der Physik for 1600\u20131900 and obtained an agreement between the corresponding distributions of scientific output (as judged by publications and discoveries) noted the same. A. I. MIKHAILOW et al.,op. cit., note 28.Scientific Communications and Informatics, Moscow, 1976, p. 184)."},{"key":"BF02016597_CR30","unstructured":"D. CRANE,ibid., Invisible Colleges. Diffusion of Knowledge in Scientific Communities, Chicago, 1972. A. I. MIKHAILOV et al.,op. cit. Scientific Communications and Informatics, Moscow, 1976, p. 213."},{"key":"BF02016597_CR31","unstructured":"The concept of hierarchic structure as a way of ensuring stability of a complex system under development with the presence of external limitations or the existence of contradictory requirements of centralized and decentralized control is quite widely spread in modern system analysis (see, for example, N. N. MOISEEV, The Mathematician Asks Questions ... Moscow, 1974.)."},{"key":"BF02016597_CR32","unstructured":"A. J. MIKHAILOV et al.,op. cit., note 28,Scientific Communications and Informatics, Moscow, 1976, p. 66."},{"key":"BF02016597_CR33","unstructured":"A. J. YABLONSKY,op. cit., note 9. Statistical models of scientific activity. In:Systems Research Yearbook \u2014 1975, Moscow, 1976."},{"key":"BF02016597_CR34","unstructured":"A. J. YABLONSKY,ibid. Statistical models of scientific activity. In:Systems Research Yearbook \u2014 1975, Moscow, 1976."},{"key":"BF02016597_CR35","volume-title":"An Introduction to Probability Theory and its Applications","author":"W. Feller","year":"1966","unstructured":"W. FELLER,An Introduction to Probability Theory and its Applications, Vol. 2. J. Wiley & Sons, New York\u2014London\u2014Sydney, 1966; B. V. GNEDENKO, A. N. KOLMOGOROV,Limiting Distributions for Sums of Independent Random Variables, Moscow-Leningrad, 1949."},{"key":"BF02016597_CR36","unstructured":"See: A. J. YABLONSKY,op. cit., note 9, Statistical models of scientific activity. In:Systems Research Yearbook \u2014 1975, Moscow, 1976. for the analysis of the scientological aspects of this connection."},{"key":"BF02016597_CR37","first-page":"4","volume":"124","author":"M. G. Kendall","year":"1964","unstructured":"M. G. KENDALL, Natural law in the social sciences,Journal of the Royal Statistical Society, 124 (1964) part 1, p. 4.","journal-title":"Journal of the Royal Statistical Society"},{"key":"BF02016597_CR38","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1086\/258792","volume":"71","author":"B. Mandelbrot","year":"1963","unstructured":"See. e.g., B. MANDELBROT,.","journal-title":"Journal of Political Economy"},{"key":"BF02016597_CR39","unstructured":"A. J. YABLONSKY. The development of science as an open system. In:Systems Research Yearbook \u2014 1978, Moscow, 1978."},{"key":"BF02016597_CR40","first-page":"4","volume":"24","author":"M. G. Kendall","year":"1964","unstructured":"M. G. KENDALL, ; G. K. ZIPF,Human Behaviour and the Principle of Least Effort, Cambridge, 1949.","journal-title":"Journal of the Royal Statistical Society"},{"key":"BF02016597_CR41","first-page":"109","volume":"1","author":"J. Vlach\u00fd","year":"1978","unstructured":"J. VLACH\u00dd,.","journal-title":"Scientometrics"},{"key":"BF02016597_CR42","unstructured":"Yu. K. ORLOV, On the statistical structure of communications optimal for human perception (on the formulation of the question),Nauchno-tekhnicheskaya informatsiya, Ser. 2, 1970, No. 8."},{"key":"BF02016597_CR43","unstructured":"Yu. A. SHREIDER, Complex systems and cosmological principles. In:Systems Research Yearbook \u2014 1975, Moscow, 1976."},{"key":"BF02016597_CR44","volume-title":"I am a Mathematician","author":"N. Wiener","year":"1956","unstructured":"N. WIENER,I am a Mathematician. Doubleday Book Co., Inc., Garden-City, New York, 1956; A. A. IGNAT'EV, A. I. YABLONSKY, Analytic structures of scientific communication. In:Systems Research Yearbook \u2014 1975, Moscow, 1976: A. J. YABLONSKY,."},{"key":"BF02016597_CR45","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-51866-9","volume-title":"The Theory of Branching Processes","author":"T. E. Harris","year":"1963","unstructured":"T. E. HARRIS,The Theory of Branching Processes, Springer-Verlag, Berlin\u2014Gottingen\u2014Heidelberg, 1963."},{"key":"BF02016597_CR46","volume-title":"Elements of the Theory of Markov Processes and their Applications","author":"A. T. Bharucha-Reid","year":"1960","unstructured":"A. T. BHARUCHA-REID,Elements of the Theory of Markov Processes and their Applications, McGraw-Hill Book Co., Inc., New York\u2014Toronto\u2014London, 1960."},{"key":"BF02016597_CR47","doi-asserted-by":"crossref","first-page":"425","DOI":"10.1093\/biomet\/42.3-4.425","volume":"42","author":"H. A. Simon","year":"1955","unstructured":"H. A. 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PRICE, A general theory of bibliometric and other cumulative advantage processes,Journal of the American Society for Informations Science, 27 (1976) No. 5, 292\u2013306] obtained the same distribution on the basis of somewhat different considerations (depending, as well asSimon's approach on finding a stable solution of the finite difference equation for the dynamics of the author) calls it \u201cthe cumulative advantage distribution\u201d.","journal-title":"Journal of the American Society for Informations Science"},{"key":"BF02016597_CR50","unstructured":"A. J. YABLONSKY,op. cit., note 9. Statistical models of scientific activity. In:Systems Research Yearbook \u2014 1975, Moscow, 1976."},{"issue":"No. 5","key":"BF02016597_CR51","doi-asserted-by":"crossref","first-page":"292","DOI":"10.1002\/asi.4630270505","volume":"27","author":"D. de Sollaprice","year":"1976","unstructured":"D. de SOLLAPRICE.","journal-title":"Journal of the American Society for Information Science"},{"key":"BF02016597_CR52","volume-title":"Science and Information Theory","author":"L. Brillouin","year":"1956","unstructured":"See, e.g., L. BRILLOUIN,Science and Information Theory, Academic Press, Inc., New York, 1956."},{"key":"BF02016597_CR53","unstructured":"See, e.g., A. Avramescu, Contribution to the foundation of bibliometric laws,Studii si cercetarii de documentare, 15 (1973) No. 1."},{"key":"BF02016597_CR54","unstructured":"W. Goffman, K. S. 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