Scientometric study of biochemical literature of Nigeria, 1970–1984: Application of Lotka's law and the 80/20-Rule

A bibliography of biochemical literature of Nigeria for the period, 1970–1984 containing a total of 500 items, was analysed to test the applicability of Lotka's law and 80/20-rule to the author productivity distribution patterns. Four different files were created out of the data on author productivity: one for the publication of all the authors, second for the publications by first authors only, third for single authors and fourth for the contributions of only coauthors. Lotka's law could apply in all the four cases with different values of . The Kolmogorov-Smirnov test was applied to test the applicability of Lotka's law at 0.01 level of significance. Egghe's theory and formula were used to test 80/20-rule and it was found that the rule did not apply to any of the four data sets.     

Author productivity patterns in theoretical population genetics (1900–1980)

Focuses on the validity of Lotka's law and the negative binomial distribution model to author productivity data in different time periods in theoretical population genetics speciality. Finds out if there is any relation between applicability of a statistical distribution and the development of speciality. Looks at the linkages between inequality/concentration measures and the development of speciality. Explores the relevance and applicability of the two generalisations, namely Price Square, Root Law and 80/20 Rule to the author productivity data and their relation with development of theoretical population genetics. Finally, a study of the growth of practitioners in the field with different productivity levels is conducted, and the emergence of core authors in the speciality is explored.     

Lotka's law and productivity patterns of entomological research in Nigeria for the period, 1900–1973

A bibliography of entomological research in Nigeria, 1900–1973 totally 1720 publications was analysed to study the author productivity patterns and to test the applicability of Lotka's law for the obtained distributions. Four different files were generated, one for the publications of all the authors, second for the publications by first authors, third for single authors and fourth for coauthors. Lotka's law in its original form as inverse square law does not apply to any of the four data sets. However, it does apply in its generalised form with the calculated values of characteristic exponent . The values of were found to be 1.9, 1.8, 2.2 and 2.4 for the four different data sets. K-S statistical test was aplied to test the applicability of generalised form of Lotka's law. The maximum difference in the observed and estimated values of the proportions of authors was found to be highly insignificant at 0.01 level of significance in each of the four cases.     

Bibliometric study of bioinformatics literature

Bioinformatics is a multidisciplinary and comparatively new area of science that has made a significant impact within a short period. A systematic analysis of the rise in bioinformatics literature is, however, not available. This study analyses the growth of the scientific literature in this area as available from NCBI PubMed using standard bibliometric techniques. Bradford's law of scattering was used to identify core journals and Lotka's law employed to analyze author's productivity pattern. Study also explored publication type, language and the country of publication. Twenty core journals were identified and the primary mode of dissemination of information was through journal articles. Authors with single publication were more predominant (73.58%) contrary to that predicted by Lotka's law. The study provides useful information to scientists wishing to undertake work in this area.     

A bibliometric analysis of productivity patterns of biomedical authors of Nigeria during 1967-2002

Summary Bibliographic data on biomedical literature of Nigeria drawn from articles listed in Medline covering the period 1967-2002, and numbering 6820 were analysed to study the pattern of productivity of various author categories using Lotka's law. The total of 2184 authors who wrote the papers was divided into four different files, namely all authors, first authors, non-collaborative authors and co-authors. We hypothesized that the productivity patterns of each of the categories of authors differed from Lotka's inverse power law. The results showed that only the co-author category differed from the inverse power version of the law, while the other categories did not, although they yielded various exponents.     

An exact calculation of Price's law for the law of Lotka

Price's law asserts — in its simpliest version — that authors produce half of the papers made by the total ofN authors. More generally: the topN (0<<1) authors produce a fraction (0<<1) of the papers made by the total ofN authors and the Price's law says that . In this paper — using Lotka's law — we prove a mathematical relationship of in function of and the parameter (the mean number of papers per author) and investigate when . More-over our reasoning uses the theory of the 80/20 rule as developed in: L. EGGHE, On the 80/20-rule,Scientometrics, 10 (1986) 55–68, thereby also showing the relation betwwen the 80/20-rules (being an arithmetical form of measuring elitarism) and Price's law (being a geometric form of measuring elitarism).     

Power laws of research output. Evidence for journals of economics

In this paper we examine the validity of Lotka's law and Zipf'slaw for research output in 15 top journals of economics in the period 1977to 1997. Our data for individual authors satisfy a general form of Lotka'slaw. We find increasing competition over time among economists on the individuallevel. However, publications in top journals are concentrated heavily whenthe institutional level is under consideration. Research output of institutionscan be fit adequately by Zipf's law. This revised version was published online in June 2006 with corrections to the Cover Date.     

Stable non-Gaussian distributions in scientometrics

A mathematical treatment is given for the family of scientometric laws (usually referred to as the Zipf-Pareto law) that have been described byPrice and do not conform with the usual Gaussian view of empirical distributions. An analysis of the Zipf-Pareto law in relationship with stable non Gaussian distributions. An analysis of the Zipf-Pareto law in relationship with stable non Gaussian distributions reveals, in particular, that the truncated Cauchy distribution asymptotically coincides with Lotka's law, the most well-known frequency form of the Zipf-Pareto law. The mathematical theory of stable non Gaussian distributions, as applied to the analysis of the Zipf-Pareto law, leads to several conclusions on the mechanism of their genesis, the specific methods of processing empirical data, etc. The use of non-Gaussian processes in scientometric models suggests that this approach may result in a general mathematical theory describing the distribution of science related variables.     

A Bibliometric Study of Semiconductor Literature, 1978–1997

Semiconductor is the key element for information industry. The present study investigated the growth of semiconductor literature based on the database of INSPEC. Well-established bibliometric techniques, such as Bradford-Zipf's plot and Lotka's law have been employed to further explore the characteristics of semiconductor literature. Quantitative results on the literature growth, form of publication, research treatment, publishing country and language, author productivity and affiliate are reported. Moreover, from the Bradford-Zipf's plot, 25 core journals in semiconductor were identified and analyzed.     

A comparision of productivity of male and female scientists of CSIR

The paper examines the scientific productivity of male and female scientistts working in the Council of Scientific and Industrial Research (CSIR), India at the overall agency level and at the group of laboratories level, characterized by three broad subjects of physical, biological, and engineering sciences. The productivity of scientists is evaluated on the basis of three parameters: the extent of scientists not publishing any paper, the average number of papers per scientist, and using Lotka's approach. In order to find out whether there is any significant difference between male and female productivity distributions, a Chi-square test is used. Studies the applicability of Lotka's inverse power law and some other statistical models in the distribution of scientific productivity of male and female scientists. Concludes that no significant difference exists between productivity distributions of male and female scientists.     

Productivity differences fields of learning,and Lotka's law

The paper examines whether productivity differences among individual researchers are larger in some fields of learning than in others. Productivity patterns in the natural sciences, the medical sciences, the social sciences, and the humanities are compared by the use of unweighted and weighted publication counts. Irrespective of whether total number of publications or a refined indicator taking account of type of publication and multiple authorship are used, there are no essential differences in publishing inequality between the various fields. About 20% of the tenured faculty at Norwegian universities produce 50% of the total output, and the most prolific half of the researchers account for almost 85% of the output. The results are discussed in relation to Lotka's law.     

Collaboration and author productivity: A study with a new variable in Lotka's law

The paper explores the possibility of using a new variable represented by the number of collaborators per author as a substitute for the number of papers in Lotka's distribution to predict the productivity strata. On the basis of a case study in theoretical population genetics it is concluded that the number of collaborators per author has not proved to be a good substitute in the Lotka's distribution, which is in contrast to Qin's results.     

On the modelling of complex anisotropic frictional contact laws

In this paper, the formulation of complex anisotropic frictional models with orthotropic friction condition and non-associated sliding rule is discussed. The friction law is described by a superellipse, which allow to consider a wide range of convex friction condition by simply varying the roundness factor affecting the shape of the limit surface. The sliding potential is also a superellipse but with a different semi-axis ratio, which lead to a non-associated sliding rule. For bodies in contact, the Signorini conditions can be formulated in terms of velocities and combined with the sliding rule to give the frictional contact law describing interfacial interactions. Its is shown that the frictional contact law as well as its inverse can be derived from the same scalar valued function called bi-potential. Due to the non-associated nature of the law, this relation is implicit. The advantage of the present formulation lies in the existence of stationary points of a functional, called bi-functional, that depends on both the displacements and the stresses.     

An incremental formulation for the prediction of two-dimensional fatigue crack growth with curved paths

This paper presents a new incremental formulation for predicting the curved growth paths of two-dimensional fatigue cracks. The displacement and traction boundary integral equations (BIEs) are employed to calculate responses of a linear elastic cracked body. The Paris law and the principle of local symmetry are adopted for defining the growth rate and direction of a fatigue crack, respectively. The three governing equations, i.e. the BIEs, the Paris law and the local symmetry condition, are non-linear with respect to the crack growth path and unknowns on the boundary. Iterative forms of three governing equations are derived to solve problems of the fatigue crack growth by the Newton–Raphson method. The incremental crack path is modelled as a parabola defined by the crack-tip position, and the trapezoidal rule is employed to integrate the Paris law. The validity of the proposed method is demonstrated by two numerical examples of plates with an edge crack. Copyright © 2007 John Wiley & Sons, Ltd.     

Three‐dimensional finite element computations for frictional contact problems with non‐associated sliding rule

This paper presents an algorithm for solving anisotropic frictional contact problems where the sliding rule is non‐associated.The algorithm is based on a variational formulation of the complex interface model that combine the classical unilateral contact law and an anisotropic friction model with a non‐associated slip rule. Both the friction condition and the sliding potential are elliptical and have the same principal axes but with different semi‐axes ratio. The frictional contact law and its inverse are derived from a single non‐differentiable scalar‐valued function, called a bi‐potential. The convexity properties of the bi‐potential permit to associate stationary principles with initial/boundary value problems. With the present formulation, the time‐integration of the frictional contact law takes the form of a projection onto a convex set and only one predictor–corrector step addresses all cases (sticking, sliding, no‐contact). A solution algorithm is presented and tested on a simple example that shows the strong influence of the slip rule on the frictional behaviour. Copyright 2004 John Wiley & Sons, Ltd.     

A criterion to avoid starvation zones for convection–diffusion–reaction problem inside a porous biological pellet under oscillatory flow

The behavior of nutrient transport inside a porous spherical pellet in an oscillatory Stokes flow is investigated analytically. Unsteady Stokes equations are used for the flow outside the porous pellet and Darcy’s law is used inside the pellet. A solenoidal decomposition method is employed for the derivation of the flow field outside the pellet. The corresponding convection–diffusion–reaction problem is formulated and solved analytically for a zeroth-order nutrient consumption rate. From the obtained solution a general condition between the Peclet number and Thiele modulus is derived to obviate the nutrient reduction everywhere in the pellet. For the correct modeling of the processes involving flow through biological catalysts this becomes a necessary and sufficient condition.     

Scientific production: A statistical analysis of authors in physics, 1800-1900

We show that scientific production can be described by two variables: rate of production (rateof publications) and career duration. For 19^th century physicists, we show that the time pattern ofproduction is random and Poisson distributed, contrary to the theory of cumulative advantage. Weshow that the exponential distribution provides excellent goodness-of-fit to rate of production andcareer duration. The good fits to these distributions can be explained naturally from the statisticsof exceedances. Thus, more powerful statistical tests and a better theoretical foundation isobtained for rate of production and career duration than has been the case for Lotka's Law.     

Lotka's law reconsidered: The evolution of publication and citation distributions in scientific fields

This paper reports early steps in research that seeks to clarify how publications of scientists interact dynamically with citations and reputation in shaping the evolution of scientific fields. We assume that Lotka's modified law holds for scientific fields. A primary approach to model publication productivity was published by Yablonsky. In contrast to Yablonsky's unfinished mathematical approach, our simulation approach is not predominantly driven by insight into the formal generation mechanisms of certain processes but more theory driven. It considers the evolution of publication and citation distributions over the histories of scientific fields using both simulated and real historical data.     

Scientific production: A statistical analysis of authors in mathematical logic

We show that scientific production can be described by two variables: rate of production (rate of publications) and career duration. For mathematical logicians, we show that the time pattern of production is random and Poisson distributed, contrary to the theory of cumulative advantage. We show that the exponential distribution provides excellent goodness-of-fit to rate of production and a reasonable fit to career duration. The good fits to these distributions can be explained naturally from the statistics of exceedances. Thus, more powerful statistical tests and a better theoretical foundation is obtained for rate of production and career duration than has been the case for Lotka's Law.     

Correlations among growth law of small cracks,low-cycle fatigue law and applicability of miner's rule

The initiation and propagation process of a small crack in low-cycle fatigue of a medium carbon steel is observed in detail by the plastic replica method. It is found that the Manson-Coffin relation is virtually the same as the crack growth law of a small crack; more than 90% (almost 100%) of the fatigue life of plain specimens is occupied by the crack propagation process. From this viewpoint, the ambiguity in the definition of the initiation of “an engineering-size crack” can be removed.The effects of prior fatigue history on the growth rate of a small crack are investigated systematically using special specimens containing an artificial small hole with diameters of 40, 100 and 200 μ m.Prior fatigue history which may be accumulated at the region where a crack will later propagate hardly influences the crack growth rate, i.e. prior fatigue history itself should not be regarded as fatigue damage. This is an essential condition for Miner's rule to apply.