THE DEPENDENCE OF LOTKA'S LAW ON THE SELECTION OF TIME PERIODS IN THE DEVELOPMENT OF SCIENTIFIC AREAS AND AUTHORS

The Lotka distribution of the productivity of authors is highly dependent on the selection of the period of investigation. If many authors are covered only fractionally, the slope of the distribution is steeper than the slope of the distribution covering the complete publication output of a group of authors. We show this in a special branch of mathematics, namely mathematical logic from 1874 to 1990. If one compares authors with the same number of years spent in scientific activity, the characteristic form of the Lotka distribution completely vanishes. The time effect can be intensified if a scientific area features major expansion and the portion of new authors with few contributions is high; this is demonstrated in two special areas of logic. One may try to explain differences of the Lotka distributions of the phases of a scientific area by means of a simple learning model, taking into consideration that the learning curves of scientists in the birth, in the ‘pioneering’, and in the fulfilment stages of an area must be different.