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A New Conceptual Mathematical Model of the Scientific Capital and Its Empirical Test
The paper puts forth an axiomatic description of the complexity of an object of sociological investigation. The proposed axioms allow us to determine complexity within the framework of mathematical sociology such as the variational principle, which is formed relative to the state of the object of sociological investigation. On the basis of this principle we can conclude the equation of state, which coincides with the stationary forward Kolmogorov equation. Based on the results of an empirical study of Russian doctorate holders, a scientific capital value was determined for each respondent by calculating an empirical distribution function for each respondent’s active properties. The goal of this study is to develop a phenomenological theory of Scientific Capital in the form of a hierarchy of variational principles. On the micro level, the principle of the maximum enables us to examine the numerous meanings of Scientific Capital based on the measurement of the actual (i.e., factually realized) distribution of active properties of a scientific field’s agent among the multitude of possible distributions. On the macro level, the principle of the minimum energy functional describes the distribution of Scientific Capital among the agents of a scientific field.