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Of all publications in the section: 2
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Article
Schofield N., Claassen C., Ozdemir U. et al. International Journal of Mathematics and Mathematical Sciences. 2010. P. 1-30.

Previous empirical research has developed stochastic electoral models for Israel, Turkey, and other polities. The work suggests that convergence to an electoral center (often predicted by electoral models) is a nongeneric phenomenon. In an attempt to explain nonconvergence, a formal model based on intrinsic valence is presented. This theory showed that there are necessary and sufficient conditions for convergence. The necessary condition is that a convergence coefficient c is bounded above by the dimension w of the policy space, while a sufficient condition is that the coefficient is bounded above by 1. This coefficient is defined in terms of the difference in exogenous valences, the “spatial coefficient”, and the electoral variance. The theoretical model is then applied to empirical analyses of elections in the United States and Britain. These empirical models include sociodemographic valence and electoral perceptions of character trait. It is shown that the model implies convergence to positions close to the electoral origin. To explain party divergence, the model is then extended to incorporate activist valences. This extension gives a first-order balance condition that allows the party to calculate the optimal marginal condition to maximize vote share. We argue that the equilibrium positions of presidential candidates in US elections and by party leaders in British elections are principally due to the influence of activists, rather than the centripetal effect of the electorate.

Added: Nov 14, 2012
Article
Natalia A. Shmatko, Katchanov Y. L. International Journal of Mathematics and Mathematical Sciences. 2014. Vol. 2014. No. ID 785058.

The paper intends to contribute to a better understanding of the phenomenon of scientific capital. Scientific capital is a well-known concept for measuring and assessing the accumulated recognition and the specific scientific power. The concept of scientific capital developed by Pierre Bourdieu is used in international social science research to explain a set of scholarly properties and practices. Mathematical modeling is applied as a lens through which to address the scientific capital. The principal contribution of this paper is an axiomatic characterization of scientific capital in terms of natural axioms. The application of the axiomatic method to scientific capital reveals novel insights into problem still not covered by mathematical modeling. Proposed model embraces the interrelations between separate sociological variables, providing a unified sociological view of science. Suggested micro variational principle is based upon postulate, which affirms that (under suitable conditions) the observed state of the agent in a scientific field maximizes scientific capital. Its value can be roughly imagined as a volume of social differences. According the considered macro variational principle, the actual state of a scientific field makes so-called energy functional (which is associated with the distribution of scientific capital) minimal.

Added: Jun 13, 2013