Edgeworth expansions in operator form

An operator form of asymptotic expansions for Markov chains is established. Coefficients are given explicitly. Such expansions require a certain modification of the classical spectral method. They prove to be extremely useful within the context of large deviations.Comment: 12 page

A general correlation inequality and the Almost Sure Local Limit Theorem for random sequences in the domain of attraction of a stable law

In the present paper we obtain a new correlation inequality and use it for the purpose of extending the theory of the Almost Sure Local Limit Theorem to the case of lattice random sequences in the domain of attraction of a stable law. In particular, we prove ASLLT in the case of the normal domain of attraction of $\alpha$--stable law, $\alpha\in(1,2)$

Strongly sequentially separable function spaces, via selection principles

A separable space is strongly sequentially separable if, for each countable dense set, every point in the space is a limit of a sequence from the dense set. We consider this and related properties, for the spaces of continous and Borel real-valued functions on Tychonoff spaces, with the topology of pointwise convergence. Our results solve a problem stated by Gartside, Lo, and Marsh.Comment: 9 page

The System of Management of Regional Development in Poland: New Legal and Administrative Proposals

This paper describes the new proposal being advanced regarding the legal and administrative aspects of regional development in Poland, presenting a smallscale survey of part of the legal system as it pertains to regional development. It outlines the new legal proposal for implementation with regard to the preparation of solutions necessary for the next programming period (2014–2020). The results of the analysis suggest that the solutions proposed may be effective and may contribute to improving the system

Jak zmierzyć demokrację? Skale pomiaru demokracji politycznej stosowane w politologii porównawczej

The author reviews and characterizes the most important scales for measuring the democracy of political systems, applied in Western, mainly Anglo-Saxon, comparative political science. He refers to his article published in a back issue of Przegl¹d Polityczny, where the fundamental theoretical and methodological issues of democracy measuring were presented, and tries to indicate how these issues are dealt with by various researchers whose scales and data bases are most common and most frequently referred to in research into political comparative studies. The paper describes S. Huntington’s analyses, the Freedom House scale, the IDEA assessment of the quality of democracy, the EIU democracy index, Bollen’s scale, the Political Regimes Project, the Polity Project, T. Vanhanen’s democracy index and the scale of polyarchy by Coppedge and Reinicke. As the author analyzes one scale and database after another, he tries to identify their strengths and weaknesses, determine the most characteristic properties of each proposal, and assess their applicability in comparative analyses, pointing to their potential benefits and the threats of using them. In conclusion, he recommends caution in the selection of a scale to become a foundation for potential analyses, while he acknowledges that this theoretical and methodological tool is highly useful