We calculate characteristic polynomials of operators explicitly represented as polynomials of rank $1$ operators. Applications of the results obtained include a generalization of the Forman--Kenyon's formula for a determinant of the graph Laplacian and also provide its level $2$ analog involving summation over triangulated nodal surfaces with boundary.
In his article Vladimir Kantor explores the destiny of Russia intelligentsia within the context of cultural crisis that took place at the turn of XIX and XX centuries, analyzing the Vekhovs, a group of leading intellectuals who ran a collection of essays, titled "Vekhi", studying their relationship towards that Russian cultural phenomenon. To author, the intelligentsia is considered as a critical factor in the development of Russian history. Within a context of the struggle around the "Vekhi", by referring to famous philosophical and literature books, published in 1909, the author focuses on relationships between intelligentsia and ordinary people, their attractive and repulsive interaction, which represents the key theme of the Russian destiny. Any historical movement occurs through tragedy; heroes who move the history have to sacrifice themselves to provide that movement. Confirmation to that idea would be rejection and exclusion of the Russian intelligentsia from the country's mentality throughout a number of generations which ultimately led to its tragic being.
We address the external effects on public sector efficiency measures acquired using Data Envelopment Analysis. We use the health care system in Russian regions in 2011 to evaluate modern approaches to accounting for external effects. We propose a promising method of correcting DEA efficiency measures. Despite the multiple advantages DEA offers, the usage of this approach carries with it a number of methodological difficulties. Accounting for multiple factors of efficiency calls for more complex methods, among which the most promising are DMU clustering and calculating local production possibility frontiers. Using regression models for estimate correction requires further study due to possible systematic errors during estimation. A mixture of data correction and DMU clustering together with multi-stage DEA seems most promising at the moment. Analyzing several stages of transforming society’s resources into social welfare will allow for picking out the weak points in a state agency’s work.