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.
Several approaches to the concept of fatherhood present in Western sociological tradition are analyzed and compared: biological determinism, social constructivism and biosocial theory. The problematics of fatherhood and men’s parental practices is marginalized in modern Russian social research devoted to family and this fact makes the traditional inequality in family relations, when the father’s role is considered secondary compared to that of mother, even stronger. However, in Western critical men’s studies several stages can be outlined: the development of “sex roles” paradigm (biological determinism), the emergence of the hegemonic masculinity concept, inter-disciplinary stage (biosocial theory). According to the approach of biological determinism, the role of a father is that of the patriarch, he continues the family line and serves as a model for his ascendants. Social constructivism looks into man’s functions in the family from the point of view of masculine pressure and establishing hegemony over a woman and children. Biosocial theory aims to unite the biological determinacy of fatherhood with social, cultural and personal context. It is shown that these approaches are directly connected with the level of the society development, marriage and family perceptions, the level of egality of gender order.