Reinventing the Russian monarchy in the 1550s: Ivan the Terrible, the dynasty, and the church

Reinventing the Russian Monarchy in the 1550s: Ivan the Terrible, the Dynasty, and the Church by Sergei Bogatyrev This article focuses on the political and cultural priorities of the Daniilovichi dynasty in the middle of the sixteenth century. In the late 1540s to 1550s Ivan IV faced two interrelated challenges: strengthening the prestige of the dynasty and securing succession for his heir. Using the relations with the Orthodox East, the court functionaries, apparently actively supported by Ivan, launched an ambitious dynastic project which was focused on the antiquity of the Muscovite dynasty, the confirmation of Ivan's title of tsar by the patriarch, and the commemoration of members of the dynasty in ancient ccntres of Orthodoxy. The 'Greek project' of Ivan the Terrible was a major step in turning the Muscovite monarchy into a dynastic state

Integral equations PS-3 and moduli of pants

More than a hundred years ago H.Poincare and V.A.Steklov considered a problem for the Laplace equation with spectral parameter in the boundary conditions. Today similar problems for two adjacent domains with the spectral parameter in the conditions on the common boundary of the domains arises in a variety of situations: in justification and optimization of domain decomposition method, simple 2D models of oil extraction, (thermo)conductivity of composite materials. Singular 1D integral Poincare-Steklov equation with spectral parameter naturally emerges after reducing this 2D problem to the common boundary of the domains. We present a constructive representation for the eigenvalues and eigenfunctions of this integral equation in terms of moduli of explicitly constructed pants, one of the simplest Riemann surfaces with boundary. Essentially the solution of integral equation is reduced to the solution of three transcendent equations with three unknown numbers, moduli of pants. The discreet spectrum of the equation is related to certain surgery procedure ('grafting') invented by B.Maskit (1969), D.Hejhal (1975) and D.Sullivan- W.Thurston (1983).Comment: 27 pages, 13 figure

Pictorial Representation for Antisymmetric Eigenfunctions of PS-3 Integral Equations

Eigenvalue problem for Poincare-Steklov-3 integral equation is reduced to the solution of three transcendential equations for three unknown numbers, moduli of pants. The complete list of antisymmetric eigenfunctions of integral equation in terms of Kleinian membranes is given.Comment: 33 pages, 13 figures. This paper is an extended version of CV/061173

Novgorod

Novgorod’s crucial positioning between the Baltic and the north-eastern Rus principalities yielded a textual culture that was highly distinctive, especially in its use of birchbark documents, yet widely connected. This chapter examines cultural exchange and creative writing in Novgorod in the fourteenth and early fifteenth centuries by focusing on the work of various scriptoria which produced liturgical books, local chronicles and devotional literature. The paper also discusses the interaction of various literary traditions in the birchbark documents