On the Conditions for the Solvability of Boundary-Value Problems for Higher-Order Equations with Discontinuous Coefficients

Mathematical Notes - A Dirichlet-type problem for an equation of high even order with discontinuous coefficients is studied. A criterion for the uniqueness of the solution is given. The solution in...     

Spectral problem for an equation of high even order

We study an eigenvalue problem for an equation of even order in a rectangular domain. We investigate distribution and asymptotics of eigenvalues and explore their difference under variation of the potential q(x, y).     

Construction of new heteroacenes based on benzo[b]thieno[2,3-d]thiophene / quinoline or 1,8-naphthyridine systems using the Friedländer reaction

Two new classes of heteroacenes, namely benzo[4′,5′]thieno[2′,3′:4,5]thieno[3,2-b]quinolines and benzo[4′,5′]thieno[2′,3′:4,5]thieno[3,2-b][1,8]naphthyridines, have been formed using the Friedländer reaction to annulate the benzo[b]thieno[2,3-d]thiophene scaffold to quinoline or 1,8-naphthyridine fragments. In accordance with this synthetic strategy, benzo[b]thieno[2,3-d]thiophen-3(2H)-ones were treated with 2-aminobenzaldehydes or 2-aminonicotinaldehyde in the presence of pyrrolidine in glacial acetic acid at reflux to give the desired quinoline- or 1,8-naphthyridine-fused compounds, respectively. The optical and electrochemical properties of selected heteroacenes were determined.