Crystal structure and Hirshfeld surface analysis of 5, 7-diphenyl-1, 2, 3, 5, 6, 7-hexahydroimidazo [1, 2-a] pyridine-6, 6, 8-tricarbonitrile methanol monosolvate

TARAMAWOSWOS:000661118800004TARAMAPUBMEDTARAMASCOPUSIn the title compound, C22H17N5·CH4O, the imidazolidine ring of the 1,2,3,5,6,7-hexahydroimidazo[1,2-a]pyridine ring system is a twisted envelope, while the 1,2,3,4-tetrahydropyridine ring adopts a twisted boat conformation. In the crystal, pairs of molecules are linked by O—H⋯N and N—H⋯O hydrogen bonds via two methanol molecules, forming a centrosymmetric R44(16) ring motif. These motifs are connected to each other by C—H⋯N hydrogen bonds and form columns along the a axis. The columns form a stable molecular packing, being connected to each other by van der Waals interactions. A Hirshfeld surface analysis indicates that the most significant contributions to the crystal packing are from H⋯H (43.8%), N⋯H/H⋯N (31.7%) and C⋯H/H⋯C (18.4%) contacts

Qualitative analysis of eigenvalues and eigenfunctions of one boundary value-transmission problem

WOS: 000374243400001The aim of this study is to investigate various qualitative properties of eigenvalues and corresponding eigenfunctions of one Sturm-Liouville problem with an interior singular point. We introduce a new Hilbert space and integral operator in it such a way that the problem under consideration can be interpreted as a spectral problem of this operator. By using our own approaches we investigate such properties as uniform convergence of the eigenfunction expansions, the Parseval equality, the Rayleigh-Ritz formula, the minimax principle, and the monotonicity of eigenvalues for the considered boundary value-transmission problem (BVTP)