1-[6-(9H-Carbazol-9-yl)hex­yl]-2-phenyl-1H-benzimidazole

The mol­ecule of the title compound, C31H29N3, contains a hexyl chain, a coordination unit (benzimidazole) and a functional group (carbazole). The benzimidazole ring is not coplanar with either the phenyl ring or the carbazole system, making dihedral angles of 43.26 (3) and 39.03 (2)°, respectively. The dihedral angle between the phenyl ring and the carbazole system is 24.42 (3)°. The hexyl Cβ atom (with respect to benzimidazole) deviates by 1.124 (2) Å from the benzimidazole plane, although the Cα atom lies in the plane. The hexyl Cβ atom (with respect to carbazole) deviates by 1.315 (1) Å from the carbazole plane, although the Cα atom lies in the plane. The crystal structure is stabilized by inter­molecular C—H⋯π inter­actions

Toeplitz Operators on the Weighted Pluriharmonic Bergman Space with Radial Symbols

We construct an operator R whose restriction onto weighted pluriharmonic Bergman Space bμ2(Bn) is an isometric isomorphism between bμ2(Bn) and l2#. Furthermore, using the operator R we prove that each Toeplitz operator Ta with radial symbols is unitary to the multication operator γa,μI. Meanwhile, the Wick function of a Toeplitz operator with radial symbol gives complete information about the operator, providing its spectral decomposition

6-Hy­droxy-4-(pyridin-3-yl)-5-(2-thienyl­carbon­yl)-6-trifluoro­meth­yl-3,4,5,6-tetra­hydro­pyrimidin-2(1H)-one

In the title compound, C15H12F3N3O3S, the pyrimidine ring adopts a half-chair conformation with the mean plane formed by the ring atoms excluding the C atom bonded to thio­phene-2-carbonyl group lying nearly perpendicular to the pyridine and thio­phene rings, making dihedral angles of 84.91 (4) and 87.40 (5)°, respectively. The dihedral angle between the pyridine and thio­phene rings is 54.44 (5)°. The crystal structure is stabilized by inter­molecular O—H⋯O and N—H⋯N hydrogen bonds and weak C—H⋯O inter­actions further consolidate the structure

1,3-Bis(4-meth­oxy­benz­yl)-6-methyl­pyrimidine-2,4(1H,3H)-dione

The title compound, C21H22N2O4, was prepared by reaction of 6-methyl­pyrimidine-2,4(1H,3H)-dione and 1-chloro­methyl-4-meth­oxy­benzene. In the title mol­ecule, the central pyrimidine ring forms dihedral angles of 62.16 (4) and 69.77 (3)° with the two benzene rings. In the crystal, weak inter­molecular C—H⋯O hydrogen bonds link the mol­ecules into chains