INTERPOLATING BLASCHKE PRODUCTS AND ANGULAR DERIVATIVES

We show that to each inner function, there corresponds at least one interpolating Blaschke product whose angular derivatives have precisely the same behavior as the given inner function. We characterize the Blaschke products invertible in the closed algebra H-infinity[(b) over bar : b has finite angular derivative everywhere. We study the most well-known example of a Blaschke product with infinite angular derivative everywhere and show that it is an interpolating Blaschke product. We conclude the paper with a method for constructing thin Blaschke products with infinite angular derivative everywhere.

5a-Butyl-1,3,8,10-tetra-chloro-7,13-bis-(4-nitro-benzo-yl)-5a,6a,12a,12b-tetra-hydro-7H,13H-thieno[2,3-b:4,5-b']bis-(1,4-benzoxazine)

The title compound, C(34)H(24)Cl(4)N(4)O(8)S, is a linear penta-cyclic system formed of two substituted benzoxazinyl groups fused to 2-n-butyl-tetra-hydro-thio-phene. The oxazine ring, which is fused to the n-butyl-substituted side of the thio-phene ring, is in a boat conformation. The other fused oxazine ring and the tetra-hydro-thiene ring are each in an envelope conformation. The bridgehead C atom alpha to both the S and N atoms forms the flap of each envelope. This results in a twist of the penta-cyclic system such that the dihedral angle between the terminal dichloro-benzene rings is 82.92 (8)°. In the crystal, inversion-related mol-ecules form a weakly hydrogen-bonded dimer, with two C-H⋯O inter-actions between an H atom on the oxazine ring and an amide O atom. Additionally, C-H⋯O inter-actions occur between an H atom on a screw-related nitro-benzene ring and an O atom on the nitro-benzene ring of one mol-ecule. One of the Cl atoms and the butyl group are disordered over two sets of sites with occupancy ratios of 0.94 (2):0.06 (2) and 0.624 (4):0.376 (4), respectively.

Interpolating Blaschke Products and Angular Derivatives

We show that to each inner function, there corresponds at least one interpolating Blaschke product whose angular derivatives have precisely the same behavior as the given inner function. We characterize the Blaschke products invertible in the closed algebra generated by the algebra of bounded analytic functions and the conjugates of Blaschke products with angular derivative finite everywhere. We study the most well-known example of a Blaschke product with infinite angular derivative everywhere and show that it is an interpolating Blaschke product. We conclude the paper with a method for constructing thin Blaschke products with infinite angular derivative everywhere.

Spirocyclic Acylphloroglucinol Derivatives from Hypericum pyramidatum

Five spirocyclic acylphloroglucinol derivatives (1-5) have been isolated from a hexanes extract of the leaves of Hypericum pyramidatum. Pyramidatones A-D (1-3, 5) are new, and chipericumin C (4) has been previously reported. The acylphloroglucinols were characterized based on spectroscopic (NMR, IR, UV-VIS) and mass spectrometric data.