On Modular Forms Arising from a Differential Equation of Hypergeometric Type

Modular and quasimodular solutions of a specific second order differential equation in the upper-half plane, which originates from a study of supersingular j-invariants in the first author's work with Don Zagier, are given explicitly. Positivity of Fourier coefficients of some of the solutions as well as a characterization of the differential equation are also discussed.     

Stereoselective synthesis of (25R)-25,26-dihydroxy-23-oxovitamin D3 and its enzymatic conversion to (25R)-1α,25,26-trihydroxy-23-oxovitamin D3, a putative metabolite of vitamin D3

(25$\text{R}$)-25,26-Dihydroxy-23-oxovitamin D₃ was synthesized efficiently and stereoselectively, and it was converted enzymatically to (25$\text{R}$)-1α,25,26-trihydroxy-23-oxovitamin D₃, a putative metabolite of 1α,25-dihydroxyvitamin D₃. The spectral and chemical properties of (25$\text{R}$)-25,26-dihydroxy-23-oxovitamin D₃ and its 1α,hydroxylated derivative disagree with those reported for the isolated metabolite.     

Rapid racemization of chiral non-racemic sec-alcohols catalyzed by (η-C5(CH3)5)Ru complexes bearing tertiary phosphine-primary amine chelate ligands

A ternary catalyst system of Cp*RuCl(cod)-2-diphenylphosphinoethylamine-KOt-Bu (Cp*=η⁵-C₅(CH₃)₅, cod=1,5-cyclooctadiene) causes rapid racemization of chiral non-racemic sec-alcohols, which results from the reversible hydrogen transfer between sec-alcohols and ketones. Both tertiary phosphine and primary amine functionalities in the ligand are responsible for the high rate.     

A new synthesis of indoloquinolizines by Pictet-Spengler reaction of tryptamine type 1,2-dihydropyridines utilizing sec-nitrodienamine

The Pictet-Spengler reaction of tryptamine type 1,2-dihydropyridine 5c derived from the cycloaddition of the sec-nitrodienamine 3c with acetaldehyde afforded the indoloquinolizine derivatives 6 and 7.     

Lactone and cyclic ether analogues of platelet-activating factor. Synthesis and biological activities

Six-membered lactone and tetrahydropyran analogues of platelet-activating factor (PAF), 4-11, and related antagonistic derivatives 41-46 were synthesized. None of the delta-lactones 4-7 showed PAF-like activities, while the corresponding cyclic ethers 8, 9 and 11 were slightly active. Some of the cyclic antagonists showed more potent inhibitory activities than the open chain antagonist CV-3988 against platelet aggregation (rabbit platelet-rich plasma, IC50) and hypotension (rat, ID50) induced by C16-PAF: e.g. dl-3-[6-[O-(trans-3-heptadecylcarbamoyloxytetrahydropyran-2- yl)methyl]phosphonoxy]hexylthiazolium (inner salt) (41d) (IC50 5.5 x 10(-7) M, ID50 0.046 mg/kg, i.v.); dl-3-[5-[O-(cis-3-heptadecylcarbamoylthiotetrahydropyran-2- yl)methyl]phosphonoxy]pentylthiazolium (inner salt) (43c) (IC50 5.7 x 10(-7) M, ID50 0.076 mg/kg, i.v.).