Tetrahydropyran-2,4-diones in the Synthesis of Fused N,O-Heterocycles

Condensation of 6-methyl(or phenyl)-tetrahydropyran-2,4-diones with 2-aminonaphthalene or 6-aminoquinoline and aromatic aldehydes in an aliphatic alcohol gave 5-aryl-2,2-dimethyl(or 2-phenyl)-1,2,5,6-tetrahydro-4H-benzo[f]pyrano[3,4-c]quinolin-4-ones and 5-aryl-2-methyl-1,2,5,6-tetrahydro-4H-pyrano[4,3-a][4,7]phenanthrolin-4-ones which are new N,O-heterocyclic systems containing fused aza- and diazaphenanthrene moieties and a 2-pyranone ring.     

Synthesis of 3- and 5-Alkyl-6-alkyl(aryl)tetrahydropyran-2,4-diones by the Condensation of β-Oxo Acid Esters with Aldehydes and Ketones

A method is proposed for obtaining 3- and 5-alkyl-6-alkyl(aryl)tetrahydropyran-2,4-diones based on the condensation of the dianion of alkyl(dialkyl)acetoacetic ester with aldehydes and ketones.     

Constants of Strong Uniqueness of Minimal Projections onto Hyperplanes in the Space ℓ∞ n (n≥3)

In this paper, we obtain the maximum values of the constants of strong uniqueness of minimal projections with nonunit norm on hyperplanes in the space #x2113; ⁿ (n3)