Geometry of Quantum Principal Bundles I

A theory of principal bundles possessing quantum structure groups and classical base manifolds is presented. Structural analysis of such quantum principal bundles is performed. A differential calculus is constructed, combining differential forms on the base manifold with an appropriate differential calculus on the structure quantum group. Relations between the calculus on the group and the calculus on the bundle are investigated. A concept of (pseudo)tensoriality is formulated. The formalism of connections is developed. In particular, operators of horizontal projection, covariant derivative and curvature are constructed and analyzed. Generalizations of the first structure equation and of the Bianchi identity are found. Illustrative examples are presented.Comment: 64 pages, AMS-LaTeX, To appear in CM

Improvement of supercritical CO2 and n-hexane extraction of wild growing pomegranate seed oil by microwave pretreatment

Microwave radiation was suggested as a pretreatment technique to increase the yield of pomegranate seed oil. Seeds were pretreated at 100, 250 and 600 W during 2 and 6 min and then extracted by supercritical carbon dioxide (scCO(2)) in high pressure unit as well as by n-hexane in Soxhlet apparatus. Even at the lowest microwave pretreatment parameters applied (100 W for 2 min) increased the yield of seed oil obtained by both extraction techniques compared with untreated seeds (from 27.7 to 34.0% and from 21.6 to 25.5% for Soxhlet and scCO(2) extractions, respectively). Maximal oil yield in Soxhlet extraction (36.3%) was obtained with microwave radiation of 600 W for 6 min while for scCO(2) extraction maximal oil yield (27.2%) was with 250 W for 6 min microwave radiation pretreatment. The qualitative and quantitative composition of fatty acids of the obtained oils was determined by gas chromatography/flame ionization detection and gas chromatography/mass spectrometry. Punicic acid was the most abundant fatty acid in pomegranate seed oil ( gt 60%). Microwave pretreatment of seeds showed negligible influence on profile and the amount of fatty acids in obtained extracts, compared with its significant influence on extraction yield. Our results recognize microwave pretreatment as a promising technique for intensification of oil extraction from pomegranate seeds