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

Zinc complex-based determination of rutin in dietary supplements

The aim of this study was to develop and validate a simple, rapid, sensitive and low-cost method for determination of rutin in tablets. The proposed spectrophotometric method is based on the formation of the Zn2+-rutin complex in methanol 70% (v/v) at pH 8.52, and detection at λmax= 410 nm. The concentration range over which the response was linear was 0.3-12.2 μg ml-1. The limit of detection (LOD) and the limit of quantification (LOQ) were 0.21 μg ml-1 and 0.63 μg ml-1, respectively. The proposed method was successfully applied to the determination of rutin in herbal dietary supplements. The reliability of the method was checked by comparison with results obtained by the established RP-HPLC/UV method. The proposed method fulfills all aimed requirements