Fibrations of Simplicial Sets

There are infinitely many variants of the notion of Kan fibration that, together with suitable choices of cofibrations and the usual notion of weak equivalence of simplicial sets, satisfy Quillen’s axioms for a homotopy model category. The combinatorics underlying these fibrations is purely finitary and seems interesting both for its own sake and for its interaction with homotopy types. To show that these notions of fibration are indeed distinct, one needs to understand how iterates of Kan’s Ex functor act on graphs and on nerves of small categories.     

Effects of fluorescent light and vacuum packaging on the rate of decomposition of pigments in paprika (Capsicum annuum) powder determined by reversed-phase high-performance liquid chromatography.

The effect of storage time, the presence of light and oxygen on the decomposition rate of carotenoid pigments in paprika (Capsicum annuum) powders was determined by reversed-phase high-performance liquid chromatography (RP-HPLC). The similarities and dissimilarities of pigment composition of samples under various storage conditions was elucidated by principal component analysis (PCA) and stepwise regression analysis (SRA). Calculations proved that the overall decomposition rate of pigment sections equally depended on the storage time and on the presence of light and oxygen, the effect of storage time being the most decisive factor while the impact of oxygen was the lowest. The selectivity of decomposition also depended on the storage time and on the presence of oxygen the influence of storage time being the most important. RP-HPLC followed by PCA and SRA can be successfully used for the study of the impact of environmental conditions on the decomposition of carotenoid pigments of paprika powders.     

Axially symmetric static solutions of four-dimensional SU(N) σ-models by the inverse scattering method

A systematic framework is derived for constructing a superpotential in static, axially symmetric four-dimensional SU(N) principal σ-models by applying an inverse scattering method.     

Inclusion complexing by water-soluble β-cyclodextrin polymers

Cross-linked -cyclodextrin with a molecular weight of less than 10000 has good solubility in water, and it is a better inclusion complexing agent than the parent -cyclodextrin. By including lipophilic guest molecules into the apolar cyclodextrin cavity, their apparent lipophilicity is reduced because the outer surface of the molecular wrapping (the crosslinked -CD) is highly hydrophilic. The relative stability of the inclusion complexes can be rapidly determined by reversed-phase thin-layer chromatography. The reversed-phase TLC behaviour of 25 triphenylmethane derivatives and analogues were studied in the presence of -cyclodextrin polymers containing neutral and carboxyl groups. Increasing the molecular weight results in an increased complex-forming capacity. The carboxyl group modifies the accessibility of the CD cavity which in turn results in increased or decreased complex stability, depending on the guest molecule. The presence of organic solvents diminishes the stability of the CD complexes.     

Theoretical studies on the conformation of saccharides. V. Hydration of the acetal segment in glycosides

Hydration sites of the acetal segment were studied in five of the most stable conformers of 2-methoxy-tetrahydropyran (MTHP) as the first step in the determination of the hydration scheme of glycosides. The intramolecular geometries of a supermolecule formed with MTHP and water were calculated by a PCILO quantum-chemical method. The hydration sites determined can be classified into two groups: (a) individual sites, in which water interacts with one oxygen only, and (b) bridging sites, in which water interacts with both oxygens. The interaction energies of the individual sites are approximately 22 kJ mol^?1, and 26 and 29 kJ mol^?1 in the bridging sites. An increase of the number of water molecules in the hydration shell of MTHP showed that monohydration of the glycosidic linkage oxygens was most advantageous. Despite of the fact that the hydration shell have various structures in the individual MTHP conformers, the obtained results indicate that the hydration does not operate against the anomeric or exoanomeric effects, i.e., it does not influence the equilibrium of the MTHP conformers in favor of the trans arrangements of a glycosidic bond. Therefore, the experimentally observed stabilization of the trans positions in aqueous solutions should be considered as a result of influence of water being a dielectric continuum.     

Synthesis, chiroptical properties, and solid-state structure determination of two new chiral dipyrrin difluoroboryl chelates

Two new types of optically active BODIPY fluorophores bearing chiral phenyl substituents either at the meso-position or at both external alpha-positions have been synthesized. Their chiroptical properties are strongly dependent both on the position of the chiral group and on the protonation of the chromophore. The solid-state structures of one of the difluoroboryl chelates bearing the chiral phenyl substituent at the meso-position (9a) as well as of the corresponding ligand (8a) and its perchlorate have been determined by X-ray diffraction analysis. These are, to the best of our knowledge, the first crystal structures of a dipyrrin free base and of a dipyrrin salt which have been obtained by X-ray diffraction analysis. Hence, for the first time, the helical structure of a protonated dipyrrin chromophore has been proved experimentally.