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.     

Adsorption of 1-octanol at the free water surface as studied by Monte Carlo simulation

The adsorption of 1-octanol at the free water surface has been investigated by Monte Carlo computer simulation. Six different systems, built up by an aqueous and a vapor phase, the latter also containing various number of octanol molecules, have been simulated. The number of the octanol molecules has been chosen in such a way that the octanol surface density varies in a broad range, between 0.27 and 7.83 micromol/m(2) in the six systems simulated. For reference, the interfacial system containing bulk liquid octanol in the apolar phase has also been simulated. The results have shown that the formation of hydrogen bonds between the interfacial water and adsorbed octanol molecules is of key importance in determining the properties of the adsorbed layer. At low octanol surface concentration values all the octanol molecules are strongly (i.e., by hydrogen bonds) bound to the aqueous phase, whereas their interaction with each other is negligibly small. Hence, they are preferentially oriented in such a way that their own binding energy (and thus their own free energy) is minimized. In this preferred orientation the O-H bond of the octanol molecule points flatly toward the aqueous phase, declining by about 30 degrees from the interfacial plane, irrespectively from whether the octanol molecule is the H-donor or the H-acceptor partner in the hydrogen bond. Hence, in its preferred orientation the octanol molecule can form at least two low energy hydrogen bonds with water: one as a H-donor and another one as a H-acceptor. Moreover, the preferred orientation of the hydrogen bonded water partners is close to one of the two preferred interfacial water alignments, in which the plane of the water molecule is parallel with the interface. When increasing the octanol surface density, the water surface gets saturated with hydrogen bonded octanols, and hence any further octanol molecule can just simply condense to the layer of the adsorbed octanols. The surface density value at which this saturation occurs is estimated to be about 1.7 micromol/m(2). Above this surface density value the hydrogen bonded octanols and their water partners are oriented in such a way that the number of the water-octanol hydrogen bonds is maximized. Hence, the preferred alignment of the O...O axes of these hydrogen bonds is perpendicular to the interface. This orientation is far from the optimal alignment of the individual octanol molecules, which is also reflected in the observed fact that, unlike in the case of many other adsorbents, the average molecular binding energy of the adsorbed octanol molecules increases (i.e., becomes less negative) with increasing octanol surface density.     

Triangle Factors In Sparse Pseudo-Random Graphs

The goal of the paper is to initiate research towards a general, Blow-up Lemma type embedding statement for pseudo-random graphs with sublinear degrees. In particular, we show that if the second eigenvalue of a d-regular graph G on 3n vertices is at most cd ³/n ² log n, for some sufficiently small constant c > 0, then G contains a triangle factor. We also show that a fractional triangle factor already exists if < 0.1d ²/n. The latter result is seen to be best possible up to a constant factor, for various values of the degree d = d(n).* Supported by a USA-Israeli BSF grant, by a grant from the Israel Science Foundation and by a Bergmann Memorial Award. Research supported in part by NSF grants DMS-0106589, CCR-9987845 and by the State of New Jersey. Research supported in part by NSF grant DMS 99-70270 and by the joint Berlin/Zurich graduate program Combinatorics, Geometry, Computation, financed by the German Science Foundation (DFG) and ETH Zürich.