On q-analogues and stability theorems

In this survey recent results about q-analogues of some classical theorems in extremal set theory are collected. They are related to determining the chromatic number of the q-analogues of Kneser graphs. For the proof one needs results on the number of 0-secant subspaces of point sets, so in the second part of the paper recent results on the structure of point sets having few 0-secant subspaces are discussed. Our attention is focussed on the planar case, where various stability results are given.     

Studies of UV photochemistry and transition moment directions of 4,5′,8-trimethyl-psoralen (TMP) by means of polarized infrared ATR spectroscopy

The UV homodimerization of 4,5′,8-trimethyl-psoralen (TMP) both in a solvent and in crystalline thin layers has been investigated.

In the crystalline phase, TMP was found to dimerize completely to the trans—anti stereoisomer. On the basis of polarized IR ATR spectra of thin layers deposited onto a KRS-5 plate, both the monomer and the dimer of TMP were found to have well-defined orientations. The directions of several transition moments have been calculated.

On irradiating TMP in solution, the photochemical reaction results in the cis—syn stereoisomer.     

On large minimal blocking sets in PG(2,q)

The size of large minimal blocking sets is bounded by the Bruen–Thas upper bound. The bound is sharp when q is a square. Here the bound is improved if q is a non‐square. On the other hand, we present some constructions of reasonably large minimal blocking sets in planes of non‐prime order. The construction can be regarded as a generalization of Buekenhout's construction of unitals. For example, if q is a cube, then our construction gives minimal blocking sets of size q^4/3 + 1 or q^4/3 + 2. Density results for the spectrum of minimal blocking sets in Galois planes of non‐prime order is also presented. The most attractive case is when q is a square, where we show that there is a minimal blocking set for any size from the interval . © 2004 Wiley Periodicals, Inc. J Combin Designs 13: 25–41, 2005.     

Microwave‐Assisted Direct Esterification of Cyclic Phosphinic Acids

It is known that phosphinic acids do not undergo direct esterification under conventional conditions. However, the reaction may take place on microwave irradiation. 1‐Hydroxy‐3‐phospholene 1‐oxides, 1‐hydroxy‐phospholane 1‐oxides, and a 1‐hydroxy‐1,2,3,4,5,6‐hexahydrophosphinine 1‐oxide were esterified with n‐pentanol, i‐pentanol, n‐octanol, and i‐octanol(2‐ethylhexanol). The phosphinates prepared in 50%–94% yield are all new compounds, and a number of them are useful intermediates.     

Complexation of hydroxamate-based siderophores with cobalt(II/III): growth inhibitory effect of cobalt(III)-desferricoprogen complex on fungi

Solution equilibrium results for Co(II) and Co(III) complexes of two natural hydroxamate-based siderophores, the exocyclic desferricrocin (DFR) and the endocyclic triacetylfusarinine (TAF) are presented. The three hydroxamate chelating functions of TAF were found to complete the octahedral coordination sphere of a Co(II) ion in stepwise processes, but following the coordination of two hydroxamates of DFR practically in one step, the third function, most probably because of sterical reasons, remained uncoordinated. A comparison with corresponding results for the previously studied acyclic desferrioxamine B (DFB) and desferricoprogen (DFC) provided some information about the effects of the molecular framework of siderophores on their cobalt-binding ability. The oxidation of the central metal ion under basic conditions and investigation of the cobalt(III) complexes by cyclic voltammetry were also made. Compared to Fe(III), by several orders of magnitude, higher stability complexes were formed with Co(III). The possibility of any effect of the Co(III)-siderophore complex on microbial Fe(III) uptake was tested by investigation of the antifungal effect of Co(III)-DFC in comparison with that of CoCl₂ on two fungi cultures, Penicillium brevicompactum and Aspergillus fumigatus.     

Demonstration of a protein with enhanced resistance to proteinase K in transmissible cytopathic condition elicited by cell-free lysate of free-living ameba Naegleria gruberi

The cell-free lysate of free-living amebae Naegleria gruberi and Naegleria fowleri were reported to elicit cytopathic effect in various cell lines that could be indefinitely transmitted by the culture media. The causative agent showed sensitivity to treatments detrimental to proteins while resisted exposures damaging to nucleic acids. Here we demonstrate that subsequent to exposure to N. gruberi lysate mild digestion with proteinase K reveals the presence of a protein band in HeLa cells absent from control cell lines. Though the small quantity of this protein with enhanced resistance to proteinase K relative to the total protein content of the sample has proved to date insufficient for its purification, we suppose that it is a human cellular protein that assumed altered conformation in a prion-like fashion. The conformational conversion could have been trigerred by an ameba protein in the lysate. In addition, we showed that HeLa cells treated with N. gruberi lysate display elevated cathepsin B activity which is assumed to be a secondary response to the accumulation of the proteinase K-resistant protein. We propose that a number of degenerative sequelae following previous microbial infections in mammals could have a similar pathomechanism. Moreover, epidemiological data strongly suggest that natural prion disease in sheep, goat and cervids may also have an etiology linked to prior infection/colonization with a microbe, as it had already been proposed by one of us.     

Nanophase separation in segmented polyurethane elastomers: Effect of specific interactions on structure and properties

Polyurethanes were prepared from 4,4′-methylenebis (phenyl isocyanate) (MDI), 1,4-butanediol (BD) and poly (tetrahydrofurane) polyether polyol (PTHF). The -OH functional group ratio of polyol/total diol was kept constant at 0.4 in all experiments, while the ratio of the isocianate and hydroxyl groups (NCO/OH) changed between 0.940 and 1.150. Melt polymerization was carried out in an internal mixer. The polymers were characterized with a number of methods including GPC, FTIR, WAXS, DSC, DMA and tensile testing. Changing stoichiometry modifies molecular weight as expected, but the relative concentration of end-groups also changes at the same time. The respective end-groups preferentially associate with each other leading to phase separation. -OH end-groups enter into weaker interactions with each other than urethane and amine groups. The extent of phase separation, as well as the size and properties of the dispersed phase depend on composition. Each property of the polymer is affected differently by molecular weight and phase separation. Melt viscosity depends mostly on the length of the molecules, ultimate tensile properties are influenced also by interactions, while stiffness is determined almost exclusively by phase structure.