Integer-valued functions and increasing unions of first countable spaces

We determine those regular cardinals κ with the property that for each increasing κ-chain of first countable spaces there is a compatible first countable topology on the union of the chain. AssumingV=L any such κ must be weakly compact. It is relatively consistent with a supercompact cardinal that each κ>w ₁ has the property. The proofs exploit the connection with interesting families of integer-valued functions. Research of the second author supported by OTKA grant no. 1805. Research of the remaining authors partially supported by NSERC of Canada.     

Spatial bistability in a pH autocatalytic system: from long to short range activation

The acid-auto-activated chlorite-tetrathionate reaction is studied in a one-side-fed spatial reactor. It was previously shown that in these conditions the unstirred reaction-diffusion system can generate oscillatory and excitable states even though under well-stirred nonequilibrium conditions only steady-state bistability is observed. Numerical simulations suggest that these temporal reaction-diffusion instabilities result from long-range activation by rapidly diffusing protons. We study here experimentally and numerically the effect of introducing into this reaction-diffusion system macromolecular carboxylate species that reduce the effective diffusivity of protons. Consistent with the original assumption, the introduction of such slow mobility proton-binding species quenches both oscillatory and excitability dynamics. Within the bistability domain the direction of the propagation of an interface between the two steady states depends on control parameter value. We elaborate on the fact that beyond a low critical concentration of macromolecular carboxylate species, the stability limit of the "thermodynamic" branch of spatial steady state does not depend on this concentration. Despite the relative simplicity of the kinetic model used in the numerical simulations, the results are in quasi-quantitative agreement with the experimental observations.     

Nanoscale probing of the enamel nanorod surface using polyamidoamine dendrimers

Although it is known that noncollagenous proteins of dental origin bind to the hydroxyapatite crystal surfaces, no measure of their binding strength has been calculated. This experiment used -COOH-capped generation 7 PAMAM dendrimers as nanoprobes of the biological hydroxyapatite nanorod surfaces. Dendrimer distribution was characterized using AFM. The results showed dendrimers to be spaced at intervals along the c-axis of the crystals. From these observations and assuming a fully ionized -COOH dendrimer, a mathematical model of the binding capacity of the crystal surface with the dendrimer was developed. The Monte Carlo method was used to simulate the binding process between the dendrimer and crystal surface, and the binding strength of the -COOH groups to the surface was calculated to be 90 +/- 20 kJ/mol. These results support the CFM studies which have described alternating bands of charge domains on the crystal surface and that the binding strength will be dependent on both the intensity of the charge on the protein and the crystal surface.     

Electronic structure of deposited monosized metal-clusters

Monosized Pt- and Au-clusters deposited on silica substrates are analyzed by photoelectron spectroscopy. The 4f-core-level energies and the valence electronic states depend on the cluster size and on the element. Au shows more uniform behavior for cluster sizes between 1 and 7 atoms than Pt does. Both materials are not yet metallic for clusters containing only a few atoms.     

Effect of variation in the chain length and number in modulating the interaction of an immunogenic lipopeptide with biomembrane models

A differential scanning calorimetry study was carried out to investigate the effect exerted by immunogenic synthetic lipopeptides obtained by the conjugation of LCMV_33–41 peptide with lipoamino acids (Laas) bearing different alkyl chain lengths (C₁₂ and C₁₆) and number of chains (2 × C₁₂) on the thermotropic behaviour of dimyristoylphosphatidylcholine (DMPC) liposomes. The aim of this work was to study the ability of these compounds to be carried by a liposomal system and released to a biomembrane model.

The examined compounds caused variations of the thermotropic parameters that characterise the liposomal system (transition temperature, T_m and enthalpy variation, ΔH), and interacted with the biomembrane models in different way. The interaction was found to be modulated by the length and number of chains present in the examined compounds. In fact, the compounds with higher number of lipid chain showed a stronger interaction with the biomembrane models with respect to the pure peptide and the compounds with a single lipid chain. These results suggest that the lipoamino acid moiety could favour the peptide to be carried by the liposomal system and released to biomembrane.     

Photoemission from laser excited semiconductors: Dynamic response of the electronic structure in Si

Using angle-resolved photoemission in coincidence with a pulsed Nd:Yag laser beam (hν_L = 2.33 eV), we have studied the dynamic rearrangement of the electronic states in Si in the presence of a large number of electron hole pairs created by laser photon excitation. We observed considerable changes in the valence band structure, a renormalization of the bandgap, and a satellite peak in the 2p core level emission due to more effective core hole screening.