Generating ultrafilters in a reasonable way

We continue investigations of reasonable ultrafilters on uncountable cardinals defined in Shelah [8]. We introduce a general scheme of generating a filter on λ from filters on smaller sets and we investigate the combinatorics of objects obtained this way. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Molecular geometry and electronic structure of molecules in free‐radical copolymerization of styrene and methyl methacrylate derived from density functional calculations

The molecular geometry and electronic structure of styrene and methyl methacrylate as well as corresponding radicals formed by the addition of a methyl radical to the β‐carbon of the monomer were determined using the density functional theory at the B3LYP/6‐311+G** level. Results were in good agreement with the theoretical and experimental data available in the literature. Full optimized molecular geometry of methyl methacrylate showed the trans form of the molecule. Monomers transformed into corresponding radicals preserved the main structural parameters of substituents whereas bonds between substituents and adjacent radical carbon atoms shortened. It was found that the correlation of the theoretically calculated electronic parameters for monomers and the corresponding radicals with the Q and e parameters from the Alfrey–Price scheme strongly depends on the level of calculations. Application of the higher level of theory including the correlation effect changes the relationship discussed in the literature between energy (E_Y) of formation of a radical from the monomer, the experimental e parameter, and the Q parameter and monomer/average electronegativity, respectively. The total atomic spin density at the radical carbon atom correlated with the radical parameter P in the Alfrey–Price scheme was computed to be higher for the methoxycarbonyl‐1‐methyl‐ethyl radical when compared with the 1‐phenyl‐propyl radical. These values are in good agreement with the localization energies and the P values determined from the kinetic measurements for macroradicals ending with styrene and methyl methacrylate monomer units. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 3761–3769, 2001     

The Symmetry Axioms in Laguerre Planes

We introduce two axioms in Laguerre geometry and prove that they provide a characterization of miquelian planes over fields of the characteristic different from 2. They allow to describe an involutory automorphism that sheds some new light on a Laguerre inversion as well as on a symmetry with respect to a pair of generators.     

Study of heating effect and acoustic properties of dextran stabilized magnetic fluid

This paper presents acoustic properties of water-based biocompatible fluids in which magnetite particles (Fe₃O₄) were coated with two layers of surfactants: sodium oleate and dextran. The attenuation coefficient of ultrasonic wave measurements shows good structural stability of the fluid under the influence of a magnetic field. Hyperthermic tests proved that the magnetic fluid is suitable for therapeutic use as an agent which can release thermal energy (hyperthermia).     

Model of prison riots

We present a model of a prison with two types of inmates. One (recidivists) is a better organized and has more influence on the formation of opinions, whereas the second one is more susceptible to the influence of internal and external pressure. We study, via computer simulations, the interplay between well-organized minority and the rest and how the final decision, like e.g. starting a riot, depends on such factors as: fraction of recidivists, their initial support of the riot and possibility of contacts among cells. We find that, as expected, the riot is more likely to start if there is more recidivists favoring it at the beginning. The influence of external factors (media) turned out to have a larger impact on the second group of prisoners. Contrary to a common practice, we show that in order to prevent riots it might be better not to block the inter-cell contacts.     

Evaluation of the inelastic mean free path (IMFP) of electrons in polyaniline and polyacetylene samples obtained from elastic peak electron spectroscopy (EPES)

The inelastic mean free path (IMFP) of electrons was determined experimentally for selected polyaniline and polyacetylene samples with Ag and Ni references using elastic peak electron spectroscopy (EPES). The surface composition was determined by XPS and density by helium pycnometry. The high resolution hemispherical ESA-31 and ADES-400 spectrometers were used for measurements in the energy range E = 0.5–3.0 keV and E =0.4 − 1.6 keV, respectively. The integrated elastic peak intensity ratios for sample and reference were calculated using the Monte Carlo (MC) algorithm based on the electron elastic scattering cross-sections database NIST SRD64 version 3.1 and applying TPP-2M IMFPs for polymers. Surface excitation parameters (SEP) and material parameters ( _ach ) for polymers were determined, using the model of Chen, from comparison of measured and MC calculated elastic peak intensity ratios. These corrections proved to be efficient in decreasing the percentage deviations between the obtained IMFPs and the TPP-2M formula IMFPs. The elastic peak of hydrogen was observed in the EPES spectra of polymers. The experimental contribution of the hydrogen to the total elastic peak was 0.58%, while this value obtained from the MC simulations was 1.98%.