Rethinking polyhedrality for lindenstrauss spaces

We present a Lindenstrauss space with an extreme point that does not contain a subspace linearly isometric to c. This example disproves a result stated by Zippin in a paper published in 1969 and it shows that some classical characterizations of polyhedral Lindenstrauss spaces, based on Zippin’s result, are false, whereas some others remain unproven; then we provide a correct proof for those characterizations. Finally, we also disprove a characterization of polyhedral Lindenstrauss spaces given by Lazar, in terms of the compact norm-preserving extension of compact operators, and we give an equivalent condition for a Banach space X to satisfy this property.     

Collective diffusion in the presence of substrate inhomogeneities and particle–particle interactions

A novel variational analytic approach to collective diffusion allowing the density dependent collective diffusion coefficient to be calculated in systems of interacting particles adsorbed on a crystalline substrate is presented. The approach, based on a kinetic lattice gas model extracts the diffusion coefficient directly from the master equations which account for the microscopic kinetics of the system in which microscopic processes underlying the diffusion are particle jumps between neighboring adsorption sites. Variational parameters minimizing the evaluated diffusional eigenvalue of the microscopic rate matrix are ‘geometrical’ and ‘correlational’ phases accounting, for the local potential energy landscape experienced by the adsorbed particle and the local correlations, respectively, i.e. an instantaneous occupation pattern of adsorption sites around the particle. Selected results, collective diffusion as a function of particle coverage, for the system of interacting particles adsorbed on a one dimensional non-homogeneous substrate with steps and for a system of non-interacting particles adsorbed on a two dimensional striped–stepped surface are presented and discussed. It is demonstrated in the latter case that the mean field approach which is known in the literature overestimates the diffusion coefficient and corresponds to the variational result in the limit of infinitely fast hopping kinetics in the direction parallel to steps.     

Asymmetric Dearomative (3+2)-Cycloaddition Involving Nitro-Substituted Benzoheteroarenes under H-Bonding Catalysis

In our studies, the organocatalytic 1,3-dipolar cycloaddition between 2-nitrobenzofurans or 2-nitrobenzothiophene and N-2,2,2-trifluoroethyl-substituted isatin imines has been developed. The reaction has been realized by employing bifunctional organocatalysis, with the use of squaramide derivative being crucial for the stereochemical efficiency of the process. The usefulness of the cycloadducts obtained has been confirmed in selected transformations, including aromative and non-aromative removal of the nitro group.     

Comparison of experimental and numerical results on metallic plates subjected to explosions

A comparative study of dynamic response including damage and rupture processes of thin metallic plates subjected to shock-wave impulses – explosions is presented. The results of the finite element numerical analysis are related to experiments. Due to high strain rate during explosions the elasto-viscoplastic Chaboche's constitutive law including damage effects has been applied. For the assumed model proper material parameters identification has been done. In the dynamic, geometrically non-linear analysis the MSC.Marc system has been used. A good correlation between numerical and experimental results has been observed. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Synthesis of aryliminoacetonitriles under FVT conditions or by dehydrogenation of arylaminoacetonitriles: an NMR and UV-photoelectron spectroscopy study

The synthesis of [(E)-arylimino]-acetonitriles 3 has been described. It was found that the title compounds can be obtained on the three ways, namely by: (i) dehydrogenation of arylaminoacetonitriles 1, (ii) thermal fragmentation of 1-aryl-4-cyano-β-lactams 4 and (iii) retro-ene reaction of (allyl-p-methoxyphenyl-amino)-acetonitrile (7a) under FVT conditions. ¹H and ¹³C NMR spectra of compounds 3, 5 and 6, and all their precursors 1 and 4, were recorded and analysed in detail using chemical shifts δ_H and δ_C [from GIAO DFT B3LYP/6-31(d) calculations] and J-couplings predicted at the DFT B3LYP/IGLO-II level. Also, UV-photoelectron spectra of 4a,d and 3a,d were measured and analysed considering the theoretical evaluation of their ionisation potentials.     

Complexes of tetra-tert-butyl-tetraazaporphine with Al(III) and Zr(IV) cations as fluoride selective ionophores

In this work, complexes of Zr(IV) and Al(III) cations with 2,7,12,17-tetra-tert-butyl-5,10,15,20-tetraazaporphine (TAP) were tested as ionophores in plasticized PVC membranes of ion-selective electrodes. It was found that both tested ionophores show enhanced affinity towards fluoride anion. High fluoride selectivity was observed in the presence of anionic or cationic additives in the membrane, which indicates that proposed compounds work according to charged or neutral carrier mechanism, depending on membrane composition and pretreatment.tert-Butyl substituents, present in the structure of tested compounds, were supposed to prevent formation of ionophore dimers within the membrane phase. This process was found to be responsible for some unfavorable potentiometric properties of electrodes based on complexes of Zr(IV) and Al(III) cations with porphyrins (compounds closely related to tetra-tert-butyl-5,10,15,20-tetraazaporphine). As it was shown using spectrophotometrical measurements, Al(III)-TAP was not susceptible to dimerization, while dimer formation was observed for Zr(IV)-TAP. In full agreement with these observations, electrodes with membranes containing Al(III)-TAP responded in near-Nernstian and fast manner towards fluoride anion, while the employment of Zr(IV)-TAP as ionophore resulted in super-Nernstian and sluggish response. Plasticized PVC membranes doped with Al(III)-TAP and 20 mol% of lipophilic anionic additives shown remarkable F⁻ selectivity, with selectivity coefficients, , as follows: −4.4 (Y⁻Br⁻), −4.3 (Cl⁻), −4.2 (NO₃⁻), −3.6 (SCN⁻), −2.9 (ClO₄⁻).     

Deoligomerization by cocomplexation: syntheses and structures of aluminum-calcium alkoxides and aryloxides

Reactions of oligomeric "Ca(dbbfo)2" and Ca9(CH3OCH2CH2O)18(CH3OCH2CH2OH)2 with Al(CH3)3 in toluene gave tetranuclear heterobimetallic [Ca(mu-dbbfo){(mu-dbbfo)(mu-CH3)Al(CH3)2}]2 (71%) and polymeric Ca{(mu-CH3OCH2CH2O)(mu-CH3)Al(CH3)2}2 (86%). The latter can be obtained as monomeric THF adduct Ca{(mu-CH3OCH2CH2O)Al(CH3)3}2(THF)2 (78%) when a mixture of solvents is used. The results, including an initial L-lactide polymerization test, are discussed in the context of calcium alkoxo cluster degradation in solution.