Inversion of the Bessel potential operator in weighted variable Lebesgue spaces

We study the inversion problem of the Bessel potential operator within the frameworks of the weighted Lebesgue spaces with variable exponent. The inverse operator is constructed by using approximative inverse operators. This generalizes some classical results to the variable exponent setting.     

Finite size effects on structure and magnetism in mass-selected CoPt nanoparticles

In this paper, the one-way absorption property in one-dimensional dielectric/metal photonic crystal structure with a dielectric defect layer is studied. The effects of incident angle and state of polarization on one-way absorption behaviour of the anti-resonant (AR) mode are investigated. The normally incident wave from left to right propagation is totally allowed to penetrate to the structure but right to left propagation totally reflected at the same wavelength. It is found that, with increasing of the incident angle, the AR mode shifts to the lower wavelengths and its intensity decreases. Simultaneously, another AR mode with reversed one-way property appears at higher wavelength. The one-way behaviour on absorption is observed at the both states of polarizations but is localized on different wavelengths. Those effects, are suggesting that the proposed structure can be used as a direction sense polarization splitter or reflector/antireflector device.     

Thermal decomposition of the [Pt(NH3)4]2+ complex in NaX zeolite

The effect of the calcination procedure on the decomposition of the [Pt(NH₃)₄]²⁺ complex in a cesium-containing NaX zeolite was studied by thermal decomposition accompanied by mass spectrometry and diffuse reflectance spectroscopy, as well as electron paramagnetic resonance and infrared spectroscopy. The decomposition of the complex took place in two steps. Under oxygen, the [Pt(NH₃)₄]²⁺ complex was first converted into the [Pt(NH₃)₂]²⁺ complex in the first step, with predominant nitrogen release. In the second step, corresponding to the decomposition of the remaining two amine ligands, NO was also formed and adsorbed. Oxygen paramagnetic species were also observed. Under He, the decomposition also occurred in two steps with H₂ release.     

Manifolds: Hausdorffness versus homogeneity

We analyze the relationship between Hausdorffness and homogeneity in the frame of manifolds not confined to be Hausdorff. We exhibit examples of homogeneous non-Hausdorff manifolds and prove that a Lindelöf homogeneous manifold is Hausdorff.

     

Thermal,structural and optical properties of Al2CoO4-Crocoite composite nanoparticles used as pigments

Novel zinc(II) complex compounds of general formula Zn(C₆H₅COO)₂·L₂ (where L=caffeine (caf) and urea (u)) were synthesized and characterized by elemental analysis and IR spectroscopy. The thermal behaviour of the complexes was studied during heating in air by thermogravimetry. It was found that the thermal decomposition of the anhydrous Zn(II) benzoate compounds with bioactive ligands was initiated by the release of organic ligands at various temperatures. On further heating of the compounds up to 400°C the thermal degradation of the benzoate anions took place. Zinc oxide was found as the final product of the thermal decomposition of all zinc(II) benzoate complex compounds heated to 600°C. Results of elemental analysis, infrared spectroscopy, mass spectroscopy and thermogravimetry are presented.     

Block separation in solvable groups

If π is a set of primes, a finite group G is block π-separated if for every two distinct irreducible complex characters α, β ∈ Irr(G) there exists a prime p ∈ π such that α and β lie in different Brauer p-blocks. A group G is block separated if it is separated by the set of prime divisors of |G|. Given a set π with n different primes, we construct an example of a solvable π-group G which is block separated but it is not separated by every proper subset of π. Received: 22 December 2004     

A separable manifold failing to have the homotopy type of a CW-complex

We show that (a variation of) the Prüfer surface, which is an example of a separable non-metrizable 2-manifold, does not have the homotopy type of a CW-complex. Received: 6 February 2007 Revised: 21 August 2007