Serre Problem for Unbounded Pseudoconvex Reinhardt Domains in ℂ<Superscript>2</Superscript>

We give a characterization of non-hyperbolic pseudoconvex Reinhardt domains in ℂ² for which the answer to the Serre problem is positive. Moreover, all non-hyperbolic pseudoconvex Reinhardt domains in ℂ² with non-compact automorphism group are explicitly described.     

Phase transformation in shape memory alloys: a numerical approach for thermomechanical modeling via peridynamics

Meccanica - The work is devoted to the numerical aspects of the modeling tool elaborated to simulate the phenomenon of solid phase transformation in shape memory alloys. Particularly, a nonlocal...     

Demixing of a binary mixture in slit-like pores at high temperatures

We investigate the fluid—fluid demixing transitions in the case of adsorption of so-called symmetric binary mixtures in slit-like pores at temperatures higher than the bulk gas—liquid critical temperature. The aim of the study is to determine how the demixing of such mixtures in the pores depends on the bulk phase composition and on the parameters characterizing the pore. The calculations have been carried out by means of a density functional theory. In the case of an equimolar bulk mixture, the demixing transition inside the pore occurs only when the adsorption potentials of both species are identical. The occurrence of this transition is manifested by a cusp in the adsorption isotherm. For nonequimolar bulk phase compositions, the transition can also take place if the adsorption energies of both components are different. However, the difference in the adsorption energies should be small enough, otherwise a continuous demixing takes place. For non-equimolar compositions two branches of the grand canonical potential intersect, whereas for equimolar bulk composition they meet tangentially. We have determined phase behaviour for several model systems.     

Photothermally Induced Bistability of Emission of Yb-doped Ca4NdO(BO3)3 Single Crystals

We report on studies of changes in the emission spectra (excited at 808 nm) of the Yb-doped Ca₄NdO(BO₃)₃ single crystals due to the photothermal effects caused by the pulsed Nd:YAG laser. Increase of the sample's surface temperature after laser treatment leads to significant enhancement of the 1040 to 1060 nm emission (ascribed to the Nd^{3+ 4}F_3/2 → ⁴I_9/2, ⁴I_11/2 transitions) and simultaneous decrease of the 975 to 1050 nm emission (corresponding to the Yb^{3+ 2}F_5/2 → ²F_7/2 transition). We explain such an increase of the Nd³⁺ luminescence by thermally activated Yb³⁺ → Nd³⁺ energy transfer.     

Spectral Studies on Cyclic Chromotropic Acid Tetramers and Their Interaction with Metal Ions

Abstract

With comparable molar quantities, chromotropic acid reacts with compounds containing aldehyde groups -CHO e.g. with formadehyde or glyoxylic acid to form cyclic compounds with rings containing four chromotropic acid fragments — cyclotetrachromotropylene derivatives. The cyclic compounds, due to the presence of a cavity in the molecule, can play the part of host and complex smaller molecules, which has been confirmed on the basis of triethylamine by the ¹H-NMR measurements. Using spectrophotometric method the stability constant of 1:1 complex formed between Ti(IV) and cyclic compound chromotropic acid with formaldehyde has been determined - K = (9,0 ± 0,1) 10⁴.     

Plasmonic enhancement of blue emission from ZnO nanorods grown on the anodic aluminum oxide (AAO) template

Luminescent properties of ZnO nanorods covered with Ag nanoparticles are examined. Nanorods were synthesized on AAO templates using Atomic Layer Deposition (ALD) technique. Two types of the samples were prepared with different arrangement of ZnO nanorods and doping conditions. Nanorods of the second type were codoped with Al, to stimulate defect-related emissions. The ZnO material fills heterogeneously the interior of the AAO nanopores and has hexagonal, wurtzite structure. Both types of structures exhibit a broad defect-related emission at about 440 nm, most probably related to recombination at zinc interstitial (Zn_i) defects. This emission in samples with a random distribution of ZnO:Al nanorods and finer Ag nanoparticles is enhanced by factor of ～2.5 upon Ag deposition. The so-obtained material is interesting from the point of view of its application in blue range emitting diodes.     

Acid-catalyzed Hydrolysis of the cis-[Cr(1,10-phenanthroline)2(O2CO)]+ Ion Studied by the u.v.–vis Stopped Flow Method

The cis-[Cr(phen)₂(O₂CO)]⁺ ion was prepared through the displacement of two molecules of water from the cis-[Cr(phen)₂(OH₂)₂]³⁺ by the bidentate carbonate anion. It underwent two-phase hydrolysis reactions under acidic conditions (0.1 < [H⁺] < 2.7 m) at 5, 10, 15, 20 and 25 °C. Via slow carbonato chelate ring opening (first step k₁^slow) and a second fast decarboxylation(k₂^fast value). The first step was preceded by protonation of the coordinate bidentate carbonate ligand. The second step exhibited no pH dependence, while k₁^slow values increased with acid concentration that suggested the presence of both protonated and deprotonated reactant species. Based on these observations we have proposed a hydrolysis mechanism featuring H₂O-induced ring-opening of the coordinate CO₃²⁻ group in the first step k₁^slow followed by loss of CO₃²⁻ from two intermediates, [Cr(phen)₂(O₂COH)]²⁺ (k₁^slow) and [Cr(phen)₂(OH₂)(O₂COH)]²⁺ (k₂^fast).     

FTIR in situ transmission studies on the kinetics of paper degradation via hydrolytic and oxidative reaction paths

This study deals with the quantitative and qualitative interpretation of transmission FTIR spectra of aged model paper samples to prepare the basis for a kinetic model of cellulose degradation involving mixed hydrolytic and oxidative mechanism. The ageing experiments were performed in situ under various conditions (pure water vapour, dried air, 100, 150 °C) to discriminate between hydrolytic and oxidative paths. Our focus was on the spectra between 1500–1900 cm^-1, where the products of paper ageing appear in the form of various carbonyl groups. A procedure of spectra standardization was used to interpret the bands area in terms of the conversion of carbon atoms in cellulose. From the time evolution of the bands the overall kinetic curves were generated. The positions of the carbonyl bands were verified by independent experiments and theoretical calculations (DFT method). A simple model involving a hydrolytic reaction route and first order kinetics was positively tested on the available experimental basis. PACS 81.05.-t; 82.20.Wt; 87.15.Rn     

Duality in the cohomology of crystalline local systems

Let k be a perfect field of a positive characteristic p, K-the fraction field of the ring of Witt vectors W(k) Let X be a smooth and proper scheme over W(k). We present a candidate for a cohomology theory with coefficients in crystalline local systems: p -adic étale local systems on X_K characterized by associating to them so called Fontaine-crystals on the crystalline site of the special fiber X _k. We show that this cohomology satysfies a duality theorem.     

Remarks on the r and Δ convolutions

In this paper we study the properties of the r–deformation introduced in [B1]. We observe that the associated convolution coming from the conditionally free convolution is associative only for r = 1 and r = 0. We give the realization of some r–Gaussian random variables and obtain Haagerup–Pisier–Buchholz type inequalities. We also study another convolution defined with the use of the r–deformation through a moment–cumulant formula [KY1] and show that it is associative and in general not positive. Partially sponsored with KBN grant no 2P03A00723 and RTN HPRN-CT-2002-00279.