On the invariant measure for the quasi‐linear Lasota equation

The problem of the existence of the invariant measure is important considering its connections with chaotic behaviour. In the papers (Zesz. Nauk. Uniw. Jagiellońskiego, Pr. Mat. 1982; 23 :117–123; Ann. Pol. Math. 1983; XLI :129–137; J. Differential Equations 2004; 196 :448–465) the existence of invariant and ergodic measures according to the dynamical system generated by the Lasota equation was proved, i.e. the equation describing the dynamics and becoming different of the population of cells. In this paper, the existence of such measure for the quasi‐linear Lasota equation is proved. This measure is the carriage of the measure described by Dawidowicz (Zesz. Nauk. Uniw. Jagiellońskiego, Pr. Mat. 1982; 23 :117–123). Copyright © 2006 John Wiley & Sons, Ltd.     

Dual Problems and Separation of Sets: Lagrange and Fenchel Duality

An extremum problem is embedded in a parametric scheme which contains, as a particular case, the classic perturbation function. The introduction of the image of the embedded problem allows one to derive a generalized duality and, in particular, Lagrangian and Fenchel duality.     

Morphological and elemental characterisation with the high-energy ion-nanoprobe LIPSION

This contribution deals with the morphological and elemental characterisation with high-energy (MeV) focused ion beams (in particular protons) with special emphasis on high spatial resolution in the sub-micrometer regime and very low minimum detection limits (sub-ppm) in trace element analysis. The most important methods like particle induced X-ray emission (PIXE), Rutherford backscattering spectrometry (RBS), as well as scanning transmission ion microscopy (STIM) and STIM-tomography will be illustrated by examples from material and life sciences.     

Activity of TiO2 deposited by the CVD method on ammoxidized surface of a carbonaceous material in hydrogenation of styrene

Hydrogenation of styrene has been applied as a test reaction to study the catalytic activity of TiO₂ deposited by the CVD (chemical vapour deposition) method on the surface of a carbonaceous material enriched in nitrogen (C_N).     

Limit cycles and Lie symmetries

Given a planar vector field U which generates the Lie symmetry of some other vector field X, we prove a new criterion to control the stability of the periodic orbits of U. The problem is linked to a classical problem proposed by A.T. Winfree in the seventies about the existence of isochrons of limit cycles (the question suggested by the study of biological clocks), already answered by Guckenheimer using a different terminology. We apply our criterion to give upper bounds of the number of limit cycles for some families of vector fields as well as to provide a class of vector fields with a prescribed number of hyperbolic limit cycles. Finally we show how this procedure solves the problem of the hyperbolicity of periodic orbits in problems where other criteria, like the classical one of the divergence, fail.     

Ricci curvature and quasiconformal deformations of a Riemannian manifold

The theory of quasiconformal deformations of a Riemannian manifold (M, g) of dimensionn leads in a natural way to the AhlforsS operator being the symmetric and trace free part of the Levi-Civita connection Δ on 1-forms, and to the Ahlfors Laplacian , whereR is the Ricci action. It is well known that there are no conformal deformations on compact Riemannian manifoldsM with negative Ricci curvature. The question arises, how close to being conformal a deformation on suchM can be, i.e. the question on the minimal constant of quasiconformality. Using spectral properties ofL, we derive several lower bounds for the constant of quasiconformality for the normalized deformations of compact manifolds with the positive definite, negative definite, or vanishing Ricci tensorR. As a result, we also obtain that there are no conformal deformations if the Ricci curvature is positive definite but small enough (Corollary 5.17).     

Vapor-particle partitioning of hydrocarbons in Western Mediterranean urban and marine atmospheres

An analytical procedure is described for a comprehensive determination of the composition of hydrocarbons in the atmosphere, based on: (a) aerosol filtration and subsequent adsorption of the vapor phase onto active charcoal and polyurethane foam; (b) GPC and HPLC fractionation of the extracts, and (c) analysis of the fractions by GC-MS under EI and NICI modes. Special emphasis is placed onn-alkanes, PAHs and their oxygenated derivatives.The characterization of samples collected in a coastal urban area (Barcelona city), and far away over the Western Mediterranean, at sea level and at 1100 m of altitude, revealed significant changes in the aerosol composition, mainly attributed to initial vapor-particle partitioning processes, influenced by ambient temperature variations, and to others taking place during long-range atmospheric transport, related with the different compound photoreactivities and with an unexplained source-decoupling phenomenon.     

Proteomic analysis of the Arabidopsis thaliana cell wall

With the completion of the Arabidopsis genome, many hypothetical proteins have been predicted without any information on their expression, subcellular localisation and function. We have performed proteomic analysis of proteins sequentially extracted from enriched Arabidopsis cell wall fractions and separated by two-dimensional gel electrophoresis (2-DE). The proteins were identified by peptide mass fingerprinting using matrix-assisted laser desorption/ionisation-time of flight (MALDI-TOF) mass spectrometry and genomic database searches. This is part of a targeted exercise to establish the entire Arabidopsis secretome database. We report evidence for new proteins of unknown function whose existence had been predicted from genomic sequences and, furthermore, localise them to the cell wall. In addition, we observed an unexpected presence in the cell wall preparations of proteins whose known biochemical activity has never been associated with this compartment hitherto. We discuss the implications of these findings and present results suggesting a possible involvement of cell wall kinases in plant responses to pathogen attack.     

Application of High Pressure-DTA for High Pressure-liquid Phase Epitaxy of Doped Mercury and Thallium HTS Formations

The fabrication method of superconducting thin films of compositions HgBa₂Ca₂Cu₃O_8+δ (Hg-1223) and Tl₂Ba₂CuO_y (2201) on single-crystalline SrTiO₃ and LaAlO₃ substrates is reported. The highest obtained T _c was 134 K and J _c over 10⁶ A cm^–2 at 77 K. High pressure DTA(HP-DTA) was applied to grow mercury- and thallium-based high-temperature superconducting crystals and thin films, to identify melting points of particular phases within these oxide systems and determine suitable processing conditions. The DTA system operates at the: maximum temperature of 1200°C, volume up to 5 cm³, working pressure up to 1.5 GPa and at a working atmosphere — inert gas with up to 25% oxygen. This revised version was published online in August 2006 with corrections to the Cover Date.