Faber-hypercyclic operators

Let Ω be a bounded domain of the complex plane whose boundary is a closed Jordan curve and (F _n ) _n≥0 the sequence of Faber polynomials of Ω. We say that a bounded linear operator T on a separable Banach space X is Ω-hypercyclic if there exists a vector x of X such that {F _n (T)x: n ≥ 0} is dense in X. We show that many of the results in the spectral theory of hypercyclic operators involving the unit disk or its boundary have Ω-hypercyclic counterparts which involve the domain Ω or its boundary. The influence of the geometry of Ω or the smoothness of its boundary on Faber-hypercyclicity is also discussed.     

Finite Genome Length Corrections for the Mean Fitness and Gene Probabilities in Evolution Models

Using the Hamilton–Jacobi equation approach to study genomes of length L, we obtain 1/L corrections for the steady state population distributions and mean fitness functions for horizontal gene transfer model, as well as for the diploid evolution model with general fitness landscapes. Our numerical solutions confirm the obtained analytic equations. Our method could be applied to the general case of nonlinear Markov models.     

Assessment of coal and ash environmental impact with the use of gamma- and X-ray spectrometry

Gamma-ray spectrometry (GS), energy dispersive X-ray fluorescence (EDXRF) analysis methods and wavelength dispersive X-ray fluorescence (WDXRF) were applied for the studies of some coal components, e.g., sulphur, light and heavy metal element concentrations and naturally occurring radioactive isotope contents. Hundred fifty coal samples originating mostly from eight different coal mines from Upper Silesian Coal Basin and 150 samples of ash obtained from these coal samples in laboratory by total combustion at final temperature of 820°C, were analyzed. Such comparitive analyses can be helpful in selection of most suitable kind of coal for burning in electrical power and heat plants to minimize the environmental pollution.     

Analysis of an optimal control problem for the three-dimensional coupled modified Navier-Stokes and Maxwell equations

The mathematical formulation and analysis of an optimal control problem associated with a viscous, incompressible, electrically conducting fluid in a bounded three-dimensional domain with fixed perfectly conducting boundaries is considered. The objective of control is the matching of the velocity and magnetic fields to given target fields; control is effected through distributed mechanical force and current controls. The existence of optimal solutions is shown, the Gâteaux differentiability for the magnetohydrodynamic system with respect to controls is proved, and the optimality system is obtained.     

Adsorption and preconcentration of divalent metal ions in fossil fuels and biofuels: gasoline, diesel, biodiesel, diesel-like and ethanol by using chitosan microspheres and thermodynamic approach

Biodiesel and diesel-like have been obtained from soybean oil by transesterification and thermal cracking process, respectively. These biofuels were characterized as according to ANP standards by using specific ASTM methods. Ethanol, gasoline, and diesel were purchased from a gas station. Deacetylation degree of chitosan was determined by three distinct methods (conductimetry, FTIR and NMR), and the average degree was 78.95%. The chitosan microspheres were prepared from chitosan by split-coating and these spheres were crosslinked using glutaraldehyde. The surface area of microspheres was determined by BET method, and the surface area of crosslinked microspheres was 9.2 m² g⁻¹. The adsorption isotherms of cooper, nickel and zinc on microspheres of chitosan were determined in petroleum derivatives (gasoline and diesel oil), as well as in biofuels (alcohol, biodiesel and diesel-like). The adsorption order in all fuels was: Cu > Ni > Zn. The elution tests presented the following preconcentration degrees: >4.5 to ethanol, >4.4 to gasoline, >4.0 to diesel, >3.8 to biodiesel and >3.6 to diesel-like. The application of chitosan microspheres in the metal ions preconcentration showed the potential of this biopolymer to enrich fuel sample in order to be analyzed by flame atomic absorption spectrometry.     

Surface Analysis of Inhibitor Film Formed by 4-Amino-N-(1,3-thiazol-2-yl) Benzene Sulfonamide on Carbon Steel Surface in Acidic Media

Inhibitive properties of the antibacterial sulfa drug sulfathiazole—IUPAC name being 4-amino-N-(1,3-thiazol-2-yl) benzene sulfonamide—on the corrosion of carbon steel in 1.0 M HCl solution were investigated using weight loss measurements, electrochemical impedance spectroscopy (EIS), scanning electron microscopy (SEM), and X-ray photoelectron spectroscopy (XPS). Sulfathiazole is a good adsorption inhibitor, and the inhibition efficiency increases with increasing concentration. Adsorption is spontaneous and is best described by Temkin isotherm. XPS analysis showed, at this stage, that the main product of corrosion is a nonstoichiometric Fe³⁺ oxide/oxyhydroxide consisting of a mixture of Fe₂O₃, α, and γ-FeO(OH) and/or Fe(OH)₃, where α, γ-FeO(OH) is the main phase.     

Laboratory set-up for X-ray diffraction at high pressures

We describe here a simple set-up for X-ray diffraction under high pressure using a diamond anvil cell employing a sealed tube. The set-up works in angular dispersive geometry and is built using rather common components that are available in a research laboratory. We show that using this set-up one can routinely acquire good-quality data for the determination of structural properties under pressure and the equations of state. Technical details are presented along with examples of experimental results for sodium chloride and LiV₂O₄.     

Analysis and discretization of an optimal control problem for the time-periodic MHD equations

We consider the mathematical formulation and analysis of an optimal control problem associated with the tracking of the velocity and the magnetic field of a viscous, incompressible, electrically conducting fluid in a bounded two-dimensional domain through the adjustment of distributed controls. Existence of optimal solutions is proved and first-order necessary conditions for optimality are used to derive an optimality system of partial differential equations whose solutions provide optimal states and controls. Semidiscrete-in-time approximations are defined and their convergence to the exact optimal solutions is shown.     

Generalized inverses and the maximal radius of regularity of a Fredholm operator

Operators possessing analytic generalized inverses satisfying the resolvent identity are studied. Several characterizations and necessary conditions are obtained. The maximal radius of regularity for a Fredholm operatorT is computed in terms of the spectral radius of a generalized inverse ofT. This provides a partial answer to a conjecture of J. Zemánek.