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.     

<Emphasis Type="Italic">N</Emphasis>-Alkoxy-3,5-dinitro-4-aminobenzoic acid derivatives with controlled physico-chemical properties

Starting from 4-chloro-3,5-dinitrobenzoic acid 1, compounds 2–10 (N-alkoxy-3,5-dinitro-4-aminobenzoic acid esters where alkoxy stands for methoxy, carboxymethoxy, triphenylmethoxy, or corresponding amides) have been obtained, from which compounds 3–5 and 7–10 are new, and for the known compounds 2 and 6 the synthetic procedure has been improved. The new derivatives have been characterized by appropriate means (IR, UV–Vis, ¹H- and ¹³C-NMR, fluorescence) and their properties were studied. Thus, depending on their structure, the compounds have acid properties, fluorescence and complexing properties with alkaline cations.     

New N-aryloxy-phthalimide derivatives. Synthesis,physico-chemical properties,and QSPR studies

Starting from N-hydroxyphthalimide 1 and the reactive fluoro- or chloro-nitroaryl derivatives 2, 3 and 4a-e (2-chloro-3,5-dinitropyridine; 3, NBD-chloride; 4a, 1-fluoro-2,4-dinitrobenzene; 4b, picryl chloride; 4c, 4-chloro-3,5-dinitrobenzotrifluoride; 4d, 2-chloro-3,5- dinitrobenzotrifluoride; 4e, 4-chloro-3,5-dinitrobenzoic acid) the corresponding N-(2-nitroaryloxy)-phthalimide derivatives 5a-e, or 6 and 7 were obtained and characterized by IR, UV-Vis ¹H-NMR and ¹³C-NMR spectroscopy. The TLC behavior and the hydrophobicity of these derivatives have been experimentally evaluated by R_M0 parameters (using RP-TLC). The experimental R_M0 parameters were compared with the calculated partition coefficient, log P. A QSPR study was also performed to establish possible correlations between the structure and physical properties (λ_max and R_M0) of compounds 5a-e, 6, and 7.      

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.     

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.     

Chemical isolation of element 106 from aqueous solutions according to model experiments with short-lived tungsten isotopes

The short-lived isotopes of W and their descendants have been isolated from the products of the bombardment of¹⁴⁴Sm with²⁴Mg by a fast continuous ion-exchange method, using HF solution media. The feasibility of this method for isolation of element 106 is discussed.     

Fast and continuous chemical isolation of short-lived isotopes of Hf,Ta and W as homologs of elements 104, 105 and 106

Some short-lived isotopes of Hf, Ta and W, synthesized at the U-400 cyclotron of JINR-Dubna, have been isolated using a previously elaborated fast continuous method of chemical isolation of element 104 from nuclear reaction products. The products were transported by a NaCl aerosol jet, from the irradiated targets to a separation device in which Hf, Ta and W were isolated by using three coupled ion-exchange columns.     

Neutron-neutron correlation approach for 11Li halo structure investigation

The preemission of neutrons from ¹¹Li halo nuclei is considered. The present problems of investigation of ¹¹Li halo nucleus structure by means of the C _nn correlation function are briefly presented. The influence of the target screening on the halo neutron preemission is described. It is shown that, owing to the diminishing of the screening effect, the yield of preemission neutron pairs is expected to be much larger in the case of ¹²C than in the case of Si target. It is shown that a new experiment on a ¹²C target will allow one to solve the standing problems of C _nn and to test experimentally a recent new theory of C _nn. The text was submitted by the authors in English.