Coupling leads to chaos

The main goal of this paper is to prove analytically the existence of strange attractors in a family of vector fields consisting of two Brusselators linearly coupled by diffusion. We will show that such a family contains a generic unfolding of a 4-dimensional nilpotent singularity of codimension 4. On the other hand, we will prove that in any generic unfolding Xμ of an n-dimensional nilpotent singularity of codimension n there are bifurcation curves of (n−1)-dimensional nilpotent singularities of codimension n−1 which are in turn generically unfolded by Xμ. Arguments conclude recalling that any generic unfolding of the 3-dimensional nilpotent singularity of codimension 3 exhibits strange attractors.     

Interactions of xanthines with activated carbon: II. The adsorption equilibrium

In the present work, we have studied the adsorption of xanthine derivatives by activated carbon sorbents in aqueous solutions. The study comprised both kinetic, equilibrium and thermodynamic aspects. The kinetic results were reported in a previous paper; the equilibrium-related results are discussed here. The two types of carbon used exhibit some differences but the equilibrium isotherms obtained are all of the H-3 type in the classification of Giles. This suggests a high affinity of the sorbents for the sorbates. We also found that the overall adsorption process comprises more than one individual adsorption-desorption process of which one leads to the formation of a “monolayer” and the other to the “precipitation” of the sorbate on the sorbent surface (multilayer adsorption); the amount of sorbate adsorbed in monolayer form was seemingly greater in C-A14.     

Aluminum(III) complexes containing O,O chelating ligand

The stoichiometric reactions of trimethylaluminum with 2,6‐(MeOCH₂)₂C₆H₃OH (LH) revealed compounds L₃Al ( 1 ) and L₂AlMe ( 2 ). On the other hand reaction of 1 equiv. of LH with trimethylaluminum did not lead to the formation of complex LAlMe₂ ( 3 ), rather 2 together with Me₃Al were observed as a result of a disproportionation of 3 . Compounds 1 and 2 were characterized by elemental analysis, ¹H and ¹³C NMR spectroscopy and in the case of 1 by X‐ray diffraction. Derivative 2 underwent transmetalation with Ph₃SnOH, giving LSnPh₃ ( 4 ) as the result of a migration of ligand L from the aluminum to the tin atom. The identity of 4 was established by elemental analysis, ¹H, ¹³C and ¹¹⁹Sn NMR spectroscopy and ¹H, ¹¹⁹Sn HMBC experiments. The system 2 and B(C₆F₅)₃ in a 1:1 molar ratio was shown to be active in the polymerization of propylene oxide and ε‐caprolactone. Copyright © 2007 John Wiley & Sons, Ltd.     

The temperature and pressure in the plasma parallel plate accelerator

This paper presents the results of plasma temperature and pressure calculations in the parallel plate accelerator during the accelerating process. The plasma pressure is calculated by means in Dalton's law.     

Application of extraction disks in dissolution tests of clenbuterol and levothyroxine tablets by capillary electrophoresis

Sample preparation procedures using octadecyl (C₁₈) extraction disks were developed to obtain accurate and reproducible results for determinations of clenbuterol (20 μg per dose) and levothyroxine (100 μg per dose) in dissolution media of solid oral dosage forms. Preconcentration of samples allowed final concentrations of 1.1 μg/ml of clenbuterol and 4.0 μg/ml of levothyroxine to be reached prior to CE analysis. The results obtained by CE were in good agreement with those of HPLC. The precision of the migration time, peak area, peak height and accuracy were determined in both intea-day (n = 6) and inter-day (n =18) assays. Linearity was demonstrated over the ranges 0.5–80.0 μg/ml of clenbuterol and 1.0–30.0 μg/ml of levothyroxine. The mean recoveries were higher than 94.0%, ranging from 50 to 125% levels with respect to dose potencies. The proposed methodology may be generally applied to determine drugs at ng/ml concentrations.     

On the solutions of a functional equation of dhombres

Continuous solutions of the functional equation ?(x?(x)) = (?(x))² for x ∈ [0,∞) have been characterized by Dhombres. They form a simple, two-parametric family and the result can be easily extended to solutions on the whole real line. However, the class of all solutions is much larger. We show that there is a solution ? whose graph has, among others, the full outer two-dimensional Lebesgue measure. It turns out that partial restrictions, like boundedness, monotonicity and/or continuity on a subinterval do not imply the continuity of solutions. In particular, the class of monotonic solutions has interesting properties. We provide some techniques of constructing such solutions and show that, among others, there is a strictly increasing solution ? whose points of discontinuity form a dense set in R.     

Wind tunnel simulation of air pollution dispersion in a street canyon

Physical simulation was used to study pollution dispersion in a street canyon. The street canyon model was designed to study the effect of measuring flow and concentration fields. A method of C02-laser photoacoustic spectrometry was applied for detection of trace concentration of gas pollution. The advantage of this method is its high sensitivity and broad dynamic range, permitting monitoring of concentrations from trace to saturation values. Application of this method enabled us to propose a simple model based on line permeation pollutant source, developed on the principle of concentration standards, to ensure high precision and homogeneity of the concentration flow. Spatial measurement of the concentration distribution inside the street canyon was performed on the model with reference velocity of 1.5 m/s.