A new regularization of equilibrium problems on Hadamard manifolds: applications to theories of desires

In this paper, we introduce a new proximal algorithm for equilibrium problems on a genuine Hadamard manifold, using a new regularization term. We first extend recent existence results by considering pseudomonotone bifunctions and a weaker sufficient condition than the coercivity assumption. Then, we consider the convergence of this proximal-like algorithm which can be applied to genuinely Hadamard manifolds and not only to specific ones, as in the recent literature. A striking point is that our new regularization term have a clear interpretation in a recent “variational rationality” approach of human behavior. It represents the resistance to change aspects of such human dynamics driven by motivation to change aspects. This allows us to give an application to the theories of desires, showing how an agent must escape to a succession of temporary traps to be able to reach, at the end, his desires.

     

Hair color changes and protein damage caused by ultraviolet radiation

Ultraviolet and visible radiations are known to damage hair. However, quantitative data relating damage to hair type, proteins and color to the radiation wavelength are missing. We studied the effect of UV plus visible, UVA plus visible, visible mercury-vapor lamp radiation and sunlight on (blended) virgin dark-brown, blond and red hair and (one head) virgin black and curly dark-brown hair. All hair types showed a substantial increase in protein loss in water after lamp and sun irradiation. The damaging effect of UVB was about 2-5 times higher than that of UVA plus visible radiation, depending on the hair type. Significant color changes were also observed in every hair type, after lamp and sun irradiation, being more pronounced for the light colored hairs. The luminosity difference parameter was the major contributor to the hair color changes, but significant changes in the red-green and yellow-blue parameters of every hair were observed. In this case, the damaging effect is ascribable mainly to UVA radiation. No significant changes in the mechanical properties or topography were observed in any case. We discuss these results in terms of hair type and composition and melanin types.     

The inclusion of rhodium(II)α-methyl-cinnamate in β-cyclodextrin

The preparation and characterization of the 1:1 inclusion compound of rhodium(II) -methyl cinnamate in -cyclodextrin is reported. Evidence of inclusion was obtained from X-ray powder diffraction results, Raman, IR and UV-Vis spectroscopic studies and thermal analysis. Given the potential antitumor activity of the rhodium(II) carboxylate and its virtual insolubility in water, its inclusion in -cyclodextrin opens the possibility for its transference to the aqueous phase.     

Spectrophotometric determination of zinc in copper-base alloys with TAN

TAN reacts with zinc(II) forming a red complex with composition 1:2 Zn(II)-TAN and absorption maximum at 582 nm. Zinc can be determined with this reagent in the presence of Triton X-100, in the pH range 6.20-8.00 with a molar absorptivity of 4.5×10⁴ l/mol/cm Beer's Law was obeyed up to least 1.55 g/ml. Copper interference was eliminated with a mixture of thiosulfate and ascorbic acid and nickel separated by precipitation with dimethylglyoxime. The proposed method was used for zinc determination in several copper-base alloys and the results of analysis in comparison with certified values indicated that the procedure was accurate and precise. A derivative procedure is also proposed, allowing zinc determination with high sensitivity (5-400 ng/ml).     

An Efficient and Simple Entry to N-Substituted beta-Enamino Acid Derivatives from 2-Alkyl-2-oxazolines and 2-Alkyl-2-thiazolines

Reaction of azaenolates of 2-alkyl-oxa(thia)zolines 6 with imidoyl chlorides 7 as electrophiles to furnish masked N-substituted beta-enamino acid derivatives 1-2 in 70-90% yield is described. Alternative routes are discussed. Compounds 1-2 generally appear in one tautomeric form, imino or enamino, depending on the nature of the imidoyl chloride. The configuration of the enamino moiety (Z) and the conformation (s-cis) of compounds 1-2 obtained were established by an NMR study and unequivocally set by nuclear Overhauser effect difference experiments. An X-ray structure of compound 1e is also reported, showing a strong intramolecular NH.N hydrogen bond. Ab initio calculations (HF/3-21G and HF/3-21+G) have been carried out on several representative examples (1e, 1p, and 1l) in an attempt to support and provide the correct geometry of these derivatives. Structural considerations among the possible isomers of compounds 1 are discussed. From these studies it was concluded that the theoretical calculations agree with the experimental results. In addition, a very simple one-pot procedure for the preparation of masked N-substituted alpha-alkylated beta-enamino acid derivatives 2 from 6, 7, and different alkyl halides (R(3)Y) is described.