Extreme points, support points and the Loewner variation in several complex variables

In this paper we consider extreme points and support points for compact subclasses of normalized biholomorphic mappings of the Euclidean unit ball Bn in Cn. We consider the class S0(Bn) of biholomorphic mappings on Bn which have parametric representation, i.e., they are the initial elements f (·, 0) of a Loewner chain f (z, t) = etz + ··· such that {e-tf (·, t)}t 0 is a normal family on Bn. We show that if f (·, 0) is an extreme point (respectively a support point) of S0(Bn), then e-tf (·, t) is an extreme point of S0(Bn) for t 0 (respectively a support point of S0(Bn) for t ∈[0, t0] and some t0 > 0). This is a generalization to the n-dimensional case of work due to Pell. Also, we prove analogous results for mappings which belong to S0(Bn) and which are bounded in the norm by a fixed constant. We relate the study of this class to reachable sets in control theory generalizing work of Roth. Finally we consider extreme points and support points for biholomorphic mappings of Bn generated by using extension operators that preserve Loewner chains.     

Design and DNA binding of an extended triple-stranded metallo-supramolecular cylinder

A new tetracationic triple-stranded supramolecular cylinder is prepared from a bis(pyridylimine) ligand containing a diphenylmethane and two ketimine groups in the spacer. The cylinder is longer and slightly wider than the corresponding cylinder containing just diphenylmethane spacers. Inter-strand CH...pi interactions are not observed and this affects the relay of the chiral information within the cylinder; a mixture of rac and meso isomers results, with the meso isomer being the dominant solution species and characterised in the solid state by crystallography. This new cylinder does bind to DNA as confirmed by induced circular dichroism signals in both the metal-to-ligand charge transfer (MLCT) and in-ligand bands of the cylinder. Flow linear dichroism demonstrates that the cylinder binds to DNA in a specific orientation(s) and is consistent with (major) groove-binding as seen for the shorter cylinder. Some DNA bending/coiling is observed but the effect is much less dramatic than observed for the cylinder with diphenylmethane spacers confirming that coiling is not solely a consequence of the tetracationic charge, but rather is related to the precise size and shape of the cylinder.     

Synthesis of nanosized zinc and magnesium chromites starting from PVA–metal nitrate solutions

In this article, we present a detailed study regarding the preparation of nanosized zinc and magnesium chromites starting from a 4% poly(vinyl)alcohol (PVA) aqueous solution and metal nitrates. The controlled thermal treatment of these solutions has permitted the isolation of an intermediary solid product, used as precursor of the preferred mixed oxides: zinc and magnesium chromites. The as-obtained precursors were characterized by FT-IR spectrometry and thermal analysis. FT-IR spectrometry has evidenced the disappearance of the NO₃ ^? anions at 140?°C, due to the redox interaction with PVA. The thermal decompositions of the synthesized precursors were different, as resulted from both thermal analysis and FT-IR spectrometry. Thus, while ZnCrPVA precursor decomposes up to 400?°C with formation of zinc chromite, the precursor MgCrPVA decomposes up to 500?°C, with formation of MgCrO₄ as intermediary amorphous phase. By thermal decomposition of MgCrO₄ at 500?°C, weakly crystallized MgCr₂O₄ powder is obtained. The obtained chromite powders consist of fine nanoparticles with diameters ranging from 10 to 30?nm at 500?°C; on raising the annealing temperature to 1000?°C, chromite particles become octahedral, with diameter up to 500?nm, but with no sign of sintering.     

A DNA-binding copper(I) metallosupramolecular cylinder that acts as an artificial nuclease

The DNA binding of a dicationic pyridylimine-based dicopper(I) metallosupramolecular cylinder is reported together with its ability to act as an artificial nuclease. The cylinder binds strongly to DNA; more strongly than the spherical dication [Ru(phen)(3)](2+) (phen=1,10-phenanthroline), but more weakly than the corresponding tetracationic cylinders. DNA coiling effects are not observed with this dication, in contrast to the situation with the previously reported tetracationic cylinder involving a similar ligand. Linear dichroism (LD) data suggests that the dicopper cylinder binds in a different orientation from that of the tetracationic iron cylinder. Furthermore, the dicopper cylinder shows DNA-cleavage activity in the presence of peroxide. Of particular note is that the cylinder displays a marked and unusual ability to cleave both DNA strands at the same site, probably reflecting its dinuclear nature and possibly its mode of binding to the DNA.     

In vitro antioxidant and in vivo photoprotective effects of an association of bioflavonoids with liposoluble vitamins

A new tendency in cosmetic formulations is the association of botanical extracts and vitamins to improve skin conditions by synergic effects. The objective of this study was to determine the antioxidant activity of associated bioflavonoids, retinyl palmitate (RP), tocopheryl acetate (TA) and ascorbyl tetraisopalmitate (ATIP), as well as their photoprotective effects in preventing increased erythema, transepidermal water loss (TEWL) and sunburn cell formation in hairless mouse skin. The antioxidant activity of solutions containing the association or each substance separately was evaluated in vitro by a chemiluminescence assay. The photoprotective effect was evaluated by means of in vivo tests. Dorsal skin of hairless mice was treated daily by topical applications for 5 days with formulations containing or not containing (vehicle) the flavonoid-vitamins association (5%). The skin was irradiated (UVA/B) 15 minutes after the last application. The results showed that bioflavonoids had in vitro antioxidant properties and also that when they were associated with vitamins their antioxidant activity was more pronounced. On the other hand, erythema and UV damage to the permeability barrier function (TEWL) was not significantly reduced by previous treatment with the flavonoid-vitamin-association formulations, when compared to the irradiated vehicle-treated area. However, the treatment protected the skin from UV damage because it reduced the number of sunburn cells, when compared to the vehicle-treated area. Finally, the association of vitamins and bioflavonoids added to a dermocosmetic formulation showed a relevant biological activity in terms of photoprotection, because the association of bioflavonoids and vitamins acted by different mechanisms, such as antioxidation and absorption of UV radiation, which suggests its use in antiaging and photoprotective products.     

Vibrational spectroscopy at high pressure of the permanganate anion trapped in potassium bromide and potassium perchlorate matrices

The effect of high pressure on the resonance Raman spectra of the permanganate ion isolated in potassium bromide and potassium perchlorate matrices has been investigated at room temperature for pressures up to 50 kbar. The pressure dependences of the anharmonicity constants and harmonic frequencies have been determined from the overtones of the totally symmetric nu1(A1) mode of the permanganate ion. For both matrices, as the pressure increases, the anharmonicity constants decrease slightly, while the harmonic frequencies increase steadily. The effect of the potassium bromide phase transition from a face-centered to a body-centered structure was observed on the permanganate ion Raman spectrum at approximately 24 kbar. The perchlorate matrix does not exhibit any phase transition under the experimental conditions used in this study.     

A (2 + )-Approximation Scheme for Minimum Domination on Circle Graphs

The main result of this paper is a (2 + )-approximation scheme for the minimum dominating set problem on circle graphs. We first present an O(n²) time 8-approximation algorithm for this problem and then extend it to an time (2 + )-approximation scheme for this problem. Here n and m are the number of vertices and the number of edges of the circle graph. We then present simple modifications to this algorithm that yield (3 + )-approximation schemes for the minimum connected and the minimum total dominating set problems on circle graphs. Keil (1993, Discrete Appl. Math.42, 51–63) shows that these problems are NP-complete for circle graphs and leaves open the problem of devising approximation algorithms for them. These are the first O(1)-approximation algorithms for domination problems on circle graphs.