The Formulation of Four-Components Practically Perfluorinated Microemulsions

Microheterogeneous systems consisting of sodium perfluorooctanoate ( 1 ), 2, 2, 3, 3, 4, 4, 4-heptafluoro-1-butanol ( 2 ), perfluorohexane ( 3 ) and water, representing the first practically perfluorinated microemulsions based on ionic surfactants have been formulated. A pseudoternary phase diagram shows a central region of turbid or transparent gels and two regions of monophasic systems (O/W- and W/O-microemulsions) which have been characterized by NMR. spectroscopy.     

Colourful and Fractional (p,q)-theorems

Let p≥q≥d+1 be positive integers and let ${\mathcal{F}}$ be a finite family of convex sets in ${\mathbb{R}}^{d}$ . Assume that the elements of ${\mathcal{F}}$ are coloured with p colours. A p-element subset of ${\mathcal{F}}$ is heterochromatic if it contains exactly one element of each colour. The family ${\mathcal{F}}$ has the heterochromatic (p,q)-property if in every heterochromatic p-element subset there are at least q elements that have a point in common. We show that, under the heterochromatic (p,q)-condition, some colour class can be pierced by a finite set whose size we estimate from above in terms of d,p, and q. This is a colourful version of the famous (p,q)-theorem. (We prove a colourful variant of the fractional Helly theorem along the way.) A fractional version of the same problem is when the (p,q)-condition holds for all but an α fraction of the p-tuples in ${\mathcal{F}}$ . We show that, in the case that d=1, all but a β fraction of the elements of ${\mathcal{F}}$ can be pierced by p?q+1 points. Here β depends on α and p,q, and β→0 as α goes to zero.     

Oxidation of Tyrosine Photoinduced by Pterin in Aqueous Solution

Pterins, heterocyclic compounds widespread in biological systems, accumulate in the skin of patients suffering from vitiligo, a chronic depigmentation disorder. Pterins have been previously identified as good photosensitizers under UV‐A irradiation. In this work, we have investigated the ability of pterin (Ptr), the parent compound of oxidized pterins, to photosensitize the oxidation of tyrosine (Tyr) in aqueous solutions. Tyr is an important target in the study of the photodynamic effects of UV‐A radiation because it is oxidized by singlet oxygen (¹O₂) and plays a key role in polymerization and cross‐linking of proteins. Steady UV‐A irradiation of solutions containing Ptr and Tyr led to the consumption of Tyr and dissolved O₂, whereas the Ptr concentration remained unchanged. Concomitantly, hydrogen peroxide (H₂O₂) was produced. By combining different analytical techniques, we could establish that the mechanism of the photosensitized process involves an electron transfer from Tyr to the triplet excited state of Ptr. Mass spectrometry, chromatography and fluorescence were used to analyze the photoproducts. In particular, oxygenated and dimeric compounds were identified.     

Infrared cut-off proposal for the holographic density

We propose an infrared cut-off for the holographic dark energy, which besides the square of the Hubble scale also contains the time derivative of the Hubble scale. This avoids the problem of causality which appears using the event horizon area as the cut-off, and solves the coincidence problem.