The Ramsey property for Banach spaces and Choquet simplices,and applications

We show that the class of finite-dimensional Banach spaces and the class of finite-dimensional Choquet simplices have the Ramsey property. As an application, we show that the group $\mathrm{Aut}(\mathbb{G})$ of surjective linear isometries of the Gurarij space $\mathbb{G}$ is extremely amenable, and that the canonical action $\mathrm{Aut}(\mathbb{P})?\mathbb{P}$ is the universal minimal flow of the group $\mathrm{Aut}(\mathbb{P})$ of affine homeomorphisms of the Poulsen simplex $\mathbb{P}$. This answers questions of Melleray–Tsankov and Conley–Törnquist.     

Topical Photodynamic Therapy Using Different Porphyrin Precursors Leads to Differences in Vascular Photosensitization and Vascular Damage in Normal Mouse Skin

Different distributions of hexyl aminolevulinate (HAL), aminolevulinic acid (ALA) and methyl aminolevulinate (MAL) in the superficial vasculature are not well studied but they are hypothesized to play an important role in topical photodynamic therapy (PDT). The colocalization of fluorescent CD31 and protoporphyrin IX (PpIX) was calculated using confocal microscopy of mouse skin sections to investigate the vascular distribution after topical application. Vascular damage leads to disruption of the normal endothelial adherens junction complex, of which CD144 is an integral component. Therefore, normal CD31 combined with loss of normal fluorescent CD144 staining was visually scored to assess vascular damage. Both the vascular PpIX concentration and the vascular damage were highest for HAL, then ALA and then MAL. Vascular damage in MAL was not different from normal contralateral control skin. This pattern is consistent with literature data on vasoconstriction after PDT, and with the hypothesis that the vasculature plays a role in light fractionation that increases efficacy for HAL and ALA‐PDT but not for MAL. These findings indicate that endothelial cells of superficial blood vessels synthesize biologically relevant PpIX concentrations, leading to vascular damage. Such vascular effects are expected to influence the oxygenation of tissue after PDT which can be important for treatment efficacy.     

Inertial Manifolds on Squeezed Domains

Let be an arbitrary smooth bounded domain in and > 0 be arbitrary. Squeeze by the factor in the y-direction to obtain the squeezed domain = {(x,y)(x,y)}. In this paper we study the family of reaction-diffusion equations

(2,3)-Generation of SL(n,q).I. cases n=5,6,7

In this paper we prove that the groupws SL(n,q), q=p^m, are factors of the modular groups PSL(2,Z) When n=5,6,7 and P≠2, q≠9     

An algebraic approach to the study of multipartite entanglement

We introduce a simple algebraic approach to the study of multipartite entanglement for pure states together with a class of suitable functionals able to detect the entanglement. On this basis, we reproduce some known results. Indeed, by investigating the properties of the introduced functionals, we show that a subset of such class is strictly connected to the purity. Moreover, we provide a direct and basic solution to the problem of simultaneous maximization of three appropriate functionals for three-qubit states, confirming that the simultaneous maximization of the entanglement for all possible bipartitions is compatible only with the structure of the GHZ states.     

Magnetic properties of jet-printer inks containing dispersed magnetite nanoparticles

Two ferrofluid inks for jet-printing, containing magnetite NPs of slightly different average radius (sample A: 6 nm; sample B: 8 nm) were prepared by adding a dispersion of magnetite nanopowders in n-hexane to an insulating ink. Isothermal magnetization loops of inks were measured by means of a vibrating sample magnetometer in the temperature interval 5–300 K up to 70 kOe. The inks were then ejected at room temperature on standard paper by means of either a thermal ink jet head (TIJ; sample A) or a piezoelectric ink jet head (PIJ; sample B). Magnetic properties of prints on paper (FC/ZFC curves, isothermal magnetic loops and related hysteretic properties) were measured between 10 and 300 K using an alternating gradient force magnetometer up to 20 kOe. The inks display a different magnetic behavior with respect to both prints. In particular, the dispersed NPs are characterized by an effective radius (and ensuing magnetic interaction) larger than expected on the basis of the properties of the starting powders. Instead, the NP radii in both prints are closer to the starting values. The printed magnetic films show an almost perfect superparamagnetic (SP) response around room temperature; however, at temperatures lower than 100 K the SP scaling is not observed and both samples behave as interacting superparamagnetic (ISP) materials. The evolution from the SP to the ISP regime is marked by a steady increase in the hysteretic properties of both samples. Particular attention will be paid to the study of magnetic interactions occurring among NPs. The effect of the ejection process on the degree of aggregation of magnetite NPs will be here studied.     

High-order Levi curvatures and classification results

In this paper we write some differential formulas involving the high-order Levi curvatures of a real hypersurface in a complex space form. As application we get a classification result under suitable assumptions.     

Preparation of Nd:YAG nanopowder in a confined environment

Nanopowder of yttrium aluminum garnet (YAG, Y3Al5O12) doped with neodymium ions (Nd:YAG) was prepared in the water/cetyltrimethylammonium bromide/1-butanol/n-heptane system. Aluminum, yttrium, and neodymium nitrates were used as starting materials, and ammonia was used as a precipitating agent. Coprecipitate hydroxide precursors where thermally treated at 900 degrees C to achieve the garnet phase. The starting system with and without reactants was characterized by means of the small-angle neutron scattering technique. The system, without reactants, is constituted by a bicontinuous structure laying near the borderline with the lamellar phase region. The introduction of nitrates stabilizes the bicontinuous structure, while the presence of ammonia induces a transformation from the bicontinuous phase to a lamellar phase. Nd:YAG nanopowder was characterized by wide-angle X-ray scattering, transmission electron microscopy, gas adsorption, and photoluminescence spectroscopy. By comparison with a sample prepared by the conventional coprecipitation method, the obtained Nd:YAG nanopowder is constituted by smaller crystalline nanoparticles showing a lower tendency to agglomerate. In addition, the nanoparticles present a well-defined spherical shape. Photoluminescence spectroscopy confirms that the doping Nd3+ ions substitute Y3+ ions in the YAG crystalline lattice. The Nd3+ lifetime value, obtained from the luminescence decay curves, was 286 +/- 10 micros, higher than the single-crystal value (255 micros) and much higher than the nanopowder value obtained by the conventional coprecipitation method (75 micros).     

Direct products of finite groups as unions of proper subgroups

We determine all the ways in which a direct product of two finite groups can be expressed as the set-theoretical union of proper subgroups in a family of minimal cardinality.