Entire radial and nonradial solutions for systems with critical growth

In this paper we establish existence of radial and nonradial solutions to the system

$$\begin{aligned} {\left\{ \begin{array}{ll} \displaystyle -\Delta u_1 = F_1(u_1,u_2) &{}\quad \text {in }{\mathbb R}^N,\\ -\Delta u_2 = F_2(u_1,u_2) &{}\quad \text {in }{\mathbb R}^N,\\ u_1\geqslant 0,\ u_2\geqslant 0 &{}\quad \text {in }{\mathbb R}^N,\\ u_1,u_2\in D^{1,2}({\mathbb R}^N), \end{array}\right. } \end{aligned}$$

where \(F_1,F_2\) are nonlinearities with critical behavior.

     

On the shape factor of interaction laws for a non-local approximation of the Sobolev norm and the total variation

We consider the family of non-local and non-convex functionals introduced by H. Brézis and H.-M. Nguyen in a recent paper. These functionals Gamma-converge to a multiple of the Sobolev norm or the total variation, depending on a summability exponent, but the exact values of the constants are unknown in many cases.We describe a new approach to the Gamma-convergence result that leads in some special cases to the exact value of the constants, and to the existence of smooth recovery families.     

Memoriam to James K. Knowles (1931–2009)

Obituary

Memoriam to James K. Knowles (1931–2009)     

Zinc Oxide Thin Films for Memristive Devices: A Review

Zinc Oxide (ZnO) thin films have been addressed as promising candidates for the fabrication of Resistive Random Access Memory devices, which are alternative to conventional charge-based flash memories. According to the filamentary conducting model and charge trapping/detrapping theory developed in the last decade, the memristive behavior of ZnO thin films is explained in terms of conducting filaments formed by metallic ions and/or oxygen vacancies, and their breaking through electrochemical redox reactions and/or recombination of oxygen vacancies/ions. A comparative review of the memristive properties of ZnO thin films grown by sputtering, atomic layer deposition (ALD), pulsed laser deposition (PLD), and sol-gel methods is here proposed. Sputtered ZnO thin films show promising resistive switching behaviors, showing high on/off ratios (10–10⁴), good endurance, and low operating voltages. ALD is also indicated to be useful for growing conformal ZnO layers with atomic thickness control, resulting in important resistive switching characteristics, such as relatively high on/off ratios and low operating voltages. High insulating epitaxial ZnO thin films can be obtained by PLD, showing reliable switching properties at low voltages and with good retention. On the contrary, the sol-gel approach generally results in ZnO thin films with poor resistive switching behaviors. Nevertheless, thin films derived from ZnO NPs show improved switching performances, with higher on/off ratios and lower operating voltages. Independently of the synthetic approach, doped ZnO thin films exhibit better resistive switching behaviors than pristine ones, coupling a strong increase of the on/off ratio with a more stable switching response.     

On the longitudinal librations of Hyperion

We study a nonlinear, second order ordinary differential equation that models the longitudinal librations of the longest axis L of a satellite with respect to the planet-satellite center line C. Combining theoretical arguments and numerical evidence we prove that, in the case of Hyperion, a satellite of Saturn, the angle A between L and C can change in a chaotic manner at the moments when the distance from Hyperion to Saturn reaches its minimum value. More precisely, given an arbitrary sequence of zeros and ones, we show that there is at least one initial velocity of A such that its successive positions reproduce the given sequence.      

Acute‐phase proteins investigation based on lectins affinity capture prior to 2‐DE separation: Application to serum from multiple sclerosis patients

Plasma acute‐phase proteins (APPs) glyco‐isoforms are important biomarkers of inflammatory processes such as those occurring in multiple sclerosis (MS). Specific analysis of these proteins is often hampered by sample biochemical complexity. The aim of our study was to set up a method to accurately visualize, identify and quantify APPs glyco‐isoforms in human serum. An enrichment strategy based on affinity chromatography using the carbohydrate‐binding proteins concanavalin A (ConA) and erythrina cristagalli lectin (ECL) was applied to pooled serum samples from 15 patients and 9 healthy individuals. Image analysis of 2‐DE detected 30 spots with a fold change higher than 1.5. A total of 14 were statistically significant (p value<0.05): 7 up‐regulated and 7 down‐regulated in MS samples. ESI LC‐Nanospray IT mass spectrometry analysis confirmed that all of them were APPs isoforms supporting the idea that the accurate analysis of differential glycosylation profiles in these biomarkers is instrumental to distinguish between MS patients and healthy subjects. Additionally, overlaps in ConA/ECL maps protein patterns suggest how the used lectins are able to bind sugars harbored by the same oligosaccharide structure. Among identified proteins, the presence of complex and/or hybrid type N‐linked sugar structures is well known. Performing galectin‐3 binding and Western blotting, we were able to demonstrate a correlation between hybrid type glyco‐isoforms of β‐haptoglobin and MS. In conclusion, although the patho‐physiological role of the identified species still remains unclear and further validations are needed, these findings may have a relevant impact on disease‐specific marker identification approaches.     

Enantioseparation of 2-aryloxypropionic acids on chiral porous monolithic columns by capillary electrochromatography. Evaluation of column performance and enantioselectivity

The enantioseparation of 2-aryloxypropionic acids by capillary electrochromatography was tested on columns with a monolithic stationary phase prepared from silanized fused-silica capillaries (100 microm I.D.) by in situ copolymerization of glycidyl methacrylate, ethylene glycol dimethacrylate and methyl methacrylate in the presence of formamide and 1-propanol as the porogen solvents. The porous chiral monolithic stationary phases were prepared by reaction of the epoxy-groups at the surface of the monolith with (+)-1-(4-aminobutyl)-(5R,8S,10R)-terguride. To attain the minimum HETP values for the enantiodiscrimination of 2-phenoxypropionic acid, the influence of the composition of polymerization solution on column total porosity and efficiency was investigated. Optimum mobile phase conditions were found for all analytes tested using acetonitrile-methanol mixtures containing triethylamine and acetic acid as the buffer components. Furthermore, the chemical and mechanical stabilities of the columns were satisfactory, allowing hundreds of analyses.     

Single and double pH-driven Cu2+ translocation with molecular rearrangement in alkyne-functionalized polyamino polyamido ligands

A new series of ligands, containing one (L1H(2)-L4H(2)) or two (L5H(4)-L6H(4)) 1,4,8,11-tetraaza-5,7-dione units and functionalized with a propargyl group on the C atom between the C=O moieties, has been synthesized. Protonation constants for the ligands and formation constants of their Cu(2+) complexes have been determined in water, and the coordination geometry of the complexes existing at various pH values has been investigated by coupled pH-metric and spectrophotometric titrations. Ligands capable of simple uptake of Cu(2+) with the formation of neutral, square-planar complexes containing the -2-charged diamino-diimido donor sets and ligands containing further coordinating groups (quinoline or pyridine) capable of single and double cation translocation have been investigated. The role of the substituents on the amino groups and the structural role played by the propargyl group have been examined as regards Cu(2+) complexation and translocation. In the double-translocating ligand L6H(4), when the two Cu(2+) ions move inside the diamino-diamido donor set, the slim propargyl group allows an unprecedented folding of the whole ligand with apical coordination of one pyridine to form a five-coordinate, square-pyramidal Cu(2+) ion. The crystal and molecular structures of this unusual [L6Cu(2)] complex have been determined by X-ray diffraction. Finally, oxidation of Cu(2+) to Cu(3+) has been studied by cyclic voltammetry in water, which revealed that the redox reaction occurs only when the copper cation is within the diamino-diimido compartment. Moreover, both functionalization of the primary amines with bulky substituents and apical coordination of Cu(2+) make access to the 3+ oxidation state more difficult and disrupt the reversibility of the electrochemical process.     

Supramolecular hybrids of [60]fullerene and single-wall carbon nanotubes

Noncovalent interactions between purified HiPCO single-wall carbon nanotubes (SWNT) and a [60]fullerene-pyrene dyad, synthesized through a regioselective double-cyclopropanation process, produce stable suspensions in which the tubes are very well dispersed, as evidenced by microscopy characterization. Cyclic voltammetry experiments and photophysical characterization of the suspensions in organic solvents are all indicative of sizeable interactions of the pyrene moiety with the SWNT and, therefore, of the prevalence in solution of [60]fullerene-pyreneSWNT hybrids.     

Dynamically induced effective interaction in periodically driven granular mixtures

We show that a granular mixture subject to horizontal oscillations can be reduced to a monodisperse system of particles interacting via an effective interaction. This interaction is attractive at short distances and strongly anisotropic, and its features explain the system rich phenomenology, including segregation and stripe pattern formation. Finally, we show that a modified Cahn-Hilliard equation, which takes into account the characteristics of the effective interaction, is capable of describing the dynamics of the mixture.