Positive solutions for nonlinear periodic problems with concave terms

We consider a nonlinear periodic problem, driven by the scalar p-Laplacian, with a parametric concave term and a Carathéodory perturbation whose potential (primitive) exhibits a p-superlinear growth near +∞, without satisfying the usual in such cases Ambrosetti-Rabinowitz condition. Using critical point theory and truncation techniques, we prove a bifurcation-type theorem describing the nonexistence, existence and multiplicity of positive solutions as the parameter varies.     

On the uniqueness of smooth,stationary black holes in vacuum

A fundamental conjecture in general relativity asserts that the domain of outer communication of a regular, stationary, four dimensional, vacuum black hole solution is isometrically diffeomorphic to the domain of outer communication of a Kerr black hole. So far the conjecture has been resolved, by combining results of Hawking [17], Carter [4] and Robinson [28], under the additional hypothesis of non-degenerate horizons and real analyticity of the space-time. We develop a new strategy to bypass analyticity based on a tensorial characterization of the Kerr solutions, due to Mars [24], and new geometric Carleman estimates. We prove, under a technical assumption (an identity relating the Ernst potential and the Killing scalar) on the bifurcate sphere of the event horizon, that the domain of outer communication of a smooth, regular, stationary Einstein vacuum spacetime of dimension 4 is locally isometric to the domain of outer communication of a Kerr spacetime.     

Fractional nonholonomic Ricci flows

We formulate the fractional Ricci flow theory for (pseudo) Riemannian geometries enabled with nonholonomic distributions defining fractional integro-differential structures, for non-integer dimensions. There are constructed fractional analogs of Perelman’s functionals and derived the corresponding fractional evolution (Hamilton’s) equations. We apply in fractional calculus the nonlinear connection formalism originally elaborated in Finsler geometry and generalizations and recently applied to classical and quantum gravity theories. There are also analyzed the fractional operators for the entropy and fundamental thermodynamic values.     

Hetero di- and trinuclear Cu-Gd complexes with trifluoroacetate bridges: synthesis, structural and magnetic studies

The synthesis, structural determinations and magnetic properties of an original dinuclear Cu-Gd and two trinuclear Cu-Ln-Cu complexes (Ln = Gd or Dy) made with a Schiff base ligand and carboxylate ligands are reported. In each complex, the copper and gadolinium or dysprosium ions are linked by a double phenoxo bridge and a eta1:eta1:mu trifluoroacetato bridge. The dinuclear Cu-Gd complex exhibits the usual ferromagnetic interaction while the trinuclear (Cu-Gd-Cu) complexes can not be fitted with a simple Hamiltonian that only takes into account the Cu-Gd interaction. Introduction into the Hamiltonian of a Cu-Cu interaction between the terminal copper ions gives a nice fit in the case of a ferromagnetic Cu-Cu interaction (J'(Cu-Cu) = 8.3 and 9.8 cm(-1)). For the first time, the occurrence of a ferromagnetic interaction between the copper ions of the trinuclear entities is evidenced and supported by the field dependence of the magnetization. As there is no direct proof for the existence of an interaction between two centers through a third magnetic center located in between them, we can conclude that the existence of pi-pi stacking interactions through the phenyl rings of the ligands are responsible for the presence of these interactions.     

A new photoluminescent silica aerogel based on N-hydroxysuccinimide–Tb(III) complex

The paper describes the preparation of a new photoluminescent silica aerogel by embedding a new Tb(III) complex in a silica matrix by using N-hydroxysuccinimide as ligand. The Tb(III) complex prepared at a metal to ligand ratio of 1:3 (mol%) exhibits strong photoluminescence as a result of specific radiative transitions within the Tb(III) cation with the most intense peak located at 543 nm due to ⁵D₄ → ⁷F₅ transition. The synthesized complex was doped in the silica matrix through a catalyzed sol–gel process. After ageing in ethanol, the alcogel was dried under supercritical regime by exchanging the ethanol with liquid carbon dioxide followed by supercritical evaporation. The leaching of the free complex from the alcogel during ageing and solvent exchange phases was found to be minimal most likely due to the interactions between chemical groups of complex with those specific to silica matrix. The obtained regular shaped monolithic aerogel preserved the remarkable photoluminescent properties and also improved the thermal stability of the free complex. Both, the free complex and doped aerogel were characterized through thermal analysis, FT-IR, powder X-ray diffraction, Scanning electron microscopy and fluorescence spectroscopy. For comparison purposes, an undoped silica aerogel was also prepared and investigated through FT-IR, BET analysis and powder X-ray diffraction. The excellent photoluminescent properties might recommend the prepared aerogel for applications in optoelectronic devices where photonic conversion materials are required.     

New high-pressures vapor-liquid equilibrium data for the carbon dioxide + 2-methyl-1-propanol (isobutanol) binary system

New vapor-liquid equilibria (VLE) data at 333.15, 343.15, and 353.15 K and pressures up to 130.0 bar are reported for the carbon dioxide + 2-methyl-1-propanol (isobutanol) system. The experimental method used in this work was a static analytical method with liquid and vapor phases sampling using a rapid online sampler injector (ROLSITM) coupled to a gas chromatograph (GC) for analysis. Measured VLE data and literature data for carbon dioxide + 2-methyl-1-propanol system were modeled with the Soave-Redlich-Kwong (SRK) cubic equation of state with classical van der Waals (two-parameter conventional mixing rule, 2PCMR) mixing rules. A single set of interaction parameters that lead to a correct phase behavior was used in this work to model the new VLE data and critical points of the mixtures in a wide range of temperature and pressure. The SRK prediction results were compared to the new data measured in this study and to available literature data.

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Synthesis,structure and toxicity evaluation of ethanolamine nitro/chloronitrobenzoates: a combined experimental and theoretical study

Background

Nitroaromatic and chloronitroaromatic compounds have been a subject of great interest in industry and recently in medical-pharmaceutic field. 2-Chloro-4-nitro/2-chloro-5-nitrobenzoic acids and 4-nitrobenzoic acid are promising new agents for the treatment of main infectious killing diseases in the world: immunodeficiency diseases and tuberculosis.

Results

New ethanolamine nitro/chloronitrobenzoates were synthesized and characterized by X-ray crystallography, UV–vis, FT-IR and elementary analysis techniques. The toxicity of the compounds prepared and correspondent components was evaluated using Hydractinia echinata as test system. A significant lower toxicity was observed for nitro-derivative compared with chloronitro-derivatives and individual components. Crystallographic studies, together with the chemical reactivity and stability profiles resulted from density functional theory and ab initio molecular orbital calculations, explain the particular behavior of ethanolamine 4-nitrobenzoate in biological test.

Conclusions

The experimental and theoretical data reveal the potential of these compounds to contribute to the design of new active pharmaceutical ingredients with lower toxicity.