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.     

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.

     

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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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.     

Parameter identification in nonlocal nonlinear evolution equations

We develop an approximation framework for identifying parameters in a general class of nonautonomous, nonlocal and nonlinear evolution equations. After establishing existence and uniqueness of solutions, we present a convergence theory for Galerkin approximations to inverse problems involving these equations. Our approach relies on the theory of maximal monotone operators in Banach spaces. An application to a nonautonomous nonlinear integral equation arising in heat flow is also discussed.     

Locally Anisotropic Structures and Nonlinear Connections in Einstein and Gauge Gravity

We analyze locally anisotropic configurations modeled by anholonomic frames with associated nonlinear connections in general relativity, affine–Poincarè and/or de Sitter gauge gravity and Kaluza–Klein theories. A suitable geometrical formalism for theories with higher order anisotropies and non compactified extra dimensions is introduced. We give a mostly self–containing review of some aspects of gauge models of gravity and discuss their anholonomic generalizations and the conditions of equivalence with the Einstein gravity in arbitrary dimensions. New classes of cosmological solutions describing Friedmann–Robertson–Walker like universes with resolution ellipsoid or torus symmetry.     

A physical space approach to wave equation bilinear estimates

Bilinear estimates for the wave equation in Minkowski space are normally proven using the Fourier transform and Plancherel’s theorem. However, such methods are difficult to carry over to non-flat situations (such as wave equations with rough metrics or connections with non-zero curvature). In this note, we describe an alternative physical space approach which relies on vector fields, energy estimates as well as tube localization, splitting into coarse and fine scales, and induction on scales (in the spirit of Wolff [29], [30]).     

Magnetic cellulosic materials based on TEMPO-oxidized viscose fibers

A simple method for preparation of magnetic cellulose fibers by coating (2,2,6,6-tetramethylpiperidin-1-yl)oxyl (TEMPO)-oxidized viscose with oleic-acid-coated or uncoated, freshly prepared magnetic nanoparticles (MNp) is presented. MNp attachment was facilitated by chemical activation of the cellulose fibers through introduction of negatively charged carboxylic groups using the well-established TEMPO-mediated oxidation protocol. The resulting composite materials preserved the intrinsic properties of the cellulose fibers, but gained notable specific features due to the presence of magnetic nanoparticles. The obtained composite materials were characterized using spectral (Fourier-transform infrared spectroscopy) and microscopic (scanning electron microscopy) methods. Thermogravimetric analyses were carried out to evaluate the thermal stability of the magnetic fibers. The magnetic properties were evaluated using vibrating-sample magnetometry.     

The resolution of the bounded L2 curvature conjecture in general relativity

This paper reports on the recent proof of the bounded L² curvature conjecture. More precisely we show that the time of existence of a classical solution to the Einstein-vacuum equations depends only on the L²-norm of the curvature and a lower bound of the volume radius of the corresponding initial data set.     

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.