Monotonicity of solutions of quasilinear degenerate elliptic equation in half-spaces

We prove a weak comparison principle in narrow unbounded domains for solutions to $-\Delta _p u=f(u)$ in the case $2<p< 3$ and $f(\cdot )$ is a power-type nonlinearity, or in the case $p>2$ and $f(\cdot )$ is super-linear. We exploit it to prove the monotonicity of positive solutions to $-\Delta _p u=f(u)$ in half spaces (with zero Dirichlet assumption) and therefore to prove some Liouville-type theorems.     

Characterisation by liquid chromatography-electrospray tandem mass spectrometry of anthocyanins in extracts of Myrtus communis L. berries used for the preparation of myrtle liqueur

Anthocyanins in extracts of berries of Myrtus communis, prepared following a typical Sardinia myrtle liqueur recipe, were identified and quantified by HPLC coupled with electrospray/tandem mass spectrometry using, respectively, an ion trap and a triple quadrupole mass analyser. The fragmentation patterns of the anthocyanidins were dependent on the MS technique employed, and differed considerably from those previously reported. The anthocyanin profile of five anthocyanin glucosides and four anthocyanin arabinosides, the latter not previously identified in this specie, was specific for myrtle berry extracts. The quantitative compositions of extracts of myrtle berries derived from different geographical areas in Italy were compared.     

Tuning the Adsorption Properties of Isoreticular Pyrazolate-Based Metal-Organic Frameworks through Ligand Modification

Two isoreticular series of pyrazolate-based 3D open metal-organic frameworks, MBDP_X, adopting the NiBDP and ZnBDP structure types [H(2)BDP = 1,4-bis(1H-pyrazol-4-yl)benzene], were synthesized with the new tagged organic linkers H(2)BDP_X (X = -NO(2), -NH(2), -OH). All of the MBDP_X materials have been characterized through a combination of techniques. IR spectroscopy proved the effective presence of tags, while X-ray powder diffraction (XRPD) witnessed their isoreticular nature. Simultaneous TG/DSC analyses (STA) demonstrated their remarkable thermal stability, while variable-temperature XRPD experiments highlighted their high degree of flexibility related to guest-induced fit processes of the solvent molecules included in the channels. A structural isomer of the parent NiBDP was obtained with a sulfonate tagged ligand, H(2)BDP_SO(3)H. Structure solution from powder diffraction data collected at three different temperatures (room temperature, 90, and 250 °C) allowed the determination of its structure and the comprehension of its solvent-related flexible behavior. Finally, the potential application of the tagged MOFs in selective adsorption processes for gas separation and purification purposes was investigated by conventional single component adsorption isotherms, as well as by advanced experiments of pulse gas chromatography and breakthrough curve measurements. Noteworthy, the results show that functionalization does not improve the adsorption selectivity (partition coefficients) for the resolution of gas mixtures characterized by similar high quadrupole moments (e.g., CO(2)/C(2)H(2)); however, the resolution of gas mixtures containing molecules with highly differentiated polarities (i.e., N(2)/CO(2) or CH(4)/CO(2)) is highly improved.     

Temperature effects on the fluorescence of indolic molecules in polar solvents. Anomalous stokes shift

The fluorescence Stokes shift of polar solutions of indole is explained on the basis of the interaction of solute-solvent hydrogen-bonded complexes with their polar cages. Temperature dependence of N-methylindole versus indole fluorescence is used in this study.     

Barbier-type diastereoselective allylation of alpha-amino aldehydes with an enantiopure 2-sulfinylallyl building block.

An optimized procedure for the diastereoselective allylation under aqueous Barbier conditions of a series of alpha-amino aldehydes with our new chiral building block (S(s))-3-chloro-2-(p-tolylsulfinyl)-1-propene [(S(s))-1a] to afford enantiomerically pure sulfinylamino alcohols in good yields and diastereoselectivites is reported. High levels of diastereoinduction can be achieved from alpha-amino aldehydes configurationally related to natural alpha-amino acids.     

Liquid chromatography/tandem mass spectrometry of unusual phenols from Yucca schidigera bark: comparison with other analytical techniques

Qualitative and quantitative analyses of phenolic compounds are of interest for both medicinal and food plants. In the present work, the phenolic fraction from Yucca schidigera, a plant bearing the GRAS (Generally Recognized as Safe) label approved by the US Food and Drug Administration, was studied. Crude extracts of Y. schidigera bark were investigated by liquid chromatography/UV spectrophotometry with diode-array detection, liquid chromatography/electrospray ionization mass spectrometry (LC/ESI-MS) and liquid chromatography/electrospray ionization tandem mass spectrometry (LC/ESI-MS/MS), in order to develop and optimize simple and rapid techniques to determine both stilbenes and yuccaols for the purposes of quality control of collected material. With optimal LC and MS conditions, stilbenes and yuccaols were quantified with all the proposed methods and the results were compared. Sensitivity was evaluated and the results indicated that MS/MS detection in the multiple reaction monitoring mode is easily applicable to this plant and allows the rapid and direct identification and quantification of these peculiar compounds in crude plant extracts.     

On the moving plane method for nonlocal problems in bounded domains

We consider a nonlocal problem involving the fractional Laplacian and the Hardy potential in bounded smooth domains. Exploiting the moving plane method and some weak and strong comparison principles, we deduce symmetry and monotonicity properties of positive solutions under zero Dirichlet boundary conditions.     

Existence and qualitative properties of solutions to a quasilinear elliptic equation involving the Hardy–Leray potential

In this work we deal with the existence and qualitative properties of the solutions to a supercritical problem involving the −_Δp(⋅)$-{\mathrm{\Delta }}_p(\cdot )$ operator and the Hardy–Leray potential. Assuming 0∈Ω$0\in \Omega$, we study the regularizing effect due to the addition of a first order nonlinear term, which provides the existence of solutions with a breaking of resonance. Once we have proved the existence of a solution, we study the qualitative properties of the solutions such as regularity, monotonicity and symmetry.