Elliptic systems with nonlinearity q greater or equal than two with controlled growth. Global Hölder continuity of solutions to the Dirichlet problem

Hölder regularity up to the boundary of the solutions to the Dirichlet problem for second order elliptic systems with nonlinearity q>2 and with controlled growth is proved when n?q+2.     

Positive solutions for a quasilinear degenerate elliptic equation inR n

In questa nota proviamo un teorema di esistenza di soluzioni positive su tuttoR ⁿ della equazionediv(|Du| ^p?2Du)+f(u)=0.     

Metodi variazionali nello studio di problemi al contorno con parte non lineare discontinua

The main purpose of this paper is to use variational methods in the study of problems of following type: $$\left\{ {\begin{array}{*{20}c} {Lu = \lambda f(x,u) in \Omega } \\ {u = 0 on \partial \Omega } \\ \end{array} } \right.$$ Here Ω is supposed to be a bounded domain with smooth boundary ? Ω,L an elliptic operator, λ∈IR andf(x, t) a real function defined on \(\tilde \Omega \times IR\) having one or several simple discontinuities ont. Mainly we are interested in solutions which satisfy (.) a. e., which are most meaningful in physical problems, and we prove various existence theorems for several choices ofL, f and λ. The main difficulty consists in the fact that the functionals related to (.) are not Fréchet differentiable in every point, sincef is discontinuous.     

Reductive lithiation of alkoxy-substituted benzyl methyl ethers and connection with cross-coupling reactions

2-and 4-Ethoxymethoxybenzyl methyl ethers were employied as useful starting materials for the synthesis of 1,2- or 1,4-dicarbo-substituted benzenes. The proposed reaction sequence involves connection between the reductive lithiation of benzyl alkyl ethers and the metal-catalyzed cross-coupling reaction of aromatic triflates.     

Quantification methods of amorphous/crystalline fractions in high-energy ball milled pharmaceutical products

In this work, thermoanalytical, diffractometry, and microscopy measurements have been performed in order to characterize the effect of high energy milling on a drug active in the migraine prophylaxis and smoke cessation. We can assert that the mechanical treatment induces only a partial amorphisation of the solid phase, in particular it reduces the crystal order by producing lattice defects which propagate from the surface to the bulk crystal. For this reason, the DSC is able to detect the presence of ordered solid, while the powder X-ray diffractometry, because of its low penetration depth, does not reach the crystalline core of the particles.     

Studies on crude oil‐water biphasic mixtures by low‐field NMR

Low‐field ¹H NMR was used in this work for the analysis of mixtures involving crude oils and water. CPMG experiments were performed to determine the transverse relaxation time (T₂) distribution curves, which were computed by the inverse Laplace transform of the echo decay data. The instrument's ability of quantifying water and petroleum in biphasic mixtures following different methodologies was tested. For mixtures between deionized water and petroleum, one achieved excellent results, with root mean squared error of cross‐validation (RMSECV) of 0.8% for a regression between the water content (wt %) and the relative area of the water peak in the T₂ distribution curve, or a standard deviation of 0.9% for the relationship between the water content and the relative water peak area, corrected by the relative hydrogen index of the crude. In the case of biphasic mixtures of Mn²⁺‐doped water and crude oils, the best result of RMSECV = 1.6% was achieved by using the raw magnetization decay data for a partial least squares regression. Copyright © 2012 John Wiley & Sons, Ltd.     

CHIRAL VARIANTS OF ARYLALKYL SULFUR REAGENTS. (R)-CAMPHOR KETIMINES OF OGIOVANNA AMINOTHIOETHERS AND OXIDES

Abstract

Ketimines la-d derived from ortho-aminosubstituted phenylthioethers were prepared in order to determine the degree of chirality transfer from the chiral auxiliary to the sulfur atom in the formation of the sulfoxide or to the α-carbon atom in the reaction of the anion with alkyl halides or benzaldehyde. Oxidation to the sulfoxide occurred with little or no asymmetric induction. The crystalline benzyl sulfone 4c was deprotonated by alkyllithium or Grignard reagents and reacted with alkyl halides and benzaldehyde, in all cases with little to fair transfer of chirality. The major diastereoisomer from methylation of the anion of 4c with methyl iodide, was isolated, and afforded the enantiomerically pure amine 5 after removal of the chiral auxiliary. An X-ray structure determination of 4d allowed the assignment of the absolute configuration of the asymmetric carbon and revealed that the conformation of the ketimine in the crystal state is not homogeneous.     

Probenecid and benzamide: DSC applied to the study of an “impossible” pharmaceutical system

Journal of Thermal Analysis and Calorimetry - The study of the binary system probenecid–benzamide is an excellent example of the power and the limits of thermal analysis applied to the...