Existence of strong minimizers for the Griffith static fracture model in dimension two

We consider the Griffith fracture model in two spatial dimensions, and prove existence of strong minimizers, with closed jump set and continuously differentiable deformation fields. One key ingredient, which is the object of the present paper, is a generalization to the vectorial situation of the decay estimate by De Giorgi, Carriero, and Leaci. This is based on replacing the coarea formula by a method to approximate $SB{D}^p$ functions with small jump set by Sobolev functions, and is restricted to two dimensions. The other two ingredients will appear in companion papers and consist respectively in regularity results for vectorial elliptic problems of the elasticity type and in a method to approximate in energy $GSB{D}^p$ functions by $SB{V}^p$ ones.     

A rapid and sensitive UHPLC–MS/MS method for the determination of celosin A in rat plasma with application to pharmacokinetic study

Celosin A (CA), a natural compound isolated from Celosia argentea L., has been shown significant hepatoprotective effect on AHNP‐induced liver injury. This study described a rapid and sensitive ultra‐high‐pressure liquid chromatography–tandem mass spectrometry (UHPLC–MS/MS) assay for determination of CA in rat plasma. Methanol‐mediated precipitation was used for sample pretreatment. Chromatographic separation was achieved on a T3 column with gradient elution using water and acetonitrile as mobile phase. Determination was obtained using an electrospray ionization source in negative selected reaction monitoring mode at the transitions of m/z 793.3 → m/z 661.2 and m/z 955.6 → m/z 793.2 for CA and IS, respectively. The assay was linear over the concentration range 0.25–2500 ng/mL (r > 0.995) with a lowest limit of quantification (LLOQ) of 0.25 ng/mL. The intra‐ and inter‐day precisions (RSD) were 1.65–9.84 and 2.46–13.49%, respectively, while accuracy (RR) ranged from 96.21 to 99.45%, respectively. The recovery ranged from 95.09 to 102.22% and the matrix effect from 98.29 to 100.13%. The analyte was stable under the tested storage conditions. The method has been successfully applied to a preclinical pharmacokinetic study in rats after a single intravenous (2 mg/kg) or oral (50 mg/kg) administration. The oral bioavailability of CA was ~1.94%; in addition, there was no difference between male and female rats. This is the first time of the use of an UHPLC–MS/MS method for determination of CA concentration in rat plasma and for evaluation of its pharmacokinetic behavior.     

Structural and luminescence characteristics of CuAlxIn1−xSe2 (0 < x ≤ 0.30) chalcopyrite solid solutions

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On images of locally finite derivations and E-derivations

Some cases of the LFED Conjecture, proposed by the second author [15], for certain integral domains are proved. In particular, the LFED Conjecture is completely established for the field of fractions $k(x)$ of the polynomial algebra $k[x]$, the formal power series algebra $k[[x]]$ and the Laurent formal power series algebra $k[[x]][x^{?1}]$, where $x=(x_1,x_2,\dots ,x_n)$ denotes n commutative free variables and k a field of characteristic zero. Furthermore, the relation between the LFED Conjecture and the Duistermaat–van der Kallen Theorem [3] is also discussed and emphasized.     

On the limit Sobolev regularity for Dirichlet and Neumann problems on Lipschitz domains

We construct a bounded C¹ domain Ω in for which the regularity for the Dirichlet and Neumann problems for the Laplacian cannot be improved, that is, there exists f in such that the solution of in Ω and either on or on is contained in but not in for any . An analogous result holds for Sobolev spaces with .     

A note on the eigenvalues of p‐fractional Hardy–Sobolev operator with indefinite weight

In this article, we study the eigenvalues of p‐fractional Hardy operator where , , , and Ω is an unbounded domain in with Lipschitz boundary containing 0. The weight function V may change sign and may have singular points. We also show that the least positive eigenvalue is simple and it is uniquely associated to a nonnegative eigenfunction. Moreover, we proved that there exists a sequence of eigenvalues as .     

Silver chloride supported on Vitamin B1 -Organometallic magnetic catalyst: synthesis,density functional theory study and application in A3-coupling reactions

A highly efficient Fe₃O₄@VitB₁–Ag(I) magnetic catalyst has been obtained using surface modification of Fe₃O₄. To this end, silver chloride was immobilized on Fe₃O₄ nanoparticles via vitamin B₁ biomolecules. The synthesized biocompatible magnetic catalyst was applied in an A³-coupling reaction in the presence of aldehyde, amine and phenyl acetylene under solvent-free conditions and afforded the desired products in excellent yields. Also, interactions between metal and ligand in the Fe₃O₄@VitB₁–Ag(I) were studied using theoretical calculations.     

New insights into the extraction of uranium(VI) by an N,N-dialkylamide

This paper presents the methodology developed in order to thoroughly characterise a solvent extraction system containing high solute concentrations. The chemical system selected is N,N-(2-ethylhexyl)isobutyramide (DEHiBA) diluted in one alkane with increasing concentration of uranium(VI). Combining experiments with theoretical calculations allowed a deeper understanding of the extraction mechanism. A thermodynamic study was performed by the classical van't Hoff method and also by direct calorimetry to provide the enthalpies of extraction and specific heats. Dedicated methods like vapour pressure osmometry and electrospray ionisation mass spectrometry analysis provide information about the stoichiometry of the extracted species. Spectroscopic investigations with ultraviolet–visible and Fourier transform infrared probed the uranium coordination. Finally, a combination of molecular dynamics simulations, and small and wide-angle X-ray scattering experiments investigated the organisation in the organic phase beyond the molecular scale. It was shown that the high concentrations of uranium extracted have no influence on the stoichiometry of the complexes and the coordination of uranium in the inner sphere. The thermodynamic properties related to the extraction process and obtained with a fine consideration of the activity coefficients showed to be the same as those found with trace concentration. However, an unexpected organisation beyond the molecular scale was observed with an important role of nitrates as bridging ligands which could explain some physico-chemical properties. This approach could be applied to other chemical systems (other N,N-dialkylamides or other cations) to identify the origin of the different affinities between ligands and the difference of selectivity between cations.