Concentration on minimal submanifolds for a singularly perturbed Neumann problem

We consider the equation −ε²Δu+u=up in Ω⊆RN, where Ω is open, smooth and bounded, and we prove concentration of solutions along k-dimensional minimal submanifolds of ∂Ω, for N?3 and for k∈{1,…,N−2}. We impose Neumann boundary conditions, assuming 1<p<(N−k+2)/(N−k−2) and ε→⁰⁺. This result settles in full generality a phenomenon previously considered only in the particular case N=3 and k=1.     

Capillary electrophoretic analysis of sulfur and cyanicides speciation during cyanidation of gold complex sulfidic ores

A capillary electrophoretic protocol for the separation and quantification of the most important species potentially liberated during the cyanidation of gold sulfide‐rich ores was accomplished in this study. The separation of 11 ions: S₂O₃^2–, Cu(CN)₃^2–, Fe(CN)₆^4–, Fe(CN)₆^3–, SCN^–, Au(CN)₂^–, Ag(CN)₂^–, SO₄^2–, OCN^–, SO₃^2–, and HS^– was achieved using an indirect UV detection method. The robustness of the analytical protocol was tested by analyzing ions speciation during the cyanidation of two gold sulfide‐rich ores. The 1‐h cyanidation of the two ores released up to six complexes into solution: S₂O₃^2–, Cu(CN)₃^2–, SCN^–, Fe(CN)₆^4–, OCN^–, and SO₄^2–. The mineralogy of the ore was found to influence directly the nature and the amount of the dissolved species. Conserving the cyanidation solution for 72 h after sampling resulted in 96% total sulfur recovery. These results allow us to conclude that the analytical protocol developed in this study can become very useful for the optimization of precious‐metals cyanidation plants.     

Stark broadening of isolated lines: calculation of the diagonal multiplet factor for complex configurations (n1l1 n n2l2 m n3l3 p)

Owing to the increasing sensitivity of detectors, accurate line profiles are needed for accurate stellar atmospheres modelling and for laboratory and technological plasmas as well. So, Stark broadening parameters of isolated lines of complex atoms and ions within the impact and quasistatic approximation are needed, even if the atomic abundance of the considered element is low. Angular factors of the diagonal line strength entering the quadrupole term appearing in the semi-classical expression of the width of line broadened by electron or ion perturbers, are needed. The aim of this paper is to extend the previous calculations of this diagonal multiplet factor which were obtained for configurations of the type lⁿ and l₁ ⁿl₂ ^m to more complex configurations in LS coupling. To study the Stark broadening of isolated lines in the impact and quasistatic approximation, we use the semi-classical-perturbation treatment, including both dipole and quadrupole contribution in the expansion of the electrostatic interaction between the optical electron and the perturber. We also use the Fano-Racah algebra. Angular factors of the diagonal line strength entering the quadrupole term appearing in the semi-classical expression of the width of line broadened by electron or ion perturbers, are calculated. New diagonal multiplet factor formulae for more complicated configurations such as (n₁l₁ ⁿ(L_nS_n)n₂l₂ ^m(L_mS_m)n₃l₃ ^p(L_pS_p)) are provided. These formulae can enter the computer Stark semi-classical perturbation codes.     

Regioselective bond cleavage in the dissociative electron transfer to benzyl thiocyanates

The electrochemical reduction of benzyl thiocyanate and p-nitrobenzyl thiocyanate was investigated in acetonitrile at an inert electrode. These two compounds reveal a change in the reductive cleavage mechanism, and more interestingly, they show a clear-cut example of a regioselective bond dissociation. Both phenomena may be understood on the basis of the dissociative ET theory and its extension to the formation/dissociation reactions of radical ions. While the effect of the standard oxidation potential of the leaving group seems to be predominant in understanding the change in the ET mechanism by changing the driving force, the regioselective cleavage is dictated by changes in the intrinsic barrier related to the nature of the substituent on the aryl moiety.