Local Convergence Properties of Douglas–Rachford and Alternating Direction Method of Multipliers

The Douglas–Rachford and alternating direction method of multipliers are two proximal splitting algorithms designed to minimize the sum of two proper lower semi-continuous convex functions whose proximity operators are easy to compute. The goal of this work is to understand the local linear convergence behaviour of Douglas–Rachford (resp. alternating direction method of multipliers) when the involved functions (resp. their Legendre–Fenchel conjugates) are moreover partly smooth. More precisely, when the two functions (resp. their conjugates) are partly smooth relative to their respective smooth submanifolds, we show that Douglas–Rachford (resp. alternating direction method of multipliers) (i) identifies these manifolds in finite time; (ii) enters a local linear convergence regime. When both functions are locally polyhedral, we show that the optimal convergence radius is given in terms of the cosine of the Friedrichs angle between the tangent spaces of the identified submanifolds. Under polyhedrality of both functions, we also provide conditions sufficient for finite convergence. The obtained results are illustrated by several concrete examples and supported by numerical experiments.     

In situ Raman and UV-vis spectroscopic studies of polypyrrole and poly(pyrrole-2,6-dimethyl-β-cyclodextrin)

Polypyrrole (PPy) and poly(pyrrole-2,6-dimethyl-β-cyclodextrin) [P(Py-β-DMCD)] films prepared by potential cycling in aqueous acidic solutions on indium tin oxide (ITO)-coated glass and gold electrodes were studied by in situ UV-vis and Raman spectroscopy. Characteristic UV-vis and Raman bands were identified and their dependencies on the electrode potential have been discussed. Spectroelectrochemical results reveal differences both in the position of the spectral bands and their potential dependence for PPy and P(Py-β-DMCD) films indicating interactions between polymer chains and CDs during electropolymerization process. The films were also characterized by cyclic voltammetry and FT-IR spectroscopy.     

Catalytic study of the copper-based magnetic nanocatalyst on the aerobic oxidation of alcohols in water

A copper-based magnetic nanocatalyst has been prepared by co-precipitation method and characterized by FESEM, EDS, TEM, XRD, XRF, ICP–OES, FTIR, and BET analysis. This new nanocatalyst displays a good activity toward the aerobic oxidation of a wide range of alcohols in water. Moreover, it is recyclable up to five following runs by simple filtration without any significant loss of its catalytic activity.

     

Study of kinetic,thermodynamic, and isotherm of Sr adsorption from aqueous solutions on graphene oxide (GO) and (aminomethyl)phosphonic acid–graphene oxide (AMPA–GO)

Journal of Radioanalytical and Nuclear Chemistry - In this work, graphene oxide (GO) and (aminomethyl)phosphonic acid–Graphene oxide (AMPA–GO) adsorbents were prepared by the modified...     

Ab initio and density functional theory studies of peri- and regioselectivity in 1,3-dipolar cycloaddition reaction of 1,2-diazepine with nitrile oxide

The first systematic study of all dipolarophile sites of 1,2-diazepine towards nitrile oxide as dipole via 1,3-dipolar cycloaddition reactions has been carried out. To this end, the structural and energetic aspects of seventy-two isomers were determined by means of ab initio and density functional theory methods at different levels of accuracy were performed on all peri- and regio-isomeric forms. The agreement between the calculated and the experimental geometries, regio- and periselectivity of the studied reaction is good in all instances. The dipole condensation with the norcaradiene dipolarophile has been considered seemingly for the first time. The bis-cycloadduct 3a,3b,7,10a-tetrahydro-10 H-[1,2] oxazolo [4,5-d] [1,2,4] oxadiazolo [4,5-b] [1,2] diazepine is the most stable one as predicted by all methods used in this work. However, the tautomerization study of all forms of 1,2-diazepine seems to rule out the existence of the tautomeric form that provides the above mentioned cycloadduct. Consequently, the bis-cycloadduct 5,10-dioxa-1,2,4,11-tetrazatricyclo[7,3,1,0^2,6]trideca-3,7,11-triene is the favored product of this reaction.     

Formation of negative oxidation states of platinum and gold in redox ionic liquid: Electrochemical evidence

The electrochemical reduction of noble metal electrodes in the presence of redox ionic liquid, 1-ferrocenylethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide, [FcEMIM][TFSI], was investigated by cyclic voltammetry. Our experiments suggest the formation of metal with negative oxidation states, in the cases of platinum and gold electrodes [M_n⁻, FcEMIM⁺]. By analogy with the previous work, the formation of these phases is concomitant with the insertion of the supporting electrolyte; which correspond in our experimental condition to the redox cation of the ionic liquid. As an exciting result, the electrochemical investigations of the reduced electrode in electrolytic solution, containing solvent and supporting electrolyte, evidence the presence of the ferrocene groups at the electrode surface. Moreover, the reduced electrode exhibits the presence of the ferrocene even after, contact with air, after ultrasound, and after physical polishing, highlighting the large stability of this organo-metallic phases formed in this media. The AFM investigations demonstrate the morphological change of the platinum surface after the reduction process. Finally, our works bring a formal electrochemical proof of the presence of the ionic liquid cation inside the electrode material after the cathodic treatment in this media.     

Excess molar volume and viscosity deviation for binary mixtures of polyethylene glycol dimethyl ether 250 with 1,2-alkanediols (C3–C6) at T = (293.15 to 323.15) K

In this work, density and viscosity have been determined for (polyethylene glycol dimethyl ether 250 + 1,2-propanediol, or 1,2-butanediol, or 1,2-pentanediol, or 1,2-hexanediol) binary systems over the whole concentration range at temperatures of (293.15, 303.15, 313.15, 323.15) K and atmospheric pressure. Experimental data of mixtures were used to calculate the excess molar volumes V^E, and viscosity deviations Δη. These results were fitted by the Redlich–Kister polynomial relation to obtain the coefficients and standard deviations.