Some new extragradient iterative methods for variational inequalities

In this paper, we suggest and analyze some new extragradient iterative methods for finding the common element of the fixed points of a nonexpansive mapping and the solution set of the variational inequality for an inverse strongly monotone mapping in a Hilbert space. We also consider the strong convergence of the proposed method under some mild conditions. Several special cases are also discussed. Results proved in this paper may be viewed as improvement and refinement of the previously known results.     

Synthesis and Characterization of New Thiacalix[4]arenes Bearing Semicarbazide and Thiosemicarbazide Fragments at the Lower Rim

Starting from thiacalixarene tetraacetates, tetraacetohydrazides have been prepared and then used for the introduction of semicarbazide and thiosemicarbazide fragments into the lower rim by the reaction with phenyl isocyanate and phenyl isothiocyanate in dry toluene. The structures of the prepared compounds were investigated by FT‐IR, FAB‐MS, ¹H NMR, and X‐ray crystallography, and their receptor properties were examined by liquid liquid extraction of dichromate anions.     

A New Inexactness Criterion for Approximate Logarithmic-Quadratic Proximal Methods

Recently,a class of logarithmic-quadratic proximal(LQP)methods was intro- duced by Auslender,Teboulle and Ben-Tiba.The inexact versions of these methods solve the sub-problems in each iteration approximately.In this paper,we present a practical inexactness criterion for the inexact version of these methods.     

A modified inexact operator splitting method for monotone variational inequalities

The Douglas–Peaceman–Rachford–Varga operator splitting methods (DPRV methods) are attractive methods for monotone variational inequalities. He et al. [Numer. Math. 94, 715–737 (2003)] proposed an inexact self-adaptive operator splitting method based on DPRV. This paper relaxes the inexactness restriction further. And numerical experiments indicate the improvement of this relaxation.      

A new projection and contraction method for linear variational inequalities

In this paper, we presented a new projection and contraction method for linear variational inequalities, which can be regarded as an extension of He's method. The proposed method includes several new methods as special cases. We used a self-adaptive technique to adjust parameter β at each iteration. This method is simple, the global convergence is proved under the same assumptions as He's method. Some preliminary computational results are given to illustrate the efficiency of the proposed method.     

Reversible photomagnetic properties of the molecular compound [{Cu(bipy)2}2{Mo(CN)8}]·9H2O·CH3OH

The optical and photomagnetic properties of [{Cu^II(bipy)₂}₂{Mo^IV(CN)₈}]·9H₂O·CH₃OH (1) have been reinvestigated. A comparison between spectra in solution and in the solid state revealed the presence of an intervalence band (or Metal–Metal Charge Transfer, hereafter noted MMCT) at 570 nm. The photomagnetic properties have been performed in a Superconducting QUantum Interference Device at 10 K with irradiation in the range of the MMCT: 488 nm, 520 nm and 647 nm at 10 K. An important increase of the magnetic signal has been measured after 1 h of irradiation at 488 nm, whereas a weaker increase has been obtained for the irradiation at 520 nm in the same conditions. Moreover, after an excitation at 488 nm, an irradiation at 647 nm has induced a decrease of the magnetic moment, which corresponds to a partial deexcitation. The complete characterization of the photoproduct has been realised after an irradiation of 4 h at 488 nm. The photomagnetic properties have shown an increase of the paramagnetism of 1 at low temperature. After a thermal heating at 300 K, the material goes back to its initial state before irradiation. It is the first time that a fully reversible photomagnetic behaviour for the compound [{Cu^II(bipy)₂}₂{Mo^IV(CN)₈}]·9H₂O·CH₃OH has been described. The observed properties have been discussed in terms of an electron transfer mechanism Mo → Cu.     

Étude de l'écoulement plan d'un fluide visqueux et incompressible autour et au travers de coques cylindriques poreuses, á faibles nombres de Reynolds

Résumé On étudie par voies numérique et expérimentale l'écoulement plan engendré par la translation uniforme en régime de Stokes d'une coque poreuse cylindrique à mi-distance entre deux parois parallèles. On donne des résultats fiables et détaillés concernant le champ hydrodynamique en formulant avec précision les conditions de raccordement aux interfaces entre le milieu poreux et le milieu fluide.

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The two-dimensionnal flow induced by the uniform translation of a porous shell cylinder midway between two parallel plane walls is investigated, for the Stokes regime, both numerically and experimentally. Reliable and detailed results relative to the hydrodynamic field are given formulating the conditions of junction between porous and fluid media.