Self-adaptive methods for mixed quasi-variational inequalities

It is well known that the variational inequalities involving the nonlinear term φ are equivalent to the fixed-point problems and the resolvent equations. In this paper, we use these alternative equivalent formulations to suggest and analyze some new self-adaptive iterative methods for solving mixed quasi-variational inequalities. Our results can be viewed as significant extensions of the previously known results for mixed quasi-variational inequalities. An example is given to illustrate the efficiency of the proposed method.     

A self-adaptive method for solving general mixed variational inequalities

The general mixed variational inequality containing a nonlinear term φ is a useful and an important generalization of variational inequalities. The projection method cannot be applied to solve this problem due to the presence of the nonlinear term. To overcome this disadvantage, Noor [M.A. Noor, Pseudomonotone general mixed variational inequalities, Appl. Math. Comput. 141 (2003) 529-540] used the resolvent equations technique to suggest and analyze an iterative method for solving general mixed variational inequalities. In this paper, we present a new self-adaptive iterative method which can be viewed as a refinement and improvement of the method of Noor. Global convergence of the new method is proved under the same assumptions as Noor's method. Some preliminary computational results are given.     

Hypersurfaces compactes d'un fibré vectoriel riemannien à courbure moyenne prescriteCompact hypersurfaces of a Riemannian vector bundle with prescribed mean curvature

Let M be a compact Riemannian manifold, E a Riemannian vector bundle on M and Σ the sphere subbundle of E. We look for embeddings of Σ into E admitting prescribed mean curvatures of various types. To cite this article: P. Cherrier, A. Hanani, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 525–528.     

Global solutions and self-similar solutions of semilinear wave equation

We prove existence, uniqueness and regularity results for the global solutions of the semilinear wave equations. In particular, we show existence of regular self-similar solutions. Also, we build some finite-energy asymptotically self-similar solutions. Received: 20 September 1999; in final form: 10 May 2000 / Published online: 25 June 2001     

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.     

A regiodivergent synthesis of ring a C-prenylflavones

Capitalizing on the use of orthogonal protecting groups and the development of a modified Robinson flavone synthesis that avoids harsh acidic conditions, a regioselective synthesis of 6- and 8-prenylflavones from the same prenylated disilylated phloracetophenone (9) has been developed, targeting cannflavin B (1d), the COX-inhibiting principle of marijuana, and its unnatural isomer isocannflavin B (1e) as model compounds.     

Dynamic near three-to-one internal resonance in composite stiffened panels

Nonlinear dynamic of composite stiffened panels to parametric and three-to-one internal resonances is investigated. The ordinary differential equation of two mode shapes is established by using Galerkin method and the condition of three-to-one internal resonance between the first mode (1,3) and the second mode (3,1) is examined near the principal resonance 2:1 of the first mode. Then, the nonlinear behavior of the two buckling mode shapes is analyzed using a perturbation analysis. We show the existence of jump phenomena for the two modes indicating a complex dynamic of the structure near the three-to-one internal resonance for the HM Graphite/epoxy materials.     

Novel pyrazoline and pyrazole porphyrin derivatives: synthesis and photophysical properties

2-Vinyl-5,10,15,20-tetraphenylporphyrinatozinc(II) reacts with nitrile imines, generated in situ from ethyl hydrazono-α-bromoglyoxylates, affording the corresponding pyrazolines in good to excellent yields. Treatment of pyrazoline derivatives with DDQ affords the corresponding pyrazole derivatives with moderate to excellent yields. When the hydrolysis of ester group in the pyrazoline derivatives was considered, it was observed the concomitant oxidation of the heterocyclic unit, which allowed directly obtaining porphyrin-pyrazole derivatives with a carboxylic group, in very good yields.The photophysical properties of the pyrazoline and pyrazole porphyrin derivatives show that the influence of the heterocyclic substituents is limited by the tendency of these molecules to aggregate. All other properties and especially the triplet kinetics remain unaffected. The adducts with low tendency to aggregate showed very high singlet oxygen yield, which makes these compounds interesting for their use as photosensitizers for PDT.     

A DFT calculation of electronic structures,magnetic, and thermoelectric properties of the new equiatomic quaternary Heusler alloy RuTiCrSi

The stabilities, mechanical, electronic, and magnetic properties of the new equiatomic quaternary Heusler alloy (EQHA) RuTiCrSi were investigated using the Kohn-Sham DFT (KS-DFT) calculations within the generalized gradient approach (GGA), the modified version of the exchange potential introduced by Becke and Johnson in addition to the GGA (mBJ-GGA), and Heyd-Scuseria-Ernzerhof (HSE06) hybrid functional. The ground-state equilibrium energy reveals that the ferromagnetic with type 2 structure is the more stable. The RuTiCrSi is energetically, mechanically, and dynamically stable. The calculated self-consistent total magnetic moment is 2 μB and agrees well with the Slater-Pauling rule of $M_{\mathrm{t}}=\left|Z_{\mathrm{t}}-24\right|$. The electronic structure results from mBJ-GGA and HSE06 functionals show a half-metallic behavior. A high Curie temperature is obtained using the mean-field approximation. The thermoelectric response was calculated using the semi-classical Boltzmann transport equation under constant relaxation time. The maximum value of Seebeck coefficient is observed at the ambient temperature of $741\mathrm{\mu V}{\mathrm{K}}^{-1}$. It was also observed that the power factor increases significantly as temperature rises. Therefore, the new EQHA RuTiCrSi seems to be a potential candidate for spintronic thermoelectric applications.