A common fixed point theorem with applications to vector equilibrium problems

In this paper, using the Brouwer fixed point theorem, we establish a common fixed point theorem for a family of set-valued mappings. As applications of this result we obtain existence theorems for the solutions of two types of vector equilibrium problems, a Ky Fan-type minimax inequality and a generalization of a known result due to Iohvidov.     

Self-commutator inequalities in higher dimension

Three natural multi-dimensional substitutes for the self-commutator of a Hilbert space operator are introduced and generalizations of Putnam's inequality to tuples of operators with semidefinite self-commutators are indicated. In addition, a Riesz transform model is developed and investigated.

     

Analysis of lumped models with contact and friction

We consider two mathematical models that describe the vibrations of spring-mass-damper systems with contact and friction. In the first model, both the contact and frictional boundary conditions are described with subdifferentials of nonconvex functions. In the second model, the contact is modeled with a Lipschitz continuous function, and the restitution force is described by a differential equation involving a Volterra integral term. The two models lead to second-order differential inclusions with and without an integral term, in which the unknowns are the positions of the masses. For each model, we prove the existence of a solution by using an abstract result for first-order differential inclusions in finite dimensional spaces. For the second model, in addition, we prove the uniqueness of the solution by using a fixed point argument. Finally, we provide examples of systems with contact and friction conditions for which our results are valid.     

Analysis of viscoelastic contact with normal compliance,friction and wear diffusionAnalyse d'un problème viscoélastique avec compliance normale,frottement et diffusion d'usure

We consider a quasistatic problem of frictional contact between a viscoelastic body and a moving foundation. The contact is with wear and is modeled by normal compliance and a law of dry friction. The novelty in the model is that it allows for the diffusion of the wear debris over the potential contact surface. Such kind of phenomena arise in orthopaedic biomechanics and influence the properties of joint prosthesis. We derive a weak formulation of the problem and state that, under a smallness assumption on the problem data, there exists a unique weak solution for the model. To cite this article: M. Shillor et al., C. R. Mecanique 331 (2003).     

Antibunching in the emission of a single tetrachromophoric dendritic system

The photophysics of a dendrimer containing four chromophores are investigated at the single-molecule level. First, the multichromophoric character of single dendrimers' absorption is probed by modulating the linear polarization of the excitation beam. Subsequently, using circular polarization, the same dendrimers are excited, and their fluorescence transients are recorded. Using pulsed excitation in combination with the classical Hanbury-Brown and Twiss coincidence setup the presented data demonstrate that efficient singlet-singlet annihilation ensures that always only one photon is emitted even when several excitations are generated in an individual multichromophoric molecule.     

Nanoporous carbon allotropes by septupling map operations

Spongy carbon nanostructures, also called schwarzites, have been synthesized. They consist of highly connected covalent networks, periodic in the three dimensions of Euclidean space. The intimate structure of schwarzites has a topology of triply periodic minimal surfaces. They can be tessellated by some geometric operations on maps, including the newly proposed septupling operations. Formulas for calculating the lattice parameters of iteratively transformed maps are presented. Examples are given for both finite/closed cages and infinite/open all-sp2 carbon structures. Strain energy calculations for structures, consisting of thousands of atoms, show that such carbon allotropes are very relaxed and approach to the non-strained graphite sheet.     

Polyaniline/Maleic Acid Copolymers Composites: Synthesis and Characterization

Summary: Polyaniline/maleic acid copolymers composites were synthesized by chemical in situ polymerization of aniline using ammonium peroxidisulfate as oxidant, in the presence of water soluble copolymers containing carboxylic groups. Fine dispersions of composite materials, soluble in N,N-dimethylformamide or dimethyl sulfoxide were obtained which can be processed as thin films and membranes for application as proton-conductive materials for electrolyte membranes of fuel cells. The composites were characterized by FTIR spectroscopy and thermal methods.     

Studies regarding the formation from metal nitrates and diol of NiM 2 III O4 spinels, inside a silica matrix

The present study deals with preparation and characterization of spinel mixed oxide systems NiM ₂ ^III O₄, where M^III?=?Fe^III, Cr^III. In order to obtain 50% NiFe₂O₄/50% SiO₂ and 50% NiCr₂O₄/50% SiO₂ nanocomposite, we have used a versatile route based on the thermal decomposition inside the SiO₂ matrix, of some particular precursors, coordination compounds of the involved M^II and M^III cations with dicarboxylate ligands. The ligands form in the redox reaction between metal nitrates mixture and 1,3-propanediol at the heating around 140?°C of the gels (tetraethylorthosilicate?Cmetal nitrates?C1,3-propanediol?Cwater). The as-obtained precursors, embedded in silica gels, have been characterized by FT-IR spectrometry and thermal analysis. Both precursors thermally decompose up to 350?°C leading to the formation of the corresponding metal oxides inside the silica matrix. X-ray diffraction of the annealed powders have evidenced the formation of NiFe₂O₄ starting with 600?°C, and NiCr₂O₄ starting with 400?°C. This behavior can be explained by the fact that, by thermal decomposition of the Fe(III) carboxylate at 300?°C, the spinelic phase ??-Fe₂O₃ is formed, which interacts with the NiO, forming the ferrite nuclei. By thermal decomposition of chromium carboxylate, a nonstoichiometric chromium oxide (Cr₂O_3+x ) is formed. In the range 380?C400?°C, Cr₂O_3+x turns into Cr₂O₃ which immediately interacts with NiO leading to the formation of nickel chromites nuclei inside the pores of silica matrix. Both spinels have been obtained as nanocrystalites homogenously dispersed as resulted from XRD and TEM data.