Sufficient conditions of non‐uniqueness for the Coulomb friction problem

We consider the Signorini problem with Coulomb friction in elasticity. Sufficient conditions of non‐uniqueness are obtained for the continuous model. These conditions are linked to the existence of real eigenvalues of an operator in a Hilbert space. We prove that, under appropriate conditions, real eigenvalues exist for a non‐local Coulomb friction model. Finite element approximation of the eigenvalue problem is considered and numerical experiments are performed. Copyright © 2003 John Wiley & Sons, Ltd.     

On Genuine Bernstein–Durrmeyer Operators

We continue the studies on the so–called genuine Bernstein–Durrmeyer operators U _n by establishing a recurrence formula for the moments and by investigating the semigroup T(t) approximated by U _n . Moreover, for sufficiently smooth functions the degree of this convergence is estimated. We also determine the eigenstructure of U _n , compute the moments of T(t) and establish asymptotic formulas. Received: January 26, 2007.     

The Cosmological Constant in the Framework of Gravito-Magnetodynamic Waves in Weak Gravitational Fields

Using the linearization of Einstein's equations for weak gravitational fields, a specific model of gravito-magnetofluid is elaborated. The study of wave formation and propagation in such a medium is necessarily connected to the existence of the cosmological constant.     

Maximal σ‐polynomials of connected 3‐chromatic graphs

In the set of graphs of order n and chromatic number k the following partial order relation is defined. One says that a graph G is less than a graph H if c_i(G) ≤ c_i(H) holds for every i, k ≤ i ≤ n and at least one inequality is strict, where c_i(G) denotes the number of i‐color partitions of G. In this paper the first ? n/2 ? levels of the diagram of the partially ordered set of connected 3‐chromatic graphs of order n are described. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 210–222, 2003     

Synthesis and characterization of mid‐ and end‐chain functional telechelics by controlled polymerization methods and coupling processes

Well‐defined polystyrene‐ (PSt) or poly(ε‐caprolactone) (PCL)‐based polymers containing mid‐ or end‐chain 2,5 or 3,5‐ dibromobenzene moieties were prepared by controlled polymerization methods, such as atom transfer radical polymerization (ATRP) or ring opening polymerization (ROP). 1,4‐Dibromo‐2‐(bromomethyl)benzene, 1,3‐dibromo‐5‐(bromomethyl)benzene, and 1,4‐dibromo‐2,5‐di(bromomethyl)benzene were used as initiators in ATRP of styrene (St) in conjunction with CuBr/2,2′‐bipyridine as catalyst. 2,5‐Dibromo‐1,4‐(dihydroxymethyl)benzene initiated the ROP of ε‐caprolactone (CL) in the presence of stannous octoate (Sn(Oct)₂) catalyst. The reaction of these polymers with amino‐ or aldehyde‐functionalized monoboronic acids, in Suzuki‐type couplings, afforded the corresponding telechelics. Further functionalization with oxidable groups such as 2‐pyrrolyl or 1‐naphthyl was attained by condensation reactions of the amino or aldehyde groups with low molecular weight aldehydes or amines, respectively, with the formation of azomethine linkages. Preliminary attempts for the synthesis of fully conjugated poly(Schiff base) with polymeric segments as substituents, by oxidative polymerization of the macromonomers, are presented. All the starting, intermediate, or final polymers were structurally analyzed by spectral methods (¹H NMR, ¹³C NMR, and IR). © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 727–743, 2006     

Synthesis and characterization of PAni–SiO2 and PTh–SiO2 nanocomposites' thin films by plasma polymerization

In the present work, we explore the possibility to deposit polyaniline–silicon dioxide (PAni–SiO₂) and polythiophene–silicon dioxide (PTh–SiO₂) nanocomposites through a plasma polymerization route. The films were generated by spraying of mixtures of nano-sized silica particles dispersed in the liquid monomer into a plasma stream of the DC-plasma discharge reactor. The silica in the resulted polymer matrix changes the conduction mechanisms varying from ohmic to ballistic and traps inducing the space charged limited currents (SCLC). The silica modifies the morphology and composition of the deposited films.     

Parametric analysis of oscillatory oxidation reactions

A complete parametric analysis, concerning an overall kinetic model for oscillating catalytic deep oxidation of alcohols, carbon monoxide or hydrogen, is presented. The model contains four parameters.     

Isomerisation of ω-hydroxyalkenes under hydroxycarbonylation conditions in palladium catalysed aqueous phase systems

The ω-hydroxyolefins 3-buten-1-ol, 3-buten-1-methyl-1-ol and 4-penten-1-ol were subjected to hydroxycarbonylation conditions in water in the presence of PdCl₂(PhCN)₂ and 4-8 equiv. of water soluble tris(3-sodiumsulfonatophenyl)phosphine (TPPTS), or N-bis(N′,N′-diethyl-2-aminoethyl)-4-aminomethylphenyl-diphenylphosphine (N3P). Under conditions of high conversion, the olefins primarily undergo isomerisation through a chain walking mechanism with selectivities for aldehyde ranging from 65% to 98%, with the lower values for longer chain alcohols. The lactones formed as the minor product are almost exclusively branched, indicating that in the first step 2,1-insertion is strongly favoured over 1,2-insertion. In the N3P system also linear lactone is produced at lower conversion. Running the reaction in D₂O produces multiple deuterium incorporation in all positions of the carbon chain. A mechanism is discussed.     

Analytical contributions to the evaluation of painting authenticity from Princely church of Curtea de Arges

The present study contains the analyses performed for pigment samples taken from the Princely church of Curtea de Arges, one of the oldest churches in Romania. The results of our investigations have shown the source of these samples, thus being identified the pigments: natural ultramarine, cinnabar, red earth, and calcium carbonate in the painting from the 14th century, the pigments: lead white, zinc white, and Prussian blue in the repainting from the 19th century and the pigments zinc white, titanium dioxide white, bone white, yellow ochre, red ochre, green earth, artificial ultramarine, and mars red in the interventions carried out in the 20th century. The analyses consisted of light microscopy (LM) and microchemical tests, as well as energy dispersive X-ray (EDX) analysis. This system of analyses allows one to precisely determine the authenticity of certain pigments, thus avoiding the dating errors for different interventions carried out on the original mural painting from the Saint Nicholas Princely church of Curtea de Arges.