Pointwise stabilization of strings with non‐linear feedback

We consider an initial and boundary value problem for a homogenous string subject to an internal pointwise control. The solution resulting from a non‐linear feedback is studied. We give various explicit decay estimates depending on the control position and the feedback non‐linearity. Copyright © 2004 John Wiley & Sons, Ltd.     

Comparative Study of Surface Functionalization of Hydroxyapatite by One‐pot Grafting of Organophosphonates Species

The ability to graft apatite surface by specific ligand fields creates powerful new technology applications. Thus, grafted organophosphonate can provide an effective route to modify the surface properties of apatite materials. The ability to decorate the apatite surface with the desired functionality requires covalent attachment to solid interface; most commonly achieved using organophosphonate self‐assembly. The current study shows that various phosphonates can react with calcium ions and control the formation of the porous apatite with high surface areas as well as the porosity. The structural and surface properties are given some importance in this review.     

Stabilization of unbounded bilinear control systems in Hilbert space

We consider bilinear control systems of the form y^′(t)=Ay(t)+u(t)By(t) where A generates a strongly continuous semigroup of contraction (etA)_t?0 on an infinite-dimensional Hilbert space Y whose scalar product is denoted by 〈.,.〉. We suppose that this system is unbounded in the sense that the linear operator B is unbounded from the state Y into itself. Tacking into account eventual control saturation, we study the problem of stabilization by (possibly nonquadratic) feedback of the form u(t)=−f(〈By(t),y(t)〉). Applications to the heat equation is considered.     

Novel palladium nanoparticles supported on mesoporous natural phosphate: Catalytic ability for the preparation of aromatic hydrocarbons from natural terpenes

Various ratios of palladium nanoparticles supported on mesoporous natural phosphate (Pd@NP) were prepared using the wetness impregnation method. The prepared catalysts were characterized by IR, XRD, CV, SEM, EDX, XRF, TEM and BET analysis. The reduction and preparation of the palladium nanoparticles afford a crystallite size of 10.88 nm. The performance of the synthesized catalyst was investigated in the solvent-free dehydroaromatization of α-, β- and γ-himachalene mixture from Cedrus atlantica oil as a model substrate. In order to achieve an efficient and selective catalysis, the catalytic dehydroaromatization of various terpenes such as limonene, limonaketone, carvone, carveol and perillyl alcohol was studied. The Pd@NP catalyst performed a high catalytic activity, selectivity and recyclability in the terpenes dehydroaromatization reaction.     

Friedel-Craft acylation of ar-himachalene: synthesis of acyl-ar-himachalene and a new acyl-hydroperoxide

Friedel-Craft acylation at 100 °C of 2,5,9,9-tetramethyl-6,7,8,9-tetrahydro-5H-benzocycloheptene [ar-himachalene], a sesquiterpenic hydrocarbon obtained by catalytic dehydrogenation of α-, β- and γ-himachalenes, produces a mixture of two compounds: (3,5,5,9-tetramethyl-6,7,8,9-tetrahydro-5H-benzocyclohepten-2-yl)-ethanone (2, in 69% yield), with a conserved reactant backbone, and 3, with a different skeleton, in 21% yield. The crystal structure of 3 reveals it to be 1-(8-ethyl-8-hydroperoxy-3,5,5-trimethyl-5,6,7,8-tetrahydronaphthalen-2-yl)-ethanone. In this compound O-H…O bonds form dimers. These hydrogen-bonds, in conjunction with weaker C-H…O interactions, form a more extended supramolecular arrangement in the crystal.     

Efficient Synthesis of New 2H‐Chromene Retinoids Hybrid Derivatives by Suzuki Cross‐coupling Reactions

In an attempt to improve anticancer activity, a series of retinoids–chromene hybrids was described. The novel heterocyclic chromene–retinoids hybrid including oxygen as a heteroatom in a six‐membered cyclic ring (2H‐chromene or 2H‐1‐benzopyran) was designed and synthesized by introducing different groups such as an aromatic or styrylphenyl ring in 6‐position of 2H‐chromene. These novel compounds were synthesized by using the efficient cascades one‐pot process involving Wittig–Horner–Emmons reaction and Suzuki–Miyaura cross‐coupling pallado‐catalyzed reactions with 60% to 90% overall yields. These new compounds were tested against glioblastoma multiforme brain cancer, medulloblastoma, neuroblastoma cell lines, and breast cancer MCF‐7 cell lines. Two of them exhibited an appreciable anti‐tumor activity in the low micromolar range, which opens new perspectives for therapeutic application on humans.     

Compacité des opérateurs de Dunford–Pettis positifs sur les treillis de Banach

We establish some sufficient and necessary conditions which give the compactness of positive Dunford–Pettis operators on Banach lattices. To cite this article: B. Aqzzouz et al., C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

Impedance spectroscopy and conductometric biosensing for probing catalase reaction with cyanide as ligand and inhibitor

In this work, a new biosensor was prepared through immobilization of bovine liver catalase in a photoreticulated poly (vinyl alcohol) membrane at the surface of a conductometric transducer. This biosensor was used to study the kinetics of catalase–H₂0₂ reaction and its inhibition by cyanide. Immobilized catalase exhibited a Michaelis–Menten behaviour at low H₂0₂ concentrations (< 100 mM) with apparent constant K_M^app = 84 ± 3 mM and maximal initial velocity V_M^app = 13.4 μS min^? 1. Inhibition by cyanide was found to be non-competitive and inhibition binding constant K_i was 13.9 ± 0.3 μM. The decrease of the biosensor response by increasing cyanide concentration was linear up to 50 μM, with a cyanide detection limit of 6 μM. In parallel, electrochemical characteristics of the catalase/PVA biomembrane and its interaction with cyanide were studied by cyclic voltammetry and impedance spectroscopy. Addition of the biomembrane onto the gold electrodes induced a significant increase of the interfacial polarization resistance R_P. On the contrary, cyanide binding resulted in a decrease of Rp proportional to KCN concentration in the 4 to 50 μM range. Inhibition coefficient I₅₀ calculated by this powerful label-free and substrate-free technique (24.3 μM) was in good agreement with that determined from the substrate-dependent conductometric biosensor (24.9 μM).     

Retention Time of Unretained Compound Calculation and Determination of Retention Indices of Some Monosubstituted Benzenes Using a Multiparametric Method in Binary, Ternary and Quaternary Solvent RP-LC Systems

In reversed phase liquid chromatography (RP-LC), the validity of a multiparametric (MP) non-linear least-squares regression iterative method has been evaluated for 14 different aqueous mobile phases modified with one, two or three organic solvents [acetonitrile (ACN), methanol (MeOH), or tetrahydrofuran (THF)] for calculating the retention time of unretained compound t _M and the regression parameter (slope b), based on the use of alkan-2-ones and alkyl aryl ketones homologous series. The determination of t _M and b has been studied for eight binary (ACN?CH₂O or MeOH?CH₂O), 3 ternary (ACN?CMeOH?CH₂O) and 3 quaternary (ACN?CMeOH?CTHF?CH₂O) mobile phase systems on an Omnispher C₁₈ column. The multiparametric calculated t _M and b values were compared with those obtained by Guardino??s, and Grobler??s methods. The MP retention indices (RI) of ten monosubstituted benzenes with different functionality (hydroxyl, carbonyl, nitro, etc.) based on the alkan-2-ones retention index standards have been determined and compared for the different mobile phase compositions studied. The influence of organic modifier type, the nature of mobile phase system and water content on the variation of retention parameter studied in this work were discussed.     

On the duality problem of positive Dunford-Pettis operators on Banach lattices

We give some sufficient and necessary conditions for that a positive Dunford-Pettis operator admits a dual operator which is also Dunford-Pettis, and conversely.