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.     

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.     

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.     

Correlation between chemical composition and antibacterial activity of essential oils from fifteen Eucalyptus species growing in the Korbous and Jbel Abderrahman arboreta (North East Tunisia)

The essential oils of fifteen Eucalyptus species harvested from the Jbel Abderrahman and Korbous arboreta (North East Tunisia) were screened for their antibacterial activities by the agar disc diffusion method. Eighteen major components as identified by GC/FID and GC/MS were selected for a study of the chemical and biological activity variability. The main one was 1,8-cineole, followed by spathulenol, trans-pinocarveol, α-pinene, p-cymene, globulol, cryptone, β-phellandrene, viridiflorol, borneol, limonene and isospathulenol. The chemical principal component analysis identified five species groups and subgroups, where each group constituted a chemotype, however that of the values of zone diameter of the inhibition (zdi) identified six groups of Eucalyptus oils, characterized by their antibacterial inhibition ability. The strongest activity was shown by E. platypus oil against Enterococcus faecalis and by E. lamannii oil against Staphylococcus aureus, Pseudomonas aeruginosa and Escherichia coli. A correlation between the levels of some major components and the antibacterial activities was observed.     

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).     

A ruthenium(II) complex with p‐cymene and (S)‐2‐(anilinomethyl)pyrrolidine

The title compound, [(S)‐2‐(anilino­methyl)­pyrrolidine‐N,N′]‐chloro(η⁶‐para‐cymene)­ruthenium(II) chloride, [RuCl‐(C₁₀H₁₄)(C₁₁H₁₆N₂)]Cl, has been synthesized by the reaction of [RuCl₂(p‐cymene)]₂ (p‐cymene is para‐iso­propyl­toluene) with (S)‐2‐(anilinomethyl)­pyrrolidine in triethyl­amine/2‐propanol. The Ru atom is in a pseudo‐tetrahedral environment coordinated by a chloride ligand, the aromatic hydro­carbon is linked in a η⁶ manner and the amine is linked via its two N atoms. The chloride anion is involved in hydrogen bonding with the di­amine moieties through N—H?Cl interactions, with N?Cl distances of 3.273 (4) and 3.352 (4) Å.     

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.     

Ni(0)-CMC-Na - nickel colloids in sodium carboxymethyl-cellulose: catalytic evaluation in hydrogenation reactions

A recyclable catalyst, Ni(0)-CMC-Na, composed of nickel colloids dispersed in a water soluble bioorganic polymer, sodium carboxymethylcellulose (CMC-Na), was synthesized by a simple procedure from readily available reagents. The catalyst thus obtained is stable and highly active in alkene hydrogenations.     

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.