Some inequalities involving quadratic forms of operator means

Let T and S be two self-adjoint positive invertible operators of a complex Hilbert space H. In this paper, we investigate some inequalities involving the quadratic forms of the weighted arithmetic and harmonic means of T and S. Application for operator entropies is also discussed.     

Inversion transformation of Stokes flows bounded by parallel planes

The positive inversion transformation applied to a two-dimensional Stokes flow around bodies leads alike to a Stokes flow. This fact can be exploited to find new two-dimensional Stokes flow solutions around inverse bodies. Some features of this method, such as the relations between the reference and inverse fluid velocity fields, are presented followed by an application to examples of cellular flow between two parallel plates induced by rotating or translating cylinder. Thus hydrodynamic characteristics of flow around circular bodies obtained by inversion of the plates are straightforward deduced. Typical fluid flow patterns around two circular cylinders in contact placed in the centre of a rotating or a translating circular cylinder are thus illustrated.     

Stability of the Kaluza-Klein wormhole soliton

We show that the electrically charged wormhole soliton solution of sourceless five-dimensional general relativity is classically stable against radial perturbations, except in the special case of a massless soliton.On leave of absence from: Département de Physique Théorique, Université de Constantine, Constantine, Algeria     

Indefinite Stochastic Linear Quadratic Control with Markovian Jumps in Infinite Time Horizon

This paper studies a stochastic linear quadratic (LQ) control problem in the infinite time horizon with Markovian jumps in parameter values. In contrast to the deterministic case, the cost weighting matrices of the state and control are allowed to be indinifite here. When the generator matrix of the jump process – which is assumed to be a Markov chain – is known and time-invariant, the well-posedness of the indefinite stochastic LQ problem is shown to be equivalent to the solvability of a system of coupled generalized algebraic Riccati equations (CGAREs) that involves equality and inequality constraints. To analyze the CGAREs, linear matrix inequalities (LMIs) are utilized, and the equivalence between the feasibility of the LMIs and the solvability of the CGAREs is established. Finally, an LMI-based algorithm is devised to slove the CGAREs via a semidefinite programming, and numerical results are presented to illustrate the proposed algorithm.     

Calorimetric studies of poly (2-phenoxyethylacrylate)/5CB mixtures

The thermophysical properties of mixtures of poly (2-phenoxyethylacrylate) and 4-cyano-4'-pentyl-biphenyl, 5CB, are investigated using polarizing optical microscopy (POM) and differential scanning calorimetry (DSC). The polymer has a molar mass M w = 181 000 g mol -1 ; the low molecular mass liquid crystal exhibits a nematic to isotropic transition at 35.3°C and crystallizes below 23°C. The phase diagram exhibits miscibility gaps in certain regions of temperature and composition where coexisting nematic and isotropic phases are found. From a practical point of view when considering the electro-optical applications of these systems, it proves to be useful to know precisely the amount of small liquid crystal molecules dissolved in the polymer matrix and the concentration of polymer in the nematic phase. The former quantity has a mechanical impact due to a plasticizing effect, an optical impact since it changes the polymer refractive index, while the polymer in the nematic phase shifts the transition temperatures influencing the electro-optical response of the liquid crystal. The present work addresses these important aspects using POM and DSC.     

The acyclic dienamine-indoloacrylate addition route to catharanthine

Condensation of methyl 3-benzyl-1,2,3,4,5,6-hexahydroazepino[4,5-b]indole-5-carboxylate (3) with methyl Z-4-formylhex-3-enoate (6) gave cis-fused dimethyl 5-benzyl-4-ethyl-2,4a,5,6,7,12-hexahydro-1H-benzo[2,3]azepino[4,5-b]indole-2,12b-dicarboxylate and its trans-fused diastereomer. Selective reduction of the less hindered ester group with sodium borohydride to an alcohol ester, tosylation, debenzylation, and cyclization gave racemic catharanthine (1).     

On collisionless transport semigroups with boundary operators of norm one

We deal with streaming operators T _H defined in L ¹ spaces by the directional derivative with positive boundary operator H of norm 1 relating the incoming and outgoing fluxes. It is known that T _H need not be a generator but there exists a contraction semigroup generated by an extension A of T _H . This paper deals with the total mass carried by individual trajectories {e ^tA f; t ≥ 0} for nonnegative initial data f and related topics. In particular, our analysis covers the problem of (the lack of) stochasticity of {e ^tA ; t ≥ 0} for conservative boundary operator H.      

Redox isomerisation of allylic alcohols catalysed by water-soluble ruthenium complexes in aqueous systems

The process of catalytic isomerisation of various allylic alcohols (alk-1-en-3-ols) into saturated ketones under mild conditions is reported. The water-soluble Na₄[{RuCl₂(mtppms)₂}₂] complex, previously reported by us as a precursor to very active hydrogenation catalysts was also found an active catalyst of the redox isomerisation of allylic alcohols in aqueous media. The new Na[Ru(CO)Cp(mtppms)₂] as well as Na₄[{RuCl(μ-Cl)(CCCPh₂)(mtppms)₂}₂] and Na₂[RuClCp(mtppms)₂] also showed good to excellent catalytic activities for redox isomerisations in aqueous systems at 50-80 °C under inert atmosphere.     

Aluminium substitution in iron(II-III)-layered double hydroxides: Formation and cationic order

The formation and the modifications of the structural properties of an aluminium-substituted iron(II-III)-layered double hydroxide (LDH) of formula (OH)₁₂ SO₄, 8H₂O are followed by pH titration curves, Mössbauer spectroscopy and high-resolution X-ray powder diffraction using synchrotron radiation. Rietveld refinements allow to build a structural model for hydroxysulphate green rust, GR(SO₄²⁻), i.e. y=0, in which a bilayer of sulphate anions points to the Fe³⁺ species. A cationic order is proposed to occur in both GR(SO₄²⁻) and aluminium-substituted hydroxysulphate green rust when y<0.08. Variation of the cell parameters and a sharp decrease in average crystal size and anisotropy are detected for an aluminium content as low as y=0.01. The formation of Al-GR(SO₄²⁻) is preceded by the successive precipitation of Fe^III and Al^III (oxy)hydroxides. Adsorption of more soluble Al^III species onto the initially formed ferric oxyhydroxide may be responsible for this slowdown of crystal growth. Therefore, the insertion of low aluminium amount (y∼0.01) could be an interesting way for increasing the surface reactivity of iron(II-III) LDH that maintains constant the quantity of the reactive Fe^II species of the material.     

Large deviations from a macroscopic scaling limit for particle systems with Kac interaction and random potential

We consider a lattice gas in a periodic d-dimensional lattice of width γ⁻¹, γ>0, interacting via a Kac's type interaction, with range and strength γ^d, and under the influence of a random one body potential given by independent, bounded, random variables with translational invariant distribution. The system evolves through a conservative dynamics, i.e. particles jump to nearest neighbor empty sites, with rates satisfying detailed balance with respect to the equilibrium measures. In [M. Mourragui, E. Orlandi, E. Saada, Macroscopic evolution of particles systems with random field Kac interactions, Nonlinearity 16 (2003) 2123–2147] it has been shown that rescaling space as γ⁻¹ and time as γ⁻², in the limit γ→0, for dimensions d3, the macroscopic density profile ρ satisfies, a.s. with respect to the random field, a non-linear integral partial differential equation, having the diffusion matrix determined by the statistical properties of the external random field. Here we show an almost sure (with respect to the random field) large deviations principle for the empirical measures of such a process. The rate function, which depends on the statistical properties of the external random field, is lower semicontinuous and has compact level sets.