Design of polyethers,thioethers, and amines with pendent iron moieties

Soluble organoiron polyethers, thioethers, and amines were synthesized via nucleophilic aromatic substitution reactions. The synthesis of these classes of organometallic polymers involved either the reaction of cyclopentadienyliron complexes of dichloroarenes with various oxygen and sulfur dinucleophiles or the reaction of ether‐ or amine‐containing diiron complexes with dithiols. Polymerization reactions with the diiron complexes gave rise to organoiron polymers with alternating ether/thioether or amine/thioether bridges. Removal of the iron moieties from the backbone of these polymers allowed for the production of the corresponding organic materials. Furthermore, the organometallic polymers had much higher solubilities than their organic analogues. Thermogravimetric analysis of the organoiron polymers indicated that the polymers lost their metallic moieties at approximately 200 °C, whereas degradation of the polymer backbones occurred around 500 °C. © 2001 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 39: 1216–1231, 2001     

Robin-type boundary control problems for the nonlinear Boussinesq type equations

In this paper, we study a linear and a nonlinear boundary control problems arising from viscous flows. The equations are of nonlinear Navier-Stokes type for the velocity and pressure, of transport-diffusion type for the temperature and the salinity. The essential difficulties are due to the nonlinear nature of a part of the boundary conditions and to the nature of the equations: time-dependent, coupled and nonlinear. The existence and the conditions of the uniqueness of the solution, for the variational problem, are studied. The control is of linear or nonlinear Robin-type and acts on a part of the boundary during a time T. The cost function measures the distance between the observed and the computed vorticity. The existence of an optimal control in the admissible set of states and controls is proved. A first order necessary conditions of optimality are obtained.     

Justification of the kinematic assumptions for thin-walled rods with shallow profile

In this Note we present a justification of the kinematic assumptions for thin-walled rods with shallow profile. These assumptions are fundamental to writing the one-dimensional equilibrium equations for such structures. The obtained kinematics are different from the Vlassov case, which is only valid for strongly curved profiles. They are also different from the that classically used in shell theory. The justification given in this Note is based on an asymptotic approach. To cite this article: L. Grillet et al., C. R. Mecanique 333 (2005).     

Subgrid models preserving the symmetry group of the Navier–Stokes equations

In order to preserve the physical properties of the flow (scaling laws, conservation laws, …) during the simulation, a class of subgrid models respecting the symmetry group of the Navier–Stokes equations is built. The class is then refined such that models satisfy the second law of thermodynamics and are suited to take into account the inverse energy cascade. A simple model belonging to the class is tested and a better result than those provided by Smagorinsky and dynamic models is obtained. To cite this article: D. Razafindralandy, A. Hamdouni, C. R. Mecanique 333 (2005).     

Real-time tracking of hydrogen peroxide secreted by live cells using MnO2 nanoparticles intercalated layered doubled hydroxide nanohybrids

We report a facile and green method for the fabrication of new type of electrocatalysts based on MnO₂ nanoparticles incorporated on MgAl LDH P-type semiconductive channel and explore its practical applications as high-performance electrode materials for electrochemical biosensor. A series of MgAl layered doubled hydroxide (LDH) nanohybrids with fixed Mg/Al (M²⁺/M³⁺ atomic ratio of 3) and varied amount of MnCl₂.4H₂O are fabricated by a facile co-precipitation method. This approach demonstrates the combination of distinct properties including excellent intercalation features of LDH for entrapping nanoparticles and high loading of MnO₂ nanoparticles in the host layers of LDH. Among all samples, Mn5–MgAl with 0.04% loaded manganese has a good crystalline morphology. A well-dispersed MnO₂ nanoparticles encapsulated into the host matrix of hydrotalcite exhibit enhanced electrocatalytic activity towards the reduction of H₂O₂ as well as excellent stability, selectivity and reproducibility due to synergistic effect of good catalytic ability of MnO₂ and conductive MgAl LDH. Glass carbon electrode (GCE) modified with Mn5–MgAl possesses a wide linear range of 0.05–78 mM, lowest detection limit 5 μM (S/N = 3) and detection sensitivity of 0.9352 μAmM⁻¹. This outstanding performance enables it to be used for real-time tracking of H₂O₂ secreted by live HeLa cells. This work may provide new insight in clinical diagnosis, on-site environmental analysis and point of care testing devices.     

Some characterizations of almost limited operators

In this paper we give several characterizations of almost limited operators. Mainly, it is proved that an operator \(T:X\rightarrow E\) from a Banach space X into a \(\sigma \)-Dedekind complete Banach lattice E is almost limited if and only if \(\left\| T^{*}\left( f_{n}\right) \right\| \rightarrow 0\) for every positive weak\(^{*}\) null sequence \(\left( f_{n}\right) \) of \(E^{*}\). Moreover, we present some interesting connections between almost limited, almost Dunford–Pettis and limited operators.     

The behavior of a gas bubble in a shock wave

The phenomenon of thermal relaxation of the gas bubbles in a fluid behind a shock front is analyzed. The approach to solving the problem of heat transfer between a gas bubble and a fluid developed by the author is used to obtain a solution describing the initial stage of bubble collapse behind the shock front.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 187–189, September–October, 1993.     

Exponential Behavior of Solutions to Stochastic Integrodifferential Equations with Distributed Delays

In this work, we study the existence, uniqueness, and exponential asymptotic behavior of mild solutions to stochastic integrodifferential delay evolution equations. We assume that the non-delay part generates a C₀-semigroup.