Piecewise multiplier method and nonlinear integral inequalities for Petrowsky equation with nonlinear dissipation

This work is concerned with obtention of energy decay estimates for Petrowsky equation with a nonlinear dissipation which is active only in an interior subset of the domain. We prove that the piecewise multiplier method as introduced by [20] and [22] for the wave equation can be extended to the Petrowsky equation. Moreover, we also apply some recent results by the author to obtain precise decay rate estimates for the energy, without specifying the growth of the nonlinear dissipation close to the origin by means of convex properties and nonlinear integral inequalities for the energy of the solutions.     

General decay for a class of viscoelastic problem with not necessarily decreasing kernel

In this paper, a problem which arises in a class of viscoelasticity is considered. We obtain the decay rate of the energy, for certain class of relaxation functions not necessarily exponentially or polynomially decaying to zero.     

Anion Directed Self‐Assembly of One‐Dimensional and Two‐Dimensional Coordination Polymers Containing Bridging Diphosphine Ligands

The reactions of 1,2‐bis(diphenylphosphanyl)ethane (dppe) with different silver(I) salts facilitated the formation of 1D and 2D coordination polymers, [Ag(dppe)(OAc)]_n · nH₂O ( 1 ) and [Ag₂(dppe)_1.5(NO₃)₂]_n ( 2 ), respectively. The complexes were characterized by elemental analysis, ATR‐IR spectroscopy, ¹H NMR, ¹³C NMR, and ³¹P NMR spectroscopy, and single‐crystal X‐ray diffraction. Structural analysis revealed that complex 1 exhibits a 1D infinite wavy structure, in which each silver(I) ion is bridged by dppe ligands. Structure 2 has a 2D topologically promising architecture that displays a 6.6.6 graphitic net, which corresponds to hnd topology. The nitrate ions and dppe ligands are in a μ₂ bridging mode and support the formation of this net. Moreover, significant π–π interactions between the phenyl rings in the apertures of (6,3) grid stabilized complex 2 .     

Efficient multicomponent synthesis of 2-aminopyridines catalysed by basic mesoporous materials

Research on Chemical Intermediates - An efficient and green procedure for the synthesis of 2-aminopyridines derivatives via four-component reaction of acetophenone, malononitrile, triethoxymethane...     

A general formula for decay rates of nonlinear dissipative systems

This work is concerned with stabilization of hyperbolic systems by a nonlinear feedback which can be localized on part of the boundary or locally distributed. We present here a general formula which gives the energy decay rates in terms of the behavior of the nonlinear feedback close to the origin. This formula allows us to unify for instance the cases where the feedback has a polynomial growth at the origin, with the cases where it goes exponentially fast to zero at the origin. We give also two other significant examples of nonpolynomial growth at the origin. We also show that we either obtain or improve significantly the decay rates of Lasiecka and Tataru (Differential Integral Equations 8 (1993) 507–533) and Martinez (Rev. Mat. Comput. 12 (1999) 251–283). To cite this article: F. Alabau-Boussouira, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Investigation of 3D Contour Map and Intermolecular Interaction of Dopamine with β-Cyclodextrin and 2-Hydroxypropyl-β-cyclodextrin

The interactions of the neurotransmitter dopamine (DA) with β-cyclodextrin and 2-hydroxypropyl-β-cyclodextrin (HP-β-CD) was characterized using UV–visible, 2D fluorescence, 3D fluorescence, FT–IR, PXRD and SEM techniques. PM3, PM7 and DFT methods were used to optimize the structures of the inclusion complexes in the gas phase. The absorbance and fluorescence intensities of DA increased in the presence of CDs in aqueous solution. The binding energy, HOMO–LUMO energy gap and Mulliken atomic charges were computed for the inclusion complexes. NBO analysis revealed a greater number of intermolecular hydrogen bonds in DA:HP-β-CD. Experimental and theoretical results suggested that the DA molecule is deeply embedded in the cavities of both CDs.     

Structural properties of the one-dimensional drift-diffusion models for semiconductors

This paper is devoted to the analysis of the one-dimensional current and voltage drift-diffusion models for arbitrary types of semiconductor devices and under the assumption of vanishing generation recombination. We show in the course of this paper, that these models satisfy structural properties, which are due to the particular form of the coupling of the involved systems. These structural properties allow us to prove an existence and uniqueness result for the solutions of the current driven model together with monotonicity properties with respect to the total current , of the electron and hole current densities and of the electric field at the contacts. We also prove analytic dependence of the solutions on . These results allow us to establish several qualitative properties of the current voltage characteristic. In particular, we give the nature of the (possible) bifurcation points of this curve, we show that the voltage function is an analytic function of the total current and we characterize the asymptotic behavior of the currents for large voltages. As a consequence, we show that the currents never saturate as the voltage goes to , contrary to what was predicted by numerical simulations by M. S. Mock (Compel. 1 (1982), pp. 165--174). We also analyze the drift-diffusion models under the assumption of quasi-neutral approximation. We show, in particular, that the reduced current driven model has at most one solution, but that it does not always have a solution. Then, we compare the full and the reduced voltage driven models and we show that, in general, the quasi-neutral approximation is not accurate for large voltages, even if no saturation phenomenon occurs. Finally, we prove a local existence and uniqueness result for the current driven model in the case of small generation recombination terms.

     

Effect of surfactant and mineral additive on the efficiency of lead-acid battery positive active material

The effect of Sodium tripolyphosphate (STPP) and mineral additive on the performance of the lead-acid battery positive plate has been investigated. The addition of alumina-silicate to the positive paste and STPP to the electrolyte modifies the shape and size of PbO₂ crystals and improves the utilization of the positive active material (PAM). The electrochemical performance of the positive active material was determined using galvanostatic discharge and electrochemical impedance spectroscopy (EIS). The crystal structure and morphology of the PAM (PbO₂) were characterized by X-ray diffraction (XRD) and scanning electron microscopy (SEM). The water content of the PAM was calculated using Thermogravimetric analysis (TGA) technique. The results showed that the addition of surfactant and mineral additive changes the morphology and the crystallite size of the PAM. We observe a remarkable improvement of the discharge capacity of the PAM when the surfactant (STPP) is added in the electrolyte. The discharge capacity increases with the decrease of the crystallite size and the charge transfer resistance R_ct of the PAM. This shows that the addition of mineral additive and the surfactant together improves the electrical performance of lead-acid battery.     

Eigenproblem for p-Laplacian and nonlinear elliptic equation with nonlinear boundary conditions

In this article, we study the solvability of nonlinear problem for p-Laplacian with nonlinear boundary conditions. We give some characterization of the first eigenvalue of an intermediary eigenvalue problem as simplicity, isolation and its strict monotonicity. Afterward, we character also the second eigenvalue and its strictly partial monotony. On the other hand, in some sense, we establish the non-resonance below the first and furthermore between the first and second eigenvalues of nonlinear Steklov–Robin.     

Exponential and polynomial stability of a wave equation for boundary memory damping with singular kernels

This work is concerned with stabilization of a wave equation stabilized by a boundary feedback. When the feedback is both frictional and with memory, we prove exponential stability of the solutions. In case of a boundary feedback which is only of memory type, uniform stability is not expected. We prove in this latter case, that the solutions decay polynomially. The method is new and uses the method of higher order energies (see [F. Alabau-Boussouira, J. Prüss, R. Zacher, Exponential and polynomial stabilization of wave equations subjected to boundary-memory dissipation with singular kernels, in preparation; F. Alabau, Stabilisation frontière indirecte de systèmes faiblement couplés, C. R. Acad. Sci. Paris Sér. I Math. 328 (1999) 1015–1020; F. Alabau, P. Cannarsa, V. Komornik, Indirect internal damping of coupled systems, J. Evolution Equations 2 (2002) 127–150; F. Alabau, Indirect boundary stabilization of weakly coupled systems, SIAM J. Control Optim. 41 (2002) 511–541]), the multiplier method and the properties of a large class of singular kernels. Moreover, our method can be extended to include cases of nonsingular kernels (see [V. Vergara, R. Zacher, Lyapunov functions and convergence to steady state for differential equations of fractional order, Math. Z. 259 (2008) 287–309; R. Zacher, Convergence to equilibrium for second order differential equations with weak damping of memory type, preprint.]). To cite this article: F. Alabau-Boussouira et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009).