New integrable cases of a Cremona transformation: a finite-order orbits analysis

We analyse the properties of a particular birational mapping of two variables (Cremona transformation) depending on two free parameters ( and ), associated with the action of a discrete group of non-linear (birational) transformations on the entries of a q × q matrix. This mapping originates from the analysis of birational transformations obtained from very simple algebraic calculations, namely taking the inverse of q × q matrices and permuting some of the entries of these matrices. It has been seen to yield weak chaos and integrability. We have found new integrable cases of this Cremona transformation, corresponding to the values of = 0 when , besides the already known values = 0 and = −1, and also arbitrary when = 0. For these cases, one has a foliation of the parameter space in elliptic curves. We give the equations of these elliptic curves. Based on this very example we show how one can find these integrability cases of the Cremona transformation and actually integrate it using a method based on the systematic study of the finite-order conditions of the Cremona transformation. The method is shown to be efficient and straightforward. The various integrability cases are revisited using many different representations of this very mapping (birational transformations, recursion in one variable, …).     

Experimental Determination of the Longitudinal Dispersivity During the Injection of a Micro-Cement Grout in a One-Dimensional Soil Column

In order to describe the basic phenomenon of miscible grout propagation during the injection in a saturated and deformable porous medium, a general mathematical model was proposed, which accounts for the existing coupling between the fluid flow analysis, the miscible grout transport, and the solid skeleton deformation, leading to a realistic prediction of the injected zone. The development of the model was made concurrently with laboratory experiments to determine the model parameters. This paper describes the determination of the longitudinal dispersivity during the transport of a micro-cement grout injected in a one-dimensional soil column, by relying on image processing analysis. The application concerned here is the injection of soils for improving their properties, that is, to reduce permeability, increase mechanical strength or reduce the deformability. The longitudinal dispersion coefficient is an essential parameter governing the mixing process and the evolution of the transition zone, and thus the injection efficiency. Finally, the comparison between simulated results from the developed model and experimental data, essential to validate the model from a phenomenological standpoint, is made.     

Global synchronization of fractional‐order and integer‐order N component reaction diffusion systems: Application to biochemical models

This study considers the problem of control and synchronization between fractional‐order and integer‐order, N‐components reaction‐diffusion systems with nonidentical coefficients and different nonlinear parts. The control scheme is designed using the Lyapunov direct method. The results are exemplified by two significant biochemical models, namely, the fractional‐order Lengyel‐Epstein model and the Gray‐Scott model. To illustrate the effectiveness of the proposed scheme, numerical simulations are performed in one and two space dimensions using Homotopy Analysis Method (HAM).     

Discrete symmetry groups of vertex models in statistical mechanics

We analyze discrete symmetry groups of vertex models in lattice statistical mechanics represented as groups of birational transformations. They can be seen as generated by involutions corresponding respectively to two kinds of transformations onq×q matrices: the inversion of theq×q matrix and an (involutive) permutation of the entries of the matrix. We show that the analysis of the factorizations of the iterations of these transformations is a precious tool in the study of lattice models in statistical mechanics. This approach enables one to analyze two-dimensionalq ⁴-state vertex models as simply as three-dimensional vertex models, or higher-dimensional vertex models. Various examples of birational symmetries of vertex models are analyzed. A particular emphasis is devoted to a three-dimensional vertex model, the 64-state cubic vertex model, which exhibits a polynomial growth of the complexity of the calculations. A subcase of this general model is seen to yield integrable recursion relations. We also concentrate on a specific two-dimensional vertex model to see how the generic exponential growth of the calculations reduces to a polynomial growth when the model becomes Yang-Baxter integrable. It is also underlined that a polynomial growth of the complexity of these iterations can occur even for transformations yielding algebraic surfaces, or higher-dimensional algebraic varieties.     

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.