Feedback Stabilization for a Reaction-Diffusion System with Nonlocal Reaction Term

We consider a two-component reaction-diffusion system with a nonlocal reaction term. A necessary condition and a sufficient condition for the internal stabilizability to zero of one of the two components of the solution while preserving the nonnegativity of both components have been established in [6 S. Ani?a , W.-E. Fitzgibbon , and M. Langlais ( 2009 ). Global existence and internal stabilization for a class of predator-prey systems posed on non coincident spatial domains . Discrete Cont. Dynam. Syst. B 11 : 805 – 822 .[Crossref], [Web of Science ®] , [Google Scholar]]. In case of stabilizability, a feedback stabilizing control of harvesting type has been indicated. The rate of stabilization (for the indicated feedback control) is given by the principal eigenvalue of a certain non-selfadjoint operator. A large principal eigenvalue leads to a fast stabilization. The first main goal of this article is to approximate this principal eigenvalue. This is done in two steps. First, we investigate the large-time behavior of the solution to a logistic population dynamics with migration, and next we derive as a consequence a method to approximate the principal eigenvalue. The other main goal is to derive a conceptual iterative algorithm to improve the position of the support of the control in order to get a faster stabilization. Our results apply to prey-predator systems.     

Toward an understanding of the acceleration of Diels-Alder reactions by a pseudo-intramolecular process achieved by molecular recognition. A DFT study

The pseudo-intramolecular Diels-Alder (DA) reaction between a 2-substituted furan (1) and a N-maleimide derivative (2) has been analyzed using DFT methods. Formation of two hydrogen bonds between the appendages on furan and maleimide derivatives favors thermodynamically the formation of a molecular complex (MC1) through an efficient molecular recognition process. The large enthalpy stabilization associated with the molecular recognition overcomes the unfavorable activation entropy associated with the bimolecular process. As a consequence, the subsequent DA reaction is clearly accelerated through a pseudo-intramolecular process.     

Synchronization and secure communication of chaotic systems via robust adaptive high-gain fuzzy observer

This paper proposes an alternative robust adaptive high-gain fuzzy observer design scheme and its application to synchronization and secure communication of chaotic systems. It is assumed that their states are immeasurable and their parameters are unknown. The structure of the proposed observer is represented by Takagi–Sugeno fuzzy model and has the integrator of the estimation error. It improves the performance of high-gain observer and makes the proposed observer robust against noisy measurements, uncertainties and parameter perturbations as well. Using Lyapunov stability theory, an adaptive law is derived to estimate the unknown parameters and the stability of the proposed observer is analyzed. Some simulation result of synchronization and secure communication of chaotic systems is given to present the validity of theoretical derivations and the performance of the proposed observer as an application.     

Convergence results for a nonlinear parabolic control problem

We investigate a general control problem for a class of nonlinear parabolic evolution equations. Applications are related to solid-solid and solid-liquid phase transitions.

We prove compactness of the solution operators, existence of optimal controls and show convergence of the finite-dimensional approximate control problem to the original one.     

Pyridine-2-thionate as a versatile ligand in Pd(II) and Pt(II) chemistry: the presence of three different co-ordination modes in [Pd2(micro2-S,N-C5H4SN)(micro2-kappa2S-C5H4SN)(micro2-dppm)(S-C5H4SN)2

Reactions of [MCl2(L-L)], M = Pt, Pd; L-L = bis(diphenylphosphino)methane (dppm) or bis(diphenylphosphino)ethane (dppe), with NaC5H4SN in a 1 : 2 molar ratio lead to mononuclear species [M(S-C5H4SN)2(P-P)], M = Pt; L-L = dppm (1) or dppe (2) and M = Pd; L-L = dppe (3), as well as to the dinuclear [Pd2(micro2-S,N-C5H4SN)(micro2-kappa2S-C5H4SN)(micro2-dppm)(S-C5H4SN)2] (4). In contrast, reaction of [MCl2(dppm)] with NaC5H4SN in a 1 : 1 molar ratio leads to [Pd2(micro2-S,N-C5H4SN)3(micro2-dppm)]Cl (5) and trans-[Pt(S-C5H4SN)2(PPh2Me)2] (6) respectively. The latter is formed in low yield by cleavage of the dppm ligand. The dinuclear derivatives 4 and 5 present an A-frame and lantern structure, respectively. The former showing three different co-ordination modes in the same molecule with a short Pd-Pd distance of 2.9583 (9) A and the latter with three bridging S,N thionate ligands showing a shorter Pd-Pd distance of 2.7291 (13) A. Both distances could be imposed by the bridging ligands or point to some sort of metal-metal interaction.     

A wavelet-based method for multifractal image analysis. I. Methodology and test applications on isotropic and anisotropic random rough surfaces

We generalize the so-called wavelet transform modulus maxima (WTMM) method to multifractal image analysis. We show that the implementation of this method provides very efficient numerical techniques to characterize statistically the roughness fluctuations of fractal surfaces. We emphasize the wide range of potential applications of this wavelet-based image processing method in fundamental as well as applied sciences. This paper is the first one of a series of three articles. It is mainly devoted to the methodology and to test applications on random self-affine surfaces (e.g., isotropic fractional Brownian surfaces and anisotropic monofractal rough surfaces). Besides its ability to characterize point-wise regularity, the WTMM method is definitely a multiscale edge detection method which can be equally used for pattern recognition, detection of contours and image denoising. Paper II (N. Decoster, S.G. Roux, A. Arnéodo, to be published in Eur. Phys. J. B 15 (2000)) will be devoted to some applications of the WTMM method to synthetic multifractal rough surfaces. In paper III (S.G. Roux, A. Arnéodo, N. Decoster, to be published in Eur. Phys. J. 15 (2000)), we will report the results of a comparative experimental analysis of high-resolution satellite images of cloudy scenes. Received 8 July 1999     

The Specific Heat of Tetramethylammonium Salts

New measurements of the (N(CH₃ )₄ )₂ MnBr₄ specific heat by adiabatic calorimetry around the ferro- paraelastic phase transition shown by the crystal around 276 K are compared with previous calorimetric studies on similar tetramethylammonium bromide compounds. The thermodynamic behaviour of the tribromides and tetrabromides derivatives together with the influence on the phase transition parameters of the cation and halogen molecular substitutions are examined. The thermal relaxation experiments permit to study the behaviour of the crystals thermal conduction as a function of the temperature. Finally, the Landau theory for second order phase transitions is used to describe the thermodynamic behaviour of some of these crystals. This revised version was published online in July 2006 with corrections to the Cover Date.     

Diffusion-enhanced resonance energy transfer shows that linker-DNA accessibility decreases during salt-induced chromatin condensation

Accessibility of linker-DNA chromatin during salt-induced condensation of chicken erythrocytes chromatin was studied by diffusion-enhanced resonance energy transfer. A terbium complex was covalently bound to linker-DNA and fluorescein molecules bound to latex particles with diameters ranging from 14 to 2470 nm were used as acceptor. The accessibility of linker-DNA to molecules with a diameter superior to 14 nm diminished during condensation, but for an acceptor diameter of 14 nm or less, no accessibility variation was observed. It can be concluded that (1) linker-DNA is located inside the fiber when chromatin is in the condensed state, (2) chromatin condensation can prevent the approach to DNA due to steric hindrance, (3) salt-induced chromatin condensation is a gradual process, and (4) condensed chromatin models containing a central cavity are more likely.Abbreviations DTPA diethylene tetramine pentacetic acid - FDL-DERET fast diffusion limit of diffusion-enhanced resonance energy transfer - Pso-Tb psoralen-terbium complex - PAS paraamino salicylic acid - TREF time-resolved emission of fluorescence     

Multi-Regge cluster model versus multiparticle experimental data

Zeitschrift für Physik C Particles and Fields - We perform an analysis of predictions of the multi-Regge cluster model and compare them with available longitudinal and transverse data. We show...