Control analysis for water quality problem

The optimal control of water quality model is considered. We analyze a regularized version of the pointwise control. A numerical algorithm is presented. The solution approach is a combination of a TVD scheme for the shallow water equations and a purley deterministic particle method for the pollutant problem. We present some computational results. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Matched asymptotic expansions for the determination of the electromagnetic field near the edge of a patch antenna

We consider a simple but representative model incorporating the main behavior of the electromagnetic field near the edge of a patch antenna. Recall that this kind of antenna is obtained by a metal patch laying on a dielectric substrate covering a ground metallic plane. The functioning principle of such an electric device is based on the matching of an N-dimensional behavior of the field outside the antenna with an (N-1)-dimensional one inside the zone limited by the patch and the ground plane, N = 3 or 2 according to the considered model. In this study, we make use of the technique of matched asymptotic expansions and computation of singularities to describe this behavior for the two-dimensional case. Proved error estimates enable us to give a rigorous background to the underlying asymptotic analysis. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

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...     

Structural and electrochemical properties of LiCoO2 and LiAlyCo1−yO2 (y=0.1 and 0.2) oxides: A comparative study of electrodes prepared by the citrate precursor route

We present the characterization and electrode behavior of LiCoO₂ and Al-doped LiAl_yCo_1−yO₂ (y=0.1 and 0.2) oxides prepared by wet-chemical method from the citrate precursor route. We study the phase evolution as a function of the aluminum substitution and the modification on the intercalation and deintercalation of Li ions. Characterization methods include XRD, SEM, and FTIR. X-ray diffraction patterns show that samples belong to the LiCoO₂-LiAlO₂ solid solution and have the layered α-NaFeO₂ structure. FT-infrared vibrational spectroscopy indicates the slight modification in the local structure related to the short-range environment of oxygen coordination around the cations in oxide lattices. The frequencies and relative intensities of the bands are sensitive to the covalency of the (Al, Co)O₂ slabs. The overall electrochemical capacity of the LiAl_yCo_1−yO₂ oxides have been reduced due to the sp metal substitution, however, a more stable charge-discharge cycling performances have been observed when electrodes are charged to 4.3 V as compared to the performances of the native oxide. Differences and similarities between LiCoO₂ and Al-substituted oxides are discussed therefrom. Paper presented at the 9th EuroConference on Ionics, Ixia, Rhodes, Greece, Sept. 15–21, 2002.     

Densité des vecteurs propres généralisés d'une classe d'opérateurs compacts non auto-adjoints et applications

We consider a closed densely defined linear operatorT in a Hilbert spaceE, and assume the existence of ₀ (T) such thatK = (T - ₀ I)^-1 is compact and the existence ofp>0 such thats _n (K)=o((n ^–1/p)), whereS _n (K) denotes the sequence of non-zero eigenvalues of the compact hermitian operator . In this work, sufficient conditions (announced in [1]) are introduced to assure that the closed subspace ofE spanned by the generalized eigenvectors ofT coincides withE. These conditions are in particular verified by a family of non-self-adjoint operators arising in reggeon's field theory.     

Etude spectrale d'une famille d'opérateurs non-symétriques intervenant dans la théorie des champs de reggeons

In this paper, we study a few spectral properties of a non-symmetrical operator arising in the Gribov theory. The first and second section are devoted to Bargmann's representation and the study of general spectral properties of the operator: $$\begin{gathered} H_{\lambda ',\mu ,\lambda ,\alpha } = \lambda '\sum\limits_{j = 1}^N {A_j^{ * 2} A_j^2 + \mu \sum\limits_{j = 1}^N {A_j^ * A_j + i\lambda \sum\limits_{j = 1}^N {A_j^ * (A_j + A_j^ * )A_j } } } \hfill \\ + \alpha \sum\limits_{j = 1}^{N - 1} {(A_{j + 1}^ * A_j + A_j^ * A_{j + 1} ),} \hfill \\ \end{gathered}$$ whereA* _j andA _j ,j∈[1,N] are the creation and annihilation operators. In the third section, we restrict our study to the case of nul transverse dimension (N=1). Following the study done in [1], we consider the operator: $$H_{\lambda ',\mu ,\lambda } = \lambda 'A^{ * 2} A^2 + \mu A^ * A + i\lambda A^ * (A + A^ * )A,$$ whereA* andA are the creation and annihilation operators. For λ′>0 and λ′²≦μλ′+λ². We prove that the solutions of the equationu′(t)+H _{λ′, μ,λ} u(t)=0 are expandable in series of the eigenvectors ofH _λ′,μ,λ fort>0. In the last section, we show that the smallest eigenvalue σ(α) of the operatorH _{λ′,μ,λ,α} is analytic in α, and thus admits an expansion: σ(α)=σ₀+ασ₁+α²σ₂+..., where σ₀ is the smallest eigenvalue of the operatorH _{λ′,μ,λ,0}.     

Cycloaddition reactions in aqueous systems: A two-decade trend endeavor

Cycloaddition reactions are an integral and weighty part of organic chemistry in pedagogy and research as well. The wealthy literature on cycloaddition reactions from their birth up to now, unequivocally witnesses to their leading chemistry. The so-called “conventional solvents” are organic solvents that have indubitably promoted their success. Yet, the toxicity facet of these solvents impedes their use freely and with no fear. Not only is the operating chemist uncomfortable while experimenting, but also the environment is equally threatened. Working out the cycloaddition reactions and other organic ones in aqueous systems would certainly bring some relief to the chemist and to the environment as well. Unusual outcomes in terms of yield, reactivity and selectivity compared to those performed in organic solvents were commonly observed, and have overwhelmed the chemists with surprise indeed. In this review, homo Diels–Alder reactions in aqueous media include those involving the following dienophiles: maleimides, α,β-unsaturated esters, p-benzoquinones, vinyl ketones, phenyl-1-(2-pyridyl)-2-propen-1-one, α,β-unsaturated esters. A special case is the organocatalysis of Diels–Alder cycloaddition of α,β-unsaturated ketones (aldehydes). Of no less importance, some hetero Diels–Alder cycloaddition reactions in water systems are delineated. The impact of additives (salts, organic and inorganic chemicals), micellar catalysis and Lewis/Brønstëd acid catalysis on outcomes of such cycloaddition reactions is discussed. The 1,3-dipolar cycloaddition methodology applied to aqueous media has brought forth a number of heterocyclic compounds, usually with a regio- and stereoselectivity pecularity. These heterocycles include triazoles, tetrazoles, pyrazoles, isoxazoles, isoxazolidines, pyrroles and pyrrolidines. The superiority of copper(I) catalysis in the azide-alkyne cycloaddition (Huisgen cycloaddition) in water is endorsed by a number of examples.