Synthesis of new (pyrazol-1-yl)(7-nitro-1h-indol-2-yl)ketone derivatives

The condensation of 7-nitroindole-2-carbohydrazide derivatives with acetylacetone lead to (pyrazol-1-yl)(7-nitroindol-2-yl)ketones.     

Newton's method for the common eigenvector problem

In El Ghazi et al. [Backward error for the common eigenvector problem, CERFACS Report TR/PA/06/16, Toulouse, France, 2006], we have proved the sensitivity of computing the common eigenvector of two matrices A and B, and we have designed a new approach to solve this problem based on the notion of the backward error.If one of the two matrices (saying A) has n eigenvectors then to find the common eigenvector we have just to write the matrix B in the basis formed by the eigenvectors of A. But if there is eigenvectors with multiplicity >1, the common vector belong to vector space of dimension >1 and such strategy would not help compute it.In this paper we use Newton's method to compute a common eigenvector for two matrices, taking the backward error as a stopping criteria.We mention that no assumptions are made on the matrices A and B.     

Reaction of Aminobenzimidazoles with 4-Hydroxy-6-methyl-2-pyrone and 4-Hydroxycoumarine

6- and 7-(4-hydroxy-6-methyl-2-oxo-1-pyridyl)benzimidazoles and 1-(6- and 7-benzimidazolyl)-4-hydroxy-2-oxoquinolines were synthesized by reaction of aminobenzimidazoles with 4-hydroxy-6-methyl-2-pyrone and 4-hydroxycoumarine.     

Influence of anion substitution on hydrogen‐bonding patterns of salt compounds: cytosinium hydrogen sulfate and cytosinium perchlorate

In the two title compounds, cytosinium hydrogen sulfate, C₄H₆N₃O⁺·HSO₄⁻, (I), and cytosinium perchlorate, C₄H₆N₃O⁺·ClO₄⁻, (II), the asymmetric units comprise a cytosinium cation with hydrogen sulfate and perchlorate anions, respectively. The crystal structures of (I) and (II) are similar; that of (I) is characterized by a three‐dimensional N—H...O, O—H...O and C—H...O hydrogen‐bonded network. In (I) and (II), two‐dimensional layers are formed by N—H...O and C—H...O hydrogen bonds and, in the case of (I), they are linked by O—H...O hydrogen bonds where the anion acts as a donor and the cation as an acceptor. The hydrogen‐bonded sheets in (II) form an angle of 87.1°.     

Electro-fenton and photoelectro-fenton degradation of sulfanilic acid using a boron-doped diamond anode and an air diffusion cathode

The mineralization of sulfanilic acid has been studied by electro-Fenton (EF) and photoelectro-Fenton (PEF) reaction with UVA light using an undivided electrochemical cell with a boron-doped diamond (BDD) anode and an air diffusion cathode able to generate H(2)O(2). Organics were then oxidized by hydroxyl radicals formed at the anode surface from water oxidation and in the bulk from Fenton's reaction between generated H(2)O(2) and added Fe(2+). The UVA irradiation in PEF enhanced the production of hydroxyl radicals in the bulk, accelerating the removal of organics and photodecomposed intermediates like Fe(III)-carboxylate complexes. Partial decontamination of 1.39 mM sulfanilic acid solutions was achieved by EF until 100 mA cm(-2) at optimum conditions of 0.4 mM Fe(2+) and pH 3.0. The increase in current density and substrate content led to an almost total mineralization. In contrast, the PEF process was more powerful, yielding almost complete mineralization in less electrolysis time under comparable conditions. The kinetics for sulfanilic acid decay always followed a pseudo-first-order reaction. Hydroquinone and p-benzoquinone were detected as aromatic intermediates, whereas acetic, maleic, formic, oxalic, and oxamic acids were identified as generated carboxylic acids. NH(4)(+) ion was preferentially released in both treatments, along with NO(3)(-) ion in smaller proportion.     

Kinetics, mechanism, and computational studies of rhenium-catalyzed desulfurization reactions of thiiranes (thioepoxides)

The oxorhenium(V) dimer {MeReO(edt)}2 (1; where edt = 1,2-ethanedithiolate) catalyzes S atom transfer from thiiranes to triarylphosphines and triarylarsines. Despite the fact that phosphines are more nucleophilic than arsines, phosphines are less effective because they rapidly convert the dimer catalyst to the much less reactive catalyst [MeReO(edt)(PAr3)] (2). With AsAr3, which does not yield the monomer, the rate law is given by v = k[thiirane][1], independent of the arsine concentration. The values of k at 25.0 degrees C in CDCl3 are 5.58 +/- 0.08 L mol(-1) s(-1) for cyclohexene sulfide and ca. 2 L mol(-1) s(-1) for propylene sulfide. The activation parameters for cyclohexene sulfide are deltaH(double dagger) = 10.0 +/- 0.9 kcal mol(-1) and deltaS(double dagger) = -21 +/- 3 cal K(-1) mol(-1). Arsine enters the catalytic cycle after the rate-controlling release of alkene, undergoing a reaction with the Re(VII)(O)(S) intermediate that is so rapid in comparison that it cannot be studied directly. The use of a kinetic competition method provided relative rate constants and a Hammett reaction constant, rho = -1.0. Computations showed that there is little thermodynamic selectivity for arsine attack at O or S of the intermediate. There is, however, a large kinetic selectivity in favor of Ar3AsS formation: the calculated values of deltaH(double dagger) for attack of AsAr3 at Re=O vs Re=S in Re(VII)(O)(S) are 23.2 and 1.1 kcal mol(-1), respectively.     

On a Pre-Lie Algebra Defined by Insertion of Rooted Trees

Let K be a field of characteristic zero. For \({n \in \mathbb{N}^{*}}\) , let \({\mathcal{T}^{\,\prime}_{n}}\) be the vector space of non-planar rooted trees with n vertices (Foissy in Bull Sci Math 126, no. 3, 193–239; no. 4, 249–288, 2002). Let \({\vartriangleright}\) be the left pre-Lie product of insertion of a tree inside another defined on infinitesimal characters of the graded Hopf algebra \({\mathcal{H}}\) introduced by Calaque, Ebrahimi-Fard and Manchon. Let \({\mathcal{T}^{\,\prime}=\oplus_{n\geq 2}\mathcal{T}^{\,\prime}_{n}}\) . In this work, we first prove that \({(\mathcal{T}^{\,\prime}, \vartriangleright)}\) a pre-Lie algebra generated by the two ladders E ₁ and E ₂ where E ₁ is the ladder with one edge and E ₂ is the ladder with two edges. Second, we prove that \({(\mathcal{T}^{\,\prime}, \vartriangleright)}\) is not a free pre-Lie algebra, and we exhibit a family of relations.     

Synthesis of Tacrine Analogs Derived from N-Aryl-5-amino-4-cyanopyrazoles

Synthesis of 11 tacrine analogs derived from N-aryl-5-amino-4-cyanopyrazoles, by a Friedländer type reaction, is described. Their structures were confirmed by ¹H and ¹³C NMR spectroscopy, elemental analysis, and/or mass spectrometry.     

Théorèmes de trace de type Szegö dans le cas singulier

Let f be a function eiθ→f(eiθ)=|1−eiθ|^2αf₁(eiθ) with f₁ a regular strictly positive function and a real number α in ]−1/2,1/2[?{0}. In a previous paper for such a number α we have obtained the asymptotic behaviour of the entries of the inverse of the Toeplitz matrix TN,f when N goes to infinity. These results allow us to give trace formulas, which extend a classical expression of Szegö's limits theorems.     

Coupling proximal methods and variational convergence

An approximation method which combines a data perturbation by variational convergence with the proximal point algorithm, is presented. Conditions which guarantee convergence, are provided and an application to the partial inverse method is given.