On Finite and Strong Convergence of a Proximal Method for Equilibrium Problems

We introduce the notions of conditioning and well-posedness for equilibrium problems. Using these concepts, we obtain finite and strong convergence results for the proximal method that improve, develop, and unify several theorems in optimization and nonlinear analysis.     

Thymoquinone Lowers Blood Glucose and Reduces Oxidative Stress in a Rat Model of Diabetes

The aim of the present study was to assess the short-term effects of Thymoquinone (TQ) on oxidative stress, glycaemic control, and renal functions in diabetic rats. DM was induced in groups II and III with a single dose of streptozotocin (STZ), while group I received no medication (control). The rats in groups I and II were then given distilled water, while the rats in group III were given TQ at a dose of 50 mg/kg body weight/day for 4 weeks. Lipid peroxidase, nitric oxide (NO), total antioxidant capacity (TAC), glycated haemoglobin (HbA1c), lipid profiles, and renal function were assessed. Moreover, the renal tissues were used for histopathological examination. STZ increased the levels of HbA1c, lipid peroxidase, NO, and creatinine in STZ-induced diabetic rats in comparison to control rats. TAC was lower in STZ-induced diabetic rats than in the control group. Furthermore, rats treated with TQ exhibited significantly lower levels of HbA1c, lipid peroxidase, and NO than did untreated diabetic rats. TAC was higher in diabetic rats treated with TQ than in untreated diabetic rats. The histopathological results showed that treatment with TQ greatly attenuated the effect of STZ-induced diabetic nephropathy. TQ effectively adjusts glycaemic control and reduces oxidative stress in STZ-induced diabetic rats without significant damaging effects on the renal function.     

Estimateur hiérarchique robuste pour un problème de perturbation singulière

In this Note, we show that a modified and simplified version of the estimator of Bank–Weiser can be used to define a robust a posteriori error estimator for singularly perturbed problem. We prove without comparison with a residual estimator or saturation assumption, the equivalence of the estimator with the error in the energy norm and the robusteness with respect to the diffusion coefficient. To cite this article: B. Achchab et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Syntheses and crystal structures of two magnesium–tetrazole compounds in salt and polymeric forms

Two alkaline earth–tetrazole compounds, namely catena‐poly[[[triaquamagnesium(II)]‐μ‐5,5′‐(azanediyl)ditetrazolato‐κ³N¹,N^1′:N⁵] hemi{bis[μ‐5,5′‐(azanediyl)ditetrazolato‐κ³N¹,N^1′:N²]bis[triaquamagnesium(II)]} monohydrate], {[Mg(C₂HN₉)(H₂O)₃][Mg₂(C₂HN₉)₂(H₂O)₆]_0.5·H₂O}_n, (I), and bis[5‐(pyrazin‐2‐yl)tetrazolate] hexaaquamagnesium(II), (C₅H₃N₆)[Mg(H₂O)₆], (II), have been prepared under hydrothermal conditions. Compound (I) is a mixed dimer–polymer based on magnesium ion centres and can be regarded as the first example of a magnesium–tetrazolate polymer in the crystalline form. The structure shows a complex three‐dimensional hydrogen‐bonded network that involves magnesium–tetrazolate dimers, solvent water molecules and one‐dimensional magnesium–tetrazolate polymeric chains. The intrinsic cohesion in the polymer chains is ensured by N—H...N hydrogen bonds, which form R₂²(7) rings, thus reinforcing the propagation of the polymer chain along the a axis. The crystal structure of magnesium tetrazole salt (II) reveals a mixed ribbon of hydrogen‐bonded rings, of types R₂²(7), R₂²(9) and R₂⁴(10), running along the c axis, which are linked by R₂⁴(16) rings, generating a 4,8‐c flu net.     

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°.     

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.     

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.     

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.     

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.     

Surjective linear maps preserving local spectra

Let B(X) be the algebra of all bounded linear operators on an infinite dimensional complex Banach space X. We characterize linear surjective and continuous maps on B(X) preserving different local spectral quantities at a nonzero fixed vector.