Étude d'un système non linéaire de Boussinesq–Stefan

We give a few existence results for solutions for a class of Boussinesq–Stefan systems, with suitable conditions on the forcing terms in the right-hand side of the momentum equation depending on the temperature. To cite this article: A. Attaoui, C. R. Acad. Sci. Paris, Ser. I 347 (2009).     

Novel syntheses of pyrrolone and pyrrolopyridine derivatives

4-Arylmethylene-2-phenyl-2-oxazolin-5-ones 1a , b reacted with some active methylene reagents to afford pyrrolidine-3,5-dione, pyrrolo[2,3-b]pyridine and pyrrolinone derivatives. The cinnamate ester, obtained from 1a and sodium ethoxide, could be converted into a pyrrolidinone derivative having an active methylene group. This compound coupled with diazonium salts to afford the corresponding azo coupling products.     

A two parameter mixed interior-exterior penalty algorithm

In this paper, we analyze the mixed penalty methods introduced in the classic book of Fiacco and McCormick usingtwo distinct penalty parametersr, t. The two penalty coefficients induce a two-parameter differentiable trajectory. We analyze the numerical behaviour of an extrapolation strategy that follows the path of the two-parameter trajectory. We show also how to remove the ill-conditioning by suitable transformations of the equations. In the resulting theory, we show that function values as well as distances to the optimum are both governed by the same behaviour as interior methods (two-step superlinearly convergent, with limiting exponent 4/3).Research partially supported by NSERC grant OGP0036512.Research partially supported by NSERC grant OGP0005491.     

Screening effect of Ti ions on the electrical conductivity and thermoelectric power of Mg ferrite

The samples Mg_1+xTi_xFe_2−2xO₄ were prepared in a single phase spinel structure as indicated from X-ray analysis. The preference of Mg²⁺ ions to the octahedral site decreases the ratio of the normal spinel in the investigated ferrite where the Mg²⁺ increases on the expense of the Fe³⁺ ions on the same site. The increase in the conductivity was found to be due to thermally activated mobility of charge carriers. The mobility data enhances the use of Verway model of conductivity which depends on the electron exchange between iron ions of different valences located on the same crystallographic sites. The existence of Ti⁴⁺ ions on the octahedral site screens the polarization and decreases the conductivity of the samples. Peculiar behavior was obtained for Ti content of 0.7 and 0.8 due to the presence of secondary phases.     

TMSCH(2)Li and TMSCH(2)Li-LiDMAE: efficient reagents for noncryogenic halogen-lithium exchange in bromopyridines

TMSCH(2)Li and TMSCH(2)Li-LiDMAE have been used efficiently for bromine-lithium exchange in 2-bromo-, 3-bromo-, and 2,5-dibromopyridines under noncryogenic conditions, while low temperatures (-78 to -100 degrees C) are always needed with n-BuLi. The aminoalkoxide LiDMAE induced a remarkable C-2 selectivity with 2,5-dibromopyridines in toluene at 0 degrees C, which was unprecedented at such a temperature. The lithiopyridines were successfully reacted with electrophiles also under noncryogenic conditions giving the expected adducts in good yields.     

Total Synthesis of Δ12‐Prostaglandin J3: Evolution of Synthetic Strategies to a Streamlined Process

The total synthesis of Δ¹²‐prostaglandin J₃ (Δ¹²‐PGJ₃, 1 ), a reported leukemia stem cell ablator, through a number of strategies and tactics is described. The signature cross‐conjugated dienone structural motif of 1 was forged by an aldol reaction/dehydration sequence from key building blocks enone 13 and aldehyde 14 , whose lone stereocenters were generated by an asymmetric Tsuji–Trost reaction and an asymmetric Mukaiyama aldol reaction, respectively. During this program, a substituent‐governed regioselectivity pattern for the Rh‐catalyzed C?H functionalization of cyclopentenes and related olefins was discovered. The evolution of the synthesis of 1 from the original strategy to the final streamlined process proceeded through improvements in the construction of both fragments 13 and 14 , exploration of the chemistry of the hitherto underutilized chiral lactone synthon 57 , and a diastereoselective alkylation of a cyclopentenone intermediate. The described chemistry sets the stage for large‐scale production of Δ¹²‐PGJ₃ and designed analogues for further biological and pharmacological studies.     

Coupling reaction between electron-rich pyrimidinones and α-amino acids promoted by phosphonium salts

Coupling reaction between electron-rich 2-morpholino-4(3H)-pyrimidinone and nucleophilic side chains of several natural α-amino acids promoted by phosphonium salt has been developed to prepare new optically active pyrimidin-4-yl amino acids. The best results were obtained using a two-step method through the easily available benzotriazolyl-1-oxy intermediate. A detailed optimization study of this reaction is discussed.