The Determination of Protonation Constants of Some Amino Acids and Their Esters by Potentiometry in Different Media

In this study, stoichiometric protonation constants of L-tyrosine, L-cysteine, L-tryptophane, L-lysine, and L-histidine, and their methyl and ethyl esters in water and ethanol–water mixtures of 30, 50, and 70% ethanol (v/v), were determined potentiometrically using a combined pH electrode system calibrated as the concentration of hydrogen ion. Titrations were performed at 25^∘C and the ionic strength of the medium was maintained at 0.10 mol⋅L⁻¹ using sodium chloride. Protonation constants were calculated by using the BEST computer program. The effect of solvent composition on the protonation constants is discussed. The log₁₀ K₂ values of esters generally decreased with increasing ethanol content. However, the log₁₀ K₁ values of the esters of L-tyrosine, L-cysteine, and L-tryptophane were found to increase with increasing ethanol content in contrast those of L-lysine and L-histidine esters.     

Non-explosion en temps grand et stabilité de solutions globales des équations de Navier–StokesNon-blowup at large times and stability for global solutions to the Navier–Stokes equations

Suppose there exists a global solution u to the incompressible Navier–Stokes equations, such that $\text{u∈}\text{C}{}_{\mathrm{t}}\text{(}\text{H}\text{?}{}^{\mathrm{1/2}}\text{)}$. We prove that its $\text{H}\text{?}{}^{\mathrm{1/2}}$ norm goes to 0 at infinity. We next use this fact to control the $\text{L}{}^2{}_{\mathrm{t}}\text{(}\text{H}\text{?}{}^{\mathrm{3/2}}\text{)}$ norm of u, and finally we prove that such a solution is stable. To cite this article: I. Gallagher et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 289–292.     

Erratum: Synthesis and characterization of diorganotin(IV) complexes of Schiff bases with ONO‐type donors and crystal structure of [N‐(2‐hydroxy‐4‐nitrophenyl)‐3‐ethoxysalicylideneiminato]diphenyltin(IV)

The article referenced above was first published online on 30 August 2007 with incorrect pagination; the pagination has now been corrected online and in print. Copyright © 2007 John Wiley & Sons, Ltd.     

On Genuine Bernstein–Durrmeyer Operators

We continue the studies on the so–called genuine Bernstein–Durrmeyer operators U _n by establishing a recurrence formula for the moments and by investigating the semigroup T(t) approximated by U _n . Moreover, for sufficiently smooth functions the degree of this convergence is estimated. We also determine the eigenstructure of U _n , compute the moments of T(t) and establish asymptotic formulas. Received: January 26, 2007.     

On the S-procedure and Some Variants

We give a concise review and extension of S-procedure that is an instrumental tool in control theory and robust optimization analysis. We also discuss the approximate S-Lemma as well as its applications in robust optimization.The many suggestions and detailed corrections of an anonymous referee are gratefully acknowledged.     

Adsorption of the Cu<Superscript>2+</Superscript> ions from aqueous solutions on the active carbon oxidized with hydrogen peroxide and impregnated with nitrogen-containing compounds

Adsorption of the copper ions from aqueous solutions, benzene, and water on the active carbon obtained by chemical activation from walnut shells was studied. The active carbon was additionally oxidized with hydrogen peroxide and then impregnated with nitrogen-containing compounds. As a result of impregnation with melamine, a secondary porosity is formed within the oxidized active carbon, leading to an increase in the specific surface of the sorbent. A modified carbon surface is heterogeneous, and the carbons themselves exhibit catalytic activity in the oxidation of luminol and decomposition of hydrogen peroxide.     

Synthesis and characterization of mid‐ and end‐chain functional telechelics by controlled polymerization methods and coupling processes

Well‐defined polystyrene‐ (PSt) or poly(ε‐caprolactone) (PCL)‐based polymers containing mid‐ or end‐chain 2,5 or 3,5‐ dibromobenzene moieties were prepared by controlled polymerization methods, such as atom transfer radical polymerization (ATRP) or ring opening polymerization (ROP). 1,4‐Dibromo‐2‐(bromomethyl)benzene, 1,3‐dibromo‐5‐(bromomethyl)benzene, and 1,4‐dibromo‐2,5‐di(bromomethyl)benzene were used as initiators in ATRP of styrene (St) in conjunction with CuBr/2,2′‐bipyridine as catalyst. 2,5‐Dibromo‐1,4‐(dihydroxymethyl)benzene initiated the ROP of ε‐caprolactone (CL) in the presence of stannous octoate (Sn(Oct)₂) catalyst. The reaction of these polymers with amino‐ or aldehyde‐functionalized monoboronic acids, in Suzuki‐type couplings, afforded the corresponding telechelics. Further functionalization with oxidable groups such as 2‐pyrrolyl or 1‐naphthyl was attained by condensation reactions of the amino or aldehyde groups with low molecular weight aldehydes or amines, respectively, with the formation of azomethine linkages. Preliminary attempts for the synthesis of fully conjugated poly(Schiff base) with polymeric segments as substituents, by oxidative polymerization of the macromonomers, are presented. All the starting, intermediate, or final polymers were structurally analyzed by spectral methods (¹H NMR, ¹³C NMR, and IR). © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 727–743, 2006