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.     

The matrix equation AX-YB=C and related problems

The main result of the paper is a theorem, using which a new proof of Roth’s theorem is obtained, a new solvability criterion for the matrix equation AX-YB = C is proved, a formula for a particular solution of the latter is derived, and the least of the orders of square nonsingular matrices containing a given rectangular matrix as a submatrix is determined. Bibliography: 5 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 323, 2005, pp. 15–23.     

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.     

Selective extraction of iron(III) from aqueous nitrate solution in the presence of cobalt(II), copper(II) and nickel(II) ions using bis(delta2-2-imidazolinyl)-5,5'-dioxime.

The feasibility of using bis(delta2-2-imidazolinyl)-5,5'-dioxime (H2L) for the selective extraction of iron(III) from aqueous solutions was investigated by employing an solvent-extraction technique. The extraction of iron(III) from an aqueous nitrate solution in the presence of metal ions, such as cobalt(II), copper(II) and nickel(II), was carried out using H2L in binary and multicomponent mixtures. Iron(III) extraction has been studied as a function of the pH, equilibrium time and extractant concentration. From the extracted complex species in the organic phase, iron(III) was stripped with 2 M HNO3, and later determined using atomic-absorption spectrometry. The extraction was found to significantly depend on the aqueous solution pH. The extraction of iron(III) with H2L increases with the pH value, reaching a maximum in the zone of pH 2.0, remaining constant between 2 and 3.5 and subsequently decreasing. The quantitative extraction of iron(III) with 5 x 10(-30 M H2L in toluene is observed at pH 2.0. H2L was found to react with iron(III) to form ligand complex having a composition of 1:2 (Fe:H2L).     

A Novel Cardiac Glycoside from Parepigynum funingesis

From the dried aerial part ofParepigynumfuningesis Tsiang et P. T. Li (Apocynaceae),a new cardiac glucoside, named parefuningoside (1) had been isolated. Its structure was determined by means of hydrolysis and spectral analysis.     

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 a Modified Subgradient Algorithm for Dual Problems via Sharp Augmented Lagrangian*

We study convergence properties of a modified subgradient algorithm, applied to the dual problem defined by the sharp augmented Lagrangian. The primal problem we consider is nonconvex and nondifferentiable, with equality constraints. We obtain primal and dual convergence results, as well as a condition for existence of a dual solution. Using a practical selection of the step-size parameters, we demonstrate the algorithm and its advantages on test problems, including an integer programming and an optimal control problem. *Partially Supported by 2003 UniSA ITEE Small Research Grant Ero2. Supported by CAPES, Brazil, Grant No. 0664-02/2, during her visit to the School of Mathematics and Statistics, UniSA.