Infinite dimensional duality and applications

The usual duality theory cannot be applied to infinite dimensional problems because the underlying constraint set mostly has an empty interior and the constraints are possibly nonlinear. In this paper we present an infinite dimensional nonlinear duality theory obtained by using new separation theorems based on the notion of quasi-relative interior, which, in all the concrete problems considered, is nonempty. We apply this theory to solve the until now unsolved problem of finding, in the infinite dimensional case, the Lagrange multipliers associated to optimization problems or to variational inequalities. As an example, we find the Lagrange multiplier associated to a general elastic–plastic torsion problem.     

Binding of hexacyanoferrate(II) by aliphatic amines in aqueous solution

The stability of hexacyanoferrate(II)-amine(methylamine, ethylenediamine, diethylenetriamine and tetraethylenepentamine) was determined potentiometrically. Species Fe(CN)₆(A)H _j ^(j–4) (A=amine) are formed in all the systems investigated, with j=1...n+2 (n=number of aminogroups). Some other complexes Fe(CN)₆(A)_iH_j (with i>1) were also found. The stability of these complexes is fairly high: the full protonated amine species, show for the reaction Fe(CN)₆ ^4- + H_nAⁿ⁺ = Fe(CN)₆(A)H_n ^(n-4) an equilibrium constant given by logK=0.686+2.10n. Factors affecting the stability are discussed in comparison with similar systems, together with the importance of interferences.     

Interaction of l-malic acid with alkaline metals and open chain polyammonium cations in aqueous solution

This work reports a potentiometric, calorimetric and spectropolarimetric ultraviolet circular dichroism (UV/CD) study of the interaction of l-malic acid with alkaline metals or (poly)ammonium (methylamine, ethylenediamine, diethylenetriamine, triethylenetetramine, spermine, tetraethylenepentamine and pentaethylenehexamine) cations. Stability data (logK, DeltaG(0)) were obtained potentiometrically for the l-malic acid with (poly)ammonium cations systems; calorimetric measurements (25 degrees C) made it possible to obtain DeltaH(0) and TDeltaS(0) values for the complexes formed in the systems under examination. logK values calculated (for the reaction: H(i)A(i+)+H(j)L((j-z))=ALH(r)((i+j-z)), with r=i+j) range between 0.8 and 4.6, i.e., the interactions are from weak to fairly strong while maximum stability for each system is given by the species with the highest z(anion)xz(cation) (z=charge) value. Enthalpy changes associated with reactions H(n)A(n+)+L(2-)=ALH(n)((n-2)) and H(n)A(n+)+HL(-)=ALH(n+1)((n-1)) are always positive and increase progressively with n. The same is valid for T DeltaS(0) values, which indicate that these species are entropically stabilized, as expected for electrostatic interactions. It was verified that the UV/CD signal depends on both ionic medium and ionic strength value; for comparison, we used the l-malic acid signal recorded in tetramethylammonium chloride as baseline background salt (as in potentiometry). UV/CD spectra were recorded for solutions containing both cationic and anionic species. When the cation was a protonated polyamine, CD spectra calculations were performed for most stable ion pairs: the results show remarkable differences in Deltaepsilon (dm(3) mol(-1) cm(-1)) values at 205 nm (which is the l-malate UV/CD lambda(max)) between the chiral ligand and its complex with a polyamine.     

Formation and stability of pyrophosphate complexes with aliphatic amines in aqueous solution

The complex formation between pyrophosphate (P(2)O(7)(4-)) and protonated methylamine, ethylenediamine, diethylenetriamine, triethylenetetramine, tetraethylenepentamine and pentaethylenehexamine, has been studied potentiometrically, in aqueous solution, at 25 degrees C. It was found that the species ALH(q)(A = amine, L = P(2)O(7)(4-)) are formed with q = 1 ... n(n = 3, 5, 6, 7, 7 and 8 for the above amines respectively). Mono- and di-amines form species A(p)LH(q) too. The stability of these species is quite high [e.g. H(4)A(4+) + HL(3-)ALH(5)(+): log K = 8.1 (A = pentaethylenehexamine)] and depends strictly on the charges involved in the formation reaction. Charges of reactants being equal, the stability trend is penten > tetren > trien > dien > en > meta and cationic mixed species are more stable than anionic ones. These results are discussed in relation to speciation problems in natural and biological fluids.     

The retention of some open-chain diamines on a strong cation-exchange resin in ion chromatography as a function of their structure

This work reports the results of a study of the influence of the structure of some open-chain diamines on their retention in high-performance ion chromatography (HPIC). We examine a set of eight diamines, in which the N atoms are separated by two C atoms and are differently N- and C-alkyl substituted; four of these diamines have the same formula weight. In the other two sets, the diamines are different from each other, either in terms of the length of the alkyl chain between the N atoms or in terms of the length of the substituent(s) on the nitrogen atom(s). The mobile phase is a mixture of HClO4 0.100 mol/L, 0.160 < C(NaClO4) < 1.50 mol/L, and 0 < acetonitrile% < or = 15 (v/v). The amines are detected by integrated amperometry. Interpretation of experimental data shows that (a) elution occurs for both ionic and hydrophobic interactions and is dependent on all the components of the mobile phase, (b) the diamines are eluted in any case as dications, and (c) steric hindrance significantly influences elution times. Some examples of separation are proposed.     

Interaction of methyltin(IV) compounds with carboxylate ligands. Part 2: formation thermodynamic parameters,predictive relationships and sequestering ability

Thermodynamic data of mono‐, di‐ and tri‐methyltin(IV)‐carboxylate complexes (acetate, malonate, succinate, oxydiacetate, diethylenetrioxydiacetate, malate, citrate, 1,2,3‐tricarballylate, 1,2,3,4‐butanetetracarboxylate, 1,2,3,4,5,6‐benzenehexacarboxylate) in aqueous solution are reported at t = 25 °C and I = 0 mol l⁻¹. Thermodynamic parameters obtained were analysed to formulate empirical predictive relationships as a function of different parameters, such as the number of carboxylate groups of the ligand and the charge of the alkyltin(IV) cation. Sequestration diagrams of citrate and 1,2,3‐tricarballylate towards alkyltin(IV) cations at different pH values are also reported and discussed. Copyright © 2007 John Wiley & Sons, Ltd.     

Oxazolidinone Antibiotics: Chemical,Biological and Analytical Aspects

This review covers the main aspects concerning the chemistry, the biological activity and the analytical determination of oxazolidinones, the only new class of synthetic antibiotics advanced in clinical use over the past 50 years. They are characterized by a chemical structure including the oxazolidone ring with the S configuration of substituent at C5, the acylaminomethyl group linked to C5 and the N-aryl substituent. The synthesis of oxazolidinones has gained increasing interest due to their unique mechanism of action that assures high antibiotic efficiency and low susceptibility to resistance mechanisms. Here, the main features of oxazolidinone antibiotics licensed or under development, such as Linezolid, Sutezolid, Eperezolid, Radezolid, Contezolid, Posizolid, Tedizolid, Delpazolid and TBI-223, are discussed. As they are protein synthesis inhibitors active against a wide spectrum of multidrug-resistant Gram-positive bacteria, their biological activity is carefully analyzed, together with the drug delivery systems recently developed to overcome the poor oxazolidinone water solubility. Finally, the most employed analytical techniques for oxazolidinone determination in different matrices, such as biological fluids, tissues, drugs and natural waters, are reviewed. Most are based on HPLC (High Performance Liquid Chromatography) coupled with UV-Vis or mass spectrometer detectors, but, to a lesser extent are also based on spectrofluorimetry or voltammetry.     

Global regularity for solutions to Dirichlet problem for discontinuous elliptic systems with nonlinearity q > 1 and with natural growth

In this paper we deal with the Hölder regularity up to the boundary of the solutions to a nonhomogeneous Dirichlet problem for second-order discontinuous elliptic systems with nonlinearity q > 1 and with natural growth. The aim of the paper is to clarify that the solutions of the above problem are always global Hölder continuous in the case of the dimension n = q without any kind of regularity assumptions on the coefficients. As a consequence of this sharp result, the singular sets $\Omega_0 \subset \OmegaIn this paper we deal with the H?lder regularity up to the boundary of the solutions to a nonhomogeneous Dirichlet problem for second-order discontinuous elliptic systems with nonlinearity q > 1 and with natural growth. The aim of the paper is to clarify that the solutions of the above problem are always global H?lder continuous in the case of the dimension n = q without any kind of regularity assumptions on the coefficients. As a consequence of this sharp result, the singular sets , are always empty for n = q. Moreover we show that also for 1 < q < 2, but q close enough to 2, the solutions are global H?lder continuous for n = 2.