The Singular Set of Minima of Integral Functionals

In this paper we provide upper bounds for the Hausdorff dimension of the singular set of minima of general variational integrals where F is suitably convex with respect to Dv and Hölder continuous with respect to (x,v). In particular, we prove that the Hausdorff dimension of the singular set is always strictly less than n, where .     

Optimal Potentials for Problems with Changing Sign Data

The main purpose of this paper is to study the duality and penalty method for a constrained nonconvex vector optimization problem. Following along with the image space analysis, a Lagrange-type duality for a constrained nonconvex vector optimization problem is proposed by virtue of the class of vector-valued regular weak separation functions in the image space. Simultaneously, some equivalent characterizations to the zero duality gap property are established including the Lagrange multiplier, the Lagrange saddle point and the regular separation. Moreover, an exact penalization is also obtained by means of a local image regularity condition and a class of particular regular weak separation functions in the image space.     

The zero-electron-mass limit in the hydrodynamic model for plasmas

The limit of the vanishing ratio of the electron mass to the ion mass in the isentropic transient Euler-Poisson equations with periodic boundary conditions is proved. The equations consist of the balance laws for the electron density and current density for a given ion density, coupled to the Poisson equation for the electrostatic potential. The limit is related to the low-Mach-number limit of Klainerman and Majda. In particular, the limit velocity satisfies the incompressible Euler equations with damping. The difference to the zero-Mach-number limit comes from the electrostatic potential which needs to be controlled. This is done by a reformulation of the equations in terms of the enthalpy, higher-order energy estimates and a careful use of the Poisson equation.     

Gradient continuity estimates

We consider degenerate elliptic equations of p-Laplacean type

$$-{\rm{div}}\, (\gamma(x)|Du|^{p-2}Du)=\mu\,,$$

and give a sufficient condition for the continuity of Du in terms of a natural non-linear Wolff potential of the right-hand side measure μ. As a corollary we identify borderline condition for the continuity of Du in terms of the data: namely μ belongs to the Lorentz space L(n, 1/(p ? 1)), and γ(x) is a Dini continuous elliptic coefficient. This last result, together with pointwise gradient bounds via non-linear potentials, extends to the non homogeneous p-Laplacean system, thereby giving a positive answer in the vectorial case to a conjecture of Verbitsky. Continuity conditions related to the density of μ, or to the decay rate of its L ⁿ -norm on small balls, are identified as well as corollaries of the main non-linear potential criterium.

     

On gap functions for nonsmooth multiobjective optimization problems

A set-valued gap function, \(\phi \), existing in the literature for smooth and nonsmooth multiobjective optimization problems is dealt with. It is known that \(0\in \phi (x^*)\) is a sufficient condition for efficiency of a feasible solution \(x^*\), while the converse does not hold. In the current work, the converse of this assertion is proved for properly efficient solutions. Afterwards, to avoid the complexities of set-valued maps some new single-valued gap functions, for nonsmooth multiobjective optimization problems with locally Lipschitz data are introduced. Important properties of the new gap functions are established.     

Correlation between different clean-up methods and analytical techniques performances to detect Ochratoxin A in wine

Three different clean-up methods and two analytical techniques were compared to determine Ochratoxin A (OTA) in wines. The first clean-up used a MycoSep column, the second an immunoaffinity column (IAC) and the third consisted in a liquid-liquid extraction (LLE) using dichloromethane in acid conditions. Meanwhile, two different OTA determination techniques were also evaluated: a HPLC analysis using a fluorescence detector and an enzyme-linked immunosorbent assays (ELISA) method.Correlations between clean-up methods and analytical techniques to determine OTA in wine were made evaluating linearity, accuracy and precision.Both the two first clean-up methods (solid-phase extraction, SPE) showed a good linear fit (r² = about 0.9999), followed by LLE. The use of immunoaffinity columns showed the best recoveries, even if also the SPE with MycoSep showed good recoveries while the LLE recoveries were the worst ones. The HPLC analysis showed good precision and accuracy, while ELISA method, even with a sufficient linearity, generally underestimated OTA content in wines.     

The Meyer-Schuster rearrangement: a new synthetic strategy leading to prostaglandins and their drug analogs, Bimatoprost and Latanoprost

Gold(I) mediated Meyer-Schuster rearrangement for the installation of the ‘lower’ side chain of prostaglandins and their analogs has been developed. This Au-mediated rearrangement, featuring a low catalyst loading and mild reaction conditions, has been demonstrated to be an efficient alternative to the standard Horner-Wadsworth-Emmons reaction in prostaglandin chemistry. Moreover, the present results provide a new synthetic process leading to pharmacologically active prostanoids: Latanoprost and Bimatoprost, that continue to hold key positions in the anti-glaucoma drug market.     

Lectin recognition of a new SOD mimic bioconjugate studied with surface plasmon resonance imaging

Surface plasmon resonance imaging is used to demonstrate the recognition by the Ricinus communis agglutinin of a new SOD mimic, a bioconjugate of the manganese(II) complex of 1,4,7,10,13-pentaazacyclopentadecane with galactose.