On the existence of ground state solutions to nonlinear Schrödinger equations with multisingular inverse-square anisotropic potentials

A class of nonlinear Schrödinger equations with critical power-nonlinearities and potentials exhibiting multiple anisotropic inverse square singularities is investigated. Conditions on strength, location, and orientation of singularities are given for the minimum of the associated Rayleigh quotient to be achieved, both in ? ^N and in bounded domains.     

Necessary and sufficient global optimality conditions for NLP reformulations of linear SDP problems

In this paper we consider the standard linear SDP problem, and its low rank nonlinear programming reformulation, based on a Gramian representation of a positive semidefinite matrix. For this nonconvex quadratic problem with quadratic equality constraints, we give necessary and sufficient conditions of global optimality expressed in terms of the Lagrangian function.     

Solvent systems for countercurrent chromatography: an aqueous two phase liquid system based on a room temperature ionic liquid

A new aqueous two phase liquid system (ATPS) based on the ionic liquid 1-butyl-3-methyl imidazolium chloride (BMIM Cl), potassium dibasic phosphate (K(2)HPO(4)) and water was recently proposed in the literature. The full phase diagram of this ATPS was prepared and some tie lines were fully determined. It was compared to classical ATPSs based on polyethylene glycol with an average molecular mass of 1000 (PEG 1000) and 10,000 (PEG 10000) and K(2)HPO(4). Two countercurrent chromatography (CCC) columns, a hydrostatic Sanki and a J type hydrodynamic CCC columns were used to test the liquid phase retention of these ATPSs in all possible configurations. It was found that the BMIM Cl ATPS liquid phases were much easier to retain in the two CCC columns than the PEG 1000 ATPS phases. Using protein and alcohol solutes, it was established that the BMIM Cl ATPS has a polarity completely different from that of the PEG 1000 ATPS. For example, ovalbumin partitions equally between the two phases of the PEG 1000 ATPS (K(D)=1.4) when it is completely located in the BMIM Cl upper phase of the ionic liquid ATPS (K(D)=180). The discrimination factor of the ionic liquid system and its intrinsic hydrophobicity were respectively found three times higher and ten times lower than the respective values of the PEG 1000 ATPS.     

NMR study of the adsorption-desorption kinetics of dissolved tetraalanine in MCM-41 mesoporous material

In this study we show how deuterium magic-angle spinning NMR spectroscopy can be used to investigate the adsorption-desorption kinetics of molecules in solution at surface-liquid interfaces. An aqueous solution of deuterium-labeled tetraalanine is inserted in the pores of MCM-41 mesoporous material, and its 2H MAS NMR spectrum is measured as a function of temperature and fraction of filling of the pores. Prior to this study, the different types of water in MCM-41 are characterized as a function of water loading of the pores. Analysis of 2H MAS sideband line shapes enabled the determination of the adsorption and desorption rates and the activation energies of desorption.     

Light-emitting iridium(III) and ruthenium(II) polypyridyl complexes containing quadruple hydrogen-bonding moieties

A novel compound containing both a 2,2'-bipyridine as well as a 2-ureido-4[1H]-ureidopyrimidinone supramolecular moiety (3) has been synthesised and fully characterized by 1H-NMR, MALDI-TOFMS, UV-vis and IR spectroscopy. Subsequent coordination to iridium and ruthenium polypyridyl precursors allowed the formation of iridium(III) and ruthenium(II) polypyridyl dimers (5 and 7) assembled via quadruple hydrogen-bonding as well as metal coordination interactions. The syntheses and complete characterization of these materials by means of two-dimensional NMR techniques (1H-1H COSY and 1H-1H DOSY) as well as IR and MALDI-TOFMS are described in detail. Comparative studies of the optical properties of the luminescent model complexes (5' and '7) and the dimer species (5 and 7) are also illustrated. In addition, good processability of the materials has been demonstrated by inkjet printing leading to thin films revealing their potential for light-emitting devices.     

A Note on Local Asymptotics of Solutions to Singular Elliptic Equations via Monotonicity Methods

This paper concerns the asymptotic behavior of solutions and their gradients to linear and nonlinear elliptic equations with singular coefficients of fuchsian type.