Effects of neutron skin on the excitation of isovector modes of neutron-rich nuclei

The existence of a neutron skin in neutron-rich nuclei is discussed in connection with the excitation of isovector dipole and quadrupole giant modes via isoscalar nuclear probes. In the case of large neutron excess, important contributions are obtained from the nuclear excitation, which may even become predominant according to proper kinematical conditions. At variance with the usual situation encountered in inelastic processes, constructive interference can be found between nuclear and Coulomb contributions.     

The exterior magnetic field for the multilayer ellipsoidal model of the brain

The magnetic induction field in the exterior of an ellipsoidallyinhomogeneous, four-conducting-layer model of the human headis obtained analytically up to its quadrupole approximation.The interior ellipsoidal core represents the homogeneous brainwhile each one of the shells represents the cerebrospinal fluid,the skull and the scalp, all characterized by different conductivities.The inhomogeneities of these four domains, together with theanisotropy imposed by the use of the ellipsoidal geometry, providethe most realistic physical and geometrical model of the brainfor which an analytic solution of the biomagnetic forward problemis possible. It is shown that in contrast to the spherical model,where shells of different conductivity are magnetically invisible,the magnetic induction field in ellipsoidal geometry is stronglydependent on the conductivity supports. The fact that sphericalshells of different conductivity are invisible has enhancedthe common belief that the biomagnetic forward solution doesnot depend on the conductivity profiles. As we demonstrate inthe present work, this is not true. Hence, the proposed multilayeredellipsoidal model provides a qualitative improvement of therealistic interpretation of magnetoencephalography (MEG) measurements.We show that the presence of the shells of different conductivitycan be incorporated in the form of the dipole vector for thehomogeneous model. Numerical investigations show that the effectsof shell inhomogeneities are almost as sound as the level ofMEG measurements themselves. The degenerate cases, where eitherthe differences of the conductivities within the shells disappear,or the ellipsoidal geometry is reduced to the spherical one,are also considered.     

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.     

Sparse generalized Fourier transforms

Block-diagonalization of sparse equivariant discretization matrices is studied. Such matrices typically arise when partial differential equations that evolve in symmetric geometries are discretized via the finite element method or via finite differences. By considering sparse equivariant matrices as equivariant graphs, we identify a condition for when block-diagonalization via a sparse variant of a generalized Fourier transform (GFT) becomes particularly simple and fast. Characterizations for finite element triangulations of a symmetric domain are given, and formulas for assembling the block-diagonalized matrix directly are presented. It is emphasized that the GFT preserves symmetric (Hermitian) properties of an equivariant matrix. By simulating the heat equation at the surface of a sphere discretized by an icosahedral grid, it is demonstrated that the block-diagonalization is beneficial. The gain is significant for a direct method, and modest for an iterative method. A comparison with a block-diagonalization approach based upon the continuous formulation is made. It is found that the sparse GFT method is an appropriate way to discretize the resulting continuous subsystems, since the spectrum and the symmetry are preserved. AMS subject classification (2000)  43A30, 65T99, 20B25     

Adsorption of dicarboxylates on nano-sized gibbsite particles: effects of ligand structure on bonding mechanisms

The adsorption of the dicarboxylates o-phthalate, maleate, fumarate, malonate, and oxalate (representing ligands with the general composition ⁻O₂C---C_n---CO₂⁻; n=0, 1, or 2) on gibbsite were studied by means of quantitative batch adsorption experiments and attenuated total reflectance Fourier transform infrared (ATR-FTIR) spectroscopy. The interpretations of ATR-FTIR spectra were aided by comparison with IR spectra of solution species and by results from theoretical frequency calculations. The main objectives of the study were to identify the molecular level bonding mechanisms of the dicarboxylates to gibbsite, and to investigate how these were influenced by the composition and structure of the ligands. Carboxylates with n=2 formed predominantly outer sphere complexes, whereas the importance of inner sphere complexes progressively increased for n=1 and 0. The inner sphere structures were identified as mononuclear chelates with one oxygen from each carboxylate group bonded to Al(III) at the surface. This showed the importance of chelate ring structure for the formation of inner sphere surface complexes, with stabilities of the complexes increasing in the order seven-membered ring less than six-membered ring less than five-membered ring. For ligands with n=2 only small variations in surface speciation were observed as a function of steric factors; irrespective of the relative positions of the carboxylate groups and bulkiness of the ligands outer sphere bonding is the dominating adsorption mode. Adsorption experiments were also conducted with gibbsite particles exhibiting differences in shape and surface roughness. These experiments showed that inner sphere complexes were favored on the less well-developed and more irregular gibbsite particles.     

Carbon nanotube array-based biosensor

Aligned multi-wall carbon nanotubes (MWNT) grown on platinum substrate are used for the development of an amperometric biosensor. The opening and functionalization by oxidation of the nanotube array allows for the efficient immobilization of the model enzyme, glucose oxidase. The carboxylated open-ends of nanotubes are used for the immobilization of the enzymes, while the platinum substrate provides the direct transduction platform for signal monitoring. It is also shown that carbon nanotubes can play a dual role, both as immobilization matrices and as mediators, allowing for the development of a third generation of biosensor systems, with good overall analytical characteristics.     

Squeezing the [Cu-OH...H2O-Cu]3+ bridge by cryptate encapsulation

Treatment of cryptand L(1) with Cu(II) generates a H3O2(-)-bridged dicopper(II) cryptate, 2, where the guest anion has responded to steric constraint by a significant shortening of the O-O distance to 2.325(9) A; computational optimization at the B3LYP/6-31(d) level suggests that the bridging O-H...O H-bond is bent (approximately 157 degrees) but that the barrier to interchange of the bridging H atom is low (<4 kJ mol(-1)). This cryptate, rather than the [Cu2L(1)muCN]3+ species recently claimed to derive from cleavage of the C-C bond of the solvent, is the product of acetonitrile recrystallization of the initially formed reaction product, 1.     

Di-2-pyridylmethylamine-based palladium complexes as new catalysts for Heck,Suzuki, and Sonogashira reactions in organic and aqueous solvents

A new palladium-dipyridylmethylamine complex is an excellent catalyst for C-C bond-forming processes such as the Heck, Suzuki, and Sonogashira reactions in organic and aqueous solvents under homogeneous conditions. [reaction: see text]