ENERGY OF GLOBAL FRAMES

The energy of a unit vector field X on a closed Riemannian manifold M is defined as the energy of the section into T(1) M determined by X. For odd-dimensional spheres, the energy functional has an infimum for each dimension 2k + 1 which is not attained by any non-singular vector field for k > 1. For k = 1, Hopf vector fields are the unique minima. In this paper we show that for any closed Riemannian manifold, the energy of a frame defined on the manifold, possibly except on a finite subset, admits a lower bound in terms of the total scalar curvature of the manifold. In particular, for odd-dimensional spheres this lower bound is attained by a family of frames defined on the sphere minus one point and consisting of vector fields parallel along geodesics.

On a Gromoll-Meyer type theorem in globally hyperbolic stationary spacetimes

Following the lines of the celebrated Riemannian result of Gromoll and Meyer, we use infinite dimensional equivariant Morse theory to establish the existence of infinitely many geometrically distinct closed geodesics in a class of globally hyperbolic stationary Lorentzian manifolds.

On the semi-Riemannian bumpy metric theorem

We prove the semi-Riemannian bumpy metric theorem using equivariant variational genericity. The theorem states that, on a given compact manifold M, the set of semi-Riemannian metrics that admit only nondegenerate closed geodesics is generic relatively to the C(k)-topology, k=2, ..., infinity, in the set of metrics of a given index on M. A higher-order genericity Riemannian result of Klingenberg and Takens is extended to semi-Riemannian geometry.

Protoporphyrin IX Nanoparticle Carrier: Preparation, Optical Properties, and Singlet Oxygen Generation

The present study is focused on developing a nanoparticle carrier for the photosensitizer protoporphyrin IX for use in photodynamic therapy. The entrapment of protoporphyrin IX (Pp IX) in silica spheres was achieved by modification of Pp IX molecules with an organosilane reagent. The immobilized drug preserved its optical properties and the capacity to generate singlet oxygen, which was detected by a direct method from its characteristic phosphorescence decay curve at near-infrared and by a chemical method using 1,3-diphenylisobenzofuran to trap singlet oxygen. The lifetime of singlet oxygen when a suspension of Pp IX-loaded particles in acetonitrile was excited at 532 nm was determined as 52 mu s, which is in good agreement with the value determined for methylene blue in acetonitrile solution under the same conditions. The Pp IX-loaded silica particles have an efficiency of singlet oxygen generation (eta Delta) higher than the quantum yield of free porphyrins. This high efficiency of singlet oxygen generation was attributed to changes on the monomer-dimer equilibrium after photosentisizer immobilization.

Photoluminescence study of new lanthanide complexes with benzeneseleninic acids

New lanthanide complexes with benzeneseleninic (ABSe) and 4-chloro-benzeneseleninic (ABSeCl) acids have been synthesized and characterized by elemental analysis, infrared and UV-visible spectroscopies. The emission spectra of the trivalent europium complexes presented the typical electronic (5)D(0) -> (7)F(j) transitions of the ion (J = 0-4). The ground-state geometries of the europium complexes have been calculated by using the Sparkle/AM1 model. From these results, the 4f-4f intensity parameters and energies of the ligand singlet and triplet excited states have been obtained. The lower emission quantum yield for the [Eu(ABSe)(3)(H(2)O)(2)](H(2)O)(2) compound, as compared to the [Eu(Al(3)SeCl)(3)(H(2)O)(2)] one, can be associated to the higher numbers of water molecules, in the first and second coordination spheres, that contribute to the luminescence quenching. The [Eu(Al(3)Se)(3)(H(2)O)(2)](H(2)O)(2) complex presents an intermediate state whose energy difference with respect to the first excited singlet state is resonant with three phonons from the water molecules, favouring a multiphonon relaxation process from the singlet state followed by a fast internal conversion process; this effect is less pronounced in the complex with the ABSeCl ligand. The luminescence decay curves of the gadolinium complexes indicate that the level responsible for the intramolecular energy transfer process has a triplet character for both compounds. The nephelauxetic effect in these compounds was investigated under the light of a recently proposed covalency scale based on the concept of overlap polarizability of the chemical bond. (C) 2009 Elsevier B.V. All rights reserved.

Formation of out of plane oxime metallacycles in [Cu(2)] and [Cu(4)] complexes

The reaction Of Cu(ClO(4))(2)center dot 6H(2)O with dimethylglyoxime (H(2)dmg) in a 1:1 mole ratio in aqueous methanol at room temperature affords the dinuclear complex [Cu(2)(mu-Hdmg)(4)] (1). Reaction of 1 with [Cu(bpy)(H(2)O)(2)](ClO(4))(2) (bpy = 2,2`-bipyridine) in a 1:1 mole ratio in aqueous methanol at room temperature yields the tetranuclear complex [Cu(2)(mu-HdMg)(2)(mu-dMg)(2)(bpy)(2)(H(2)O)(2)](ClO(4))(2) (2). The direct reaction of Cu(ClO(4))(2)center dot 6H(2)O with H(2)dmg and bpy in a 2:21 mole ratio in aqueous methanol at room temperature also yields 2 quantitatively. The complexes 1 and 2 were structurally characterized by X-ray crystallography. Unlike the binding in Ni/Co-dmg, two different types of N-O bridging modes during the oxime based metallacycle formation and stacking of square planar units have been identified in these complexes. The neutral dinuclear complex 1 has CuN(4)O coordination spheres and complex 2 consists of a dicationic [Cu(2)(mu-HdMg)(2)(mu-dMg)(2)(bpy)(2)(H(2)O)(2)](2+) unit and two uncoordinated ClO(4)(-) anions having CuN(4)O and CuN(2)O(3) coordination spheres. The two copper(II) ions are at a distance of 3.846(8) angstrom in 1 for the trans out of plane link and at 3.419(10) and 3.684(10) angstrom in 2 for the trans out of plane and cis in plane arrangements, respectively. The average Cu-N(oxime) distances are 1.953 and 1.935 angstrom, respectively. The average basal and apical Cu-N(oxime) distances are 1.945, 2.295 and 2.429 angstrom. The UV-Vis spectra of 2 is similar to the spectrum of the reaction mixture of 1 and [Cu(bpy)(H(2)O)(2)](2+). Variable temperature magnetic properties measurement shows that the interaction between the paramagnetic copper centers in complex I is antiferromagnetic in nature. The EPR spectra of frozen solution of the complexes at 77 K consist of axially symmetric fine-structure transitions (Delta M(S) = 1) and half-field signals (Delta M(S) = 2) at ca. 1600 G, suggesting the presence of appreciable Cu-Cu interactions. (C) 2009 Elsevier Ltd. All rights reserved.

Using Polycarbonate Membranes as Templates for the Preparation of Au Nanostructures for Surface-Enhanced Raman Scattering

Polycarbonate membranes (PCM) of various pores sizes (400, 200, 100 and 50 nm) were used as templates for gold deposition. The electrodeposition from gold ions resulted in the formation of gold nanotubes when large pores size PCMs (400 and 200 nm) were used. On the other hand, gold nanowires were predominant for the PCMs with smaller pores size (100 and 50 nm). Surface-enhanced Raman scattering (SERS) from the probe molecule 4-mercaptopyridine (4-MPy) was obtained from all these nanostructures. The SERS efficiency of the substrates produced using the PC M templates were compared to two commonly used SERS platforms: a roughened gold electrode and gold nanostructures electrodeposited through organized polystyrene spheres (PSS). The SERS signal of the probe molecule increased as the pore diameter of the PCM template decreased. Moreover, the SERS efficiency from the nanostructures produced using 50 nm PCM templates was four and two times better than the signal from the roughened gold electrode and the PSS template, respectively. The SERS substrates prepared using PCM templates were more homogenous over a larger area (ca. 1 cm(2)), presented better spatial and sample to sample reproducibility than the other substrates. These results show that SERS substrates prepared using PCM templates are promising for the fabrication of planar SERS platforms for analytical/bioanalytical applications.

Oxorhenium(V) Complexes with 2,3-Dihydroxynaphthalene

2,3-Dihydroxynaphthalene (H(2)dhn) reacts with [ReOCl(3)-(PPh(3))(2)] or [ReOBr(3)(PPh(3))(2)] in a 1:1 molar ratio with formation of the isostructural complexes [ReOCl(2)(PPh(3))(2)(Hdhn)] (4) and [ReOBr(2)-(PPh(3))(2)(Hdhn)] (5). They have distorted octahedral coordination spheres with the halide and the triphenylphosphine ligands arranged in equatorial trans positions to each other. The Hdhn-ligand coordinates monodentately in trans position to the oxo ligand. Intramolecular hydrogen bonds between the Hdhn and the halogeno ligands stabilize this coordination mode. The products represent the first examples of oxorhenium(V) complexes with monodentate catecholate-type ligands.

Cationic and neutral phenylmercury(II) complexes with heterocyclic thione ligands. X-ray structures of [HgPh(dmpymtH)][BF(4)] center dot H(2)O and [{HgPh}(2)(mu-dtu)]

The neutral complex [HgPh(dmpymt)] 1 (dmpymtH = 4,6-dimethylpyrimidine-2(1H)-thione) reacts with HBF(4) to give the cationic complex [HgPh(dmpymtH)][BF(4)] 2. The X-ray molecular structure of the later revealed a [2+1] coordination sphere about the mercury(II) atom (C-Hg-S and Hg center dot center dot center dot N). In the dinuclear complex [(HgPh)(2)(mu-dtu)] 3 [dtuH(2) = 2,4(1H,3H)-pyrimidinedithione or dithiouracil] the coordination spheres are also [2+1] although dissimilar regarding the Hg center dot center dot center dot N secondary bonds. NMR spectroscopy ((1)H, (13)C and (199)Hg) studies were undertaken in solution and the results discussed in the light of the X-ray structures. (C) 2008 Elsevier B. V. All rights reserved.