Weakly Z symmetric manifolds

We introduce a new kind of Riemannian manifold that includes weakly-, pseudo- and pseudo projective- Ricci symmetric manifolds. The manifold is defined through a generalization of the so called Z tensor; it is named "weakly Z symmetric" and denoted by (WZS)_n. If the Z tensor is singular we give conditions for the existence of a proper concircular vector. For non singular Z tensor, we study the closedness property of the associated covectors and give sufficient conditions for the existence of a proper concircular vector in the conformally harmonic case, and the general form of the Ricci tensor. For conformally flat (WZS)_n manifolds, we derive the local form of the metric tensor.Comment: 13 page

Synthesis of a functionalized europium complex and deposition of luminescent Langmuir-Blodgett (LB) films

The synthesis, characterization and formation of Langmuir-Blodgett (LB)films for the luminescent [(C12H25)(2)(CH3)(2)N][Eu(tta)(4)] complex, where [(C12H25)(2)(CH3)(2)](N+) is didodecyldimethylammonium and the tta ligand is thenoyltrifluoroacetone, are reported. The coordination of tta ligands to the Eu3+ ion was confirmed by FTIR spectroscopy and the emission spectrum comprised bands corresponding to D-5(0) -> F-7(0-4) transitions. The lifetime (tau) from the emission state (D-5(0))was 0.41 ms, measured by monitoring the hypersensitive D-5(0) -> F-7(2) transition, with the curve being fitted with a first-order exponential function. The surface pressure-area isotherm indicated that the anionic complex may form condensed structures at the air-water interface due to the amphiphilic properties of the counter ion and the beta-diketone ligand. Y-type LB films of [(C12H25)(2)(CH3)(2)N][Eu(tta)(4)] were deposited on quartz substrates, with preserved luminescence and a band assigned to the D-5(0) -> F-7(2) transition. The molecular arrangement at the air/water interface and the preserved luminescence in LB films are consistent with theoretical predictions using a semi-empirical Sparkle/AM1 calculation method for the molecule in vacuum. These tools were used for the first time to predict the behavior of organized films.CAPESCAPESCNPqCNPqFAPESPFAPES