Isometric immersions into a homogeneous Lorentzian Heisenberg group and rigidity

In this paper we prove an existence result for local and global isometric immersions of semi-Riemannian surfaces into the three dimensional Heisenberg group endowed with a homogeneous left-invariant Lorentzian metric. As a corollary, we prove a rigidity result for such immersions.

Rigidity theorems for complete spacelike hypersurfaces with constant scalar curvature in De Sitter space

In this paper we give a partially affirmative answer to the following question posed by Haizhong Li: is a complete spacelike hypersurface in De Sitter space S(1)(n+1)(c), n >= 3, with constant normalized scalar curvature R satisfying n-2/nc <= R <= c totally umbilical? (C) 2008 Elsevier B.V. All rights reserved.

Photoswitches and Luminescent Rigidity Sensors Based on fac-[Re(CO)(3)(Me(4)phen)(L)](+)

The fac-[Re(CO)(3)(Me(4)phen)(trans-L)](+) complexes, Me(4)phen = 3,4,7,8-tetramethyl-1,10-phenanthroline and L = 4-styrylpyridine, stpy, or 1,2-bis(4-pyridyl)ethylene, bpe, were synthesized and characterized by their spectroscopic, photochemical, and photophysical properties. The complexes exhibit trans-to-cis isomerization upon 313, 334, 365, and 404 nm irradiation, and the true quantum yields can be efficiently determined by absorption changes combined with (1)H NMR data. For fac-[Re(CO)(3)(Me(4)phen)(trans-bpe)](+) similar quantum yields were determined at all wavelengths investigated. However, a lower value (phi(true) = 0.35) was determined for fac-[Re(CO)(3)(Me(4)phen)(trans-stpy)](+) at 404 nm irradiation, which indicates different pathways for the photoisomerization process. The photoproducts, fac-[Re(CO)(3)(Me(4)phen)(cis-L)](+), exhibit luminescence at room temperature with two maxima ascribed to the (3)IL(Me4phen) and (3)MLCT(Re -> Me4phen) excited states. The luminescence properties were investigated in different media, and the behavior in glassy EPA at 77 K showed that the contribution of each emissive state is dependent on the excitation wavelength. The photochemical and photophysical behavior of the complexes were rationalized in terms of the energy gap of excited states and can be exploited in photoswitchable luminescent rigidity sensors.

Reappraisal of the effective elastic thickness for the sub-Andes using 3-D finite element flexural modelling, gravity and geological constraints

P>Estimates of effective elastic thickness (T(e)) for the western portion of the South American Plate using, independently, forward flexural modelling and coherence analysis, suggest different thermomechanical properties for the same continental lithosphere. We present a review of these T(e) estimates and carry out a critical reappraisal using a common methodology of 3-D finite element method to solve a differential equation for the bending of a thin elastic plate. The finite element flexural model incorporates lateral variations of T(e) and the Andes topography as the load. Three T(e) maps for the entire Andes were analysed: Stewart & Watts (1997), Tassara et al. (2007) and Perez-Gussinye et al. (2007). The predicted flexural deformation obtained for each T(e) map was compared with the depth to the base of the foreland basin sequence. Likewise, the gravity effect of flexurally induced crust-mantle deformation was compared with the observed Bouguer gravity. T(e) estimates using forward flexural modelling by Stewart & Watts (1997) better predict the geological and gravity data for most of the Andean system, particularly in the Central Andes, where T(e) ranges from greater than 70 km in the sub-Andes to less than 15 km under the Andes Cordillera. The misfit between the calculated and observed foreland basin subsidence and the gravity anomaly for the Maranon basin in Peru and the Bermejo basin in Argentina, regardless of the assumed T(e) map, may be due to a dynamic topography component associated with the shallow subduction of the Nazca Plate beneath the Andes at these latitudes.

Transitivity of codimension-one Anosov actions of R(k) on closed manifolds

We consider Anosov actions of R(k), k >= 2, on a closed connected orientable manifold M, of codimension one, i.e. such that the unstable foliation associated to some element of R(k) has dimension one. We prove that if the ambient manifold has dimension greater than k + 2, then the action is topologically transitive. This generalizes a result of Verjovsky for codimension-one Anosov flows.

Perturbation treatment of symmetry breaking within random matrix theory

We discuss the applicability, within the random matrix theory, of perturbative treatment of symmetry breaking to the experimental data on the flip symmetry breaking in quartz crystal. We found that the values of the parameter that measures this breaking are different for the spacing distribution as compared to those for the spectral rigidity. We consider both two-fold and three-fold symmetries. The latter was found to account better for the spectral rigidity than the former. Both cases, however, underestimate the experimental spectral rigidity at large L. This discrepancy can be resolved if an appropriate number of eigenfrequencies is considered to be missing in the sample. Our findings are relevant for symmetry violation studies in general. (C) 2008 Elsevier B.V. All rights reserved.

Transition metal atoms encapsulated in adamantane molecules

We performed a first principles total energy investigation on the structural, electronic, and magnetic properties of 3d-transition metal-encapsulated adamantane molecules (TM@C(10)H(16). with TM = Cr, Mn, Fe, Co, and Ni). We find that the C-C interactions are strong enough to maintain the molecular rigidity upon TM incorporation, although outward relaxations and formation energies are large. We built a microscopic model that explains the electronic structure of those molecules. (C) 2011 Elsevier B.V. All rights reserved.

Magnetic-field asymmetry of nonlinear transport in a small ring

We have investigated the magnetic-field asymmetry of the conductance in the nonlinear regime in a small Aharonov-Bohm ring. We have found that the odd-in B and linear in V (the DC bias) correlation function of the differential conductance exhibits periodical oscillations with the Aharonov-Bohm flux. We have deduced the electron interaction constant and analyzed the phase rigidity of the Aharonov-Bohm oscillations in the nonlinear regime. Copyright (C) EPLA, 2009

Crystal Engineering of an Anti-HIV Drug Based on the Recognition of Assembling Molecular Frameworks

A rational strategy was employed for design of an orthorhombic structure of lamivudine with maleic acid. On the basis of the lamivudine saccharinate structure reported in the literature, maleic acid was chosen to synthesize a salt with the anti-HIV drug because of the structural similarities between the salt formers. Maleic acid has an acid-ionization constant of the anti first proton and an arrangement of their hydrogen bonding functionalities similar to those of saccharin. Likewise, there is a saccharin-like conformational rigidity in maleic acid because of the hydrogen-bonded ring formation and the Z-configuration around the C=C double bond. As was conceivably predicted, lamivudine maleate assembles into a structure whose intermolecular architecture is related to that of saccharinate salt of the drug. Therefore, a molecular framework responsible for crystal assembly into a lamivudine saccharinate-like structure could be recognized in the salt formers. Furthermore, structural correlations and structure-solubility relationships were established for lamivudine maleate and saccharinate. Although there is a same molecular framework in maleic acid and saccharin, these salt formers are Structurally different in some aspects. When compared to saccharin, neither out-of-plane SO(2) oxygens nor a benzene group occur in maleic acid. Both features could be related to higher solubility of lamivudine maleate. Here, we also anticipate that multicomponent molecular crystals of lamivudine with other salt formers possessing the molecular framework responsible for crystal assembly can be engineered successfully.

NEW CHARACTERIZATIONS OF COMPLETE SPACELIKE SUBMANIFOLDS IN SEMI-RIEMANNIAN SPACE FORMS

In this paper we study n-dimensional complete spacelike submanifolds with constant normalized scalar curvature immersed in semi-Riemannian space forms. By extending Cheng-Yau`s technique to these ambients, we obtain results to such submanifolds satisfying certain conditions on both the squared norm of the second fundamental form and the mean curvature. We also characterize compact non-negatively curved submanifolds in De Sitter space of index p.

Ruled Weingarten hypersurfaces in Sn+1

In this paper we classify the connected ruled Weingarten hypersurfaces in Sn+1, n >= 3.

Henon-like maps with arbitrary stationary combinatorics

We extend the renormalization operator introduced in [A. de Carvalho, M. Martens and M. Lyubich. Renormalization in the Henon family, I: universality but non-rigidity. J. Stat. Phys. 121(5/6) (2005), 611-669] from period-doubling Henon-like maps to Henon-like maps with arbitrary stationary combinatorics. We show that the renonnalization picture also holds in this case if the maps are taken to be strongly dissipative. We study infinitely renormalizable maps F and show that they have an invariant Cantor set O on which F acts like a p-adic adding machine for some p > 1. We then show, as for the period-doubling case in the work of de Carvalho, Martens and Lyubich [Renormalization in the Henon family, I: universality but non-rigidity. J. Stat. Phys. 121(5/6) (2005), 611-669], that the sequence of renormalizations has a universal form, but that the invariant Cantor set O is non-rigid. We also show that O cannot possess a continuous invariant line field.