Actions of Noncompact Semisimple Groups on Lorentz Manifolds

The above title is the same, but with “semisimple” instead of “simple,” as that of a notice by Nadine Kowalsky. There, she announced many theorems on the subject of actions of simple Lie groups preserving a Lorentz structure. Unfortunately, she published proofs for essentially only half of the announced results before her premature death. Here, using a different, geometric approach, we generalize her results to the semisimple case, and give proofs of all her announced results. Received: May 2006, Revision: February 2007, Accepted: March 2007     

Influence of the nature of the polycation on the adsorption kinetics and on exchange processes in polyelectrolyte multilayer films

The deposition of polyelectrolyte multilayer films (PEMs) appears more and more as a versatile tool to functionalize a broad range of materials with coatings having controlled thicknesses and properties. To increase the control over the properties of such coatings, a good knowledge of their deposition mechanism is required. Since Cohen Stuart et al. (Langmuir 18 (2002) 5607-5612) showed that the adsorption of one polyelectrolyte could induce desorption of polyelectrolyte complexes instead of regular deposition, more and more findings highlight peculiarities in the deposition of such films. Herein we demonstrate that the association of sodium polyphosphate (PSP) as the polyanion and either poly(-L-lysine hydrobromide) (PLL) or poly(allylamine chloride) (PAH) as the polycations may lead to non-monotonous film deposition as a function of time. Complementary, films containing PSP and PLL can be obtained from a (PLL-HA)(n) template films after the exchange of HA (hyaluronic acid) from the sacrificial template by PSP from the solution. This exchange is accompanied by pronounced film erosion. However, when starting from a (PAH-HA)(n) template, the film erosion and exchange due to the contact with PSP is by far less pronounced, nevertheless the film morphology changes. These findings show that the nature of the polycation used to deposit the PEM film may have a profound influence of the film's response to a competing polyanion.     

Theoretical study of the νO–H IR spectra for the hydrogen bond dimers from the polarized spectra of glutaric and 1-naphthoic acid crystals: Fermi resonances effects

A full quantum theoretical model is proposed to study the ν_O–H experimental IR line shapes of polarized crystalline glutaric and 1-naphthoic acid dimer crystals at room and liquid nitrogen temperatures. This work is an application of a previous model [M. E-A. Benmalti, D. Chamma, P. Blaise, and O. Henri-Rousseau, J. Mol. Struct. 785 (2006) 27–31] by accounting for Fermi resonances. The approach is dealing with the strong anharmonic coupling, Davydov coupling, multiple Fermi resonances between the first harmonics of some bending modes and the first excited state of the symmetric combination of the two ν_O–H modes and the quantum direct and indirect relaxation.Numerical results show that mixing of all these effects allows to reproduce satisfactorily the main features of the experimental IR line shapes of crystalline hydrogenated and deuterated glutaric and 1-naphthoic acid crystals and are expected to provide efficient of Fermi resonances effects.     

Global rigidity of holomorphic Riemannian metrics on compact complex 3-manifolds

We study compact complex 3-manifolds M admitting a (locally homogeneous) holomorphic Riemannian metric g. We prove the following: (i) If the Killing Lie algebra of g has a non trivial semi-simple part, then it preserves some holomorphic Riemannian metric on M with constant sectional curvature; (ii) If the Killing Lie algebra of g is solvable, then, up to a finite unramified cover, M is a quotient Γ\G, where Γ is a lattice in G and G is either the complex Heisenberg group, or the complex SOL group. S. Dumitrescu was partially supported by the ANR Grant BLAN 06-3-137237.     

Modeling Wormholes Generated by Dark Matter Galactic Halos in f(R)$f(R)$ Modified Gravity

Wormholes (WHs) are hypothetical topologically non-trivial spacetime structures that can be freely traversed by observers and connect two asymptotic regions or infinities. From the current theoretical development, the prospect of their existence is challenging but cannot be excluded. In this paper, generalized Ellis–Bronikov (GEB) traversable WH geometries for static and spherically symmetric spacetime in the background of $f(R)$ gravity is explored. First, the Tsujikawa-like $f(R)$ model and the shape function for the GEB model is considered, which depend on a sequence of simple Lorentzian WHs with two parameters: a free even integer exponent, n, besides the throat radius, r₀. One also consider that these WHs are generated by dark matter galactic halos (DMGHs), based on the three most common phenomenological models, viz., Navarro–Frenk–White (NFW), Thomas–Fermi (TF), and pseudo-isothermal (PI). In this concern, the satisfaction of the energy conditions (ECs) which are dependent on the dark matter (DM) models, viz., dominant energy condition (DEC) and strong energy condition (SEC) and those which are not dependent viz., null energy condition (NEC) and WEC at the WH throat and its neighborhood is investigated. Finally, the presence of exotic matter is confirmed by the violation of the NEC in all cases, revealing the supremacy and physical acceptability to support the existence of the WHs and making them compatible and traversable in Tsujikawa's-like $f(R)$ model.