Formalization of the “Twin Paradox” for Non-uniformly Accelerated Motions

The use of hyperbolic numbers for studying space-time geometry and trigonometry is extended for demonstrating the Frenet’s formulas in space-time. By means of this introduction the twin paradox for non-uniformly accelerated motions is formalized in a straightforward way.     

Non-linear Stark effect and molecular localization

We consider a non-linear Stark effect as a model for localization and symmetry breaking of a molecule in a gas. By a comparison method with respect to the linear Stark effect, we prove the existence of level bifurcation and symmetry breaking at a critical value of the gas pressure exponentially small for large nuclear masses. Extending the Davies results, we confirm the predictions of Claverie-Jona Lasinio for pyramidal molecules as the ammonia one.     

Exterior products of forms and the cohomology ring of a complex space

In recent publications, we have defined complexes of differential forms on analytic spaces which are resolutions of the constant sheaf. These complexes were used to prove the existence of a mixed Hodge structure on the cohomology of analytic spaces which possess kählerian hypercoverings, in particular, projective algebraic varieties. We define an exterior product on these forms, which induces the cup product on the cohomology of analytic spaces. The main difficulty is to prove that this exterior product is functorial with respect to morphisms of analytic spaces. This exterior product can be used to prove that the cup product is compatible with the mixed Hodge structure on the cohomology.     

Luminescence Properties of Eu3+ Complexes of Tripode and Tetrapode Ligands Containing 2,2′-Bipyridine Units

The Eu³⁺ complexes of the tripode and tetrapode ligands 1 and 2 , respectively, containing 2,2′-bipyridine coordinating units have been prepared. The UV absorption and luminescence spectra, lifetimes, and quantum yields have been measured under a variety of experimental conditions. The contributions of different paths to the decay of the luminescent excited state are evaluated, and the structures of the complexes are discussed on the basis of spectroscopic and photophysical data.     

Theory of thin-film, narrowband, linear-polarization rejection filters with superlattice structure

A device to be obtained by depositing a columnar thin-film on a transparent substrate decorated periodically by an array of rectangular grooves is proposed as a narrowband, linear-polarization rejection filter. The rigorous coupled-wave approach is harnessed to calculate the reflectances and transmittances. High-quality filters of chosen materials and with less than 2 nm bandwidths can be designed with a vapor flux angle for deposition of the columnar thin-film as the controlling parameter.     

Chloroform sorption in nanoporous crystalline and amorphous phases of syndiotactic polystyrene

The transport of chloroform in films of atactic polystyrene and of semicrystalline syndiotactic polystyrene in its nanoporous form (δ‐form) has been investigated by gravimetric analysis. Experimental tests have been performed at 35, 49, and 56 °C and at several vapor pressures ranging from 0.5 to 100 Torr. Nonequilibrium lattice fluid prediction of the amorphous sorption behavior was used to enucleate the sorption contribution of the crystalline nanoporous phase from semicrystalline samples. Sorption behavior of the crystalline phase has been interpreted on the basis of Langmuir equation. Moreover, the chloroform sorption at low activities in the crystalline nanoporous phase has been predicted by using Grand Canonical Monte Carlo molecular simulations. Isosteric heats of sorption were also experimentally evaluated for the crystalline phase, and compared with the corresponding prediction of molecular simulation. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 8–15, 2008