Non-unitary representations and fourier transform on the poincaré group

Two families of representations of the Poincaré group $\text{P}$ associated to complex orbits (with complex linear momenta) are introduced. The conditions for equivalence and irreducibility are stated. Fourier transforms related to them are defined and inversion formulas obtained for functions infinitely differentiable and of compact support on $\text{P}$.     

Systematics of the isoscalar giant monopole resonance from 60 MeV inelastic proton scattering

Evidence for an isoscalar giant monopole resonance is provided for seven nuclei with A ? 58. The resonance excitation energy is $\text{≈ 80 × A}{}^{\mathrm{<mtext>?1</mtext><mtext>3</mtext>}}\text{MeV}$. For nuclei with A ? 0, nearly 100% of the L = 0, T = 0 energy-weighted sum rule is depleted in the resonance, in agreement with earlier work on ²⁰⁸Pb and ¹⁴⁴Sm. Only ≈30% is found in ⁵⁸Ni, and no clear evidence is found for localized monopole strength in ⁴⁰Ca.     

Quantum fields and poisson processes II: Interaction of boson-boson and boson-fermion fields with a cut-off

Quantum field evolutions are written as expectation values with respect to Poisson processes in two simple models: interaction of two boson fields (with conservation of the number of particles in one field) and interaction of a boson with a fermion field. The introduction of a cut-off ensures that the expectation values are well-defined.     

Reactivite des derives de cyclopropylidene-3 propyle-I: Synthese d'alcools β-cyclopropylideniques

A series of β-cyclopropylidenic alcohols has been synthesized through the following sequence: (i) Wittig condensation between cyclopropylidenetriphenylphosphorane with appropriate monoprotected 1,3-dicarbonyl compounds; (ii) smooth hydrolysis of acetals (after a necessary transacetalization step) and ketals thus formed; (iii) LAH reduction of aldehydes and ketones (yielding primary and secondary alcohols respectively) or treatment of ketones with methyllithium (yielding tertiary alcohols).     

Orienting the Demixion of a Diblock‐copolymer Using 193 nm Interferometric Lithography for the Controlled Deposition of Nanoparticles

DUV interferometric lithography and diblock copolymer self‐organization have successfully been combined to provide a simple and highly collective nanopatterning technique enabling the organization of nanoparticles over several orders of magnitude, from nanometre to millimetre. The nanostructural changes at the surface of the polymer film after thermal annealing have been monitored by AFM and the process parameters optimized for obtaining a long‐range organization of the lamellar domains. In particular, the impact of the annealing conditions and geometric parameters of the substrate patterns have been investigated. The nanopatterns resulting from the lamellar demixion of (PS‐b‐MMA) were used for a controlled deposition of nanoparticles. The affinity of the hydrophobic particles for the PS block was demonstrated, opening new doors towards the preparation of high‐density arrays of nanoparticles with potential applications in data storage.

     

Interactions between oscillatory modes near a 2:3 resonant Hopf-Hopf bifurcation

In this paper, the dynamics near a 2:3 resonant Hopf-Hopf bifurcation is studied. The main result is the identification of a distinctive structure connecting 1:2 and 1:3 strong resonances of limit cycles. This structure is found near the Hopf-Hopf point revealing that it may be associated to the resonant case, and may provide useful information about the dynamics generated by this codimension 3 bifurcation.     

Thermotropic lanthanidomesogens

Due to their high and variable coordination numbers leading to poorly predictable three-dimensional coordination spheres, the trivalent lanthanide metal ions are challenging molecular objects for introduction into thermotropic liquid crystals. Conversely, their predictive electronic, optical and magnetic metal-centred properties make them particularly attractive for being incorporated into switchable macroscopic materials responding to external electric and magnetic stimuli. We briefly describe here some of the important concepts and strategies leading to the recent successful preparation of luminescent thermotropic lanthanide-containing mesophases, for which the generic term lanthanidomesogens is proposed.