Flexible Structures Based on a Short Pitch Cholesteric Liquid Crystals

We report on the realization and characterization of electro-responsive and pressure sensitive polydimethylsiloxane (PDMS) conductive photonic structures combined with the reconfigurable properties of short pitch cholesteric liquid crystals (aligned in Grandjean configuration). By combining ion-implantation process and surface chemistry functionalization, we have overcome the insulating properties of PDMS and induced long range organization of cholesteric liquid crystals, thus controlling both diffraction and selective Bragg reflection of light by means of external perturbations (electric field, pressure). We have characterized our devices in terms of morphological, optical and electro-optical properties.     

Stationary entanglement between macroscopic mechanical oscillators

We show that the optomechanical coupling between an optical cavity mode and two movable cavity mirrors is able to entangle two different macroscopic oscillation modes of the mirrors. This continuous variable entanglement is maintained by the light bouncing between the mirrors and is robust against thermal noise. In fact, it could be experimentally demonstrated using present technology. Received 2 September 2002 / Received in final form 10 October 2002 Published online 7 January 2003     

Infinite dimensional duality and applications

The usual duality theory cannot be applied to infinite dimensional problems because the underlying constraint set mostly has an empty interior and the constraints are possibly nonlinear. In this paper we present an infinite dimensional nonlinear duality theory obtained by using new separation theorems based on the notion of quasi-relative interior, which, in all the concrete problems considered, is nonempty. We apply this theory to solve the until now unsolved problem of finding, in the infinite dimensional case, the Lagrange multipliers associated to optimization problems or to variational inequalities. As an example, we find the Lagrange multiplier associated to a general elastic–plastic torsion problem.     

Quantum teleportation with continuous variables: A survey

Very recently, we took part in a new development of quantum information, the so-called continuous variable (CV) quantum information theory. Such a further development is mainly due to the experimental and theoretical advantages offered by CV systems, i.e., quantum systems described by a set of observables, like position and momentum, which have a continuous spectrum of eigenvalues. According to this novel trend, quantum information protocols like quantum teleportation have been suitably extended to the CV framework. Here, we briefly review some mathematical tools relative to CV systems, and we consequently develop the concepts of quantum entanglement and teleportation in the CV framework by analogy with the qubit-based approach. Some connections between teleportation fidelity and entanglement properties of the underlying quantum channel are inspected. Next, we address the study of CV quantum teleportation networks where more users share a multipartite state and an arbitrary pair of them performs quantum teleportation. In this context, we show alternative protocols, and we investigate the optimal strategy that maximizes the performance of the network.     

151Eu Mössbauer studies on Eu1+x Ba2−x Cu3O7+δ oxide systems

Mössbauer parameters of¹⁵¹Eu in Eu_1+x Ba_2?x Cu₃O_7+δ have been studied as a function of temperature, forx=0.15 andx=0.25. The areas of the absorption spectra for the two samples are almost equal. This could mean that thef-Mössbauer factor for¹⁵¹Eu at the barium sites is much smaller than that for¹⁵¹Eu at the rare earth sites, i.e. we only observe the spectra of the latter sites. According to this, the fits of the spectra with a single quadrupolar pattern and with two quadrupolar patterns have given equivalent χ² values.     

Elliptic systems with nonlinearity q greater or equal than two with controlled growth. Global Hölder continuity of solutions to the Dirichlet problem

Hölder regularity up to the boundary of the solutions to the Dirichlet problem for second order elliptic systems with nonlinearity q>2 and with controlled growth is proved when n?q+2.     

The activation energy as guiding factor in the fragmentation of substituted diphenylmethanes

The mass spectra of a series of substituted diphenylmethanes were obtained. The mass spectral features were compared with those of the corresponding 1,2 diphenylethanes and discussed in terms of the factors which influence the electron-impact fragmentation. In the series examined, it is shown that the activation energy is the most important factor in determining cracking patterns. The meaning of the averaged rate constants is criticised.     

Positive solutions for a quasilinear degenerate elliptic equation inR n

In questa nota proviamo un teorema di esistenza di soluzioni positive su tuttoR ⁿ della equazionediv(|Du| ^p?2Du)+f(u)=0.     

A Formal Total Synthesis of (+)-Methyl Trachyloban-18-oate and (+)-Methyl 16-Oxo-17-norkauran-18-oate: Regio- and Diastereoselective Preparation of Methyl (13S)-13-Hydroxyisoatisiren-18-oate from (−)-Abietic Acid

A novel preparation of methyl (13S)-13-hydroxyisoatisiren-18-oate ( 4 ), a key-intermediate in a synthesis of (+)-methyl trachyloban-18-oate ((+)- 1 ), from (?)-abietic acid, is described. Since (?)- 1 has been previously converted into (?)-methyl 16-oxo-17-norkauran-18-oate ((?)- 16 ), our preparation of 4 constitutes also a formal total synthesis, from (?)-abietic acid, of (+)- 16 . Key steps in this approach were the allene photoaddition to podocarp-8(14)-en-13-one ( 5 ) and the conversion of the endo-toluene-4-sulfonate 11 into the exo-benzoate 12b .