Effect of molecular structure on the phase behaviour of some liquid crystalline compounds and their mixtures XII. Binary mixtures of homologues of unsymmetrical 1,4-phenylene bis (4-substituted benzoates)

Twentyfour liquid crystalline esters of the type 4-(n-C_nH_2n+1O)C₆H₄COOC₆H₄OOCC₆H₄-X-4 have been investigated for their phase behaviour. These compounds constitute six homologous series that differ from each other by the substituent X. The latter varies between CH₃O, CH₃, Cl, CN, NO₂, and n-C_nH_2n+1O, and the number (n) of carbons varies, within a homologous series, between 6, 8, 14, and 16. All possible binary mixtures made from any two homologues were prepared and characterized for their mesophase behaviour by differential scanning calorimetry and polarizing optical microscopy.     

Q-Complete domains with corners in {\mathbb{P}^n} and extension of line bundles

We show that if a compact set X in ${\mathbb P^n}$ is laminated by holomorphic submanifolds of dimension q, then ${\mathbb P^n{\setminus}X}$ is (q + 1)-complete with corners. Consider a manifold U, q-complete with corners. Let ${\mathcal N}$ be a holomorphic line bundle in the complement of a compact in U. We study when ${\mathcal N}$ extends as a holomorphic line bundle in U. We give applications to the non existence of some Levi-flat foliations in open sets in ${\mathbb P^n}$ . The results apply in particular when U is a Stein manifold of dimension n ≥ 3, then every holomorphic line bundle in the complement of a compact extends holomorphically to U.     

Super-potentials of positive closed currents,intersection theory and dynamics

We introduce a notion of super-potential for positive closed currents of bidegree (p, p) on projective spaces. This gives a calculus on positive closed currents of arbitrary bidegree. We define in particular the intersection of such currents and the pull-back operator by meromorphic maps. One of the main tools is the introduction of structural discs in the space of positive closed currents which gives a “geometry” on that space. We apply the theory of super-potentials to construct Green currents for rational maps and to study equidistribution problems for holomorphic endomorphisms and for polynomial automorphisms.     

Sur la frontière de Shilov des domaines de ℂ n

Sans résumé     

Sobolev embedding in ℂn and the\overline \partial - equation

We prove a Sobolev embedding theorem for functions that are in a Sobolev space while their is in L^t, fort large enough. This allows us to deduceL ^p or Lipschitz estimates with loss from classical Sobolev estimates for the solution of in weakly pseudo-convex domains.     

Strong light‐matter coupling between a molecular vibrational mode in a PMMA film and a low‐loss mid‐IR microcavity

Microcavity devices exhibiting strong light‐matter coupling in the mid‐infrared spectral range offer the potential to explore exciting open physical questions pertaining to energy transfer between heat and light and can lead to a new generation of efficient wavelength tunable mid‐infrared sources of coherent light based on polariton Bose‐Einstein Condensation. Vibrational transitions of organic molecules, which often have strong absorption peaks in the infrared and considerably narrower linewidths than organic excitonic resonances, can generate polaritonic states in the mid‐infrared spectral range using microcavity devices. Here, narrow linewidth polaritonic resonances are exhibited in the mid‐infrared by coupling the carbonyl stretch vibrational transition of a polymethyl methacrylate film to the photonic resonance of a low optical‐loss mid‐infrared microcavity, which consisted of two Ge/ZnS dielectric Bragg reflectors. Rabi‐splitting of 14.3 meV is observed, with a 4.4 meV polariton linewidth at anti‐crossing. The large Rabi‐splitting relative to linewidth indicates efficient impedance‐matching between the bare vibrational and photonic states, and suggests molecular‐vibration polaritons incorporated in dielectric microcavities can be an enabling step towards realizing polariton optical switching and polariton condensation in the mid‐infrared spectral range.     

The Effect of the Compatibilization Route of PA/PO Blends on the Physico-chemical Phenomena Developing Along a Twin-screw Extruder

The effect of the compatibilization method (ex-situ, in-situ, cross linking) on the chemical conversion, morphological and rheological evolution of polyamide/polyolefin blends along a twin screw extruder is investigated. For this purpose, samples were quickly collected from the extruder at specific barrel locations, quenched and subsequently characterized off-line. While significant changes occur very quickly in the melting zone for the ex-situ and in-situ routes, changes of the cross linking system could be detected along all the extruder. Correlations between chemical conversion, particle size and linear viscoelastic response could be established.     

Equidistribution for meromorphic transforms and the dd~c-method

In this paper we give an introduction to the notion of meromorphic transform. We describe some equidistribution problems and their solution, using the ddc-method. In particular, we give some statistical properties of the equilibrium measure for meromorphic maps on compact Kahler manifolds: K-mixing, exponential decay of correlations and central limit theorem.     

The ¯∂-equation on a positive current

We study the induced ˉ∂-equation on a positive current in a complex manifold. We extend the L ²-estimates for the ˉ∂-equation to harmonic currents of bidimension (1,1), satisfying a Frobenius type condition. We also show that the L ²-estimates are satisfied for the ˉ∂-equation on a positive closed current of bidegree (1,1) on a pseudoconvex domain in ℂ ⁿ . Oblatum 7-XII-2000 & 28-VI-2001?Published online: 24 September 2001