1- Products in the method of orbits for nilpotent groups

On each orbit W of the coadjoint representation of any nilpotent (connected, simply connected) Lie group G, we construct 1-products and associated Von Neumann algebras $\text{G}$. G acts canonically on $\text{G}$ by automorphisms. In the unique faithful, irreducible representation of $\text{G}$, this action is implemented by the unitary irreducible representation of G corresponding to W by the Kirillov method. This construction is uniquely determined by W and gives the classification of all unitary irreducible representations of G.     

Self-Nucleation Behavior of the Polyethylene Block as Function of the Confinement Degree in Polyethylene-Block-Polystyrene Diblock Copolymers

A series of well defined polyethylene-b-polystyrene diblock copolymers (E_xS_y^z, where x and y represent the composition in weight % and z the molecular weight in Kg/mol) has been synthesized in a wide composition range by sequential anionic polymerization. The molecular weight of the PE block was kept constant. A fractionated crystallization behavior was observed for the PE block within E₂₆S₇₄¹⁰⁵ (PE cylinders) and E₁₁S₈₉²⁴⁴ (PE spheres). When the PE blocks form a continuous or percolated phase (PE, E₇₉S₂₁⁴¹ and E₅₃S₄₇⁵¹), a “classic” self-nucleation behavior (where the usual three self-nucleation domains are obtained) was observed. When the PE block is located within isolated microphases (having dimensions on the nanometer scale) and a fractionated crystallization was detected (E₂₆S₇₄¹⁰⁵ and E₁₁S₈₉²⁴⁴), the fraction of crystals formed at higher temperatures exhibits a “classic” self-nucleation behavior, while those crystals that crystallized at the largest supercooling (lower exotherms) can only be self-nucleated at lower temperatures where annealing of unmolten material has already started. An unusual fractionated crystallization behavior for isolated, spherical PE microphases (E₁₁S₈₉²⁴⁴) is reported.     

Synthesis and Characterization of Triblock Terpolymers with three Potentially Crystallisable Blocks: Polyethylene-b-poly(ethylene oxide)-b-poly(ε-caprolactone)

A first attempt was made to produce novel ABC triblock terpolymers with three potentially crystallisable blocks: polyethylene (PE), poly(ethylene oxide) (PEO), and poly(ε-caprolactone) (PCL). Polybutadiene-b-poly(ethylene oxide) diblock copolymers were synthesized by living anionic polymerization. Then, a non-catalyzed thermal polymerization of ε-caprolactone from the hydroxyl end group of the PB-b-PEO diblock precursors was performed. Finally, hydrogenation by Wilkinson catalyst produced PE-b-PEO-b-PCL triblock terpolymers. Side reactions were detected that lead to the formation of undesired PCL-b-PEO diblock copolymers, however, these impurities were successfully removed by purification. A range of triblock terpolymers with PCL and PEO minor components were prepared. Topological restrictions on the PEO middle block prevented this block from crystallizing while the complex crystallization behavior of the PE and PCL blocks was documented by DSC and WAXS measurements.     

Nilpotent Fourier transform and applications

We study the nilpotent Fourier transform on spaces of distributions. We use it to prove the equivalence between ^*-products on g^* for nilpotent g.     

Poisson Action and Formality

Using a formality on a Poisson manifold, we construct a star product and for each Poisson vector field a derivation of this star product. Starting with a Poisson action of a Lie group, we are able under a natural cohomological assumption to define a representation of its Lie algebra in the space of derivations of the star product. Finally, we use these results to define some generically tangential star products on duals of Lie algebra as in [1] but in a more realistic context. This work was supported by the CMCU contract 00 F 15 02.     

Alkalien

Ohne Zusammenfassung     

Nachweis und Bestimmung des Aluminiums

Ohne Zusammenfassung