$$\partial \overline{\partial }$$-Complex symplectic and Calabi–Yau manifolds: Albanese map,deformations and period maps

Wintgen ideal submanifolds in space forms are those ones attaining equality pointwise in the so-called DDVV inequality which relates the scalar curvature, the mean curvature and the scalar normal curvature. As conformal invariant objects, they are suitable to study in the framework of Möbius geometry. This paper continues our previous work in this program, showing that Wintgen ideal submanifolds can be divided into three classes: the reducible ones, the irreducible minimal ones in space forms (up to Möbius transformations), and the generic (irreducible) ones. The reducible Wintgen ideal submanifolds have a specific low-dimensional integrable distribution, which allows us to get the most general reduction theorem, saying that they are Möbius equivalent to cones, cylinders, or rotational surfaces generated by minimal Wintgen ideal submanifolds in lower-dimensional space forms.     

A chiral electrophilic selenium reagent to promote the kinetic resolution of racemic allylic alcohols

[reaction: see text] The first example of a kinetic resolution process promoted by electrophilic selenium reagents is reported. Racemic allylic alcohols react with half equivalents of a selenenylating agent in methanol leading to the regiospecific formation of the corresponding addition products with a very high level of facial selectivity (from 95:5 to 98:2 dr). The unreacted alcohols can be recovered in an optically enriched form (from 90 to 94% ee).     

Production of hollow cylindrical plasmas for laser guiding in acceleration experiments

One of the major tasks for the progress of laser acceleration of electrons in plasmas is the guiding of focused pulses along path lengths much larger than the depth of focus. We have tested experimentally the production of hollow plasmas in gas to be used as guiding medium. We induced optical breakdown in Helium with a nanosecond laser pulse similar to the Amplified Spontaneous Emission (ASE) pedestal of a powerful ultrashort laser pulse. The plasma produced in this way was carefully characterized by high resolution interferometry. Plasma channels several millimeters in length whose density, depth and width match the requirements for an efficient guiding have been obtained. Channels with a variety of parameters can be created according to the well-known dynamics of the plasmas produced by optical breakdown. PACS 42.82.Et; 52.50.Jm; 41.75.Jv     

Sulle trasformazioni continue

Sunto Si dimostra che ogni trasformazione piana, rappresentata da funzioni assolutamente continue secondoTonelli con dervate parziali prime integrabiliL ²→ α con α>0, sono a variazione limitata e assolutamente continue secondoBanach eVitali. Si danno inoltre esempi effettivi di trasformazioni piane, rappresentate da funzioni assolutamente continue secondoTonelli con derivate parziali prime integrabiliL ², che non sono ne a variazione limitata ne assolutamente continue secondoBanacheVitali. Lavoro eseguito nel Seminario Matematico della R. Scuola Normale Superiore di Pisa.     

Maximally homogeneous para-CR manifolds

We define the notion of a (weak) almost para-CR structure on a manifold M as a distribution HM ⊂ TM together with a field K ∈ Γ(End(HM)) of involutive endomorphisms of HM. If K satisfies integrability conditions, then (HM, K) is called a (weak) para-CR structure. Under some regularity conditions, an almost para-CR structure can be identified with a Tanaka structure. The notion of maximally homogeneous almost para-CR structure of a semisimple type is defined. A classification of such maximally homogeneous almost para-CR structures is given in terms of appropriate gradations of real semisimple Lie algebras. All such maximally homogeneous structures of depth two (which correspond to depth two gradations) are listed and the integrability conditions are verified.Mathematics Subject Classifications (1991): 53C15, 53D99, 58A14     

Thiol-mediated free radical cyclisations of isocyanides on solid support

Three novel polymer-supported isocyanides have been synthesised, from commercial Wang and HMBA-AM resins, and reacted under radical conditions with 2-mercaptoethanol and ethanethiol to give the corresponding pyrrolidine or pyroglutamic acid derivatives in good yields.