Poisson–Nijenhuis structures on quiver path algebras

We introduce a notion of noncommutative Poisson–Nijenhuis structure on the path algebra of a quiver. In particular, we focus on the case when the Poisson bracket arises from a noncommutative symplectic form. The formalism is then applied to the study of the Calogero–Moser and Gibbons–Hermsen integrable systems. In the former case, we give a new interpretation of the bihamiltonian reduction performed in Bartocci et al. (Int Math Res Not 2010:279–296, 2010. arXiv:0902.0953).     

SiC bonding in ( C 60 ) n Si m clusters

This paper deals with a new type of SiC bonding where silicon atom seems to bridge C₆₀ molecules. We have studied films obtained by deposition of (C₆₀)_nSi_m clusters prepared in a laser vaporization source. Prior deposition, free ionized clusters were studied in a time-of-flight mass spectrometer. Mixed clusters (C₆₀)_nSi_m were clearly observed. Abundance and photofragmentation mass spectroscopies revealed the relatively high stability of the (C₆₀)_nSi _n ⁺ , (C₆₀)_nSi _{n - 1} ⁺ and (C₆₀)_nSi _{n - 2} ⁺ species. This observation is in favor of the arrangement of these complexes as polymers where the C₆₀ cages may be bridged by a silicon atom. Free neutral clusters are then deposited onto substrate making up a nanogranular thin film (≃ 100 nm). The film is probed by Auger and X-ray photoemission spectroscopies, but above all by surface enhanced Raman scattering. The results suggest an unusual chemical bonding between silicon and carbon and the environment of the silicon atom is expected to be totally different from the sp³ lattice: ten or twelve carbon neighbors might surround silicon atom. The bonding is discussed to the light of the so-called fullerene polymerization as observed for pure fullerite upon laser irradiation. This opens a new route for bridging C₆₀ molecules together with an appreciable energy bonding, since the usual van der Waals bonding in fullerite could be replaced by an ionocovalent bond. Such an assumption must be checked in the future by XAS and EXAFS experiments. Received 15 November 2000     

Neural markers of a greater female responsiveness to social stimuli

Background  

There is fMRI evidence that women are neurally predisposed to process infant laughter and crying. Other findings show that women might be more empathic and sensitive than men to emotional facial expressions. However, no gender difference in the brain responses to persons and unanimated scenes has hitherto been demonstrated.     

A countable class of non-homeomorphic homology spheres with Heegaard genus two

We construct a countable set of prime non-homeomorphic homology spheres with Heegaard genus 2.

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Sunto Si prova l'esistenza di una classe numerabile di sfere omologiche prime non omeomorfe con genere di Heegaard 2.

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Work performed under the auspicies of the G.N.S.A.G.A. of the C.N.R. (National Research Council of Italy) and within the project Geometria delle Varietà Differenziabili of the M.P.I. (Italy).     

Rigid cohomology via the tilting equivalence

We define a de Rham cohomology theory for analytic varieties over a valued field $K^{?}$ of equal characteristic p with coefficients in a chosen untilt of the perfection of $K^{?}$ by means of the motivic version of Scholze's tilting equivalence. We show that this definition generalizes the usual rigid cohomology in case the variety has good reduction. We also prove a conjecture of Ayoub yielding an equivalence between rigid analytic motives with good reduction and unipotent algebraic motives over the residue field, also in mixed characteristic.     

Computational Study of Cage Like (ZnO)12 Cluster Using Hybrid and Hybrid Meta Functionals

Density Functional Theory employing hybrid and M06 functionals in combination with three different basis sets is used to calculate the ground state of a cage like (ZnO)₁₂ nanocluster which has been consistently reported as the more stable cluster for its particular size. B3LYP and B3PW91 hybrid functionals combined with 6‐31+G*, Lanl2dz and SDD basis sets are employed to treat the ZnO molecular system. Alternatively, three M06 functionals in combination with three basis sets are employed in the nanostructure calculations. Results obtained by treating ZnO sodalite cage nanocluster with M06 functionals demonstrated comparable quality to results obtained with hybrid functionals. Within this study, efficient theoretical DFT methods with the widely known hybrid and the recently created M06 meta‐hybrid functionals are employed to study nanostructured ZnO. Our resulting parameters provide a fresh approach performance wise on the different theoretical methods to treat transition metal nanostructures, particularly, ZnO nanoclusters geometry and electronic structure.