A characterization of Fourier series of Stepanov almost-periodic functions

We show by example that the classical characterization of the Fourier series of periodic functions in L^p, 1<p≤+∞, as those trigonometric series whose Abel or Fejér means are uniformly bounded in L^p does not hold for general (non-periodic) trigonometric series in relation to Stepanov-almost-periodic functions, but that it does hold under the additional hypothesis that the means are translation equicontinuous. We exhibit a bounded, infinitely differentiable function that belongs to every class of Besicovitch-almost-periodic functions but is not equivalent in the metric of Besicovitch-almost-periodic functions to any Stepanov-almost-periodic function.     

Rank two fundamental groups of positively curved manifolds

This paper deals with the construction of previously unknown fundamental groups for positively curved manifolds.     

On the stability of the behavior of random walks on groups

We show that, for random walks on Cayley graphs, the long time behavior of the probability of return after 2n steps is invariant by quasi-isometry.     

Adapted complex structures in a neighborhood of an isotropic embedding

Let (X, ω) be a symplectic manifold and ι: M ? X an isotropic embedding, ι*ω = 0. The isotropie embedding theorem gives a local normal form of X in a neighborhood of M, in particular a natural potential α of ω, ?dα = ω. Now, given certain geometrical structures on M and on the symplectic normal bundle of M, in particular inducing a natural energy momentum function H in a neighborhood of M, we construct a natural complex structure J in a neighborhood of M satisfying certain initial conditions associated to the given initial data along M and satisfying the equation (in J): d^c H = α. This generalizes a theorem of Guillemin-Stenzel and Lempert-Szöke in the Lagrangean case.     

Defect and evaluations

Let S be a generic submanifold of C ^N of real codimension m. In this paper we continue the study, carried over by various authors, of the set of analytic discs attached to S. Moreover, we look at the subspaces of C ^N obtained by evaluating at given points, holomorphic maps which are infinitesimal deformations of analytic discs attached to S.     

Kähler-Einstein metrics and projective embeddings

We prove that the complex projective space equipped with its Fubini-Study metric admits no compact Kähler-Einstein submanifold with nonpositive Einstein constant. In particular, the Calabi-Yau metrics carried by an algebraic K3 surface cannot be realized by projective embeddings.     

Sintering of titanium dioxide nanoparticles: a comparison between molecular dynamics and phenomenological modeling

Molecular dynamics simulations were used to determine the melting points of anatase and rutile nanoparticles. The melting points decrease with decrease in particle diameter and are in reasonable agreement with the empirical formula derived by Buffat and Borel. The phenomenological model of Koch and Friedlander is unable to predict the temperature rise during initial stages of sintering with acceptable accuracy. It is argued that the Koch and Friedlander assumption of linear surface reduction rate upon sintering may be inadequate for the time scales under consideration. A theoretical model using direct area measurement from molecular dynamics simulations and a single adjustable parameter is able to predict temperature rise during initial stages of sintering within acceptable error limits.     

On the structure of finite perimeter sets in step 2 Carnot groups

In this article we study codimension 1 rectifiable sets in Carnot groups and we extend classical De Giorgi ’s rectifiability and divergence theorems to the setting of step 2 groups. Related problems in higher step Carnot groups are discussed, pointing on new phenomena related to the blow up procedure. First author was supported by University of Bologna, Italy, funds for selected research topics; second and third authors were supported by MURST, Italy, and University of Trento, Italy.     

Generalized Wiman and Arima theorems for<Emphasis Type="Italic">n</Emphasis>-subharmonic functions on cones

Theorems of Wiman and Arima about entire holomorphic functions of a complex variable are generalized to the case of n—subharmonic functions on spherical n-dimensional cones.