Divisorial Zariski decomposition and algebraic Morse inequalities

In this note we use the divisorial Zariski decomposition to give a more intrinsic version of the algebraic Morse inequalities.Comment: In this version we correct some misprints

Locally convex quasi C*-algebras and noncommutative integration

In this paper we continue the analysis undertaken in a series of previous papers on structures arising as completions of C*-algebras under topologies coarser that their norm and we focus our attention on the so-called {\em locally convex quasi C*-algebras}. We show, in particular, that any strongly *-semisimple locally convex quasi C*-algebra (\X,\Ao), can be represented in a class of noncommutative local $L^2$-spaces.Comment: 12 page

A compact, multi-pixel parametric light source

The features of a compact, single pass, multi-pixel optical parametric generator are discussed. Several hundreds of independent high spatial-quality tunable ultrashort pulses were produced by pumping a bulk lithium triborate crystal with an array of tightly focussed intense beams. The array of beams was produced by shining a microlenses array with a large pump beam. Overall conversion efficiency to signal and idler up to 30% of the pump beam has been reported. Shot-to-shot energy fluctuation down to 3% was achieved for the generated radiation.Comment: 11 pages, 6 figures, submitted to "Optics Communications

Sequential testing for structural stability in approximate factor models

We develop a monitoring procedure to detect changes in a large approximate factor model. Letting $r$ be the number of common factors, we base our statistics on the fact that the $\left( r+1\right)$-th eigenvalue of the sample covariance matrix is bounded under the null of no change, whereas it becomes spiked under changes. Given that sample eigenvalues cannot be estimated consistently under the null, we randomise the test statistic, obtaining a sequence of \textit{i.i.d} statistics, which are used for the monitoring scheme. Numerical evidence shows a very small probability of false detections, and tight detection times of change-points

Quasi-negative holomorphic sectional curvature and positivity of the canonical bundle

We show that if a compact complex manifold admits a K\"ahler metric whose holomorphic sectional curvature is everywhere non positive and strictly negative in at least one point, then its canonical bundle is positive.Comment: 12 pages, no figures, final version, to appear on J. Differential Geo

Estimates of Weil-Petersson volumes via effective divisors

We study the asymptotics of the Weil-Petersson volumes of the moduli spaces of compact Riemann surfaces of genus $g$ with $n$ punctures, for fixed $n$ as $g \to \infty$

Riesz-like bases in rigged Hilbert spaces

The notions of Bessel sequence, Riesz-Fischer sequence and Riesz basis are generalized to a rigged Hilbert space \D[t] \subset \H \subset \D^\times[t^\times]. A Riesz-like basis, in particular, is obtained by considering a sequence \{\xi_n\}\subset \D which is mapped by a one-to-one continuous operator T:\D[t]\to\H[\|\cdot\|] into an orthonormal basis of the central Hilbert space \H of the triplet. The operator $T$ is, in general, an unbounded operator in \H. If $T$ has a bounded inverse then the rigged Hilbert space is shown to be equivalent to a triplet of Hilbert spaces