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M. Mazzocco

Publications and source records attributed to M. Mazzocco.

24 records · Page 2Linked to original sources
arXiv2005

New Mass and Lifetime Measurements of $^{152}$Sm Projectile Fragments with Time-Resolved Schottky Mass Spectrometry

The FRS-ESR facilities at GSI provide unique conditions for precision measurements with stored exotic nuclei over a large range in the chart of nuclides. In the present experiment the exotic nuclei were produced via fragmentation of $^{152}$Sm projectiles in a thick beryllium target at 500-600 MeV/u, separated in-flight with the fragment separator FRS, and injected into the storage-cooler ring ESR. Mass and lifetime measurements have been performed with bare and few-electron ions. The experiment and first results will be presented in this contribution.

nucl-ex↗
arXiv2004

Rational Solutions of the Painleve' VI Equation

In this paper, we classify all values of the parameters $α$, $β$, $γ$ and $δ$ of the Painlevé VI equation such that there are rational solutions. We give a formula for them up to the birational canonical transformations and the symmetries of the Painlevé VI equation.

nlin.SI↗
arXiv2002

Existence and Uniqueness of Tri-tronquée Solutions of the second Painlevé hierarchy

The first five classical Painlevé equations are known to have solutions described by divergent asymptotic power series near infinity. Here we prove that such solutions also exist for the infinite hierarchy of equations associated with the second Painlevé equation. Moreover we prove that these are unique in certain sectors near infinity.

math.CA↗
arXiv1999

Picard and Chazy solutions to the Painleve' VI equation

I study the solutions of a particular family of Painlevé VI equations with the parameters $β=γ=0, δ=1/2$ and $2α=(2μ-1)^2$, for $2μ\in\interi$. I show that the case of half-integer $μ$ is integrable and that the solutions are of two types: the so-called Picard solutions and the so-called Chazy solutions. I give explicit formulae for them and completely determine their asymptotic behaviour near the singular points $0,1,\infty$ and their nonlinear monodromy. I study the structure of analytic continuation of the solutions to the PVI$μ$ equation for any $μ$ such that $2μ\in\interi$. As an application, I classify all the algebraic solutions. For $μ$ half-integer, I show that they are in one to one correspondence with regular polygons or star-polygons in the plane. For $μ$ integer, I show that all algebraic solutions belong to a one-parameter family of rational solutions.

math.AG↗
arXiv1998

Monodromy of certain Painleve' VI transcendents and reflection groups

We study the global analytic properties of the solutions of a particular family of Painleve' VI equations with the parameters $β=γ=0$, $δ={1\over2}$ and $α$ arbitrary. We introduce a class of solutions having critical behaviour of algebraic type, and completely compute the structure of the analytic continuation of these solutions in terms of an auxiliary reflection group in the three dimensional space. The analytic continuation is given in terms of an action of the braid group on the triples of generators of the reflection group. This result is used to classify all the algebraic solutions of our Painleve' VI equation.

math.AG↗