arXiv subjects

DL Ferrario

Publications and source records attributed to DL Ferrario.

2 recordsLinked to original sources

arXiv2026

On Certain Pfaffians Connected with the Inverse Problem for Collinear Central Configurations

A. Albouy and R. Moeckel in 2000 found some interesting inequalities related to the inverse problem for collinear (Moulton) central configurations: the Pfaffian of a certain matrix is positive since all coefficients of some polynomials are positive, for the Newtonian (interaction potential $1/r$ and $n\leq 6$). They conjectured that for all $n$ such Pfaffians, for the Newtonian case, are positive. In this article we analyze further the problem, and we prove that such inequalities hold true in more general cases (potentials with log-convex derivative, such as those with homogeneity parameters $\alpha>0$, for all even $n\leq 14$).

math.DS↗

arXiv2020

Pfaffians and the inverse problem for collinear central configurations

We consider, after Albouy-Moeckel, the inverse problem for collinear central configurations: given a collinear configuration of $n$ bodies, find positive masses which make it central. We give some new estimates concerning the positivity of Albouy-Moeckel pfaffians: we show that for any homogeneity $\alpha$ and $n\leq 6$ or $n\leq 10$ and $\alpha=1$ (computer-assisted) the pfaffians are positive. Moreover, for the inverse problem with positive masses, we show that for any homogeneity and $n\geq 4$ there are explicit regions of the configuration space without solutions of the inverse problem.

math.DS↗