On the displacement function of isometries of Euclidean buildings

In this note we study the displacement function $d_g(x):=d(gx,x)$ of an isometry $g$ of a Euclidean building. We give a lower bound for $d_g(x)$ depending on the distance from $x$ to the minimal set of $g$

Discrete moving breather collisions in a Klein-Gordon chain of oscillators

We study collision processes of moving breathers with the same frequency, traveling with opposite directions within a Klein-Gordon chain of oscillators. Two types of collisions have been analyzed: symmetric and non-symmetric, head-on collisions. For low enough frequency the outcome is strongly dependent of the dynamical states of the two colliding breathers just before the collision. For symmetric collisions, several results can be observed: breather generation, with the formation of a trapped breather and two new moving breathers; breather reflection; generation of two new moving breathers; and breather fusion bringing about a trapped breather. For non-symmetric collisions the possible results are: breather generation, with the formation of three new moving breathers; breather fusion, originating a new moving breather; breather trapping with also breather reflection; generation of two new moving breathers; and two new moving breathers traveling as a ligand state. Breather annihilation has never been observed.Comment: 19 pages, 12 figure

A Practical Guide to the Assessment of the Vulnerability of the Non-Financial Private Sector

The paper proposes a practical guide to the evaluation of the financial and non-financial vulnerability of the private sector (excluding financial entities). It describes step by step the sequence of issues that should be examined to assess the level of vulnerability of the private sector, including factors arising from the financial markets, country-risk, common risk management practices in the corporate sector, and the general environment for corporate restructuring and governance. The paper also provides useful references for those seeking further information on a specific aspect of the vulnerability of the non-financial private sector.financial vulnerability; financial risk; country risk; corporate restructuring; corporate governance