Bounding regions to plane steepest descent curves of quasi convex families

Two dimensional steepest descent curves (SDC) for a quasi convex family are considered; the problem of their extensions (with constraints) outside of a convex body $K$ is studied. It is shown that possible extensions are constrained to lie inside of suitable bounding regions depending on $K$. These regions are bounded by arcs of involutes of the boundary of $K$ and satisfy many inclusions properties. The involutes of the boundary of an arbitrary plane convex body are defined and written by their support function. Extensions SDC of minimal length are constructed. Self contracting sets (with opposite orientation) are considered, necessary and/or sufficients conditions for them to be subsets of a SDC are proved.Comment: 34 pages, 4 figure

On the complements of union of open balls of fixed radius in the Euclidean space

Let an $R$-body be the complement of the union of open balls of radius $R$ in $\mathbb{E}^d$. The $R$-hulloid of a closed not empty set $A$, the minimal $R$-body containing $A$, is investigated; if $A$ is the set of the vertices of a simplex, the $R$-hulloid of $A$ is completely described (if $d=2$) and if $d> 2$ special examples are studied. The class of $R$-bodies is compact in the Hausdorff metric if $d =2$, but not compact if $d>2$.Comment: 1 figur

Sistemi di assistenza in condizioni di emergenza

The aim of this project is to make a preliminary analysis and to formulate proposals about the rescue in emergency of persons with disabilities. Rescue teams, both emergency workers in the workplace and Firefighters, often underestimate the complexity and difficulties encountered in the management of emergencies in which there are people with special needs. The project method starts by analyzing briefly some real cases: the exodus in the World Trade Center during the terrorist attack of September 11, 2001, and the critical issues arisen during the Katrina hurricane, 2005. Afterwards, by using an observational method, critical issues that occurs in a special caseate studied; management and emergency planning in an Italian healthcare facility, specifically a retirement home in residential regime are observed. More precisely, the study carries out an analysis of simulated emergency in a department of the nursing home where guests with disabilities live. The emergency is analyzed conducting two simulations. The first one takes place in the current condition, the second one after the introduction of some corrective measures. The results relate to: development of a model to determine the maximum evacuation time from a department of a nursing home or hospital where there are people with walking impairment; determination of measures, not present in specialist literature, such as speed and time of preparation and deposition of people not self sufficient who use assistive devices; a proposal to modification of the Italian regulation that provides mandatory information on emergency management in work places where there are people with disabilities. The suggestion is based on the factors that led to improvements in the planning and execution of the exodus in the simulations. The conclusions recommend the importance of planning the emergency exodus when there are people with disabilities and suggest some points to consider in emergencies that require the evacuation of vulnerable people

Arnaldo da Villanova e i papi del suo tempo : tra religione e politica

Estratto da: Studi romani, anno VII, n. 2, 195

An extension of a theorem by M. I. Freidlin to good solutions to elliptic nondivergence equations

In the context of second order linear uniformly elliptic equations with measurable coefficients, a result of Freidlin [9], which deals with homogenization type properties for elliptic equations with smooth periodic coefficients, is extended to generalized solutions for equations with measurable coefficients