1,721,058 research outputs found
Convex intersection bodies in three and four dimensions
No full textThe paper shows that no origin-symmetric convex polyhedron in R^3 is the intersection body of a star body. It is shown also that every origin-symmetric convex body in R^d, for d = 3 and 4, can be seen as the intersection body of a star-shaped set whose radial function satisfies conditions related to suitable non-integer Sobolev classes
Recovering a centred body from the areas of its shadows: a stability estimate
No full textThe main result of this paper is an estimate of the Hausdorff distance between two centrally symmetric bodies T1 and T2 of R3 by the L2 -norm of A(T1; z) - A(T2; z). Here A(Ti; z), i=1, 2, is the area of the orthogonal projection of Ti in the direction z. © 1988 Fondazione Annali di Matematica Pura ed Applicata
On projection bodies of order one
No full textAbstract. The projection body of order one of a convex body K in R^n is the body whose support function is, up to a constant, the average mean width of the orthogonal projections of K onto
hyperplanes through the origin. The paper contains an inequality for the support function of the projection body of order one of K which implies in particular that such a function is strictly convex, unless K has dimension one or two. Furthermore, an existence problem related to the reconstruction of a convex body is discussed to highlight the different behavior of the area measures of order one and of order n − 1
Extremal convex sets for Sylvester-Busemann type functionals
No full textThe Sylvester (d+2)-points problem deals with the probability S(K) that d+2 random points taken from a convex compact subset K of R^d are not the vertices of any convex polytope and asks for which sets S(K) is minimal or maximal. While it is known that ellipsoids are the only minimizers of S(K) , the problem of the maximum is still open, unless d=2 .
In this paper we study generalizations of S(K) , which include the Busemann functional and a functional introduced by Bourgain, Meyer and Pajor in connection with the local theory of Banach spaces. We show that also for these functionals ellipsoids are the only minimizers and for d=2 triangles (or parallelograms, in the symmetric case) are maximizers
On the reverse Lp-Busemann-Petty centroid inequality
No full textThe volume of the L-p-centroid body of a convex body K subset of R-d is a convex function of a time-like parameter when each chord of K parallel to a fixed direction moves with constant speed. This fact is used to study extrema of some affine invariant functionals involving the volume of the L-p-centroid body and related to classical open problems like the slicing problem. Some variants of the L-p-Busemann-Petty centroid inequality are established. The reverse form of these inequalities is proved in the two-dimensional case
Organizzazioni for profit e not for profit: creazione di valore sociale e corporate social responsibility
No full textOrganizational Boundaries in Childcare Service System and the Promotion of NPO Networks by Local Public Agencies in an Italian Metropolitan Area
No full textResearch in organization has recently focused on the issue of cross-boundary processes. In this paper we approached the study of this topic from the perspective of the organizations that work in the field of social services. Discussions have been carried out illustrating three different cases of change in the way the Local Public Agency in Genoa Metropolitan Area manages its relations with some of the non-profit organizations that operate in the field of social childcare. Each of the cases has been discussed from different theoretical standpoints: the Contingency approach, the Transactional view and the Organizational Action Theory. The heuristic contribution of the Organizational Action Theory has been underlined and considerations has been made in order to evaluate if this innovative analytical framework could help researchers to better understand how Local Public Agencies and Non-Profit Organizations relate to one another in the field of social childcare. On the basis of our analyses the heuristic power of the Organizational Action Theory is confirmed and a more wide-ranging adoption of this approach in researching this field is welcomed
- …
