The evolution of the Australian ‘ndrangheta. An historical perspective

This paper explores the phenomenon of the ‘ndrangheta – a criminal organisation from Calabria, South of Italy and allegedly the most powerful among the Italian mafias – through its migrating routes. In particular, by focusing on the peculiar case of Australia, the paper aims to show the overlapping of migrating flows with criminal colonisation, which has proven to be a strategy of this particular mafia. The paper uses the very thin literature on the subject alongside official reports and newspaper articles on migration and crime, mainly from Italian sources, to trace an historical journey on the migration of people from Calabria to Australia in various moments of the last century. The aim is to present the evolution and growth of Calabrian clans in Australia. The topic is largely unexplored and is still underreported among Australian institutions and scholars, which is why the paper chooses an historical approach to describe the principal paths in this very new field of research

Inverse scale space decomposition

We investigate the inverse scale space flow as a decomposition method for decomposing data into generalised singular vectors. We show that the inverse scale space flow, based on convex and absolutely one-homogeneous regularisation functionals, can decompose data represented by the application of a forward operator to a linear combination of generalised singular vectors into its individual singular vectors. We verify that for this decomposition to hold true, two additional conditions on the singular vectors are sufficient: orthogonality in the data space and inclusion of partial sums of the subgradients of the singular vectors in the subdifferential of the regularisation functional at zero. We also address the converse question of when the inverse scale space flow returns a generalised singular vector given that the initial data is arbitrary (and therefore not necessarily in the range of the forward operator). We prove that the inverse scale space flow is guaranteed to return a singular vector if the data satisfies a novel dual singular vector condition. We conclude the paper with numerical results that validate the theoretical results and that demonstrate the importance of the additional conditions required to guarantee the decomposition result

Fractional p-eigenvalues

We discuss some basic properties of the eigenfunctions of a class of nonlocal operators whose model is the fractional p-Laplacian

An anisotropic eigenvalue problem of Stekloff type and weighted Wulff inequalities

We study the Stekloff eigenvalue problem for the so-called pseudo p-Laplacian operator. After proving the existence of an unbounded sequence of eigenvalues, we focus on the first nontrivial eigenvalue $\sigma_{2,p}$ providing various equivalent characterizations for it. We also prove an upper bound for $\sigma_{2,p}$ in terms of geometric quantities. The latter can be seen as the nonlinear analogue of the Brock-Weinstock inequality for the first nontrivial Stekloff eigenvalue of the (standard) Laplacian. Such an estimate is obtained by exploiting a family of sharp weighted Wulff inequalities, which are here derived and appear to be interesting in themselves. Copyright 2013 Springer Basel

Convexity properties of Dirichlet integrals and Picone-type inequalities

We focus on three different convexity principles for local and nonlocal variational integrals. We prove various generalizations of them, as well as their equivalences. Some applications to nonlinear eigenvalue problems and Hardy-type inequalities are given. We also prove a measure-theoretic minimum principle for nonlocal and non- linear positive eigenfunctions. \ua9 2014, Tokyo Institute of Technology. All rights reserved