On the monotonicity of perimeter of convex bodies

Let $n\ge2$ and let $\Phi\colon\mathbb{R}^n\to[0,\infty)$ be a positively $1$-homogeneous and convex function. Given two convex bodies $A\subset B$ in $\mathbb{R}^n$, the monotonicity of anisotropic $\Phi$-perimeters holds, i.e. $P_\Phi(A)\le P_\Phi(B)$. In this note, we prove a quantitative lower bound on the difference of the $\Phi$-perimeters of $A$ and $B$ in terms of their Hausdorff distance.Comment: 8 page

On human dignity and State sovereignty: The Italian Constitutional Court's 238/2014 judgment on State immunity for international crimes

Judgment 238/2014 of the Italian Constitutional Court has flatly contravened the decision of the ICJ on Jurisdictional Immunity of States (Germany v. Italy: Greece intervening) of 2012, ruling that the customary norm on State immunity from civil suits before a foreign court as ascertained in the ICJ decision never entered the domestic legal order, because it is incompatible with core principles of the Italian Constitution. In execution of the Constitutional Court ruling, in 2015, some Italian tribunals have condemned Germany to pay damages to former Italian military internees victim of international crimes during World War II, thus integrating an international wrongful act on the part of Italy. The 238/2014 judgment has been criticised from many angles. Much criticism was addressed to its alleged dualist approach that seemed to insulate Italy. The paper argues that the 2014 judgment of the Italian court is rather a reasoned response to the ICJ decision, grounded on principles common to the Italian and the international law, and a call for a consistent application of State obligations concerning the effective implementation of human rights. From this perspective it constitutes a valuable contribution towards a principled and open-minded debate over the structure and function of international la

Products of ideals may not be Golod

We exhibit an example of a product of two proper monomial ideals such that the residue class ring is not Golod. We also discuss the strongly Golod property for rational powers of monomial ideals, and introduce some sufficient conditions for weak Golodness of monomial ideals. Along the way, we ask some related questions.Comment: 18 pages, minor changes from first versio

A counterexample to a conjecture of Ding

We give a counterexample to a conjecture posed by S. Ding regarding the index of a Gorenstein local ring by exhibiting several examples of one dimensional local complete intersections of embedding dimension three with index 5 and generalized L\"oewy length 6.Comment: 9 pages, a few changes from the first versio

Effective use of communication and information technology: Bridging the skills gap

There is a revolutionary culture change taking place within higher education in the United Kingdom. Part of this change is the adoption of new communication and information technologies (C&IT), such as the World Wide Web (WWW), for teaching, learning and assessment. Many academics have limited experience of the WWW for teaching and learning and perceive that the use of new technologies involves transferring traditional teaching methods into an electronic format, with no regard for the underlying pedagogical implications. Our current research with teaching staff has given insight into essential skills and competencies required to empower the use of C&IT bearing in mind the importance of the underlying pedagogy. In this paper we present an analysis of research carried out with academic staff members to determine the nature of staff and student skills needs regarding the use of C&IT in teaching and learning. This analysis is followed by a case study of how these findings were incorporated into the development and implementation of a staff development programme aimed at encouraging innovative teaching at the University of Strathclyde

spotlight europe 20120/05, August 2012: Confronting the crisis

The euro crisis has not gone away on holiday. In fact, it continues to generate a never-ending string of horrific headlines. Where is it all going to end? In this article we describe the proposed remedies that are currently being discussed, and what blue and red eurobonds, euro bills, FIRE and the debt redemption fund can actually achieve

Labour Market Outcomes of Second Generation Immigrants: How Heterogeneous Are They Really?

The second and third generation of immigrants have been the centre of a lively debate about the economic integration of immigrants into their host societies, but there is little empirical evidence on the German case. In this study I comprehensively portray the labour market outcomes of second generation immigrants in Germany. Special attention is attributed to observable heterogeneity in terms of country of origin and unobservable heterogeneity in terms of parental human capital, neighbourhood effects, and mixed marriage background. Pooled, static and dynamic panel data models, and a decomposition analysis are used to estimate and explain the average differences in hourly wages and unemployment probabilities separately for men and women. The results suggest that the second generation cannot be considered as one homogeneous group; some groups perform better, equally or worse than comparable German natives. Also, relative outcomes in wages depend mainly on observable characteristics, whereas relative unemployment risks are mainly driven by unobservable factors.Panel data, second generation immigrants, labour market outcomes, random effects, dynamic models, decomposition analysis

Improved Lipschitz approximation of HH-perimeter minimizing boundaries

We prove two new approximation results of $H$-perimeter minimizing boundaries by means of intrinsic Lipschitz functions in the setting of the Heisenberg group $\mathbb{H}^n$ with $n\ge2$. The first one is an improvement of a result of Monti and is the natural reformulation in $\mathbb{H}^n$ of the classical Lipschitz approximation in $\mathbb{R}^n$. The second one is an adaptation of the approximation via maximal function developed by De Lellis and Spadaro.Comment: 25 page