DPW Potentials for Compact Symmetric CMC Surfaces in S3\mathbb{S}^3

Inspired by the work of Heller [12], we show that there exists a DPW potential for the Lawson surface $\xi_{k-1, l-1}$ from which it is possible to reconstruct the minimal immersion $f: \xi_{k-1, l-1} \to \mathbb{S}^3$ via the DPW method. Moreover, we extend the result to surfaces immersed in the 3-sphere with constant mean curvature which satisfy a certain symmetric condition.Comment: 20 pages, to appear in Journal of Geometry and Physic

On the lexicographic representation of numbers

It is proven that, contrarily to the common belief, the notion of zero is not necessary for having positional representations of numbers. Namely, for any positive integer $k$, a positional representation with the symbols for $1, 2, \ldots, k$ is given that retains all the essential properties of the usual positional representation of base $k$ (over symbols for $0, 1, 2 \ldots, k-1$). Moreover, in this zero-free representation, a sequence of symbols identifies the number that corresponds to the order number that the sequence has in the ordering where shorter sequences precede the longer ones, and among sequences of the same length the usual lexicographic ordering of dictionaries is considered. The main properties of this lexicographic representation are proven and conversion algorithms between lexicographic and classical positional representations are given. Zero-free positional representations are relevantt in the perspective of the history of mathematics, as well as, in the perspective of emergent computation models, and of unconventional representations of genomes.Comment: 15 page

Studies of Open Charm and Charmonium Production at LHCb

We present recent results from charmonium and open charm production at the LHCb experiment at CERN, Geneva. We concentrate on studies for the measurement of the cross section pp ->JPsi+X in its decay channel with two muons, showing the agreement of the simulation with the data in few key distributions. We also show the reconstructed modes of D0->K-pi+, D0 K-pi+pi0, LambdaC+ -> p K-pi+ and D+ ->Ks0 pi+ and their prospects.Comment: Proceedings to 11th International Workshop on Meson Production, Properties and Interaction, KRAK\'OW, POLAND, 10 - 15 June 201

Technology Catching-up and the Role of Institutions

The aim of the paper is to investigate the role played by differences in Institutional Quality on the process of technology catch-up across countries. Empirical evidence shows how countries endowed with better institutions are those experiencing higher TFP growth rates, faster rates of technology adoption and hence being those more rapidly closing the gap with the frontier. Conversely, countries lacking some minimum institutional level are shown to diverge in the long run and not to catch-up. Some institutions, however, play an ambiguous role in the creation and adoption of technology. We find that the tightening of Intellectual Property Rights reduces the ability of followers to freely imitate technology slowing down their catch-up rate. This negative effect is stronger the farther the countries are found from the frontier. Other institutional categories such as openness to trade, instead, benefit both leaders and followers.TFP, Growth, Institutions, IPRs