A Fermat-Like Sequence and Primes of the Form 2h.3n+12h.3^n+1

Fermat numbers are a classical topic in elementary number theory. Fermat introduced them and claimed that all these numbers are prime. This claim was disproofed by Euler who gave a property on the eventual divisors of the Fermat numbers. In this article we exhibit another serie whose definition is close to the one of Fermat numbers and which exhibit similar properties. This problem will lead us to the sets of covering congruences for numbers $2h.3^n+1$ as similarly Fermat numbers lead to Sierpinski's problem

HESS J1632-478: an energetic relic

HESS J1632-478 is an extended and still unidentified TeV source in the galactic plane. In order to identify the source of the very high energy emission and to constrain its spectral energy distribution, we used a deep observation of the field obtained with XMM-Newton together with data from Molonglo, Spitzer and Fermi to detect counterparts at other wavelengths. The flux density emitted by HESS J1632-478 peaks at very high energies and is more than 20 times weaker at all other wavelengths probed. The source spectrum features two large prominent bumps with the synchrotron emission peaking in the ultraviolet and the external inverse Compton emission peaking in the TeV. HESS J1632-478 is an energetic pulsar wind nebula with an age of the order of 10^4 years. Its bolometric (mostly GeV-TeV) luminosity reaches 10% of the current pulsar spin down power. The synchrotron nebula has a size of 1 pc and contains an unresolved point-like X-ray source, probably the pulsar with its wind termination shock.Comment: A&A accepted, 9 pages, 5 figures, 4 table

High speed low complexity radix-16 Max-Log-MAP SISO decoder

International audienceAt present, the main challenge for hardware implementation turbo decoders is to achieve the high data rates required by current and future communication system standards. In order to address this challenge, a low complexity radix-16 SISO decoder for the Max-Log- MAP algorithm is proposed in this paper. Based on the elimination of parallel paths in the radix-16 trellis diagram, architectural solutions to reduce the hardware complexity of the different blocks of a SISO decoder are detailed. Moreover, two complementary techniques are introduced order to overcome BER/FER performance degradation when turbo decoders based on the proposed SISO decoder are considered. Thus, a penalty lower than 0.05dB is observed for a 8 state binary turbo code with respect to a traditional radix-2 turbo decoder for 6 decoding iterations

Improving Sustainability and Circularity of European Food Waste Management with a Life Cycle Approach

In the past years, several research initiatives have been promoted in the area of food waste. Many of these were focused on the identification of key drivers of food wastage and on the quantification of food waste generation. While these initiatives provided fairly accurate information over European food waste generation and management routes, they did not always deliver comprehensive and comparable knowledge on the sustainability of food waste management and on ways to mitigate negative consequences at environmental, economic and social levels. Building on most recent methodological advancement and policy needs, the work presented in this report aims at providing policy/decision makers and waste managers with a life-cycle based framework methodology to quantify the environmental and economic sustainability performance of European food waste management. This methodology can help identify options for improvement of such performance, thus can offer relevant insight to the decision making process. A numerical case study is also developed. This is meant to give an example of simplified application of the proposed methodology to a fictitious European waste management context. The environmental dimension has been evaluated with the Life Cycle Assessment (LCA) software EASETECH, while the economic assessment is conducted based on a number of different indicators expressing the costs associated with food waste management. This methodology makes use of multi-objective optimization and Pareto optimality concepts in order to help identify most sustainable management options for food waste, intended as those that minimize environmental and economic impacts. In any case, the proposed methodology is meant to only provide relevant information that can support science-based decision making. The final choice will in fact depend on a number of additional aspects that are beyond the scope of this report and also depends on the preferences of the decision maker.JRC.H.8-Sustainability Assessmen

Is the Riemann zeta function in a short interval a 1-RSB spin glass ?

Fyodorov, Hiary & Keating established an intriguing connection between the maxima of log-correlated processes and the ones of the Riemann zeta function on a short interval of the critical line. In particular, they suggest that the analogue of the free energy of the Riemann zeta function is identical to the one of the Random Energy Model in spin glasses. In this paper, the connection between spin glasses and the Riemann zeta function is explored further. We study a random model of the Riemann zeta function and show that its two-overlap distribution corresponds to the one of a one-step replica symmetry breaking (1-RSB) spin glass. This provides evidence that the local maxima of the zeta function are strongly clustered.Comment: 20 pages, 1 figure, Minor corrections, References update

Energy use in the EU food sector: State of play and opportunities for improvement

The amount of energy necessary to cultivate, process, pack and bring the food to European citizens tables accounts for the 17 % of the EU's gross energy consumption, equivalent to about 26 % of the EU's final energy consumption in 2013. Challenges and solutions for decreasing energy consumption and increasing the use of renewable energy in the European food sector are presented and discussed.JRC.F.7-Renewables and Energy Efficienc