17 resultados para curva ellittica cubica liscia Nagell-Lutz Mordell legge di gruppo punti razionali


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The collection of the data for this volume formed part of the work of the European Science Foundation project on Writing National Histories. I was a member of the Research Team (1) which produced the volume. I also wrote two contributions for the Atlas. I collected the data and wrote the section on academic historians in Ireland. I also wrote a synthesis of the data on academic women historians in Europe, 1815-2005.

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Irreversibility is one of the most intriguing concepts in physics. While microscopic physical laws are perfectly reversible, macroscopic average behavior has a preferred direction of time. According to the second law of thermodynamics, this arrow of time is associated with a positive mean entropy production. Using a nuclear magnetic resonance setup, we measure the nonequilibrium entropy produced in an isolated spin-1/2 system following fast quenches of an external magnetic field and experimentally demonstrate that it is equal to the entropic distance, expressed by the Kullback-Leibler divergence, between a microscopic process and its time-reverse. Our result addresses the concept of irreversibility from a microscopic quantum standpoint.