Evaluating VudV_{ud} from neutron beta decays

Although well studied, the neutron still offers a unique laboratory for precise tests of Standard Model (SM) predictions. Neutron decay is free of nuclear structure corrections present in nuclear beta decays, and, with a $10^8$ times larger branching ratio than the theoretically cleaner pion beta decay, it is more readily accessible to experimental study than the latter. Measurements at sufficient precision of the neutron lifetime, and of correlations in free neutron beta decay, offer several stringent tests of the SM, including the weak quark couplings (quark-lepton universality), and certain extensions beyond the standard $V-A$ weak interaction theory. This paper focuses on the long-running free neutron beta decay experimental program aimed at obtaining an independent determination of the Cabibbo-Kobayashi-Maskawa (CKM) mixing matrix element $V_{ud}$. We discuss the present state of precision achieved in this program and briefly review the currently active projects, as well as the expected near-term improvements in the field.Comment: 6 pages, 3 figures, 1 table, presented at the 9th International Workshop on the CKM Unitarity Triangle, 28 November - 3 December 2016, Tata Institute for Fundamental Research (TIFR), Mumbai, India; to appear in Proceeding of Science, PoS(CKM2016

On fuzzy non-discrimination

We show that the incompatibility between the Pareto principle and the notion of non-discrimination as presented in Xu (2000) continues to hold when the individuals have exact preferences and the social preference relation is allowed to be a reflexive and transitive fuzzy binary relation. Our result can be seen as a strengthening of the result of Xu in two directions: (1) the range of the aggregation rule is enlarged and (2) a weaker condition on non-discrimination is used.fuzzy preferences

Top coalitions, common rankings, and semistrict core stability

The top coalition property of Banerjee et al. (2001) and the common ranking property of Farrell and Scotchmer (1988) are sufficient conditions for core stability in hedonic games. We introduce the semistrict core as a stronger stability concept than the core, and show that the top coalition property guarantees the existence of semistrictly core stable coalition structures. Moreover, for each game satisfying the common ranking property, the core and the semistrict core coincide.coalition formation

On top coalitions, common rankings, and semistrict core stability

The top coalition property of Banerjee et al. (2001) and the common ranking property of Farrell and Scotchmer (1988) are sufficient conditions for core stability in hedonic games. We introduce the semistrict core as a stronger stability concept than the core, and show that the top coalition property guarantees the existence of semistrictly core stable coalition structures. Moreover, for each game satisfying the common ranking property, the core and the semistrict core coincide.coalition formation, common ranking property, hedonic games, semistrict core, top coalition property

Dichotomous Preferences and Power Set Extensions

This paper is devoted to the study of how to extend a dichotomous partition of a universal set X into good and bad objects to an ordering on the power set of X. We introduce a family of rules that naturally take into account the number of good objects and the number of bad objects, and provide axiomatic characterizations of two rules for ranking sets in such a context