Vacuum stability conditions of the economical 3-3-1 model from copositivity

By applying copositivity criterion to the scalar potential of the economical $3-3-1$ model, we derive necessary and sufficient bounded-from-below conditions at tree level. Although these are a large number of intricate inequalities for the dimensionless parameters of the scalar potential, we present general enlightening relations in this work. Additionally, we use constraints coming from the minimization of the scalar potential by means of the orbit space method, the positivity of the squared masses of the extra scalars, the Higgs boson mass, the $Z'$ gauge boson mass and its mixing angle with the SM $Z$ boson in order to further restrict the parameter space of this model.Comment: 22 pages, 7 figures, added text and references. Matches published versio

Cultural Anthropology. Global Forces, Local Lives.

Book revie

The unbearable lightness of tourism … as violence: an afterword

This Afterword reviews the special issue of the Journal of Sustainable Tourism on Critical Geographies, which focuses on the intricate relationships between tourism and various forms of tourism related violence. It notes the slippery and complex concept of violence in tourism, and that it is typically seen from the viewpoint of the tourist, with researchers working from the anthropological host and guests relationship model as a way of negotiating kinship and friendship between societies, with broader aspects of tourism's power play with socio-cultural change perhaps conveniently forgotten. Tourism and tourists are seen as hiding their corporate and personal violence behind destination branding, tourism imaginaries and saleable commodification. While the innovative approaches adopted by papers in the special issue are commended, two key and still outstanding issues are highlighted. Tourism researchers must find ways to share their work more effectively across all stakeholders, as well as publishing in academic journals. And researchers should become more self reflexive and critical of themselves, seeking to address the complex practical challenges for sustainable tourism thinkers and doers of creating better links between the visitors and businesses of developed societies, and the culture and communities of developing societies

Improved bounds for the crossing numbers of K_m,n and K_n

It has been long--conjectured that the crossing number cr(K_m,n) of the complete bipartite graph K_m,n equals the Zarankiewicz Number Z(m,n):= floor((m-1)/2) floor(m/2) floor((n-1)/2) floor(n/2). Another long--standing conjecture states that the crossing number cr(K_n) of the complete graph K_n equals Z(n):= floor(n/2) floor((n-1)/2) floor((n-2)/2) floor((n-3)/2)/4. In this paper we show the following improved bounds on the asymptotic ratios of these crossing numbers and their conjectured values: (i) for each fixed m >= 9, lim_{n->infty} cr(K_m,n)/Z(m,n) >= 0.83m/(m-1); (ii) lim_{n->infty} cr(K_n,n)/Z(n,n) >= 0.83; and (iii) lim_{n->infty} cr(K_n)/Z(n) >= 0.83. The previous best known lower bounds were 0.8m/(m-1), 0.8, and 0.8, respectively. These improved bounds are obtained as a consequence of the new bound cr(K_{7,n}) >= 2.1796n^2 - 4.5n. To obtain this improved lower bound for cr(K_{7,n}), we use some elementary topological facts on drawings of K_{2,7} to set up a quadratic program on 6! variables whose minimum p satisfies cr(K_{7,n}) >= (p/2)n^2 - 4.5n, and then use state--of--the--art quadratic optimization techniques combined with a bit of invariant theory of permutation groups to show that p >= 4.3593.Comment: LaTeX, 18 pages, 2 figure