13,532 research outputs found
Vacuum stability conditions of the economical 3-3-1 model from copositivity
By applying copositivity criterion to the scalar potential of the economical
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 gauge boson mass and its mixing angle with the SM
boson in order to further restrict the parameter space of this model.Comment: 22 pages, 7 figures, added text and references. Matches published
versio
The unbearable lightness of tourism ā¦ 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
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