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A nonlinear elliptic problem with terms concentrating in the boundary
In this paper we investigate the behavior of a family of steady state
solutions of a nonlinear reaction diffusion equation when some reaction and
potential terms are concentrated in a -neighborhood of a portion
of the boundary. We assume that this -neighborhood shrinks
to as the small parameter goes to zero. Also, we suppose
the upper boundary of this -strip presents a highly oscillatory
behavior. Our main goal here is to show that this family of solutions converges
to the solutions of a limit problem, a nonlinear elliptic equation that
captures the oscillatory behavior. Indeed, the reaction term and concentrating
potential are transformed into a flux condition and a potential on ,
which depends on the oscillating neighborhood
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Addressing food and nutrition security in South Africa: A review of policy responses since 2002
Since 2002, a range of South African policies have attempted to address the disproportionate burden of food and nutrition insecurity on the population. Yet malnutrition among the poor has worsened. This study reviewed policies to examine their implications for food security and the treatment of malnutrition. Policies enacted between 2002 and 2017 were retrieved from government departments and the data were thematically analysed. A preliminary analysis shows that policy has aided production through input provision and capacity building. Taxation, school nutrition programmes and social grants are some of the food access initiatives, whilst micronutrient supplementation, breastfeeding campaigns and food fortification are policies specifically focused on nutrition. However, despite these interventions, food insecurity has remained due to gaps in and contradictions among policies and the lack of coordination in policy development and implementation, especially across sectors. To improve food and nutrition security, government must better engage with ideas about how to address food and nutrition security systemically, and develop the appropriate coordination mechanisms for a more holistic approach to this challenge
Isotropization of the universe during inflation
A primordial inflationary phase allows one to erase any possible anisotropic
expansion thanks to the cosmic no-hair theorem. If there is no global
anisotropic stress, then the anisotropic expansion rate tends to decrease. What
are the observational consequences of a possible early anisotropic phase? We
first review the dynamics of anisotropic universes and report analytic
approximations. We then discuss the structure of dynamical equations for
perturbations and the statistical properties of observables, as well as the
implication of a primordial anisotropy on the quantization of these
perturbations during inflation. Finally we briefly review models based on
primordial vector field which evade the cosmic no-hair theorem.Comment: 9 pages, 3 figures. Invited review article for the French Academy of
Scienc
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