241 research outputs found
Quantization for an elliptic equation of order 2m with critical exponential non-linearity
On a smoothly bounded domain we consider a sequence of
positive solutions in to
the equation subject to Dirichlet
boundary conditions, where . Assuming that
we
prove that is an integer multiple of
\Lambda_1:=(2m-1)!\vol(S^{2m}), the total -curvature of the standard
-dimensional sphere.Comment: 33 page
Biomaterial-mediated factor delivery for spinal cord injury treatment
Spinal cord injury (SCI) is an injurious process that begins with immediate physical damage to the spinal cord and associated tissues during an acute traumatic event. However, the tissue damage expands in both intensity and volume in the subsequent subacute phase. At this stage, numerous events exacerbate the pathological condition, and therein lies the main cause of post-traumatic neural degeneration, which then ends with the chronic phase. In recent years, therapeutic interventions addressing different neurodegenerative mechanisms have been proposed, but have met with limited success when translated into clinical settings. The underlying reasons for this are that the pathogenesis of SCI is a continued multifactorial disease, and the treatment of only one factor is not sufficient to curb neural degeneration and resulting paralysis. Recent advances have led to the development of biomaterials aiming to promote in situ combinatorial strategies using drugs/biomolecules to achieve a maximized multitarget approach. This review provides an overview of single and combinatorial regenerative-factor-based treatments as well as potential delivery options to treat SCIs
Spherical harmonics and integration in superspace
In this paper the classical theory of spherical harmonics in R^m is extended
to superspace using techniques from Clifford analysis. After defining a
super-Laplace operator and studying some basic properties of polynomial
null-solutions of this operator, a new type of integration over the supersphere
is introduced by exploiting the formal equivalence with an old result of
Pizzetti. This integral is then used to prove orthogonality of spherical
harmonics of different degree, Green-like theorems and also an extension of the
important Funk-Hecke theorem to superspace. Finally, this integration over the
supersphere is used to define an integral over the whole superspace and it is
proven that this is equivalent with the Berezin integral, thus providing a more
sound definition of the Berezin integral.Comment: 22 pages, accepted for publication in J. Phys.
A threshold phenomenon for embeddings of into Orlicz spaces
We consider a sequence of positive smooth critical points of the
Adams-Moser-Trudinger embedding of into Orlicz spaces. We study its
concentration-compactness behavior and show that if the sequence is not
precompact, then the liminf of the -norms of the functions is greater
than or equal to a positive geometric constant.Comment: 14 Page
The right to food and food diversity in the Italian Constitution
Il contributo analizza la tutela apprestata dalla Costituzione italiana al diritto al cibo che, pur non essendo espressamente menzionato, viene ricavato attraverso l'analisi di principi ed azioni sottese alla nostra Carta che ne riconoscono il valore: il principio lavorista, la lotta alla povertà, la retribuzione del lavoratore...
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