2,079 research outputs found
A variational nonlinear Hausdorff-Young inequality in the discrete setting
Following the works of Lyons and Oberlin, Seeger, Tao, Thiele and Wright, we
relate the variation of certain discrete curves on the Lie group
to the corresponding variation of their linearized versions on
the Lie algebra. Combining this with a discrete variational
Menshov-Paley-Zygmund theorem, we establish a variational Hausdorff-Young
inequality for a discrete version of the nonlinear Fourier transform on
.Comment: 16 page
Combining hyaluronic acid with chitosan enhances gene delivery
The low gene transfer efficiency of chitosan-DNA polyplexes is a consequence of their high stability and consequent slow DNA release. The incorporation of an anionic polymer is believed to loosen chitosan interactions with DNA and thus promote higher transfection efficiencies. In this work, several formulations of chitosan-DNA polyplexes incorporating hyaluronic acid were prepared and characterized for their gene transfection efficiency on both HEK293 and retinal pigment epithelial cells. The different polyplex formulations showed morphology, size, and charge compatible with a role in gene delivery. The incorporation of hyaluronic acid rendered the formulations less stable, as was the goal, but it did not affect the loading and protection of the DNA. Compared with chitosan alone, the transfection efficiency had a 4-fold improvement, which was attributed to the presence of hyaluronic acid. Overall, our hybrid chitosan-hyaluronic acid polyplexes showed a significant improvement of the efficiency of chitosan-based nonviral vectors in vitro, suggesting that this strategy can further improve the transfection efficiency of nonviral vectors.Fundacao para a Ciencia e Tecnologia [SFRH/BD/52424/2013]; Marie Curie Reintegration Grant [PIRG-GA-2009-249314
A variational restriction theorem
We establish variational estimates related to the problem of restricting the
Fourier transform of a three-dimensional function to the two-dimensional
Euclidean sphere. At the same time, we give a short survey of the recent field
of maximal Fourier restriction theory.Comment: 10 pages, v2: bibliography is updated, a short survey of the maximal
Fourier restriction is include
Chitosan-Hyaluronic acid hybrid vectors for retinal gene therapy
info:eu-repo/semantics/publishedVersio
A sharp nonlinear Hausdorff-Young inequality for small potentials
The nonlinear Hausdorff-Young inequality follows from the work of Christ and
Kiselev. Later Muscalu, Tao, and Thiele asked if the constants can be chosen
independently of the exponent. We show that the nonlinear Hausdorff-Young
quotient admits an even better upper bound than the linear one, provided that
the function is sufficiently small in the norm. The proof combines
perturbative techniques with the sharpened version of the linear
Hausdorff-Young inequality due to Christ.Comment: 14 pages, v2: referee's suggestions incorporate
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