On the Graded Identities for Elementary Gradings in Matrix Algebras over Infinite Fields

We find a basis for the $G$-graded identities of the $n\times n$ matrix algebra $M_n(K)$ over an infinite field $K$ of characteristic $p>0$ with an elementary grading such that the neutral component corresponds to the diagonal of $M_n(K)$

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 $\text{SU}(1,1)$ 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 $\text{SU}(1,1)$.Comment: 16 page

A Contribution to the Modal Identification of the Damping Factor based on the Dissipated Energy

ABSTRACT: The identification of the modal parameters from frequency response functions is a subject that is not new. However, the starting point often comes from the equations that govern the dynamic motion. In this paper, a novel approach is shown, resulting from an analysis that starts on the dissipated energy per cycle of vibration. For lightly damped systems with conveniently spaced modes, it produced quite accurate results in comparison to the direct application of the method of the inverse, both in the numerical and in the experimental examples. It also is a simple technique that can be used to produce quick estimates of the modal damping factors. Furthermore, this is also a contribution to further developments on modal analysis and identification methods as, up to today, the developed technique has not yet been proposed.Final Published versio

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