On the behavior of clamped plates under large compression

We determine the asymptotic behavior of eigenvalues of clamped plates under large compression by relating this problem to eigenvalues of the Laplacian with Robin boundary conditions. Using the method of fundamental solutions, we then carry out a numerical study of the extremal domains for the first eigenvalue, from which we see that these depend on the value of the compression, and start developing a boundary structure as this parameter is increased. The corresponding number of nodal domains of the first eigenfunction of the extremal domain also increases with the compression.This work was partially supported by the Funda ̧c ̃ao para a Ciˆencia e a Tecnologia(Portugal) through the program “Investigador FCT” with reference IF/00177/2013 and the projectExtremal spectral quantities and related problems(PTDC/MAT-CAL/4334/2014).info:eu-repo/semantics/publishedVersio

Analyticity and criticality results for the eigenvalues of the biharmonic operator

We consider the eigenvalues of the biharmonic operator subject to several homogeneous boundary conditions (Dirichlet, Neumann, Navier, Steklov). We show that simple eigenvalues and elementary symmetric functions of multiple eigenvalues are real analytic, and provide Hadamard-type formulas for the corresponding shape derivatives. After recalling the known results in shape optimization, we prove that balls are always critical domains under volume constraint.Comment: To appear on the proceedings of the conference "Geometric Properties for Parabolic and Elliptic PDE's - 4th Italian-Japanese Workshop" held in Palinuro (Italy), May 25-29, 201

On a classical spectral optimization problem in linear elasticity

We consider a classical shape optimization problem for the eigenvalues of elliptic operators with homogeneous boundary conditions on domains in the $N$-dimensional Euclidean space. We survey recent results concerning the analytic dependence of the elementary symmetric functions of the eigenvalues upon domain perturbation and the role of balls as critical points of such functions subject to volume constraint. Our discussion concerns Dirichlet and buckling-type problems for polyharmonic operators, the Neumann and the intermediate problems for the biharmonic operator, the Lam\'{e} and the Reissner-Mindlin systems.Comment: To appear in the proceedings of the workshop `New Trends in Shape Optimization', Friedrich-Alexander Universit\"{a}t Erlangen-Nuremberg, 23-27 September 201

On the stability of some isoperimetric inequalities for the fundamental tones of free plates

We provide a quantitative version of the isoperimetric inequality for the fundamental tone of a biharmonic Neumann problem. Such an inequality has been recently established by Chasman adapting Weinberger's argument for the corresponding second order problem. Following a scheme introduced by Brasco and Pratelli for the second order case, we prove that a similar quantitative inequality holds also for the biharmonic operator. We also prove the sharpness of both such an inequality and the corresponding one for the biharmonic Steklov problem

Cortisol-induced SRSF3 expression promotes GR splicing, RACK1 expression and breast cancer cells migration

Recent data have demonstrated that triple negative breast cancer (TNBC) with high glucocorticoid receptor (GR) expression are associated to therapy resistance and increased mortality. Given that GR alternative splicing generates mainly GRα, responsible of glucocorticoids action, we investigated its role in the regulation of RACK1 (Receptor for Activated C Kinase 1), a scaffolding protein with a GRE (Glucocorticoid Response Element) site on its promoter and involved in breast cancer cells migration and invasion. We provide the first evidence that GRα transcriptionally regulates RACK1 by a mechanism connected to SRSF3 splicing factor, which promotes GRα, essential for RACK1 transcriptional regulation and consequently for cells migration. We also establish that this mechanism can be positively regulated by cortisol. Hence, our data elucidate RACK1 transcriptional regulation and demonstrate that SRSF3 involvement in cells migration implies its role in controlling different pathways thus highlighting that new players have to be considered in GR-positive TNBC

Spectral analysis of the biharmonic operator subject to Neumann boundary conditions on dumbbell domains

We consider the biharmonic operator subject to homogeneous boundary conditions of Neumann type on a planar dumbbell domain which consists of two disjoint domains connected by a thin channel. We analyse the spectral behaviour of the operator, characterizing the limit of the eigenvalues and of the eigenprojections as the thickness of the channel goes to zero. In applications to linear elasticity, the fourth order operator under consideration is related to the deformation of a free elastic plate, a part of which shrinks to a segment. In contrast to what happens with the classical second order case, it turns out that the limiting equation is here distorted by a strange factor depending on a parameter which plays the role of the Poisson coefficient of the represented plate.Comment: To appear in "Integral Equations and Operator Theory

A mechanistic mathematical model for describing and predicting the dynamics of high-affinity nitrate intake into roots of maize and other plant species

A fully mechanistic dynamical model for plant nitrate uptake is presented. Based on physiological and regulatory pathways and based on physical laws, we form a dynamic system mathematically described by seven differential equations. The model evidences the presence of a short-term positive feedback on the high-affinity nitrate uptake, triggered by the presence of nitrate around the roots, which induces its intaking. In the long run, this positive feedback is overridden by two long-term negative feedback loops which drastically reduces the nitrate uptake capacity. These two negative feedbacks are due to the generation of ammonium and amino acids, respectively, and inhibit the synthesis and the activity of high-affinity nitrate transporters. This model faithfully predicts the typical spiking behavior of the nitrate uptake, in which an initial strong increase of nitrate absorption capacity is followed by a drop, which regulates the absorption down to the initial value. The model outcome was compared with experimental data and they fit quite nicely. The model predicts that after the initial exposure of the roots with nitrate, the absorption of the anion strongly increases and that, on the contrary, the intensity of the absorption is limited in presence of ammonium around the roots

Conformational altered p53 affects neuronal function: relevance for the response to toxic insult and growth-associated protein 43 expression

The role of p53 in neurodegenerative diseases is essentially associated with neuronal death. Recently an alternative point of view is emerging, as altered p53 conformation and impaired protein function have been found in fibroblasts and blood cells derived from Alzheimer's disease patients. Here, using stable transfected SH-SY5Y cells overexpressing APP751wt (SY5Y-APP) we demonstrated that the expression of an unfolded p53 conformation compromised neuronal functionality. In particular, these cells showed (i) augmented expression of amyloid precursor protein (APP) and its metabolites, including the C-terminal fragments C99 and C83 and β-amyloid peptide (ii) high levels of oxidative markers, such as 4-hydroxy-2-nonenal Michael-adducts and 3-nitro-tyrosine and (iii) altered p53 conformation, mainly due to nitration of its tyrosine residues. The consequences of high-unfolded p53 expression resulted in loss of p53 pro-apoptotic activity, and reduction of growth-associated protein 43 (GAP-43) mRNA and protein levels. The role of unfolded p53 in cell death resistance and lack of GAP-43 transcription was demonstrated by ZnCl(2) treatment. Zinc supplementation reverted p53 wild-type tertiary structure, increased cells sensitivity to acute cytotoxic injury and GAP-43 levels in SY5Y-APP clone