Peterson's Deformations of Higher Dimensional Quadrics

We provide the first explicit examples of deformations of higher dimensional quadrics: a straightforward generalization of Peterson's explicit 1-dimensional family of deformations in $\mathbb{C}^3$ of 2-dimensional general quadrics with common conjugate system given by the spherical coordinates on the complex sphere $\mathbb{S}^2\subset\mathbb{C}^3$ to an explicit $(n-1)$-dimensional family of deformations in $\mathbb{C}^{2n-1}$ of $n$-dimensional general quadrics with common conjugate system given by the spherical coordinates on the complex sphere $\mathbb{S}^n\subset\mathbb{C}^{n+1}$ and non-degenerate joined second fundamental forms. It is then proven that this family is maximal

The B\"{a}cklund transforms of Peterson's isometric deformations of diagonal higher dimensional quadrics without center

We provide the B\"{a}cklund transforms of Peterson's isometric deformations of diagonal higher dimensional quadrics without center. These are found explicitly. can be iterated via the Bianchi Permutability Theorem and can be further iterated via the $3$-M\"{o}bius configuration, thus producing explicit solutions depending on arbitrarily many constants.Comment: arXiv admin note: substantial text overlap with arXiv:0808.2007, arXiv:2208.11419; text overlap with arXiv:0905.0216, arXiv:0902.142

Nanocomposites as Advanced Materials for Aerospace Industry

Polymer nanocomposites, consisting of nanoparticles dispersed in polymer matrix, have gained interest due to the attractive properties of nanostructured fillers, as carbon nanotubes and layered silicates. Low volume additions (1- 5%) of nanoparticles provide properties enhancements comparable to those achieved by conventional loadings (15- 40%) of traditional fillers.Structural nanocomposites represent reinforcement structures based on carbon or glass fibers embedded into polymeric matrix modified with nanofillers.Structural composites are the most important application of nanaocomposites, in aerospace field, as, laminates and sandwich structures. Also, they can by used as anti-lightning, anti-radar protectors and paints. The paper presents the effects of sonic dispersion of carbon nanotubes and montmorrilonite on the mechanical, electrical, rheological and trybological properties of epoxy polymers and laminated composites, with carbon or glass fiber reinforcement, with nanoadditivated epoxy matrix. One significant observation is that nanoclay contents higher than 2% wt generate an increase of the resin viscosity, from 1500 to 50000- 100000 cP, making the matrix impossible to use in high performance composites.Also, carbon nanotubes provide the resin important electrical properties, passing from dielectric to semi- conductive class. These effects have also been observed for fiber reinforced composites.Contrarily to some opinions in literature, the results of carbon nanotubes or nanoclays addition on the mechanical characteristics of glass or carbon fiber composites seem to be rather low