Weak helix submanifolds of euclidean spaces

It is shown that there exist nonstrong weak 2-helix surfaces of R

Constant Angle Surfaces in \H^2\times \R

In this paper we classify constant angle surfaces in \H^2\times\R, where \H^2 is the hyperbolic plane.Comment: 9 Latex page

On certain surfaces in the Euclidean space E3{\mathbb{E}}^3

In the present paper we classify all surfaces in \E^3 with a canonical principal direction. Examples of these type of surfaces are constructed. We prove that the only minimal surface with a canonical principal direction in the Euclidean space ${\mathbb{E}}^3$ is the catenoid.Comment: 13 Latex page

From Golden Spirals to Constant Slope Surfaces

In this paper, we find all constant slope surfaces in the Euclidean 3-space, namely those surfaces for which the position vector of a point of the surface makes constant angle with the normal at the surface in that point. These surfaces could be thought as the bi-dimensional analogue of the generalized helices. Some pictures are drawn by using the parametric equations we found.Comment: 11 pages, 8 figure

On weak r-Helix submanifolds

In this paper, we investigate special curves on a weak r-helix submanifold in Euclidean n-space E^{n}. Also, we give the important relations between weak r-helix submanifolds and the special curves such as line of curvature, asymptotic curve and helix line.Comment: arXiv admin note: text overlap with arXiv:1203.160

Symmetric Jacobians

This article is about polynomial maps with a certain symmetry and/or antisymmetry in their Jacobians, and whether the Jacobian Conjecture is satisfied for such maps, or whether it is sufficient to prove the Jacobian Conjecture for such maps. For instance, we show that it suffices to prove the Jacobian conjecture for polynomial maps x + H over C such that JH satisfies all symmetries of the square, where H is homogeneous of arbitrary degree d >= 3.Comment: 18 pages, minor corrections, grayscale eepic boxes have been replaced by colorful tikz boxe

Controlled Anisotropic Deformation of Ag Nanoparticles by Si Ion Irradiation

The shape and alignment of silver nanoparticles embedded in a glass matrix is controlled using silicon ion irradiation. Symmetric silver nanoparticles are transformed into anisotropic particles whose larger axis is along the ion beam. Upon irradiation, the surface plasmon resonance of symmetric particles splits into two resonances whose separation depends on the fluence of the ion irradiation. Simulations of the optical absorbance show that the anisotropy is caused by the deformation and alignment of the nanoparticles, and that both properties are controlled with the irradiation fluence.Comment: Submitted to Phys. Rev. Lett. (October 14, 2005