We propose a kind of anisotropic planar metasurface, which has capacity to manipulate the orthogonally-polarized electromagnetic waves independently in the reflection mode. The metasurface is composed of orthogonally I-shaped structures and a metal-grounded plane spaced by a dielectric isolator, with the thickness of about 1/15 wavelength. The normally incident linear-polarized waves will be to...

The rational solutions with as denominators powers of to the elliptic diophantine equation y x x are determined An idea of Yuri Bilu is applied which avoids Thue and Thue Mahler equations and deduces four term S unit equations with special properties that are solved by linear forms in real and p adic logarithms Introduction In a recent paper SW my colleague R J Stroeker and I determined the com...

in this present work, the kudryashov method and the functional variable method are used to construct exact solutions of the complex kdv equation. the kudryashov method and the functional variable method are powerful methods for obtaining exact solutions of nonlinear evolution equations.

We consider the Allen-Cahn equation ε∆u+(1−u)u = 0 in a bounded, smooth domain Ω in R, under zero Neumann boundary conditions, where ε > 0 is a small parameter. Let Γ0 be a segment contained in Ω, connecting orthogonally the boundary. Under certain non-degeneracy and non-minimality assumptions for Γ0, satisfied for instance by the short axis in an ellipse, we construct, for any given N ≥ 1, a s...

Carbon nanotubes (CNTs) have been readily functionalized by microwave activation using two different reactions affording functional derivatives characterized by two orthogonally protected amino groups. The doubly functionalized CNTs can serve as multipurpose, versatile synthons in materials science and biological applications.