By using the notion of a quantum double we introduce analogs partial derivatives on Reflection Equation algebra, associated with Hecke symmetry GL(N) type. We construct matrix L=MD, where M is generating algebra and D composed prove that matrices M, L satisfy identity, called Capelli one. Upon applying trace, it becomes scalar relation, which far-reaching generalization classical identity. Also...

Expressions for displacements on the surface of a layered half-space due to point force are given in terms of generalized reflection and transmission coefficient matrices (Kennett, 1980) and the discrete wavenumber summation method (Bouchon, 1981). The Bouchon method with complex frequencies yields accurate near-field dynamic and static solutions. The algorithm is extended to include simultaneo...

Fresnel reflection amplitude coefficients (fractional amplitudes) at the surface of an isotropic, intrinsically nonmagnetic chiral medium are derived on the basis of the Drude–Condon model of optical activity. The eigenvalue–eigenvector solution is obtained with use of Berreman’s 4 3 4 matrix method. Self-consistent results are obtained when the calculations are based on a new 4 3 4 matrix for ...

The effect of single and double-layer anti-reflective coatings on efficiency enhancement of silicon solar cells was investigated. The reflectance of different anti-reflection structures were calculated using the transfer matrix method and then to predict the performance of solar cells coated by these structures, the weighted average reflectance curves were used as an input of a PC1D simulation....

The q-generalizations of the two fundamental statements of matrix algebra – the Cayley-Hamilton theorem and the Newton relations – to the cases of quantum matrix algebras of an ”RTT-” and of a ”Reflection equation” types have been obtained in [2]–[6]. We construct a family of matrix identities which we call Cayley-HamiltonNewton identities and which underlie the characteristic identity as well ...

In this paper, free longitudinal vibration of nanorods is investigated from the wave viewpoint. The Eringen’s nonlocal elasticity theory is used for nanorods modelling. Wave propagation in a medium has a similar formulation as vibrations and thus,  it can be used to describe the vibration behavior. Boundaries reflect the propagating waves after incident. Firstly, the governing quation of nanoro...