Position vector of spacelike biharmonic curves in the Lorentzian Heisenberg group Heis 3
In this paper, we study spacelike biharmonic curves in the Lorentzian Heisenberg group Heis 3 . We show that spacelike biharmonic curves are general helices. We characterize position vector of spacelike biharmonic general helices in terms of their curvature and torsion.
Null biharmonic curves in the Lorentzian Heinsenberg group Heis3
In this paper, we study biharmonic curves and we characterize null biharmonic curves in terms of their curvature and torsion in the Lorentzian Heisenberg group Heis. We give necessary and sufficient conditions for null biharmonic curves in the Lorentzian Heisenberg group Heis. Finally, we prove that all of null biharmonic curves are helices and we give their explicit parametrizations. key words. Heisenberg group, biharmonic curve, null curve, helices. AMS subject classifications. 58E20.
Reflection coefficient of inhomogeneous anisotropic impedance plane
Solved the problem of constructive synthesis of an inhomogeneous anisotropic impedance plane reflecting a homogeneous plane wave in two different preset directions on a matched and cross polarization. Obtained the reflection coefficients and expressions for the scattering diagrams. The impedance is implemented by the frequent array of orthogonal strips. The law of distribution of the reactance was obtained in an explicit form. It is shown that for arbitrarily given (unequal) directions of reflections on matched and cross polarizations, the orientation of the reactance strips turns out to be variable along the plane. Formulated restrictions on class of implemented scattering diagrams. Shown the results of numerical studies.