‎In this paper,  the sufficient conditions for the linear combinations of slanted half-plane harmonic mappings to be univalent and convex in the direction of $(-gamma) $ are studied. Our result improves some recent works. Furthermore, a illustrative example and imagine domains of the linear combinations satisfying the desired conditions are enumerated.

The present article deals with the study of propagation of plane waves in isotropic generalized thermoelastic diffusion with voids under initial stress. It is found that, for two dimensional model of isotropic generalized thermoelastic diffusion with voids under initial stress, there exists four coupled waves namely, P wave, Mass Diffusion (MD) wave, thermal (T) wave and Volume Fraction (VF) wa...

Consider a time-harmonic electromagnetic plane wave incident on a biperiodic structure in R. The periodic structure separates two homogeneous regions. The medium inside the structure is chiral and nonhomogeneous. In this paper, variational formulations coupling finite element methods in the chiral medium with a method of integral equations on the periodic interfaces are studied. The well-posedn...

A variational method is given for determining the essential supremum of the surface conductivity of a partially coated anisotropic dielectric medium from a knowledge of the far field pattern of the time-harmonic electric field at fixed frequency corresponding to an incident plane wave. It is assumed that the shape of the scatterer has been determined (e.g. by solving the far field equation and ...

Consider a plane monochromatic wave incident on a semi-infinite periodic structure. What happens if the normal component of the transmitted wave group velocity vanishes? At first sight, zero normal component of the transmitted wave group velocity simply implies total reflection of the incident wave. But we demonstrate that total reflection is not the only possible outcome. Instead, the transmit...

Consider a plane monochromatic wave incident on a semi-infinite periodic structure. What happens if the normal component of the transmitted wave group velocity vanishes? At first sight, zero normal component of the transmitted wave group velocity simply implies total reflection of the incident wave. But we demonstrate that total reflection is not the only possible outcome. Instead, the transmit...

in almost all of the present mathematical models, the upstream subbasins, with overland flow as the dominant type of flow, are simulated as a rectangular plane. however, the converging plane is the closest shape to an actual upstream subbasin. the intricate nature of the governing equations of the overland flow on a converging plane is the cause of prolonged absence of an analytical or semi ana...

This paper concerns the switching on of two-dimensional time-harmonic scalar waves. We first review the switch-on problem for a point source in free space, then proceed to analyse the analogous problem for the diffraction of a plane wave by a half-line (the ‘Sommerfeld problem’), determining in both cases the conditions under which the field is well-approximated by the solution of the correspon...

We consider scattering of a time-harmonic acoustic plane wave by a sound-soft convex polygon. To achieve good approximation at high frequencies with a relatively low number of degrees of freedom, we recently proposed a novel Galerkin boundary element method, for which the approximation space consists of piecewise polynomials supported on a graded mesh, with smaller elements adjacent to the corn...

– The superconducting current-phase relation (CPR) of Nb/Au/(001)YBa2Cu3Ox heterojunctions prepared on epitaxial c-axis oriented YBa2Cu3Ox thin films has been measured in a single-junction interferometer. For the first time, the second harmonic of the CPR of such junctions has been observed. The appearance of the second harmonic and the relative sign of the first and second harmonics of the CPR...