We consider Maxwell’s equations for an isomagnetic anisotropic, non-stationary and inhomogeneous medium in two dimensions. We discuss an inverse problem of determining the permittivity tensor   ε1 ε2 ε2 ε3   and the permeability μ in the constitutive relations from a finite number of lateral boundary measurements. Applying a Carleman estimate, we prove an estimate of the Lipschitz type for ...

The Casimir effect is considered for a wedge with opening angle α, with perfectly conducting walls, when the interior region is filled with an isotropic and nondispersive medium with permittivity ǫ and permeability μ. The electromagnetic energy-momentum tensor in the bulk is calculated, together with the surface stress on the walls. A discussion is given on the possibilities for measuring the i...

Negative refractive index characteristics of a uniaxial anisotropic slab with a negative component of the permeability tensor are first confirmed. A two-dimensional array of metallic spirals is fabricated on a dielectric substrate and the wave propagation guided by the structure is measured by near-field measurements at 4.5 GHz band. The ω-β relation is obtained by the measured phase distributi...

a projective parameter of a geodesic as solution of certain ode is defined to be a parameter which is invariant under projective change of metric. using projective parameter and poincaré metric, an intrinsic projectively invariant pseudo-distance can be constructed. in the present work, solutions of the above ode are characterized with respect to the sign of parallel ricci tensor on a finsler s...

In this paper, we first show that the tensor product of a finite number of standard g-frames (resp. fusion frames, frames) is a standard g-frame (resp. fusion frame, frame) for the tensor product of Hilbert $C^ast-$ modules and vice versa, then we consider tensor products of g-Bessel multipliers, Bessel multipliers and Bessel fusion multipliers in Hilbert $C^ast-$modules. Moreover, we obtain so...

A = Jacobian matrix a = speed of sound, m∕s C = source term vector E = total energy, J∕kg e = internal energy vector, J∕kg F = inviscid flux tensor Fd = diffusive flux tensor Fo = Forchheimer number G = flux tensor, F − Fd − uU h = enthalpy, J∕kg h = species enthalpy vector, J∕kg hr = recovery enthalpy, J∕kg I = identity matrix J = directional species diffusion flux tensor, kg∕m K = permeabilit...

‎We consider Albeverio's linear representations of the braid groups $B_3$ and $B_4$‎. ‎We specialize the indeterminates used in defining these representations to non zero complex numbers‎. ‎We then consider the tensor products of the representations of $B_3$ and the tensor products of those of $B_4$‎. ‎We then determine necessary and sufficient conditions that guarantee the irreducibility of th...

Accurate modeling of contamination in subsurface flow and water aquifers is crucial for agriculture environmental protection. Here, we demonstrate a parallel algorithm to quantify the propagation uncertainty dispersal pollution flow. Specifically, consider density-driven estimate how from permeability porosity propagates solution. We take two-dimensional Elder-like problem as numerical benchmar...