Abstract: A complete spectral representation for the
electromagnetic field of planar multilayered waveguides
inhomogeneously filled with omega media is presented. The problem
of guided electromagnetic propagation is reduced to an eigenvalue
equation related to a 2 ´ 2 matrix differential operator. Using the
concept of adjoint waveguide, general bi-orthogonality relations for
the hybrid modes (either from the discrete or from the continuous
spectrum) are derived. For the special case of homogeneous layers
the linear operator formalism is reduced to a simple 2 ´ 2 coupling
matrix eigenvalue problem. Finally, as an example of application, the
surface and the radiation modes of a grounded omega slab waveguide
are analyzed.
Abstract: The paper considered the construction of BIBDs using potential Lotto Designs (LDs) earlier derived from qualifying parent BIBDs. The study utilized Li’s condition pr t−1 ( t−1 2 ) + pr− pr t−1 (t−1) 2 < ( p 2 ) λ, to determine the qualification of a parent BIBD (v, b, r, k, λ) as LD (n, k, p, t) constrained on v ≥ k, v ≥ p, t ≤ min{k, p} and then considered the case k = t since t is the smallest number of tickets that can guarantee a win in a lottery. The (15, 140, 28, 3, 4) and (7, 7, 3, 3, 1) BIBDs were selected as parent BIBDs to illustrate the procedure. These BIBDs yielded three potential LDs each. Each of the LDs was completely generated and their properties studied. The three LDs from the (15, 140, 28, 3, 4) produced (9, 84, 28, 3, 7), (10, 120, 36, 3, 8) and (11, 165, 45, 3, 9) BIBDs while those from the (7, 7, 3, 3, 1) produced the (5, 10, 6, 3, 3), (6, 20, 10, 3, 4) and (7, 35, 15, 3, 5) BIBDs. The produced BIBDs follow the generalization (v + 1, b + r + λ + 1, r +λ+1, k, λ+1) where (v, b, r, k, λ) are the parameters of the (9, 84, 28, 3, 7) and (5, 10, 6, 3, 3) BIBDs. All the BIBDs produced are unreduced designs.