let be a set and let be the set of subsets of . the pair in which is a collection of elements of (blocks) is called a design if every element of appears in , times. is called a symmetric design if . in a symmetric design, each element of appears times in blocks of . a mapping between two designs and is an isomorphism if is a one-to-one correspondence and . every isomorphism of a design, , to it...

We present a study of the lensing properties of two-dimensional (2-D) photonic quasicrystal (PQC) slabs made of dielectric cylinders arranged according to a 12fold-symmetric square-triangle aperiodic tiling. Our full-wave numerical analysis confirms the results recently emerged in the technical literature and, in particular, the possibility of achieving focusing effects within several frequency...

We study quantum field theories with sextic interactions in $3\ensuremath{-}\ensuremath{\epsilon}$ dimensions, where the scalar fields ${\ensuremath{\phi}}^{ab}$ form irreducible representations under $O(N{)}^{2}$ or $O(N)$ global symmetry group. calculate beta functions up to four-loop order and find renormalization group (RG) fixed points. In an example of large $N$ equivalence, parent theory...

Discretization of the Stokes equations produces a symmetric indefinite system of linear equations. For stable discretizatiom a variety of numerical methods have been proposed that have rates of convergence independent of the mesh size used in the dkretization. In this paper we compare the performance of four such methods, namely variants of the Uzawa, preconditioned conjugate gradient, precondi...