In this paper, the optical properties of one dimensional fractal structures are investigated. We consider six typical fractal photonic structures: the symmetric dual cantor-like fractal structure, the asymmetric dual cantor-like fractal structure, the single cantor-like fractal structure, the symmetric dual golden-section fractal structure, the asymmetric dual golden-section fractal structure a...

In this thesis I study reconstruction of orthogonal polyhedral surfaces and orthogonal polyhedra from partial information about their boundaries. There are three main questions for which I provide novel results. The first question is “Given the dual graph, facial angles and edge lengths of an orthogonal polyhedral surface or polyhedron, is it possible to reconstruct the dihedral angles?” The se...

We characterize orthogonal matrix polynomials (Pn)n whose differences (∇ Pn+1)n are also orthogonal by means of a discrete Pearson equation for the weight matrix W with respect to which the polynomials (Pn)n are orthogonal. We also construct some illustrative examples. In particular, we show that contrary to what happens in the scalar case, in the matrix orthogonality the discrete Pearson equat...

b∈B μ ◦σ b . There are two a priori candidates for an associated orthogonal harmonic analysis : (i) the existence of some subset Λ in R such that the exponentials {e}λ∈Λ form an orthogonal basis for L (μ); and (ii) the existence of a certain dual pair of representations of the C-algebra ON where N is the cardinality of the set B. (For each N , the C-algebra ON is known to be simple; it is also ...

Dual scattering channel schemes extend the transmission line matrix numerical method (Johns’ TLM algorithm) in two directions. For one point, transmission line links are replaced by abstract scattering channels in terms of paired distributions (characteristic impedances are thus neither needed, nor in general defined, e.g.). In the second place, non-trivial cell interface scattering is admitted...

Dual scattering channel schemes extend the transmission line matrix numerical method (Johns’ TLM algorithm) in two directions. For one point, transmission line links are replaced by abstract scattering channels in terms of paired distributions (characteristic impedances are thus neither needed, nor in general defined, e.g.). In the second place, non-trivial cell interface scattering is admitted...

the microstructure of dual phase steels can be considered as a matrix of ferrite phase reinforced by martensite particles. recent measurements show that the mechanical properties of the ferrite phase are changed with the distance from the martensite grains. in this paper, a new method has been proposed to consider this phenomenon in finite element modeling of dual phase steels microstructure. i...

In this paper we present several types of orthogonal matrix decompositions used in systems and control. We focus on those related to eigenvalue and singular value problems and include generalizations to several matrices.