Quasiperiodicity is the concept of order without translation symmetry. The discovery of quasiperiodic order in natural materials transformed the way scientists examine and define ordered structure. We show and verify experimentally that quasiperiodicity can be observed by scattering processes from a periodic structure, provided the interaction area is of finite width. This is made through a mom...

We demonstrate how to design thin-film multilayer structures that separate multiple wavelength channels with a single stack by spatial dispersion, thus allowing compact manufacturable wavelength multiplexers and demultiplexers and possibly beam-steering or dispersion-control devices. We discuss four types of structure--periodic one-dimensional photonic crystal superprism structures, double-chir...

In this paper, a delayed predator–prey system with stage structure is investigated. Sufficient conditions for the system to have multiple periodic solutions are obtained when the delay is sufficiently large by applying Bendixson’s criterion. Further, some numerical examples are given. Keywords—Predator-prey system, Stage structure, Hopf bifurcation, Periodic solutions.

We prove an algebraic preservation theorem for positive Horn definability in א0-categorical structures. In particular, we define and study a construction which we call the periodic power of a structure, and define a periomorphism of a structure to be a homomorphism from the periodic power of the structure to the structure itself. Our preservation theorem states that, over an א0-categorical stru...

Abstract. In this paper, we provide a new formulation for the generalized periodic Toda lattice. Since the work of Kostant, Adler and Symes, it has been known that the Toda lattice is related to the structure of simple Lie algebras. Indeed, the non-periodic and the periodic Toda lattices can be expressed as Hamiltonian systems on coadjoint orbits: the former of a simple Lie group and the latter...

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...

We prove a preservation theorem for positive Horn definability inא0-categorical structures.In particular, we define and study a construction which we call the periodic power of a structure, anddefine a periomorphism of a structure to be a homomorphism from the periodic power of the structureto the structure itself. Our preservation theorem states that, over anא0-categorical ...

We study the stability of a four parameter family of spatially periodic traveling wave solutions of the generalized Benjamin-Bona-Mahony equation to two classes of perturbations: periodic perturbations with the same periodic structure as the underlying wave, and long-wavelength localized perturbations. In particular, we derive necessary conditions for spectral instability to perturbations to bo...

The algorithmic construction of formula periodic tables for polycyclic conjugated hydrocarbons is detailed. The symmetries associated with this construction are identified. The formula periodic table for benzenoids (Table PAH6) exhibits a one-to-one mapping onto the formula periodic table for fluorenoids/fluoranthenoids minus the constant-isomer fluorenoid/fluoranthenoid formulas and the formul...

A study is presented of right (left) coprime decompositions of a collection of N -periodic rational matrices, with some ordered structure. From a block-ordered right coprime decomposition of a rational matrix of the given periodic collection, the corresponding block-ordered right coprime decompositions of the remaining matrices of the collection are constructed. In addition, those decomposition...