相关论文: General unit-disk representation for periodic mult…

The reflection and transmission amplitudes of waves in disordered multimode waveguides are studied by means of numerical simulations based on the invariant embedding equations. In particular, we analyze the influence of surface-type…

We study periodic representations in number systems with an algebraic base $\beta$ (not a rational integer). We show that if $\beta$ has no Galois conjugate on the unit circle, then there exists a finite integer alphabet $\mathcal A$ such…

Many quantum systems may have the same classical limit. We argue that in the classical limit their traces do not necessarily converge one to another. The trace formula allows to express quantum traces by means of classical quantities as…

We consider a class of discontinuous piecewise linear differential systems in $\mathbb{R}^3$ with two pieces separated by a plane. In this class we show that there exist differential systems having: a unique limit cycle, a unique…

We study the combinatorial types of periodic orbits of the standard covering endomorphisms ${\mathbf m}_k(x)=k x \ (\text{mod} \ {\mathbb Z})$ of the circle for integers $k \geq 2$ and the frequency with which they occur. For any $q$-cycle…

Polyadic systems and their representations are reviewed and a classification of general polyadic systems is presented. A new multiplace generalization of associativity preserving homomorphisms, a 'heteromorphism' which connects polyadic…

We present here a generalization of the scattering-matrix approach for the description of the propagation of electromagnetic waves in nanostructured magneto-optical systems. Our formalism allows us to describe all the key magneto-optical…

The spectral theory of quantum graphs is related via an exact trace formula with the spectrum of the lengths of periodic orbits (cycles) on the graphs. The latter is a degenerate spectrum, and understanding its structure (i.e.,finding out…

Even after several decades of systematic usage of X-ray diffraction as one of the major analytical tool for epitaxic layers, the vision of the reciprocal space of these materials is still a simple superposition of two reciprocal lattices,…

Topologically protected states can be found in physical systems, that show singularities in some energy contour diagram. These singularities can be characterized by winding numbers, defined on a classification surface, which maps physical…

In this paper we show how rotational bands of resonances can be described by using trajectories of poles of the scattering amplitude in the complex angular momentum plane: each band of resonances is represented by the evolution of a single…

It is shown that total reflection for all incident angles does not require a two- or three-dimensional photonic crystal. We demonstrate that a one-dimensional photonic crystal can exhibit total omni-directional reflection for any incident…

We consider the space of all representations of the commutator subgroup of a knot group into Z/p, p is prime. As proven by D. Silver and S. Williams, this space can be completely described by a finite oriented graph. We describe the lengths…

It is well known that not every combinatorial configuration admits a geometric realization with points and lines. Moreover, some of them do not even admit realizations with pseudoline arrangements, i.e., they are not topological. In this…

A unitary (Euclidean) representation of a quiver is given by assigning to each vertex a unitary (Euclidean) vector space and to each arrow a linear mapping of the corresponding vector spaces. We recall an algorithm for reducing the matrices…

We study the propagation of surface electromagnetic waves along the metallic surface covered by various layered dielectric structures. We show that strong radiative losses typical for the scattering of the surface wave can be considerably…

We construct C-algebras for a class of surfaces that are inverse images of certain polynomials of arbitrary degree. By using the directed graph associated to a matrix, the representation theory can be understood in terms of ``loop'' and…

Transversal structures (also known as regular edge labelings) are combinatorial structures defined over 4-connected plane triangulations with quadrangular outer-face. They have been intensively studied and used for many applications…

The constitutive characterization of the uniformity and homogeneity of binary elastic composites is presented in terms of a combination of the material groupoids of the individual constituents. The incorporation of these two groupoids…

For a given family of similar shapes, what we call a "unit shape" strongly analogizes the role of the unit circle within the family of all circles. Within many such families of similar shapes, we present what we believe is naturally and…