Related papers: Iwasawa Effects in Multi-layer Optics
Iwasawa theory of Heegner points on abelian varieties of GL_2 type has been studied by, among others, Mazur, Perrin-Riou, Bertolini and Howard. The purpose of this paper is to describe extensions of some of their results in which abelian…
We develop a transfer-matrix formulation of the scattering of electromagnetic waves by a general isotropic medium which makes use of a notion of electromagnetic transfer matrix $\mathbf{M}$ that does not involve slicing of the scattering…
Nature is imbued with mathematics, manifested through its stunning patterns, symmetries, and structures. Here, we unveil that in a multilayered framework of twisted birefringent optical components, a recursive number pattern of Pascal's…
We study gravitational lensing when plasma surrounds the lens. An extra deflection angle is induced by the plasma in addition to the deflection generated by gravity. An inhomogeneous plasma distribution generates a greater effect than a…
Matrix weights satisfying a Muckenhoupt $A_p$-condition relative to a family of anisotropic balls in $\mathbb{R}^d$ defined by a pseudo-metric are studied. It is shown that such matrix weights satisfy a doubling condition and a reverse…
This paper presents a theoretical study of the phenomenon of acoustic imaging by sonic crystals, which are made of two-dimensional regular arrays of rigid cylinders placed in parallel in air. The scattering of acoustic waves is computed…
We present an algorithm to reduce the computational effort for the multiplication of a given matrix with an unknown column vector. The algorithm decomposes the given matrix into a product of matrices whose entries are either zero or integer…
Predicting the optical response of macroscopic arrangements of individual scatterers is a computational challenge, as the problem involves length scales across multiple orders of magnitude. We present a full-wave optical method to highly…
The aim of this paper is to describe efficient algorithms for computing Maass waveforms on subgroups of the modular group PSL(2,Z) with general multiplier systems and real weight. A selection of numerical results obtained with these…
The meaning of quantum group transformation properties is discussed in some detail by comparing the (co)actions of the quantum group with those of the corresponding Lie group, both of which have the same algebraic (matrix) form of the…
Abstr.: The classical r-matrix implied by the quantum k-Poincare algebra of Lukierski,Nowicki and Ruegg is used to generate a Poisson structure on the ISL(2,C) group. A quantum deformation of the ISL(2,C) group ( on the Hopf algebra level )…
Neutron and X-ray reflectometry are important methods for studying thin multilayer systems. The Parratt method and the method of characteristic matrices, also referred to as transfer matrices, are used for simulation, evaluation of…
The integrated Sachs-Wolfe (ISW) effect in a Lambda dominated universe can be an important factor in the evolution of cosmic microwave background fluctuations. With the inclusion of cosmological constant we present the complete analytic…
This paper examines the use of Lie group and Lie Algebra theory to construct the geometry of pairwise comparisons matrices. The Hadamard product (also known as coordinatewise, coordinate-wise, elementwise, or element-wise product) is…
We study the average behaviour of the Iwasawa invariants for Selmer groups of elliptic curves. These results lie at the intersection of arithmetic statistics and Iwasawa theory. We obtain unconditional lower bounds for the density of…
In this paper we deal with the global properties of Willmore surfaces in spheres via the harmonic conformal Gauss map using loop groups. We first derive a global description of those harmonic maps which can be realized as conformal Gauss…
We compute the Schwartzman group associated with an ergodic affine automorphism of a compact connected abelian group given by the composition of an automorphism of the group and a translation by an element in the path component of the…
We study the average behaviour of the Iwasawa invariants for the Selmer groups of elliptic curves, setting out new directions in arithmetic statistics and Iwasawa theory.
Wave effects in lensing form a rich phenomenon at the intersection of classical caustic singularities and quantum interference, yet are notoriously difficult to model. A large number of recently observed pulsars and fast radio bursts in…
We introduce a numerical method that enables efficient modelling of light scattering by large, disordered ensembles of non-spherical particles incorporated in stratified media, including when the particles are in close vicinity to each…