Related papers: Singular Mueller matrices
A transversal matroid $M$ of rank $r$ on $[n]$ can be associated to a family of binary matrices corresponding to different presentations of $M$. We describe those matrices which arise from unique maximal presentations of size $r$- giving a…
Polarizability tensor of a strongly magnetized plasma and the polarization vectors and opacities of normal electromagnetic waves are studied for the conditions typical of neutron star atmospheres, taking account of partial ionization…
The dark matter may consist not of one elementary particle but of different species, each of them contributing a fraction of the observed dark matter density. A major theoretical difficulty with this scenario --dubbed multi-component dark…
The possibility of a polarization sounding of the pulsar magnetosphere is examined, using intrinsic pulsar emission as a probe signal, for modern radio telescopes operating in the meter and decameter wavelength range. Different models of…
We investigate the cluster-tilted algebras of finite representation type over an algebraically closed field. We give an explicit description of the relations for the quivers for finite representation type. As a consequence we show that a…
A new property, the strong singular value property, is introduced, developed, and utilized to study the problem of which lists of nonnegative real numbers occur as the singular values of a matrix with a prescribed zero-nonzero pattern.
We present an overview of characteristic identities for Lie algebras and superalgebras. We outline methods that employ these characteristic identities to deduce matrix elements of finite dimensional representations. To demonstrate the…
Polarized light-matter interactions are mathematically described by the Mueller matrix (MM)-valued polarized bidirectional reflectance distribution function (pBRDF). A pBRDF is parameterized by 16 degrees of freedom that depend upon…
We study the family of depolarizations of a squarefree monomial ideal $I$, i.e. all monomial ideals whose polarization is $I$. We describe a method to find all depolarizations of $I$ and study some of the properties they share and some they…
In this paper, we study the two natural polarizations, namely the standard polarization and the box polarization, of the d-th power of the maximal ideal in a polynomial ring. We show that these polarizations correspond to smooth points in…
While dealing with the nontrivial task of classifying Mueller matrices, of special interest is the study of the degenerate Mueller matrices (matrices with vanishing determinant, for which the law of multiplication holds, but there exists no…
We consider the origin of unpolarised light resulting from the backscattering of circularly polarized light by random turbid tissue-like disperse medium. We reveal the dynamics of the backscattered fraction of unpolarized light, disclosing…
Totally equimodular matrices generalize totally unimodular matrices and arise in the context of box-total dual integral polyhedra. This work further explores the parallels between these two classes and introduces foundational building…
Spin dependencies of the intensity and polarization of the synchrotron radiation of the longitudinally polarized particle performing uniform circular motion in the magnetic field are investigated.
Singularities, such as poles and branch points, play a crucial role in investigating the analytic properties of scattering amplitudes that inform new computational techniques. In this note, we point out that scattering amplitudes can also…
We propose a formal resource-theoretic approach to quantify the degree of polarization of two and three-dimensional random electromagnetic fields. This endows the space of spectral polarization matrices with the orders induced by…
An isolated hypersurface singularity comes equipped with many different pairings on different spaces, the intersection form and the Seifert form on the Milnor lattice, a polarizing form for a mixed Hodge structure on a dual space, and a…
Calculations are performed for the linear polarization of starlight due to extinction by aligned dust grains when the starlight traverses a medium with irregular magnetic fields. This medium is intended to represent the optically thick…
We present a comprehensive investigation of the radio polarization properties within the theory of natural electromagnetic wave modes in pulsar magnetospheres. Taking into account the curvature of the field lines, aberration effects and…
Determinantal singularities are an important class of singularities, generalizing complete intersections, which recently have seen a large amount of interest. They are defined as preimage of $M^{t}_{m,n}$ the sets of matrices of rank less…