Related papers: Two-vector representation of a nondepolarizing Mue…
The degree of polarimetric purity is an invariant dimensionless quantity that characterizes the closeness of a polarization state of a wave to a pure state and is related to the Von Neumann entropy. The polarimetric purity of a plane wave…
New degrees of freedom having the form of a unit vector are identified for characterizing the spin polarization of free electron. It is shown that when only the spin is considered, the non-commutativity of the Cartesian components of the…
We demonstrate the existence of topological insulators in one dimension protected by mirror and time-reversal symmetries. They are characterized by a nontrivial $\mathbb{Z}_2$ topological invariant defined in terms of the "partial"…
A model of randomly distributed overlapping spheres of different radii is represented to describe a heterogeneous porous medium. Two-particle correlation function of the relative position of pores of different radii in the medium space was…
If for a vector space V of dimension g over a characteristic zero field we denote by $\wedge^iV$ its alternating powers, and by $V^\vee$ its linear dual, then there are natural Poincar\'e isomorphisms: $\wedge^i V^\vee \cong \wedge^{g-i}…
General expressions for the unpolarized differential cross section and for various polarization observables in the coherent pseudoscalar meson photo- and electroproduction on the deuteron target have been obtained in one-photon-exchange…
In this paper polynomial maps are represented by the use of matrices whose entries are numbered by pair of multiindices and a new product of such matrices is introduced. A matrix representation of composition of polynomial maps is given. In…
A non associative, noncommutative algebra is defined that may be interpreted as a set of vector modules over a noncommutative surface of rotation. Two of these vector modules are identified with the analogues of the tangent and cotangent…
Linearly polarized emission is described, in general, in terms of the Stokes parameters $Q$ and $U$, from which the polarization intensity and polarization angle can be determined. Although the polarization intensity and polarization angle…
We describe a method for an explicit determination of indecomposable preprojective and preinjective representations for extended Dynkin quivers by vector spaces and matrices. This method uses tilting theory and the explicit knowledge of…
A proper set of indices characterizing the polarimetric purity of light and material media is defined from the eigenvalues of the corresponding coherency matrix. A simple and generalizable relation of these indices with the current…
To represent real $m$-dimensional vectors, a positional vector system given by a non-singular matrix $M \in \mathbb{Z}^{m \times m}$ and a digit set $\mathcal{D} \subset \mathbb{Z}^m$ is used. If $m = 1$, the system coincides with the well…
This paper offers a number of examples showing that in the case of two independent variables the uniform ellipticity of a linear system of differential equations with partial derivatives of the second order, which fulfills condition (3), do…
Many books on polarization give tables of Mueller matrices. Here we give a table of Mueller matrices M, coherency matrices C, and coherency matrix factors F for different polarization components. F is not given for some complicated cases.…
The two-by-two representation of the SL(2,c) group is for spin-1/2 particles. Starting from this two-by-two representation, it is possible to construct the four-by-four matrices for spin-1 particles. For massless particles, it is possible…
We study the modular representation theory of the symmetric and alternating groups. One of the most natural ways to label the irreducible representations of a given group or algebra in the modular case is to show the unitriangularity of the…
We provide sharp lower bounds for the multiplicity of a local holomorphic foliation defined in a complex surface in terms of data associated to a germ of invariant curve. Then we apply our methods to invariant curves whose branches are…
The ideal imaging system would efficiently capture information about all fundamental properties light: intensity, direction, wavelength, and polarization. Most common imaging systems only map the spatial degrees of freedom of light onto a…
Mueller polarized bi-directional scattering distribution functions (pBSDFs) are 4x4 matrix-valued functions which depend on acquisition geometry. The most popular pBSDF is a weighted sum between a Fresnel matrix and an ideal depolarizer.…
General relativity predicts the existence of only two tensorial gravitational wave polarizations, while a generic metric theories of gravity can possess up to four additional polarizations, including two vector and two scalar ones. These…