Related papers: Binary Representations of ABCD Matrices
The set of linear, differential operators preserving the vector space of couples of polynomials of degrees n and n-2 in one real variable leads to an abstract associative graded algebra A(2). The irreducible, finite dimensional…
We propose an Analytical method of Blind Separation (ABS) of cosmic magnification from the intrinsic fluctuations of galaxy number density in the observed galaxy number density distribution. The ABS method utilizes the different dependences…
An alternating sign matrix is a square matrix satisfying (i) all entries are equal to 1, -1 or 0; (ii) every row and column has sum 1; (iii) in every row and column the non-zero entries alternate in sign. The 8-element group of symmetries…
We reconsider the basic properties of ray-transfer matrices for first-order optical systems from a geometrical viewpoint. In the paraxial regime of scalar wave optics, there is a wide family of beams for which the action of a ray-transfer…
We construct the representations of affine sl(2,R) starting from the unitary representations of the loop ax+b-group. Our approach involves a combinatorial analysis of the correlation functions of the generators and renormalization of the…
We consider a hierarchy of many particle systems on the line with polynomial potentials separable in parabolic coordinates. Using the Lax representation, written in terms of $2\times 2$ matrices for the whole hierarchy, we construct the…
For paraxial light beams and electromagnetic fields, the Stokes vector and polarization matrix provide equivalent scalar measures of optical chirality, widely used in linear optics. However, growing interest in non-paraxial fields, with…
To a finite quadratic module, that is, a finite abelian group D together with a non-singular quadratic form Q:D --> Q/Z, it is possible to associate a representation of either the modular group, SL(2,Z), or its metaplectic cover, Mp(2,Z),…
A spectrograph is an optical instrument that disperses photons of different energies into distinct directions and space locations, and images photon spectra on a position-sensitive detector. Spectrographs consist of collimating, angular…
The versatility of optics enables the design of a wide range of elegant beam instrumentation. Multiple properties of particle beams can be precisely measured by various optical techniques, which include: direct sampling of optical radiation…
Binary Parseval frames share many structural properties with real and complex ones. On the other hand, there are subtle differences, for example that the Gramian of a binary Parseval frame is characterized as a symmetric idempotent whose…
This paper deals with the theory and application of 2-Dimensional, nine-neighborhood, null- boundary, uniform as well as hybrid Cellular Automata (2D CA) linear rules in image processing. These rules are classified into nine groups…
We show that multiple filamentation patterns in high-power laser beams, can be described by means of two statistical physics concepts, namely self-similarity of the patterns over two nested scales, and nearest-neighbor interactions of…
The Type D asymmetric simple exclusion process (ASEP) is a particle system involving two classes of particles that can be viewed from both a probabilistic and an algebraic perspective (arXiv:2011.13473). From a probabilistic perspective, we…
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…
A non-binary Constraint Satisfaction Problem (CSP) can be solved directly using extended versions of binary techniques. Alternatively, the non-binary problem can be translated into an equivalent binary one. In this case, it is generally…
Collaborative representation-based classification (CRC) has demonstrated remarkable progress in the past few years because of its closed-form analytical solutions. However, the existing CRC methods are incapable of processing the nonlinear…
In this tutorial, exponentiation and factorization (decomposition) formulas are derived and discussed for common matrix operators that arise in studies of classical dynamics, linear and nonlinear optics, and special relativity. To…
We show that all spin groups of non-definite, quinary quadratic forms over a field with characteristic 0 can be represented as 2 by 2 matrices with entries in an associated quaternion algebra. Over local and global fields, we further study…
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…