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We propose superfield equations in tensorial N-extended superspaces to describe the N=2,4,8 supersymmetric generalizations of free conformal higher spin theories. These can be obtained by quantizing a superparticle model in N-extended…
In this paper we study the boundedness of extension operators associated with spheres in vector spaces over finite fields.In even dimensions, we estimate the number of incidences between spheres and points in the translated set from a…
Many physically interesting quantities of the electromagnetic field can be computed using the electromagnetic scalar product. However, none of the existing expressions for such scalar product are directly applicable when the fields are only…
There has been enormous progress in the last few years in designing neural networks that respect the fundamental symmetries and coordinate freedoms of physical law. Some of these frameworks make use of irreducible representations, some make…
Wavelet based algorithms in numerical analysis are similar to other transform methods in that vectors and operators are expanded into a basis and the computations take place in this new system of coordinates. However, due to the recursive…
The generalized Maxwell equations including an additional scalar field are considered in the first-order formalism. The gauge invariance of the Lagrangian and equations is broken resulting the appearance of a scalar field. We find the…
We outline a regular way for solving Maxwell's equations. We take, as the starting point, the notion of vector potentials. The rationale for introducing this notion in electrodynamics is that the set of Maxwell's equations is seemingly…
We give a representation of the classical theory of multiplicative arithmetic functions (MF)in the ring of symmetric polynomials. The basis of the ring of symmetric polynomials that we use is the isobaric basis, a basis especially sensitive…
The three-dimensional galaxy power spectrum is a powerful probe of primordial non-Gaussianity and additional general relativistic effects, which become important on large scales. At the same time, wide-angle (WA) effects due to differing…
Many applications in science call for the numerical simulation of systems on manifolds with spherical topology. Through use of integer spin weighted spherical harmonics we present a method which allows for the implementation of arbitrary…
We present a review of recent developments of simulations of the Vlasov-Maxwell system of equations using a Fourier transform method in velocity space. In this method, the distribution functions for electrons and ions are Fourier…
The Cartesian coordinate system is the most commonly used system in computer visualization. This is due to its ease of use and processing speed. However, it is not always suitable for a given problem. Angular measures often allow us to…
We calculate the Fourier transform of a spherically symmetric exponential function. Our evaluation is much simpler than the known one. We use the polar coordinates and reduce the Fourier transform to the integral of a rational function of…
We present a unified approach for constructing Slepian functions - also known as prolate spheroidal wave functions - on the sphere for arbitrary tensor ranks including scalar, vectorial, and rank 2 tensorial Slepian functions, using…
The wave equation for vectors and symmetric tensors in spherical coordinates is studied under the divergence-free constraint. We describe a numerical method, based on the spectral decomposition of vector/tensor components onto spherical…
A general theory of matrix-spherical functions for dual Hopf algebras and right coideal subalgebras is developed. We establish their existence and define their orthogonality relations. When specialized to Kolb and Letzter's quantum…
Many flexible parameterizations exist to represent data on the sphere. In addition to the venerable spherical harmonics, we have the Slepian basis, harmonic splines, wavelets and wavelet-like Slepian frames. In this paper we focus on the…
We provide an algorithm for the construction of orthonormal multivariate polynomials that are symmetric with respect to the interchange of any two coordinates on the unit hypercube and are constrained to the hyperplane where the sum of the…
A set of exactly computable orthonormal basis functions that are useful in computations involving constituent quarks is presented. These basis functions are distinguished by the property that they fall off algebraically in momentum space…
We present a framework for the construction of linearizations for scalar and matrix polynomials based on dual bases which, in the case of orthogonal polynomials, can be described by the associated recurrence relations. The framework…