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We extend the spherical tensorial formalism for polarization to the treatment of electric- and magnetic-multipole transitions of any order. We rely on the spherical-wave expansion to derive the tensor form of the operator describing the…
The perfectly matched layer is very important for the elastic wave problem in the frequency domain. Generally, the formulas of the elasticity tensor in the perfectly matched layers are derived from the transformed momentum equation. In this…
Arc permutations, which were originally introduced in the study of triangulations and characters, have recently been shown to have interesting combinatorial properties. The first part of this paper continues their study by providing signed…
A unified field theory for the description of matter in a curved space is discussed. The description is based on a standard Lagrangianian formalism in a pseudo-Euclidian 4D continuum using a 3-index tensor as independent variables. The…
A brief overview of some computer algebra methods for computations with nested integrals is given. The focus is on nested integrals over integrands involving square roots. Rewrite rules for conversion to and from associated nested sums are…
Discriminative latent-variable models are typically learned using EM or gradient-based optimization, which suffer from local optima. In this paper, we develop a new computationally efficient and provably consistent estimator for a mixture…
Everyone knows that the Euler characteristic of a combinatorial manifold is given by the alternating sum of its numbers of simplices. It is shown that there are other linear combinations of the numbers of simplices which are combinatorial…
We introduce a new type of reduction of inversive difference polynomials that is associated with a partition of the basic set of automorphisms $\sigma$ and uses a generalization of the concept of effective order of a difference polynomial.…
We introduce a sub-symmetry of a differential system as an infinitesimal transformation of a subset of the system that leaves the subset invariant on the solution set of the entire system. We discuss the geometrical meaning and properties…
A numerical approach to compute tensor integrals in one-loop calculations is presented. The algorithm is based on a recursion relation which allows to express high rank tensor integrals as a function of lower rank ones. At each level of…
In this article, we introduce and study various V-line transforms (VLTs) defined on symmetric 2-tensor fields in $\mathbb{R}^2$. The operators of interest include the longitudinal, transverse, and mixed VLTs, their integral moments, and the…
We initiate a study of the inversion of the geodesic X-ray transform $I_m$ over symmetric $m$-tensor fields on asymptotically hyperbolic surfaces. This operator has a non-trivial kernel whenever $m\ge 1$. To propose a gauge representative…
In the first part of the paper kernels are constructed which meromorphically extend the Macdonald-Koornwinder polynomials in their degrees. In the second part of the paper the kernels associated with rank one root systems are used to define…
We consider restricted light ray transforms arising from an inverse problem of finding cosmic strings. We construct a relative left parametrix for the transform on two tensors, which recovers the space-like and some light-like singularities…
We consider first generation scalar-tensor theories of gravitation in a completely generic form, keeping the transformation functions of the local rescaling of the metric and the scalar field redefinition explicitly distinct from the…
In this paper we introduce an intermediate field representation for random matrices and random tensors with positive (stable) interactions of degree higher than 4. This representation respects the symmetry axis responsible for positivity.…
The most important purpose of this article is to investigate perfect reconstruction underlying range space of operators in finite dimensional Hilbert spaces by matrix methods. To this end, first we obtain more structures of the canonical…
We show that Mandell's inverse $K$-theory functor is a categorically-enriched non-symmetric multifunctor. In particular, it preserves algebraic structures parametrized by non-symmetric operads. As applications, we describe how ring…
In this paper, we analyze the nonlinear single pixel X-ray transform $K$ and study the reconstruction of $f$ from the measurement $Kf$. Different from the well-known X-ray transform, the transform $K$ is a nonlinear operator and uses a…
In natural and laboratory magnetized plasmas, an equilibrium electric field may exist perpendicular to the background magnetic field. In such a situation all the plasma species experience a common drift and the unperturbed distribution…