Related papers: Inversion formula, Unique continuation property, a…
We derive explicit reconstruction formulas for the attenuated geodesic X-ray transform over functions and, in the case of non-vanishing attenuation, vector fields, on a class of simple Riemannian surfaces with boundary. These formulas…
Let R be the local ring of a point on a variety X over an algebraically closed field k. We make a connection between the notion of mixed (Samuel) multiplicity of m-primary ideals in R and intersection theory of subspaces of rational…
The star transform is a generalized Radon transform mapping a function of two variables to its integrals along "star-shaped" trajectories, which consist of a finite number of rays emanating from a common vertex. Such operators appear in…
We survey recent progress in the problem of recovering a tensor field from its integrals along geodesics. We also propose several open problems.
In this review paper we carry on our investigations on Schroedinger operators with inverse square potentials on the half-line. Depending on several parameters, such operators possess either a finite number of complex eigenvalues, or an…
In this paper we present an invariant formulation of special relativity, i.e., the ''true transformations relativity.'' It deals either with true tensor quantities (when no basis has been introduced) or equivalently with coordinate- based…
We discuss the properties and the permutation behaviour of the reversed Dickson polynomials of the $(k+1)$-th kind $D_{n,k}(1,x)$ over finite fields. The results in this paper unify and generalize several recently discovered results on…
We solve a combinatorial question concerning eigenvalues of the universal intertwining endomorphism of a subset representation. This is then applied to justify the evaluation of the Eisenbud-Levine-Khimshiashvili (ELK) signature formula for…
Algebraically special gravitational fields are described using algebraic and differential invariants of the Weyl tensor. A type III invariant is also given and calculated for Robinson-Trautman spaces.
The development of energy selective, photon counting X-ray detectors allows for a wide range of new possibilities in the area of computed tomographic image formation. Under the assumption of perfect energy resolution, here we propose a…
It is known that the Funk transform (the Funk-Radon transform) is invertible in the class of even (symmetric) continuous functions defined on the unit 2-sphere S^2. In this article, for the reconstruction of f from C(S^2) (can be non-even),…
We present a unified algebraic framework utilizing the formal Bell transform to bridge the Dirichlet convolution of arithmetic functions with the combinatorial structure of infinite Euler-type products. By analyzing the logarithmic…
In the paper "Confinement of matroid representations to subsets of partial fields" (arXiv:0806.4487) we introduced the Hydra-k partial fields to study quinary matroids with inequivalent representations. The proofs of some results on these…
In the last decades the Moore-Penrose pseudoinverse has found a wide range of applications in many areas of Science and became a useful tool for physicists dealing, for instance, with optimization problems, with data analysis, with the…
In a previous article [J. Comp. Phys. $\mathbf{357}$ (2018) 282-304], the mixed mimetic spectral element method was used to solve the rotating shallow water equations in an idealized geometry. Here the method is extended to a smoothly…
In Tensor Field Theory (TFT), observables are defined through tensor field contractions that produce unitary invariants for complex-valued tensor fields. Traditionally, these observables are constructed using tensor fields of a fixed order…
A method of approximating the inverse Radon transform on the plane by integrating against a smooth kernel is investigated. For piecewise smooth integrable functions, convergence theorems are proven and Gibbs phenomena are ruled out.…
This article studies the inverse problem of recovering a vector field supported in $\mathbb{D}_R$, the disk of radius $R$ centered at the origin, through a set of generalized broken ray/V-line transforms, namely longitudinal and transverse…
Interactions of $a_2, K^*_2, f_2$ and $f_2'$ tensor-mesons with low-energy $\pi, K, \eta, \eta'$ pseudo-scalar mesons are constrained by chiral symmetry. We derive a chiral Lagrangian of tensor mesons in which the tensor mesons are treated…
In a previous paper we proposed a new method based on resummations for studying radiation reaction of an electron in a plane-wave electromagnetic field. In this paper we use this method to study the electron momentum expectation value for a…