Related papers: V-line 2-tensor tomography in the plane
Currently, theory of ray transforms of vector and tensor fields is well developed, but the Radon transforms of such fields have not been fully analyzed. We thus consider linearly weighted and unweighted longitudinal and transversal Radon…
In this paper we try to prepare a framework for field quantization. To this end, we aim to replace the field of scalars R by self-adjoint elements of a commutative C-algebra, and reach an appropriate generalization of geometrical concepts…
In this paper the properties of right invertible row operators, i.e., of 1X2 surjective operator matrices are studied. This investigation is based on a specific space decomposition. Using this decomposition, we characterize the…
An inversion technique has been developed to recover LTE one-dimensional model photospheres for late-type stars from very high-resolution high signal-to-noise stellar line profiles. It is successfully applied to the Sun using a set of…
In this paper, we consider a special V-line transform. It integrates a given function f over the V-lines whose centers are on a circle centered at the origin and the symmetric axes pass through the origin. We derive two sampling scheme of…
We review a recently developed transfer matrix formulation of the stationary scattering in two and three dimensions where the transfer matrix is a linear operator acting in an infinite-dimensional function space. We discuss its utility in…
Torse-forming vector fields are generalizations of some important vector fields. In this paper, we present some techniques to transform a proper torse-forming vector field into its special cases. Concrete examples are given.
A theory of an optical vector pulsing soliton of self-induced transparency in an ensemble of semiconductor quantum dots is investigated. It is shown that a distribution of the excitonic ground-state transition dipole moments of the quantum…
Braided vector fields on spatial subdomains homeomorphic to the cylinder play a crucial role in applications such as solar and plasma physics, relativistic astrophysics, fluid and vortex dynamics, elasticity, and bio-elasticity. Often the…
Modified Volterra lattice admits two vector generalizations. One of them is studied for the first time. The zero curvature representations, B\"acklund transformations, nonlinear superposition principle and the simplest explicit solutions of…
We reformulate the action of Verlinde line operators on conformal blocks in a 3d TFT language and extend it to line operators labelled by open paths joining punctures on the Riemann surface. We discuss the possible applications of open…
This paper constructs a semi-discrete tight frame of tensor needlets associated with a quadrature rule for tangent vector fields on the unit sphere $\mathbb{S}^2$ of $\mathbb{R}^3$ --- tensor needlets. The proposed tight tensor needlets…
Let $M$ be an $n$-dimensional manifold, $V$ the space of a representation $\rho: GL(n)\longrightarrow GL(V)$. Locally, let $T(V)$ be the space of sections of the tensor bundle with fiber $V$ over a sufficiently small open set $U\subset M$,…
In this paper we show the invertibility of the geodesic X-ray transform on one forms and 2-tensors on asymptotically conic manifolds, up to the natural obstruction, allowing existence of certain kinds of conjugate points. We use the 1-cusp…
We present general formulas for transverse and transverse-traceless (TT) symmetric tensors in flat spaces. TT tensors in conformally flat spaces can be obtained by means of a conformal transformation.
We study the $T\overline{T}$ deformation of two dimensional quantum field theories from a Hamiltonian point of view, focusing on aspects of the theory in Lorentzian signature. Our starting point is a simple rewriting of the spatial integral…
Trivially-acting symmetries in two-dimensional conformal field theory include twist fields of dimension zero which are local topological operators. We investigate the consequences of regarding these operators as part of the global symmetry…
We construct the defining data of two-dimensional topological field theories (TFTs) enriched by non-invertible symmetries/topological defect lines. Simple formulae for the three-point functions and the lasso two-point functions are derived,…
We study a solenoidal-potential type decomposition of a symmetric $m$-tensor field in $\Rb^2$, and its implications to injectivity questions for the momentum and elastic ray transforms. For symmetric tensor fields, a general decomposition…
Topo-Tomography (TT) is a synchrotron-based X-ray diffraction imaging technique used to characterize grain shape and crystal orientation in polycrystalline samples. This work aims to provide a decisive and fundamental understanding of 3D…