Related papers: Imaging of complex-valued tensors for two-dimensio…
We consider the boundary rigidity problem for asymptotically hyperbolic manifolds. We show injectivity of the X-ray transform in several cases and consider the non-linear inverse problem which consists of recovering a metric from boundary…
A two-fluid model is derived from the plasma kinetic equations using the moment model reduction method. The moment method we adopt was recently developed with a globally hyperbolic regularization where the moment model attained is locally…
We introduce a method for transforming low-order tensors into higher-order tensors and apply it to tensors defined by graphs and hypergraphs. The transformation proceeds according to a surgery-like procedure that splits vertices, creates…
Modeling time-harmonic Maxwell problems in heterogeneous media presents significant mathematical and computational challenges. Due to the inherent non-elliptic structure and non-coercive nature of Maxwell equations, conventional methods…
We consider for the time-dependent Maxwell's equations the inverse problem of identifying locations and certain properties of small electromagnetic inhomogeneities in a homogeneous background medium from dynamic measurements of the…
We study the inverse conductivity problem of how to reconstruct an isotropic electrical conductivity distribution $\gamma$ in an object from static electrical measurements on the boundary of the object. We give an exact reconstruction…
This paper studies an inverse boundary value problem for a semilinear Helmholtz equation with Neumann boundary conditions in a bounded domain $\Omega \subset \mathbb{R}^n$ ($n\ge2$). The objective is to recover the unknown linear and…
This paper extends approach of our joint paper with K\"{a}hler and recent paper of the author, published in 2021, on problems of the static Maxwell system in three dimensional inhomogeneous media. Applied pseudoanalytic function theory…
We introduce an algorithm to decide isomorphism between tensors. The algorithm uses the Lie algebra of derivations of a tensor to compress the space in which the search takes place to a so-called densor space. To make the method practicable…
The Maxwell field equations relative to a uniformly accelerated frame, and the variational principle from which they are obtained, are formulated in terms of the technique of geometrical gauge invariant potentials. They refer to the…
In recent literature on holographic QCD, the consideration of the five-dimensional Einstein-dilaton-Maxwell models has played a crucial role. Typically, one Maxwell field is associated with the chemical potential, while additional Maxwell…
We consider for the full time-dependent Maxwell's equations the inverse problem of identifying locations and certain properties of small electromagnetic inhomogeneities in a homogeneous background medium from dynamic boundary measurements…
Consider a compact Riemannian manifold in dimension $n\geq 3$ with strictly convex boundary. We show that the transverse ray transform of $1$ tensors and the mixed ray transform of $1+1$ tensors are invertible, up to natural obstructions,…
In this paper, we study the complexity factor for a charged anisotropic self-gravitating object. We formulate the Einstein-Maxwell field equations, Tolman-Opphenheimer-Volkoff equation, and the mass function. We form the structure scalars…
It is known that in the four-dimensional Riemannian space the complex bispinor generates a number of tensors: scalar, pseudo-scalar, vector, pseudo-vector, antisymmetric tensor. This paper solves the inverse problem: the above tensors are…
We prove a sharp stability estimate for the problem of reconstructing a symmetric 2-tensor from its integrals along all maximal geodesics on a simple manifold.
We use the Holder regularity analysis to study the symmetry breaking and recovery due to a parametric potential generated via the strictly isospectral factorization method. The initial potential is two-dimensional and periodic in the two…
The transverse anisotropy constant and the related D\"oring mass density are key parameters of the one-dimensional model to describe the motion of magnetic domain walls. So far, no general framework is available to determine these…
In this paper, a restricted transverse ray transform acting on vector and symmetric $m$-tensor fields is studied. We developed inversion algorithms using restricted transverse ray transform data to recover symmetric $m$-tensor fields in…
We consider the inverse problem of recovering a potential from the Dirichlet to Neumann map at a large fixed frequency on certain Riemannian manifolds. We extend the earlier result of [G. Uhlmann and Y. Wang, arXiv:2104.03477] to the case…