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This article proves the uniqueness for two kinds of inverse problems of identifying fractional orders in diffusion equations with multiple time-fractional derivatives by pointwise observation. By means of eigenfunction expansion and Laplace…
We consider the inverse Calder\'on problem consisting of determining the conductivity inside a medium by electrical measurements on its surface. Ideally, these measurements determine the Dirichlet-to-Neumann map and, therefore, one usually…
In this work, an inverse problem in the fractional diffusion equation with random source is considered. Statistical moments are used of the realizations of single point observation $u(x_0,t,\omega).$ We build the representation of the…
In this paper, we first discuss the concept of an emission wave. In the history of science, this is the first time we have discovered a new way in which (transverse) waves are realized in nature. It can therefore be expected to lead to…
We consider an inverse boundary value problem for a nonlinear elastic wave equation which was studied in [de Hoop, Uhlmann, Wang. Math. Ann. (2019) doi:10.1007/s00208-018-01796-y]. We show that all the parameters appearing in the equation…
We consider an inverse boundary problem for the dynamical Maxwell's equations. We show that the electric permittivity, conductivity, and magnetic permeability can be uniquely determined locally if there is a strictly convex foliation with…
The problem of inverting a system in presence of a series-defined output is analyzed. Inverse models are derived that consist of a set of algebraic equations. The inversion is performed explicitly for an output trajectory functional, which…
In this paper, we empirically reveal an invariance over images-images share a set of one-way wave equations with latent speeds. Each image is uniquely associated with a solution to these wave equations, allowing for its reconstruction with…
The well-known Dixmier conjecture asks if every algebra endomorphism of the first Weyl algebra over a characteristic zero field is an automorphism. We bring a hopefully easier to solve conjecture, called the $\gamma,\delta$ conjecture, and…
We consider an inverse problem arising in thermo-/photo- acoustic tomography that amounts to reconstructing a function $f$ from its circular or spherical means with the centers lying on a given measurement surface. (Equivalently, these…
The Inverse problem for an electromagnetic field produced by a dipole is solved. It is assumed that the field of an arbitrary changing dipole is known. Obtained formulae allow calculation of the position and dynamics of the dipole which…
Maxwell's equations hold in inertial reference frames in uniform translational motion relative to one another. In conjunction with the Lorentz coordinate transformation equations, the transformation equations for the electric and magnetic…
We consider the inverse problem of determining different type of information about a diffusion process, described by ordinary or fractional diffusion equations stated on a bounded domain, like the density of the medium or the velocity field…
We consider fractional diffusion equations and study the stability of the inverse problem of determining the time-dependent parameter in a source term or a coefficient of zero-th order term from observations of the solution at one point in…
The goal of inversion is to estimate the model which generates the data of observations with a specific modeling equation. One general approach to inversion is to use optimization methods which are algebraic in nature to define an objective…
Texture is the term used to characterize the surface of a given object or phenomenon and is an important feature used in image processing and pattern recognition. Our aim is to compare various Texture analyzing methods and compare the…
In this paper we introduce the functional framework and the necessary conditions for the well-posedness of an inverse problem arising in the mathematical modeling of disease transmission. The direct problem is given by an initial boundary…
We study the inverse scattering problem of determining a magnetic field and electric potential from scattering measurements corresponding to finitely many plane waves. The main result shows that the coefficients are uniquely determined by…
We show that part I of uniform Martin's conjecture follows from a local phenomenon, namely that if a non-constant Turing invariant function goes from the Turing degree $\boldsymbol x$ to the Turing degree $\boldsymbol y$, then $\boldsymbol…
In this paper, we consider several geometric inverse problems for linear elliptic systems. We prove uniqueness and stability results. In particular, we show the way that the observation depends on the perturbations of the domain. In some…