Related papers: A uniqueness theorem in potential theory with impl…
This paper is concerned with uniqueness in inverse acoustic scattering with phaseless far-field data at a fixed frequency. The main difficulty of this problem is the so-called translation invariance property of the modulus of the far-field…
Reconstructing magnetizations from measurements of the generated magnetic potential is generally non-unique. The non-uniqueness still remains if one restricts the magnetization to those induced by an ambient magnetic dipole field (i.e., the…
The inverse source problem where an unknown source is to be identified from the knowledge of its radiated wave is studied. The focus is placed on the effect that multi-frequency data has on establishing uniqueness. In particular, it is…
We consider Sturm-Liouville operators on geometrical graphs without cycles (trees) with singular potentials from the class $W_2^{-1}$. We suppose that the potentials are known on a part of the graph, and study the so-called partial inverse…
This work establishes a strong uniqueness property for a class of planar locally integrable vector fields. A result on pointwise convergence to the boundary value is also proved for bounded solutions.
A Bayesian approach is developed to determine quantum mechanical potentials from empirical data. Bayesian methods, combining empirical measurements and "a priori" information, provide flexible tools for such empirical learning problems. The…
Time-distance helioseismology is a set of powerful tools to study features below the Sun's surface. Inverse methods are needed to interpret time-distance measurements, with many examples in the literature. However, techniques that utilize a…
We present a new method for renormalisation group improvement of the effective potential of a quantum field theory with an arbitrary number of scalar fields. The method amounts to solving the renormalisation group equation for the effective…
It is shown that the operator algebraic setting of local quantum physics leads to a uniqueness proof for the inverse scattering problem. The important mathematical tool is the thermal KMS aspect of wedge-localized operator algebras and its…
The behavior of the magnetic potential near a point charge (fluxon) located at a curved regular boundary surface is shown to be essentially different from that of a volume point charge. In addition to the usual inverse distance singularity,…
This work investigates both direct and inverse problems of the variable-exponent sub-diffusion model, which attracts increasing attentions in both practical applications and theoretical aspects. Based on the perturbation method, which…
In this paper, we prove a sharp uniqueness result for the singular Schr\"odinger equation with an inverse square potential. This will be done without assuming geometrical restrictions on the observation region. The proof relies on a recent…
Inverse analysis, such as model calibration, often suffers from a lack of informative data in complex real-world scenarios. The standard remedy, designing new experimental setups, is often costly and time-consuming, while readily available…
Quantum theory makes the most accurate empirical predictions and yet it lacks simple, comprehensible physical principles from which the theory can be uniquely derived. A broad class of probabilistic theories exist which all share some…
This paper is concerned with the uniqueness of inverse acoustic scattering problem for cavities with the modulus of the near-fields. With the aid of the reference ball technique and the superpositions of two point sources as the incident…
We consider the formally determined inverse problem of recovering an unknown time-dependent potential function from the knowledge of the restriction of the solution of the wave equation to a small subset, subject to a single external…
This paper is concerned with the unique identification of the shape of a scatterer through a single far-field pattern in an inverse elastic medium scattering problem with a generalized transmission boundary condition. The uniqueness issue…
Diffraction tomography aims to recover an object's scattering potential from measured wave fields. In the classical setting, the object is illuminated by plane waves from many directions, and the Fourier diffraction theorem provides a…
We show that the direction of renormalization in effective field theory is constrained by fundamental principles in the infrared$\unicode{x2014}$unitarity, analyticity, and Lorentz invariance. Our theorem, in the spirit of the $a$-theorem…
It is shown that, contrary to widely held beliefs, the potentials of spin-density-functional theory (SDFT) are not unique functionals of the spin densities. Explicit examples of distinct sets of potentials with the same ground-state…