Related papers: On the Inverse Problem Relative to Dynamics of the…
Inverse problems in statistical physics are motivated by the challenges of `big data' in different fields, in particular high-throughput experiments in biology. In inverse problems, the usual procedure of statistical physics needs to be…
The determination of Parton Distribution Functions from a finite set of data is a typical example of an inverse problem. Inverse problems are notoriously difficult to solve, in particular when a robust determination of the uncertainty in…
We consider inverse dynamic and spectral problems for the one dimensional Dirac system on a finite tree. Our aim will be to recover the topology of a tree (lengths and connectivity of edges) as well as matrix potentials on each edge. As…
In this paper we consider new regularization methods for linear inverse problems of dynamic type. These methods are based on dynamic programming techniques for linear quadratic optimal control problems. Two different approaches are…
In this paper, we investigate the inverse quasi-variational inequality problem in finite-dimensional spaces. First, we introduce a second-order dynamical system whose trajectory converges exponentially to the solution of the inverse…
The Lambert W function, implicitly defined by W(x) exp{W(x)}=x, is a "new" special function that has recently been the subject of an extended upsurge in interest and applications. In this note, I point out that the Lambert W function can…
The Lambert $W$ function, giving the solutions of a simple transcendental equation, has become a famous function and arises in many applications in combinatorics, physics, or population dyamics just to mention a few. In the last decade it…
We study the relationship between numerical solutions for inverting Tippe Top and the structure of the dynamical equations. The numerical solutions confirm oscillatory behaviour of the inclination angle $\theta(t)$ for the symmetry axis of…
We establish H\"older stability of an inverse hyperbolic obstacle problem. Mainly, we study the problem of reconstructing an unknown function defined on the boundary of the obstacle from two measurements taken on the boundary of a domain…
We consider the inverse problem for the wave equation which consists of determining an unknown space-dependent force function acting on a vibrating structure from Cauchy boundary data. Since only boundary data are used as measurements, the…
We consider the inverse dynamical problem for the dynamical system with discrete time associated with the semi-infinite Jacobi matrix. We solve the inverse problem for such a system and answer a question on the characterization of the…
The Wigner functions on the one dimensional lattice are studied. Contrary to the previous claim in literature, Wigner functions exist on the lattice with any number of sites, whether it is even or odd. There are infinitely many solutions…
We consider dynamic inverse problems for a dynamical system associated with a finite Jacobi matrix and for a system describing propagation of waves in a finite Krein-Stieltjes string. We offer three methods of recovering unknown parameters:…
We study the inverse problem for the fractional Laplace equation with multiple nonlinear lower order terms. We show that the direct problem is well-posed and the inverse problem is uniquely solvable. More specifically, the unknown…
In this paper, we consider a discontinuous Dirac operator depending polynomially on the spectral parameter and a finite number of transmission conditions. We get some properties of eigenvalues and eigenfunctions. Then, we investigate some…
The Lambert W function has utility for solving various exponential and logarithmic equations arranged in the form of $g(x)e^{g(x)}$. Using the Lambert W function and tetration, a variety of categorized inversion formulas are presented.…
Inverse problems, where in broad sense the task is to learn from the noisy response about some unknown function, usually represented as the argument of some known functional form, has received wide attention in the general scientific…
We revisit the standard representation of the (inverse) Radon transform which is well-known in the mathematical literature. We extend this representation to the case involving the parton distributions. We have found the new additional…
The present work is a brief review of the progressive search of improper delta-functions which are of interest in Quantum Mechanics and in the problem of motion in General Relativity Theory.
In the study of discrete dynamical systems, we typically start with a function from a space into itself, and ask questions about the properties of sequences of iterates of the function. In this paper we reverse the direction of this study.…