Related papers: On the Inverse Problem Relative to Dynamics of the…

Finding a computationally efficient algorithm for the inverse continuous wavelet transform is a fundamental topic in applications. In this paper, we show the convergence of the inverse wavelet transform.

The area of inverse problems in mathematics is highly interdisciplinary. In various fields of science, engineering, medicine, and industry, there arises a need to reconstruct information about unknown entities that cannot be directly…

We show the equivalence of inverse problems for different dynamical systems and corresponding canonical systems. For canonical system with general Hamiltonian we outline the strategy of studying the dynamic inverse problem and procedure of…

We provide a necessary and sufficient condition for a rough control driving a differential equation to be reconstructable, to some order, from observing the resulting controlled evolution. Physical examples and applications in stochastic…

The subject of this paper is the history of the Minkowski-Funk Transform. After introducing the Minkowski-Funk Transform as well as its dual transform and a generalization of both, we will present an inversion formula of the Minkowski-Funk…

The motion in the complex plane of the zeros to various zeta functions is investigated numerically. First the Hurwitz zeta function is considered and an accurate formula for the distribution of its zeros is suggested. Then functions which…

Using a new technique involving integration it is possible to find the exact roots of simple functions. In this case, simple functions are defined as smooth functions having an inverse, and that inverse having an antiderivative. This…

We analyse a mechanical system in two-dimensional relative motion with friction. Although the system is simple, the peculiar interplay between two kinetic friction forces and gravity leads to the wide range of admissible solutions exceeding…

In this review, we extend the Boundary Control method\, -- \,an approach to inverse problems based on control theory for dynamical systems \, -- \,to inverse problems for discrete dynamical systems. We apply our results to classical moment…

A non-classical Weyl theory is developed for Dirac systems with rectangular matrix potentials. The notion of the Weyl function is introduced and the corresponding direct problem is treated. Furthermore, explicit solutions of the direct and…

We study an inverse problem for the fractional Allen-Cahn equation. Our formulation and arguments rely on the asymptotics for the fractional equation and unique continuation properties.

We consider the functional inverse of the Gamma function in the complex plane, where it is multi-valued, and define a set of suitable branches by proposing a natural extension from the real case.

This work considers the algebras of functions in the quantum matrix ball. An explicit formula for a positive invariant integral is presented.

We develop a geometric version of the inverse problem of the calculus of variations for discrete mechanics and constrained discrete mechanics. The geometric approach consists of using suitable Lagrangian and isotropic submanifolds. We also…

The paper contains the inversion formula for the weighted spherical mean. The interest to reconstruction a function by its integral by sphere grews tremendously in the last six decades, stimulated by the spectrum of new problems and methods…

In this paper, we will discuss several radii problems related to Wright Function involving four parameters.

We consider a variable order differential operator on a graph with a cycle. We study the inverse spectral problem for this operator by the system of spectra. The main results of the paper are the uniqueness theorem and the constructive…

We first formulate an inverse problem for a linear fractional Lam\'e system. We determine the Lam\'e parameters from exterior partial measurements of the Dirichlet-to-Neumann map. We further study an inverse obstacle problem as well as an…

Some properties and relations satisfied by the polynomial solutions of the bispectral problem are studied. Given a differential operator, under certain restrictions its polynomial eigenfunctions are explicitly obtained, as well as the…

The purpose of this paper is to introduce a curious function of two variables, expressable via the employment of the Lambert W Funtion, which can be generalized to satisfy Euler's Equation of Inviscid Motion over a specific domain, with…