Related papers: The inverse problem within free Electrodynamics an…
We carry on the approach used in [Sch] to provide a solution for the inverse problem of the calculus of variations for Maxwell equations in vacuum and we provide an abstract theory including all implicit differential equations that can be…
The inverse problem of the calculus of variations consists in determining if the solutions of a given system of second order differential equations correspond with the solutions of the Euler-Lagrange equations for some regular Lagrangian.…
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…
We prove an implicit function theorem and an inverse function theorem for free noncommutative functions over operator spaces and on the set of nilpotent matrices. We apply these results to study dependence of the solution of the initial…
The electron and photon transport processes in spectroscopy techniques described by the invariant embedding theory is here revisited. We report a convergence method to obtain closed analytical solutions to the 3D integro-differential…
Tools of the intrinsic analysis on manifolds, helpful in solving the invariant inverse problem of the calculus of variations are being presented comprising a combined approach which consists in the simultaneous imposition of symmetry…
The free motion of charged colloids within ionic solutions and in the vicinity of charged boundaries, is a phenomenon that occurs in various natural, biological and industrial settings. Here, we develop an electrohydrodynamic lubrication…
In this paper we have chosen to work with two different approaches to solving the inverse problem of the calculus of variation. The first approach is based on an integral representation of the Lagrangian function that uses the first…
Quantum electrodynamics near a boundary is investigated by considering the inertial mass shift of an electron near a dielectric or conducting surface. We show that in all tractable cases the shift can be written in terms of integrals over…
A matrix inverse free method to solve time-dependent Schrodinger equation is presented. The method is not subject to form of Hamiltonian and adopting real space grid system such as structured and unstructured grid, and achieves the order N…
The paper deals with the problem of integration of equations of motion in nonholonomic systems. By means of well-known theory of the differential equations with an invariant measure the new integrable systems are discovered. Among them…
We extend the theory of exterior differential systems from manifolds and their tangent bundles to Lie algebroids. In particular, we define the concept of an integral manifold of such an exterior differential system. We support our…
We consider the time-harmonic elastic wave scattering from a general (possibly anisotropic) inhomogeneous medium with an embedded impenetrable obstacle. We show that the impenetrable obstacle can be effectively approximated by an isotropic…
A complete solution to the multiplier version of the inverse problem of the calculus of variations is given for a class of hyperbolic systems of second-order partial differential equations in two independent variables. The necessary and…
In this work we consider the inverse elastic scattering problem by an inclusion in two dimensions. The elastic inclusion is placed in an isotropic homogeneous elastic medium. The inverse problem, using the third Betti's formula (direct…
The aim of this paper is to establish the framework of the enclosure method for some class of inverse problems whose governing equations are given by parabolic equations with discontinuous coefficients. The framework is given by considering…
It is shown that nonlinear electrodynamics of the Born--Infeld theory type may be exploited to shed insight into a few fundamental problems in theoretical physics, including rendering electromagnetic asymmetry to energetically exclude…
In this paper we apply a scaling invariance analysis to reduce a class of parabolic moving boundary problems to free boundary problems governed by ordinary differential equations. As well known free boundary problems are always non-linear…
We give a solution to the inverse moment problem for a certain class of Hessenberg and symmetric matrices related to integrable lattices of Toda type.
We present a novel approach for the inverse problem in electrical impedance tomography based on regularized quadratic regression. Our contribution introduces a new formulation for the forward model in the form of a nonlinear integral…