In this paper, an approach for human-following robot control is investigated. The approach is based on velocity potential fields that permit to generate velocity vector commands that drive the robot at a safe distance with regard to the human while avoiding obstacles. Velocity potential fields are known for not crating local minima present in the case of artificial potential fields. The approac...

This paper deals with the scattering problem by an inhomogeneous object embedded in a chiral medium. A combined Hilbert space and integral equation method is employed to prove the existence and uniqueness of the solutions to the scattering problem. It is shown that the classical Silver-M uller radiation condition remains valid in chiral media.

In this article, we present some results concerning the harmonicity on tangent bundle equipped with vertical rescaled metric. We establish necessary and sufficient conditions under which a vector field is harmonic respect to metric construct examples of fields. also study along map between Riemannian manifolds, target manifold its bundle. Next discuss composition projection from into another ma...

In the context of Lebesgue integration, we derive the divergence theorem for unbounded vector fields that can have singularities at every point of a compact set whose Minkowski content of codimension greater than two is finite. The resulting integration by parts theorem is applied to removable sets of holomorphic and harmonic functions. In the context of Lebesgue integration, powerful divergenc...

Inverse problems arising in (geo)magnetism are typically ill-posed, particular {they exhibit non-uniqueness}. Nevertheless, there exist nontrivial model spaces on which the problem is uniquely solvable. Our goal here to describe such that accommodate constraints suited for applications. In this paper we treat inverse magnetization a Lipschitz domain with fairly general topology. We characterize...

Abstract This paper addresses the approximation of fractional harmonic maps. Besides a unit-length constraint, one has to tackle difficulty nonlocality. We establish weak compactness results for critical points Dirichlet energy on vector fields. devise and analyze numerical methods various partial differential equations related The imply convergence approximations. Numerical examples spin chain...

We develop a large-scale regularity theory of higher order for divergence-form elliptic equations with heterogeneous coefficient fields a in the context of stochastic homogenization. The large-scale regularity of a-harmonic functions is encoded by Liouville principles: The space of a-harmonic functions that grow at most like a polynomial of degree k has the same dimension as in the constant-coe...

In this article, we generalize the concept of the Lie algebra of vector fields to the set of smooth sections of a T-bundle which is by definition a canonical generalization of the concept of a tangent bundle. We define a Lie bracket multiplication on this set so that it becomes a Lie algebra. In the particular case of tangent bundles this Lie algebra coincides with the Lie algebra of vector fie...

The Hamiltonian structure of spacetimes with two commuting Killing vector fields is analyzed for the purpose of addressing the various problems of time that arise in canonical gravity. Two specific models are considered: (i) cylindrically symmetric spacetimes, and (ii) toroidally symmetric spacetimes, which respectively involve open and closed universe boundary conditions. For each model canoni...