117 research outputs found
The spectral properties of the magnetic polarizability tensor for metallic object characterisation
The measurement of time‐harmonic perturbed field data, at a range of frequencies, is beneficial for practical metal detection, where the goal is to locate and identify hidden targets. In particular, these benefits are realised when frequency‐dependent magnetic polarizability tensors (MPTs) are used to provide an economical characterisation of conducting permeable objects, and a dictionary‐based classifier is employed. However, despite the advantages shown in dictionary‐based classifiers, the behaviour of the MPT coefficients with frequency is not properly understood. In this paper, we rigorously analyse, for the first time, the spectral properties of the coefficients of the MPT. This analysis has the potential to improve existing algorithms and design new approaches for object location and identification in metal detection. Our analysis also enables the response transient response from a conducting permeable object to be predicted for more general forms of excitation
Physics in Riemann's mathematical papers
Riemann's mathematical papers contain many ideas that arise from physics, and
some of them are motivated by problems from physics. In fact, it is not easy to
separate Riemann's ideas in mathematics from those in physics. Furthermore,
Riemann's philosophical ideas are often in the background of his work on
science. The aim of this chapter is to give an overview of Riemann's
mathematical results based on physical reasoning or motivated by physics. We
also elaborate on the relation with philosophy. While we discuss some of
Riemann's philosophical points of view, we review some ideas on the same
subjects emitted by Riemann's predecessors, and in particular Greek
philosophers, mainly the pre-socratics and Aristotle. The final version of this
paper will appear in the book: From Riemann to differential geometry and
relativity (L. Ji, A. Papadopoulos and S. Yamada, ed.) Berlin: Springer, 2017
Looking backward: From Euler to Riemann
We survey the main ideas in the early history of the subjects on which
Riemann worked and that led to some of his most important discoveries. The
subjects discussed include the theory of functions of a complex variable,
elliptic and Abelian integrals, the hypergeometric series, the zeta function,
topology, differential geometry, integration, and the notion of space. We shall
see that among Riemann's predecessors in all these fields, one name occupies a
prominent place, this is Leonhard Euler. The final version of this paper will
appear in the book \emph{From Riemann to differential geometry and relativity}
(L. Ji, A. Papadopoulos and S. Yamada, ed.) Berlin: Springer, 2017
REMOVABLE SETS FOR LIPSCHITZ HARMONIC FUNCTIONS ON CARNOT GROUPS
Abstract. Let G be a Carnot group with homogeneous dimension Q ≥ 3 and let L be a sub-Laplacian on G. We prove that the critical dimension for removable sets of Lipschitz L-harmonic functions is (Q − 1). Moreover we construct self-similar sets with positive and finite H Q−1 measure which are removable. 1
Generalized gradients on Lie algebroids
Generalized O(n) -gradients for connections on Lie algebroids are derived
A glimpse into Thurston's work
We present an overview of some significant results of Thurston and their
impact on mathematics. The final version of this paper will appear as Chapter 1
of the book "In the tradition of Thurston: Geometry and topology", edited by K.
Ohshika and A. Papadopoulos (Springer, 2020)
A note on the Königs domain of compact composition operators on the Bloch space
Let D be the unit disk in the complex plane. We define B0 to be the little Bloch space of functions f analytic in D which satisfy lim┬(|z|→1)〖(1- |z|^2 )|f^' (z) |=0.〗 If φ:D→D is analytic then the composition operator C_φ:f→f∘φ is a continuous operator that maps B0 into itself. In this paper, we show that the compactness of C_φ, as and operator on B0, can be modelled geometrically by its principle eigenfunction. In particular, under certain necessary conditions, we relate the compactness of C_φto the geometry of Ω=σ(D) where σ satisfies Schroder’s functional equation σ∘φ=φ^' (0)σ
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