Search results for "Conformal"

Quasiconformal distortion on arcs

1994

Homeomorphisms of Finite Distortion

2013

In this chapter we establish the optimal regularity of the inverse mapping in higher dimensions and optimal Sobolev regularity for composites. Moreover, we establish optimal moduli of continuity for mappings in our classes and we discuss orientation preservation and approximation of Sobolev homeomorphisms.

Conformal transformations and weak field limit of scalar-tensor gravity

2013

The weak field limit of scalar tensor theories of gravity is discussed in view of conformal transformations. Specifically, we consider how physical quantities, like gravitational potentials derived in the Newtonian approximation for the same scalar-tensor theory, behave in the Jordan and in the Einstein frame. The approach allows to discriminate features that are invariant under conformal transformations and gives contributions in the debate of selecting the true physical frame. As a particular example, the case of $f(R)$ gravity is considered.

Modular, customisable, accomodation-friendly antenna system for satellite avionics: Development, prototyping and validation

2014

In the frame of ESA program AO/1- 6737/11/NL/MH, an innovative X-band antenna system for satellite avionics has been studied, demonstrated and validated at Proof of Concept Model level. The innovative contribution of such an antenna system relies on modularity, customizability and accommodation friendliness. The antenna concept is based on a Plug and Play architecture, where the basic module is a 2.7 cm-cube with a mass of 53 gr, which can be clustered in array configuration. A catalogue of predefined and ready-to-use clusters could be developed with the possibility of adapting the antenna systems to various platform types by tuning just a few control parameters. Different levels of customi…

Application of spaces of subspheres to conformal invariants of curves and canal surfaces

2013

Extremal length and Hölder continuity of conformal mappings

1986

Elastic Wave Near-Cloaking

2020

Cloaking elastic waves has, in contrast to the cloaking of electromagnetic waves, remained a fundamental challenge: the latter successfully uses the invariance of Maxwell's equations, from which the field of transformational optics has emerged, whereas the elastic Navier equations are not invariant under coordinate transformations. Our aim is to overcome this challenge, at least in practical terms, and thereby unlock applications in mechanics, ultrasound, vibration mitigation, non-destructive evaluation and elastic wave control. We achieve near-cloaking by recognising that, despite the lack of invariance, a decoupling into a system of form invariant potential equations together with a quant…

An Introduction to Geometric Algebra and Conics

2016

This chapter introduces the conics and characterizes them from an algebraic perspective. While in depth geometrical aspects of the conics lie outside the scopes of this chapter, this chapter is an opportunity to revisit concepts studied in other chapters such as matrix and determinant and assign a new geometric characterization to them.

Affine varieties and lie algebras of vector fields

1993

In this article, we associate to affine algebraic or local analytic varieties their tangent algebra. This is the Lie algebra of all vector fields on the ambient space which are tangent to the variety. Properties of the relation between varieties and tangent algebras are studied. Being the tangent algebra of some variety is shown to be equivalent to a purely Lie algebra theoretic property of subalgebras of the Lie algebra of all vector fields on the ambient space. This allows to prove that the isomorphism type of the variety is determinde by its tangent algebra.

Algebras of pseudodifferential operators on complete manifolds

2003

In several influential works, Melrose has studied examples of non-compact manifolds M 0 M_0 whose large scale geometry is described by a Lie algebra of vector fields V ⊂ Γ ( M ; T M ) \mathcal V \subset \Gamma (M;TM) on a compactification of M 0 M_0 to a manifold with corners M M . The geometry of these manifolds—called “manifolds with a Lie structure at infinity”—was studied from an axiomatic point of view in a previous paper of ours. In this paper, we define and study an algebra Ψ 1 , 0 , V ∞ ( M 0 ) \Psi _{1,0,\mathcal V}^\infty (M_0) of pseudodifferential operators canonically associated to a manifold M 0 M_0 with a Lie structure at infinity V ⊂ Γ ( M ; T M ) \mathcal V \subset \Gamma (…