Computing Volume Bounds of Inclusions by EIT Measurements

The size estimates approach for Electrical Impedance Tomography (EIT) allows for estimating the size (area or volume) of an unknown inclusion in an electrical conductor by means of one pair of boundary measurements of voltage and current. In this paper we show by numerical simulations how to obtain such bounds for practical application of the method. The computations are carried out both in a 2D and a 3D setting.Comment: 20 pages with figure

Globally diffeomorphic σ -harmonic mappings

Given a two-dimensional mapping U whose components solve a divergence structure elliptic equation,we give necessary and sufficient conditions on the boundary so that U is a global diffeomorphism

Seismic Station Installations and Their Impact on the Recorded Signals and Derived Quantities

The role of local geology in controlling ground motion has long been acknowledged. Consequently, increasing attention is paid to the assessment of the geophysical properties of the soils at the seismic stations, which impact the station recordings and a series of related quantities, particularly those referring to seismic hazard estimates. Not the same level of attention is commonly dedicated to the seismic station installation, to the point that it is generally believed that housings and shelters containing seismic instruments are of no interest, because they can only affect frequencies well above the engineering range of interest. Using examples from seismometric and accelerometric stations, we describe the (1) housing, (2) foundation, and (3) pillar effects on the seismic records. We propose a simple working scheme to identify the existence of potential installation-related issues and to assess the frequency fidelity range of response of a seismic station to ground motion. Our scheme is developed mostly on ambient noise recordings and, thus, surface waves. The hope is that, besides the parameters that start to be routinely introduced in the seismic archives (VS30, soil classes, etc.), the assessment of the maximum reliable frequency, under which no soil–structure interaction is expected, also becomes a mandatory information. In our experience, for some installation sites, the maximum reliable frequency can even be less than a very few hert

Sewing Constraints and Non-Orientable Open Strings

We extend to non-orientable surfaces previous work on sewing constraints in Conformal Field Theory. A new constraint, related to the real projective plane, is described and is used to illustrate the correspondence with a previous construction of open-string spectra.Comment: phyzzx, 11 pages and 4 figures, ROM2F-93/3

Characterization of ellipses as uniformly dense sets with respect to a family of convex bodies

Let K \subset R^N be a convex body containing the origin. A measurable set G \subset R^N with positive Lebesgue measure is said to be uniformly K-dense if, for any fixed r > 0, the measure of G \cap (x + rK) is constant when x varies on the boundary of G (here, x + rK denotes a translation of a dilation of K). We first prove that G must always be strictly convex and at least C1,1-regular; also, if K is centrally symmetric, K must be strictly convex, C1,1-regular and such that K = G - G up to homotheties; this implies in turn that G must be C2,1- regular. Then for N = 2, we prove that G is uniformly K-dense if and only if K and G are homothetic to the same ellipse. This result was already proven by Amar, Berrone and Gianni in [3]. However, our proof removes their regularity assumptions on K and G and, more importantly, it is susceptible to be generalized to higher dimension since, by the use of Minkowski's inequality and an affine inequality, avoids the delicate computations of the higher-order terms in the Taylor expansion near r = 0 for the measure of G\cap(x+rK) (needed in [3])

Diffeomorphic approximation of Sobolev homeomorphisms

Every homeomorphism h : X -> Y between planar open sets that belongs to the Sobolev class W^{1,p}(X,Y), 1<p<\infty, can be approximated in the Sobolev norm by diffeomorphisms.Comment: 21 pages, 5 figure

Global stability for an inverse problem in soil-structure interaction

We consider the inverse problem of determining the Winkler subgrade reaction coefficient of a slab foundation modelled as a thin elastic plate clamped at the boundary. The plate is loaded by a concentrated force and its transversal deflection is measured at the interior points. We prove a global Holder stability estimate under (mild) regularity assumptions on the unknown coefficient

Path integral evaluation of Dbrane amplitudes

We extend Polchinski's evaluation of the measure for the one-loop closed string path integral to open string tree amplitudes with boundaries and crosscaps embedded in Dbranes. We explain how the nonabelian limit of near-coincident Dbranes emerges in the path integral formalism. We give a careful path integral derivation of the cylinder amplitude including the modulus dependence of the volume of the conformal Killing group.Comment: Extended version replacing hep-th/9903184, includes discussion of nonabelian limit, Latex, 10 page