Search results for "Alder"

Recent progress in the Calderón problem with partial data

2014

Exponential instability in the fractional Calder\'on problem

2017

In this note we prove the exponential instability of the fractional Calder\'on problem and thus prove the optimality of the logarithmic stability estimate from \cite{RS17}. In order to infer this result, we follow the strategy introduced by Mandache in \cite{M01} for the standard Calder\'on problem. Here we exploit a close relation between the fractional Calder\'on problem and the classical Poisson operator. Moreover, using the construction of a suitable orthonormal basis, we also prove (almost) optimality of the Runge approximation result for the fractional Laplacian, which was derived in \cite{RS17}. Finally, in one dimension, we show a close relation between the fractional Calder\'on pro…

Uniqueness and reconstruction for the fractional Calder\'on problem with a single measurement

2020

We show global uniqueness in the fractional Calder\'on problem with a single measurement and with data on arbitrary, possibly disjoint subsets of the exterior. The previous work \cite{GhoshSaloUhlmann} considered the case of infinitely many measurements. The method is again based on the strong uniqueness properties for the fractional equation, this time combined with a unique continuation principle from sets of measure zero. We also give a constructive procedure for determining an unknown potential from a single exterior measurement, based on constructive versions of the unique continuation result that involve different regularization schemes.

Calderón problem for the p-Laplace equation : First order derivative of conductivity on the boundary

2016

We recover the gradient of a scalar conductivity defined on a smooth bounded open set in Rd from the Dirichlet to Neumann map arising from the p-Laplace equation. For any boundary point we recover the gradient using Dirichlet data supported on an arbitrarily small neighbourhood of the boundary point. We use a Rellich-type identity in the proof. Our results are new when p 6 = 2. In the p = 2 case boundary determination plays a role in several methods for recovering the conductivity in the interior. peerReviewed

A characterization of Hajłasz–Sobolev and Triebel–Lizorkin spaces via grand Littlewood–Paley functions

2010

Abstract In this paper, we establish the equivalence between the Hajlasz–Sobolev spaces or classical Triebel–Lizorkin spaces and a class of grand Triebel–Lizorkin spaces on Euclidean spaces and also on metric spaces that are both doubling and reverse doubling. In particular, when p ∈ ( n / ( n + 1 ) , ∞ ) , we give a new characterization of the Hajlasz–Sobolev spaces M ˙ 1 , p ( R n ) via a grand Littlewood–Paley function.

Seismic expression of the shallow structure of The Neapolitan Yellow Tuff (NYT) caldera offshore the Campi Flegrei

2014

In this study we integrate high-resolution swath bathymetry, single-channel reflection seismic data and gravity core data, to provide new insights into the shallow structure and latest Quaternary to Holocene evolution of the submerged sector of the Neapolitan Yellow Tuff (NYT) caldera (Campi Flegrei) in the Pozzuoli Bay. The new data allow for a reconstruction of the offshore geometry of the NYT caldera collapse – ring fault system, along with the style and timing of deformation of the inner caldera resurgence. Our interpretation shows that the NYT eruption (~15 ka BP) was associated with a caldera collapse bounded by an inward-dipping ring fault system. The ring fault system consists in a …

The Neapolitan Yellow Tuff caldera offshore the Campi Flegrei: Stratal architecture and kinematic reconstruction during the last 15 ky

2014

In this study we integrate high-resolution swath bathymetry, single channel reflection seismic data and gravity core data, to provide new insights into the shallow structure and latest Quaternary to Holocene evolution of the submerged sector of the Neapolitan Yellow Tuff (NYT) caldera (Campi Flegrei) in the Pozzuoli Bay. The new data allow for a reconstruction of the offshore geometry of the NYT caldera collapse-ring fault system, along with the style and timing of deformation of the inner caldera resurgence.Our interpretation shows that the NYT eruption (~. 15. ka BP) was associated with a caldera collapse bounded by an inward-dipping ring fault system. The ring fault system consists in a …

Understanding Degassing Pathways Along the 1886 Tarawera (New Zealand) Volcanic Fissure by Combining Soil and Lake CO2 Fluxes

2019

CO2 flux measurements are often used to monitor volcanic systems, understand the cause of volcanic unrest, and map sub-surface structures. Currently, such measurements are incomplete at Tarawera (New Zealand), which erupted with little warning in 1886 and produced a ∼17 km long fissure. We combine new soil CO2 flux and C isotope measurements of Tarawera with previous data from Rotomahana and Waimangu (regions also along the 1886 fissure) to fingerprint the CO2 source, understand the current pathways for degassing, quantify the CO2 released along the entire fissure, and provide a baseline survey. The total CO2 emissions from the fissure are 1227 t⋅d–1 (742–3398 t⋅d–1 90 % confidence interval…

Syntheses of oxygenated spongiane diterpenes from carvone. Synthesis of dorisenone C

2005

Abstract The synthesis of dorisenone C, a representative member of the spongiane-type diterpene family, is described. The synthesis follows a B→AB→ABC→ABCD approach and is based on the initial preparation of the previously known hydroxy-aldehyde 14 (AB rings) from R -(−)-carvone, followed by an intramolecular Diels–Alder reaction between an oxygenated diene moiety and an acetylenic dienophile for the construction of the C ring (compound 22 ), and adequate manipulation of the Diels–Alder adduct functionality for completion of the spongiane framework.

Stereoselective construction of the tetracyclic scalarane skeleton from carvone

1999

The tetracyclic scalarane skeleton 22 has been constructed from (S)-(+)-carvone using two intramolecular Diels–Alder reactions as key synthetic steps. Abad Somovilla, Antonio, Antonio.Abad@uv.es ; Agullo Blanes, M Consuelo, Consuelo.Agullo@uv.es ; Cuñat Romero, Ana Carmen, Ana.Cunat@uv.es ; Llosa Blasco, Maria Carmen, Carmen.Llosa@uv.es