Subsidence activity maps derived from DInSAR data: Orihuela case study

A new methodology is proposed to produce subsidence activity maps based on the geostatistical analysis of persistent scatterer interferometry (PSI) data. PSI displacement measurements are interpolated based on conditional Sequential Gaussian Simulation (SGS) to calculate multiple equiprobable realizations of subsidence. The result from this process is a series of interpolated subsidence values, with an estimation of the spatial variability and a confidence level on the interpolation. These maps complement the PSI displacement map, improving the identification of wide subsiding areas at a regional scale. At a local scale, they can be used to identify buildings susceptible to suffer subsidence related damages. In order to do so, it is necessary to calculate the maximum differential settlement and the maximum angular distortion for each building of the study area. Based on PSI-derived parameters those buildings in which the serviceability limit state has been exceeded, and where in situ forensic analysis should be made, can be automatically identified. This methodology has been tested in the city of Orihuela (SE Spain) for the study of historical buildings damaged during the last two decades by subsidence due to aquifer overexploitation. The qualitative evaluation of the results from the methodology carried out in buildings where damages have been reported shows a success rate of 100%.

Cyclobutadiene automerization and rotation of ethylene: Energetics of the barriers by using Spin-polarized wave functions

Spin-projected spin polarized Møller–Plesset and spin polarized coupled clusters calculations have been made to estimate the cyclobutadiene automerization, the ethylene torsion barriers in their ground state, and the gap between the singlet and triplet states of ethylene. The results have been obtained optimizing the geometries at MP4 and/or CCSD levels, by an extensive Gaussian basis set. A comparative analysis with more complex calculations, up to MP5 and CCSDTQP, together with others from the literature, have also been made, showing the efficacy of using spin-polarized wave functions as a reference wave function for Møller–Plesset and coupled clusters calculations, in such problems.

An approximate Hahn–Banach theorem for positively homogeneous functions

This note provides an approximate version of the Hahn–Banach theorem for non-necessarily convex extended-real valued positively homogeneous functions of degree one. Given p : X → R∪{+∞} such a function defined on the real vector space X, and a linear function defined on a subspace V of X and dominated by p (i.e. (x) ≤ p(x) for all x ∈ V), we say that can approximately be p-extended to X, if is the pointwise limit of a net of linear functions on V, every one of which can be extended to a linear function defined on X and dominated by p. The main result of this note proves that can approximately be p-extended to X if and only if is dominated by p∗∗, the pointwise supremum over the family of all the linear functions on X which are dominated by p.