Integration with respect to the Lefschetz number

We develop a theory of integration with respect to the Lefschetz number in the context of o-minimal structures containing the semilinear sets. We prove several results and we apply the theory to the field of object detection using sensors

Comparación de fórmulas chilenas e internacionales para valorar el arbolado urbano

Ponce-Donoso, M (reprint author), Univ Talca, Fac Ciencias Forestales, Casilla 747, Talca, Chile.The appraisal of urban trees is a practice adopted in diverse cities of world. This survey compared international formulae: Council of Tree Landscape Appraiser (CTLA), Burnley, Helliwell and Standard Tree Evaluation Method (STEM) and three Chilean methods applied in municipalities of Concepcion, La Pintana, Maip (COPIMA), Nunoa and Penalolen, in 14 different trees located in Talca city (Chile). The objective was to identify the differences and similarities of the monetary result in the application of these formulae, which was realized by a professional. These were analyzed using a non parametric variance test of Kruskal - Wallis and the multiple comparisons Duncan test. It was possible to determine that the Chilean formulae did not present statistically significant differences with the international formulae of Burnley and CTLA; whereas Penalolen and COPIMA formulae did not present any difference when contrasted with Helliwell. In addition, the STEM formula presented differences with all the Chilean analyzed formulae. In the valuation by tree, statistically significant differences were obtained, which showed the independence of the used formula. The exception was when being applied to emblematic species or to species that stand-out in some amenity. Likewise, it was observed that the basic value continues having a high impact in the appraisal final result and the use of the statistical test applied allows extending this type of analyses

Identifying the ground state structures of point defects in solids

Point defects are a universal feature of crystalline materials. Their identification is often addressed by combining experimental measurements with theoretical models. The standard approach of simulating defects is, however, prone to missing the ground state atomic configurations associated with energy-lowering reconstructions from the idealised crystallographic environment. Missed ground states compromise the accuracy of calculated properties. To address this issue, we report an approach to efficiently navigate the defect configurational landscape using targeted bond distortions and rattling. Application of our workflow to a range of materials ($\rm CdTe$, $\rm GaAs$, $\rm Sb_2S_3$, $\rm Sb_2Se_3$, $\rm CeO_2$, $\rm In_2O_3$, $\rm ZnO$, anatase-$\rm TiO_2$) reveals symmetry breaking in each host crystal that is not found via conventional local minimisation techniques. The point defect distortions are classified by the associated physico-chemical factors. We demonstrate the impact of these defect distortions on derived properties, including formation energies, concentrations and charge transition levels. Our work presents a step forward for quantitative modelling of imperfect solids