We describe arbitrary multiplicative differential forms on Lie groupoids infinitesimally, i.e., in terms of Lie algebroid data. This description is based on the study of linear differential forms on Lie algebroids and encompasses many known integration results related to Poisson geometry. We also revisit multiplicative multivector fields and their infinitesimal counterparts, drawing a parallel between the two theories.

Abstract. We study VB-groupoids and VB-algebroids, which are vector bundles in the realm of Lie groupoids and Lie algebroids. Through a suitable reformulation of their definitions, we elucidate the Lie theory relating these objects, i.e., their relation via differentiation and integration. We also show how to extend our techniques to describe the more general Lie theory underlying double Lie algebroids and LA-groupoids.

We report here the unexpected observation of significant room-temperature ferromagnetism in a semiconductor doped with nonmagnetic impurities, Cu-doped TiO 2 thin films grown by pulsed laser deposition. The magnetic moment, calculated from the magnetization curves, resulted surprisingly large, about 1.5 B per Cu atom. A large magnetic moment was also obtained from ab initio calculations, but only if an oxygen vacancy in the nearest-neighbor shell of Cu was present. This result suggests that the role of oxygen vacancies is crucial for the appearance of ferromagnetism. The calculations also predict that Cu doping favors the formation of oxygen vacancies.

We study the relationship between multiplicative 2-forms on Lie groupoids and linear 2-forms on Lie algebroids, which leads to a new approach to the infinitesimal description of multiplicative 2-forms and to the integration of twisted Dirac manifolds.

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We give a direct, explicit and self-contained construction of a local Lie groupoid integrating a given Lie algebroid which only depends on the choice of a spray vector field lifting the underlying anchor map. This construction leads to a complete account of local Lie theory and, in particular, to a finite-dimensional proof of the fact that the category of germs of local Lie groupoids is equivalent to that of Lie algebroids.

We present an investigation of Fe-doped TiO2 anatase nanoparticles (2.8 and 5.4 at.% Fe) where Fe substitutes Ti atoms without the presence of other phases. In order to characterize these samples we used x-ray absorption experiments, 57Fe Mössbauer spectroscopy, ab initio calculations and magnetometry. Results from iron K-edge near-edge and extended x-ray absorption fine structure confirm that Fe3+ replaces Ti4+ in the TiO2 anatase structure increasing the metal-anion bond length. Mössbauer spectra recorded at room temperature show asymmetric Fe3+ broad doublets. These results agree with structural, hyperfine and magnetic properties calculated using density-functional theory, if oxygen vacancies are present in the iron–oxygen octahedra. Mössbauer and magnetic measurements indicate that samples are paramagnetic at room temperature. At low temperatures, two kind of magnetic species can be distinguished: (i) isolated paramagnetic Fe3+ ions and (ii) antiferromagnetically coupled Fe3+ ions. These results also show that substitutional Fe in nanosized anatase TiO2 does not induce ferromagnetic ordering.

Abstract-Fuzzy-logic-based inference techniques provide efficient solutions for control problems in classical and emerging applications. However, the lack of specific design tools and systematic approaches for hardware implementation of complex fuzzy controllers limits the applicability of these techniques in modern microelectronics products. This paper discusses a design strategy that eases the implementation of embedded fuzzy controllers as systems on programmable chips. The development of the controllers is carried out by means of a reconfigurable platform based on field-programmable gate arrays. This platform combines specific hardware to implement fuzzy inference modules with a general-purpose processor, thus allowing the realization of hybrid hardware/software solutions. As happens to the components of the processing system, the specific fuzzy elements are conceived as configurable intellectual property modules in order to accelerate the controller design cycle. The design methodology and tool chain presented in this paper have been applied to the realization of a control system for solving the navigation tasks of an autonomous vehicle.Index Terms-Autonomous vehicles, embedded systems, fieldprogrammable gate arrays (FPGAs), fuzzy control, intellectual property (IP).