Homotopical Algebraic Context over Differential Operators

Building on previous works, we show that the category of non-negatively graded chain complexes of $D_X$-modules -- where $X$ is a smooth affine algebraic variety over an algebraically closed field of characteristic zero -- fits into a homotopical algebraic context in the sense of Toen and Vezzosi

La tematica del corpo nelle psicologie filosofiche ‘realistiche’ del primo Ottocento tedesco: Herbart, Fries, Schleiermacher

The paper explores the relationship between body and soul in the psychologies of three German philosophers at the beginning of the 19th Century: J.F. Herbart, J.F. Fries and F.D.E. Schleiermacher. Their positions on the issue appear to be different in many way. Herbart is cautious about introspection and speaks against an identification between soul and human life; on that way, he comes close to typical contents of the Cartesian-rationalist tradition, such as the simplicity and immortality of the soul, as opposed to the mortality of the body. Fries charges Herbart with the accusation of an uncritical conception of soul. His solution is based on considering the psychological and the somatic dimensions of man as two different ways of representation, trying thus to mediate between the Leibnizian “parallelism” theory and the Kantian criticism, while from the practical points of view, however, Fries supports the doctrine of the simplicity and immortality of the soul. Schleiermacher tries to overcame a radical opposition of soul and body, and also as a theo-logian, Schleiermacher does not defend a complete independence of the soul from the body, but rather their reciprocal nexus in the flesh

CAD-CAE integration and isogeometric analysis: trivariate multipatch and applications

This PhD thesis is focused on the issues related to one of the critical steps during the lifecycle of a product design and manufacturing process: the transition between the geometrical and functional definition of a product, and the virtual prototyping with numerical simulations, also known as CAD (Computer-Aided Design) / CAE (Computer-Aided Engineering) transition. The isogeometric methodologies developed by Hughes et Al. [1, 2] has the ambition to close the gap in CAD/CAE integration, allowing the two environments to underlay on the same framework, taking advantage of the isoparametric concept, widely used in Finite Elements world, coupled with the Non-Uniform Rational B-Splines (NURBS) that are a standard in CAD systems in the mathematical representation of geometries. Even though the first paper was published 10 years ago, the method is not yet used in industrial applications and only few commercial software are able to handle isogeometric elements. In this thesis a step towards the possibility of application in industry by developing a multi-patch coupling method where the geometry at the interface does not allow a compatible mesh. This improvement opens new frontiers for applications in both static and dynamic solutions. Another issue that is analysed in this thesis is the possibility to improve the geometry-to-analysis integration by conversion of the information that comes from CAD software, in terms of representation of the external surfaces, to solid information that is necessary to be suitable for a structural simulation