We define the transgression functor which associates to a (higherdimensional) Courant algebroid on a manifold a Lie algebroid on the shifted tangent bundle of the manifold. Universidad de los Andes

No abstract

We study dg-manifolds which are R[2]-bundles over R[1]-bundles over manifolds, we calculate its symmetries, its derived symmetries and we introduce the concept of T-dual dg-manifolds. Within this framework, we construct the T-duality map as a degree -1 map between the cohomologies of the T-dual dg-manifolds and we show an explicit isomorphism between the differential graded algebra of the symmetries of the T-dual dg-manifolds. We, furthermore, show how the algebraic structure underlying Bn generalized geometry could be recovered as derived dg-Leibniz algebra of the fixed points of the T-dual automorphism acting on the symmetries of a self T-dual dgmanifold, and we show how other types of algebraic structures underlying exceptional generalized geometry could be obtained as derived symmetries of certain dg-manifolds.2010 Mathematics Subject Classification. 53D18 53D17 (primary), 55R65, 57R22 (secondary).

In this contribution, an open-source computational toolbox composed of FEniCS and complementary packages is introduced to the chemical and process engineering field by addressing two case studies. First, the oxidation of oxylene to phthalic anhydride is modelled and used as a FEniCS 0 proof-of-concept based on a comparison with the software Aspen Custom Modeler (ACM). The results show a maximum absolute error of 2% and thus a good FEniCS/ACM agreement. Second, synthetic natural gas (SNG) production through CO 2 methanation is covered in further detail. In this instance, a parametric study is performed for a tube bundle fixed-bed reactor employing a two-dimensional and transient pseudo-homogeneous model. An operating window for critical variables is evaluated, discussed, and successfully contrasted with the literature. Therefore, the computational toolbox methodology and the consistency of the results are validated, strengthening FEniCS and complements as an interesting alternative to solve mathematical models concerning chemical reaction engineering.

We describe imputation strategies resistant to outliers, through modifications of the simple imputation method proposed by Krzanowski and assess their performance. The strategies use a robust singular value decomposition, do not depend on distributional or structural assumptions and have no restrictions as to the pattern or missing data mechanisms. They are tested through the simulation of contamination and unbalance, both in artificially generated matrices and in a matrix of real data from an experiment with genotype-by-environment interaction. Their performance is assessed by means of prediction errors, the squared cosine between matrices, and a quality coefficient of fit between imputations and true values. For small matrices, the best results are obtained by applying robust decomposition directly, while for larger matrices the highest quality is obtained by eliminating the singular values of the imputation equation.