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In this paper we show that evolution algebras over any given field \Bbbk are universally finite. In other words, given any finite group G, there exist infinitely many regular evolution algebras X such that Aut(X)\cong G. The proof is built upon the construction of a covariant faithful functor from the category of finite simple (non oriented) graphs to the category of (finite dimensional) regular evolution algebras. Finally, we show that any constant finite algebraic affine group scheme \mathbf {G} over \Bbbk is isomorphic to the algebraic affine group scheme of automorphisms of a regular evolution algebra. [ABSTRACT FROM AUTHOR]

In the tensor space $${{\mathrm {Sym}}}^d \mathbb {R}^2$$ of binary forms we study the best rank k approximation problem. The critical points of the best rank 1 approximation problem are the eigenvectors and it is known that they span a hyperplane. We prove that the critical points of the best rank k approximation problem lie in the same hyperplane. As a consequence, every binary form may be written as linear combination of its critical rank 1 tensors, which extends the Spectral Theorem from quadratic forms to binary forms of any degree. In the same vein, also the best rank k approximation may be written as a linear combination of the critical rank 1 tensors, which extends the Eckart-Young theorem from matrices to binary forms. [ABSTRACT FROM AUTHOR]

Nowadays one of the main focuses of the Spanish University system is achieving the active learning paradigm in the context of its integration into the European Higher Education Area. This goal is being addressed by means of the application of novel teaching mechanisms. Among a wide variety of learning approaches, the present work focuses on peer review, understood as a collaborative learning technique where students assess other student's work and provide their own feedback. In this way, peer review has the overarching goal of improving the student learning during this process. Peer review has been successfully applied and analyzed in the literature. Indeed, many authors also recommend improving the design and implementation of self and peer review, which has been our main goal. This paper presents an empirical study based on the application of peer review assessment in different higher education BSc and MSc courses. In this way, six courses from different studies at the University of Malaga in Spain are subject to the application of peer review strategies to promote student learning and develop cross-wise skills such as critical thinking, autonomy and responsibility. Based on these experiences, a deep analysis of the results is performed, showing that a proper application of the peer review methodology provides reliable reviews (with close scores to the ones from the teacher) as well as an improvement in the students' performance. [ABSTRACT FROM AUTHOR]