In this paper, we aim to identify online teaching and learning practices that would be beneficial for blended and traditional on-campus education within STEM (Science, Technology, Engineering, and Mathematics) courses. Our university, as well as the majority of higher education institutions worldwide, has had few to no experience in delivering full online courses before 2020. The teaching process was, however, severely affected and modified by the COVID-19 pandemic, forcing an abrupt and unprepared shift towards online education. In this work, we look at the pandemic as causing a very favorable side effect that forced the university to study, test, apply, and evaluate the benefits and drawbacks of online education and assessment methods. The study is a result of joint efforts from different departments at the University of Aveiro, Portugal, connected to STEM undergraduate and graduate programs and is based on a questionnaire targeted towards students. In total, 167 valid STEM students’ answers have been collected and analyzed, both quantitatively and qualitatively. As the result, the best teaching and learning practices are identified and the main difficulties and obstacles experienced by students are detected. Some of the problems are common to many higher education institutions, such as the lack of teacher preparation in delivering quality online synchronous and asynchronous classes, technical limitations (network bandwidth/weak equipment), ineffective communication during synchronous classes, gaps in student skills, and low activity of some students and even teachers. We believe that the presented results would allow for improving future on-campus, distance, and blended learning courses, particularly through avoiding less effective teaching and assessment methods and favoring those techniques that students consider more efficient. This ultimately would lead to a more rewarding teaching/learning experience.

We study the Magnus effect: deflection of the trajectory of a spinning body moving in a gas. It is well known that in rarefied gases, the inverse Magnus effect takes place, which means that the transversal component of the force acting on the body has opposite signs in sparse and relatively dense gases. The existing works derive the inverse effect from non-elastic interaction of gas particles with the body. We propose another (complementary) mechanism of creating the transversal force owing to multiple collisions of particles in cavities of the body surface. We limit ourselves to the two-dimensional case of a rough disc moving through a zero-temperature medium on the plane, where reflections of the particles from the body are elastic and mutual interaction of the particles is neglected. We represent the force acting on the disc and the moment of this force as functionals depending on ‘shape of the roughness’, and determine the set of all admissible forces. The disc trajectory is determined for several simple cases. The study is made by means of billiard theory, Monge–Kantorovich optimal mass transport and by numerical methods.

The paper is devoted to the study of the cone ${\mathcal{C}OP}^p$ of copositive matrices. Based on the concept of immobile indices known from semi-infinite optimization, we define zero and minimal zero vectors of a subset of the cone ${\mathcal{C}OP}^p$ and use them to obtain different representations of the faces of ${\mathcal{C}OP}^p$ and the corresponding dual cones. The minimal face of ${\mathcal{C}OP}^p$ containing a given convex subset of this cone is described, and some propositions are proved that allow obtaining equivalent descriptions of the feasible sets of copositive problems.

In this paper, we study the properties of faces and exposed faces of the cone of copositive matrices (copositive cone), paying special attention to issues related to their geometric structure. Based on the concepts of zero and minimal zero vectors, we obtain several explicit representations of faces of the copositive cone and compare them. Given a face of the cone of copositive matrices, we describe the subspace generated by that face and the minimal exposed face containing it. Summarizing the results obtained in the paper, we systematically show what information can be extracted about the given copositive face in the case of incomplete data. Several examples for illustrating the main findings of the paper and also for justifying the usefulness of the developed approach to the study of the facial structure of the copositive cone are discussed.