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Aufsatz
Machine learning parameter systems, Noether normalisations and quasi-stable positions
(2024-06-25)
We discuss the use of machine learning models for finding “good coordinates” for polynomial ideals. Our main goal is to put ideals into quasi-stable position, as this generic position shares most properties of the generic initial ideal, but can be deterministically reached and verified. Furthermore, it entails a Noether normalisation and provides us with a system of parameters. Traditional approaches use either random choices which typically destroy all sparsity or rather simple human heuristics which are only ...
Aufsatz
Investigating Motivational and Cognitive Factors which Impact the Success of Engineering Students
(2021-02-06)
Engineering students particularly struggle with mathematics in the first year of their university studies. A result of these difficulties are high drop-out rates among the engineering students. There are various measures to support the students in their studies such as preparatory courses or bridging courses. The contribution of this research is to investigate the impact of certain factors on engineering students’ success in their first year of studies in a supportive environment which includes a preparatory course, ...
Aufsatz
Continuous modelling of single layer 2D carbonnanostructures based on a modified Cauchy–Born rule
(2023-09-08)
Graphene is the thinnest known structure. It consists of a single layer of carbon atoms and has unique mechanical properties. The carbon atoms form bonds with neighbouring atoms that can be described by interatomic potentials. A simulation of molecular mechanical processes can be performed by applying the formalism of the finite element method to the interatomic potentials. Neglecting local effects, a continuum formulation is an efficient alternative to a discrete model. The continuum formulation requires a connection ...
Aufsatz
A Stability Analysis of Modified Patankar–Runge–Kutta methods for a nonlinear Production–Destruction System
(2023-03-24)
Modified Patankar–Runge–Kutta (MPRK) methods preserve the positivity as well as conservativity of a production–destruction system (PDS) of ordinary differential equations for all time step sizes. As a result, higher order MPRK schemes do not belong to the class of general linear methods, i. e. the iterates are generated by a nonlinear map g even when the PDS is linear. Moreover, due to the conservativity of the method, the map g possesses non-hyperbolic fixed points.
Recently, a new theorem for the investigation of ...
Aufsatz
Promoting pre-service teachers’ professionalism in steam education and education for sustainable development through mathematical modelling activities
(2023-06-19)
To successfully solve the complex challenges facing us in the 21st century, people with expertise in the science, technology, engineering, arts and mathematics (STEAM) fields and other fields are needed, especially for their interdisciplinary way of thinking and working. These competencies should be learned in school, which first implies teacher education to that effect. In this article, a detailed theoretical reflection on the connections or overlapping areas between STEAM education and the dimension of sustainability ...
Aufsatz
Fostering diagnostic competence in prospective mathematics elementary teachers through epistemic activities
(2023-12-21)
Research on fostering teachers’ diagnostic competence and thinking has become increasingly important. To this end, research has already identified several aspects of effective fostering of teachers’ diagnostic competence. One of the aspects is assignment of the role as a teacher in interventions but, so far, assignment of the role of student has hardly been considered. Based on a model of the diagnostic thinking process, this paper operationalizes the role of the student by solving specific tasks and the role of the ...
Aufsatz
On the appearance of horseshoe chaos in a nonlinear hysteretic systems with negative stiffness
(2021-09-16)
The problem of inhibition of horseshoe chaos in a nonlinear hysteretic systems using negative stiffness is investigated in this paper. The Bouc–Wen model is used to describe the force produced by both the purely hysteretic and linear elastic springs. The analytical investigation of the Hamiltonian shows that the appearance of separatrix in the system is directly related to the parameters of the hysteretic forces. This means that the transverse intersection between the perturbed and unperturbed separatrix can be ...
Aufsatz
Auswirkungen verschachtelten Lernens auf das prozedurale und konzeptuelle Wissen von Lernenden über Zuordnungen
(2020-04-06)
Häufig werden im Mathematikunterricht Lerninhalte eher separiert behandelt. Der Ansatz des sogenannten verschachtelten Lernens geht dagegen davon aus, dass es in vielen Fällen sinnvoll ist, die Lerninhalte abwechselnd und vermischt anzuordnen, um bei den Schülerinnen und Schülern lern- und verstehensförderliche Prozesse anzuregen sowie nachhaltiges Lernen zu fördern. Verschachteltes Lernen zählt zu den wünschenswerten Erschwernissen. Das Ziel der wünschenswerten Erschwernisse ist, durch eine Erhöhung des kognitiven ...
Aufsatz
A note on dual prehomomorphisms from a group into the Margolis–Meakin expansion of a group
(2020-08-07)
We give a category-free order theoretic variant of a key result in Auinger and Szendrei (J Pure Appl Algebra 204(3):493–506, 2006) and illustrate how it might be used to compute whether a finite X-generated group H admits a canonical dual prehomomorphism into the Margolis–Meakin expansion M(G) of a finite X-generated group G. We show that for G the Klein four-group a suitable H must be of exponent 6 at least and recapture a result of Szakács.
Aufsatz
First-Order Shape Derivative of the Energy for Elastic Plates with Rigid Inclusions and Interfacial Cracks
(2020-11-16)
Within the framework of Kirchhoff–Love plate theory, we analyze a variational model for elastic plates with rigid inclusions and interfacial cracks. The main feature of the model is a fully coupled nonpenetration condition that involves both the normal component of the longitudinal displacements and the normal derivative of the transverse deflection of the crack faces. Without making any artificial assumptions on the crack geometry and shape variation, we prove that the first-order shape derivative of the potential ...