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On the implementation of large period piece-wise linear Arnold cat map
(2022-04-26)
This paper presents a piece-wise linear cat map (PWLCM) obtained by perturbing the conventional quantized Arnold cat map (QACM) with a nonlinear term. The effect of the nonlinear term on the dynamics of the QACM is investigated. We show that the eigenvalues, hence the Lyapunov exponents of the PWLCM depend on the initial conditions, which is not the case for the QACM. As a result, the proposed PWLCM is a generalized form of the QACM, whose the period exponentially increases with respect to the precision, thus taking ...
Aufsatz
Attitude maneuvers avoiding forbidden directions
(2023-06-16)
Many space missions require the execution of large-angle attitude slews during which stringent pointing constraints must be satisfied. For example, the pointing direction of a space telescope must be kept away from directions to bright objects, maintaining a prescribed safety margin. In this paper we propose an open-loop attitude control algorithm which determines a rest-to-rest maneuver between prescribed attitudes while ensuring that any of an arbitrary number of body-fixed directions of light-sensitive instruments ...
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The relationship between accuracy in numerosity estimation, math achievement, and math interest in primary school students
(2023-07-10)
Estimation is a primary activity in everyday life, so getting it “right” in primary school provides a foundational basis in mathematical reasoning. This study focuses on numerosity estimation in primary mathematics, which is one of four types of estimation reported in literature. In numerosity estimation, a non-numerical quantitative representation is typically translated into a number. While it is assumed that fostering numerosity estimation has a great impact on the development of mathematical skills, research ...
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
Covariational reasoning in Bayesian situations
(2024-01-27)
Previous studies on Bayesian situations, in which probabilistic information is used to update the probability of a hypothesis, have often focused on the calculation of a posterior probability. We argue that for an in-depth understanding of Bayesian situations, it is (apart from mere calculation) also necessary to be able to evaluate the effect of changes of parameters in the Bayesian situation and the consequences, e.g., for the posterior probability. Thus, by understanding Bayes’ formula as a function, the concept ...
Aufsatz
A material model for thick, rate-dependent adhesives with delocalized softening
(2023-10-04)
This contribution is dedicated to the development and implementation of a material model to describe the deformation behaviour of assembly adhesives. These assembly adhesives are usually used with thicknesses of several millimetres up to centimetres in order to compensate for large relative displacements of joining parts. These large displacements can be resisted by assembly adhesives, since they have a low shear modulus and thus a high strain until failur above their glass transition temperature. As a basis, the ...