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Improving Prospective Teachers’ Beliefs About a Double Discontinuity Between School Mathematics and University Mathematics
(2022-05-12)
Prospective teachers often perceive a “double discontinuity” between school mathematics and university mathematics. The first discontinuity can be described as the belief that there is no coherence between school mathematics and university mathematics, which forms part of the notoriously problematic transition from school to university. The second discontinuity can be described as a belief about the lack of relevance of university mathematics for the later professional practice of prospective teachers. Beliefs about ...
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An extendable key space integer image-cipher using 4-bit piece-wise linear cat map
(2022-09-30)
This paper presents a multiplierless image-cipher, with extendable 2048-bit key-space, based on a 4-dimensional (4D) quantized piece-wise linear cat map (PWLCM). The quantized PWLCM exhibits limit-cycles of 4-bit encoded integers with periods greater than 10⁷. The synthesis of the PWLCM in a finite state space allows to eliminate the undesirable finite precision effect due to the hardware realization. The proposed image-cipher combines chaos, modular arithmetic, and lattice-based cryptography to encrypt a color image ...
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Data Driven prediction of forced nonlinear vibrations using stabilised Autoregressive Neural Networks
(2023-03-24)
In this work, we propose a novel approach to the data-driven prediction of vibration responses of nonlinear systems. The main idea is based on Autoregressive Neural Networks (ARNN) to model the nonlinear transfer behaviour between an external excitation and the system response. We propose an autoregressive network architecture with embedded symmetry using bias-free tanh activation and guarantee Input-to-State-Stability (ISS) by enforcing a special penalty term to the weights. The resulting training procedure is ...
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An Investigation on Limiting Potentials for Damage Prediction of Viscoelastic Adhesives
(2023-03-24)
In his recent work VOLOKH introduced the energy limiting method as an alternative to continuum damage mechanics developed and envolved by KACHANOV, RABOTNOV, LEMAITRE and many more. In contrast to continuum damage mechanics, the energy limiting method is physically grounded by the process of atomistic debonding and, therefore, motivated on an energy basis. In order to use the energy limiting method within the framework of continuum mechanics, a limiting potential needs to be defined, which can be seen as a macroscopic ...
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Consideration of nonlinear multipoint constraints in finite element analyses based on a master-slave elimination scheme operating at the global level
(2023-03-24)
A method to consider nonlinear multipoint constraints in finite element analysis based on a master-slave elimination scheme operating at the global level is presented. We focus on systems with nonlinear constraints in which the number of constraints is of the same order of magnitude as the number of degrees of freedom. Therefore, we rely on the master-slave elimination which gives us the huge benefit of drastically reducing the problem size. In the literature the presented master-slave elimination schemes for linear ...
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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 ...
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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 ...
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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 ...
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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 ...