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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
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 ...
Aufsatz
On the Finite Orthogonality of q-Pseudo-Jacobi Polynomials
(2020-08-08)
Using the Sturm–Liouville theory in q-difference spaces, we prove the finite orthogonality of q-Pseudo Jacobi polynomials. Their norm square values are then explicitly computed by means of the Favard theorem.
Aufsatz
On Multivariate Bernstein Polynomials
(2020-08-21)
In this paper, we first revisit and bring together as a sort of survey, properties of Bernstein polynomials of one variable. Secondly, we extend the results from one variable to several ones, namely—uniform convergence, uniform convergence of the derivatives, order of convergence, monotonicity, fixed sign for the p-th derivative, and deduction of the upper and lower bounds of Bernstein polynomials from those of the corresponding functions.
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
A Hybrid Optimization Method Combining Network Expansion Planning and Switching State Optimization
(2020-07-01)
Combining switching state optimization (SSO) and network expansion planning (NEP) in AC systems results in a mixed-integer non-linear optimization problem. Two methodically different solution approaches are mathematical programming and heuristic methods. In this paper, we develop a hybrid optimization method combining both methods to solve the combined optimization of SSO and NEP. The presented hybrid method applies a DC programming model as an initialization strategy to reduce the search space of the heuristic. A ...
Aufsatz
A Logic Based Approach to Finding Real Singularities of Implicit Ordinary Differential Equations
(2020-06-17)
We discuss the effective computation of geometric singularities of implicit ordinary differential equations over the real numbers using methods from logic. Via the Vessiot theory of differential equations, geometric singularities can be characterised as points where the behaviour of a certain linear system of equations changes. These points can be discovered using a specifically adapted parametric generalisation of Gaussian elimination combined with heuristic simplification techniques and real quantifier elimination ...