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 ...

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, ...

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 ...

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.

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.

The vitreous is a fluid‐like viscoelastic transparent medium located in the center of the human eye and is surrounded by hyperelastic structures like the sclera, lens and iris. This naturally gives rise to a fluid‐structure interaction (FSI) problem. While the healthy vitreous is viscoelastic and described by a viscoelastic Burgers‐type equation, the aging vitreous liquefies and is therefore modeled by the Navier‐Stokes equations. We derive a monolithic variational formulation employing the arbitrary Lagrangian ...

A method to calculate the parameters for each instantaneous and relative instantaneous screw axis in an arbitrary rigid multi‐body system is presented. At first a kinematic analysis is performed which calculates the displacements of all nodes and the rotation of each body. In the next step the displacements of the nodes and the rotation of the bodies are used to calculate the instantaneous screw axis of each body. With the information on the instantaneous screw axes the instantaneous relative screw axes can be computed ...

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.

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 ...

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 ...