Evropski ucitelj: nadnacionalni pogled na politike in prakse izobrazevanja uciteljev

The future role of teachers in Europe will contribute to raising the awareness of a new expectation of what it means to be a “European Teacher”. If there is unity in diversity through national identities, the question remains: what makes a teacher “European”? Answering this unusual question, one encounters several aspects that have strong national traits of what it means to teach in a particular country (e.g. political culture), which still does not enable teachers to easily move their employment from one country to another because of differences in career structure, teacher education, selection and recruitment, etc. However, there are many similarities in general teacher competences that are required throughout Europe and beyond. This paper looks at teacher professionalism from various perspectives, attempts to discern the “Europeanness” in teachers’ work and mobility as a goal, and highlights particular policy development areas necessary to stimulate further discussions. The depiction of a European Doctorate in Teacher Education concludes the paper. (DIPF/Orig.

Trigonometric time integrators for the Zakharov system

The main challenge in the analysis of numerical schemes for the Zakharov system originates from the presence of derivatives in the nonlinearity. In this paper a new trigonometric time-integration scheme for the Zakharov system is constructed and convergence is proved. The time-step restriction is independent from a spatial discretization. Numerical experiments confirm the findings

Randomized exponential integrators for modulated nonlinear Schr\"odinger equations

We consider the nonlinear Schr\"odinger equation with dispersion modulated by a (formal) derivative of a time-dependent function with fractional Sobolev regularity of class $W^{\alpha,2}$ for some $\alpha\in (0,1)$. Due to the loss of smoothness in the problem classical numerical methods face severe order reduction. In this work, we develop and analyze a new randomized exponential integrator based on a stratified Monte Carlo approximation. The new discretization technique averages the high oscillations in the solution allowing for improved convergence rates of order $\alpha+1/2$. In addition, the new approach allows us to treat a far more general class of modulations than the available literature. Numerical results underline our theoretical findings and show the favorable error behavior of our new scheme compared to classical methods