No abstract

We report on an optimization study of percussion drilling thin metal sheets employing a high repetition rate, high power femtosecond laser with respect to the resulting heat accumulation. A specified simplex algorithm was employed to optimize the spatial drilling sequence, whereas a simplified thermal simulation using COMSOL was validated by comparing its results to the temperature measurements using an infrared camera. Optimization for drilling borehole matrices was aspired with respect to the generated temperature across the processed specimen, while the drilling strategy was altered in its spatial drilling sequence and by using multi-spot approaches generated by a spatial light modulator. As a result, we found that an optimization strategy based on limited consecutive holes in a Moore neighborhood led to reduced temperatures and the shortest process times.

In this paper the dissection of n-dimensional Euclidean simplices is investigated. Some propositions are proved about the dihedral angles of order (n -1) occurring when a simplex is cut into two subsimplices by a hyperplane. Furthermore, a description of simplices by graphs is given. If a simplex S is dissected into two subsimplices, then two graphs can be assigned to the two simplices. It is shown how these graphs are linked with the original simplex. By means of these graph-theoretical methods the dissection of four-dimensional simplices is thoroughly investigated and a new method for dissecting a four-dimensional simplex into orthoschemes is given. It is proved that 500 is an upper bound of the minimum number of orthoschernes needed.

This paper reports the concept of a preparatory mathematics course for non-traditional students in electrical engineering, and its evaluation. The blended-learning course is part of the initial study phase smoothing the transition to learning at university level. The instructional design of the preparatory course is aligned with that of the Bachelor’s study program. However, it takes place prior to the beginning of the first semester. The initial phase additionally encompasses the whole first semester with different courses meant to help students getting ready for studying. Prospective students indicated that they needed to refresh their knowledge in mathematics. Thus, a preparatory mathematics course was given priority. This course serves several purposes: Students get an impression of the requirements in mathematics necessary for the study program; they refresh their basic knowledge; they make themselves familiar with self-organized learning and the blended-learning concept of the program. Design and implementation were evaluated with a questionnaire at the end of the course and after the first semester. The results show that the course is an appropriate instrument prior to engineering studies in order to prepare and support non-traditional students. In the conclusions potential for improvement is identified.

No abstract