Generic Tropical Varieties

We show that in the constant coefficient case the generic tropical variety of a graded ideal exists. This can be seen as the analogon to the existence of the generic initial ideal in Groebner basis theory. We determine the generic tropical variety as a set in general and as a fan for principal ideals and linear ideals.Comment: 15 pages; corrected versio

Singularity avoidance for collapsing quantum dust in the Lemaitre-Tolman-Bondi model

We investigate the fate of the classical singularity in a collapsing dust cloud. For this purpose, we quantize the marginally bound Lemaitre-Tolman-Bondi model for spherically-symmetric dust collapse by considering each dust shell in the cloud individually, taking the outermost shell as a representative. Because the dust naturally provides a preferred notion of time, we can construct a quantum mechanical model for this shell and demand unitary evolution for wave packets. It turns out that the classical singularity can generically be avoided provided the quantization ambiguities fulfill some weak conditions. We demonstrate that the collapse to a singularity is replaced by a bounce followed by an expansion. We finally construct a quantum corrected spacetime describing bouncing dust collapse and calculate the time from collapse to expansion.Comment: 20 pages, 2 figure

Exteriors to bouncing collapse models

We construct a large class of spacetimes that are smoothly matched to homogeneous, spherically symmetric clouds of matter. The evolution of the clouds is left arbitrary to allow for the incorporation of modifications by quantum effects, which can in particular lead to bounces. We further discuss two simple yet illustrative examples of these spacetimes, both in general terms and for a specific form of the bounce, with a focus on horizon behavior and relevant timescales.Comment: 13 pages, 6 figure

Педагогические технологии как дидактический инструментарий подготовки специалиста в инженерном вузе

Рассмотрено понятие педагогической технологии, раскрыта сущность контекстной и задачной технологий, обоснован выбор технологий, адекватных профилю инженерного образования