RR Lyrae stars seen from space

RR Lyrae stars for a long time had the reputation of being rather simple pulsators, but the advent of high-precision space photometry has meanwhile changed this picture dramatically. This article summarizes the results obtained for two remarkable Blazhko RR Lyrae stars and discusses how our view of RR Lyrae stars has changed since the availability of ultra-precise satellite photometry as it is obtained by CoRoT and Kepler. Both stars, CoRoT 105288363 and V445 Lyrae, show a multitude of phenomena that were impossible to observe from the ground, either because of the small amplitude of the effect, or because uninterrupted long-term monitoring was required for a detection. Not only was it found that strong and irregular cycle-to-cycle changes of the Blazhko effect can occur, and that seemingly chaotic phenomena need to be accounted for when modeling the Blazhko effect, but also a rich spectrum of low-amplitude frequencies was detected in addition to the fundamental radial pusation in RRab stars. The so-called period doubling phenomenon, higher radial overtones and possibly also non-radial modes make RR Lyrae stars more multifaceted than previously thought. This article presents the various aspects of irregularity of the Blazhko effect, questioning its long-standing definition as a "periodic modulation", and also discusses the low-amplitude pulsation signatures that had been hidden in the noise of observations for centuries.Comment: 4 pages, 2 figures, accepted for publication in Astronomical Notes, proceedings of "The New Era of Helio- and Asteroseismology", 2012. 05. 20-25. Obergurgl (A

Conjugacy Growth and Conjugacy Width of Certain Branch Groups

The conjugacy growth function counts the number of distinct conjugacy classes in a ball of radius $n$. We give a lower bound for the conjugacy growth of certain branch groups, among them the Grigorchuk group. This bound is a function of intermediate growth. We further proof that certain branch groups have the property that every element can be expressed as a product of uniformly boundedly many conjugates of the generators. We call this property bounded conjugacy width. We also show how bounded conjugacy width relates to other algebraic properties of groups and apply these results to study the palindromic width of some branch groups.Comment: Final version, to appear in IJA

Using Radio Telemetry and Geographic Information Systems to Map and Estimate the Home Range Size and Daily Movement Patterns of Female Cheetahs on Namibia’s Commercial Farmland

Fewer than 10,000 cheetahs remain in the wild in Sub-Saharan Africa.Namibia has the largest population, estimated to be 4,000 cheetahs. Habitat fragmentation and prey depletion from human expansion for agriculture have pushed 90 percent of cheetahs to reside on commercial farmland where there is an absence of larger predators, but where there is conflict with the livestock farmers. Radio telemetry was used to investigate the seasonal variation in home range size among nine female cheetahs on commercial farmlands on or near the Cheetah Conservation Fund in Otjiwarongo, Namibia. ArcGIS 10.3 and Geospatial Modeling Environment were used to calculate the home range size. This was estimated for the overall, annual, monthly, and seasonal variants for each individual cheetah. Nine female cheetahs were tracked in this study; six ofthem were rewilded and three of them were wild. The wild cheetahs had a larger home range estimation compared to the rewilded cheetahs. The home range size and average distance moved (km) between GPS locations had no significance between the seasons basedon the statistical program R 3.2.1. These results in combination with further research can help formulate a long-term conservation plan for the remaining and rewilded cheetah population on Namibia\u27s commercial farmland