Long-time behavior is one of the most fundamental properties in dynamical systems. The limit behaviors flows on surfaces are captured by Poincaré-Bendixson theorem using ω-limit sets. This paper demonstrates that positive and negative long-time not independent. In fact, we show dependence between sets α-limit points surfaces, which partially generalizes theorem. Applying dependency result to so...

Given the sensitivity of current ground-based Gravitational Wave (GW) detectors, any continuous-wave signal we can realistically expect will be at a level or below the background noise. Hence, any data analysis of detector data will need to rely on statistical techniques to separate the signal from the noise. While with the current sensitivity of our detectors we do not expect to detect any tru...

A local regular behavior at almost all boundary points of a set in R representable as a locally finite union of sets with positive reach is shown. As an application, a limit formula for the volume of dilation of such a set with a small convex body is derived. MSC 2000: 53C65, 52A22