Search results for "8a"
showing 3 items of 133 documents
Shape identification in inverse medium scattering problems with a single far-field pattern
2016
Consider time-harmonic acoustic scattering from a bounded penetrable obstacle $D\subset {\mathbb R}^N$ embedded in a homogeneous background medium. The index of refraction characterizing the material inside $D$ is supposed to be Holder continuous near the corners. If $D\subset {\mathbb R}^2$ is a convex polygon, we prove that its shape and location can be uniquely determined by the far-field pattern incited by a single incident wave at a fixed frequency. In dimensions $N \geq 3$, the uniqueness applies to penetrable scatterers of rectangular type with additional assumptions on the smoothness of the contrast. Our arguments are motivated by recent studies on the absence of nonscattering waven…
A Decade of GRB Follow-Up by BOOTES in Spain (2003–2013)
2016
This article covers ten years of GRB follow-ups by the Spanish BOOTES stations: 71 follow-ups providing 23 detections. Follow-ups by BOOTES-1B from 2005 to 2008 were given in a previous article and are here reviewed and updated, and additional detection data points are included as the former article merely stated their existence. The all-sky cameras CASSANDRA have not yet detected any GRB optical afterglows, but limits are reported where available.
On arithmetic sums of Ahlfors-regular sets
2021
Let $A,B \subset \mathbb{R}$ be closed Ahlfors-regular sets with dimensions $\dim_{\mathrm{H}} A =: \alpha$ and $\dim_{\mathrm{H}} B =: \beta$. I prove that $$\dim_{\mathrm{H}} [A + \theta B] \geq \alpha + \beta \cdot \tfrac{1 - \alpha}{2 - \alpha}$$ for all $\theta \in \mathbb{R} \, \setminus \, E$, where $\dim_{\mathrm{H}} E = 0$.