Reflectionless measures and the Mattila-Melnikov-Verdera uniform rectifiability theorem

A new proof is given of the Mattila-Melnikov-Verdera theorem on the uniform rectifiability of an Ahlfors-David regular measure whose associated Cauchy transform operator is bounded.Comment: 31 pages, 5 figure

An Iterative Abstraction Algorithm for Reactive Correct-by-Construction Controller Synthesis

In this paper, we consider the problem of synthesizing correct-by-construction controllers for discrete-time dynamical systems. A commonly adopted approach in the literature is to abstract the dynamical system into a Finite Transition System (FTS) and thus convert the problem into a two player game between the environment and the system on the FTS. The controller design problem can then be solved using synthesis tools for general linear temporal logic or generalized reactivity(1) specifications. In this article, we propose a new abstraction algorithm. Instead of generating a single FTS to represent the system, we generate two FTSs, which are under- and over-approximations of the original dynamical system. We further develop an iterative abstraction scheme by exploiting the concept of winning sets, i.e., the sets of states for which there exists a winning strategy for the system. Finally, the efficiency of the new abstraction algorithm is illustrated by numerical examples.Comment: A shorter version has been accepted for publication in the 54th IEEE Conference on Decision and Control (held Tuesday through Friday, December 15-18, 2015 at the Osaka International Convention Center, Osaka, Japan

The Core-Collapse Supernova Rate in Arp299 Revisited

We present a study of the CCSN rate in nuclei A and B1 of the luminous infrared galaxy Arp299, based on 11 years of Very Large Array monitoring of their radio emission at 8.4 GHz. Significant variations in the nuclear radio flux density can be used to identify the CCSN activity in the absence of high-resolution very long baseline interferometry observations. In the case of the B1-nucleus, the small variations in its measured diffuse radio emission are below the fluxes expected from radio supernovae, thus making it well-suited to detect RSNe through flux density variability. In fact, we find strong evidence for at least three RSNe this way, which results in a lower limit for the CCSN rate of 0.28 +/- 0.16 per year. In the A-nucleus, we did not detect any significant variability and found a SN detection threshold luminosity which allows only the detection of the most luminous RSNe known. Our method is basically blind to normal CCSN explosions occurring within the A-nucleus, which result in too small variations in the nuclear flux density, remaining diluted by the strong diffuse emission of the nucleus itself. Additionally, we have attempted to find near-infrared counterparts for the earlier reported RSNe in the Arp299 nucleus A, by comparing NIR adaptive optics images from the Gemini-N telescope with contemporaneous observations from the European VLBI Network. However, we were not able to detect NIR counterparts for the reported radio SNe within the innermost regions of nucleus A. While our NIR observations were sensitive to typical CCSNe at 300 mas from the centre of the nucleus A, suffering from extinction up to A_v~15 mag, they were not sensitive to such highly obscured SNe within the innermost nuclear regions where most of the EVN sources were detected. (abridged)Comment: 12 pages, 4 figures and 7 tables. Accepted for publication in MNRA

Porosities and dimensions of measures

We introduce a concept of porosity for measures and study relations between dimensions and porosities for two classes of measures: measures on $R^n$ which satisfy the doubling condition and strongly porous measures on $R$.Comment: Jarvenpaa = J\"arvenp\"a\"

Progenitor's signatures in Type Ia supernova remnants

The remnants of Type Ia supernovae can provide important clues about their progenitor-histories. We discuss two well-observed supernova remnants (SNRs) that are believed to result from a Type Ia SN and use various tools to shed light on the possible progenitor history. We find that Kepler's SNR is consistent with a symbiotic binary progenitor consisted of a white dwarf and an AGB star. Our hydrosimulations can reproduce the observed kinematic and morphological properties. For Tycho's remnant we use the characteristics of the X-ray spectrum and the kinematics to show that the ejecta has likely interacted with dense circumstellar gas.Comment: 4 pages, 9 figures, proceedings for IAU Symposium 281, Padova, July 201

Ab initio study of point defects in CdF2

The plane-wave pseudopotential method is used to study point defects in CdF2. We present comprehensive results for the native defects as well as for dominant impurities. In addition to Fi, VCd and OF were found to be easily formed compensating acceptors. For In and Ga impurities the experimentally observed large Stokes shift could not be established, and the results rule out symmetric atomic relaxation as the mechanism leading to the bistable behavior. The limitations of the present approach utilizing density-functional theory and the local-density approximation in the case of ionic materials are addressed.Peer reviewe