Normality in terms of distances and contractions

The main purpose of this paper is to explore normality in terms of distances between points and sets. We prove some important consequences on realvalued contractions, i.e. functions not enlarging the distance, showing that as in the classical context of closures and continuous maps, normality in terms of distances based on an appropriate numerical notion of $\gamma$-separation of sets, has far reaching consequences on real valued contractive maps, where the real line is endowed with the Euclidean metric. We show that normality is equivalent to (1) separation of $\gamma$-separated sets by some Urysohn contractive map, (2) to Kat\v{e}tov-Tong's interpolation, stating that for bounded positive realvalued functions, between an upper and a larger lower regular function, there exists a contractive interpolating map and (3) to Tietze's extension theorem stating that certain contractions defined on a subspace can be contractively extended to the whole space. The appropriate setting for these investigations is the category of approach spaces, but the results have (quasi)-metric counterparts in terms of non-expansive maps. Moreover when restricted to topological spaces, classical normality and its equivalence to separation by a Urysohn continuous map, to Kat\v{e}tov-Tong's interpolation for semicontinuous maps and to Tietze's extension theorem for continuous maps are recovered

Starting resource configurations of research-based start-ups and the interaction with technology, institutional background, and industrial dynamics

We study the starting resources of start-ups, which develop and market new products or services based upon a proprietary technology or skill. We define these companies as researchbased start-ups (RBSUs). We look at how technological, financial and human resources at founding cluster together to form different starting resource configurations. Using a unique hand-collected dataset of RBSUs in Belgium, we find four different types of starting configurations: “Venture Capital-backed start-ups,” “Prospectors,” “Product start-ups” and “Transitional start-ups”. This study shows that these different types of starting resource configurations are not only empirically distinct but can also be conceptually explained by internal factors such as the entrepreneurial orientation at start-up and external factors such as the origin of the firm and the characteristics of the industry in which the firm competes

The tectonic evolution of the Chuya-Kurai zone (Siberian Altai mountains) by means of multi-method chronology

The Phanerozoic tectonic evolution of the Chuya-Kurai zone was studied by means of zircon U/Pb-dating, apatite fission track (AFT) and apatite (U-Th)/He (AHe) thermochronology performed on basement rocks. Our results suggest that multiple magmatic episodes during the Paleozoic, related to the accretion-collision tectonics in Central Asia, affected our study area. Mesozoic and Cenozoic basement cooling events are interpreted as periods of tectonic reactivation. A new tectonic model for Late Cenozoic evolution of the Chuya-Kurai zone is proposed