Generalized affine buildings:automorphisms, affine Suzuki-Ree buildings and convexity

Gebäude wurden in den 1950er und 1960er Jahren von Tits entwickelt und finden bis heute Anwendungen in vielen Bereichen der Mathematik. Bennett verallgemeinerte in den 80er Jahren Tits' Definition nicht-diskreter affiner Gebäude zu Gebäuden, die über einer angeordneten abelschen Gruppe $\Lambda$ modelliert sind. Diese allgemeine Klasse wird in der vorliegenden Arbeit untersucht. Neben dem Beweis struktureller Ergebnisse, wie zum Beispiel eines Erweiterungssatzes für ökologische Isomorphismen des Randes, enthält meine Arbeit den Beweis zweier Übertragungen des Kostantschen Konvexitätssatzes auf affine Gebäude. Der Beweis im simplizialen Fall beruht auf einer Charakterformel für Höchstgewichtsdarstellungen algebraischer Gruppen beziehungsweise im nicht-diskreten Fall auf Methoden der metrischen Geometrie. Weiter wird, mit algebraischen Methoden, die Existenz (notwendigerweise) nicht-diskreter affiner Gebäude mit Suzuki-Ree-Gebäude im Unendlichen bewiesen

\Lambda-buildings and base change functors

We prove an analog of the base change functor of \Lambda-trees in the setting of generalized affine buildings. The proof is mainly based on local and global combinatorics of the associated spherical buildings. As an application we obtain that the class of generalized affine building is closed under ultracones and asymptotic cones. Other applications involve a complex of groups decompositions and fixed point theorems for certain classes of generalized affine buildings.Comment: revised version, 29 pages, to appear in Geom. Dedicat

Möbius characterization of hemispheres

In this paper we generalize the Möbius characterization of metric spheres as obtained in Foertsch and Schroeder [4] to a corresponding Möbius characterization of metric hemispheres

Metric Möbius geometry and a characterization of spheres

We obtain a Möbius characterization of the n-dimensional spheres Sn endowed with the chordal metric d0. We show that every compact extended Ptolemy metric space with the property that every three points are contained in a circle is Möbius equivalent to (Sn, d0) for some n ≥ 1

The use of poison pills by US firms over the period 1997-2015: what has been their impact on shareholder value?

Poison pills are controversial devices for which no common conclusion as to how the market reacts to their adoption exists. This research collates 4,479 poison pill adoption events by American companies over the period 1997-2015. Statistically significant insights and positive abnormal returns were found on the day the poison pill was adopted. It is for this reason that we argue in favour of the shareholder wealth-maximization hypothesis, stating that poison pills protect shareholders by providing management a superior bargaining position. Shareholders react positively to poison pill adoption, particularly if a hostile takeover attempt is anticipated. Furthermore, shareholders seem to value the protective effect of the device, which both provides management a superior bargaining position and allows the maximal possible bid premium to be negotiated.info:eu-repo/semantics/acceptedVersio

Application of the Forgotten Effects Theory for Assessing the Public Policy on Air Pollution of the Commune of Valdivia, Chile

Environmental public policy is challenged by its complexity and uncertainty as manifested in Wicked Problems. Incentives were considered to encourage behavioural change in the public policy on air pollution in Valdivia, Chile. However, air pollution is still increasing due to extensive usage of firewood. This research aims to assess the policy within the identified incentives and behaviours by applying the Forgotten Effects theory. Empirical evidence of Forgotten Effects in the policy is provided by using data from key informant interviews. A major finding of the research is that a subsidy on transportation has no effect on reducing air pollution in residential areas. It also suggests that if people improve thermal insulation of their houses in the commune of Valdivia may contribute to a major reduction of air pollution rather than improving the quality of firewood. Education, Research and Development may also play an important role to encourage behavioural change. The latter will also contribute to the improvement of overall energy efficiency and thereby lower emissions

A flat strip theorem for Ptolemaic spaces

A metric space (X,d) is called Ptolemaic space (PT space) if the inequality |xy||zw|≤|xz||yw|+|xw||yz| holds for each quadruple of points x, y, z and w in X. Here |xy|:=d(x,y) denotes the distance of two points x and y. The main result proven in the paper is the following: If (X,d) is a PT space which is also a geodesic space (i.e., for each pair x,y there exists a geodesic connecting x and y) and if X is moreover homeomorphic to ℝ×[0,1] then X is isometric to a flat strip ℝ×[0,a]⊂ℝ 2 with its Euclidean metric. The authors also give a new short proof of the fact that a proper geodesic PT space is always strictly distance convex. (See also Th. Foertsch and V. Schroeder [Trans. Am. Math. Soc. 363, No. 6, 2891–2906 (2011; Zbl 1220.53092)]). This also indicates a positive answer to the open question if every proper geodesic PT space is also a CAT(0)-space

Orange Dogs and Memory Responses: Creativity in Spectating and Remembering

It looks cold, metallic, dangerous, but it is mesmerising. I am drawn to the floor, knowing it is made of glass, wanting to test it, try it out, measure its keep. I step onto the floor and feel the cracking underfoot. It gives way, a gentle bounce underneath whilst it creaks and splinters. I am exhilarated, and I anticipate with trepidation, that the glass will break. I hear other steps around me breaking the glass floor slowly but inexorably and here, underneath my shoe, more glass breaks. But the softness surprises me-the layers of glass cushion the step and give it that bounce. It feels alive. It is matter stretched to its limit as its molecules hold onto each other under the pressure, under the duress. It finds its strength in the mass, each sheet of glass resting on another, resisting the weight that forces it, inevitably, to break. But still, shattered, crushed, it holds its shape and the weight of my feet. It is defiant, laughing at my feeble weight, ridiculing my initial fright