We prove that if R is a domain with many units, then the natural inclusion E2(R) → E2(R[t]) induces an isomorphism in integral homology. This is a consequence of the existence of an amalgamated free product decomposition of E2(R[t]). We also use this decomposition to study the homology of E2(Z[t]) and show that a great deal of the homology of E2(Z[t]) maps nontrivially into the homology of SL2(...

We show that the Scott topology induces a topology for real-valued Lipschitz maps on Banach spaces which we call the L-topology. It is the weakest topology with respect to which the L-derivative operator, as a second order functional on the space of Lipschitz maps into the domain of non-empty, convex and weak*-compact valued functions ordered by reverse inclusion, is continuous. For finite dime...

These last years ground-based astronomy has been looking towards Antarctica, especially its summits and the internal continental plateau where the optical turbulence appears to be confined in a shallow layer close to the icy surface. Preliminary measurements have so far indicated pretty good value for the seeing above 30-35 m: 0.36” (Agabi et al. 2006), 0.27” (Lawrence et al. 2004) and 0.3” (Tr...

We show that the Scott topology induces a topology for real-valued Lipschitz maps on Banach spaces which we call the L-topology. It is the weakest topology with respect to which the L-derivative operator, as a second order functional which maps the space of Lipschitz functions into the function space of non-empty weak* compact and convex valued maps equipped with the Scott topology, is continuo...

Crime mapping has long been an integral part of the process known today as crime analysis. The New York City Police Department, for example, has traced the use of maps back to at least 1900. The traditional crime map was a jumbo representation of a jurisdiction with pins stuck in it (figure 1.1). The old pin maps were useful for showing where crimes occurred, but they had serious limitations. A...

The policy objective of safeguarding financial stability has stimulated a wave of research on systemic risk analytics, yet it still faces challenges in measurability. This paper models systemic risk by tapping into expert knowledge of financial supervisors. We decompose systemic risk into a number of interconnected segments, for which the level of vulnerability is measured. The system is modele...

Following a method by Meldrum and van der Walt, near-rings of matrix maps are defined for general near-rings, not necessarily with identity. The influence of one-sided identities is discussed. When the base near-ring is integral and planar, the near-ring of matrix maps is shown to be simple. Various types of primitivity of the near-ring of matrix maps are discussed when the base near-ring is pl...

The genus series for maps is the generating series for the number of rooted maps with a given number of vertices and faces of each degree, and a given number of edges. It captures topological information about surfaces, and appears in questions arising in statistical mechanics, topology, group rings, and certain aspects of free probability theory. An expression has been given previously for the...

The return map for planar vector fields with nilpotent linear part (having a center or a focus and under an assumption generically satisfied) is found as a convergent power series whose terms can be calculated iteratively. The first nontrivial coefficient is the value of an Abelian integral, and the following ones are explicitly given as iterated integrals built with algebraic functions.