6,339 research outputs found
A Ghost at
In the final chain of the countable powerset functor, we show that the set at
index , regarded as a transition system, is not strongly extensional
because it contains a "ghost" element that has no successor even though its
component at each successor index is inhabited. The method, adapted from a
construction of Forti and Honsell, also gives ghosts at larger ordinals in the
final chain of other subfunctors of the powerset functor. This leads to a
precise description of which sets in these final chains are strongly
extensional
Teamwork on the field and at work
One way that people learn teamwork, informal mentoring, and other workplace skills is through participating in sports. Yet, many women of my generation did not get a chance to develop these talents since they had fewer opportunities to participate in organized athletics when they were young. I came to understand the importance of sports from my own experience: My passionâall the rest is a hobbyâis coaching girlsâ soccer, something I have done for the last 15 years.Sports for women ; Mentoring
Do academic laboratories correspond to scientific communities? Evidence from a large European university.
Although acknowledged as central in the economic literature, the issue of intra academic collaboration has been, insofar, relatively overlooked. This paper fills this gap by stressing the importance of communities in academic research. By analysing the publication behavior of researchers from a large European scientific university, we argue that in certain cases, the community level constitutes a relevant level for analysing the collaborative nature of scientific investigation. Indeed, the reality of research collaborations doesnât always fit the institutional division of academic work provided by laboratories.Economics of Science, Knowledge Intensive Communities, Academic Collaborations, Social Network Analysis.
Generic singularities of nilpotent orbit closures
According to a well-known theorem of Brieskorn and Slodowy, the intersection
of the nilpotent cone of a simple Lie algebra with a transverse slice to the
subregular nilpotent orbit is a simple surface singularity. At the opposite
extremity of the nilpotent cone, the closure of the minimal nilpotent orbit is
also an isolated symplectic singularity, called a minimal singularity. For
classical Lie algebras, Kraft and Procesi showed that these two types of
singularities suffice to describe all generic singularities of nilpotent orbit
closures: specifically, any such singularity is either a simple surface
singularity, a minimal singularity, or a union of two simple surface
singularities of type . In the present paper, we complete the picture
by determining the generic singularities of all nilpotent orbit closures in
exceptional Lie algebras (up to normalization in a few cases). We summarize the
results in some graphs at the end of the paper.
In most cases, we also obtain simple surface singularities or minimal
singularities, though often with more complicated branching than occurs in the
classical types. There are, however, six singularities which do not occur in
the classical types. Three of these are unibranch non-normal singularities: an
-variety whose normalization is , an
-variety whose normalization is , and a
two-dimensional variety whose normalization is the simple surface singularity
. In addition, there are three 4-dimensional isolated singularities each
appearing once. We also study an intrinsic symmetry action on the
singularities, in analogy with Slodowy's work for the regular nilpotent orbit.Comment: 56 pages (5 figures). Minor corrections. Accepted in Advances in Mat
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