We define a bundle over a totally disconnected set such that each fiber is homeomorphic to a fractal blowup. We prove that there is a natural action of a Renault–Deaconu groupoid on our fractafold bundle and that the resulting action groupoid is a Renault– Deaconu groupoid itself. We also show that when the bundle is locally compact the associated C∗-algebra is primitive and has a densely defin...

Chain conditions, finiteness conditions, growth conditions, and other forms of finiteness, Noetherian rings and Artinian rings have been systematically studied for commutative rings and algebras since 1959. In pursuit of the deeper results of ideal theory in ordered groupoids (semigroups), it is necessary to study special classes of ordered groupoids (semigroups). Noetherian ordered groupoids (...

We use the n-globe with its skeletal filtration to define the fundamental globular ω–groupoid of a filtered space; the proofs use an analogous fundamental cubical ω–groupoid due to the author and Philip Higgins. This method also relates the construction to the fundamental crossed complex of a filtered space, and this relation allows the proof that the crossed complex associated to the free glob...

Our main aim is to associate a holonomy Lie groupoid to the connective structure of an abelian gerbe. The construction has analogies with a procedure for the holonomy Lie groupoid of a foliation, in using a locally Lie groupoid and a globalisation procedure. We show that path connections and 2–holonomy on line bundles may be formulated using the notion of a connection pair on a double category,...

OBJECTIVE To assess the association of hypoglycemic treatment regimens with cardiovascular adverse events and mortality in a large population of type 2 diabetic patients at increased cardiovascular risk. RESEARCH DESIGN AND METHODS This analysis included 8,192 overweight patients with type 2 diabetes from the Sibutramine Cardiovascular Outcomes (SCOUT) trial randomized to lifestyle interventi...

CONTEXT Adverse drug events (ADEs) are a significant and costly cause of injury during hospitalization. OBJECTIVES To evaluate the efficacy of 2 interventions for preventing nonintercepted serious medication errors, defined as those that either resulted in or had potential to result in an ADE and were not intercepted before reaching the patient. DESIGN Before-after comparison between phase ...

Many important C∗-algebras, such as AF-algebras, Cuntz-Krieger algebras, graph algebras and foliation C∗-algebras, are the C∗-algebras of r-discrete groupoids. These C∗-algebras are often associated with inverse semigroups through the C∗-algebra of the inverse semigroup [HR90] or through a crossed product construction as in Kumjian’s localization [Kum84]. Nica [Nic94] connects groupoid C∗-algeb...

The purpose of these notes is to discuss the problem of moduli for curves of genus g ≥ 3 1 and outline the construction of the (coarse) moduli scheme of stable curves due to Gieseker. The notes are broken into 4 parts. In Section 1 we discuss the general problem of constructing a moduli “space” of curves. We will also state results about its properties, some of which will be discussed in the se...

We have prepared a viscous bicontinuous microemulsion consisting of water / [20 wt% POE-GIS + 30 wt% PEPTME + 47.5 wt% POE/POP-PDMS + 2.5 wt% OA)] / DMPS system. A pseudoternary phase diagram was constructed for the mixture, and the bicontinuous microemulsion phase was characterized by means of rheometry and freeze-fracture transmission electron microscopy (FF-TEM).

The purpose of this paper is to describe orbifolds in terms of (a certain kind of) groupoids. In doing so, I hope to convince you that the theory of (Lie) groupoids provides a most convenient language for developing the foundations of the theory of orbifolds. Indeed, rather than defining all kinds of structures and invariants in a seemingly ad hoc way, often in terms of local charts, one can us...