We develop a construction of Engel structures on 4– manifolds based on decompositions of manifolds into round handles. This allows us to show that all parallelizable 4–manifolds admit an Engel structure. We also show that, given two Engel manifolds M1, M2 satisfying a certain condition on the characteristic foliations, there is an Engel structure on M1#M2#(S ×S) which is closely related to the ...

Recent molecular phylogenetic studies on Lophocoleaceae have recovered some well-supported monophyletic lineages within Chiloscyphus s. lat. that merit recognition at the generic level. As a consequence, Chiloscyphus is herein circumscribed to include only Chiloscyphus subgen. Chiloscyphus, Chiloscyphus subgen. Connati is elevated to generic rank to which the new name Cryptolophocolea is applie...

We study Thurston geometries (X, G) with contact structures and Engel structures which are compatible with the action of the isometry group G. We classify geometric contact structures and geometric Engel structures up to equivalence and we compare the geometric Engel structures with other constructions of Engel manifolds.

Objective To present a surgical series of patients with low grade temporal gliomas causing intractable epilepsy, focusing on long-term seizure outcome.Method A retrospective study was conducted with patients with temporal low-grade gliomas (LGG).Results Sixty five patients with were operated in our institution. Males were more affected than females and the mean age at surgery was 32.3 ± 8.4 (9-...

This paper develops methods for hypothesis testing in a nonparametric instrumental variables (IV) setting within a partial identification framework. I construct and derive the asymptotic distribution of a test statistic for the hypothesis that at least one element of the identified set satisfies a conjectured restriction. This procedure can be used to test for features of the model that may be ...

They imparted a value for individuals, the importance of humility, an enthusiasm for sharing knowledge, and an appreciation of history. Photo: Kellie K. Magill. fi eld, and poorer countries could also develop their own biotechnology approaches. This more democratic approach to agro-biotech could conceivably gain back some of the trust that giant companies like Monsanto and DuPont lost in the GM...

In this paper we investigate certain solvable (n+1)-Engel groups and bounded left Engel groups. We show that these (n + 1)-Engel groups can be characterized as those groups in which the normal closure of each element in the group is nilpotent of class at most n. Similarly, the bounded left Engel groups investigated can be characterized as those groups in which the normal closure of each element...