Lie completion of pseudo-groups

By far the most important class of pseudo-groups, both for theory and in essentially all applications, are the Lie pseudo-groups. In this paper we propose a definition of the Lie completion of a regular pseudo-group, and establish some of its basic properties. In particular, a pseudo-group and its Lie completion have exactly the same differential invariants and invariant differential forms. Thus, for practical purposes, one can exclusively work within the category of Lie pseudo-groups.     

Chordal Bipartite Graphs with High Boxicity

The boxicity of a graph G is defined as the minimum integer k such that G is an intersection graph of axis-parallel k-dimensional boxes. Chordal bipartite graphs are bipartite graphs that do not contain an induced cycle of length greater than 4. It was conjectured by Otachi, Okamoto and Yamazaki that chordal bipartite graphs have boxicity at most 2. We disprove this conjecture by exhibiting an infinite family of chordal bipartite graphs that have unbounded boxicity.     

Interrupted Nazarov cyclization on silica gel

Exposure of a mixture of propargyl vinyl ketone and a nucleophilic primary or secondary amine to activated dry silica gel in the absence of solvent leads to a cascade of reactions that results in the formation of an aminocyclopentenone. The reaction with triethylamine leads to a cross-conjugated cyclopentadienone.     

Addition of tethered nonaromatic carbon nucleophiles to chemoselectively activated amides

[reaction: see text] In an effort to develop new ways of synthesizing polycyclic alkaloids, we successfully added silyl enol ethers, allylsilanes, and enamines to iminium ions generated from amides. Because of their higher oxidation state, such iminiums show a yet unexploited advantage of potential double cyclizations over standard Mannich monocyclizations. We report herein the first example of tethered nonaromatic carbon nucleophiles adding to activated amides for the generation of enaminals of various ring sizes, with endo- or exo-cyclic nitrogen.     

A new quantitative analysis of significant timing differences between externally cued and self-initiated motor tasks in an fMRI study

It is generally accepted that the temporal resolution of blood oxygenation level dependent functional MRI is limited due to the inherent latency and longevity of the haemodynamic response. However, in this study we introduce a technique for measurement of timing differences from within the same brain region in two (or more) separate tasks that allows accurate determination of cortical timing differences 200 ms. Our technique, based on a novel use of linear regression analysis, is shown to yield accurate results both in simulated and experimental data. We show that cortical timing differences measured using fMRI are consistent with published electrophysiological results. Measurement of timing differences using this technique could prove a useful strategy for identifying neural network components in a wide range of cognitive paradigms.     

Synthesis of 1,3-dioxo-hexahydropyrido[1,2-c][1,3]diazepine carboxylates, a new bicyclic skeleton formed by ring expansion-RCM methodology

A short and elegant synthetic pathway was developed for the synthesis of 1,3-dioxo-hexahydropyrido[1,2-c][1,3]diazepine carboxylates, a new 1,3-diazepan-2,4-dione containing bicyclic moiety, starting from pyroglutamate esters.     

Revision of an enamine synthesis; the preparation and reactions of 2-morpholinoisoflav-3-ene.

The condensation of $\text{N}$-styrylmorpholine with salicylaldehyde does $\text{not}$ give a product that can be oxidised to isoflavone; the product is $\text{N}$-morpholino-isoflav-3-ene which can be used to prepare other compounds related to isoflavan and upon oxidation gives 3-phenylcoumarin.