Prepositions in English are a well-known challenge for language learners, and the computational analysis of preposition usage has attracted significant attention. Such research generally starts out by developing models of preposition usage for native English based on a range of features, from shallow surface evidence to deep linguistically-informed properties. While we agree that ultimately a c...

We discuss the total collision singularities of gravitational N-body problem on shape space. Shape space is relational configuration system obtained by quotienting ordinary with respect to similarity group translations, rotations, and scalings. For zero-energy gravitating system, dynamics can be constructed explicitly points collision, which are central zero momenta, analyzed in detail. It turn...

The first enantioselective total synthesis of a member of the okaramine family of bis-indole alkaloids, okaramine N (1), has been accomplished via intermediates 2-7, as outlined. The N-prenylated derivative of (S)-tryptophan methyl ester (2) was coupled with Fmoc-protected N-tert-prenylated tryptophan (3) to form the amide 4 in 70% yield. Pd(II)-mediated cyclization/rearrangement, a key step in...