Gold(I)-catalyzed rearrangement of aryl alkynylaziridines to spiro[isochroman-4,2'-pyrrolines

Alkynylaziridines carrying an aryl group could be efficiently converted to spiro[isochroman-4,2'-pyrrolines] with gold salts as catalysts. This new rearrangement involved a Friedel-Crafts type intramolecular reaction followed by cyclization of the aminoallene intermediate, both initiated by the dual σ and π Lewis acidities of gold.     

Global Dynamics of a Rapidly Forced Cart and Pendulum

In this paper, we study emergent behaviors elicited by applying open-loop, high-frequency oscillatory forcing to nonlinear control systems. First, we study hovering motions, which are periodic orbits associated with stable fixed points of the averaged system which are not fixed points of the forced system. We use the method of successive approximations to establish the existence of hovering motions, as well as compute analytical approximations of their locations, for the cart and pendulum on an inclined plane. Moreover, when small-amplitude dissipation is added, we show that the hovering motions are asymptotically stable. We compare the results for all of the local analysis with results of simulating Poincaré maps. Second, we perform a complete global analysis on this cart and pendulum system. Toward this end, the same iteration scheme we use to establish the existence of the hovering periodic orbits also yields the existence of periodic orbits near saddle equilibria of the averaged system. These latter periodic orbits are shown to be saddle periodic orbits, and in turn they have stable and unstable manifolds that form homoclinic tangles. A quantitative global analysis of these tangles is carried out. Three distinguished limiting cases are analyzed. Melnikov theory is applied in one case, and an extension of a recent result about exponentially small splitting of separatrices is developed and applied in another case. Finally, the influence of small damping is studied. This global analysis is useful in the design of open-loop control laws.     

Synthesis of 2‐Deoxy‐2‐thiophenylglucosyl Azides through 1,2 Thio Migration of Thiophenyl Mannosides

2‐Deoxy‐2‐thio glucosyl azides bearing or not bearing an azido group at the 6‐position can be conveniently obtained through a 1,2‐thio migration from thiophenyl mannoside derivatives.     

Paspalinine,a tremorgenic metabolite from Claviceps paspali Stevens et Hall

The structure of paspalinine, a tremorgenic fungal metabolite, is presented.     

K(A,B,I): II

The KABI conjecture states that double relative K-theory and cyclic homology agree, at least in characteristic zero. We show that K ₂(A, B, I) maps onto HC ₁ (A, B, I) whenever A B is a map of Q-algebras and I BIB. We also reinterpret the KABI conjecture in terms of the injectivity of the inverse limit of the map from NK(A, B, I) to the inverse limit of the truncated polynomial versions of NK(A, B, I).Supported by National Science Foundation Grant RII — 8700009.Partially supported by National Science Foundation Grants DMS — 8503018 and 8803497.     

Hodge decompositions of Loday symbols inK-theory and cyclic homology

In this paper, we study the Hodge decompositions ofK-theory and cyclic homology induced by the operations ^k and ^k , and in particular the decomposition of the Loday symbols x,y, ...z. Except in special cases, these Loday symbols do not have pure Hodge index. InK _n (A) they can project into every componentK _n ⁽ⁱ⁾ for 2in, and the projection of the Loday symbol x,y, ...,z intoK _n ⁽ⁿ⁾ is a multiple of the generalized Dennis-Stein symbol x,y, ...,z. Our calculations disprove conjectures of Beilinson and Soulé inK-theory, and of Gerstenhaber and Schack in Hochschild homology.Partially supported by National Security Agency grant MDA904-90-H-4019.Partially supported by National Science Foundation grant DMS-8803497.