Pi-envelopes of Lie superalgebras

In this paper we find necessary and sufficient conditions on a finite-dimensional Lie superalgebra under which any associative PI-envelope of is finite-dimensional. We also extend M. Scheunert's result which enables one to pass from color Lie superalgebras to the ordinary ones, to the case of gradings by an arbitrary abelian group.

     

Diffusion of asymmetric swimmers

Particles moving along curved trajectories will diffuse if the curvature fluctuates sufficiently in either magnitude or orientation. We consider particles moving at a constant speed with either a fixed or a Gaussian distributed magnitude of curvature. At small speeds the diffusivity is independent of the speed. At larger particle speeds, the diffusivity depends on the speed through a novel exponent. We apply our results to intracellular transport of vesicles. In sharp contrast to thermal diffusion, the effective diffusivity increases with vesicle size and so may provide an effective means of intracellular transport.     

Flow-induced beam steering in a single laser hot spot

The transmitted angular distribution of a 527 nm nearly diffraction-limited laser is measured after it propagates through a plasma with supersonic transverse flow. The laser beam is deflected by as much as 10 degrees and exhibits bowlike features in the flow direction, which is attributed to flow-induced beam steering. The finite interaction volume allows for direct comparison with a 3D hydrodynamic simulation, which is in good agreement with details of the experiment.     

Methylation and amination of folic acid

The methylation of folic acid (2) with excess methyl iodide resulted in the formation of dimethyl 1,3-dimethylfolate ( 4 ), whereas, methylation of dimethyl folate ( 3 ) with an equimolar amount of methyl iodide gave mainly dimethyl 3-methylfolate ( 6 ). Both 4 and 6 underwent the Dimroth rearrangement in base to give the corresponding 2-deamino-2-methyiamino folic acids 5 and 7, respectively. Amination of 2 with hydroxylamine-O-sulfonic acid in dilute base gave a low yield of 3-amino folic acid (8), which underwent Dimroth rearrangement to give 2-deamino-2-hydrazino folic acid (9) in an acidic, but not a basic, medium.     

A new two-step four-component synthesis of highly functionalized cyclohexenols by sequential nickel-catalyzed couplings

A new two-step procedure for the synthesis of cyclohexenols has been developed. A nickel-catalyzed three-component addition of an enal, alkyne, and acetylenic tin affords substituted hept-4-en-6-ynals. The products of this first step then undergo a second nickel-catalyzed reaction with organozincs or organoboranes to afford densely functionalized cyclohexenols. Variation in each of the four components is tolerated to provide access to a wide range of versatile building blocks.