Lobachevsky geometry of (super)conformal mechanics

We give a simple geometric explanation for the similarity transformation mapping one-dimensional conformal mechanics to free-particle system. Namely, we show that this transformation corresponds to the inversion of the Klein model of Lobachevsky space (non-compact complex projective plane) . We also extend this picture to the N=2k superconformal mechanics described in terms of Lobachevsky superspace .     

A simple method for asymmetric trifluoromethylation of N-acyl oxazolidinones via Ru-catalyzed radical addition to zirconium enolates

A Ru-catalyzed direct thermal trifluoromethylation and perfluoroalkylation of N-acyloxazolidinones has been developed. The reaction is experimentally simple and requires inexpensive reagents while providing good yields of products with good levels of stereocontrol. Preliminary studies have shown notable compatibility with functional groups, aromatics, and certain heteroaromatic substituents. The described method provides a useful alternative for the synthesis of fluorinated materials in an experimentally convenient manner.     

Polynomial hulls and proper analytic disks

We show how to construct the Perron–Bremermann function by using proper analytic disks. We apply this result to the polynomial hull of a compact set K defined on the boundary of the unit ball.     

On the product property of the pluricomplex Green function

We prove that the pluricomplex Green function has the product property for any domains and .

     

A convergent total synthesis of hemibrevetoxin B

A convergent biomimetic synthesis of hemibrevetoxin B from d-glucal and d-arabinose utilizes an electrophile-promoted cascade anti-Baldwin cyclization of an epoxy alcohol. The epoxy alcohol arises from a palladium-catalyzed coupling of a highly functionalized organozinc compound and an alkenyl iodide, which serve as two chiral building blocks of similar size and complexity. This first successful implementation of a cascade epoxy alcohol cyclization for the synthesis of marine polycyclic ether toxins proceeds in 39 steps and 4% overall yield.     

3,3]-Sigmatropic rearrangement/5-exo-dig cyclization reactions of benzyl alkynyl ethers: synthesis of substituted 2-indanones and indenes

Substituted benzyl alkynyl ethers, prepared from the corresponding α-alkoxy ketones in a two-step sequence involving enol triflate formation and KOtBu-induced E2 elimination, undergo [3,3]-sigmatropic rearrangement/intramolecular 5-exo-dig cyclization at 60 °C to form substituted 2-indanones in good overall yields. 1,3-cis-Disubstituted-2-indanones are formed preferentially when the benzylic substituent R(1) is bulky. Substituted indenes may be prepared from 2-indanones in high yields by Horner-Wadsworth-Emmons reaction.     

Dimroth rearrangement in the row of new pyrano[3,4-c][1,2,4]triazolo[4,3-a][1,5-a]pyridines and synthesis of new heterocyclic systems: Pyranopyrazolo[4,3-e][1,2,4]triazolopyridines

New and effective methods for the synthesis of derivatives of pyrano[3,4-c][1,2,4]triazolo[4,3-a][1,5-a]pyridines were developed. Synthesized new tetracyclic heterocyclic systems containing pyrano[3,4-c]pyridine ring unknown in the literature were obtained for the first time. The rearrangement of Dimroth in the triazolo[4,3-a]pyridine systems for the first time was studied. The possibility of rearrangement of Dimroth in the new heterocyclic system has been investigated.