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.     

Effect of Fourier transform on the streaming in quantum lattice gas algorithms

All our previous quantum lattice gas algorithms for nonlinear physics have approximated the kinetic energy operator by streaming sequences to neighboring lattice sites. Here, the kinetic energy can be treated to all orders by Fourier transforming the kinetic energy operator with interlaced Dirac-based unitary collision operators. Benchmarking against exact solutions for the 1D nonlinear Schrodinger equation shows an extended range of parameters (soliton speeds and amplitudes) over the Dirac-based near-lattice-site streaming quantum algorithm.     

Entropy of Hidden Markov Processes via Cycle Expansion

Hidden Markov Processes (HMP) is one of the basic tools of the modern probabilistic modeling. The characterization of their entropy remains however an open problem. Here the entropy of HMP is calculated via the cycle expansion of the zeta-function, a method adopted from the theory of dynamical systems. For a class of HMP this method produces exact results both for the entropy and the moment-generating function. The latter allows to estimate, via the Chernoff bound, the probabilities of large deviations for the HMP. More generally, the method offers a representation of the moment-generating function and of the entropy via convergent series.