Reductive transformations of unsaturated azabicyclic nitrolactams

Using different reducing methods unsaturated indolizidine and quinolizidine lactams substituted with a nitro group were transformed into various alkaloid-like derivatives. Hydrogen transfer and palladium catalyzed hydrogenation gave compounds of ketolactam or lactam type meanwhile the nitro group was eliminated. On the other hand, in presence of Raney-nickel catalyst the nitro compounds were reduced to diastereomeric amino derivatives whose stereochemistry was elucidated by NMR spectroscopy. Using sodium bis-dimethoxy-ethoxy-aluminum-hydride (Red-Al) as reducing agent an unexpected tricyclic azetidine was isolated and characterized.     

Computation of phase response curves via a direct method adapted to infinitesimal perturbations

A new numerical algorithm for computation of phase response curves of stable limit cycle oscillators is proposed. The idea of the algorithm originates from a direct method that is based on computation of the oscillator response to short finite pulses delivered at different phases of oscillations. Here we adapt the direct method to the case of infinitesimal perturbations and compare our algorithm with the standard algorithm based on the backward integration of the adjoint equations. In contrast to the standard algorithm, our algorithm does not require any backward integration and it is easier to program since a necessity of numerical interpolation for the Jacobian matrix is avoided. In addition, we demonstrate by examples that our algorithm is faster than the standard algorithm and this advantage is especially notable for weakly stable limit cycle oscillators.     

Zefirov's reagent and related hypervalent iodine triflates

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Transition metal-mediated oxidations utilizing monomeric iodosyl- and iodylarene species

Several transition metal-mediated oxidations using hypervalent iodine species are reported. A convenient procedure for preparation of iodylarenes via RuCl₃-catalyzed oxidation of iodoarenes has been developed. This procedure allows the generation of highly reactive monomeric iodine(V) species, which are excellent oxidants toward alcohols and hydrocarbons in situ. A broad range of substrates can be oxidized to carbonyl compounds by a tandem catalytic system based on the Ru(III)-catalyzed reoxidation of ArIO to ArIO₂ using Oxone^® as oxidant. It was shown that electrophilic iodine(III) species, originating from oligomeric iodosylbenzene sulfate (PhIO)₃SO₃, are efficient oxygenating agents in catalytic oxidation of aromatic hydrocarbons in the presence of metalloporphyrin complexes.     

Synaptic Coupling Between Two Electronic Neurons

An electrical circuit is proposed to realize an unidirectional coupling between two cells, mimicking chemical synaptic coupling. Each cell represents the FitzHugh–Nagumo (FHN) model of neuron with a modified exitability (MFHN). We present experimental results on frequency doublings and on the chaotic dynamics depending on the coupling strength in a master–slave configuration. In all experiments, we stress the influence of the coupling strength on the control of the slave neuron.     

Affine functions on CAT (κ)-spaces

We describe affine functions on spaces with an upper curvature bound.     

Some remarks on symplectic actions of compact groups

The Research was partially supported by NSF Grant DMS 8505550