Temporal differentiation of optical signals using resonant gratings

We study theoretically the possibility of performing temporal differentiation of optical signals using a resonant diffraction grating. We demonstrate that the resonant grating allows the calculation of the first-order derivative of an optical signal envelope in the vicinity of waveguide resonant frequencies in the zeroth transmitted diffraction order. The grating is shown to allow the calculation of the fractional derivative of order 1/2 in the vicinity of Rayleigh-Wood anomalies. Numerical simulations based on the rigorous coupled-wave analysis of Maxwell's equations demonstrate the high-quality differentiation of optical signals with temporal features in the picosecond range.     

Möbius characterization of the boundary at infinity of rank one symmetric spaces

Möbius structure (on a set \(X\) ) is a class of metrics having the same cross-ratios. A Möbius structure is Ptolemaic if it is invariant under inversion operations. The boundary at infinity of a \(\mathrm{CAT }(-1)\) space is in a natural way a Möbius space, which is Ptolemaic. We give a free of classification proof of the following result that characterizes the rank one symmetric spaces of noncompact type purely in terms of their Möbius geometry: Let \(X\) be a compact Ptolemy space which contains a Ptolemy circle and allows many space inversions. Then \(X\) is Möbius equivalent to the boundary at infinity of a rank one symmetric space.     

Highly alkaline electrolyte for single-stranded DNA separations by electrophoresis in bare silica capillaries.

A new, highly denaturing electrolyte system based on a solution containing 0.01 M NaOH, 0.0015 M Na2B4O5(OH)4 and a replaceable polymer sieving medium was designed for the separation of single-stranded DNA fragments in bare fused-silica capillaries. Extreme denaturing power, together with the optimized composition of the electrolyte, allows for a separation efficiency as high as 2,300,000 height equivalents to a theoretical plate per meter. Sample denaturation in alkaline solutions provides single-stranded DNA fragments without any intra- or intermolecular interactions at room temperature. Their electrophoretic mobilities were found to be twice those of fragments denatured by dimethylformamide or HCl. This can be interpreted in terms of an increased effective charge on the DNA molecules. The surprisingly weak electroosmosis (6 x 10(-10) m2 V-1 s-1) of polymer solutions at pH 12 or higher is considered to be the result of the dissolution of the silica capillary wall. A highly viscous thin layer of dissolved silica probably causes a shift of the slipping plane further away from the wall to the lower value of the zeta potential. Applications of the electrolyte in clinical diagnostics demonstrate its remarkable properties.     

Zefirov's reagent and related hypervalent iodine triflates

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A general strategy for the synthesis of difluoromethyl-containing pyrazoles, pyridines and pyrimidines

Difluoromethyl-containing heteroannulated pyridines, pyrimidines and pyrazoles are prepared by a two step method. The regioselective cyclizations of electron-excessive aminoheterocycles, hydrazines and amidines with CF₂Cl-substituted 1,3-dicarbonyl compounds provide the corresponding CF₂Cl-substituted heterocycles. Subsequent radical reactions with trimethylstannane or allyltrimethylstannane gave difluoromethyl-containing heteroannulated pyridines, pyrimidines and pyrazoles, respectively.     

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.