Redox Reaction of the Pd0 Complex Bearing the Trost Ligand with meso‐Cycloalkene‐1,4‐biscarbonates Leading to a Diamidato PdII Complex and 1,3‐Cycloalkadienes: Enantioselective Desymmetrization Versus Catalyst Deactivation

The Pd⁰ complex 1 that bears the Trost ligand 2 undergoes a facile redox reaction with 1,4‐biscarbonates 5 b – d and rac‐ 22 under formation of the diamidato–Pd^II complex 7 and the corresponding 1,3‐cycloalkadienes 8 b – d . The redox deactivation of complex 1 was the dominating pathway in the reaction of 5 b – d with HCO₃^? at room temperature. However, at 0 °C the six‐membered biscarbonate 5 b , catalytic amounts of complex 1 , and HCO₃^? mainly reacted in an allylic alkylation, which led to a highly selective desymmetrization of the substrate and gave alcohol 6 b with ≥99 % ee in 66 % yield. An increase of the catalyst loading in the reaction of 5 b with 1 and HCO₃^? afforded the bicyclic carbonate 12 b (96 % ee, 92 %). Formation of carbonate 12 b involves two consecutive inter‐ and intramolecular substitution reactions of the π‐allyl–Pd^II complexes 16 b and 18 b , respectively, with O‐nucleophiles and presumably proceeds through the hydrogen carbonate 17 b as key intermediate. The intermediate formation of 17 b is also indicated by the conversion of alcohol rac‐ 6 b to carbonate 12 b upon treatment with HCO₃^? and 1 . The Pd⁰‐catalyzed desymmetrization of 5 b with formation of 12 b and its hydrolysis allow an efficient enantioselective synthesis of diol 13 b . The reaction of the seven‐membered biscarbonate 5 c with ent‐ 1 and HCO₃^? afforded carbonate ent‐ 12 c (99 % ee, 39 %). The Pd⁰ complex 1 is stable in solution and suffers no intramolecular redox reaction with formation of complex 7 and dihydrogen as recently claimed for the similar Pd⁰ complex 9 . Instead, complex 1 is rapidly oxidized by dioxygen to give the stable Pd^II complex 7 . Thus, formation of the Pd^II complex 10 from 9 was most likely due to an oxidation by dioxygen. Oxidative workup (air) of the reaction mixture stemming from the desymmetrization of 5 c catalyzed by 1 gave the Pd^II complex 7 in high yield besides carbonate 12 c .     

Compact acousto-optic filter with beam expanders constituted by photonic crystal rows of airholes

A compact acousto-optic (AO) filter with multireflector (MR) beam expanders constituted by 32 photonic crystal rows of airholes in LiNbO(3) waveguide has been proposed and numerically studied by the two-dimensional finite-difference-time-domain method. The diameter and position of every row of holes are gradually varied along MR beam expanders in order to provide high efficiency and good sidelobe suppression. Device sizes are 70 μm × 150 μm, with an FWHM bandwidth of 4.4 nm, a tuning range of 110 nm, internal loss of -3 dB, and sidelobes of -20 dB, thus providing a unique value of 0.6 μm(2) for the product FWHM bandwidth by an AO length. It is intended for use in fiber optics telecommunications and sensing.     

Projective and generating modules over the ring of pseudorational numbers

The projective, flat, and generating modules over the ring of pseudorational numbers are described. For the projective modules, a complete independent system of invariants is constructed.     

Tri-Hamiltonian Structures of Egorov Systems of Hydrodynamic Type

We prove a simple condition under which the metric corresponding to a diagonalizable semi-Hamiltonian hydrodynamic type system belongs to the class of Egorov (potential) metrics. For Egorov diagonal hydrodynamic type systems satisfying natural semisimplicity and homogeneity conditions, we prove necessary and sufficient conditions under which the third structure is local or corresponds to a metric of constant curvature. The results are illustrated by some well-known physical examples of such systems.     

Phased Antenna Arrays Based on Vircators: Numerical Experiments

We present the results of numerical simulation of two different design schemes for phased antenna arrays (PAAs) based on vircators, i.e., microwave oscillators with virtual cathodes. The active and passive schemes of PAA design are analyzed separately. It is shown that in the case of an active PAA scheme, the degree of tuning the vircator to the master oscillator increases with increasing power of the latter, while in the case of a passive PAA scheme, the coherence degree of two vircators due to waveguide coupling increases with increase in the coupling coefficient.     

Coupled Solitons for Quantum Communication and Metrology in the Presence of Particle Dissipation

Journal of Russian Laser Research - Bright solitons represent natural information carriers for optical communication. However, particle losses create serious barriers to soliton implementation in...     

Sequences of Endomorphism Groups of Abelian Groups

In the paper, Problem 18.3 of the book “Abelian groups” (2015) by L. Fuchs is solved in the case of Abelian groups with finite p-ranks. For an Abelian group A, a sequence of groups (A_n) is considered, where A₀ = A and A_n+1 = End A_n. It is shown that, if all p-ranks of the group A are finite, then this sequence can stabilize either after A₀ or after A₁.