The dynamics of second-order equations with delayed feedback and a large coefficient of delayed control

The dynamics of second-order equations with nonlinear delayed feedback and a large coefficient of a delayed equation is investigated using asymptotic methods. Based on special methods of quasi-normal forms, a new construction is elaborated for obtaining the main terms of asymptotic expansions of asymptotic residual solutions. It is shown that the dynamical properties of the above equations are determined mostly by the behavior of the solutions of some special families of parabolic boundary value problems. A comparative analysis of the dynamics of equations with the delayed feedback of three types is carried out.     

BINOL-derived diphosphoramidites bearing unsymmetrical 1,2-diamine link and their application in asymmetric catalysis

New P,P-bidentate diastereomeric diphosphoramidite chiral ligands with mixed stereogenic elements and a C₁ backbone symmetry have been prepared from (S_a)- and (R_a)-1,1′-binaphthyl-2,2′-diol (BINOL) and (S)-N-benzyl-1-(pyrrolidin-2-yl)methanamine and are fully characterized. The use of these ligands provides up to 84% ee in the Pd-catalyzed asymmetric allylic substitution of (E)-1,3-diphenylallyl acetate and up to 95% ee in the Rh-catalyzed asymmetric hydrogenation of α-dehydrocarboxylic acid esters. The results indicate that the catalytic performance is highly affected by the axial chirality of the binaphthyl moieties of the ligand and the nature of the solvent.     

The first stable examples of compounds containing both diazonium and acyl azide,and synthesis of a new pyrazino[2′,3′:3,4]pyrazolo[5,1-c][1,2,4]triazin-4(6H)-one heterocyclic system

The first stable compound containing both N₂⁺BF₄^? and CON₃ functional groups – 8-azidocarbonyl-3-(tert-butyl)-4-oxo-4,6-dihydropyrazolo[5,1-c][1,2,4]triazine-7-diazonium tetrafluoroborate was synthesized, and its stability and reactivity discussed. The Curtius rearrangement of 7-azido-3-(tert-butyl)-4-oxo-4,6-dihydropyrazolo[5,1-c][1,2,4]triazine-8-carbonylazide was investigated, and the synthesis of a novel heterocyclic system –pyrazino[2′,3′:3,4]pyrazolo[5,1-c][1,2,4]triazin-4(6H)-one is described.