Palladium-catalyzed regiocontrolled and stereoselective alkylations of bis(trifluoroethyl) malonates with dienyl alcohols

The triethylborane-promoted and palladium-catalyzed reactions of 2,4-dienyl alcohols or the corresponding isomeric divinyl alcohols with bis(trifluoroethyl) malonates provide an improved method for the regio- and stereoselective dienylation of malonates. The phosphine ligand is an important control element in the reaction. Combinations of Pd(OAc)₂ with BIPHEP or BINAP give dienylated malonates in good yield and higher isomeric purity than the traditional combination of Pd(OAc)₂ and Ph₃P affords in the catalyzed reactions of dienyl acetates.     

Specific features of methods for obtaining Ti(III) and its concentration effect on optical properties of potassium-aluminum phosphate glass

Potassium-aluminum phosphate glasses with different concentrations of Ti(III) activator were prepared and their spectral properties were studied.     

Effect of structural permeability on the stability of a parachute with four suspension lines

The effect of various structural permeabilities (additional perforation) on the aerodynamic characteristics, shape, and stability of square parachute models with four suspension lines is studied. The parachute is made of a fabric whose air permeability coefficient is equal to zero. The shape of the parachute canopy and the force distribution along the ribbons of the canopy are discussed.     

Cycles of two-dimensional systems: Computer calculations,proofs, and experiments

One of the central problems in studying small cycles in the neighborhood of equilibrium involves computation of Lyapunov’s quantities. While Lyapunov’s first and second quantities were computed in the general form in the 1940s–1950s, Lyapunov’s third quantity was calculated only for certain special cases. In the present work, we present general formulas for calculation of Lyapunov’s third quantity. Together with the classical Lyapunov method for calculation of Lyapunov’s quantities, which is based on passing to the polar coordinates, we suggest a method developed for the Euclidian coordinates and for the time domain. The calculation of Lyapunov’s quantities by two different analytic methods involving modern software tools for symbolic computing enables us to justify the formulas obtained for Lyapunov’s third quantity. For quadratic systems in which Lyapunov’s first and second quantities vanish, while the third one does not, large cycles were calculated. In the calculations, the quadratic system was reduced to the Liénard equation, which was used to evaluate the domain of parameters corresponding to the existence of four cycles (three “small” cycles and a “large” one). This domain extends the region of parameters obtained by S.L. Shi in 1980 for a quadratic system with four limit cycles.     

A New Algorithm for a Posteriori Error Estimation for Approximate Solutions of Linear Ill-Posed Problems

Computational Mathematics and Mathematical Physics - A new algorithm for a posteriori estimation of the error in solutions to linear operator equations of the first kind in a Hilbert space is...     

Experimental enthalpies of formation and other physicochemical characteristics of compounds containing C-NO2 and C-N(O)=N-NO2 groups: a comparison

Russian Chemical Bulletin - The standard enthalpies of formation of nitro-NNO-azoxy compounds including nitro-NNO-azoxybenzene (2), 3-nitro-4-{[4-(nitro-NNO-azoxy)furazan-3-yl]-NNO-azoxy}-furazan...     

Changes in the characteristics of a high-filled polymeric compound in the area of its fastening to a rigid multilayer substrate

Changes in the characteristics of a high-filled polymeric compound are investigated in the area of its fastening to a rigid multilayer substrate. It is established that, in the fastening area, an increase in the amount of the rubber sol-fraction and the content of the high-filled polymeric compound plasticizer is observed, as well as an increase in the modulus of elasticity and a decrease in the strain of the HFPC.