Activation of free-radical polyfluoroalkylation of organic substrates with freon BrCF2CF2Br using a system of organic base-electron transfer mediator

A polyfluoroalkylation of pyrrole and phenols with freon BrCF₂CF₂Br using sulfur dioxide-substituted pyridine activating system proceeds at the aromatic nucleus by a free-radical mechanism. The essential influence of the basicity of the medium is demonstrated and discussed.     

Attractor of Smale - Williams type in an autonomous distributed system

We consider an autonomous system of partial differential equations for a one-dimensional distributed medium with periodic boundary conditions. Dynamics in time consists of alternating birth and death of patterns with spatial phases transformed from one stage of activity to another by the doubly expanding circle map. So, the attractor in the Poincaré section is uniformly hyperbolic, a kind of Smale - Williams solenoid. Finite-dimensional models are derived as ordinary differential equations for amplitudes of spatial Fourier modes (the 5D and 7D models). Correspondence of the reduced models to the original system is demonstrated numerically. Computational verification of the hyperbolicity criterion is performed for the reduced models: the distribution of angles of intersection for stable and unstable manifolds on the attractor is separated from zero, i.e., the touches are excluded. The example considered gives a partial justification for the old hopes that the chaotic behavior of autonomous distributed systems may be associated with uniformly hyperbolic attractors.     

Inverse problems on star-type graphs: differential operators of different orders on different edges

We study inverse spectral problems for ordinary differential equations on compact star-type graphs when differential equations have different orders on different edges. As the main spectral characteristics we introduce and study the so-called Weyl-type matrices which are generalizations of the Weyl function (m-function) for the classical Sturm-Liouville operator. We provide a procedure for constructing the solution of the inverse problem and prove its uniqueness.     

Gauge semi-simple extension of the Poincaré group

An approach to the cosmological term problem is proposed, using the gauge semi-simple tensor extension of the D-dimensional Poincaré group as a basis.     

A simple and convenient synthesis of 3-[5-(trifluoromethyl)-1,2,3-triazol-4-yl]cinnamic acids from 4-aryl-6-(trifluoromethyl)-2H-pyran-2-ones and sodium azide

4-Aryl-6-(trifluoromethyl)-2H-pyran-2-ones and ethyl 4-aryl-6-(trifluoromethyl)-2-oxo-2H-pyran-3-carboxylates react with sodium azide to produce highly functionalized CF₃-1,2,3-triazoles: 3-[5-(trifluoromethyl)-1,2,3-triazol-4-yl]cinnamic acids and monoethyl esters of [5-(trifluoromethyl)-1,2,3-triazol-4-yl]arylmethylidene malonic acids.