Superpositions of bounded-deterministic functions

Translated from Matematicheskie Zametki, Vol. 47, No. 3, pp. 3–10, March, 1990.     

Synthesis and properties of ferrocenylalkyl derivatives of indazole

Ferrocenylmethylation and -ferrocenylethylation of indazole were carried out for the first time. Both reactions afforded two isomers, which were characterized by physical and physicochemical methods, among them by X-ray diffraction analysis. 1-(-Ferrocenylethyl)indazole is thermally more stable than the 2-substituted isomer. Both isomers serve as ferrocenylalkylating agents with respect to s-triazole.     

Topological Invariants and Solutions with a High Complexity for Scalar Semilinear PDE

In this paper topological invariants of dynamics of scalar parabolic equations are defined. Conservation of these invariants causes persistence of complex spatially chaotic patterns in the dynamics. It implies, in particular, the existence of extremely many stable essentially different spatially complex solutions of scalar semilinear parabolic, elliptic and hyperbolic equations in the situation when coefficients of equations depend on the spatial variable strongly enough and the domain is large or unbounded, the number of different solutions exponentially depends on the volume of domain. Another implication of the conserved quantities is persistence of complexity of solutions in the dynamics.     

Controlled synthesis of new amphiphilic glycopolymers with liquid crystal grafts

A cholesterol‐based liquid crystal monomer, diethylene glycol cholesteryl ether acrylate (DEGCholA), has been successfully polymerized by atom transfer radical polymerization (ATRP) for the first time. Appropriate experimental conditions to control the polymerization of DEGCholA have been investigated using a model initiator (ethyl 2‐bromoisobutyrate) in tetrahydrofuran (THF) or toluene at 60 °C. Well‐controlled ATRP of DEGCholA was obtained using N,N,N′,N′,N″‐pentamethyldiethylenetriamine as ligand in THF at 60 °C. These conditions were then applied to initiate the ATRP of DEGCholA from multifunctional macroinitiators based on dextran. Using a protection/deprotection synthetic scheme, novel graft glycopolymers (Dex‐g‐PDEGCholA) have been synthesized. The mesomorphic properties of DEGCholA, PDEGCholA, and Dex‐g‐PDEGCholA have been studied by thermal polarizing optical microscopy, differential scanning calorimetry, and X‐ray scattering. PDEGCholA and Dex‐g‐PDEGCholA show an interdigitated smectic A phase (SmA_d) between T_g (～30 °C) and around 170 °C. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013 , 51, 3829–3839     

Exponential attractors of reaction-diffusion systems in an unbounded domain

We consider reaction-diffusion systems in unbounded domains, prove the existence of expotential attractors for such systems, and estimate their fractal dimension. The essential difference with the case of a bounded domain studied before is the continuity of the spectrum of the linear part of the equations. This difficulty is overcome by systematic use of weighted Sobolev spaces.