Reaction of methyl bromopropiolate with diamines as a method of synthesis of imidazolidine derivatives

A convenient method of synthesis of 2-(methoxycarbonylmethylene)-substituted imidazolidines and imidazolidinium bromides, and also of bicyclic diazo compounds has been developed starting from methyl bromopropiolate and ethylenediamine and its derivatives.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 9, pp. 1205–1208, September, 1991.     

A differential-geometric criterion of the kinematic integrability of nonlinear differential equations

A theorem on the existence of a G-representation and a differential-geometric criterion of the kinematic integrability for nonlinear differential equations from the Λ²-G-classes is proved. Examples of zero-curvature representations and metrics for some equations of mathematical physics are presented. __________ Translated from Fundamental’naya i Prikladnaya Matematika (Fundamental and Applied Mathematics), Vol. 11, No. 1, Geometry, 2005.     

Picosecond dynamics of intramolecular charge transfer in benzophenone amino derivatives

Institute of Molecular and Atomic Physics, Academy of Sciences of Belarus, 70 F. Skaryna Ave, Minsk 220072, Belarus. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 62, No. 3, pp. 49–55, May–June, 1995.     

Interaction between indigo and adsorbed protein as a major factor causing backstaining during cellulase treatment of cotton fabrics

A model microassay system was developed to measure indigo backstaining on cotton fabrics in the presence of enzymes on a small laboratory scale. Backstaining indexes for 11 cellulase samples were measured, and the enzymes were ranked from lower to higher backstaining. Two multienzyme cellulase preparations were separated into fractions using chromatofocusing on a Mono P column. Adsorption ability and backstaining properties of purified enzyme fractions were studied. Evidence was obtained that protein adsorption on cotton fabrics is a crucial parameter causing backstaining (both for crude cellulase samples and purified enzyme components).     

Sol–gel preparation and white up-conversion luminescence in rare-earth doped PbF<Subscript>2</Subscript> nanocrystals dissolved in silica glass

89.5(SiO₂)10(PbF₂)0.5(REF₃) silicate glasses have been prepared using room temperature sol–gel processing of Si(OCH₂CH₃)₄, Pb(CH₃COO)₂·3H₂O, RE(CH₃COO)₃·nH₂O and trifluoroacetic acid as a fluorinating agent, where RE stands for rare-earth ions, such as Yb³⁺, Er³⁺, Ho³⁺, Tm³⁺, or combinations of those ions. On heat treatment of these glasses at about 300–400 °C, the rare-earth doped spherical PbF₂ nanocrystals precipitate within SiO₂ glass matrix providing transparent nano-structured glass–ceramics, while the diameter of the nanocrystals can be set in the range from 5 to 25 nm by varying time and temperature of the heat treatment. The structural and photoluminescence studies confirm the incorporation of rare-earth ions into the PbF₂ nanocrystals and white and tuneable colour up-conversion luminescence has been detected in case of Yb³⁺-Er³⁺-Tm³⁺ and Yb³⁺-Ho³⁺-Tm³⁺ co-doped nanocrystals by varying dopant ratio and pump power.     

Interiors of sets of vector fields with shadowing corresponding to certain classes of reparameterizations

The structure of the C ¹-interiors of sets of vector fields with various forms of the shadowing property is studied. The fundamental difference between the problem under consideration and its counterpart for discrete dynamical systems generated by diffeomorphisms is the reparameterization of shadowing orbits. Depending on the type of reparameterization, Lipschitz and oriented shadowing properties are distinguished. As is known, structurally stable vector fields have the Lipschitz shadowing property. Let X be a vector field, and let p and q be its points of rest or closed orbits. Suppose that the stable manifold of p and the unstable manifold of q have a nontransversal intersection point. It is shown that, in this case, the vector field X does not have the Lipschitz shadowing property. If one of the orbits p and q is closed, then X does not have the oriented shadowing property. These assertions imply that the C ¹-interior of the set of vector fields with the Lipschitz shadowing property coincides with the set of structurally stable vector fields. If the dimension of the manifold under consideration is at most 3, then a similar result is valid for the oriented shadowing property. We study the structure of the C ¹-interiors of sets of vector fields with various forms of the shadowing property. It is shown that, in the case of the Lipschitz shadowing property, it coincides with the set of structurally stable systems. For manifolds of dimension at most 3, a similar result is valid for the oriented shadowing property.