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).     

Two-component magnetization in Pd<Subscript>99</Subscript>Fe<Subscript>01</Subscript> thin films

Magnetometry data on 5- to 40-nm-thick PdFe films are presented for the first time. It is found that the decrease in the film thickness leads not only to the lowering of the temperature of the transition from the paramagnetic to ferromagnetic state and to the decrease in the saturation magnetization but also to the drastic changes in the film properties. In particular, the type of the temperature dependence of magnetization changes, the Curie temperature becomes strongly dependent on the applied magnetic field, and two transition temperatures are observed in zero magnetic field. The observed effects are attributed to the transition from the three-dimensional distribution of ferromagnetic clusters arising around impurity iron atoms to the two-dimensional one and can be treated within the model of impurity magnetism suggested by Korenblit and Shender.     

Lower bounds on the convergence rate of the Markov symmetric random search

The convergence rate of the Markov random search algorithms designed for finding the extremizer of a function is investigated. It is shown that, for a wide class of random search methods that possess a natural symmetry property, the number of evaluations of the objective function needed to find the extremizer accurate to cannot grow slower than |ln ɛ|.