Autoresonance excitation of a breather in weak ferromagnetics

A mathematical model of the magnetodynamics of a weak ferromagnetic in an external magnetic field with variable frequency is studied. Conditions for the appearance of autoresonance are found under which the amplitude of the local magnetic inhomogeneities is considerably increased. Mathematically, the problem is to analyze the solutions to the sine-Gordon equation subject to a specific nonautonomous perturbation. For the perturbed equation, asymptotic solutions in the form of a breather with a slowly varying amplitude and a phase shift are constructed. The solutions whose amplitude increases with time from small values to quantities of order one are associated with the autoresonance phenomenon.     

Zone Structure of the Renormalization Group Flow in a Fermionic Hierarchical Model

The Gaussian part of the Hamiltonian of the four-component fermion model on a hierarchical lattice is invariant under the block-spin transformation of the renormalization group with a given degree of normalization (the renormalization group parameter). We describe the renormalization group transformation in the space of coefficients defining the Grassmann-valued density of a free measure as a homogeneous quadratic map. We interpret this space as a two-dimensional projective space and visualize it as a disk. If the renormalization group parameter is greater than the lattice dimension, then the unique attractive fixed point of the renormalization group is given by the density of the Grassmann delta function. This fixed point has two different (left and right) invariant neighborhoods. Based on this, we classify the points of the projective plane according to how they tend to the attracting point (on the left or right) under iterations of the map. We discuss the zone structure of the obtained regions and show that the global flow of the renormalization group is described simply in terms of this zone structure.     

Kinetics of oxidation of diols by ozone in aqueous solution

The kinetics of the oxidation of diols by ozone was investigated by a spectrophotometric method in the temperature interval of 277–304 K. The activation parameters of the reaction were determined.     

Isolation of ecdysterone from the inflorescences ofRhaponticum integrifolium

A method has been developed for isolating ecdysterone from the inflorescences ofRh. integrifolium. The yield is 0.15% on the weight of the raw material.Institute of the Chemistry of Plant Substances, Academy of Sciences of the Uzbek SSR, Tashkent. Translated from Khimiya Prirodnykh Soedinenii, No. 5, pp. 667–668, September–October, 1979.     

Isolation of frutitsin from the seeds ofAmorpha fruticosa

The conditions for the isolation and purification of frutitsin by various solvents and mixture of solvents have been studied. The proposed method for the isolation of frutitsin permits the yield of the substance to be increased.     

The isolation of olitoriside from jute seeds

Conclusions A polarographic method has been developed for the determination of the content of cytisine in the combined alkaloids fromThermopsis alterniflora Rgl.Khimiya Prirodnykh Soedinenii, Vol. 6, No. 1, pp. 79–82, 1970