An algebraic representation of the affine Bäcklund transformation

In 1980 Chern and Terng defined a Bäcklund transformation for affine minimal surfaces. In this paper we show that this Bäcklund transformation can be simply represented by an involution and translation of the affine conormal.     

Construction of equations for classical equilibrium correlation Green's functions on the basis of kinetic equations. II

Moscow Institute of Electronic Engineering. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 89, No. 1, pp. 132–150, October, 1991.     

A generalised model and calculation of the hyperfine interaction constant for anomalous muonium in the crystalline lattice of silicon

A new microscopic model of anomalous muonium for the elemental semiconductors is proposed. The relevant configuration consisting of both a diamagrentic molecule Si−Mu and an unpaired orbital e⁻ is contained into a semivacancy of the real lattice. By using the unrestricted Hartree-Fock computational method the principal properties of the system are established. A dynamical version of the model together with a question on the formation of such system are discussed.     

The exactly resolved nonlattice model of random media based on Markov walks with a stable law for jumps

A random-medium model which is a correlated distribution of points (particles) randomly positioned in the 3-dimensional space is considered. The construction of the medium starts from a noncorrelated (Poisson) distribution of parent particles, each of them initiates a finite Markov chain of its descendants. The complete collection of correlation functions of all orders within the scope of the model have been obtained. The use of the 3-dimensional stable law (Lévy law) as a transition probability allows us to present the correlation function in an explicit form. Proceedings of the XVII Seminar on Stability Problems for Stochastic Models, Kazan, Russian, 1995, Part II.     

Multiple Wavelength Extinction Technique for Particle Characterization in Dense Particle Clouds

In utilizing the advantages of extinction measurements in micron and especially submicron particle characterization, the properties of a multiple wavelength extinction technique have been the subject of extended theoretical studies. Furthermore, an experimental set-up was designed which provides high flexibility owing to its modular design. The performance of the technique described is demonstrated by a large variety of applications in aerosol and combustion research and in large-scale industrial systems. It was found to be a reliable tool in characterizing dense particulate systems.     

Linear systems of arbitrary genus

Kalman's theory is extended to a complete, smooth, and irreducible algebraic curve of arbitrary genus.     

Resistance of composite flywheel rim to radial tensile stresses from centrifugal forces based on results of pure bending of a rim segment

A method is proposed for evaluating the resistance of a flywheel rim to radial stresses in free rotation. The method is based on loading a rim segment in pure bending and calculating the limiting moment and the corresponding limiting angular velocity. Applicability of the method is substantiated theoretically by investigating the similarity of the radial stress diagrams in rotation and pure bending. The method is verified experimentally for the strained state of a rim segment in pure bending.Translated from Mekhanika Kompozitnykh Materialov, Vol. 29, No. 4, pp. 521–526, July–August, 1993.