Some empirical relations for electron mobility in II–VI compound semiconductors

Electron mobility has been calculated in a number of binary II–VI compound semiconductors using a displaced Maxwellian distribution function and taking the various scattering mechanisms into consideration at different lattice temperatures and for various amounts of ionized impurity concentrations. It is observed that the low field mobility values can be expressed by a cubic power relationship with lattice temperature and with ionized impurity concentration using a least mean square fit technique with an accuracy better than 5 per cent. Similarly, the field dependence of mobility can also be expressed as a power series of the applied electric field. It is suggested that these equations can be profitably used for a quick estimation of mobility values as a check on experiments and also as sufficiently accurate formulae for simulation and modelling purposes.     

Universal algebras

A survey of the development of the theory of universal algebras in the years 1976–1988. Such basic directions of development of this theory as classes of universal algebras (varieties, quasivarieties, etc.), Mal'tsev conditions, congruences, sheaves, homomorphisms, subalgebras, products of algebras, clones of operations, completeness, systems of equations in algeberas, and connections with computer mathematics show up in it. Considerable attention is given to concrete classes of algebras (p-algebras, BCK-algebras, unary algebras, etc.).Translated from Itogi Nauki i Tekhniki, Seriya Algebra, Topologiya, Geometriya, Vol. 27, pp. 45–124, 1989.     

Polynomial-time computation of the degree of a dominant morphism in zero characteristic. II

Consider a projective algebraic variety W which is an irreducible component of the set of all common zeros of a family of homogeneous polynomials of degrees less than d in n + 1 variables over a field of zero characteristic. Consider a dominant rational morphism from W to W′ given by homogeneous polynomials of degree d′. We suggest algorithms for constructing objects in general position related to this morphism. They generalize some algorithms from the first part of the paper to the case dim W > dim W′. These algorithms are deterministic and polynomial in (dd′)n and the size of the input. Bibliography: 12 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 325, 2005, pp. 181–224.     

Estimates for the Second Order Derivatives of Eigenvectors in Thin Anisotropic Plates with Variable Thickness

For the second order derivatives of eigenvectors in a thin anisotropic heterogeneous plate Ω_h, we derive estimates of their weighted L₂-norms with majorants whose dependence on the plate thickness h and on the eigenvalue number is expressed explicitly. These estimates maintain the asymptotic sharpness throughout the entire spectrum, whereas inside its low-frequency band the majorants remain bounded as h → +0. The latter is a rather unexpected fact, because for the first eigenfunction u¹ of a similar boundary-value problem for a scalar second order differential operator with variable coefficients, the norm ‖∇ _x ² u⁰; L₂(Ω_h)‖ is of order h⁻¹ and grows as h tends to zero. Bibliography: 35 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 308, 2004, pp. 161–180.     

Analogue of a spin flop phase transition for an array of magnetic moments with dipole interaction

In a two-dimensional array of magnetic moments with planar magnetization and relatively weak anisotropy in the basal plane, a stepwise phase transition is induced by an external magnetic field parallel to the easy axis of the system. This transition is similar to the spin flop phase transition in weakly anisotropic Heisenberg antiferromagnets with the significant difference that it is accompanied by the rearrangement of the sublattice structure of the magnet; i.e., it can be interpreted as a topological transition. The transition should manifest itself for arrays of submicron magnetic particles (magnetic dots) on nonmagnetic substrates, which have recently become the object of intensive research.     

Effect of Alkali Metal Cation on Copolymerization of Acrylamide with Salts of 2-Acrylamido-2-methylpropanesulfonic Acid in Aqueous Solutions

The kinetics of radical copolymerization of acrylamide with lithium, sodium, and potassium 2-acrylamido-2-methylpropanesulfonates in concentrated aqueous solutions in the presence of potassium persulfate as initiating agent at pH 9 and 50°C was studied by dilatometry.     

Behavior of Aluminum in Its Electric-Spark Dispersion in Aqueous Solutions of Some Acids

The influence exerted by the nature and concentration of a number of organic and mineral acids on the composition of products formed in electric-spark dispersion of aluminum was studied.