Mathematics

1995, Special Issue

L.M. Berkovich

THE METHOD OF AN EXACT LINEARIZATION N-ORDER ORDINARY DIFFERENTIAL EQUATIONS

In this paper necessary and sufficient conditions are found for an n-order nonlinear neautonomous ordinary differential equation to be transformed into a n-order linear ordinary differential equation with constant coefficients. These conditions are expressed in the terms of a factorization through nonlinear differential first order operators.

V.E. Voskresenskii, T.V. Fomina

THE INTEGER STRUCTURES IN ALGEBRAIC TORI

Let O be an integer domain with quotient field k, and let G be a linear algebraic group denned over the field k. By an integer form of the group G we mean a group scheme X over 0 such that k-groups and G are isomorphic. The principal results of the article is the construction of the minimal integer model of the algebraic torus defined over the field of P-adic numbers and investigation the structure of this model. To study the model in the case of ramified field of decomposition is the main problem. We describe reductions of these models on prime modules. Minimal models of tori over the ring of integers of algebraic number field are constructed. We calculate local volumes and class numbers of some models.

I.V. Demin

THE DEGREE OF THE RULED FANO MANIFOLDS

This paper gives the example of the function which bounds in each dimension the degree of Fano manifolds for which there exists a morphism onto Pⁿ whose fibers are smooth rational curves.

I.A. Andreev, V.A. Sobolev

THERMAL EXPLOSION CRITICAL CONDITIONS FOR AUTOCATALYTIC REACTION WITH REGARD TO HEAT CONDUCTIVITY

This paper is devoted to the application of the integral manifolds method and the duck-trajectories techniques for the modeling of critical phenomena in the singularly perturbed models of chemical kinetics.

S.V. Ozerskii

DECOMPOSITION OF BOUNDARY VALUE PROBLEMS WITH SINGULAR PERTURBATIONS

In this paper we are concerned with the possibility of decomposition of linear and nonlinear singularly perturbed boundary value problems to the problems of lower dimension with respect to slow and fast variables. The applicability of the considered method in the Banach spaces is examined.

E.A. Schepakina

INTEGRAL MANIFOLDS, DUCK-TRAJECTORIES AND THERMAL EXPLOSION

In this paper the class of nonlinear singularly perturbed systems of differential equations is investigated. Such systems are used for problems of combustion theory modeling.