Mathematics |
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1998, No. 4
L.M. Berkovich, I.S. Orlova
THE EXACT LINEARIZATION SOME CLASSES OF AUTONOMOUS ORDINARY DIFFERENTIAL EQUATIONS
The method of exact linearization nonlinear nonautonomous odinary differentional equations of n-order suggested by one of the authors is demonstrated in works [1] and [2]. This method is based on the factorization of nonlinear O.D.E. through nonlinear differentional the rst order`s operators, and also is based on using both point and nonpoint transformation. Exact linearization some classes the second`s, the third`s, the forth`s ordezs O.D.E is given in this work. For the rst time common form of autonomous the forth order equations is found, admitting exact linearization with using nonpoint transformation. Formulas has got in quadratures for finding common and partial solutions of investigating equations classes.
B.V. Loginov
BRANCHING OF SOLUTIONS OF NONLINEAR EQUATIONS AND GROUP SYMMETRY
A survey of the author investigations on the usage of continuous and discrete group symmetry for construction and investigation of branching equation at stationary and Andronov-Hopf bifurcation is given. The advantages of group analysis methods (RZMat 1978 11Á883K) in this direction are based. It is shown that the bifurcation theory methods allow to investigate also the stability of bifurcating solutions (RZMat 1992 7Á916). Applications to symmetry breaking problems (phase transitions theory, surface waves) are given.
S.Yu. Popov
GALOIS LATTICES AND THEIR BIRATIONAL INVARIANTS
The Picard class p(
) of a torsion-free Ï-module of finite Z-rank is a very important algebraic invariant. It defines an algebraic torus T up to stable equivalen p() is presently in incipient stage. In this paper, birational invariants 
are calculated, here is a Ï-module of low Z-rank.
M.G. Svistula
ABOUT CONNECTEDNESS OF THE RANGE OF FINITELY ADDITIVE GROUP VALUED MEASURE
It is shown that any finitely addative exhaustive quasi-monotone measure with a half property taking values in a topological abelian group without second order cyclic elements has pathwise connected range (a local compactness of the group is not required).
A.N. Stepanov
ABOUT THE PARAMETRIC MODEL OF POINT DIRECTIONAL SOURCE
The theoretical foundation of using parametric model of point directional source is considered, and the condition at satisfaction which instead of real sources with arbitrary spatial extend may be used equivalent point directional source is drawn out.
S.Ya. Shatskih, E.M. Knutova
The paper is devoted to the study of asymptotic properties of stable spherically symmetric distribution with exponent α=2/3 in Hilbertian space. Almost sure convergence of conditional distributions to normality is proved. Explicit expressions for infinite-dimensional conditional quantiles and for their distribution functions are found.