Mathematics

1998, No. 2

V.E. Voskresenskii

BIRATIONAL GEOMETRY AND ARITHMETIC OF LINEAR ALGEBRAIC GROUPS, III

The first four chapters of this work have been published in the issues of Vestnik Samara State University No. 2 and No. 4, 1997. In the fifth chapter we describe in details the construction of the famous Tamagawa measure in adele groups. Tamagawa numbers have been calculated in some important cases. We deduce Siegel formula in Tamagawa form and show its appiication for some classical examples. We give the detailed calculation of the local p-adic volumes which are necessary for obtaining the exact formulas.

V.G. Mosin

PRIMITIVE IDEALS AND SYMPLECTIC LEAVES OF QUANTUM MATRIXES (PART 2)

The dimensions of symplectic leaves on Poisson structure associated with quantum m × n -matrixes are calculated.

L.S. Pulkinа

ON SOLVABILITY OF THE NONLOCAL PROBLEM WITH INTEGRAL CONDITIONS FOR HYPERBOLIC EQUATION

In this paper the existence and uniqeness of the generalized solution of certain nonlocal problem are proved. With this end in view two-sided a priori estimates are established.

O.P. Filatov

THE EXISTENCE OF THE LIMITS OF MAXIMAL MEANS FOR ALMOST-PERIODIC FUNCTIONS OF SOME VARIABLES

It is proved that the limit , where f : R_m→R is a continuouse almost-periodic functions and the supremum is taken over all solutions of the differential inclusion , compact G⊂ R_m, alwayse exists.