We show that every automorphism of a diagonal limit of finite symmetric groups is locally inner.

Basic statements of the theory of the approximation of ordinary differential operators by other ordinary differential operators are given. Approximating operators are not the equal on the given system of functions (functional ...

A system of linear differential equations with constant coefficients is transformed to the linear-diagonal form. Explicit formulas of a nonlinear transformation of the Jordan normal form for the linear differential system ...

We consider a new class of evolutionary equations with operators constructed by non-smooth homogeneous symbols. The theory of the Cauchy problem with initial conditions which are generalized functions of the distribution ...

We investigate the best approximations eσ(f) of the integrals of functions of the spaces Lp(A,dμ) by the integrals of rank σ. We find the exact values of the upper bounds of these approximations in the case where the ...

The exact analytical solution of a stationary heat problem for two-component cylindric spaces is constructed by the method of integral transforms.

Some basic statements of the theory of the approximation of differential operators with partial derivatives by other differential operators with partial derivatives are given. The approximated and approximating operators ...

A new numerical-analytic method for investigating the boundary-value problems for nonlinear differential systems is suggested.

We develop some methods which allow studying properties of the controller of a faithful prime ideal I of the group algebra kA of a torsion-free Abelian group A of finite rank over a field k. We apply some results of the ...

We study a boundary-value problem elliptic in the sense of Petrovskii for a system of partial differential equations over a bounded domain. We prove that the operator of the problem is a Fredholm one in a refined scale of ...