On a Nation of Resurgent Function of Several Variables

The Paper presents the definition of a resurgent a resurgent function of several independent variables. The main properties of the introduced notions are investigated.     

Noncommutative elliptic theory. Examples

We study differential operators with coefficients in noncommutative algebras. As an algebra of coefficients, we consider crossed products corresponding to the action of a discrete group on a smooth manifold. We give index formulas for the Euler, signature, and Dirac operators twisted by projections over the crossed product. The index of Connes operators on the noncommutative torus is computed.     

Fourier-Maslov transform in the space of multivalued analytic functions

Translated from Matematicheskie Zametki, Vol. 49, No. 6, pp. 107–118, June, 1991.     

The canonic operator (complex case)

We present the canonic operator method for the complex case. We prove the cocyclicity of a canonic cochain and establish a fundamental theorem on commutation.     

Elliptic Operators in Subspaces and the Eta Invariant

In this paper we obtain a formula for the fractional part of the -invariant for elliptic self-adjoint operators in topological terms. The computation of the -invariant is based on the index theorem for elliptic operators in subspaces obtained by Savin and Sternin. We also apply the K-theory with coefficients _n . In particular, it is shown that the group K(T ^* M, _n ) is realized by elliptic operators (symbols) acting in appropriate subspaces.     

Boundary value problems on manifolds with fibered boundary

We define a class of boundary value problems on manifolds with fibered boundary. This class is in a certain sense a deformation between the classical boundary value problems and the Atiyah–Patodi–Singer problems in subspaces (it contains both as special cases). The boundary conditions in this theory are taken as elements of the C *‐algebra generated by pseudodifferential operators and families of pseudodifferential operators in the fibers. We prove the Fredholm property for elliptic boundary value problems and compute a topological obstruction (similar to Atiyah–Bott obstruction) to the existence of elliptic boundary conditions for a given elliptic operator. Geometric operators with trivial and nontrivial obstruction are given. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Calculating the Thrust Characteristics of Nozzles from Their Outlet Cross-Section Parameters

Within the framework of boundary-layer theory, simple formulas are presented for finding the viscous loss from the gas parameters in the nozzle outlet cross-section. The analysis is performed for ordinary Laval nozzles and spike nozzles. It is found that for nozzles with large expansion ratios the viscous loss is almost independent of the outlet cross-section parameters and is determined only by the parameter values on the nozzle contour. The effect of the longitudinal nozzle curvature on this loss is investigated. It is shown that the viscous losses calculated from the nozzle outlet parameters and by integrating along the nozzle contour with account for the longitudinal curvature fully coincide.