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)     

Elliptic translators on manifolds with multidimensional singularities

We consider translators on manifolds with many-dimensional singularities. We state the definition of ellipticity for translators, prove a finiteness (Fredholm property) theorem, and establish an index formula.     

The free charge carrier effects on elastic properties of silicon

The exact theory of the free hole contribution to the elastic moduli of p-Si taking into account all three valence bands is developed. The fair agreement is found between this theory and experimental measurements of the concentration dependence of sound velocity made for p-Si with different boron content. For n-Si analogous measurements were made and the results agree well with the theory of Keyes.     

Anderson transition criterion as found from intervalley acoustoelectron relaxation in heavily doped n-Si

Acoustic measurements are shown to be useful for the study of metal-dielectric transition in semiconductors. Squared core wave function of electron on donor centers in Si calculated from acoustic data is found to decrease at high donor densities. Critical impurity concentration is close to that obtained in other ways.     

Loss of Specific Impulse Due to Friction in Spike Nozzles

The class of nozzles with a central body, so-called spike nozzles, is considered for axisymmetric and plane central body geometries. A method of constructing the nozzle contour is outlined. The boundary layer is calculated using a three-parameter turbulence model and the loss of specific impulse due to friction in both spike nozzles and a Laval nozzle with the same expansion ratio are determined. A comparative analysis of the calculation results obtained, which makes it possible to determine the advantages and limitations of the nozzles considered, is carried out.     

The Index Locality Principle in Elliptic Theory

We prove a general theorem on the behavior of the relative index under surgery for a wide class of Fredholm operators, including relative index theorems for elliptic operators due to Gromov--Lawson, Anghel, Teleman, Booß-Bavnbek–Wojciechowski, et al. as special cases. In conjunction with some additional conditions (like symmetry conditions), this theorem permits computing the analytical index of a given operator. In particular, we obtain new index formulas for elliptic pseudodifferential operators and quantized canonical transformations on manifolds with conical singularities.     

Method of resurgent analysis in atomic collision theory

We consider the atomic collision problem in the adiabatic approximation. We show that the transition probabilities can be evaluated in this approximation using the tools of resurgent analysis. We suggest a computational algorithm for the transition probabilities and give the mathematical foundation of this algorithm. The analysis is carried out using the example of the two-level Landau-Zener model. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 112, No. 2, pp. 308–323, August, 1997.