On a class of elliptic operators with nonpolynomial degeneracy on a boundary

Rostov-on-Don. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 33, No. 5, pp. 91–99, September–October, 1992.     

An adaptive filter for gravitational-wave antennas

Summary We report on the development of an adaptive optimum filter for processing the data of a resonant bar gravitational-wave detector. This filter, based on the matched-filter theory, is adaptive in the sense that the function it realizes is derived from the actual noise spectrum of the data being analysed (instead from an idealized model of the noise). Its implementation is mostly based on frequency domain techniques. We also report on the application of the new filter to the data of the cryogenic antenna Explorer of the Rome group, with particular reference to the comparison between its performance and that of an otpimum filter with fixed values of the parameters.     

Uniformization and the diversity of Whitehead groups

Techniques of uniformization are used to prove that it is not consistent that the Whitehead groups of cardinality ℵ₁ are exactly the strongly ℵ₁-free groups. Some consequences of the assumption that every strongly ℵ₁-free group of cardinality ℵ₁ is Whitehead are derived. Other results about uniformization are also proved. Research partially supported by NSERC grant #9848. Research partially supported by the BSF. The authors thank Rutgers University for its support. Publication #441.     

Supersymmetric nonlinear graviton

Branch of Theoretical Problems, USSR Academy of Sciences, Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 26, No. 1, pp. 89–90, January–March, 1992.     

Effect of track stiffness on vibration levels in railway tunnels

The paper discusses the difficulties in comparing and drawing conclusions from vibration measurements made in different railway tunnels. A number of new measurements are presented, which have been made and analyzed on a consistent basis. The track stiffness has been determined for each of the measurements. Graphs are presented which indicate the level of rail and tunnel floor vibration likely to occur for different track stiffnesses. The variance in the measurement results also indicates the potential error in using the data to predict vibration levels in new situations.     

Initial-Boundary Value Problem for the Reynolds Lubrication Equation

The nonstationary Reynolds equation of the theory of gas lubrication is considered. The existence and uniqueness of a solution to the initial-boundary value problem for this equation are established in the case of sufficiently smooth data. Estimates for the solution are obtained for large bearing numbers. Bibliography: 8 titles.