Scientific heritage of Boris Lukich Laptev (4/23/05–1/15/89)

Biographical information on the eminent Soviet geometer Boris Lukich Laptev (4/23/05–1/15-89) is given as well as a survey of his research in the areas of differential geometry and history of mathematics.Translated from Itogi Nauki i Tekhniki, Seriya Problemy Geometrii, Vol. 21, pp.27–42, 1989.     

Self-broadening in the millimeter-wave spectrum of ozone

Self broadened widths of seven lines of ozone between 75 and 120 GHz have been measured at room temperature. The variation with temperature of the self-broadening parameter for three of these lines has been studied in the range 245–292°K.     

Conditional Time Before Ruin of an Insurance Company

The statistical characteristics of conditional time before ruin of an insurance company, including the distribution function of conditional time and its moments are examined.     

On entire nonnegative solutions of quasilinear inequalities of elliptic type that vanish on a set of positive measure

In the article, it is proved that any nonnegative solution of an elliptic quasilinear inequality that vanishes on a subset of positive measure is trivial. __________ Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 25, pp. 112–118, 2005.     

A mixed‐FEM formulation for nonlinear incompressible elasticity in the plane

This article deals with an expanded mixed finite element formulation, based on the Hu‐Washizu principle, for a nonlinear incompressible material in the plane. We follow our related previous works and introduce both the stress and the strain tensors as further unknowns, which yields a two‐fold saddle point operator equation as the corresponding variational formulation. A slight generalization of the classical Babu?ka‐Brezzi's theory is applied to prove unique solvability of the continuous and discrete formulations, and to derive the corresponding a priori error analysis. An extension of the well‐known PEERS space is used to define an stable associated Galerkin scheme. Finally, we provide an a posteriori error analysis based on the classical Bank‐Weiser approach. © 2002 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 18: 105–128, 2002