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Abstract: The inversion and convolution formulas are established for an intergral transform on [-1, 1]. Analytic properties of the images of functions defined in [-1, 0] and [0, 1] under such a transform can be applied to the solution of convolution type equations. Bibliography: 12 titles. Article History: Registration Date: 30/12/2005 Article note: Translated from Problemy Matematicheskogo Analiza, No. 31, 2005, pp. 67--93.

Byline: V. R. Krym (1) Abstract: A 5-manifold with a restricted smooth structure and an appropriate group of coordinate transformations including general relativity and gauge transformations is considered. An explicit expression for the Riemannian curvature of a 4-dimensional vector distribution is obtained, which implies the classical Einstein and Maxwell equations. Bibliography: 14 titles. Author Affiliation: (1) St.Petersburg State Agrarian University, Russia Article History: Registration Date: 22/10/2004

Byline: G. A. Seregin (1) Abstract: The initial boundary-value problem for the modified NavieraStokes equations is considered in the case of homogeneous Dirichlet boundary conditions. Under some assumptions, partial regularity for its solution is proved. It is shown that Hausdorff's dimension of the set of singular points is not greater than three. Bibliography: 8 titles. Author Affiliation: (1) St. Petersburg Department of the Steklov Mathematical Institute, Russia Article History: Registration Date: 12/10/2004

Abstract: L .sub.p-estimates for the nonstationary Stokes problem are established. Bibliography: 14 titles. Article History: Registration Date: 20/10/2004

Byline: V. G. Vyskrebtsov (1) Abstract: We investigate self-similar solutions of the Navier--Stokes equations for the axisymmetric flow of a viscous incompressible fluid. The original equations are transformed by the Slezkin method. On the basis of analysis of physical properties of the flow and the Slezkin general equation, we show that, in parallel with the known solutions of this equation, there exist several other solutions with physical meaning. We consider the simplest case of irrotational flows for which current lines may be circles, ellipses, parabolas, and hyperbolas. Unlike the Landau and Squire solutions, these flows are interpreted as nonjet flows of fluid flowing into and out of a homogeneous porous axially symmetric body. Author Affiliation: (1) Moscow Auto-Mechanical Institute, Russia Article History: Registration Date: 11/10/2004

The question of whether mathematical equations display social attributes is considered.