The classical convergence result for the additive Schwarz preconditioner with coarse grid is based on a stable decomposition. The result holds for discrete versions of the Schwarz preconditioner, and states that the preconditioned operator has a uniformly bounded condition number that depends only on the number of colors of the domain decomposition, the ratio between the average diameter of the...

A class of four-dimensional static supersymmetric black hole solutions of effective supergravity Lagrangian of IIA superstring compactified on T 6 is constructed by explicitly solving Killing spinor equations (KSEs). These solutions are dyonic black holes parametrized by four charges, with dilaton and diagonal internal metric components as the only non-zero scalar fields, and preserve 18 of N =...

The Schwarz method can be used for the iterative solution of elliptic boundary value problems on a large domain Ω. One subdivides Ω into smaller, more manageable, subdomains and solves the differential equation in these subdomains using appropriate boundary conditions. Schwarz-Robin methods use Robin conditions on the artificial interfaces for information exchange at each iteration. Optimized S...

The Schwarz map of the hypergeometric differential equation is studied first by Schwarz, and later by several authors for various generalizations of the hypergeometric equation. But up to now nothing is studied about the Schwarz map for confluent equations, mainly because such a map would produce just a chaos. Recently we defined the hyperbolic Schwarz map, and studied in several cases, includi...

The classical convergence result for the additive Schwarz preconditioner with coarse grid is based on a stable decomposition. The result holds for discrete versions of the Schwarz preconditioner, and states that the preconditioned operator has a uniformly bounded condition number that depends only on the number of colors of the domain decomposition, the ratio between the average diameter of the...

Reverses of the Schwarz, triangle and Bessel inequalities in inner product spaces that improve some earlier results are pointed out. They are applied to obtain new Grüss type inequalities. Some natural integral inequalities are also stated.

Theories of partial supersymmetry breaking N = 2 → N = 1 in four dimensions are derived by coupling the N = 2 massless gravitino multiplet to N = 2 supergravity in five dimensions and performing a generalized dimensional reduction on S/Z2 with the Scherk-Schwarz mechanism. These theories agree with results that were previously derived from four dimensions.