We study the existence and computation of extremal solutions of a system of inequations de ned over lattices. Using the Knaster-Tarski xed point theorem, we obtain su cient conditions for the existence of supremal as well as in mal solution of a given system of inequations. Iterative techniques are presented for the computation of the extremal solutions whenever they exist, and conditions under...

In this paper, the existence of solutions and extremal solutions for a perturbed hyperbolic differential inclusion is proved under the mixed generalized Lipschitz and Carathéodory’s conditions.

We describe a general three step method for constructing number fields with Lie-type Galois groups and discriminants factoring into powers of specified primes. The first step involves extremal solutions of the matrix equation ABC = I. The second step involves extremal polynomial solutions of the equation A(x) +B(x) +C(x) = 0. The third step involves integer solutions of the generalized Fermat e...

We prove several results from different areas of extremal combinatorics, giving complete or partial solutions to a number of open problems. These results, coming from areas such as extremal graph theory, Ramsey theory and additive combinatorics, have been collected together because in each case the relevant proofs are quite short.

A family of solutions to low energy string theory is found. These solutions represent waves traveling along “extremal black strings.” 2

We construct multi-center solutions for charged, dilatonic, non-extremal black holes in D = 4. When an infinite array of such non-extremal black holes are aligned periodically along an axis, the configuration becomes independent of this coordinate, which can therefore be used for Kaluza-Klein compactification. This generalises the vertical dimensional reduction procedure to include non-extremal...

We numerically construct static and spherically symmetric electrically charged black hole solutions in Einstein-Born-Infeld gravity with massive dilaton. The numerical solutions show that the dilaton potential allows many more black hole causal structures than the massless dilaton. We find that depending on the black hole mass and charge and the dilaton mass the black holes can have either one,...