Unlike the extremal Reissner-Nordström black hole in ordinary spacetime, the one in anti-de Sitter spacetime is a minimum of action and has zero entropy if quantization is carried out after extremaliza-tion. However, if extremalization is carried out after quantization, then the entropy is a quarter of the area as in the usual case. While the entropy of ordinary (non-extremal) black holes has b...

In this paper, we show a method for finding all extremal rays of polyhedral convex cones with some complementarity conditions. The polyhedral convex cone is defined as the intersection of half-spaces expressed by linear inequalities. By a complementarity extremal ray, we mean an extremal ray vector that satisfies some complementarity conditions among its elen~nts. Our method is iterative in the...

In this paper, we construct new families of graphs whose automorphism groups are transitive on 3-paths. These graphs are constructed from certain Lie algebras related to generalized Kac-Moody algebras of rank two. We will show that one particular subfamily gives new lower bounds on the number of edges in extremal graphs with no cycles of length fourteen.

A k-uniform hypergraph is s-almost intersecting if every edge is disjoint from exactly s other edges. Gerbner, Lemons, Palmer, Patkós and Szécsi conjectured that for every k, and s > s0(k), every k-uniform s-almost intersecting hypergraph has at most (s + 1) ( 2k−2 k−1 ) edges. We prove a strengthened version of this conjecture and determine the extremal graphs. We also give some related result...

The intersection shadow theorem of Katona is an important tool in extremal set theory. The original proof is purely combinatorial. The aim of the present paper is to show how it is using linear independence latently.

Let G ⊂C be a bounded simply connected domain with boundary Γ and let E ⊂G be a regular compact set with connected complement. In this paper we investigate asymptotics of the extremal constants: χn = inf p∈Pkn sup q∈Pn−kn ||pq ||E ||pq ||Γ , n = 1,2, . . . , where ‖ ·‖K is the supremum norm on a compact set K ,Pm is the set of all algebraic polynomials of degree at most m, and kn/n→ θ ∈ [0,1] a...

We study s-extremal codes over F4 or over F2. A Type I self-dual code over F4 or over F2 of length n and minimum distance d is s-extremal if the minimum weight of its shadow is largest possible. The purpose of this paper is to give some results which are missing in a series of papers by Bachoc and Gaborit [2], by Gaborit [6], and by Bautista, et. al. [1]. In particular, we give an explicit form...

Non-extremal intersecting p-brane solutions of gravity coupled with several antisymmetric fields and dilatons in various space-time dimensions are constructed. The construction uses the same algebraic method of finding solutions as in the extremal case and a modified “no-force” conditions. We justify the “deformation” prescription. It is shown that the non-extremal intersecting p-brane solution...