Given a 3-uniform hypergraph F , let ex3(n,F) denote the maximum possible size of a 3-uniform hypergraph of order n that does not contain any subhypergraph isomorphic to F . Our terminology follows that of [16] and [10], which are comprehensive survey articles of Turán-type extremal graph and hypergraph problems, respectively. Also see the monograph of Bollobás [2]. There is an extensive litera...

We discuss the nonextremal generalisation of the enhançon mechanism. We find that the nonextremal shell branch solution does not violate the Weak Energy Condition when the nonextremality parameter is small, in contrast to earlier discussions of this subject. We show that this physical shell branch solution fills the mass gap between the extremal enhançon solution and the nonextremal horizon bra...

for a bounded linear operator on hilbert space we define a sequence of the so-called weakly extremal vectors‎. ‎we study the properties of weakly extremal vectors and show that the orthogonality equation is valid for weakly extremal vectors‎. ‎also we show that any quasinilpotent operator $t$ has an hypernoncyclic vector‎, ‎and so $t$ has a nontrivial hyperinvariant subspace‎.

Recent work has demonstrated an attractor mechanism for extremal rotating black holes subject to the assumption of a near-horizon SO(2, 1) symmetry. We prove the existence of this symmetry for any extremal black hole with the same number of rotational symmetries as known four and five dimensional solutions (including black rings). The result is valid for a general two-derivative theory of gravi...

We examine the tail behaviour and extremal cluster characteristics of two-state Markov-switching autoregressive models where the first regime behaves like a random walk, the second regime is a stationary autoregression, and the generating noise is light-tailed. Under additional technical conditions we prove that the stationary solution has asymptotically exponential tail and the extremal index ...

D-brane technology has made it possible to identify and precisely count the degenerate quantum states responsible for the entropy of certain extremal, BPS-saturated black holes. Here we give a Type-II D-brane description of a class of extremal and non-extremal five-dimensional Reissner-Nordström solutions. We identify degenerate D-brane configurations that give rise to the Reissner-Nordström so...

We consider string theory corrections to 4D black holes which are solutions of the 5D vacuum Einstein equations. We find that the corrections vanish only for the extremal electric solution. We also show that for the non-extremal electric black hole the mass corrections are related to the charge corrections. The implications to string states counting and the correspondence principle for black ho...

Let α ∈ C in the upper half-plane and let I be an interval. We construct an analogue of Selberg’s majorant of the characteristic function of I that vanishes at the point α. The construction is based on the solution to an extremal problem with positivity and interpolation constraints. Moreover, the passage from the auxiliary extremal problem to the construction of Selberg’s function with vanishi...

This paper presents an approach to compute the neighboring extremal solution for an optimal switched impulsive control problem with a pre-specified sequence of modes and a large perturbation in the initial state. The decision variables – the subsystem switching times and the control parameters – are subject to inequality constraints. Since the active status of these inequality constraints may c...

We consider a multidimensional extremal problem formulated in terms of tropical mathematics. The problem is to minimize a nonlinear objective function, which is defined on a finite-dimensional semimodule over an idempotent semifield, subject to linear inequality constraints. An efficient solution approach is developed which reduces the problem to that of solving a linear inequality with an exte...