We construct and study the electrically charged, rotating black hole solution in heterotic string theory compactified on a (10 − D) dimensional torus. This black hole is characterized by its mass, angular momentum, and a (36 − 2D) dimensional electric charge vector. One of the novel features of this solution is that for D > 5, its extremal limit saturates the Bogomol’nyi bound. This is in contr...

New algorithms, based on a very efficient method to compute the A-range, have been used to extend known tables of the extremal /¡-range, to complete the solution in the case k = 3, and to find a lower bound for the extremal 2-range.

A central result in extremal set theory is the celebrated theorem of Sperner from 1928, which gives the size of the largest family of subsets of [n] not containing a 2-chain, F 1 ⊂ F 2. Erd˝ os extended this theorem to determine the largest family without a k-chain, F 1 ⊂ F 2 ⊂ · · · ⊂ F k. Erd˝ os and Katona, followed by Kleitman, asked how many chains must appear in families with sizes larger...

In this paper, we investigate extremal volumes of non-central slices of the unit cube. The case of central hyperplane sections is known and was studied in [Ha], [Ba1] [He1]. The case of non-central sections, i.e. when we dictate that the hyperplane must be a certain distance t > 0 from the center of the cube, is open in general and the same is true about sections of the unit cube by slabs, with...

A finite generalized 2d-gon of order (s, t) with d ∈ {2, 3, 4} and s 6= 1 is called extremal if t attains its maximal possible value sed , where e2 = e4 = 2 and e3 = 3. The problem of finding combinatorial conditions that are both necessary and sufficient for a finite generalized 2d-gon of order (s, t) to be extremal has so far only be solved for quadrangles and octagons. In this paper, we obta...

We discuss the stability of the extremal ground states of a two-dimensional (2D) charged black hole which carries both electric (QE) and magnetic (QM ) charges. The method is first to find the physical field and then to derive the equation of the Schrödinger type. It is found that the presenting potential to an on-coming tachyon (as a spectator) takes a barrier-well type. This provides the boun...

The purpose of this survey paper is to recall the major benchmarks of the theory of linear extremal problems in Hardy spaces and to outline the current status and open problems remaining in Bergman spaces. We focus on the model extremal problem of maximizing the norm of the linear functional associated with integration against a polynomial of finite degree, and discuss known solutions of partic...

The truncated trigonometric matrix moment problem is a well studied object. In particular, one can find in the literature the extremal value concerning the weight assigned to some point of the open unit disk within the solution set of that matrix moment problem for the so-called nondegenerate situation and some special measure which realizes the extremal value. The primary concern of the paper ...

In this paper several necessary and sufficient conditions for existence of stabilizing and antistabilizing solutions to the nonautonomous matrix Riccati differential equation (RDE) are presented. The conditions are reduced to existence of a solution to the corresponding Riccati type matrix inequality, or to existence of exponential dichotomy for the associated Hamiltonian linear differential sy...

We present new analytic and numerical results for self-gravitating SU(2)Higgs magnetic monopoles approaching the black hole threshold. Our investigation extends to large Higgs self-coupling, λ, a regime heretofore unexplored. When λ is small, the critical solution where a horizon first appears is extremal Reissner-Nordstrom outside the horizon but has a nonsingular interior. When λ is large, th...