We give in this paper some closed-form formulas for the maximal and minimal values of the rank and inertia of the Hermitian matrix expression A − BX ± (BX)∗ with respect to a variable matrix X. As applications, we derive the extremal values of the ranks/inertias of the matrices X and X ± X∗, where X is a (Hermitian) solution to the matrix equation AXB = C, respectively, and give necessary and s...

This article studies the existence of solutions and extremal solutions to partial hyperbolic differential equations of fractional order with impulses in Banach algebras under Lipschitz and Carathéodory conditions and certain monotonicity conditions.

We expand our previous analysis on fivebrane and membrane instanton solutions in the universal hypermultiplet, including near-extremal multi-centered solutions and mixed fivebranemembrane charged instantons. The results are most conveniently described in terms of a double-tensor multiplet.

In this paper, we study general extremal problems for non-vanishing functions in Bergman spaces. We show the existence and uniqueness of solutions to a wide class of such problems. In addition, we prove certain regularity results: the extremal functions in the problems considered must be in a Hardy space, and in fact must be bounded. We conjecture what the exact form of the extremal function is...

The Bak-Sneppen model displaying punctuated equilibria in biological evolution is studied on random complex networks. By using the rate equation and the random walk approaches, we obtain the analytic solution of the fitness threshold xc to be 1/((k)f+1), where (k)f=(k2)/(k) (=(k)) in the quenched (annealed) updating case, where kn is the nth moment of the degree distribution. Thus, the threshol...

We show how a recently discovered black ring solution with a rotating 2-sphere can be turned into two new solutions of Einstein–Maxwell–dilaton theory. The first is a four-dimensional solution describing a pair of oppositely charged, extremal black holes—known as a black dihole—undergoing uniform acceleration. The second is a five-dimensional solution describing a pair of concentric, static ext...

We investigate the recently proposed Kerr/CFT correspondence in the context of heterotic string theory. The Kerr/CFT correspondence states that the near-horizon states of an extremal four (or higher) dimensional black hole could be identified with a certain chiral conformal field theory under the conjecture that the central charges from the non-gravitational fields vanish. The corresponding Vir...