This paper deenes a generalization of Newton's method to deal with solution paths de-ned by polynomial homotopies that lead to extremal values. Embedding the solutions in a toric variety leads to explicit scaling relations between coeecients and solutions. Toric Newton is a symbolic-numeric algorithm where the symbolic pre-processing exploits the polyhedral structures. The numerical stage uses ...

Adopting noncommutative spacetime coordinates, we determined a new solution of Einstein equations for a static, spherically symmetric matter source. The limitations of the conventional Schwarzschild solution, due to curvature singularities, are overcome. As a result, the line element is endowed of a regular DeSitter core at the origin and of two horizons even in the considered case of electrica...

We present and contrast two distinct ways of including extremal black holes in a Lorentzian Hamiltonian quantization of spherically symmetric EinsteinMaxwell theory. First, we formulate the classical Hamiltonian dynamics with boundary conditions appropriate for extremal black holes only. The Hamiltonian contains no surface term at the internal infinity, for reasons related to the vanishing of t...

A bstract We study the information paradox for eternal black hole with charges on a doubly-holographic model in general dimensions, where charged Planck brane is coupled to baths conformal boundaries. In case of weak tension, can be treated as probe such that its backreaction bulk negligible. analytically calculate entanglement entropy radiation and obtain Page curve presence an island brane. F...

0 < A0 = A1 = A3 < A2 = A4 < 0.0319, and extremal functions for A0 and A2 exist, but extremal functions for A1, A3 and A4 they do not exist. This is a simple normal families argument; it also shows that extremal functions for A0 have the boundary of the ring {z : A0 < |z| < 1} as the natural boundary, and extremal functions for A2 have the unit circle as the natural boundary. The problem is to ...

Let G be a connected k–regular bipartite graph with bipartition V (G) = X ∪Y and adjacency matrix A. We say G is det–extremal if per(A) = |det(A)|. Det–extremal k–regular bipartite graphs exist only for k = 2 or 3. McCuaig has characterized the det–extremal 3–connected cubic bipartite graphs. We extend McCuaig’s result by determining the structure of det–extremal cubic bipartite graphs of conne...

For the most part, this article is a survey of concrete results in extremal combinatorics obtained with the method of flag algebras. But our survey is also preceded, interleaved and concluded with a few general digressions about the method itself. Also, instead of giving a plain and unannotated list of results, we try to divide our account into several connected stories that often include histo...

An extensive series of neutron diffraction experiments and molecular dynamics simulations has shown that mixtures of methanol and water exhibit extended structures in solution despite the components being fully miscible in all proportions. Of particular interest is a concentration region (methanol mole fraction between 0.27 and 0.54) where both methanol and water appear to form separate, percol...

Certain non-asymptotically flat but supersymmetric classical solution of the type IIA supergravity can be interpreted as the infinitely-boosted version of the D-particle solution along the M-theory circle. By a chain of T -dual transformations, this analysis also applies to yield non-asymptotically flat solutions from the asymptotically flat and (non)-extremal solutions with intersecting D-stri...