It is found that, when the coupling constants ?p in theory of regularized Lovelock gravity are properly chosen and number tensors p??, there exist a fairly large nonsingular (singularity free) black holes universes. Some have numerous horizons energy levels (a bit like atom) inside outer event horizon. On other hand, some universes start end two de Sitter phases. The ratio densities for phases ...

The purpose of this paper is to give basic tools for the classification of nonsingular toric Fano varieties by means of the notions of primitive collections and primitive relations due to Batyrev. By using them we can easily deal with equivariant blow-ups and blow-downs, and get an easy criterion to determine whether a given nonsingular toric variety is a Fano variety or not. As applications of...

Let SO(n) act in the standard way on C and extend this action in the usual way to C = C ⊕ C. It is shown that a nonsingular special Lagrangian submanifold L ⊂ C that is invariant under this SO(n)-action intersects the fixed C ⊂ C in a nonsingular real-analytic arc A (which may be empty). If n > 2, then A has no compact component. Conversely, an embedded, noncompact nonsingular real-analytic arc...

where P is a positive definite hermitian matrix and U is a unitary matrix. In this polar representation of the matrix A, as it is called, the two matrices P and U are unique. Since the matrix P is positive definite and nonsingular, it has the same signature as the identity matrix E while the unitary matrix U is a conjunctive automorph of E. From (1) we may deduce a somewhat similar representati...

In this note we describe how to approximate some classes of singular equations by nonsingular equations. We obtain a solution to each nonsingular problem and estimates guaranteeing that the limiting function is a solution of the original problem.

In this paper, we determine the symmetrised density of a nonsingular doubly noncentral matrix variate beta type I and II distributions under different definitions.

We analyse possible cosmological scenarios on a brane where the brane acts as a dy-namical boundary of various black holes with anti-de Sitter or de Sitter asymptotics. In many cases, the brane is found to describe completely non-singular universe. In some cases, quantum gravity era of the brane-universe can also be avoided by properly tuning bulk parameters. We further discuss the creation of ...

This paper deals with measurable stationary symmetric stable random fields indexed by R and their relationship with the ergodic theory of nonsingular R-actions. Based on the phenomenal work of Rosiński (2000), we establish extensions of some structure results of stationary SαS processes to SαS fields. Depending on the ergodic theoretical nature of the underlying action, we observe different beh...

The face ring of a simplicial complex modulo m generic linear forms is shown to have finite local cohomology if and only if the link of every face of dimension m or more is nonsingular, i.e., has the homology of a wedge of spheres of the expected dimension. This is derived from an enumerative result for local cohomology of face rings modulo generic linear forms, as compared with local cohomolog...

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...