Anti-de Sitter (AdS) space can be foliated by a family of nested surfaces homeomorphic to the boundary of the space. We propose a holographic correspondence between theories living on each surface in the foliation and quantum gravity in the enclosed volume. The flow of observables between our “interior” theories is described by a renormalization group equation. The dependence of these flows on ...

We characterize the duality of convex bodies in d-dimensional Euclidean vector space, viewed as a mapping from the space of convex bodies containing the origin in the interior into the same space. The question for such a characterization was posed by Vitali Milman. Sufficient for a characterization, up to a trivial exception and the composition with a linear transformation, is the property that...

We construct a Banach space operator T ∈ B(X) such that the set JT (0) has a nonempty interior but JT (0) 6= X. This gives a negative answer to a problem raised by G. Costakis and A. Manoussos.

In this paper we introduce the notion of interval valued hesitant fuzzy soft topological space. Also the concepts of interval valued hesitant fuzzy soft closure; interior and neighbourhood are introduced here and established some important results.

In this paper we compare two approaches to automated reasoning about metric and topology in the framework of the logicMT introduced in [10].MT -formulas are built from set variables p1, p2, . . . (for arbitrary subsets of a metric space) using the Booleans ∧, ∨, →, and ¬, the distance operators ∃ and ∃≤a, for a ∈ Q, and the topological interior and closure operators I and C. Intended models for...

Traditionally, the Lighthill-Whitham-Richards (LWR) models for homogeneous and inhomogeneous roads have been analyzed in the flux-density space with the fundamental diagram of flux-density relation. In this paper, we present a new framework for analyzing the LWR model, especially the Riemann problem at a linear boundary in which the upstream and downstream links are homogeneous and initially ca...

A spectral method is described for solving coupled elliptic problems on an interior and an exterior domain. The method is formulated and tested on the two-dimensional interior Poisson and exterior Laplace problems, whose solutions and their normal derivatives are required to be continuous across the interface. A complete basis of homogeneous solutions for the interior and exterior regions, corr...

Models of spatial relations are a key component of geographical information science (GIS). EŒorts have been made to formally deŽ ne spatial relations. The foundationmodel for such a formal presentation is the 4-intersection model proposedby Egenhofer and Franzosa (1991). In this model, the topological relations between two simple spatial entities A and B are transformed into pointset topology p...