We paste together patches of AdS6 to find solutions which describe two 4-branes intersecting on a 3-brane with non-zero tension. We construct explicitly brane arrays with Minkowski, de Sitter and Anti-de Sitter geometries intrinsic to the 3-brane, and describe how to generalize these solutions to the case of AdS4+n, n > 2, where n n + 2-branes intersect on a 3-brane. The Minkowski and de Sitter...

In a follow–up study to a previous analysis of the IRAS 1.2Jy catalogue, we quantify the morphological fluctuations in the PSCz survey. We use a variety of measures, among them the family of scalar Minkowski functionals. We confirm the existence of significant fluctuations that are discernible in volume–limited samples out to 200hMpc. In contrast to earlier findings, comparisons with cosmologic...

We present a generalization of the Phelps lemma to locally convex topological vector spaces and show the equivalence of this theorem, Ekeland's principle and Dane s' drop theorem in locally convex spaces to their Banach space counterparts and to a Pareto eeciency theorem due to Isac. Concerning the drop theorem this solves a problem proposed by G. Isac in 1997. We show that another formulation ...

We compare the volumes of projections of convex bodies and the volumes of the projections of their sections, and, dually, those of sections of convex bodies and of sections of their circumscribed cylinders. For L ⊂ R a convex body, we take n random segments in L and consider their ‘Minkowski average’ D. For fixed n, the pth moments of V (D) (1 ≤ p < ∞) are minimized, for V (L) fixed, by the ell...

A new approach to the inverse-scattering technique of Alekseev is presented which permits real-pole soliton solutions of the Ernst equations to be considered. This is achieved by adopting distinct real poles in the scattering matrix and its inverse. For the case in which the electromagnetic field vanishes, some explicit solutions are given using a Minkowski seed metric. The relation with the co...

We prove a functional version of the Brunn-Minkowski inequality for restricted sums obtained by Szarek and Voicu-lescu. We only consider Lebesgue-measurable subsets of R n , and for A ⊂ R n , we denote its volume by |A|. If A, B ⊂ R n , their Minkowski sum is defined by A + B = {x + y, (x, y) ∈ A × B}. The classical Brunn-Minkowski inequality provides a lower bound for its volume. In their stud...

In this work we investigate the behavior of the Minkowski Functionals admitted by a sequence of sets which converge to the unit ball ‘from the inside’. We begin in R2 and use this example to build intuition as we extend to the more general Rn case. We prove, in the penultimate chapter, that convergence ‘from the inside’ in this setting is equivalent to two other characterizations of the converg...

The restriction to the sphere of an homogeneous and isotropic random field defines a spherical isotropic random field. This paper derives central and non-central limit results for the first Minkowski functional subordinated to homogeneous and isotropic Gaussian and chi-squared random fields, restricted to the sphere in R. Both scenarios are motivated by their interesting applications in the ana...

The propagation of a gravitational wave (GW) through a magnetized plasma is considered. In particular, we study the excitation of fast magnetosonic waves (MSW) by a gravitational wave, using the linearized general-relativistic hydromagnetic equations. We derive the dispersion relation for the plasma, treating the gravitational wave as a perturbation in a Minkowski background space-time. We show...

We consider various inequalities for polynomials, with an emphasis on the most fundamental inequalities of approximation theory. In the sequel a key role is played by the generalized Minkowski functional α(K,x), already being used by Minkowski and contemporaries and having occurred in approximation theory in the work of Rivlin and Shapiro in the early sixties. We try to compare real, geometric ...