This is the expository paper on strong axioms of infinity and elementary embeddings origi;,ally to have been authored by Reinhardt and Solovay. It has been owed for some time and already cited with some frequency in the most recent set theoretical literature. However, for various reasons the paper did not appear in print far several years. The impetus for actual publication came from a series o...

Binary black hole coalescence produces a finite burst of gravitational radiation, which propagates toward quiescent infinity. These spacetimes are analytic about infinity and contain a dimensionless coupling constant M/s, where M denotes the total mass-energy and s is an imaginary distance. This work introduces a globally convergent Fourier series in a complex radial coordinate, allowing spectr...

We describe our present understanding of the relations between the behaviour of asymptotically flat Cauchy data for Einstein’s vacuum field equations near space-like infinity and the asymptotic behaviour of their evolution in time at null infinity.

By analyzing the local and infinitesimal behavior of degenerating polarized variations of Hodge structure the notion of infinitesimal variation of Hodge structure at infinity is introduced. It is shown that all such structures can be integrated to polarized variations of Hodge structure and that, conversely, all are limits of infinitesimal variations of Hodge structure at finite points. As an i...

We study the inverse scattering problem for electric potentials and magnetic fields in R, d ≥ 3, that are asymptotic sums of homogeneous terms at infinity. The main result is that all these terms can be uniquely reconstructed from the singularities in the forward direction of the scattering amplitude at some positive energy.

We demonstrate how an exponentially strong redshift creates a sharp boundary layer at null infinity for strong gravitational fields. This leads to saturation effects by which the gravitational energy depends only linearly on amplitude, as opposed to the quadratic dependence in the weak field case.

This paper focusses on the pioneering and influential method of Pentland which automatically estimates the direction of the “sun” from a single image. We show that, under the assumptions used in the derivation of the method, the estimate of source direction is incorrect. Specifically, we show that an image-based expression used in calculating source direction diverges to infinity as the density...

We study the behavior of p-Dirichlet optimal design problem with volume constraint for p large. As the limit as p goes to infinity, we find a limiting free boundary problem governed by the infinity-Laplacian operator. We establish a necessary and sufficient condition for uniqueness of the limiting problem and, under such a condition, we determine precisely the optimal configuration for the limi...

We consider situations where the data consist of a number of responses for each individual, which may include a mix of discrete and continuous variables. The data also include a class of predictors, where the same predictor may have different physical measurements across different experiments depending on how the predictor is measured. The goal is to select which predictors affect any of the re...

We determine the weak limit of the distribution of the random variables “height” and “range” on the set of p-watermelons without wall restriction as the number of steps tends to infinity. Additionally, we provide asymptotics for the moments of the random variable “height”.