Related papers: Universal Properties of Lens Proxy Pullbacks
In this work we investigate the weak lensing convergence using an end-to-end nonlinear general relativistic framework. Combining numerical relativity simulations of large-scale structure formation with general relativistic ray-tracing, we…
We solve the problem of best approximation by partial isometries of given rank to an arbitrary rectangular matrix, when the distance is measured in any unitarily invariant norm. In the case where the norm is strictly convex, we parametrize…
We present a detailed study of the curvature and symplectic asphericity properties of symmetric products of surfaces. We show that these spaces can be used to answer nuanced questions arising in the study of closed Riemannian manifolds with…
We study quadrangular properties of binary relations on a set $X$~--i.e., properties defined on configurations of four elements--~within an agonistic interpretation, where $xRy$ is interpreted as $x$ ``attacks''~$y$. Such relations induce a…
Taking matrix as a synonym for a numerical function on the Cartesian product of two (in general, infinite) sets, a simple purely algebraic "reciprocity property" says that the set of rows spans a finite-dim space iff the set of columns does…
In this note, we reformulate Donaldson's construction as a compactness result. Approximately holomorphic sections accumulate to "limit holomorphic sections" and uniform transversality properties of the approximately holomorphic sections…
Some aspects of basic category theory are developed in a finitely complete category $\C$, endowed with two factorization systems which determine the same discrete objects and are linked by a simple reciprocal stability law. Resting on this…
We present investigations of lens phenomenological properties of cosmic strings for deep galaxy surveys. General results that have obtained for lineic energy distribution are presented first. We stress that generically the local convergence…
Lens models appropriate for representing cusped galaxies and clusters are developed. The analogue of the odd number theorem for cusped density distributions is given. Density cusps are classified into strong, isothermal or weak, according…
We study and relate categories of modules, comodules and contramodules over a representation of a small category taking values in (co)algebras, in a manner similar to modules over a ringed space. As a result, we obtain a categorical…
Partial Isometries are important constructs that help give nontrivial solutions once a simple solution is known. We generalize this notion to Extended Partial Isometries and include operators which have right inverses but no left inverses…
The cusps of the caustics of any gravitational lens model can be classified into positive and negative ones. This distinction lies on the parity of the images involved in the creation/destruction of pairs occurring when a source crosses a…
We study the correlation between the locations of galaxy-galaxy strong lensing candidates and tracers of large-scale structure from both weak lensing or X-ray emission. The COSMOS survey is a unique data set, combining deep, high resolution…
This paper enhances and develops bridges between statistics, mechanics, and geometry. For a given system of points in $\mathbb R^k$ representing a sample of full rank, we construct an explicit pencil of confocal quadrics with the following…
Special relativity corresponds to hyperbolic geometry at constant velocity while the so-called general relativity corresponds to hyperbolic geometry of uniformly accelerated systems. Generalized expressions for angular momentum, centrifugal…
A group is combable if it can be represented by a language of words satisfying a fellow traveller property; an automatic group has a synchronous combing which is a regular language. This paper gives a systematic analysis of the properties…
The magnifications of the images in a strong gravitational lens system are sensitive to small mass clumps in the lens potential; this effect has been used to infer the amount of substructure in galaxy dark matter halos. I study the theory…
Within classical optics, one may add microscopic "roughness" to a macroscopically flat mirror so that parallel rays of a given angle are reflected at different outgoing angles. Taking the limit (as the roughness becomes increasingly…
This paper reviews a phenomenological approach to the gravitational lensing by exotic objects such as the Ellis wormhole lens, where exotic lens objects may follow a non-standard form of the equation of state or may obey a modified gravity…
We define the pull-back of a smooth principal fibre bundle, and show that it has a natural principal fibre bundle structure. Next, we analyse the relationship between pull-backs by homotopy equivalent maps. The main result of this article…