相关论文: A Universal Magnification Theorem III. Caustics Be…

Cluster lensing has become an important tool in the search for high redshift galaxies through its ability to magnify sources. In order to determine the intrinsic properties of these galaxies, lensing mass models must be constructed to…

Congruences, or $2$-parameter families of lines in $3$-space are of interest in many situations, in particular in geometric optics. In this paper we consider elements of their geometry which are invariant under affine changes of…

Generalized derivatives and infinitesimal spaces generalize the idea of derivatives to mappings which need not be differentiable. It is particularly powerful in the context of quasiregular mappings, where normal family arguments imply…

Let X be a non-singular algebraic curve of genus at least 3 and let M denote the moduli space of stable vector bundles of rank n and fixed determinant of degree d with n and d coprime. For any semistable bundle E over X, we can pull E back…

In this article we introduce generalized projective spaces (Definitions $[2.1, 2.5]$) and prove three main theorems in two different contexts. In the first context we prove, in main Theorem $A$, the surjectivity of the Chinese remainder…

For a representation of a connected compact Lie group G in a finite dimensional real vector space U and a subspace V of U, invariant under a maximal torus of G, we obtain a sufficient condition for V to meet all G-orbits in U, which is also…

We give a list of universal linear relations between the Euler characteristics of manifolds consisting of multisingularities of a generic Lagrangian map into a five-dimensional space. From these relations it follows, in particular, that the…

Studies of the inner regions of micro-lensed AGN during caustic crossing events have often relied upon the approximation that the magnification near a fold caustic is inversely proportional to the square root of the source-caustic distance.…

Gravitational lensing provides a unique and powerful probe of the mass distributions of distant galaxies. Four-image lens systems with fold and cusp configurations have two or three bright images near a critical point. Within the framework…

We prove that strong finite total curvature complete hypersurfaces of (n+1)-euclidean space are proper and diffeomorphic to a compact manifold minus finitely many points. With an additional condition, we also prove that the Gauss map of…

Galactic sized gravitational lenses are simulated by combining a cosmological N-body simulation and models for the baryonic component of the galaxy. The lens caustics, critical curves, image locations and magnification ratios are calculated…

The mathematical theory of gravitational lensing has revealed many generic and global properties. Beginning with multiple imaging, we review Morse-theoretic image counting formulas and lower bound results, and complex-algebraic upper bounds…

When a gravitationally lensed source crosses a caustic, a pair of images is created or destroyed. We calculate the mean number of such pairs of micro-images $<n>$ for a given macro-image of a gravitationally lensed point source, due to…

We investigate the extended source size effects on gravitational lensing in which a lens consists of a smooth potential and small mass clumps (``substructure lensing''). We first consider a lens model that consists of a clump modeled as a…

We prove a gravitational lensing theorem: the magnification of a source of uniform brightness by a foreground spherical lens is mu =1+pi(2R_E^2-R_L^2)/A, where A is the area of the source and R_E and R_L are the Einstein radius and size of…

The multiple images of lensed quasars provide evidence on the mass distribution of the lensing galaxy. The lensing invariants are constructed from the positions of the images, their parities and their fluxes. They depend only on the…

The {\em overlap number} of a finite $(d+1)$-uniform hypergraph $H$ is defined as the largest constant $c(H)\in (0,1]$ such that no matter how we map the vertices of $H$ into $\R^d$, there is a point covered by at least a $c(H)$-fraction of…

In this article, for generalized projective spaces with any weights, we prove four main theorems in three different contexts where the Unital Set Condition USC (Definition $2.8$) on ideals is further examined. In the first context we prove,…

We continue the work of [1, 2, 3] by analyzing the equivalence relation of bi-embeddability on various classes of countable planes, most notably the class of countable non-Desarguesian projective planes. We use constructions of the second…

The aim of this paper is to re-examine the question of the average magnification in a universe with some inhomogeneously distributed matter. We present an analytic proof, valid under rather general conditions, including clumps of any shape…