Related papers: Complex Formulation of Lensing Theory and Applicat…
In this article Ehrhart quasi-polynomials of simplices are employed to determine isospectral lens spaces in terms of a finite set of numbers. Using the natural lattice associated with a lens space the associated toric variety of a lens…
Massive structures, such as galaxies, act as strong gravitational lenses on background sources. When the background source is a quasar, several lensed images are seen, as magnified or de-magnified versions of the same object. The detailed…
We present a framework that reformulates gravitational lensing as an optical phenomenon governed by an effective refractive index, enabling exploration of modified gravity theories using undergraduate-level mathematics and optics. After…
Nonlinear field theories can be used to study both standard physics questions, or to study questions such as the emergence of order and complexity. These theories are generally derived from the symmetries of a given problem and the…
There exists a well established differential topological theory of singularities of ordinary differential equations. It has mainly studied scalar equations of low order. We propose an extension of the key concepts to arbitrary systems of…
Oftentimes, Stokes' theorem is derived by using, more or less explicitly, the invariance of the curl of the vector field with respect to translations and rotations. However, this invariance -- which is oftentimes described as the curl being…
In this study, new master theorems and general formulas of integrals are presented and implemented to solve some complicated applications in different fields of science. The proposed theorems are considered to be generators of new problems,…
It is shown that the lens equation for a binary gravitational lens being a set of two coupled real fifth-order algebraic equations (equivalent to a single complex equation of the same order) can be reduced to a single real fifth-order…
A model "remarkable" fin equation is singled out from a class of nonlinear (1+1)-dimensional fin equations. For this equation a number of exact solutions are constructed by means of using both classical Lie algorithm and different modern…
This paper provides a complete theoretical treatment of the point-mass lens perturbed by constant external shear, often called the Chang-Refsdal lens. We show that simple invariants exist for the products of the (complex) positions of the…
We discuss strong gravitational lensing by multiple objects along any line of sight. The probability for strong gravitational lensing by more than one lens is small, but a number of strong lens systems in which more than one separate lens…
A logic is presented for reasoning on iterated sequences of formulae over some given base language. The considered sequences, or "schemata", are defined inductively, on some algebraic structure (for instance the natural numbers, the lists,…
It has been recently shown that the lens equation for a binary gravitational lens, which is apparently a coupled system, can be reduced to a real fifth-order (quintic) algebraic equation. Some algebraic properties of the real quintic…
A new class of functions is presented. The structure of the algorithm, particularly the selection criteria (branching), is used to define the fundamental property of the new class. The most interesting property of the new functions is that…
We establish a general unified formulation which, using the optical theorem of electromagnetic helicity, shows that dichorism is a phenomenon arising in any scattering -or diffraction- process, elastic or not, of chiral electromagnetic…
It is shown that quadrature formulas in many different applications can be derived from rational approximation of the Cauchy transform of a weight function. Since rational approximation is now a routine technology, this provides an easy new…
A perfect focus telescope is one in which all rays parallel to the axis meet at a point and give equal magnification there. It is shown that these two conditions define the shapes of both primary and secondary mirrors. Apart from scale, the…
Prompted by an observation about the integral of exponential functions of the form $f(x)=\lambda e^{\alpha x}$, we investigate the possibility to exactly integrate families of functions generated from a given function by scaling or by…
The study of astrophysical plasma lensing, such as in the case of extreme scattering events, has typically been conducted using the geometric limit of optics, neglecting wave effects. However, for the lensing of coherent sources such as…
Singularities of caustics appeared in gravitational lensing effect are discussed analytically. Multipole expansion model of lensing object is mainly studied since it is tractable and universal. Our analyses are confirmed by numerical…