Related papers: Admissible surfaces in progressive addition lenses
Vectorial analysis relating to derivation of deflection of light is presented. Curvilinear acceleration is distinguished from the Newtonian polar conic acceleration. The difference between the two is due to the curvature term. Lorentz…
Gravitationally lensed curved arcs provide a wealth of information about the underlying lensing distortions. Extracting precise lensing information from extended sources is a key component in many studies aiming to answer fundamental…
Surface incompressibility, also called inextensibility, imposes a zero-surface-divergence constraint on the velocity of a closed deformable material surface. The well-posedness of the mechanical problem under such constraint depends on an…
We investigate strong lensing by non-singular finite isothermal ellipsoids taking into account the influence of the matter along the line of sight and in the close lens vicinity. We compare three descriptions of light propagation: the full…
We analyze the performance of a planar lens based on realistic negative index material in a generalized geometry. We demonstrate that the conventional superlens design (where the lens is centered between the object and the image) is not…
In this paper we first give a Bonnet theorem for conformal Lagrangian surfaces in complex space forms, then we show that any compact Lagrangian surface in the complex space form admits at most one other global isometric Lagrangian surface…
We propose convergent plasma lenses, possibly from current sheets, as a generic solution to strong interstellar scattering. These lenses resolve the overpressure problem by geometric alignment as noted by Goldreich and Shridhar (2006). They…
We generalize an inequality for convex lattice polygons -- aka toric surfaces -- to general rational surfaces.
We study a general elliptical potential of the form $\psi(x^2+y^2/q^2)~ (0<q\le 1)$ plus an additional shear (with an arbitrary direction) as models for the observed quadruple lenses. It is shown that a minimum additional shear is needed…
Recently there were proposed some innovative convex optimization concepts, namely, relative smoothness [1] and relative strong convexity [2,3]. These approaches have significantly expanded the class of applicability of gradient-type methods…
We prove that the natural principal parameters on a given Weingarten surface are also natural principal parameters for the parallel surfaces of the given one. As a consequence of this result we obtain that the natural PDE of any Weingarten…
We briefly review some basic concepts of parallel displacement in Finsler geometry. In general relativity, the parallel translation of objects along the congruence of the fundamental observer corresponds to the evolution in time. By…
We study the infinitesimal rigidity of equivariant minimal maps from the universal cover of a smooth oriented surface (possibly non-compact) into a Riemannian symmetric space, focusing on representations arising from cyclic harmonic…
Conformal symmetry is taken as an attribute of theories of massless fields in manifolds with specific dimensionalities. This paper shows that this is not an absolute truth; it is a consequence of the mathematical representation used for the…
We consider compressible fluid flow on an evolving surface with a piecewise Lipschitz-continuous boundary from an energetic point of view. We employ both an energetic variational approach and the first law of thermodynamics to make a…
This paper continues the study of a class of compact convex hypersurfaces in Euclidean space $R^{n+1}, ~n \geq 1$, which are boundaries of compact convex bodies obtained by taking the intersection of (solid) confocal paraboloids of…
Let M be a Q-divisor on a smooth surface over C. In this paper we give criteria for very ampleness of the adjoint of the round-up of M. (Similar results for global generation were given by Ein and Lazarsfeld and used in their proof of…
The lens surface profile is derived based on the instantaneous focal length versus the lens radius data. The lens design based on instantaneous focal length versus the lens radius data has many useful applications in software assisted image…
We introduce the notion of extended admissible dissections of a marked surface, building upon the notion of an admissible dissection of a marked surface by Amiot--Plamondon--Schroll. For each extended admissible dissection we construct a…
In this paper we discuss an extension of Perelman's comparison for quadrangles. Among applications of this new comparison theorem, we study the equidistance evolution of hypersurfaces in Alexandrov spaces with non-negative curvature. We…