Related papers: Reflection principle and envelopes of holomorphy
There is widespread interest in estimating the fluorescence properties of natural materials in an image. However, the separation between reflected and fluoresced components is difficult, because it is impossible to distinguish reflected and…
Describing the phenomenon of total internal reflection in terms of a reflection coefficient of unit magnitude, we found that, not only can propagating plane waves be total internally reflected at the planar interface of two dissimilar,…
In this note we give a positive answer to a question asked by Y. Colin de Verdi\`ere concerning the converse of the following theorem, due to A. N. Varchenko: two germs of volume forms are equivalent with respect to diffeomorphisms…
In this article, we develop an explicit categorical realization of sheafification based on colimits, products, and subobjects, emphasizing its behavior in algebraic and topological-algebraic settings. We prove that if $\mathcal{C}$ is a…
Approximate expressions for X-ray resonant and M\"ossbauer reflectivity in the total external reflection region are developed for the limiting cases of a semiinfinite mirror with a small resonant addition to the total susceptibility and for…
Light reflection plays a crucial role in a number of modern technologies. In this paper, analytical expressions for maximal reflected power in any direction and for any polarization are given for generic planar structures made of a single…
We propose a notion of critical set for two-dimensional surface diffeomorphisms as an intrinsically defined object designed to play a role analogous to that of critical points in one-dimensional dynamics.
Here we show that for a C^2 surface diffeomorphism that satisfy the hypothesis of Hayashi connecting lemma either can be approximated, in the C^1 topology, by a diffeomorphism exhibiting a homoclinic tangency or the diffeomorphism already…
The purpose of this article is to show a second main theorem with the explicit truncation level for holomorphic mappings of $ \mathbb{C} $ (or of a compact Riemann surface) into a compact complex manifold sharing divisors in subgeneral…
The theoretical description for the reflectivity properties of dielectric, metal and semiconductor plates coated with graphene is developed in the framework of the Dirac model. Graphene is described by the polarization tensor allowing the…
We propose a proof of the characterization of spherical hypersurfaces as the only strictly pseudoconvex hypersurfaces which have contracting germs of diffeomorphisms. Unlike previous proofs, our approach does not use Chern-Moser theory. It…
We present evidence supporting wave reflection in the lower solar chromosphere based on helioseismic analysis of multi-height Doppler data. This evidence is derived through a wave propagation model that incorporates both upward- and…
The notion of a "root base" together with its geometry plays a crucial role in the theory of finite and affine Lie theory. However, it is known that such a notion does not exist for the recent generalizations of finite and affine root…
Let M be a connected real-analytic hypersurface in two dimensional complex space, $\mathbb C^2$, containing a connected complex hypersurface E, and let f be a smooth CR mapping sending M into another real-analytic hypersurface M' in…
We prove finite jet determination results for smooth CR embeddings which are of constant degeneracy, using the method of complete systems. As an application, we derive a reflection principle for mappings between a Levi-nondegenerate…
Score-based diffusion models learn to reverse a stochastic differential equation that maps data to noise. However, for complex tasks, numerical error can compound and result in highly unnatural samples. Previous work mitigates this drift…
We present a novel method, based on the Saunderson corrections, to predict the reflectance between a liquid interface and a dielectric diffuser. In this method, the diffuse properties of the dielectric are characterized using a single…
Removing reflection artefacts from a single image is a problem of both theoretical and practical interest, which still presents challenges because of the massively ill-posed nature of the problem. In this work, we propose a technique based…
Scattering from conformal interfaces in two dimensions is universal in that the flux of reflected and transmitted energy does not depend on the details of the initial state. In this letter, we present the first gravitational calculation of…
This paper aims at reviewing and analysing the method of reflections. The latter is an iterative procedure designed to linear boundary value problems set in multiply connected domains. Being based on a decomposition of the domain boundary,…