相关论文: Two-mirror Schwarzschild aplanats. Basic relations

We discuss a new technology that promises large inexpensive mirrors. We argue that it should be possible to tilt a rotating viscous liquid by perhaps as much as a few tens of degrees. The tilted liquid parabolic surface is used as the…

This paper uses the Schwarzschild metric to derive an effective refractive index and acceleration vector that account for relativistic deflection of light rays, in an otherwise classical kinematic framework. The new refractive index and the…

Bringmann, Guerzhoy and Kane have shown how to correct mock modular forms by a certain linear combination of the Eichler integral of their shadows in order to obtain p-adic modular forms in the sense of Serre. In this paper, we give a new…

We consider the following geometric optics problem: Construct a system of two reflectors which transforms a spherical wavefront generated by a point source into a beam of parallel rays. This beam has a prescribed intensity distribution. We…

Albert Einstein postulated the equivalence of energy and mass, developed the theory of special relativity, explained the photoelectric effect, and described Brownian motion in five papers, all published in 1905, 100 years ago. With these…

We explain how the geometric framework introduced in arXiv:2508.11621 [math.AG] provides a universal property for the 2-rings of perfect complexes on qcqs spectral or Dirac spectral schemes. As an application, given a qcqs spectral or Dirac…

A promising way to introduce general relativity in the classroom is to study the physical implications of certain given metrics, such as the Schwarzschild one. This involves lower mathematical expenditure than an approach focusing on…

Ten years ago, Beresnevich-Dickinson-Velani initiated a project that develops the general Hausdorff measure theory of dual approximation on non-degenerate manifolds. In particular, they established the divergence part of the theory based on…

A new method for absolute polarimetric calibration of large telescopes is presented. The proposed method is highly accurate and is based on the calibration of a small sub-aperture, which is then extended to the full system by means of…

There were two famous conjectures on complete affine maximal surfaces, one due to E. Calabi, the other to S.S. Chern. Both were solved with different methods about one decade ago by studying the associated Euler-Lagrange equation. Here we…

Gravitational lensing is a well known phenomenon predicted by the General Theory of Relativity. It is now a well-developed observational technique in astronomy and is considered to be a fundamental tool for acquiring information about the…

The analysis of the shear induced by a single cluster on the images of a large number of background galaxies is all centered around the curl-free character of a well-known vector field that can be derived from the data. Such basic property…

In general relativity, an IDEAL (Intrinsic, Deductive, Explicit, ALgorithmic) characterization of a reference spacetime metric $g_0$ consists of a set of tensorial equations $T[g]=0$, constructed covariantly out of the metric $g$, its…

We report the discovery of the first example of an Einstein zig-zag lens, an extremely rare lensing configuration. In this system, J1721+8842, six images of the same background quasar are formed by two intervening galaxies, one at redshift…

Dual pseudo splines constitute a new class of refinable functions with B-splines as special examples, which was introduced in \cite{DHSS}. In this paper, we shall construct Riesz wavelet associated with dual pseudo splines. Furthermore, we…

Zernike polynomials are commonly used to represent the wavefront phase on circular optical apertures, since they form a complete and orthonormal basis on the unit disk. In [Diaz et all, 2014] we introduced a new Zernike basis for elliptic…

In the neighborhood of Sgr A*, several stars (S2, S12, S14, S1, S8, S13) enjoy an accurate determination of their orbital parameters. General Relativity predicts that the central black hole acts as a gravitational lens on these stars,…

It is shown that the problem of designing a two-reflector system transforming a plane wave front with given intensity into an output plane front with prescribed output intensity can be formulated and solved as the Monge-Kantorovich mass…

Refinements of some recent reverse inequalities for the celebrated Cauchy-Bunyakovsky-Schwarz inequality in 2-inner product spaces are given. Using this framework, applications for determinantal integral inequalities are also provided.

We present a classification of the so-called "additive symmetric 2-cocycles" of arbitrary degree and dimension over Z/p, along with a partial result and some conjectures for m-cocycles over Z/p, m > 2. This expands greatly on a result…