相关论文: Do Fresnel coefficients exist?

We obtain an essential spectral gap for $n$-dimensional convex co-compact hyperbolic manifolds with the dimension $\delta$ of the limit set close to $(n-1)/2$. The size of the gap is expressed using the additive energy of stereographic…

Using the formalism of polynomials with positive coefficients, the fact that exactly half of all subsets of a finite set have even cardinality can be generalized asymptotically.

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…

A planewave incident on an active etalon with net roundtrip gain may be expected to diverge in field amplitude, yet Maxwell's equations admit only a convergent solution. By examining a Gaussian beam obliquely incident on such a cavity, we…

We formally prove the existence of an enduring incongruence pervading a widespread interpretation of the Bell inequality and explain how to rationally avoid it with a natural assumption justified by explicit reference to a mathematical…

The concept of the diffraction limit put forth by Ernst Abbe and others has been an important guiding principle limiting our ability to tightly focus classical waves, such as light and sound, in the far field. In the past decade, numerous…

Spatial resolution of most imaging devices is fundamentally restricted by diffraction. This limitation is manifested in the loss of high spatial frequency information contained in evanescent waves. As a result, conventional far-field optics…

We are concerned with the inverse scattering problem of recovering an inhomogeneous medium by the associated acoustic wave measurement. We prove that under certain assumptions, a single far-field pattern determines the values of a…

Space-time modulation-based metamaterials have recently spurred considerable interest, owing to the fundamental addition of the time dimension to the medium parameters, and resulting novel properties and potential applications. However, the…

Recently a restriction ("quantum inequality-type relation") on the (renormalized) energy density measured by a static observer in a "globally static" (ultrastatic) spacetime has been formulated by Pfenning and Ford for the minimally coupled…

We prove Fourier restriction estimates by means of the polynomial partitioning method for compact subsets of any sufficiently smooth hyperbolic hypersurface in threedimensional euclidean space. Our approach exploits in a crucial way the…

We address the problem of super-resolution line spectrum estimation of an undersampled signal with block prior information. The component frequencies of the signal are assumed to take arbitrary continuous values in known frequency blocks.…

Recently it has been proposed that a planar slab of material, for which both the permittivity and permeability have the values of -1, could bring not only the propagating fields associated with a source to a focus, but could also refocus…

Quadratic irrationals posses a periodic continued fraction expansion. Much less is known about cubic irrationals. We do not even know if the partial quotients are bounded, even though extensive computations suggest they might follow…

The model of unstable particles with random mass is suggested to describe the finite-width effects. The phenomenological manifestation of mass smearing is discussed in the framework of the model.

We prove a quantitative isoperimetric inequality for the Gaussian fractional perimeter using extension techniques. Though the exponent of the Fraenkel asymmetry is not sharp, the constant appearing in the inequality does not depend on the…

Numerous results on self-reciprocal polynomials over finite fields have been studied. In this paper we generalize some of these to a-self reciprocal polynomials defined in [4]. We consider some properties of the divisibility of a-reciprocal…

We bound the number of electromagnetic signals which may be observed over a frequency range $[F-W,F+W]$ a time interval $[0,T]$ within a sphere of radius $R$. We show that the such constrained signals may be represented by a series…

We address an unusual problem in the theory of elasticity motivated by the problem of reconstructing the strain field from partial information obtained using X-ray diffraction. Referred to as either high-energy X-ray diffraction…

We study the problem of recovering an unknown compactly-supported multivariate function from samples of its Fourier transform that are acquired nonuniformly, i.e. not necessarily on a uniform Cartesian grid. Reconstruction problems of this…