Related papers: Trace does not preserve Reflexivity
In the scalar $\phi^4$ field model the dispersive approach to the trace anomaly is proposed. It is shown that it is impossible to get dispersion representation for all formfactors so that preserve both the translation and dilatation Ward…
Refractive optical trapping forces can be nonconservative in the vicinity of a stable equilibrium point even in the absence of radiation pressure. We discuss how nonconservative 3D force fields, in the vicinity of an equilibrium point,…
The propagation of monochromatic light through a scattering medium produces speckle patterns in reflection and transmission, and the apparent randomness of these patterns prevents direct imaging through thick turbid media. Yet, since…
The scattering of a single photon with sufficiently high energy can cause a recoil of a motional scatterer. We study its backaction on the photon's coherent transport in one dimension by modeling the motional scatterer as a two-level…
Contrary to recent claims in the literature, a simple test for reflection positivite, which we call perturbative reflection positivity in the coincidence limit, is shown to be satisfied for nonlocal field theories. Particular attention is…
We prove stable versions of trace theorems on the sphere in $L^2$ with optimal constants, thus obtaining rather precise information regarding near-extremisers. We also obtain stability for the trace theorem into $L^q$ for $q > 2$, by…
Object permanence is the concept that objects do not suddenly disappear in the physical world. Humans understand this concept at young ages and know that another person is still there, even though it is temporarily occluded. Neural networks…
Traces are used to show whether a model complies with the intended behavior. A modeler can use trace checking to ensure the preservation of the model behavior during the refinement process. In this paper, we present a trace refinement…
We derive certain constraints on the reflection matrix for reflection from a plane, nonmagnetic, optically anisotropic surface using a reciprocity theorem stated long ago by van de Hulst in the context of scattering of polarized light. The…
This paper describes how coherent backscattering is altered by an external magnetic field. In the theory presented, magneto-optical effects occur inside Mie scatterers embedded in a non-magnetic medium. Unlike previous theories based on…
We present an elementary proof concerning reciprocal transmittances and reflectances. The proof is direct, simple, and valid for the diverse objects that can be absorptive and induce diffraction and scattering, as long as the objects…
It was theoretically proposed and experimentally demonstrated that anti-reflection coating allows one to trap a high dielectric sphere, at the same time enhancing the transverse optical force. Here, by explicitly calculating the gradient…
In this article, we follow the trajectory of a photon in the human cornea. Prior to experimental evidence of the cornea's gradient refractive index (GRIN) nature, schematic eye models used a constant or average as the corneal refractive…
We prove that negative incremental resistance cannot occur on 1D spaces like the circle or the line; we construct an explicit two-dimensional model on the cylinder, and its collapse into a branched 1D backbone. We derive an accurate…
Video surveillance always had a negative connotation, among others because of the loss of privacy and because it may not automatically increase public safety. If it was able to detect atypical (i.e. dangerous) situations in real time,…
It has been shown that for left-handed metamaterials and generally for negative refraction media the refraction index cannot be entered unequivocally and cannot be considered as real, and especially as negative. This index for above…
Recently, sparse representation based visual tracking methods have attracted increasing attention in the computer vision community. Although achieve superior performance to traditional tracking methods, however, a basic problem has not been…
An example is constructed of a local ring and a module of finite type and finite projective dimension over that ring such that the module is not rigid. This shows that the rigidity conjecture is false.
Trace theorems are proved for non-isotropic Sobolev and $L^p$-Lipschitz spaces defined by vector fields satisfying H\"ormander's bracket condition of order 2. It is shown that the loss of regularity by traces is the same as in the classical…
Magnetic Faraday rotation is widely used in optics. In natural transparent materials, this effect is very weak. One way to enhance it is to incorporate the magnetic material into a periodic layered structure displaying a high-Q resonance.…