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The laws of geometric optics and their corrections are derived for scalar, electromagnetic, and gravitational waves propagating in generic curved spacetimes. Local peeling-type results are obtained, where different components of…
In this work, we obtain an unexpected geometric characterization of sphericity of a real-analytic Levi-nondegenerate hypersurface $M\subset\mathbb C^{2}$. We prove that $M$ is spherical if and only if its Segre\,(-Webster) varieties satisfy…
We study the lensing phenomena of the strong gravity regime of five-dimensional charged, equally rotating black holes with a cosmological constant, familiarly known as the Cveti\v c-L\"u-Pope black holes. These black holes are characterized…
Polarization of light is one of the fundamental concepts in optics. There are many ways to measure and characterise this feature of light but at the fundamental level it is quantum mechanics that imposes ultimate limits to such…
The intrinsic unsharpness of a quantum observable is studied by introducing the notion of resolution width. This quantification of accuracy is shown to be closely connected with the possibility of making approximately repeatable…
The properties of spin polarized pure neutron matter and symmetric nuclear matter are studied using the finite range simple effective interaction, upon its parametrization revisited. Out of the total twelve parameters involved, we now…
The paper focuses on the problem of localization in quantum mechanics. It is well known that it is not possible to define a localization observable for the photon by means of projection valued measures. Conversely, that is possible by using…
Polar coronal plumes seen during solar eclipses can now be studied with space-borne telescopes and spectrometers. We briefly discuss such observations from space with a view to understanding their plasma characteristics. Using these…
Speckle metrology is a powerful tool in the measurement of wavelength and spectra. Recently, speckle produced by multiple reflections inside an integrating sphere has been proposed and showed high performance. However, to our knowledge, a…
This is the second of two works concerning the Sobolev calculus on metric measure spaces and its applications. In this work, we focus on several approaches to vector calculus in the non-smooth setting of complete and separable metric spaces…
We analyze an experimental setup in which a quasi-monochromatic spatially coherent beam of light is used to probe a paraxial optical scatterer. We discuss the effect of the spatial coherence of the probe beam on the Mueller matrix…
Gravitational waves from compact binary mergers provide a direct measurement of luminosity distance, which, in combination with redshift information, serves as a cosmological probe. In order to statistically infer merger redshifts, the…
Spectral kernel methods are techniques for transforming data into a coordinate system that efficiently reveals the geometric structure - in particular, the "connectivity" - of the data. These methods depend on certain tuning parameters. We…
Given a Riemannian manifold $M$ endowed with a smooth metric $g$ satisfying upper and lower sectional curvature bounds, we show an equivalence property between the $\mathrm{L}^2$ norm on $M$ and the $\mathrm{L}^2$ norm on subsets $\omega$…
We develop an analytical model for calculation of optical spectra for metal nanostructures of arbitrary shape supporting localized surface plasmons (LSPs). For plasmonic systems with characteristic size below the diffraction limit, we…
Possibility of using the polarized nucleus target for testing the non-standard properties of fermionic dark matter is considered. It is assumed that the incoming dark matter scatters on the polarized nuclei in the presence of vector, axial,…
In this paper, we consider general Markov chains (MC), specified by the transition probability (kernel) $ P (x, E) $, finitely additive in the second argument. Such MC are studied within the framework of the functional operator treatment.…
A shearing interferometer is presented which uses polarization control to shear the wavefront and to modulate the interference pattern. The shear is generated by spatial walk-off in a birefringent crystal. By adjusting the orientation of…
We present theoretical and experimental studies of the optical response of L-shaped silver nanoparticles. The scattering spectrum exhibits several plasmon resonances that depend sensitively on the polarization of the incident…
In this paper we investigate the approximation properties of kernel interpolants on manifolds. The kernels we consider will be obtained by the restriction of positive definite kernels on $\R^d$, such as radial basis functions (RBFs), to a…