Related papers: Asymptotics of the $k$-free diffraction measure vi…
In this paper, we analyze several critical issues in semi-device independent quantum information processing protocol. In practical experimental realization randomness generation in that scenario is possible only if the efficiency of the…
We consider point sources in hyperbolic equations discretized by finite differences. If the source is stationary, appropriate source discretization has been shown to preserve the accuracy of the finite difference method. Moving point…
Let $f$ be an analytic polynomial of degree at most $K-1$. A classical inequality of Bernstein compares the supremum norm of $f$ over the unit circle to its supremum norm over the sampling set of the $K$-th roots of unity. Many extensions…
We calculate the distribution with respect to the vacuum state of the distance-$k$ graph of a $d$-regular tree. From this result we show that the distance-$k$ graph of a $d$-regular graphs converges to the distribution of the distance-$k$…
Light propagation in a medium made of densely packed dielectric spheres is investigated by using a rigorous diffraction theory. It is shown that a substantial suppression of the local density of states occurs in spectral domains where the…
The Rayleigh diffraction limit imposes a fundamental restriction on the resolution of direct imaging systems, hindering the identification of incoherent optical sources, such as celestial bodies in astronomy and fluorophores in bioimaging.…
In this article, recent measurements of diffraction in deep inelastic scattering are presented along with QCD fits to extract the partonic structure of the exchange. These so-called diffractive parton density functions can then be used in…
We show how to analytically determine for $g\leq 1/2$ the "Friedel oscillations" of charge density by a single impurity in a 1D Luttinger liquid of spinless electrons.
We present a technique based on multi-photon detection which leads to a strong focussing of photons scattered by independent single photon emitters. For N single photon sources it is shown that if m - 1 photons are detected in a particular…
We provide a general method to analyze the asymptotic properties of a variety of estimators of continuous time diffusion processes when the data are not only discretely sampled in time but the time separating successive observations may…
We present a method for finding the asymptotics of integrals arising in solid mechanics.
In this work, we propose an easy-to-implement fixed-point algorithm for reconstructing a space-time dependent source in a subdiffusion model from lateral boundary measurements. The numerical scheme combines a Galerkin finite element method…
Precision measurements of diffraction have been performed by the H1 and ZEUS experiments at the HERA collider with high statistics for a wide kinematic range of photon virtuality $Q^2$. The diffractive parton densities are extracted by…
Resolving sources beyond the diffraction limit is important in imaging, communications, and metrology. Current image-based methods of super-resolution require phase information (either of the source points or an added filter) and perfect…
Numerical integration of ODEs by standard numerical methods reduces a continuous time problems to discrete time problems. Discrete time problems have intrinsic properties that are absent in continuous time problems. As a result, numerical…
We consider a scalar diffusion equation with a sign-changing coefficient in its principle part. The well-posedness of such problems has already been studied extensively provided that the contrast of the coefficient is non-critical.…
Established x-ray diffraction methods allow for high-resolution structure determination of crystals, crystallized protein structures or even single molecules. While these techniques rely on coherent scattering, incoherent processes like…
We derive dispersion estimates for solutions of a one-dimensional discrete Dirac equations with a potential. In particular, we improve our previous result, weakening the conditions on the potential. To this end we also provide new results…
Consider a diffusion process X=(X_t), with t in [0,1], observed at discrete times and high frequency, solution of a stochastic differential equation whose drift and diffusion coefficients are assumed to be unknown. In this article, we focus…
Sub-GeV mass dark matter particles whose collisions with nuclei would not deposit sufficient energy to be detected, could instead be revealed through their interaction with electrons. Analyses of data from direct detection experiments…