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Using a reference system approach, we develop an analytical theory for the adsorption of random heteropolymers with exponentially decaying and/or oscillating sequence correlations on planar homogeneous surfaces. We obtain a simple equation…
Line spectral estimation is a classical signal processing problem that aims to estimate the line spectra from their signal which is contaminated by deterministic or random noise. Despite a large body of research on this subject, the…
Here we introduce a generalization of the exponential sampling series of optical physics and establish pointwise and uniform convergence theorem, also in a quantitative form. Moreover we compare the error of approximation for Mellin…
We consider special Lambert series as generating functions of divisor sums and determine their complete transseries expansion near rational roots of unity. Our methods also yield new insights into the Laurent expansions and modularity…
The problem of the one-exciton absorption spectrum is considered for the lattice of two-level interacting atoms whose initial energy splitting depends on the coordinate. It is shown that for some types of interatomic interaction, this…
We derive bounds on the volume of an inclusion in a body in two or three dimensions when the conductivities of the inclusion and the surrounding body are complex and assumed to be known. The bounds are derived in terms of average values of…
The linear and nonlinear dynamical susceptibilities of a two level system are calculated as it undergoes a transition to a decoherent state. Analogously to the Glover-Tinkham-Ferrell sum rule of superconductivity, spectral weight in the…
Motivated by observational and theoretical work which both suggest very small scale ($\lesssim 1\,$pc) structure in the circum-galactic medium of galaxies and in other environments, we study Lyman-$\alpha$ (Ly$\alpha$) radiative transfer in…
Convergence of the ensemble Kalman filter in the limit for large ensembles to the Kalman filter is proved. In each step of the filter, convergence of the ensemble sample covariance follows from a weak law of large numbers for exchangeable…
We present the study of a Lyman limit system (LLS) at $z_{\rm abs}$ = 1.5441 towards quasar J134122.50+185213.9 observed with VLT X-shooter. This is a very peculiar system with strong C I absorption seen associated with a neutral hydrogen…
The absorption and extinction spectra of sub-wavelength cylinder arrays are shown to present two different kind of resonances. Close to the Rayleigh anomalies, the diffractive coupling with the lattice periodicity leads to sharp peaks in…
The proximity effect of metal line absorption systems in spectra of high redshift quasars and quasar pairs is investigated through the distribution of \Lyalpha forests. No strong proximity effect is found down to 500 km/sec away from a…
Whether a system is to be considered complex or not depends on how one searches for correlations. We propose a general scheme for calculation of entropies in lattice systems that has high flexibility in how correlations are successively…
When polarized electrons traverse a region where the laser light is focused their polarization varies even if their energy and direction of motion are not changed. This effect is due to interference of the incoming electron wave and an…
We have obtained follow-up observations of the quasar pair LBQS 0107-025A,B and new observations of the nearby quasar LBQS 0107-0232 with the Hubble Space Telescope Faint Object Spectrograph. Extended wavelength coverage of LBQS 0107-025A…
Several studies have shown that the column densities inferred from broad absorption lines (BALs) require extremely high metallicities and phosphorus overabundances -- apparently in conflict with other abundance diagnostics. Here I use HST…
Lyman-limit absorption systems can play many important roles during and after cosmological reionization. Unfortunately, due to the prohibitively large dynamic range required, it is impossible to self-consistently include these systems in…
We study the optical response of a strongly correlated electron system near the metal-insulator transition using a mapping to the sine-Gordon model. With semiclassical quantization, the spectral weight is distributed between a Drude peak…
Absorption and scattering of electromagnetic waves by dielectric media are of fundamental importance in many branches of physics. In this Letter we analytically derived the ultimate upper limits for the absorbed and scattered powers by any…
We present new calculations of unified line profiles for hydrogen perturbed by collisions with protons. We report on new calculations of the potential energies and dipole moments which allow the evaluation of profiles for the lines of the…